ASIRI NATIONAL PROJECT PROJECT
Recommendations for the design, construction and control of rigid inclusion ground improvements
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FOREWORD
These Recommendations on the improvement of foundation soils by inserting vert ical rigid inclusions embody the achievement of the ASIRI National Project, whose research activities and studies were conducted between 2005 and 2011 with a total budget allocation of €2.7 million. This collective effort has relied on input from 39 partner rms and organizations; it has r eceived the nancial support of the French Government and steady backing from IREX for all project management aspects. This project arose from a personal initiative coordinated through IREX’s Soil Specialist Clus ter, in conjunction with public works contractors and engineering companies within France, for the purpose of accompanying the development of a new ground improvement technique. This technique rst appeared in France during the 1990’s and consists of associating a network of vertical rigid inclusions with a granular layer in order to compose the foundation platform for civil engineering works (rafts, reservoirs, ground slabs, embankments) and construction works (ground slabs). Though previous uses were already familiar and this technique beneath emem bankments had already al ready been practiced in other European countries, the increasing application of such procedures for civil engineering structures and buildings had become something of a French national specicity, owing to the dynamic role of actors within the sector (construction (c onstruction companies and consulting engineers). Yet Yet in the absence of regulatory references, a set of dedidedicated and adapted guidelines needed to be developed and implemented. The ASIRI National Project has focused on designing, conducting and interpreting a series of physical experiments and numerical models as a fundamental step to understanding the mechanisms acting in this innovative foundation system. The applied research program presented herein has been facilitated facilitate d by project participants’ broad range of competences, stemming from both academia and the professional world; the program has also greatly beneted from the physical and human resources each partner organization made available. A project database with an exceptional collection of experimental recordings and numerical results has provided a valuable support s upport tool for nine doctoral theses performed within t he scope of this very Project. A full slate of observations and model output could thus be compared for a number of varied structures. New orientations were introduced, revealing the extent to which associating such distinct elements (soil, inclusions, load transfer platform) produces an efcient and highly economical composite foundation system. These Recommendations are derived from the project’s layout, which has yielded a set of practical rules for the design, construction and control of these structures, intended for all industry actors interested in further developing this technique. Another specicity of these Project Recommendations lies in the proposed design strategy, which conforms to the general Limit State design framework set forth in the Eurocodes, espe cially Eurocode 7-1 relative to geotechnical design. This application of general principles to devise a method for ground improvement design constitutes an original and forward-looking
Foreword Forewor d
FOREWORD
These Recommendations on the improvement of foundation soils by inserting vert ical rigid inclusions embody the achievement of the ASIRI National Project, whose research activities and studies were conducted between 2005 and 2011 with a total budget allocation of €2.7 million. This collective effort has relied on input from 39 partner rms and organizations; it has r eceived the nancial support of the French Government and steady backing from IREX for all project management aspects. This project arose from a personal initiative coordinated through IREX’s Soil Specialist Clus ter, in conjunction with public works contractors and engineering companies within France, for the purpose of accompanying the development of a new ground improvement technique. This technique rst appeared in France during the 1990’s and consists of associating a network of vertical rigid inclusions with a granular layer in order to compose the foundation platform for civil engineering works (rafts, reservoirs, ground slabs, embankments) and construction works (ground slabs). Though previous uses were already familiar and this technique beneath emem bankments had already al ready been practiced in other European countries, the increasing application of such procedures for civil engineering structures and buildings had become something of a French national specicity, owing to the dynamic role of actors within the sector (construction (c onstruction companies and consulting engineers). Yet Yet in the absence of regulatory references, a set of dedidedicated and adapted guidelines needed to be developed and implemented. The ASIRI National Project has focused on designing, conducting and interpreting a series of physical experiments and numerical models as a fundamental step to understanding the mechanisms acting in this innovative foundation system. The applied research program presented herein has been facilitated facilitate d by project participants’ broad range of competences, stemming from both academia and the professional world; the program has also greatly beneted from the physical and human resources each partner organization made available. A project database with an exceptional collection of experimental recordings and numerical results has provided a valuable support s upport tool for nine doctoral theses performed within t he scope of this very Project. A full slate of observations and model output could thus be compared for a number of varied structures. New orientations were introduced, revealing the extent to which associating such distinct elements (soil, inclusions, load transfer platform) produces an efcient and highly economical composite foundation system. These Recommendations are derived from the project’s layout, which has yielded a set of practical rules for the design, construction and control of these structures, intended for all industry actors interested in further developing this technique. Another specicity of these Project Recommendations lies in the proposed design strategy, which conforms to the general Limit State design framework set forth in the Eurocodes, espe cially Eurocode 7-1 relative to geotechnical design. This application of general principles to devise a method for ground improvement design constitutes an original and forward-looking
Foreword Forewor d
approach, given that it was necessary to adopt specic rules for structures not easily identied from the foundation categories established in Eurocode 7-1. The novelty of this technique has been well substantiated, and the eld of applications foreseen thanks to this breakthrough is now wide open. This valuable contribution was made possible thanks to the support of all partner organizations, as well as to the tremendous motivation on the part of all who drove this work program so en thusiastically. Gratitude is extended to each and every one of them. B. SIMON Director of the Scientic and Technical Technical Committee
Summary
ASIRI National Project Project
Summary
Foreword ...................... ............................................ ............................................ ............................................ ............................................. .............................................3 ......................3 Partners .................... .......................................... ............................................ ............................................. ............................................. ............................................ ..........................5 ....5 Notations ...................... ............................................ ............................................ ............................................ ............................................ .............................................7 .......................7 Chapter 1. Description, history, initial developments and launching of the national project ..................................................... ........................................................................... .......................................19 .................19 Chapter 2. Operating mechanisms................................................ ...................................................................... ...........................................41 .....................41
............................................ ............................................. ............................................ ...................................91 .............91 Chapter 3. Design methods ..................... Chapter 4. Design considerations ...................................... ............................................................ ............................................ ..............................145 ........145
......................................... ............................................ ............................................ .........................................155 ...................155 Chapter 5. Justifcations ................... Chapter 6. Geotechnical investigations ........................................ ............................................................... .........................................245 ..................245
conditions..................................... ............................................. ............................................ .................................263 ...........263 Chapter 7. Execution conditions.............. Chapter 8. Controls and instrumentation .................... .......................................... ............................................ .....................................293 ...............293
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ASIRI National Project partners
ANTEA Group, BALINEAU, BOTTE Fondations, BOTTE Sondages, BOUYGUES TP, CNAM (Conservatoire national des arts et métiers), DURMEYER, EDF SEPTEN, EGIS, EIFFAGE CONSTRUCTION, École des Ponts-ParisTech (formerly ENPC), ESTP (École spéciale des travaux publics), FFB (Fédération française du bâtiment), FNTP (Fédération nationale des travaux publics), FONDASOL, FRANKI Fondations (groupe FAYAT), GTM (groupe VINCI), GTS, ICE, IFSTTAR (formerly LCPC), INCLUSOL, INERIS, INSA Lyon, KELLER Fondations Spéciales, 3SR formerly LIRIGM (Université Joseph-Fourier), MÉNARD, NAVIER NAVIER La boratory (formerly CERMES), PIEUX OUEST, PINTO, GRAND Port Maritime Mariti me du HAVRE, HAVRE, QUILLE, RFF (Réseau Ferré de France), RINCENT BTP, BTP, SAIPEM, SNCF (Société Nationale des Chemins de Fer français), SOLETANCHE BACHY, SPIE Fondations, TENCATE (formerly BIDIM Géosynthétique Géosynthétiques), s), TERRASOL. This National Project also featured an Executive Committee, presided by François SCHLOSSER assisted by his Vice Vice President Olivier COMBARIEU, along with a Scientic and a nd Technical Technical
Committee headed by Bruno SIMON. The research activities involved in this project, organized around 5 major topic areas, were coordinated by: Laurent BRIANÇON (full-scale testing), Elisabeth HAZA-ROSIER (eld tests),
Luc THOREL (physical (physical models), Daniel DIAS (numerical modeling) and Olivier COMBARIEU (Project recommendations recommendations). ). Valuable contributions to this t his project were also appreciated from: Conseil général de Seine-et-Marne (77), Ports de PARIS, SOCOTEC, SOREDAL and AXSOL France. The Recommendations comprise 8 chapters; they were crafted by ve working groups, over seen by the Scientic Committee and validated by a Review Panel.
The following individuals helped assemble and draft the recommendations set forth herein: Scientic and Technical Committee Director: B. SIMON Working groups Coordinators
O. COMBARIEU (Expert), Cl. PLUMELLE (Expert), J.-P. J.-P. IORIO (Saipem), C. POILPRE (XAmsol), L. CARPINTEIRO (Socotec) and S. LAMBER LAMBERT T (Keller Fondations Spéciales) Member
P. BERTHELOT (Veritas), T. BRET (Keller Fondations Spéciales), L. BRIANÇON (Cnam), S. BRULÉ (Ménard), C. COP COPAL AL (Keller Fondations Spéciales), J. CRÉPET (Soredal), D. DIAS (INSA Lyon), J.B. DROUET (Ménard), J.-R. GAUTHEY (Spie Fondations), M. GLANDY (Solétanche Bachy), J. GRIPON (Franki Fondations), V. V. KELLER (Durmeyer), E. LA LAVEDER VEDER
(Axsol France), B. LEGER (Quille), F. MASSÉ (Ménard), A. NANCEY (Tencate), U. OKYAY (Pinto), C. PLOMTEUX (Ménard), J. RACINAIS (Ménard), C. SIMON (EDF), and S. TURLE (Inclusol). Partners
Review Panel
President: F. SCHLOSSER (Professor Emeritus) R. KASTNER (Professor Emeritus), A. GUILLOUX (Terrasol), P. LIAUSU (Ménard), P. AGUADO (Apave) and F. BAGUELIN (Fondasol). Figures: Mr. ANIC ANTIC (Terrasol) English translation: R. SACHS
Summary
ASIRI National Project Project
Notations
Unités/ Units
Notation
Descriptif
Description
Dimension
A
Aire d’une maille (une inclusion + sol alentour)
Surface area of a mesh (inclusion + surrounding soil)
L2
(m²)
Ac
Aire de la section comprimée d’une inclusion
Surface area of the compressed cross-section of an inclusion
L2
(m²)
AS
Aire du sol compressible
Surface area of the soft soil
L2
(m²)
AP
Aire de la tête d’inclusion (dallette)
Surface area of the inclusion head
L2
(m²)
a
Longueur caractéristique de la dallette (tête d’inclusion)
Inclusion cap width
L
(m)
a, b
Espacement des inclusions dans une maille rectangulaire
Spacing between inclusions within a rectangular mesh
L
(m)
B
Dimension de référence d’une fondation superficielle
Reference dimension of a shallow foundation
L
(m)
C c
Indice de compression
Compression index
C d
Valeur limite de calcul de l’effet d’une action
Limiting design value of the effect of an action
C max
Valeur maximale de la résistance à la compression d’une inclusion tenant compte de la consistance qu’il est nécessaire de donner au béton, coulis ou mortier frais suivant la technique utilisée
Maximum value of the compressive strength of an inclusion, in recognition of the consistency that must be applied to the fresh concrete, grout or mortar depending on the technique employed
C s
Indice de recompression
Recompression index
(–)
C
Taux de consolidation secondaire
Rate of secondary consolidation
(–)
C e
Indice de fluage
Creep index
(–)
c ’
Cohésion (en termes de contrainte effective)
Cohesion (in terms of effective stress)
c k c u
Notations
(–)
ML –1T –2
ML –1T –2
Coefficient de variation du loga- Coefficient of variation of the log rithme de la perméabilité of permeability avec l’indice des vides with the void index Cohésion non drainée
Undrained shear strength
(Pa)
(Pa)
(–) ML –1T –2
(Pa)
c uu
Cohésion apparente d’un sol non saturé
Apparent cohesion of an unsaturated soil
ML –1T –2
(Pa)
c v
Coefficient de consolidation verticale
Coefficient of consolidation in the vertical direction
L2T –1
(m2/s)
D
Diamètre d’une inclusion
Inclusion diameter
L
(m)
D p
Diamètre équivalent en pointe pour une inclusion de section non circulaire
Equivalent tip diameter for an inclusion with a non-circular cross-section
L
(m)
Ds
Diamètre équivalent du fût pour une inclusion de section non circulaire
Equivalent diameter of the shaft for an inclusion with a non-circular cross-section
L
(m)
d max
Diamètre nominal du plus gros grain d’un sol
Maximum soil grain diameter
L
(m)
d i
Distance horizontale entre l’axe Horizontal distance between the d’une inclusion et le centre de la axis of an inclusion and the cenfondation ter of the foundation
L
(m)
d n
Dimension à n % (n % des parti- n percent dimension (n% of parcules en poids ont des dimenticles by weight with a dimensions inférieures à d n) sion of less than d n)
L
(m)
E
Efficacité en terme de charge
Load efficiency
(–)
E tass
Efficacité en terme de tassement
Settlement efficiency
(–)
E V
Efficacité selon le modèle Hewlett et Randolph lorsqu’elle est contrôlée par la rupture au sommet de la voûte
Efficiency according to the Hewlett and Randolph model when controlled by failure at the arch summit
(–)
E T
Efficacité selon le modèle Efficiency according to the Hewlett et Randolph lorsqu’elle Hewlett and Randolph model est contrôlée par la rupture au when controlled by failure at the pied de la voûte base of the arch
(–)
E QP
Fraction de la charge totale Proportion of total load to be à appliquer en tête de la applied at the head of a fictitious colonne fictive d’un modèle ana- column associated with an analytique d’une maille courante lytical model of a common mesh
(–)
E d
Valeur de calcul de l’effet d’une action
Design value of the effect of actions
E
Module d’Young
Young’s modulus, Modulus of elasticity
ML –1T –2
(Pa)
E *
Module de déformation apparent du sol renforcé sous chargement vertical
Apparent deformation modulus of the reinforced soil subjected to vertical loading
ML –1T –2
(Pa)
E M
Module conventionnel déterminé lors de l’essai pressiométrique Ménard normalisé
Normalized Menard pressuremeter modulus
ML –1T –2
(Pa)
E i
Module tangent du premier chargement
Tangent modulus for initial loading
ML –1T –2
(Pa)
ASIRI National Project
E oed
Module œdométrique
Oedometric modulus
ML –1T –2
(Pa)
E oedref
Valeur de référence du module Reference value of the tangent oedométrique tangent dans le oedometric modulus in the “Harmodèle Hardening soil dening soil” model
ML –1T –2
(Pa)
E oedo*
Module oedométrique équivalent du volume de sol renforcé par inclusions
Equivalent oedometric modulus of the soil volume reinforced by inclusions
ML –1T –2
(Pa)
E p
Module d’Young de l’inclusion
Young’s modulus of the inclusion
ML –1T –2
(Pa)
E s
Module de déformation apparent du sol
Apparent deformation modulus of the soil
ML –1T –2
(Pa)
E sol
Module de déformation du sol non renforcé
Deformation modulus of the non-reinforced soil
ML –1T –2
(Pa)
E 50ref
Valeur de référence du module sécant à 50 % du déviateur à rupture dans le modèle Hardening soil
Reference value of the secant modulus at 50% strength in the "Hardening soil" model
ML –1T –2
(Pa)
E ur ref
Valeur de référence du module de recompression dans le modèle Hardening soil
Reference value of the unloading-reloading modulus in the “Hardening soil” model
ML –1T –2
(Pa)
e
Indice des vides
Void ratio
(–)
e0
Indice des vides initial
Initial void ratio
(–)
emax
Indice des vides maximal (dans l’état le plus lâche)
Maximum void ratio (in the loosest state)
(–)
emin
Indice des vides minimal ( dans l’état le plus dense)
Minimum void ratio (in the densest state)
(–)
F N
Résultante du frottement négatif
Resultant of negative friction
MLT –2
(N)
f cd
Design value of the compresValeur de calcul de la résistance sive strength of the concrete, à la compression du béton, cougrout or mortar used on an inclulis ou mortier d’une inclusion sion
ML –1T –2
(Pa)
f ck
Résistance caractéristique en Characteristic value of the comcompression du béton, coulis ou pressive strength of the conmortier mesurée sur cylindres à crete, grout or mortar measured 28 jours on cylinders at 28 days
ML –1T –2
(Pa)
f ck (t )
Résistance caractéristique en Characteristic value of the comcompression du béton, coulis ou pressive strength of the conmortier mesurée sur cylindres crete, grout or mortar measured à t jours on cylinders at t days
ML –1T –2
(Pa)
f ck *
Résistance caractéristique à la compression du béton, coulis ou mortier d’une inclusion
Characteristic value of the compressive strength of the concrete, grout or mortar used on an inclusion
ML –1T –2
(Pa)
f cvd
Valeur de calcul de la résistance en cisaillement et en compression du béton, coulis ou mortier d’une inclusion
Design value of the shear and compressive strength of the concrete, grout or mortar used on an inclusion
ML –1T –2
(Pa)
Notations
f ctd
Valeur de calcul de la résistance à la traction du béton, coulis ou mortier d’une inclusion
Design value of the tensile strength of the concrete, grout or mortar used on an inclusion
ML –1T –2
(Pa)
f c 28
Valeur caractéristique de la résistance à la compression à 28 j du béton d’un dallage
Characteristic value of the compressive strength value at 28 days for the ground slab concrete
ML –1T –2
(Pa)
f t fendage28
Valeur caractéristique de la résistance en traction par fendage à 28 j du béton d’un dallage
Characteristic value of the tensile strength value by splitting at 28 days for the ground slab concrete
ML –1T –2
(Pa)
f n
Frottement négatif unitaire
Negative skin friction
ML –1T –2
(Pa)
G
Taux marginal de report d’effort Marginal load efficiency ratio on sur la tête d’une inclusion the inclusion head
G
Module de cisaillement
Shear modulus
G11,G12,
Qualificatif des missions géotechniques normalisées (norme NF P 94-500)
Qualifier of standardized geotechnical missions (NF P 94-500 Standard)
Module de cisaillement équivalent du sol renforcé
Equivalent shear modulus of the reinforced soil
Accélération de la pesanteur terrestre
Acceleration due to earth gravity
G2,G3 G4 G*
g
g g (z )
2
(g = 9,81m/s2)
(g = 9.81 m/s )
Part permanente d’une surcharge
Permanent component of a surcharge
Déplacement latéral imposé du Imposed lateral displacement of sol autour d’une inclusion the soil around an inclusion
(–) ML –1T –2
(Pa)
ML –1T –2
(Pa)
LT –2
(m/s2)
ML –1T –2
(Pa)
L
(m)
g max
Valeur maximale du déplacement latéral imposé autour d’une inclusion
Maximum imposed lateral displacement value around an inclusion
L
(m)
H
Hauteur du sol compressible
Height of the soft soil
L
(m)
He
Hauteur du plan d’égal tassement
Height of the equal settlement plane
L
(m)
H R ou hR
Hauteur du remblai
Embankment height
L
(m)
H M ou hm
Hauteur du matelas
Platform height
L
(m)
H M
Hauteur du modèle numérique plan
Height of the numerical model plane
L
(m)
H , H S
Épaisseur du sol compressible
Soft soil thickness
L
(m)
h
Épaisseur d’un dallage
Thickness of a ground slab
L
(m)
L
(m)
hc
Hauteur d’action du frottement Height of negative friction action négatif dans la couche comtaking place in the soft layer pressible (hauteur critique) (critical height)
ASIRI National Project
hi
hr , ha
Distance verticale entre le point d’intersection d’un mécanisme de rupture avec une inclusion et le centre de la fondation
Vertical distance between the point of intersection of a failure mechanism with an inclusion and the foundation center
L
(m)
Hauteur d’application du frotte- Height of negative friction appliment négatif sur la colonne cation on the fictitious column fictive surmontant la tête positioned on top d’inclusion of the inclusion head
L
(m)
L4
(m4)
I
Produit d’inertie d’une section
Product of inertia for a crosssection
I D
Indice de densité
Density index
(–)
I C
Indice de consistance
Consistency index
(–)
I p
Indice de plasticité
Plasticity index
(–)
J
Raideur d’une nappe géosynthétique
Stiffness of a geosynthetic layer
k
Coefficient de la loi de variation Coefficient of the modulus variadu module dans le modèle rhéo- tion law in the "Hardening soil" logique Hardening soil rheological model
K S ou k s
Module de réaction du sol com- Coefficient of subgrade reaction pressible (sol support) of soft soil (supporting soil)
MT –2
(N/m) (–)
ML –2T –2
(kN/m3)
K
Rapport entre contraintes horizontale et verticale
Ratio between horizontal and vertical stresses
(–)
K o
Facteur de pression des terres au repos
Coefficient of earth pressure at rest
(–)
K a
Coefficient de poussée des terres
Coefficient of active earth pressure
(–)
K p
Coefficient de butée des terres
Coefficient of passive earth pressure
(–)
K q
Coefficient de transmission d’une surcharge dans un massif non pesant
Coefficient of surcharge transmission within a weightless medium
(–)
K x
Impédance horizontale d’une fondation superficielle
Horizontal impedance of a shallow foundation
MT –2
(kN/m)
k h, k v
Coefficients de perméabilité horizontale et verticale
Coefficients of horizontal and vertical permeability
LT –1
(m/s)
k i
Module de réaction en sous face d’un dallage à proximité de l’axe d’une inclusion rigide ( r < r k )
Coefficient of subgrade reaction on the underside of a ground slab adjacent to the axis of a rigid inclusion (r < r k )
ML –2T –2
(kN/m3)
k s
Module de réaction du sol com- Coefficient of subgrade reaction pressible ou module de réaction of the soft soil or coefficient of en sous face d’un dallage à dis- subgrade reaction on the undertance de l’inclusion side of a ground slab removed (r > r k ) from the inclusion (r > r k )
ML –2T –2
(kN/m3)
Notations
k , k q
Pentes des lois de mobilisation de Frank et Zhao pour le frottement et la pointe
Slopes of the Frank and Zhao mobilization laws for both the friction and the tip
ML –1T –2
(Pa)
k 1
Empirical coefficient for determiCoefficient empirique pour la ning the design value of the détermination de la valeur de compressive strength of the calcul de la résistance en comconcrete, mortar or grout on a pression du béton, du mortier ou deep foundation (NF P 94 262 coulis d’une fondation profonde Standard); this coefficient (norme NF P 94 262) ; tient accounts for the mode of placecompte du mode de mise en ment in the soil as well as possiplace dans le sol ainsi que des ble cross-section variations variations possibles de section depending on the technique selon la technique utilisée employed
(–)
k 2
Coefficient empirique pour la Empirical coefficients for deterdétermination de la valeur de mining the design value of the calcul de la résistance en comcompressive strength of the pression du béton, du mortier ou concrete, mortar or grout on a coulis d’une fondation profonde deep foundation (NF P 94 262 (norme NF P 94 262) ; tient Standard); this coefficient compte des difficultés de béton- accounts for concreting difficulnage liées à la géométrie de ties tied to the inclusion geol’inclusion. metry
(–)
k 3
Coefficient empirique pour la détermination de la valeur de calcul de la résistance en compression du béton, du mortier ou coulis d’une fondation profonde (norme NF P 94 262) ; tient compte des contrôles d’intégrité effectués
Empirical coefficients for determining the design value of the compressive strength of the concrete, mortar or grout on a deep foundation (NF P 94 262 Standard); this coefficient accounts for the structural integrity testing conducted
(–)
L
Dimension de référence d’une fondation superficielle
Reference dimension for a shallow foundation
L
(m)
L
Longueur d’une inclusion
Inclusion length
L
(m)
L
(m)
L
(m)
Lal
Longueur nécessaire à la mobiLength required to mobilize lisation des efforts d’ancrage anchorage forces, measured as comptée à partir de la dernière of the last inclusion in the inclusion dans la direction longi- embankment longitudinal directudinale tion
L
(m)
Lat
Longueur nécessaire à la mobiLength required to mobilize lisation des efforts d’ancrage anchorage forces, measured as comptée à partir de la dernière of the last inclusion in the inclusion dans la direction embankment transverse transversale direction
L
(m)
L1
L1, L 2
Largeur de la spirale logarithmiWidth of the logarithmic spiral in que dans le mécanisme de the Prandtl mechanism Prandtl Dimensions de référence d’un dallage
Reference dimensions of a ground slab
ASIRI National Project
Lfr
Longueur d’ancrage d’une Anchorage length of a geosynnappe géosynthétique comptée thetic layer, measured from the à partir de la tête du talus top of the slope
L
(m)
Lht
Longueur disponible pour l’ancrage d’une nappe géosynthétique comptée à partir de la tête du talus
Length available for the anchorage of a geosynthetic layer, measured from the top of the slope
L
(m)
LM
Demi-largeur du modèle numérique plan
Half-width of the numerical plane-strain model
L
(m)
ML –1T –2
(Pa)
Lmax
Largeur du mécanisme de Width of the Prandtl mechanism, Prandtl comptée depuis le bord measured from the outer edge extérieur de l’inclusion of the inclusion
M
Moment d’un torseur d’effort
Net moment of a system of loads
ML2T –2
(Nm)
M
Moment fléchissant
Bending moment
ML2T –2
(Nm)
M d
Valeur de calcul du moment d’un torseur d’effort
Design value of net moment of a system of loads
ML2T –2
(Nm)
M R
Moment du torseur des réactions développées dans les inclusions pour la vérification de portance ELU
Net moment of reactions developed in inclusions, for verification of ULS load-bearing capacity
ML2T-2
(Nm)
M r
Moment radial dans une plaque
Radial moment in a plate
ML2T-2
(Nm)
M x
Moment de flexion dans une plaque autour de l’axe (0y)
Bending moment in a plate around the (0y) axis
ML2T-2
(Nm)
M y
Moment de flexion dans une plaque autour de l’axe (0x)
Bending moment in a plate around the (0x) axis
ML2T-2
(Nm)
M sup
Moment fléchissant qui sollicite la fibre supérieure du dallage en traction
Bending moment that loads the upper fiber of the ground slab in tension
ML2T-2
(Nm)
M inf
Moment fléchissant qui sollicite la fibre inférieure du dallage en traction
Bending moment that loads the lower fiber of the ground slab in tension
ML2T-2
(Nm)
MO
Teneur en matières organiques
Organic matter content
(–)
m
Exposant de la loi de variation Exponent of the modulus variadu module dans le modèle rhéo- tion law used in the “Hardening logique Hardening soil soil” rheological model
ma
Moment calculé dans un dallage continu sur sol homogénéisé équivalent
Computed moment in a continuous ground slab on an equivalent homogenized soil
ML2T –2
(Nm)
mb
Terme correctif représentant l’influence des inclusions rigides sur un dallage continu
Corrective term representing the influence of rigid i nclusionson a continuous ground slab
ML2T –2
(Nm)
mc
Terme correctif représentant les interactions entre les inclusions rigides et les joints
Corrective term representing the interactions between rigid inclusions and joints
ML2T-2
(Nm)
Notations
(–)
m , mq
Coefficients des lois de Frank et Zhao de mobilisation du frottement et du terme de pointe
Coefficients of Frank and Zhao mobilization laws for both friction and the tip term
(–)
N c , N q, N
Facteurs de capacité portante
Bearing capacity factors
(–)
N k
Facteur de corrélation entre la cohésion non drainée c u et la
Correlation factor between undrained cohesion c u and cone
(–)
résistance de pointe qc
resistance qc
N kt
Facteurs de corrélation entre la cohésion non drainée c u et la résistance de pointe piézocône qt
Correlation factors between undrained cohesion c u and cor-
(–)
rected piezocone resistance qt
n
Porosité
Porosity
(–)
P
Périmètre de l’inclusion
Inclusion perimeter
L
(m)
p
Contrainte horizontale contre une inclusion
Horizontal stress against an inclusion
ML –1T –2
(Pa)
p’
Contrainte moyenne effective = (1’ + 2’+ 3’)/3
Effective mean stress = (1’ + 2’+ 3’)/3
ML –1T –2
(Pa)
pl
Pression limite conventionnelle Standard limit pressure determidéterminée lors de l’essai pres- ned when conducting the stansiométrique Ménard normalisé dard Menard pressuremeter test
ML –1T –2
(Pa)
pl*
Pression limite conventionnelle Standard net limit pressure corcomptée à partir de la contrainte rected from the total horizontal totale horizontale régnant dans stress acting in the soil at test le sol lors de l’essai elevation
ML –1T –2
(Pa)
plim
Valeur ultime de la contrainte Ultimate value of the lateral soil horizontale contre une inclusion pressure against an inclusion
ML –1T –2
(Pa)
Q
Résultante verticale d’un torseur d’effort
Vertical net force of a system of loads
MLT –2
(N)
Qd
Valeur de calcul de la résultante verticale d’un torseur d’effort
Design value of the vertical net force of a system of loads
MLT –2
(N)
Q*
Résultante verticale des efforts appliqués (en l’absence d’inclusions)
Vertical net force of applied loads (in the absence of inclusions)
MLT –2
(N)
Q p*
Résultante verticale des efforts appliqués sur l’aire d’une tête inclusion (en l’absence d’inclusions)
Vertical net forces of applied loads over the inclusion head area (in the absence of inclusions)
MLT –2
(N)
MLT –2
(N)
MLT –2
(N)
QR
Qs(z )
Résultante verticale du torseur Vertical net force of reactions des réactions développées dans developed in inclusions, for veriles inclusions pour la vérification fication of ULS load-bearing de portance ELU capacity Résultante verticale des efforts appliqués à la section d’inclusion placée à la profondeur z sous la tête
Vertical net force of loads applied to the inclusion crosssection placed at depth z below the head
ASIRI National Project
Qs
Load applied at the corner (or Charge appliquée en angle (ou edge) of the ground slab serving en bord) de dallage qui annule to cancel out the lifting due to le soulèvement dû au retrait difthe differential shrinkage and férentiel et au gradient de temtemperature gradient pérature (DTU 13.3) (DTU 13.3)
MLT –2
(N)
Qs*
Résultante verticale des efforts appliqués sur l’aire complémentaire d’une tête d’inclusion (en l’absence d’inclusions)
Vertical net force of loads applied on the complementary area of an inclusion head (in the absence of inclusions)
MLT-2
(N)
Résultante verticale des efforts appliqués en tête d’une inclusion
Vertical net force of loads applied at the head of an i nclusion
MLT –2
(N)
QS+
Résultante verticale des efforts appliqués à la surface du sol compressible
Vertical net force of loads applied to the soft soil surface
MLT –2
(N)
q
Déviateur des contraintes
Equivalent shear stress
ML –1T –2
(Pa)
q
Part variable d’une surcharge
Variable component of a surcharge
ML –1T –2
(Pa)
q0
Contrainte appliquée en tête du profil (surcharge)
Stress applied at the profile head (excess surface load)
ML –1T –2
(Pa)
q*
Contrainte verticale s’exerçant sur le sol compressible non renforcé (sans inclusion)
Vertical stress acting upon the non-reinforced soft soil (without inclusion)
ML –1T –2
(Pa)
qa
Valeur asymptotique du dévia Asymptotic value of the hyperteur dans l’ajustement hyperbobolic fitting of stress-strain curve lique de la courbe effortin primary triaxial loading déformation d’un essai triaxial
qc
Résistance de pointe (ou résistance de cône)
Cone resistance
ML –1T –2
(Pa)
q p
Résistance limite en pointe d’une inclusion
Limit value of point resistance of an inclusion
ML –1T –2
(Pa)
qs
Frottement latéral unitaire limite
Limit value of skin friction
ML –1T –2
(Pa)
qt
Résistance de pointe (ou résistance de cône) du piézocône
Cone resistance corrected for pore water pressure (piezocone testing)
ML –1T –2
(Pa)
q p*
Contrainte appliquée sur le sol compressible à l’emplacement où se trouverait la tête d’inclusion si elle était en place
Stress applied on the soft soil at the location of the inclusion head (provided an inclusion had been placed)
ML –1T –2
(Pa)
qs*
contrainte appliquée sur le sol compressible (sans inclusion)
Stress applied on the soft soil (without an inclusion)
ML –1T –2
(Pa)
q p+
contrainte appliquée sur la tête de l’inclusion
Stress applied on the inclusion head
ML –1T –2
(Pa)
+
Valeur limite de la contrainte sur la tête de l’inclusion calculée avec le mécanisme de Prandtl
Limit value of stress on the inclusion head, as calculated using the Prandtl mechanism
ML –1T –2
(Pa)
Q p(0) ou QP + Qs(0) ou
q p (P )
Notations
q p+(L)
Valeur limite de la contrainte sur Limit value of stress on the la tête de l’inclusion calculée inclusion head, as calculated for pour un débord L de la semelle an overhang length L of the foopar rapport au bord de l’incluting relative to the inclusion sion edge
ML –1T –2
(Pa)
q p,d +
Valeur limite de calcul de la conDesign limit value of the stress trainte appliquée sur la tête de applied on the inclusion head l’inclusion
ML –1T –2
(Pa)
qs+
Contrainte appliquée à la surface du sol compressible
Stress applied to the soft soil surface
ML –1T –2
(Pa)
R
Rayon de la maille équivalente
Radius of the equivalent mesh
L
(m)
R
Rayon d’une semelle circulaire
Radius of a circular footing
L
(m)
R c
Seuil dans la courbe chargedéplacement d’une fondation sur inclusions
Threshold in the load-displacement curve of a foundation built on inclusions
MLT –2
(N)
R b
Résistance ultime de pointe de l’inclusion
Ultimate point resistance of the inclusion
MLT –2
(N)
R C
Rayon maximal du cône de diffusion
Maximum radius of the diffusion cone
L
(m)
R d
Valeur de calcul de la résistance à une action
Design value of the resistance to an action
R f
Rapport qf /qa
qf /qa ratio
R k
Valeur caractéristique de résistance
Characteristic resistance value
R s
Résistance ultime mobilisée par frottement sur le fût d’une inclusion
Ultimate resistance mobilized by friction on the shaft of an inclusion
Roc
Rapport de surconsolidation
Overconsolidation ratio
(–)
MLT –2
(N) (–)
R c ,cr ; d
Valeur de calcul de la résistance Design critical ground bearing critique (fluage) en compres- resistance value (creep) in comsion du terrain pour une inclupression for an isolated inclusion isolée sion
MLT –2
(N)
R t ; k
Valeur caractéristique de la Characteristic value of shortrésistance de traction à court term tensile strength of the geoterme du géosynthétique mesu- synthetic, as measured accorrée suivant la norme NF EN I SO ding to the NF EN ISO 10319 10319 Standard
MT –2
(N/m)
R t ; d
Valeur de calcul de la résistance Design value of the ultimate tenultime de traction du géosynthésile strength of the geosynthetic tique
MT –2
(N/m)
R t-L ; d
Valeur de calcul de la résistance Design value of the ultimate tenultime de traction du géosynthé- sile strength of the geosynthetic tique dans le sens longitudinal in the longitudinal direction of du remblai the embankment
MT –2
(N/m)
R t-T ; d
Valeur de calcul de la résistance Design value of the ultimate tenultime de traction du géosynthé- sile strength of the geosynthetic tique dans le sens transversal in the transverse direction of the du remblai embankment
MT –2
(N/m)
ASIRI National Project
R v ; d
Valeur de calcul de la résistance Design value of the ground beadu terrain sous une f ondation ring resistance beneath a shalsuperficielle low foundation
L
(m)
r k
Rayon définissant la distribution Radius defining the distribution des coefficients de réaction of coefficients of subgrade reaction k i and k s k i et k s
L
(m)
r p
Rayon de l’inclusion
Inclusion radius
L
(m)
S
Aire de la semelle
Footing area
L
(m)
Sr
Degré de saturation
Saturation ratio, degree of saturation
(–)
SRR
Taux de réduction des contraintes
Stress reduction ratio
(–)
s sc , s, sq
Entraxe des inclusions dans une Center-to-center distance of the maille carrée inclusions in a square mesh Coefficients de forme pour le calcul de la capacité portante
L
Shape coefficients for computation of the load-bearing capacity
(m) (–)
T
Résultante horizontale d’un tor- Horizontal net force of a system seur d’effort of loads
MLT –2
(N)
T d
Valeur de calcul de la résultante horizontale d’un torseur d’effort
Design value of the horizontal net force of a system of loads
MLT –2
(N)
T d
Valeur de calcul de la traction dans le géosynthétique
Design value of tension in the geosynthetic
MT –2
(N/m)
T d ; mesh
Valeur de calcul de la traction Design value of tension in the dans le géosynthétique résultant geosynthetic resulting from verdes charges verticales sur une tical loads on a mesh maille
MT –2
(N/m)
T d ; thrust
Design value of tension in the Valeur de calcul de la traction geosynthetic resulting from horidans le géosynthétique résultant zontal outward thrust of the des efforts de poussée du talus, embakment fill, as evaluated on évaluée au nu extérieur the external unfinished side of de la dernière tête d’inclusion the last inclusion head
MT –2
(N/m)
Design value of tension in the Valeur de calcul de la traction geosynthetic resulting from horidans le géosynthétique résultant zontal outward thrust of the des efforts de poussée du talus, embakment fill, as evaluated in évaluée à l’aplomb de la crête alignment with the slope ridge du talus line
MT –2
(N/m)
Valeur de calcul de la résistance de la nappe géosynthétique
MT –2
(N/m)
T geo, long
Valeur de calcul de la résistance Design value of geosynthetic de la nappe géosynthétique layer resistance in the longitudidans le sens longitudinal nal direction
MT –2
(N/m)
T geo, trans
Valeur de calcul de la résistance de la nappe géosynthétique dans le sens transversal
MT –2
(N/m)
T d ; thrust ; max
T geo
Notations
Design value of geosynthetic layer resistance
Design value of geosynthetic layer resistance in the transverse direction
Résultante horizontale du tor- Horizontal net force of the reacseur des réactions développées tions developed in inclusions, dans les inclusions pour la vérifi- for verification of ULS load-beacation de portance ELU ring capacity
MLT –2
(N)
T
Effort tranchant dans une inclusion
Shear force in an inclusion
MLT –2
(N)
T v
Facteur temps œdométrique
Time factor
U
Degré de consolidation
Degree of consolidation, consolidation ratio
u
Pression interstitielle, surpression interstitielle
Pore pressure, excess pore pressure
ML –1T –2
(Pa)
V
Vitesse d’un bloc rigide
Velocity of a rigid block
LT –1
(m/s)
V
Volume spécifique = (1 + e)
Specific volume = (1 + e)
V BS
Valeur de bleu de méthylène d’un sol
Methylene blue value of a soil
V i
Effort vertical appliqué en pied d’un rack
Vertical force applied at foot of a rack
MLT-2
(N)
v
Déplacement latéral
Lateral displacement
L
(m)
W
Poids du volume de matelas d’une maille élémentaire
Weight of the load platform for a unit cell
MLT –2
(N)
W p
Poids du matelas supporté Weight of the load platform suppar la tête d’une inclusion dans ported by an inclusion head in a une maille unit cell
MLT –2
(N)
W T
Charge verticale supportée par une nappe géosynthétique entre deux inclusions
Vertical load supported by a geosynthetic layer placed between two inclusions
MLT –2
(N)
w (z )
Déplacement relatif entre le sol et l’inclusion ; = y s(z ) – y p(z )
Relative displacement between the soil and the inclusion = ys(z) - yp(z)
L
(m)
w
Teneur en eau
Water content
(–)
w n
Teneur en eau naturelle
Natural water content
(-)
w L
Limite de liquidité
Liquid limit
(–)
w P
Limite de plasticité
Plastic limit
(–)
y
Tassement
Settlement
L
(m)
y s
Tassement du sol
Soil settlement
L
(m)
y p
Tassement de l’inclusion
Inclusion settlement
L
(m)
y M
Tassement à la surface du matelas
Settlement at the load platform surface
L
(m)
T R
(–)
(g/100 g of soil)
ASIRI National Project
Taux de couverture
Coverage area ratio/Area replacement ratio/Area ratio
(–)
Déformation angulaire d’une fondation
Angular deformation of a foundation
(rad)
Coefficient réducteur du frottement de l’interface sol-géosynthétique
Reduction coefficient of friction at the soil-geosynthetic interface
(–)
cc
Coefficient pour le calcul de la résistance caractéristique du béton
Coefficient for the characteristic concrete strength computation
(–)
Angle de diffusion des efforts
Diffusion angle of forces
(°)
Coefficient correcteur pour évaluer le module apparent du sol renforcé
Correction coefficient for evaluating the apparent modulus of reinforced soil
(–)
Rotation relative d’une fondation
Relative foundation rotation
(–)
Déflexion d’une fondation
Foundation deflection
(–)
Déformation
Strain
(–)
1 ou a
Déformation axiale
Axial strain
(–)
v
Déformation volumique
Volume strain
(–)
’
Angle de frottement interne effectif
Angle of shearing resistance (in terms of effective stress),effective angle of shearing resistance
(°)
’crit
Angle de frottement interne à l’état critique
Angle of shearing resistance at critical state
(°)
geo
Angle de frottement de l’interface sol-géosynthétique
Angle of friction at the soil-geosynthetic interface
(°)
’NC
Angle de frottement interne effectif dans le domaine normalement consolidé
Effective angle of shearing resistance within the normally consolidated domain
(°)
’pic
Angle de frottement interne effectif au pic
Peak angle of shearing resistance
(°)
’SC
Angle de frottement interne effectif dans le domaine surconsolidé
Effective angle of shearing resistance within the overconsolidated domain
(°)
Angle de dilatance
Angle of dilatancy
(°)
Facteur de proportionnalité entre les valeurs maximales du déplacement horizontal et vertical du sol autour d’une inclusion
Proportionality factor between the maximum horizontal and vertical displacement values for the soil around an inclusion
(–)
Notations
flu
Coefficient partiel lié au comportement en fonction du temps des géosynthétiques ; flu = 1/flu tel que défini dans la norme NF P 94270 annexe F.4.3.
deg
Coefficient partiel lié au vieillissement des produits géosynthétiques, par exemple par hydrolyse ou oxydation, dépendant des conditions d’environnement du produit ; deg = 1/ deg tel que défini dans la norme NF P 94270 annexe F.4.4.
end
Coefficient partiel correspondant à l’endommagement des renforcements géosynthétiques produit par leur installation et le compactage des remblais. end = 1/ end tel que défini dans la norme NF P 94270 annexe F.4.2
Partial coefficient related to the behavior over time of geosynthetics; flu =1/flu, as defined in
(–)
the NF P 94270 Standard, Appendix F.4.3 Partial coefficient related to the aging of geosynthetic products, e.g. by means of hydrolysis or oxidation, as a function of product environmental conditions; deg = 1/ deg, as defined in the
(–)
NF P 94270 Standard, Appendix F.4.4 Partial coefficient corresponding to the damage of geosynthetic reinforcements caused by their installation and embankment compaction; end = 1/ end, as defined in the
(–)
NF P 94270 Standard, Appendix F.4.2
Poids volumique du sol
Soil unit weight
ML –2T –2
(kN/m3)
’
Poids volumique déjaugé
Submerged unit weight of soil
ML –2T –2
(kN/m3)
C
Coefficient partiel relatif au béton (NF EN 1992-1-1 2.4.2.4)
Partial coefficient relative to concrete (NF EN 1992-1-1 2.4.2.4 Standard)
(–)
G
Facteur partiel pour une action permanente
Partial factor for a permanent action
(–)
M ; t
Facteur partiel du matériau géosynthétique
Partial factor of the geosynthetic material
(–)
Q
Facteur partiel pour une action variable
Partial factor for a variable action
(–)
R;h
Facteur partiel pour la résistance au glissement
Partial factor for sliding resistance
(–)
R ;d
Facteur partiel pour l’incertitude dans un modèle de résistance
Partial factor for the level of uncertainty in a resistance model
(–)
R ; f
Facteur partiel pour la résistance d’interaction sol-géosynthétique
Partial factor for the soil-geosynthetic interaction resistance
(–)
R ; v
Facteur partiel pour la portance (résistance)
Partial factor for the load-bearing capacity (resistance)
(–)
b
Facteur partiel pour la résistance de pointe d’une inclusion
Partial factor for the inclusion point resistance
(–)
ASIRI National Project
c’
Facteur partiel pour la cohésion effective
Partial factor for effective cohesion
(–)
cu
Facteur partiel pour la cohésion non drainée
Partial factor for undrained cohesion
(–)
geo
Facteur partiel de sécurité sur la résistance de la nappe géosynthétique
Partial safety factor on the geosynthetic resistance
s
Facteur partiel pour la résistance par frottement sur le fût d’une inclusion
Partial factor for resistance by friction on the inclusion shaft
(–)
’
Facteur partiel pour l’angle de frottement interne (tan’)
Partial factor for the angle of internal friction (tan’)
(–)
Facteur partiel pour le poids volumique
Partial factor for the unit weight
(–)
r
Poids volumique du remblai
Unit weight of the embankment
ML –2T –2
(kN/m3)
s
Poids volumique du sol
Unit weight of the soil
ML –2T –2
(kN/m3)
p
Poids volumique du pieu
Unit weight of the pile
ML –2T –2
(kN/m3)
w
Poids volumique de l’eau
Unit weight of water
ML –2T –2
(kN/m3)
*
Indice de décompression recompression dans modèle de comportement Soft soil = 2C s /2,3 (1 + e)
Unloading-reloading index in the constitutive soft soil model = 2C s /2.3 (1 + e)
Coefficient d’accrochage dans la méthode de Combarieu
Latching coefficient used in Combarieu’s method
*
Indice de compression dans modèle de comportement Soft Soil = C c /2,3 (1 + e)
Compression index used in the constitutive Soft Soil model = C c /2.3 (1 + e)
Facteur d’augmentation de la cohésion non drainée c u en
Undrained cohesion c u increase
cu
fonction de l’augmentation de contrainte de consolidation
(–)
(–)
factor as a function of consolidation stress
µ
Coefficient de l’équation différentielle dans la méthode de Combarieu
Coefficient of the differential equation used in Combarieu’s method
*
Indice de fluage dans modèle de comportement Soft Soil = C e /2,3 (1 + e)
Creep index used in the constitutive Soft Soil model = C e /2.3
Coefficient de Poisson
Poisson’s ratio
Contrainte totale
Total stress
ML –1T –2
(Pa)
c
Pression de confinement
Confinement stress
ML –1T –2
(Pa)
h
Contrainte horizontale
Horizontal stress
ML –1T –2
(Pa)
i
Contrainte verticale supposée uniforme sur le disque r r k
Vertical stress assumed uniform over the disc r r k on the
ML –1T –2
(Pa)
en sous-face du dallage
ground slab underside
Notations
M –1
1/m
(1 + e) (–)
s
Contrainte verticale supposée uniforme sur l’anneau r k r R en sous-face du dallage
Vertical stress assumed uniform over the ring r k r R on the
ML –1T –2
(Pa)
ground slab underside
c ’
Contrainte de consolidation isotrope durant un essai triaxial
Isotropic consolidation stress during a triaxial test
ML –1T –2
(Pa)
v
Contrainte verticale totale
Total vertical stress
ML –1T –2
(Pa)
v ’
Contrainte verticale effective
Effective vertical stress
ML-1T –2
(Pa)
v
Contrainte verticale effective moyenne dans une section horizontale
Average effective vertical stress within a horizontal cross-section
ML –1T –2
(Pa)
v , d
Valeur de calcul de la contrainte verticale limite à la surface du sol
Design value of the ultimate vertical stress at the soil surface
ML –1T –2
(Pa)
v , geo
Contrainte verticale appliquée sur la nappe géosynthétique
Vertical stress applied on the geosynthetic layer
ML –1T –2
(Pa)
Contraintes principales totales
Principal total stresses
ML –1T –2
(Pa)
Contraintes principales effectives
Principal effective stresses
ML-1T-2
(Pa)
’
Contrainte verticale effective libre dans le terrain à l’état final, calculée sans tenir compte de la présence de l’inclusion (dans le modèle du frottement négatif selon Combarieu)
Effective vertical stress in free field in the final state, as calculated without taking into account the presence of the inclusion (within the negative friction model, according to Combarieu)
ML –1T –2
(Pa)
ELS
Contrainte de traction dans un dallage non armé
Tensile stress in a non-reinforced ground slab
ML –1T –2
(Pa)
Contrainte de cisaillement
Shear stress
ML –1T –2
(Pa)
cp
Valeur de calcul de la contrainte de cisaillement dans l’inclusion
Design value of shear stress in inclusion
ML –1T –2
(Pa)
Rotation d’une fondation
Rotation of a foundation
(rad)
1, 2
Facteurs de corrélation pour évaluer les résultats des essais de chargement statique d’inclusions
Correlation factors for evaluating the results of inclusion static loading tests
(–)
, 4
Facteurs de corrélation pour dériver la résistance d’une inclusion des résultats de reconnaissance du terrain à l’exclusion d’essais de chargement d’inclusions.
Correlation factors for deriving the resistance of an inclusion from field investigation results, with the exception of inclusion loading tests
(–)
Inclinaison d’une fondation
Inclination of a foundation
(rad)
1, 2, 3 ’ ’ ’
ASIRI National Project
Acronyms/abbreviations
ASIRI: Soil improvement by vertical rigid inclusions
CSTB: Scientic and Technical Resource Centre for the Building Industry DTU:
Unied Technical Document
DPM:
Special Contract Documents
ELS:
Serviceability Limit State (SLS)
ELU:
Ultimate Limit State (ULS)
G11, G12, G2, G3, G4, G5: Standardized geotechnical missions (NF P 94 500) ICEDA: Active Waste Conditioning and Storage Facility (project conducted by France’s EDF electric utility company at its Bugey site) MV1, MV2, MV3: Simplied models for computing footings on rigid inclusions, subjected to a vertical loading MH1, MH2, MH3: Simplied models for computing footings on rigid inclusions, subjected to a lateral loading ma: Result of the ground slab computation on an equivalent homogenized soil (DTU 13.3, Appendix C) mb: Inuence of rigid inclusions on a continuous ground slab mc: Interaction between the rigid inclusions and the joints OPM:
Optimum value found by Modied Proctor compaction test
Soed(SJ): Computation result of a continuous ground slab resting on an equivalent homog enized soil Soed(JT): Computation result of a ground slab with joints resting on an equivalent homogenized soil
IR(SJ): sions
Computation result of a continuous ground slab resting on a network of rigid inclu-
IR(JT): sions
Computation result of a ground slab with joints resting on a network of rigid inclu-
Summary
CHAPTER 1
Descriptions, history, initial developments and launch of the national project
The concept of installing a foundation on a soil reinforced by rigid inclusions constitutes one of the recent techniques for soil improvement and reinforcement. It is used to significantly reduce the settlement of the foundation block subjected to applied loads, while increasing its stability in resisting punching. This technique does not necessarily improve the soil in and of itself, as in most cases the actual mechanical characteristics remain unchanged following implementation of the inclusions. In reality, the soil is reinforced by means of creating a composite in which the loads applied are distributed between soil and inclusions. This foundation concept requires the presence of a inclusions and the structure they are supporting.
load transfer platform between the
1. RIGID INCLUSIONS AND FOUNDATION TYPES
It is helpful at this point to place the foundation concept of a soil reinforced by rigid inclusions into the general framework of major structural foundation principles (see Fig. 1.1): the shallow foundation solution is obviously preferable if the foundation soil provides a guarantee of stability and yields settlements acceptable for the structure; if at least one of these two criteria is not met, then the conventional alternative would consist of using deep foundations that have been designed to carry the entire load. Load is transmitted to the piles via a rigid element, which performs the role of distributing forces among the piles: this element is known as the pile group cap or the slab where piles are embedded. Yet, many intermediate situations can be found of average-quality soils and/or structures tolerating small deformations, whereby the shallow foundation solution is not acceptable while the deep foundation solution is overdesigned in comparison with what would be strictly necessary. This situation can be solved by simultaneously taking into account the respective load-bearing capacities of the cap and the piles, in considering that a part of the loads introduced by the structure is actually being transferred to the soil underneath the cap. This concept, referred to as a piled raft foundation, is attractive for soils featuring average and homogeneous characteristics. It leads to a fully satisfactory intermediate foundation system, in which a rigid connection exists between the piles and the pile cap. The advantage is to decrease the load transferred at each pile head (since a part of the load is transmitted by the cap to the soil underneath it), leading to a reduction in the required pile length or diameter. The piled raft foundation approach has unfortunately only been used sparingly in France, as opposed to other countries like Germany.
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The foundation on rigid inclusions approach is somewhat similar to the piled raft foundation approach, in that it associates rigid vertical elements, i.e. inclusions, with a flexible cap layer, yet without any rigid mechanical link placed between the two. From a purely theoretical standpoint, the rigid inclusion concept remains pertinent once the conventional rigid linkage between pile cap and piles disappears in the piled raft foundation configuration. In practice, this transition from piled raft foundation to a foundation on rigid inclusions is reflected by a combined geometric and mechanical discontinuity, along with the introduction of a relatively thin mattress, generally a granular layer, called the load transfer platform.
Figure 1.1: The various types of foundations.
This concept comprises various modes of interaction between: 1) the inclusions, each possibly topped by a cap; 2) the load transfer platform directly supporting the foundation; and 3) the foundation soil between the inclusions. The diagram in Figure 1.2 effectively summarizes this range of interactions, with a differential settlement at the load transfer platform base, which generates both a load transfer onto the inclusion caps via an arching effect taking place in the load transfer platform and a negative friction along the inclusions over the upper part of the soil between the inclusions. This load transfer by negative skin friction thus constitutes the critical component of this concept and will be developed at length in Chapter 2.
Figure 1.2: The four components of a complete foundation on rigid inclusions.
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2. DEFINITION OF A RIGID INCLUSION
Rigid inclusions, in the strict sense of the term, contain elements that are slender, often cylindrical in shape, mechanically continuous and typically vertical. They are laid out according to a regular mesh pattern, which must be adapted both to the nature and geometry of applied loads and to soil conditions. The cross-section of an inclusion is in theory constant, except for the cap, which features a larger cross-section. For vertical inclusions, the term group is employed, and the present Recommendations are intended solely for groups. Should the inclusions be slanted, in most cases at variable angles, then the term network is introduced.
The adjective rigid is required whenever the component material displays a strong permanent cohesion, thereby generating a level of stiffness significantly greater than that of the surrounding soil. Nonetheless, this stiffness may vary widely depending on the type of inclusion developed, ranging from the lime column to the metal section, yet still includes the gravel column injected with a cement slurry, mortar or concrete (whether reinforced or not). The rigid inclusion concept supposes that column stability is provided without any lateral confinement of the surrounding soil, which sharply contrasts with the concept of stone columns, whose justification would be totally different when adopting a rigid inclusion approach.
The force to be applied at the cap, for a given cross-section, depends on the intrinsic strength of the material composing the inclusion and thus varies from one type of inclusion to the next. The various types of inclusions described in Chapter 7 reveal the presence of large families, as characterized by both their stiffness and intrinsic capacity. As such, the design of a reinforcement using rigid inclusions requires a minimum internal strength of inclusion material and moreover must incorporate interactions with the surrounding soil: shaft friction, and forces at the top and tip. Consequently, the inclusion dimensions themselves prove to be highly variable. In most cases, their length extends to at least the thickness of the relevant soft soils, in recognizing that shorter inclusions would be less efficient due to a lack of load-bearing capacity. The diameter or transverse dimensions may also vary considerably since current techniques, and those practiced in France in particular, have led to installing diameters that routinely range from 250 mm to 800 mm for elements bored by a hollow auger, with these latter applications involving a technology identical to that derived for piles. Using the larger diameter from this range, 30-m long inclusions could be produced along the banks of the Loire River in Montoir-de-Bretagne ( Loire Atlantique Department). As an exceptional case, metal tube elements 2 m in diameter were placed by pile-driving for the foundations of the Rion-Antirion Bridge in Greece (Pecker, 2004). Smaller diameter inclusions should still be anticipated in the outcome of the structural design calculations or as validated by extensive practice. This is the case when introducing wood, such as bamboo, in the Far East or casting in place 15 cm diameter mortar elements reinforced by a metal section immediately driven into the mortar, as has been tested and used in Germany.
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As revealed in their mechanistic study (see Chapters 2 through 5), inclusions are intended to carry a significant fraction of the loads applied to a soft soil volume. They must therefore be designed to effectively withstand such loads; when given an appropriate cross-section, inclusions are most often stopped in a ground layer exhibiting sufficient strength. Typically not reinforced (especially in the presence of vertical loads), inclusions may sometimes receive rebar additions in order to resist the eventual transverse forces being exerted. This occurs, for example, when reinforcing the base of a tall embankment slope on a soft or compressible soil, where sliding stability is a prerequisite. Under this kind of scenario, in addition to placing rebar into the inclusions, it may be requested to introduce above the pile caps, or inside the embankment body, other reinforcements like horizontal geosynthetic sheets that absorb forces through traction and thus limit vertical forces transmitted to the inclusions. Furthermore, the lack of a rigid bond between inclusions and the supported structure, along with the absence of any group effect, is indeed favorable in the event of seismic loading (Chapter 2). 3. PILE CAPS
The pile cap lies at the summit of the rigid inclusion. The surface area of its cross-section divided by that of the reinforcement grid determines what is referred to as the " . This parameter, whose value often ranges between 2% and 10%, is an essential factor of reinforcement efficiency. In the majority of more common cases, the inclusion is simply embedded into the load transfer platform; under certain conditions and for the purpose of raising this coverage rate, the pile cap diameter may be increased or else the cap may be topped by a small slab. The choice is available between uniform inclusions laid out in a relatively dense pattern and elements sized with a diameter identical to the uniform inclusion but with greater spacing and topped by a cap. Both cases offer the same cover rate. Economic considerations however also play a role in the choice of cap type. 4. LOAD TRANSFER PLATFORM
The rigid inclusion concept implies that inclusion caps are not structurally bound to the supported structure, as opposed to what is traditionally practiced for a foundation on piles embedded into a tie raft. In contrast, bonding is created by interspersing between the caps and structure a distribution layer (or platform), on which the designed structure lies. The presence of this layer, called the load transfer platform and most often composed of gravel, determines the specificity of the rigid inclusion reinforcement technique. Inclusion placement, combined with covering their caps by a load transfer platform, ultimately leads to a composite or reinforced soil volume, which tends to be stronger and less deformable than the initial soil volume, allowing the structure to lay on a shallow foundation.
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A minimum load transfer platform thickness is necessary to allow for appropriate load transfer between inclusions and soil, as well as to limit forces within the supported structure (slabs, base plates, etc.). This thickness, often on the order of 40 to 80 cm, proves essential in deriving an optimal design for the supported structure, particularly with the aim of reducing bending moments in the slabs. The load transfer platform may be composed of the following, depending on the application: a simple layer of well-compacted granular material; a layer of soil treated with hydraulic binder; or a layer of soil reinforced by horizontal geosynthetic sheets. In the case of a granular material layer, the objective consists of obtaining a high level of compactness, which in turn yields a high modulus of deformation. In the case of materials treated with hydraulic binder (lime or cement-lime mortar), the treated layer must retain sufficient flexibility in order to avoid cracking; an extreme condition would be described as a slab supported by deep foundations, whereby the principle of foundations on inclusions would no longer apply. A load transfer platform composed of a granular soil reinforced by geosynthetic sheets is widespread in Anglo-Saxon countries. Geotextiles laid out in one or more horizontal sheets within the load transfer platform are less commonly used in France, since they have been deemed too easily deformable, especially when placed beneath slabs. The use of stiffer geosynthetics, such as geogrids or reinforcing steel meshes, is more efficient given that smaller deformations are sufficient to mobilize major forces. These horizontal reinforcements can also be laid out in one or more sheets either inside the load transfer platform or at the base of a homogeneous embankment, in which case they sit directly on the caps. For a given load transfer platform thickness, the use of geosynthetics serves to lower the cover rate value. The designer therefore has access to a wide array of potential solutions that would need to be optimized as part of a comprehensive technical-economic approach aimed at improving the design. 5. APPLICABLE SOILS
According to its underlying principle, the rigid inclusion system may be applied to all types of soil conditions. In practice however, its economic benefit remains confined to soft or medium soils, which are most often compressible, i.e. clay, silt or peat. Let's point out however that peat and, more generally, all materials containing organic matter require special attention due to the fact that they are subjected to secondary compression settlements. The type of soil, which is often saturated, along with its index parameters, loading history and mechanical properties are contributing factors in the choice of rigid inclusion production mode, and some of these modes, like for piles, might not be advised. The most widespread applications relate mainly to the limits of conventional soil improvement techniques because of their inability to guarantee the necessary settlement criteria or their requirement of a minimum quality threshold for the surrounding soil.
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Reinforcement by rigid inclusions can also be effective for the purpose of building on former waste storage sites. An analysis of such sites, in terms of chemical aggressiveness and evolution, becomes critical when dealing with organic soils. Settlements, especially when delayed, must be treated with special attention. The procedure for incorporating these elements will be discussed in Chapter 6. Under all circumstances, it is essential to recall that a foundation on rigid inclusions will undergo settlement on the order of a few centimeters. 6. FIELDS OF APPLICATION
All structures, regardless of their nature, require both internal and external design in order to ensure integrity throughout the construction period and then during the service life. This integrity relies on whether the deformations, settlements, horizontal displacements and distortions remain permissible, in recognizing the difficulty often involved when setting exact thresholds. European standardization also prescribes for geotechnical structures a specific deformation design. Until recently, this step primarily revolved around: justifications at the point of failure and the application of normal safety factors leading to relatively acceptable deformations for the structures. Only very severe deformation conditions would motivate undertaking a complete deformation design, which is often complex and ultimately results in choosing higher safety factors than usually admitted. The foundation design, notably for compressible soils, consists of identifying the most relevant solution that satisfies both stability and deformation objectives while seeking to optimize construction costs and scheduling. When the preliminary design of a structure reveals that the foundation soil in its current state is incapable of carrying the loads transmitted by this structure without either excessive settlement or incurring the risk of failure, then the designer must plan for a backup with deep foundations or preliminary ground improvement or reinforcement. The choice of solution thus depends on: the type of structure, type of applied loads (either distributed or point), structure sensitivity to settlement, type of foundation soil, and construction scheduling duration. From a general standpoint, soil improvement solutions are more likely to be reserved for structures with a large footprint and loads primarily of the distributed type. As an example, a very tall building with a strong concentrated load on a poor quality foundation soil will typically remain in the domain of more conventional deep foundations with piles or diaphragm wall barrettes. Conversely, many structures transmit distributed loads over large surface areas on the foundation soil, as: slabs and foundations of industrial and commercial buildings; storage reservoirs (water, oil products or liquid chemicals), treatment plant basins and retention facilities; highway embankments or railway embankments for high-speed trains.
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For all these categories of structures, the implementation of soil improvement or reinforcement solutions often proves well adapted and leads to savings when compared with other potential solutions. Under which conditions should rigid inclusions be favored over other soil improvement solutions such as vertical drains with preloading, stone columns, dynamic compaction or compaction by vibration? For the most part, this choice will be guided by soil conditions, type of structure with its maximum settlement specifications, the construction timetable and, lastly, execution costs. As regards soil conditions, it is a well-known fact that, for example, cohesive soils cannot be improved using dynamic methods such as dynamic compaction or vibroflotation. The previous section also observed that some very soft soils (e.g. silt) or organic soils could prohibit the use of a non-cement soil reinforcement technique like stone columns. The depth of such a poor quality soil layer is another element to be taken into consideration since some techniques become inefficient beyond a certain depth, whereas the technology for producing rigid inclusions is closely tied to that of piles and allows reaching greater depths using the right set of tools. Rigid inclusions will tend to be well adapted therefore in cases of soft or very soft soils, whether natural or manmade, with an adequate thickness. As for the structure, it is obvious that reliance on a rigid inclusion solution will become necessary in the presence of relatively heavy loads (e.g. a heavily-loaded slab, a tall reservoir) rather than a solution calling for flexible inclusions of the stone column type, which would not sufficiently reduce the predicted settlements. The acknowledgment of construction time frames may be a determinant factor as well. In the example of building an embankment on compressible soil, a preloading solution with vertical drainage is often adapted and economical, yet still requires a large span of available time to cover: vertical drain installation, embankment placement at its final height raised by the level of settlement compensation and temporary excess load (potentially requiring a phase-by phase rise if stability cannot be guaranteed), the waiting period for consolidation, and removal of the residual overload. A works program does not always offer this time frame, whereas a rigid inclusion solution will allow for quickly raising the embankment and immediately mobilizing the corresponding settlements. Moreover, the solution cost obviously remains a key selection criterion, with the solution ultimately chosen needing to be more competitive for the Project Owner. Let's also mention that in some cases, several solutions might be technically feasible, thus making it useful to compare the costs of these various options while not overlooking that this cost depends on both the type and density of inclusions required as well as the performance of the tooling proposed by contractors.
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a: Slabs and foundations of industrial buildings
b: Embankment used to access a bridge
c: Tanks and basins
Figure 1.3: Examples of structures reinforced by rigid inclusions.
What are the specificities of these various types of structures for which rigid inclusion solutions are commonly preferred?
For the first category, i.e. industrial and commercial building slabs, the problem to be solved is basically one of limiting settlements, since the soil is typically capable of carrying these distributed loads without any risk of failure. For these structures, special attention is paid during load transfer platform design since the slab structure tends to be thin and sensitive to the bending moments eventually created. Furthermore, let's not overlook the fact that the operating load on the slab will not necessarily be uniform (strips with fluctuating loads, traffic corridors, rack bases, etc.), all of which serves to complicate the design step, as will be discussed in Chapter 5. 26
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Let's also point out that should the slab foundation problem actually lead to a rigid inclusion solution, then the same technology may be used as a complement underneath the structural foundation footings.
For the second category, i.e. reservoirs, tanks and basins, the design criterion often stays focused on settlements, whose magnitude is greater due to significantly higher stresses than those found in the first category. Given the presence of load contributed by a liquid, the operating stress will be perfectly uniform, except under the walls or skirts of tanks where different localized reinforcements will be required. Nonetheless, it must be noted that certain structures of the metal tank type are capable of withstanding even greater settlements while remaining fully functional. For taller and more heavily-loaded tanks, the problem of load-bearing capacity might also need to be addressed.
In the third and last category, i.e. embankments, these structures for the most part are loaded in a permanent manner and by the embankment itself, with the extra operating load due to road or rail traffic being relatively small. In this instance, it is difficult to identify a specific structure, as opposed to the first two categories, and the embankment base is the target of a specific treatment to ensure that the load transfer platform role is being fulfilled. For this reason, full-scale testing undertaken within the scope of the ASIRI project has been divided into two distinct full-scale experiments on inclusions: under slabs and under embankments. For lower embankments, the design criterion will be based on settlements, while for taller ones the stability problem will become predominant and generate the parasite horizontal forces in the inclusions that need to be evaluated and taken into account. 7. A BRIEF HISTORY OF RIGID INCLUSIONS
Besides all available foundation soil improvement techniques, rigid inclusion reinforcement offers a new and efficient technique. Yet in reality, this technique has already been used many times over throughout history for building on difficult sites, such as marshy zones, without necessarily a solid understanding of its mechanism and behavior. It has longtime been observed that wood piles driven into the ground have served as foundations for increasingly heavy structures over the ages. However, only when a sand layer or stick bundle is positioned in between these piles and the structure can the thought be entertained that rigid inclusion reinforcement is actually at work. Noteworthy herein is the paper by Kerisel (1986), who cited an interesting publication by Coles (1986) relative to the construction of Neolithic roads in England. The ingenious underlying principle is as follows: long wood piles are driven at an angle in order to form a succession of trestles, on top of which a traffic lane built on planks is placed, yet this configuration can also comprise a line of vertical piles not aligned with the planks and placed along a central axis, as shown to the right in Figure 1.4.
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Figure 1.4: Foundation of Neolithic roads (England).
In the case described above, the planks are perforated with holes along the central axis to enable the vertical piles to slide freely. While the trestles alone were in no way able to offer a "foundation on rigid inclusions", the entire road foundation presented on the right-hand side of the above figure provides a very clever example. The forces exerted on the traffic lane to both sides of the central axis load the vertical piles with negative skin friction subsequent to a soil settlement caused by the trestles. This mode of operations is similar to what was adopted for certain buildings in Mexico City, as will be seen further below. The modern period has led to technical and scientific improvements in the potential of these foundation systems. A justification was provided with the study on negative skin friction Zeevaert (1957) undertook in Mexico. Since Spain s 16th-century conquest, Mexico City has faced acute problems regarding the behavior of its edifices. A very thick layer of soft volcanic clay (ash), which is both saturated and compressible, lies underneath the external loads and experiences settlements up to several meters. These settlements were triggered and intensified as of the beginning of the 20 th century by the permanent pumping of water into deeper layers.
From the 1960's on, the technical literature provides many examples where both the negative friction phenomenon and group effect are used advantageously, demonstrating that exterior piles contribute more than piles located in the interior. The few original examples that follow seem to have won only slight recognition. A more subtle justification technique would be the so-called overlapping piles introduced in Mexico by Girault (1969); Figure I.5 provides the corresponding diagram. The building rests on piles A that do not reach as deep as the substratum but instead stop in the deformable layers, in order to limit the substantial differential settlements occurring between the building and the surrounding soil, which winds up being compacted. These building settlements nonetheless require ensuring that any evolution diminishes over the time period following construction. Short, type B inclusions, called piles for this purpose, are dropped into the resistant layer and allow absorbing a fraction of the forces by means of the vault effect and by mobilizing negative skin friction along their shaft. This set-up results in a notable decrease in settlements and the appearance of significant forces in the type B inclusions.
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Figure 1.5: Building supported on "overlapping piles" (Mexico).
Correa (1961), as related by Broms (1969) and Auvinet et al. (2006), designed buildings set on an apron, with the combination resting on compressible soils undergoing consolidation. Inside these soils were vertical piles lying on the substratum layer, the top of which crossed the base of a hollow raft that had been designed as a box. This raft base was placed so as to slide along the piles (see Fig. 1.6) which were acting like rigid inclusions. The uniform load transmitted to the soil by the raft is then partially transferred onto the inclusions via negative skin friction and the group effect. These inclusions have been designed relative to the soil with a low safety factor and can be bonded to the raft without any technical difficulty should it be sought to definitively stop the settlements.
Figure 1.6: Inclusions independent of the supported structure (Mexico).
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In 1904 however, an engineer had proposed to support the Mexican Parliament palace building on driven metal inclusions not bonded to the structure. At present, Mexico City is the site of many construction projects featuring several thousand non-reinforced concrete inclusions, where justifications have been conducted by applying a finite element calculation method developed for this specific purpose. In Japan, Okabe (1977) performed a full-scale study, on behalf of the Japanese Railways, of groups of piles subjected to negative friction. The test site, containing 40 m of soft clay, displayed an annual settlement of 10 cm due to water pumping in the depth. Isolated metal piles, 60 cm in diameter, were able to bear up to 6,000 kN of undesirable forces due to negative skin friction. Some heavier structures were supported on pile groups, which themselves were surrounded by rigid inclusions independent of the pile group cap. The recorded measurements confirmed transfer of the majority of parasite friction onto the inclusions, with an unloading of piles bonded to the structure. At the European level, the first papers on the subject of structures supported on rigid inclusions relate to road or rail embankments. In this respect, Broms (1979) in Sweden supplied abacuses to proceed with designing pile groups, with the use of expanded pile caps being specified. Along these same lines, Rathmayer (1975) in Finland produced a series of similar recommendations with applications for road embankments. Several embankments for accessing bridges were built in Scotland in 1983 based on recommendations featuring the simultaneous use of geotextile reinforcement sheets above expanded prefabricated pile caps. Let's add the construction, for West Germany's railway system, beginning in 1976 of a 7 m embankment on rigid inclusions topped by prefabricated caps, as part of a layout designed by Smoltczyk (1976). All observations and measurements performed during the construction of these various structures have demonstrated the efficiency of reinforcement by rigid inclusions. In France, the first publication on reinforcement by rigid inclusions, presented in Figure 1.7, is credited to Gigan (1975), who used the technique without taking account of the mechanism. Nonetheless, discussions held with the specialized contractor, as recounted by the author, reveal the emergence of new ideas in the field of foundations. In the case studied, the focus was to improve the characteristics of former embankments, clayey silts then sandy silts, by means of driving cast-in-place piles without bonding them to the structures. This pile-driving step actually led to very significantly enhancing the characteristics of in situ soils, which were then deemed sufficient to accommodate a direct foundation. Designers however questioned one another over the complementary role played by piles, which despite being isolated from the base plates by a sand-gravel platform obviously performed like foundations on rigid inclusions and not like conventional piles, as had been suggested.
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Figure 1.7: Improvement in foundation soil characteristics thanks to the installation of piles (France).
The foundations presented in Figure 1.8 were designed in 1982 in Indonesia for reinforced earth protection walls nearly 10 meters high by 6.5 m wide on a set of liquefied natural gas retention reservoirs. These foundations are more technically sophisticated and rest on a 20 to 30-meter compressible clay layer. The walls are supported on open metal tubes 0.40 m in diameter, with each one covered by a square metal plate 0.50 m to a side. The group of piles is backfilled by a 1-m thick granular platform that had been horizontally stiffened by a continuous structure of metal reinforcement strips merging and covering the driven pile caps. While the rigid inclusions term had not been introduced at that time, this in fact was the applied technique, though it was poorly understood 20 years ago. Simon and Schlosser (2006) presented a paper on this case at an international congress on foundation soil reinforcement held in Mexico City.
Figure 1.8: Reservoir foundation on rigid inclusions (Indonesia).
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Two consecutive publications on the analytical design of rigid inclusion groups by Combarieu (1988, 1990), built upon the findings of two highly detailed studies (theoretical, experimental and bibliographical), were devoted to negative skin friction on piles. These works served to boost popularity in France of the foundation soil reinforcement technique using rigid inclusions. The first study examined the construction of embankments on mediocre quality soils; it provided a thoroughly justifying approach for the mesh pattern of a rigid inclusion groups and for the resistant inclusion embedment, in addition to determining compressible soil settlement. The second study related to calculating the inclusion groups for either large-sized flexible structures or rigid shallow foundations. For these latter elements, a more targeted justification had been proposed, dedicated to both load-bearing capacity and settlement, with this justification being close to that developed for piled spread footing foundations. These methods have been compared with the several existing European regulations as well as with the experimental results of embankments on soft soils supported by rigid inclusions (some of these results have already been cited). For rigid footings, the loading tests carried out on a plate on sand reinforced by rigid inclusions, as conducted by Plumelle (1985) in a large tank at the CEBTP testing facility, yielded results that match predictions fairly well. The transition into practice occurred in 1989 at the time of an initial project, namely the Carrère junction (Fig. 1.9), near the Lamentin-en-Martinique Airport (Combarieu et al., 1994). These works were, technically speaking, conservative, with the objective of building bridge access embankments consisting of Reinforced Earth abutments 6 to 7 m high. The footings of these abutments were supported by HP piles crossing both the Reinforced Earth walls and in situ soil.
Figure 1.9: Carrère junction abutment (Martinique).
The foundation soils were slightly sandy, saturated clays over a depth of 6 to 7 meters. Without being treated, these soils would have led to a settlement of 40 cm. The 124 inclusions were cast in place using a recovered metal tube and lost tip. Equipped with a central reinforcement rod, these inclusions were all between 8 and 9 m long, with a 30 cm diameter and 2.20 m spacing; they were subsequently covered by small, square prefabricated reinforced concrete caps 0.80 m to a side. At the embankment base, a 10 cm thick concrete slab,
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reinforced by a metallic latticework, was cast 20 cm above the pile caps. The settlements observed at the end of the works period were equal to 5 cm, without any subsequent evolution. More difficult projects ensued, with thicker and highly compressible soils that even contained substantial peat layers. The outstanding problems became more complicated while at the same time calculation methods underwent various changes, some significant examples of which will be cited below. In 1990, Simon and D Apolito (1991) studied the foundations and access embankments of an upper section over the A43 motorway, near Chambery in France (Fig. 1.10). This structure was intended to double the existing facility with a foundation composed of heavily-loaded piles on which any additional force impact needed to be prevented. Without special precautions, the 7 meters of new embankment would have generated 80 cm of settlement and an 11-cm horizontal displacement of the foundation soil, composed of 12 m of clayey soil.
The proposed solution consisted of foundation soil reinforcement by rigid inclusions, 37 cm diameter and 15 m long, performed by using the soil mixing technique and supporting both the new embankment and the shallow foundation of the new structure.
Figure 1.10: Abutment and embankment on rigid inclusions for the A43 motorway section, Chambéry (France).
Also during 1990, at Mandelieu on the A8 motorway (Bustamante and Gouvenot, 1991), annual deformations of 15 cm reaching the surface and affecting the upper 15 m of 30 m high marl embankments have been stopped using rigid inclusions. This significant highway operations obstacle was in fact due to successive pavement thickness increases. Bored rigid inclusions injected under high pressure over a height of approx. 18 m and then stopped in the lower part of the embankment (built with high-quality materials) allowed absorbing by negative skin friction the majority of the load due to the embankment's upper 15 m. All movements were practically stopped since the residual deformation only measured 3 mm over a 6-month period. In 1999, the Nantes - Saint-Nazaire Port authority built a container dock on piles, in Montoirde-Bretagne on the banks of the Loire River (Combarieu and Frossard, 2003). The transition between a slab on piles and the unstable riverbank was handled by floating rigid inclusions 30 meters long (Fig. 1.11) embedded into alluvial silts featuring 40-m power and average characteristics at these depths.
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The inclusions, with a 3.50-m spacing and 54-cm diameter, were produced using a continuous auger and composed of fiber-reinforced concrete. They were topped with 1.40 m 1.40 m prefabricated caps, which themselves were covered by a sheet of welded metallic latticework laid out in the granular load transfer platform. The calculated settlement, in the absence of any foundation soil treatment, was 1 m, and reduced to 20 cm with the rigid inclusions. In reality, the measured settlements were between 5 and 10 cm.
Figure 1.11: Transition zone on inclusions between a dock on piles and the riverbank (Montoir-de-Bretagne, France).
En 2000, it was proposed to found a closed frame made of reinforced concrete plus its corresponding 6 m high access embankments on rigid inclusions, at the exit of France s A15 motorway in Rouen, (Combarieu and Pioline, 2004). Use of this technique resulted in successfully meeting the requirements of an imperative 4 month schedule for opening the new lane to traffic. With 10 m of highly compressible soils, including peat, rigid inclusions 15 m long and 40 cm in diameter, produced with a hollow auger and topped by caps, brought settlements on the structure and its access ramps down to 4 cm in a homogeneous manner, a feat that could not have been accomplished by deep foundations placed exclusively beneath the concrete frame. The ICEDA (French acronym for Conditioning Installation and Storage of Active Wastes) project conducted in 2010 by France's electricity utility EDF at the Bugey site is a building intended to temporarily store wastes from dismantled 1 st-generation nuclear power plants and the Super-Phenix reactor, plus wastes produced from sections of the pressurized water reactor in operation. The predicted life span for this installation is 50 years. Its dimensions are on the order of 120 m by 60-70 m, and average loads range from 140 kPa (under the space used to store packages of waste) to 240 kPa (under the packaging workshop). Prior to these works, the ICEDA project zone stratigraphy was as follows: An average 5 m of sand-gravel alluvia offering high geotechnical quality; 35 to 55 m of silty clay; A molasse substratum located at a depth of between approx. 40 to 60 meters (pitch of the layer top on the order of 15%).
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The settlements evaluated during the preliminary design phase, of roughly 25 cm, were deemed excessive, and a solution to reinforce the compressible clay layer by means of rigid inclusions was adopted. This solution comprised (Fig. 1.12): 292 reinforced concrete inclusions 1 meter in diameter, with heads at least 2 meters below the underside of the rafts and tips reaching the weathered molasse (i.e. a length of between ~37 m and ~57 m), with spacing varying between 3 m and 6 m; A load transfer platform 2 to 2.75 m thick, composed of site alluvia homogenized and carefully compacted. The building settlement calculation on the reinforced soil led to values on the order of 4 cm.
Figure 1.12: Reinforcement by inclusions under the ICEDA project (Bugey).
This historical perspective will be concluded with the earthquake-resistant foundations implemented on the exceptional structure of the Rion-Antirion Bridge crossing the Strait of Corinth in Greece. This structure, built on a seismically active site with potential tectonic movement and accommodating a heavy maritime navigation route, rests on very thick soils with weak to average resistance and a highly heterogeneous composition (sands, silts, gravels, clays). The foundation soil, for three of the bridge supports, was reinforced by rigid inclusions composed of large-diameter (2 m) open metal tubes, driven over a depth of 25 to 30 m, filled with sand and then covered by a 2.80-m thick gravel embankment, thus forming the load transfer platform. The foundation, comprising a 90 m diameter box girder prefabricated and transported to the site by flotation, lies directly on the reinforced soil at the sea floor under 90 m of water. This foundation system, proposed in Pecker (2004), proved during the design phase to be much better adapted technically than a conventional foundation on piles, and this was especially so relative to the earthquake risk. The insertion of a very thick granular load transfer platform in fact created a fuse capable of absorbing by shear a large portion of the lateral forces caused by an earthquake, with the caisson foundation then capable of sliding more than 1 meter on its base without generating any significant impact on the structure. Figures I.13 and I.14 provide a glimpse of these exceptional foundations.
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Figure 1.13: The Rion-Antirion Bridge - Principle of the foundation solution on inclusions (Greece).
Figure 1.14: The Rion-Antirion Bridge - Cut-away diagram of the foundations.
These examples illustrate a few of the varied geotechnical problems that the new technique involving rigid inclusions has been able to solve. While up until 2000 the building of foundations using this process remained relatively infrequent, the number of such projects has increased since then significantly. This concept is now being proposed by the majority of contractors specialized in foundation works and soil treatment and moreover has been accepted by structural inspection bodies and insurance companies, provided that the contractors have been given a relevant set of specifications. Project Owners and Architects alike have found in this technique an effective response to project deadline constraints. The introduction of a slab and raft foundation has generated a number of attractive applications. Alongside these advances, many computation models have been developed in France, by either contractors or geotechnical design firms, entailing the use of analytical models relying on the concept of negative friction or numerical models incorporating the finite element method. 8. THE ASIRI NATIONAL PROJECT
As of the end of the 1990 s, many projects could already be cited in which rigid inclusions constituted the foundation system. Their use has only expanded since that time and the claims rate recorded through use of this technique remains, at present, comparable to that of more
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conventional soil or foundation reinforcement techniques. Though reassuring, this observation is still not sufficient. As indicated above however, a great diversity can be found within the set of implementation techniques, component materials and justification methods. As such, it seemed both useful and necessary to the French geotechnical engineering community to undertake a study intended to better understand the mechanisms and behavior of reinforcement by means of rigid inclusions, as well as to develop reliable design methods calibrated on the results derived from a wide array of instrumentation. At the end of 1999, a proposal was forwarded to the Institute for Applied Research and Experimentation in Civil Engineering (IREX), through its Soil Expertise Unit that interfaces with the geotechnical engineering community, by B. Simon with the firm Terrasol suggesting a national project on the topic. Three preparatory stages preceded the official launch of this project. A feasibility stage was initiated and officially commissioned in August 2000 to IREX by the Directorate for Research and Scientific and Technical Actions (DRAST) of the national Public Works Ministry. The working group coordinated by B. Simon (Terrasol) assembled representatives of project architects, design firms, structural inspection offices and specialized contractors, namely: SETRA (G. Haïun), LRPC de Rouen (O. Combarieu), Scétauroute (A. Morbois), Bureau Véritas (P. Berthelot), Ménard Sol Traitement (P. Liausu), Botte Fondations (D. Thiriat), Keller France (M. Naidji), Bouygues Offshore (which has since become Saipem) (J.P. Iorio) and Solétanche (T. Kretz). The feasibility report (IREX, 2000) was presented in January 2001 and underscored the strong interest behind reinforcing soils by rigid inclusions, through displaying the portfolio of completed and potential projects. A collection of the points critical to improving understanding of the phenomena involved has guided this proposal towards seeking a certification that will rely upon: A state-of-the-art assessment of practices both in France and abroad; An evaluation of the performance realized by the use of various inclusion techniques; a determination, via experimental campaigns (full scale, in a centrifuge and in a calibration chamber) of contributions from the various interaction mechanisms introduced into the process, and comparison of these observations with different models; Drafting of recommendations for field use with foundations, encompassing all aspects: choice of techniques, design and control methods. An initial program outline, covering 4 years, was presented along with a preliminary analysis of the bibliography. Based on the feasibility study, DRAST commissioned to IREX in October 2001 the task of establishing, as a preparatory step to a National Project, a state-of-the-art on soil reinforcement by rigid inclusions both in France and abroad, with this assessment jointly coordinated by R. Kastner (INSA Lyon) and B. Simon (Terrasol). L. Briançon executed this work program over the period February-July 2002, under close monitoring of a committee of experts, composed of: S. Borel, O. Combarieu, J. Garnier, E. Haza, Ph. Liausu, A. Morbois and L. Thorel. Another step, carried out simultaneously in Lyon and focusing on 3D modeling, gave rise to a Master4s degree dissertation, which was successfully defended in October 2002 (Laurent,
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2002). The memoranda on these accomplishments then resulted in an IREX report published in November 2002 (Briançon, 2002) offering a view of the current state of practices, by highlighting outstanding project developments / experiments and relying on the results of a survey conducted among specialized French firms. The general program adopted by the National Project was presented on February 4 th, 2005. This R&D project was planned to span a 4 year period, with the first three years being devoted to establishing and then implementing experimental and numerical protocols as well as an analysis of the initial experimental data, and the final year spent synthesizing all data collected, validating the various design methods and producing a document containing recommendations. The launch of this project was timed to coincide with the completion of the doctoral thesis defended by Orianne Jenck, in November 2005 at the INSA de Lyon institution, dealing with the physical and numerical modeling of the technique of reinforcement by rigid inclusions. During the first Executive Committee meeting held on March 29 th, 2005 at the FNTP offices under the aegis of IREX, the National Project (abbreviated under the French acronym ASIRI, for Soil Improvement by Rigid Inclusions) designated the following officers: President F. Schlosser, Vice President O. Combarieu, and Scientific Director B. Simon. Five working topics shape the scope of this project: Topic 1: Full-scale experiments, hosted by C. Plumelle and L. Briançon (Geotechnical Engineering Chair at the Cnam). This topic treats full-scale experimental campaigns in an extremely thorough manner and solely to satisfy research needs. Topic 2: Experimental sites, hosted by E. Haza (CER Rouen). This topic will focus on the limited instrumentation built for actual project sites, with the aim of compiling results. Topic 3: Laboratory testing, hosted by L Thorel (IFSSTAR Nantes). The scope here covers all tests intended to characterize materials and develop centrifuge-based tests. Topic 4: Numerical modeling, hosted by D. Dias and R. Kastner (INSA Lyon). Topic 5: Recommendations, hosted by O. Combarieu.
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References
Auvinet G., Rodriguez J.-F. Rigid inclusions in Mexico City soft soils: History and perspectives. Symposium Rigid inclusions in difficult subsoil conditions, ISSMGE TC36, Sociedad Mexicana de Mecanica de Suelos, UNAM, Mexico, 2006. Briançon L. « Renforcement des sols par inclusions rigides. art en France et à étranger ». Irex, opération du Réseau génie civil et urbain, 2002. Broms B.B. - Design of piles group with respect to negative skin friction; Specialty session on negative skin friction and 7 th.ICSMFE , Mexico, 1969. Broms B.B. - Problems and solutions to c Proc. 6th Asian regional conference on soil mechanics and foundation engineering , Singapore, vol. 2, 1979, p 2830. Bustamante M., Gouvenot D. « a nde hauteur par injection ». 10e conférence internationale de mécanique des sols et travaux de fondation, Florence, mai 1991. Coles J. - Sweet track to Glastonbury. Thames and Hudson, Londres, 1986. Combarieu O. - « Amélioration des sols par inclusions rigides verticales. Application à ». Revue française de géotechnique n° 44, 1988, p. 57-79. Combarieu O. « Fondations superficielles sur sol amélioré par inclusions rigides verticales ». Revue française de géotechnique n° 53, 1990, p. 33-44. Combarieu O., Frossard A. « Amélioration des sols des berges de Loire par inclusions ». 13e Congrès européen de mécanique des sols et fondations, Prague, 2003. Combarieu O., Gestin F., Pioline M. - « Remblais sur sols améliorés par inclusions rigides. Premiers chantiers ». Bulletin des laboratoires des ponts et chaussées n° 191, 1994, p. 5562. Combarieu O., Pioline M. - « sol amélioré par inclusions rigides » amélioration des sols en place, ASEPGI , 9-10 sept. 2004, Paris. Gigan J.-P. - « ». Bulletin des laboratoires des ponts et chaussées n° 78, 1975, p. 12-16. Girault P. Proc. Conf. on deep foundations, Mexican society of soils mechanics; Mexico, 1969, vol. 1. IREX - Pôle Compétence Sols. Utilisation des inclusions rigides pour le renforcement des sols de fonda ouvrages et de remblais. un projet national, 2000. Jenck O. - Le renforcement des sols par inclusions rigides verticales. Modélisation physique et numérique. Thèse de doctorat INSA Lyon, 2005. Kerisel J. - « Angleterre ; décou ». Revue Archéologia n° 292, 1986, p 56-60. Laurent Y. - Renforcement des massifs de fondation par inclusions rigides verticales, Étude bibliographique et numérique. Mémoire DEA INSA Lyon, 2002. Okabe.T. Large negative skin friction 9th ICSFME , Tokyo, vol. 1, 1977. Pecker A. « Le pont de Rion-Antirion en Grèce, le défi sismique ». 550 e conférence, . Plumelle C. - « Renforcement ». Revue française de géotechnique n° 30, 1985, p.47-57. Rathmayer H. « Piled embankment supported by single pile caps ». Proc. Istanbul conference on soil mechanics and foundation engineering , 1975, 8 p.
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Simon B. - « ns rigides en déformation ». XV e Congrès international de mécanique des sols et fondations, Istanbul, vol. 2, 2000, p. 1007-1010. « eur fondé sur pieux ayant subi des efforts parasites importants ». Colloque international fondations profondes , ENPC, Paris, mai 1991, p.285-292. Simon B., Schlosser F. - « Soil reinforcement by vertical stiff inclusions in France ». Symposium Rigid inclusions in difficult subsoil conditions, ISSMGE TC36 , Sociedad Mexicana de Mecanica de Suelos, UNAM, Mexico, 2006. e Smoltczyk - 6 Congrès européen de mécanique des sols et fondations, Vienne, 1976, vol. 3. Zeevaert L. Discussion on negative friction and reduction of Proc. 4th.ICSMFE , 1957, vol. 3.
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Summary
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CHAPTER 2
Operating mechanisms
This chapter presents the operating mechanisms applicable to a group of inclusions, which serves as an essential prerequisite to raising the notions of Design and Dimensioning in subsequent chapters. These mechanisms, which pertain to load transfer and subsequent impact on settlements, rely to a considerable extent on full-scale experiments, in addition to physical and numerical models, conducted within the scope of the ASIRI National Project; however, they also incorporate previous results, especially as regards the negative skin friction model proposed by Combarieu (1974). According to its underlying principle, the soil reinforcement technique using rigid inclusions introduces a whole sequence of complex interactions, from the structure being supported down to the substratum layer: Interaction between the structure and the load transfer platform, depending on both platform thickness and foundation stiffness; Interaction between the transfer platform and the reinforced soil block composed of the soft soil layer and rigid inclusions; Interaction at the interface between the soft soil and the inclusions, where successively negative then positive friction develops over the depth; Lastly, interaction between inclusion tip and load-bearing soil. Once these interaction mechanisms have been demonstrated, attention will focus on explaining the negative skin friction model, as well as load transfer mechanisms and the associated settlements and deformations. In order to trim the length of Chapters 3 and 5, dedicated respectively to design considerations and justifications, the analytical formulations related to negative skin friction and load transfer in the platform will be developed in this chapter. As a conclusion to this chapter, lessons will be drawn from full-scale field experiments, which are considered an essential step towards producing an effective design, along with a review of seismic loadings as set forth in the Guide on Soil Improvement and Reinforcement Processes under Seismic Action, published with the support of the French Earthquake Engineering Association (AFPS). 1. THE STRUCTURE - TRANSFER PLATFORM - INCLUSION HEAD INTERACTION 1.1. Interaction between the Reinforced soil and the Load transfer platform
Using the set of notations selected for the ASIRI National Project framework, the load transfer mechanism on inclusions within the granular platform can be quantified by means of the following parameters (Fig. 2.1):
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The forc load 1
and defined as the ratio of load Q p acting on the rigid inclusion head to the total vertical load applied on the element mesh (W+Q), where W is the dead load of the transfer platform and Q the force due to the surcharge applied; The marginal load transfer rate G, which represents the capacity of the granular platform to transfer surcharges towards the rigid inclusions, is defined as the ratio of load increment QP applied at the rigid inclusions to the incremental vertical surcharge Q applied.
Figure 2.1: Forces included in the efficiency calculation.
These two parameters can be written as follows: E
Qp Qp and G Q W Q
(2.1)
In order to describe the transfer mechanisms, it would be useful to distinguish the case of an embankment from that of a ground slab or shallow foundation. 1.1.1. Case of an embankment
The simplest case would be that of a load transfer platform composed of a granular material inserted at the base of an embankment; this case has been studied in simplified form by considering a uniform load exerted on the transfer platform. In using for this transfer platform a three-dimensional model built with discrete elements, results demonstrate that, for a given configuration, efficiency E increases with load until reaching a threshold value. This point corresponds to the gradual mobilization of shear strength in the granular material, through saturation. Moreover, calculations indicate the presence of tapered and relatively stationary zones within the transfer platform on top of the inclusion heads, where shear concentrates at the edge (Fig. 2.2, Chevalier et al., 2010). By this shear, load is transferred from peripheral zones towards the inclusion heads, with only slight displacements associated. The opening of cones is correlated with the peak friction angle of the granular material (or else with the critical state friction angle should the surrounding soil be highly compressible). 1
Also defined her eff Etass: see Section 5.
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Figure 2.2: Displacement fields (top view and vertical cross-section between rigid inclusions) for various granular transfer platform thicknesses (h m = 0.5 m, left) and (hm = 1.0 m, right).
The ultimate load efficiency increases with transfer platform thickness h m until reaching a threshold that defines a critical thickness. This thickness value may be interpreted as the height from which the cones meet; it also corresponds to the complete development of stress chains related to the most heavily-loaded grains in the granular medium that form like arches inside the load transfer platform (Fig. 2.3, Chevalier et al., 2010). The critical thickness depends on both the spacing between inclusions and mechanical characteristics (deformation modulus and friction angle) of the load transfer platform. A series of centrifuge experiments by Baudouin (2010) enables evaluating this thickness. Among other findings, these tests demonstrated that the critical thickness is found for an h m/(s - a) ratio value close to 2/3, with h m being the transfer platform thickness, and (s - a) the clear span spacing between inclusions.
Figure 2.3: Stress chain networks inside the granular transfer platform (h m = 1.0 m).
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In continuous numerical models, this phenomenon corresponds to the full rotation of principal stresses at the top of the transfer platform halfway between the inclusions. Jenck's two-dimensional model (2005), which yields access to the displacement field in the load transfer platform, highlighted that increasing the platform thickness mitigates the differential settlements at the surface. This is illustrated in Figure 2.4, where the evolution of settlements in the transfer platform is plotted, both in alignment with an inclusion and between two of them. According to this two-dimensional model, a relative transfer platform thickness hm/(s - a) equal to 1.3 prevents complete development of the arch, which is reflected by a persistent differential settlement at the surface. A relative thickness h m/(s - a) equal to 2.0 would enable completing the arching development, as reflected by a quick equalization of settlements within the load transfer platform. It should be pointed out that these values of 1.3 and 2.0 are taken only as examples due to the model limitations.
Figure 2.4: Vertical displacement of the two-dimensional model in alignment with an inclusion and between two successive inclusions, during consolidation at an area ratio = 22%.
From a general standpoint, Jenck (2005) and the series of physical models developed within the scope of the ASIRI National Project (Jenck et al., 2006) suggest that compressibility of the surrounding soil exerts no significant influence on efficiency E, as long as the soil is capable of providing the required level of confinement around the inclusion heads. When this confinement risks no longer being sufficient, the discrete models reveal the beneficial role played by a geosynthetic reinforcement placed at the base of the transfer platform. The following graphs (Fig. 2.5), extracted from Chevalier (2008), illustrate this role of geosynthetic reinforcement in the case of no downdrag effect between the soft soil and inclusions. They also display the evolution in efficiency E vs. applied loading with two values of stiffness J for the geosynthetic and a surrounding soil of variable deformability. It can be observed that the primary contribution of the geosynthetic becomes tangible for the most highly-compressible supporting soils. In this case, the geosynthetic, provided it offers adequate stiffness, is able to mobilize sufficient tension to allow confining the transfer platform base.
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Figure 2.5: Efficiency of the granular transfer platform E vs. surcharge q0 for various coefficients of subgrade reaction; h m = 0.5 m without a ground slab (discrete 3D model).
1.1.2. Case of a ground slab or shallow foundation
A shallow foundation, ground slab or footing, if encountered, plays a vital role in load distribution whenever the transfer platform thickness is less than the critical thickness defined above. In the case of a ground slab, the slab through its stiffness tends to make the settlements uniform and initiates a significant load transfer in alignment with the inclusions, along with the development of bending stresses in the slab. For a given transfer platform thickness, of less than critical height, the ultimate efficiency E with a ground slab is always greater than the value without a ground slab. Besides, efficiency E drops as transfer platform thickness increases, combined with a positive consequence, namely a decrease in bending stresses within the ground slab. This finding would suggest the existence of an optimal design for the platform-slab complex. The following series of graphs (Fig. 2.6), all extracted from Dinh s thesis (2009), display the trends in efficiency E vs. surcharge (see Fig. 2.6a), as well as the ultimate efficiency vs. transfer platform ground slab cases. It can be observed that ultimate efficiencies converge on a single value (obtained at the critical case). This observation would explain why the role of ground slab, as a load transfer element, becomes negligible from a certain transfer platform thickness.
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Figure 2.6: Evolution of boundary efficiencies vs. transfer platform thickness for the "embankment" and "ground slab" cases (physical model run in a calibration chamber).
The following diagrams (Fig. 2.7) illustrate the load transfer mechanism underneath both an embankment and a ground slab based on the results of a continuous 3D model using the Flac software (Laurent, 2002). case
(Fig. 2.7a), load transfer is driven by shear inside the embankment, with a rotation of the principal stresses that reflects arching development. ground
slab case (Fig. 2.7b), load transfer is governed by slab stiffness and leads to a stress concentration in the transfer platform columns situated on top of the inclusion. These columns become preferred zones in the development of stress chain networks. The stability of each column is provided by the confinement existing in the transfer platform as well as by the underlying soil reaction. Insufficient confinement degrades system operations. This point must always give rise to a specific verification in the ground slab case. In both cases at the level of the transfer platform base, it is noticed that the settlement gradient is localized in the immediate vicinity of inclusion heads, with settlement being relatively uniform between inclusions.
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Figure 2.7: Comparison of load transfer mechanisms underneath an embankment and ground slab (continuous 3D model).
case, efficiency under a ground slab or shallow foundation
is slightly improved with more highly compressible soils (Chevalier, 2008). 1.1.3. Special case of a transfer platform treated with hydraulic binder
Whenever mechanical properties, in particular shear strength, of the transfer platform component material prove inadequate, a soil treatment with hydraulic binder offers remedial action. The specificity of materials treated with hydraulic binder (i.e. lime or cement) is their ability to reach a significant tensile strength, in contrast with granular materials. Depending on the soil treatment type or formula employed, the associated behavior may be of either the type (case of lime- (a predominantly cement treatment). This consideration yields a different load transfer evolution at the inclusion head, as shown below in the centrifuge test results, whereby a mobile tray simulates the soil settlement (Fig. 2.8, extracted from Okyay, 2010).
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Figure 2.8: Mobile tray set-up for centrifuge tests and simulation principle for soil settlement.
1.1.3.1. Ductile behavior (lime-based treatment) The standard case of ductile behavior is that of a lime-treated silt. The material sets rather quickly and acquires its definitive strength after a relatively long hardening period. When the load is applied, the maximum efficiency E is gradually reached as the soft soil settles. Despite local cracking of the load transfer platform, this maximum efficiency is in fact very high (Fig. 2.9a). It can be concluded that the treated transfer platform partially plays the role that would be provided by a ground slab. In the absence of a large-sized ground slab or shallow foundation, the transfer platform thickness exerts a major influence due to the cracking risk associated with insufficient thickness.
1.1.3.2. Fragile behavior (cement-based treatment) As opposed to the lime-based treatment, a cement treatment quickly stiffens the soil in an irreversible manner and yields higher strengths. The behavior however is fragile and brittle. When load is applied, the maximum efficiency E is attained with very limited soft soil settlement (Fig. 2.9b), at a level observed to be less than that associated with lime-treated soil.
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Figure 2.9: Evolution in the load applied at the inclusion head with soil settlement (comparison between lime treatment and cement treatment) (Okyay, 2010).
Nearly all load is transmitted onto the heads of rigid inclusions. For higher loads, once the transfer platform has been damaged, efficiency drops instantaneously. This phenomenon is correlated with the transfer platforms fragile behavior. Given the considerable stiffness of transfer platforms composed of cement-treated material, the stresses transmitted prior to failure on the soft soil may be very small, or even nonexistent. The load transfer platform behaves like a slab loaded in bending. If the transfer platform is covered by a ground slab or raft, then the bending loadings will be distributed between this structural element and the transfer platform in proportion with their respective stiffness and according to the interface bonding condition. Transfer platform behavior may be influenced by actual placement conditions. An ineffectual treatment during reworking of the successive layers can considerably affect transfer platform homogeneity as a result of inadequate adhesion. 1.1.4. Edge effect
At the edge of the structure, interactions between the load transfer platform and inclusion heads are modified relative to conditions existing in the central part of the structure, due to the following factors: Asymmetry between the loading zone and the exterior unloaded zone, which necessarily causes significant stress field variations in the transfer platform; Limited extension of the load transfer platform around the inclusion; The transfer platform's reduced lateral confinement capacity; The transfer platform's vertical confinement limited to the structural footprint (ground slab or footing); A non-uniform stress distribution on the underside of a stiff foundation (stress peak at the foundation edge). These factors can induce specific failure mechanisms with, as a consequence, a lower load limit capable of being applied at the inclusion head. The continuous 3D model that served to justify the ICEDA project (as described in Chapter 1, Section 7) illustrates that the stress field at the head of the peripheral row can be distinguished Operating mechanisms
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from that of the interior rows, which appears to be independent of position (Fig. 2.10). In this project, the inclusions were 1 m in diameter, with 6 m spacing, and the load transfer platform was 2 m thick. The present calculation assumes a 200 kPa load (including the weight of the raft).
Figure 2.10: Example of a stress field at the periphery of the structure (ICEDA project).
1.2. Reinforced soil - Ground slab Interaction 1.2.1. Definition
As opposed to the ground slab placed on a homogeneous soil that, subjected to a uniform load, undergoes a uniform reaction across the standard section, the ground slab on a soil reinforced by rigid inclusions undergoes a non-uniform reaction whenever transfer platform thickness is less than the critical thickness. This reaction is stronger in alignment with each inclusion and then weaker in the area between inclusions (Fig. 2.11). Ground slab loading depends on how these reactions are distributed. A minimum transfer platform thickness is recommended, while recognizing that an increase in the relative transfer platform thickness tends to standardize these reactions. From another standpoint, a calculation performed that neglects the soil reaction between inclusions (as a suspended floor calculation) would turn out to be very conservative. This reaction distribution is to be evaluated by an appropriate calculation model able to take account of the following parameters: Deformation modulus of the inclusion; Deformation modulus of the load transfer platform, soft soil and inclusion embedment layer; Interactions of shear and/or shear failure between the various elements; Transfer platform thickness relative to inclusion spacing. Figure 2.11 shows the total stress measurements performed on the full-scale field experiment at Saint-Ouen-Aumône (2006). These measurements lead to the following observations, which effectively illustrate the interaction mechanisms between reinforced soil and the ground slab: 50
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In this case, which corresponds to a relatively thin transfer platform, nearly the same
stresses have been measured on the rigid inclusion as on the underside of the ground slab in alignment with the inclusion: the bulk of load transfer thus takes place through the ground slab; As consequence, stresses measured under the ground slab are sharply lower between inclusions than when aligned with them: the distribution of reactions is therefore nonuniform, a finding that must be taken into account when designing ground slabs.
Figure 2.11: The Saint-Ouen-l'Aumône experimental campaign (2006): Stresses measured on the 3D test section (ground slab and displacement inclusions).
Experimental and numerical studies have demonstrated that a thinner transfer platform enhances the efficiency of rigid inclusions in the presence of a ground slab, inasmuch as the ground slab will participate in the load transfer process. Compared to an infinitely thick transfer platform, in which failure shear mechanisms cannot extend to the upper part of the transfer platform, the presence of a ground slab on a thin transfer platform modifies how these mechanisms develop through loading of the ground slab itself. If a limited transfer platform thickness were associated with high mechanical characteristics (modulus of compressibility, friction angle, cohesion), it would be possible to obtain optimal efficiency, leading in turn to a maximum stress concentration on inclusion heads and therefore a maximum decrease of settlements. In exchange, the ground slab would be more heavily loaded in bending, as indicated in Figures 2.12 and 2.13 (Okyay, 2010). The characteristics of both transfer platform and ground slab need to be defined so as to identify an optimum between loadings in ground slab and settlements.
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Figure 2.12: Influence of the transfer platform modulus of elasticity on efficiency, settlements and loadings in a ground slab.
Ground slab: thickness = 20 cm; Transfer platform: height = 60 cm and friction angle = 31°, variable modulus of elasticity; Inclusions: diameter = 35 cm and spacing = 2 m.
Figure 2.13: Influence of the transfer platform friction angle and cohesion on bending moments in the ground slab (Okyay, 2010; Okyay and Dias, 2010).
Ground slab: thickness = 20 cm; Transfer platform: height = 60 cm and modulus E = 70 MPa, variable friction angle or cohesion; Inclusions: diameter = 35 cm and spacing = 2 m.
The definition and control of the transfer platform component material, as well as its level of compaction and aptitude for eventual treatment, are all keys to ensuring effective operations of this transfer platform on a group of rigid inclusions. It would seem essential to define a range of minimum and maximum values for the transfer platform s mechanical characteristics, while acknowledging the placement conditions and their eventual evolution (e.g. lime-treated soil, whose characteristics vary according to moisture conditions). The
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upper values derived typically correspond to an upper bound of structural element loadings, and lower values are associated with an upper bound of settlements. The soil study executed in accordance with the sequence of geotechnical engineering missions (see NF P 94-500 Standard, December 2006) is expected to establish a succession of soil and fill layers, along with the values of parameters required as input for the calculation model (Chapters 4 and 6). 1.2.2. Design considerations
Ground slab design and computation rely on DTU 13.3 (Standard NF P 11-213), yet still need to incorporate the specific type of non-uniform distribution of reactions on the ground slab underside. Along these lines, the simplified method for evaluating displacements and loadings, as detailed in Appendix C of DTU 13.3, can only be applied to a reinforcement configuration by rigid inclusions provided the corrective terms have been integrated. Such an approach will be explained in Chapter 5. These principles will now be applied by distinguishing inclusion meshes in a standard ground slab section (central zone removed from the edges and joints) from meshes at the periphery of the structure or joints and meshes positioned at a corner (Fig. 2.14).
Figure 2.14: Distinct zones to be considered for ground slab design and calculation.
The cases of point loads will also be determinant in the ground slab design process. In practice, ground slab stiffness relative to the foundation base will imply a redistribution of point forces on each mesh. The behavior of the foundation base (reinforced soil + transfer platform) will remain controlled by the resultant of various reactions derived (by analogy with Barré de Saint-s regularization principle for beams). Along these lines, the behavior of the foundation base below the ground slab can be related to the behavior found below a uniform loading with the same mesh resultant. Under these conditions, the ground slab needs to be studied when exposed to a combination of point loads at the ground slab surface, along with the reactions calculated on the underside. Such reactions are estimated for an equivalent uniform loading applied to each mesh (see Chapter 5: Justifications).
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1.3. Reinforced soil - Footing Interaction 1.3.1. Definition
Whenever foundation elements with strong inertia (i.e. footing, raft) are submitted to loadings that are not vertical and centered (moments, horizontal forces), the role of the transfer platform extends beyond distributing uniform vertical loads: it must provide for an effective distribution and transmission of forces, both vertical and transverse, between inclusion heads and surrounding soil. The transfer platform between the foundation base and inclusion heads allows for: Reducing, at the inclusion head, the axial and shear forces, and below, the compressive and tensile stresses tied to bending; in turn, this may serve to avoid having to install rebar or reinforcement elements (cage, section or tube); Better distributing the non-centered, vertical footing loadings on the inclusions; Limiting the parasitic forces relative to inclusion offset problems under the footing; Returning to a spread footing design, provided verification of sufficient transfer platform thickness to prevent inducing bending loads in the footing. 1.3.2. Design considerations
The rigid inclusion design is inextricably tied to the characteristics of both the soil to be reinforced and the load transfer platform. The justifications to be provided in design calculations pertain, in the general case, to the two following criteria: Maximum loads on the block of reinforced soil, and justification of the various types of foundations with respect to failure; Absolute settlement of the various structural elements within the given structure, justification of differential settlements either within the structure or between structure and ground slab, depending on the allowable tolerances specific to each structure as well as current regulations. The tolerance on inclusion execution (as will be defined in Chapter 7) must be taken into account during design of the footing and supported structure. Above this value, justification must be provided that behavior remains compatible with the structural configuration. 2. SURROUNDING SOIL - INCLUSION INTERACTION 2.1. Foreword
The interaction between surrounding soil and inclusion remains closely tied to the load transfer mechanism via a transfer platform. The role of the inclusions is to transmit the load resulting from structural dead load and service loads in deep soil layers offering greater load-bearing capacity. The purpose here is to increase load-bearing capacity while reducing structural settlements, for which the rigid inclusions will be designed in order to reach a load-bearing layer at depth.
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Inclusions are mobilized not only by the load directly applied on their head, but also by the friction of the surrounding soil, subjected to settlement under the loading applied by the weight of the structure. Over the upper part of the reinforced soil, the soil settles to a greater extent than the inclusions, whereas at the base the inclusions settle more than the soil. A depth therefore exists where both soil and inclusions settle to the same extent: this is known as the neutral point. In the upper part, this effect takes the form of a negative friction loading the inclusion, until reaching a maximum compressive load at the neutral point (Fig. 2.15).
Figure 2.15: Schematic of positive and negative friction.
This load is absorbed below the neutral point by means of positive friction and tip resistance. The incorporation of soft soil action on the inclusions is complex since it involves a combination of the following types of behavior: Transfer of forces by means of friction from the inclusion towards the soil and away from the soil; Transfer of forces at the inclusion tip; Soil settlement between inclusions; Inclusion settlement by elastic shortening and tip penetration. The main parameters to be integrated into the operating mechanism that describes this soilinclusion interaction are as follows: Area ratio; Soil overconsolidation ratio; Deformability of the soft soil; Deformability of the load-bearing soil; Eventual creep rate of the soft soil (case of organic soils, peat, etc.); Modulus of elasticity of the inclusion; Soil-inclusion shaft friction, negative as well as positive, and tip resistance.
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All these parameters exert an influence on both the stress distribution and differential settlements between the soil and rigid inclusions. Remark : An
evaluation of the shaft friction and tip resistance parameters must take into account the type of inclusion and its installation technique, by distinguishing those inclusions performed without soil displacement bored piles) from those executed with soil displacement driven steel pipe piles ). 2.2. Negative skin friction 2.2.1. Underlying principles
Negative skin friction is produced when soil settlement along the rigid inclusion shaft exceeds the vertical displacement of the rigid inclusion itself. In contrast with the pile, rigid inclusions do not experience negative skin friction like a parasitic force, but instead the negative friction serves to relieve the soft soil layer of the residual stress existing at the transfer platform base. Such transfer onto the inclusions occurs gradually with depth. 2.2.2. Neutral point
The equality between the rigid inclusion vertical displacement and the vertical soil settlement along the rigid inclusion serves to define the depth h c of the neutral point N. Above this point N, friction is negative, while below it turns positive (Fig. 2.15). At its head, the rigid inclusion absorbs a load Q P(0). At point N, the rigid inclusion is subjected to this load Q P(0) increased by the negative skin friction force F N (F N = 0hc (z).D.dz) between the rigid inclusion head and point N. The axial force in the rigid inclusion therefore rises between inclusion head and neutral point. This total force [Q P(0) + F N] must then be balanced by the positive friction force F P below point N plus the tip force QP(L) (Fig. 2.15): QP(0) + F N = FP + Q P(L). In the vicinity of the inclusion shaft, v thus decreases with depth since a portion of the ground weight is transmitted to the inclusion via the negative skin friction mobilized above this given point: such an effect is known as the downdrag effect. 2.2.3. Mobilization over both time and depth
The maximum negative skin friction depends on: Soil settlement (as a function of its compressibility and consolidation time); Inclusion displacement (as a function of its rigidity and embedment stiffness); Surcharges compared to the set of initial conditions; Soil-inclusion interface conditions; Boundary conditions (single inclusion vs. inclusion within a group).
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The negative skin friction stress f n increases with relative soil-inclusion displacement y until reaching a threshold value q s for relative displacement yc (on the order of a few millimeters), hence a very small amount (Fig. 2.16). Given the consolidation process, this negative skin friction f n is maximized in the long term and must be calculated on the basis of effective stresses.
Figure 2.16: Simplified mobilization law of unit shaft friction q s.
The methods typically implemented to evaluate the forces due to negative skin friction do not explicitly introduce a mobilization law for these forces as a function of relative soil-pile displacement; instead, these methods tend to be failure methods. The relationship between effective vertical and horizontal stresses can be written as follows: h v (z) (2.2) with K being the earth pressure coefficient at the soil-pile boundary. soil-pile friction angle, which depends on both the type of pile and soil characteristics. The shear stress due to negative skin friction is then expressed as: f n(z) = K. v (z). Tan (2.3.)
Negative skin friction may appear in cases other than surcharges on a soft soil, namely: Natural or artificial soils (recent embankments) settling under their own weight; Lowering of the water table; Liquefiable soils or loose soils that may settle by either saturation or densification in the presence of seismic effects. A detailed description of the protocol for calculating negative skin friction around a pile (or an inclusion), whether single or in a group, will be provided below (see Section 3 of this chapter), with reference to the model proposed by Combarieu (1974, 1985). 2.3. Soil resistance mobilization
The resistant part of the inclusion located below the neutral point, also called the resisting length, allows absorbing, through positive friction and tip resistance, the maximum inclusion load at the neutral point. Mobilization of the positive unit shaft friction depends on relative displacement between inclusion and surrounding soil, should the inclusion displacement be greater than soil displacement. The resisting length of the inclusion will be calculated according to methods specifically devised for deep foundations. The safety factors however will be deliberately selected at
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lower values (without applying a reduction factor to the creep load), given that a higher displacement can be accepted for an inclusion than for a deep foundation. 2.4. Inclusion settlement
Loading tests have demonstrated that, like for piles, the vertical settlement of a single inclusion bearing on a stiff layer is weak under a service load. Frank and Zhao (1982) provided a method for calculating these settlements based on pressuremeter characteristics. The settlement of an inclusion results from both its tip settlement and elastic shortening. Elastic shortening of the various types of inclusions tends to be small in comparison with soft soil settlement. Examples of characteristic deformation modulus values for inclusions are given in Chapter 7 (Section 3.4). As explained in Section 5 of this chapter, the settlement of a group of inclusions will be calculated as the sum of two primary components: settlement of the actual reinforced soil (including transfer platform settlement), combined with the settlement of non-reinforced deep layers. 2.5. Loadings other than vertical and centered 2.5.1. Asymmetrical loading
In the case of large-sized foundations, the predominant vertical direction of loads to be absorbed and the type of interaction mechanisms between soil and inclusions lead to primarily compressive forces in the inclusions. Only those inclusions placed at the periphery of a loaded zone would be able to accommodate additional bending loadings (i.e. the edge effect). In the example of a small group of inclusions underneath a single footing (Fig. 2.17), the edge effect that already exists in the presence of a vertical load becomes predominant when the footing is exposed to a combined loading (i.e. transverse force and moment). A specific study is needed to define the geometry and mechanical characteristics of the transfer platform that yield a sufficient reduction in loadings in the inclusions so as to avoid, if applicable, reinforcing the inclusions.
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Figure 2.17: Example of asymmetrical loading leading to a non-uniform distribution of forces in the inclusions.
Under large-scale foundations, edge effects are to be taken into consideration, and this leads to calculating the inclusions close to edges differently from those located in the central zones, whose loadings tend more often to be uniform. As an example, under tall embankments, bending loadings may appear at the heads of inclusions placed below the slope, in addition to compressive loadings developed along the embankment axis. This condition might justify the incorporation of reinforcement layers (geosynthetics, geogrids) at the embankment base in order to reduce the horizontal displacement and its influence on inclusion heads. The asymmetry of embankment loads leads moreover to a non-uniform distribution of vertical forces within the inclusions. 2.5.2. Transverse loading
As opposed to footings placed on piles (where transverse forces are fully distributed at the pile heads), the granular transfer platform absorbs a portion of deformations, which could produce the beneficial impact of decreasing displacements at the inclusion heads. The transverse forces exerted on the foundation are distributed, via the granular transfer platform, between the inclusions and the soil.
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These lower forces applied at inclusion heads, when combined with the fact that inclusions are free head, explain why the loadings induced in inclusions are typically significantly lower than in the case of a footing installed on piles. 3. LOAD TRANSFER MECHANISMS
Load transfer mechanisms rely heavily on the model Combarieu (1974, 1985) proposed in order to describe negative skin friction either around a single pile or on a group of piles. In the case of reinforcement by rigid inclusions, this original model is only applicable to the height of soft soil around the inclusions. Combarieu subsequently proposed extending this model to the soil located above inclusion heads in order to study load transfers within the platform, specifically in the following cases: Embankments lying directly over the inclusions (piled embankments) (1988, 2007); Load transfer platforms in the case of flexible ground slabs or rigid footings lying on soils reinforced by inclusions (1990, 2007). Other methods have also been proposed to study load transfer inside the platform, including method. 3.1. Negative skin friction over the soft soil height 3.1.1. Single inclusion or single pile
The model was developed to calculate the negative skin friction acting on structural piles. Conventional methods consist of estimating the critical height h c, which corresponds to the inclusion length actually subjected to negative skin friction (Fig. 2.18), and then calculating the intensity of this negative friction based on the following relation: hc
F N 2 r p K tan ' v ( z , r p ) dz
(2.4)
0
in assuming v (z, r p) in the soil along the inclusion is not disturbed by the presence of the inclusion itself and is identified with 1 (z), the effective vertical stress in free field without inclusions.
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Figure 2.18: Negative skin friction calculation diagram.
The height hc over which negative skin friction . K.tan is the term that relates shear stress and vertical stress along the inclusion shaft. According to Combarieu s proposal, which complies with those of many specialists, the two terms need not be differentiated (i.e. K: earth pressure coefficient, tan : coefficient of soil-pile friction), but instead their product is to be treated like a single parameter whose value depends on the type of pile (or inclusion) and on soft soil properties. These values were determined experimentally on piles. When F N is calculated using this method, its value always remains overestimated due to the fact of overvaluing v (z, r p). Combarieu (1974) proposed a more satisfactory approach for dealing with negative skin friction, by introducing a modification in the state of stresses along the inclusion shaft as a result of the downdrag effect. This modification reflects the fact that, with the pile or inclusion taking a negative skin friction force, the soil around the inclusion becomes unloaded. The effective vertical stress along the inclusion is thus locally reduced and its value less than that derived in the absence of an inclusion. This force transfer is manifested by a stress v (z, r) being variable and increasing with distance r to the inclusion axis. This variation describes a shear that develops as a function of surface areas concentric to the inclusion. The approach can also be extended to groups of inclusions and enables determining the critical height hc. This method does not impose any other hypotheses than a sufficient level of soil compressibility, so that the settlement allows attaining the ultimate negative skin friction value.
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Combarieu (1985) went on to define a radial variation law for vertical stress at height z, by introducing the notion of downdrag effect of soft soil around the inclusion (Fig. 2.19).
Figure 2.19: Distribution of stress v (z, r).
For r > r p: r r p r ' v ( z , r ) ' v ( z ) ' 1 ( z ) ' v ( z )1 e p
(2.5)
where: 1 (z) is the effective vertical stress in free field within the ground in the final state, as calculated without taking into account the presence of the inclusion; v (z) = v (z, r p) is the effective vertical stress at the inclusion contact in the final state, while taking into account the downdrag effect; v (z, r) is the actual effective vertical stress at a distance r from the inclusion axis, in taking into account the disturbance due to the presence of the inclusion; is the so-called downdrag coefficient that characterizes the magnitude of the downdrag effect around the inclusion. The downdrag coefficient is assigned the following values, all of which have been obtained experimentally (Fig. 2.20).
Figure 2.20: Abacus used to determine the value of (Standard NF P 94-262).
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1 0.5 0.25 K tan
0.385 K tan
0
if if if
K.tan 0.15 0.15 K.tan 0.385 K.tan 0.385
The case = 0, i.e. maximum downdrag effect, corresponds to the simplifying hypothesis of zero reduction in vertical stresses due to the presence of inclusions. The values of K.tan , which are correlated with the type of inclusion or pile as well as with the nature and characteristics of the surrounding soil, stem from full-scale experiments conducted on deep foundations exposed to typically strong intensities of the final negative skin friction that is necessary for a successful interpretation (only obtained after what are often long consolidation periods). Table 2.1 below lists the values of K.tan proposed in 1985 for piles (which could also constitute rigid inclusions), by focusing on those piles whose mode of execution is applicable to current inclusion types of smaller dimensions. Table 2.2 provides the values of K.tan proposed in the NF P 94-262 Standard (Appendix H: Evaluation of negative skin friction on a foundation element ). The various types of inclusions currently performed on sites have been introduced into this table as well. It must nonetheless be noted that in justifying a group of inclusions, the major part of forces is absorbed at the inclusion heads; forces absorbed in the soft soil by means of negative skin friction are relatively weak, and the influence of the term K.tan thus remains limited. Table 2.1: Recommended values of parameter K.tan.
Piles or inclusions executed by displacement or under pressure, in fine-grained soils with a liquid to soft consistency or in organic soils *reduced to 0.15 for open elements Piles or inclusions bored into fine-grained soils with a liquid to soft consistency or into organic soils *reduced to 0.10 for the lost casing method Piles or inclusions executed by displacement or under pressure, in fine-grained soils with firm to stiff consistency *reduced to 0.20 for open elements Piles or inclusions bored into fine-grained soils with firm to stiff consistency *reduced to 0.15 for the lost casing method Piles or inclusions executed by displacement or bored, in sands and gravels
0.20* 0.15* 0.30* 0.20* 0.35-1 (depending on compaction grade)
Table 2.2: Values of the K.tan parameter (Standard NF P 94-262).
Peat Clays and silts Sands and gravels
Organic soils Soft soils Firm / stiff soils Very loose Loose Dense
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Bored cased piles 0.10 0.10 0.15
Bored piles 0.15 0.15 0.20 0.35 0.45 1.00
Driven piles 0.20 0.20 0.30
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The principle of vertical force conservation in the model yields the following differential equation, written using stress v (z) as the variable (Combarieu, 1985): d ' v ( z ) d ' ( z ) ( ) ' v ( z ) 1 dz dz
(2.6.)
with:
( )
² K tan 1 r p
(2.7)
The solution to this equation results in the general expression of effective vertical stress v(z) at the soil-pile interface, over intervals where d 1(z)/dz can be assumed constant: 1 d ' 1 ( z ) 1 d ' 1 ( z ) ' v ( z ) e ( ) z ' v ( 0 ) (2.8) ( ) dz ( ) dz In the special case of a homogeneous, saturated soft soil layer with groundwater at the surface d ' ( z ) ' in the final state. and subjected to a uniform surcharge q 0, d1(z)/dz is constant: 1 dz
Hence, after consolidation, 1 (z) can be expressed as: '1 z ' z q0 , where submerged unit weight of the soil. This simple case leads to the following: ' ' (2.9) ' v ( z ) e ( ) z q0 ( ) ( ) and the height h c over which negative skin friction is exerted, i.e. from the inclusion head to the neutral point as determined v (hc) = c, verifies the relation: ( ) hc 1 e ( ) hc q ( ) 0 1 ' which, as a preference, is to be solved graphically. If the calculated hc value is less than H (i.e. the soft soil thickness), then the negative skin 2 r p K tan friction resultant is written as: F N q0 , ( ) meaning that proportionality exists between F N and q0. If the calculated hc value is greater than H, then F N is to be applied over the entire soft soil thickness H, with the negative skin friction resultant being expressed as: 2 r p K tan F N ' hc q0 ' v (hc ) ( ) v (hc) is given by: ' ' h ' v (hc ) e ( ) c q 0 ( ) ( ) It is shown that F N, which reaches its maximum value at the end of the consolidation period, is very simply correlated with the degree of consolidation whenever h c is less than height H.
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3.1.2. Inclusion within a group
In the presence of many inclusions, the group effect, which increases as the mesh becomes tighter, combines with the downdrag effect. Let's take a group of rigid inclusions regularly distributed in an unlimited number (Fig. 2.21).
Figure 2.21: Layout of the group of rigid inclusions.
The following parameters are to be defined: a and b: distances between inclusion axes along two orthogonal directions, r p: inclusion radius. The calculation is comparable to that of a single inclusion, merely expressing the conservation of forces applied at the element mesh A = ab (zone of influence). This element mesh is related to a cylindrical mesh of radius R, radius of influence (Fig. 2.22): R
ab
Figure 2.22: Zone of influence of one pile in an unlimited group.
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Figure 2.23 schematically illustrates the negative skin friction model being studied along with its associated notations.
Figure 2.23: Negative skin friction model according to Combarieu (1985).
This analysis results in a differential equation identical to that in (2.6), which makes it possible to determine v (z, r p) (Combarieu, 1985): d ' v ( z , r p ) dz
( , R ) ' v ( z , r p )
d ' 1 ( z )
(2.10)
dz
with:
( , R )
²
K tan
R 1 1 r p e
R r p r p
r p
if 0
(2.11)
or:
( 0 , R )
2
K tan
R 2 1 r p
r p
if 0
(2.12)
These relations are also given in the form of an abacus (Fig. 2.24).
Figure 2.24: -262).
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A solution is feasible in situations where the term
d ' 1 ( z ) (homogeneous at a unit weight) dz
can be considered as constant, i.e. cases in which the profile 1 (z) can be linearized by layer. Both the critical height determination and total negative skin friction force calculation are carried out in the same manner as for a single inclusion. A number of software programs have been developed for this purpose. The vertical stress profile v (z, r) is obtained by solving (2.10), which is a first-order linear differential equation. This solution uses as input the vertical stress profile 1 (z) that would be obtained without any inclusion and the values of the two coefficients K.tan and , which serve to characterize the downdrag effect around the inclusions (by which vertical stress at the inclusion contact v (z, r p) decreases). The negative skin friction along the inclusion is expressed like for the single inclusion, with () being replaced , R/r p), where ) corresponds to the limit derived for R/r p = In assuming, as is the case with older conventional methods, that the vertical stress 1 (z) is not disturbed by the presence of rigid elements, this would be equivalent to a maximum downdrag effect = 0, which does not prevent the group effect from intervening. Integrating equation (2.10) yields the solution provided by Zeevaert in 1957, which constitutes a specific solution of the proposed more general solution. The average vertical stress v*(z) between inclusions is expressed, over the height where negative skin friction is applied, as follows:
v * ( z ) ' 1 ( z ) ' 1 ( z ) ' v ( z , r p )
2 K tan r p
R r p ( , Rr ) p 2
(2.13)
2
The critical height h c is often determined by adopting the hypothesis that negative skin friction only acts if the stress in contact with v (z, r p) is greater than the initial stress v0 (z). The negative skin friction force acting on the inclusion can then be calculated by the expression in (2.8) over the height h c or H. Simon (2001) suggested an alternative whereby negative skin friction only develops upon reaching a depth where the average vertical stress between inclusio v*(z) remains greater than or equal to the initial stress v0 (z). Combarieu's approach is based on ultimate stresses, where inclusions are only slightly deformable, while the soil settlement is sufficient for shear stresses in contact with the inclusions to reach their ultimate values (z); these ultimate values are obtained for relative displacements between soil and inclusion (or pile) on the order of 0.01 D (where D is the element diameter). They stem from experimental tests on negative skin friction. In order to verify method applicability, a study of deformations without inclusions must be performed. More specifically, this method produces: The shear stress at all points on the inclusion shaft; (z) = K.tan . v (z, r p); * The average vertical stress v (z), as used in the settlement calculation; depth hc of the neutral point.
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3.1.3. Inclusion in a group with a limited number of inclusions
In the case of a limited group of inclusions, the proposed rules are semi-empirical and have been calibrated on centrifuge test results (Cartier, 1994). In order to evaluate the negative skin friction on any element in a limited group of inclusions, the single file case (Fig. 2.25) must be distinguished from that of several rows (Fig. 2.26) and then the following parameters need to be determined: F N (): total negative skin friction force on a single inclusion; F N (R): total negative skin friction force on an inclusion in an unlimited group. The negative skin friction on each group inclusion (whether interior, exterior or placed in the corner) is obtained by a linear combination of the terms F N ( ) and F N (R); this combination is defined by separating either the single file case or the several row case. 3.1.3.1. Single file F Na
1 2 F N ( R) F N () 3 3
F Ne
2 1 F N ( R) F N () 3 3 Figure 2.25: Layout of an inclusion in a single file.
3.1.3.2. Several rows
F Ni F N ( R)
F Na
(i) interior
7 5 F N ( R ) F N () (a) corner 12 12
5 1 F Ne F N ( R) F N () 6 6
(e) exterior
Figure 2.26: Layout of an inclusion in several rows.
3.1.4. Model limitations
The following limitations need to be taken into consideration: The shape of the selected v (z, r) field implies that shear on the cylinder of radius R is nonzero at the edge of the cylinder equivalent to the mesh. This point contradicts the fact that at the mesh edge, for reasons of symmetry, the shear must equal zero; The method only applies to the volume where the negative skin friction actually develops; it does not allow analyzing force distribution below the neutral point. Under the horizontal 68
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plane passing at this level ("neutral plane of equal settlement"), friction is positive and contributes to increasing the load transmitted to the soil between inclusions by means of reducing the force being supported by these specific inclusions. The resulting settlement of the surrounding soil can therefore only be estimated in an approximate manner based on a set of complementary hypotheses; Soil stiffness under the inclusion tip and deep layer stiffness also prove to be major factors since they determine the magnitude of differential settlement between the inclusion tip and surrounding soil, thereby justifying the implicit hypothesis of Combarieu s method, according to which relative soil-inclusion displacements in a standard cross-section are of sufficient magnitude for the negative skin friction to reach its ultimate values. 3.2. Load transfer in the platform
Among the various analytical methods available to evaluate load transfer in the platform, the ASIRI National Project forwards the two following tested methods: The fictitious inclusion method (developed by Combarieu), which offers the advantage of providing a homogeneous approach consistent with the negative skin friction evaluation method described above, based on the same set of principles (downdrag effect on fictitious columns in the embankment); The diffusion cone method, which entails an approach compliant with the mechanisms exposed during the various experiments and modeling exercises conducted within the scope of the ASIRI National Project (i.e. load transfer by diffusion above the inclusion), as detailed in Section 1 of this chapter. These two methods and their limitations will be discussed below. 3.2.1. The fictitious inclusion method
3.2.1.1. Description Combarieu (1988) proposed modeling the phenomena involved in load transfer above the inclusion heads by assimilation with the negative skin friction that would have developed, had these inclusions been fictitiously extended over the same height h r as that where this negative friction has been exerted (Fig. 2.27). Parameter h r is thus equal to the thickness H R of the embankment or load transfer platform supporting a flexible structure subjected to a uniform load of intensity q0. In the special case of cohesionless materials, it is suggested to set the value of r = 1 r : embankment friction angle), yielding the value = 0 for the downdrag coefficient. The vertical stress in the soil between inclusions is then uniform and given by: q S
r r
( 1 e r hr ) q 0 e r hr
(2.14)
with: r
2 r p K tan r R² r p ²
where: r p: inclusion radius, R: equivalent mesh radius (or 2R: spacing between inclusions).
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In the special case of embankments made with cohesionless materials, this expression is the same as that exposed by Terzaghi in his study on the silo effect for sands.
Figure 2.27: s approach (1988).
In its general form, µ r is also a function of (directly related to K.tan), the downdrag coefficient introduced for negative skin friction and set equal to zero for a high-quality embankment (granular material). The expression yielding q s+ makes it possible to study the influence of the various geometric parameters (r p/R, HR /R) on system efficiency. Moreover, in the calculation performed in accordance with Combarieu's method, it has been verified that the load absorbed by an inclusion is bounded by the load value corresponding to its zone of influence. By applying Combarieu's model to the embankment with fictitious elements featuring the same cross-section as the inclusions in soft soil, a comprehensive approach can be established for the design of reinforcement by rigid inclusions, through setting an objective of minimizing the stress applied on the soft soil. From a general standpoint, it is sought to limit the stress q s+ on the soil between inclusions, with the aim of limiting settlements. By setting an appropriate value for the stress reduction rate (SRR) = qs+ / r .hr , it becomes possible to determine an acceptable mesh geometry for a fixed inclusion radius r p. Each inclusion is then subjected to the following force at the head: (F N + r p2.r .hr ), where F N is the negative skin friction developed over height h r . 3.2.1.2. Limitations and improvements introduced The original method proposed by Combarieu in 1988 to treat the fictitious inclusion presented the disadvantage of leading to stress reduction rate (SRR) increasing with embankment height HR , which contradicts both the observations recorded on reduced-scale models and the theoretical results established by Hewlett or Kempton (which indicate that this rate actually reaches a threshold value vs. increasing embankment heights).
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In reality, the method to be applied is based on the position of an upper plane of equal settlement in the embankment, and not based on the upper surface position of the embankment. For the work carried out in the ASIRI National Project, the method has been modified (Combarieu, 2007, 2008) as regards its extension to the calculation of forces passing through the embankment above the inclusion heads. For this purpose, an empirical formulation has been introduced to provide the active height h a between inclusion heads and the upper plane of equal settlement (Fig. 2.27), vs. radius R of the equivalent circular mesh, i.e.: ha R R 10 0.4(6 )² if < 6 r p r p r p ha R 10 and if 6 r p r p It is also proposed to evaluate the coefficient K.tan in the embankment by means of the following empirical relation: K.tan = 1.1 e E/E0 (2.15) based on the deformation modulus E of the layer of thickness h a (with E0 = 50 MPa). This modulus value E is equal to the E v2 modulus measured at the 60-cm diameter plate, which may also be estimated from correlations with other deformability measurements. The residual stress between inclusions can now be written under these conditions: q s q( ha )
r r
( 1 e r ha ) r ( hr ha )e r ha
(2.16)
If the calculated value of h a exceeds H R , then it is necessary to set h a = H R . The SRR ratio of residual stress q s+ to applied stress r .hr tends towards the finite value e r ha as hr increases indefinitely. Introduction of the plane of equal settlement causes a rise in q s+ and, consequently, a smaller force at the inclusion head. Conversely, negative friction along the shaft, generated by q s+ using a consistent mode of calculation, subsequently rises. On the whole, for efficient groups of inclusions, this situation leads, relative to the 1988 proposals, to just a slight drop in efficiency. In the case of ground slabs, the upper plane of equal settlement can be related to the ground slab underside. 3.2.1.3. Evaluation The fictitious inclusion model is capable of describing load transfer in the platform, provided taking into account the specific points raised in the previous section (e.g. identification of an upper plane of equal settlement). Chapter 3 will detail the requirements inherent in analytical type calculation models.
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3.2.2. Diffusion cone method
Load transfer can be modeled by means of diffusion above the inclusion, with reference to the mechanisms highlighted in the various experimental and modeling studies conducted as part of the ASIRI National Project (Chevalier et al., 2010, 2011). As explained in Section 1 of this chapter, it is important to recall that the load transfer mechanism depends on the specific type of structure under consideration: Case of an embankment: diffusion occurs according to the model of the capital slanted at the friction angle of the transfer platform material; Case of a ground slab or shallow foundation installed on a granular transfer platform: load transfer occurs via the structural element (ground slab or shallow foundation), the vertical transfer platform column on top of the inclusion and, to a lesser extent, the immediate vicinity of this column. In the case of an embankment on a granular transfer platform, load transfer takes place via shear along a truncated cone derived from the inclusion head and forming a solid equal to the peak friction angle of the transfer platform material. From angle , made by the diffusion zone with the vertical direction, it is possible to evaluate load transfer in the direction of inclusions by considering that the displaced block is transmitting both its dead load and the load it receives directly to the soft soil. This hypothesis, based on numerical simulation results, is compatible with the kinematic approach calculation by the yield design theory of this rigid block in displacement: the angle must be equal to the friction angle of the material in order to obtain a vertical displacement of this block, which happens to be the only kinematically admissible direction (Fig. 2.28).
Figure 2.28: Kinematic approach of the failure calculation applied to determining soil bearing resistance between inclusions.
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Figure 2.29: The proposed load transfer mechanisms.
Based on the proposed geometry (Fig. 2.29), a determination can now be made of the share of surcharge Q p and weight W p of the granular layer being redirected towards the inclusions via the load transfer zone. Both the efficiency E and capacity G of the granular transfer platform relaying surcharges towards the inclusions can also be deduced in the case of square-section inclusions or pile caps. Q p q a 2 4 a hm tan hm2 tan 2 for hm h *
s a 2 tan
s a W p a 2 hm 2 a hm2 tan hm3 tan 2 for h m h * 3 2 tan
E
W p Q p s 2 hm q
and
(2.17)
a 2 4 a hm tan hm2 tan 2 G s 2
(2.18)
(2.19)
For circular-section inclusions or pile caps, with diameter a, the following are obtained: W p
hm a / 22 a / 2 hm tan 2 a a / 2 hm tan / 2 3
Q p q a / 2 hm tan 2 for hm h*
W Q p E 2 p s hm q
and
s a 2 tan
a / 2 hm tan 2 G s 2
(2.20)
(2.21) (2.22)
Angle is typically set equal to the peak friction angle p of the granular material in order to assess the maximum efficiency capable of being mobilized for a given loading. In comparison with numerical simulations using discrete elements run for a load transfer platform of thickness hm = 1.0 m and 0.5 m, it is observed in Figure 2.30 that the proposed analytical formulations serve to approximate, in a satisfactory manner, the range of load Operating mechanisms
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transfer mechanisms. For small granular layer displacements, the friction angle to be considered in the analytical formulations is indeed the peak friction angle of the granular material introduced. For greater deformations however, it could be assumed that particle disorganization would require adopting smaller friction angles.
Figure 2.30: Comparison between load efficiencies E and G obtained by discrete numerical simulations and analytical calculations (Chevalier et al ., 2010) (Case of an embankment, with square inclusions a = 0.37 m, a 2.5- 22%)
4. BASIC MECHANISMS 4.1. Overall mechanism of reinforcement by rigid inclusions s
recall that in comparison with foundations on piles or a reinforcement by flexible inclusions of the stone columns type, a foundation soil reinforcement by rigid inclusions features as its primary mechanism the distribution of loads between the inclusions and the surrounding soft soil while minimizing settlements. This mechanism is also observed with stone columns, though with the difference that stone columns produce equal settlements at the column head and at the top of the surrounding soil. Rigid inclusions thus serve to: Channel the stresses due to embankments, loads on ground slabs or rafts, towards the deeper stiff soil strata; Reduce stresses in the soft soil in order to limit settlements; Eventually shorten consolidation time by lowering stresses in the soft soil, depending on its overconsolidation ratio. 4.2. Behavior of the single rigid inclusion
The single rigid inclusion functions like a small pile. During loading of the rigid inclusion head, shaft friction is quickly mobilized and then the process occurs more slowly for the tip until reaching the ultimate resistance conventionally set at a head displacement equal to onetenth the inclusion diameter (Fig. 2.31).
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Figure 2.31: Mobilization of total and tip resistance for a rigid inclusion.
As regards embedding the inclusion in layers beneath the soft soil layers, it would be necessary to differentiate two very distinct cases: Domain no. 1: Inclusions are required for the stability and load-bearing capacity of the structure. In this case, prescriptions from the Standard NF P 94-262 "Deep foundations" need to be applied with, in general, a minimum embedment of 3 diameters for piles whose diameter is less than 0.50 m. This lower embedment limit may be reduced to the minimum value of 0.50 m, provided the foundation contractor is able to guarantee execution of this pile tip embedding operation within the load-bearing layer by either extracting samples, or introducing a trepan or using a core sampler. Domain no. 2: The rigid inclusions are primarily intended to decrease settlements and are not required to justify the stability or load-bearing capacity of the structure. From a general standpoint, a limitation will be imposed of a minimum one-diameter embedment in the load bearing layer, provided a relevant evaluation has been performed of the load-bearing factor (with respect to Standard NF P 94-262) along with a strict execution quality control (such as a systematic recording of installation parameters), thus making it possible to guarantee generating this minimum embedment for all inclusions. In the absence of a true load-bearing layer, so- inclusions may be envisaged, albeit subjected to the condition of specific justifications. 4.3. Behavior of a rigid inclusion within a group
Under the effect of soft soil settlement around grouped rigid inclusions, a negative skin friction develops over the upper part of each inclusion; this friction increases with either the embankment height or the surcharge. In this part, the vertical displacement of the neighboring soil is greater than that of the inclusion itself. In contrast, over the lower part, the friction is positive and moreover at each level, the vertical displacement of the rigid inclusion is greater than that of the surrounding soil. A level of inclusion therefore exists at which the displacements of both the inclusion and surrounding soil are identical; this level is referred to as the and corresponds to where the shear stress due to shaft friction equals zero, and the normal force is maximized in the inclusion. Two other neutral planes, located respectively above the inclusion heads and below the inclusion tips, are typically defined as well (see Fig. 2.32):
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Figure 2.32: Position of the 3 neutral planes determined from the shear stress profile along the inclusion.
The upper neutral plane is the most interesting to study, since above it the settlements are uniform and, as such, the upper embankment surface will not be subjected to egg carton type deformations (Fig. 2.33).
The lower neutral plane is located beneath the inclusions in the bearing soil, at a level where soil settlement becomes uniform once again.
Figure 2.33: Pavement on rigid inclusions disp surface.
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4.4. Soil behavior around the rigid inclusion within a group
In a reinforcement configuration using rigid inclusions, the soft soil, once relieved of a portion of the stresses contributed by the embankment or ground slab, settles less than unreinforced soil. The inclusion head reveals a sudden variation in settlement that quickly becomes uniform away from the rigid inclusion shaft (Fig. 2.34).
Figure 2.34: Soil displacements at the level of the inclusion head.
It thus proves necessary to introduce a thick enough transfer platform to avoid differential displacements at the top of an embankment or hard points under a ground slab. An insufficient transfer platform thickness leads, in the case of an embankment, to failure within a soil volume above the inclusion head penetrating the surface (compare Figs. 2.35 and 2.36) or alternatively, in the case of a ground slab, to high stresses inside it.
Figure 2.35: Volume of soil at failure under 1 m of cover.
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Figure 2.36: Confined volume of soil at failure under 7 m of cover.
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4.5. Consolidation of saturated soft soil in a rigid inclusion group
The consolidation of a soft soil reinforced by rigid inclusions may occur much faster than the consolidation of unreinforced soil. This finding is due to the decrease in vertical stresses within the reinforced soft soil, causing most of the load applied in the overconsolidated domain, where settling happens more quickly than in the normally consolidated domain. The reduced settlements are thus generally accompanied by a shorter consolidation period (Figs. 2.37 and 2.38). These results once again recall the importance of conducting a comprehensive study of the mechanical and hydraulic characteristics of the soft soil prior to any reinforcement project.
Figure 2.37: Settlement curves for an overconsolidated soil both with and without reinforcement.
Figure 2.38: Dissipation of excess pore pressure for an overconsolidated soil, with and without reinforcement (U = 90%).
5. SETTLEMENTS AND DEFORMATIONS
The decision to reinforce a foundation soil stems from an observation that the settlement of the structure on a virgin soil is not compatible with its intended purpose. The initial task then will be to calculate the expected settlement in the absence of all reinforcement. If necessary, the group of inclusions will be designed to reduce this settlement to an admissible value, by means of applying the operating mechanisms described below. 78
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In addition to load efficiency E (as defined in Section 1.1 of this chapter), it is common practice for engineers to consider a settlement efficiency E tass that specifically expresses the capacity of the process to satisfy the settlement criteria required for the structure. This efficiency is established via the expression: Etass = 1 yM / y0 (2.23) with: yM: settlement of the soil reinforced by rigid inclusions, as evaluated or measured at the surface of the load transfer platform; y0: settlement of the virgin soil (i.e. without inclusions), as evaluated based on site investigation data. The reinforced soil settlement may be: Either calculated based on data derived from site investigation results and the calculation methods proposed in these Recommendations (see Chapters 3, 4 and 5); Or measured using appropriate instrumentation implemented within the scope of the control testing campaign. The settlement of a shallow foundation such as an embankment, footing, ground slab or raft on soil reinforced by rigid inclusions is defined as the sum of two components, i.e.: The actual settlement experienced by the reinforced soil, including the settlement of the load transfer platform; The settlement of deeper, non-reinforced layers. 5.1. Settlement of reinforced soil
A reinforcement by rigid inclusions is reflected, and such is the intended purpose, by a reduction (most often of large magnitude) of settlements over the entire reinforced soil height; this reduction depends on both the reinforcement mesh and characteristics of the granular transfer platform (thickness, deformability and eventual presence of a structural additive like a geogrid). These settlements could be lowered thanks to a substantial transfer of applied load onto the inclusions that occurs at two levels, as already described in the previous sections, namely: A load concentration at the inclusion head resulting from shear mechanisms in the transfer platform and capable of leading, due to the induced stress rotation, to the creation of force arches through which forces can be channeled, and possibly complemented by permanent cohesion of the platform constituent material or by the membrane effect of geogrid(s) laid out on the inclusion heads; A negative friction effect of the soft soil acting on the inclusion, according to the set of mechanisms analyzed by O. Combarieu, as governed by parameters including , in combining the group and downdrag effects. This load transfer yields a significant drop in the additional stress applied at the top of the soft soil and inside it, hence leading to a very noticeable decrease in settlement, which after all is the intended goal. In recognizing that a sizable portion of the load is transferred onto the inclusions and moreover that these inclusions display relatively high stiffness, final settlement reduction will be even more pronounced if the inclusion tip rests on a load-bearing resistant layer such as a stiff substratum or a layer of sand or gravel of adequate thickness. Operating mechanisms
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In this respect, it would be necessary to accurately distinguish the case of inclusions stopping in the soft soil layer, which can be qualified as floating inclusions, from the case of inclusions resting on a resistant layer. With the aim of optimizing reinforcement efficiency in terms of settlement reduction, it is highly recommended, in common cases, to allocate reinforcement over the entire soft soil layer height and then embed the inclusions on a load-bearing level, while acknowledging that relatively short floating inclusions would display a near-zero efficiency. In the presence of organic soils (peat, household waste, etc.), the residual surcharge applied on the soil could cause creep settlements and thereby limit the phenomenon of downdrag. 5.2. Settlement of deeper, unreinforced layers
Depending on the mechanism described above, inclusions play the role of deep-seated load transfer elements. This surcharge, transferred at the level of the inclusion base, winds up causing settlements in the underlying layers (remaining in a virgin state given their lack of reinforcement), in the same way as settlements potentially occurring under a group of piles (even though the transfer mechanism is substantially different in the case of piles) (Fig. 2.39).
Figure 2.39: Necessity of verification for the load transfer influence under the inclusion tip.
It should nonetheless be pointed out that these deep layers tend to be relatively incompressible, meaning that settlements induced at the surface are small and often uniform at the scale of the structure examined. Yet this examination of settlement within the deeper layers must not be overlooked. 5.3. Geotechnical investigations
As regards site investigations, it will be necessary to plan a series of boreholes with suitable laboratory or in situ testing to allow evaluating soil compressibility characteristics. This will require reaching a sufficient depth, relative to the targeted reinforcement area and depth, and with a sufficient number of borings to determine the potential variations in these characteristics at the scale of the structure, with the aim of assessing both total and differential settlements.
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The reader is referred to Chapter 6 for a detailed description of the relevant boreholes and tests. 5.4. Determinant parameters
As a complement to in situ soil compressibility characteristics, the following key parameters, which will be showcased in the calculation methods described in Chapters 3, 4 and 5, are determinant to settlement evaluations: Granular transfer platform characteristics (thickness, deformability, friction angle, eventual cohesion), including if applicable the characteristics of additives used as reinforcement layers; Inclusion characteristics (head diameter and diameter of the standard cross-section, deformation modulus, length compared to soft soil thickness); The area ratio, i.e. ratio of the head cross-sectional area to the element mesh area. Searching for the best combination of these parameters allows deriving an optimal design that satisfies the settlement criteria. 6. LESSONS FROM THE FULL-SCALE EXPERIMENTS
As a complement to the description of fundamental mechanisms, it seems important to highlight a number of observations or lessons from the two full-scale experiments (SaintOuen-Aumône and Chelles) conducted within the scope of the ASIRI National Project. These lessons are deemed to be particularly useful in producing an effective design or carrying out a realistic preliminary design of reinforcement by rigid inclusions during the early project design stage. 6.1. Inclusion behavior
As for inclusion head loads and settlements, the Saint-Ouen- Aumône (Fig. 2.40) and Chelles (Fig. 2.41) experiments demonstrate that the behavior of an inclusion underneath the structure (embankment, ground slab) is the same as that of the tip of a single rigid inclusion subjected to a loading test. This outcome reveals that the load exerted at the head of an inclusion is close to that exerted in the vicinity of its tip. Such a finding expresses the fact that the positive and negative friction resultants along the inclusion shaft are more or less balanced, and that consequently inclusion efficiency is basically governed by its load-bearing capacity at the tip. These results expose the need to determine this capacity and then accurately model the inclusion tip behavior in order to obtain realistic results at the top of a structure on soil reinforced by rigid inclusions. This result can be considered as valid solely for groups of inclusions lying on a resistant substratum (and in theory does not apply to the floating inclusions).
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Figure 2.40: The Saint-Ouen- Aumône experiment Ground slabs - (2006) Load and settlement measurements at the head of inclusions placed at the center of the 2D and 3D test sections (displacement inclusions).
Figure 2.41: The Chelles experiment - Embankments - (2007) Load and settlement measurements at the head of inclusions placed at the center of the 2R, 3R and 4R test sections.
6.2. Load transfer
The Chelles experiment (2007), which contained a granular transfer platform, shows a decrease in applied stress on the soft soil, compared to the stress contributed by the embankment. This observation was not recorded above the transfer platform, which proves that the load transfer mechanisms are effectively activated in the granular platform. If the embankment material is of high quality, then the load transfer mechanisms can also occur at the embankment base, in which case the base acts as a load transfer platform. Should the upper layer of reinforced soil be of good quality, then it also participates in the load transfer by means of friction, in which case the solution of pile caps placed at the head of
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inclusions may not be optimal, given that it is capable of constraining this friction-based transfer mechanism. The step of cutting off inclusions at the base of the granular transfer platform could reduce load transfer in that the soil aligned with the inclusion might not be compacted like the rest of the load transfer platform. In this respect, appropriate arrangements are required in order to guarantee the homogeneity of transfer platform compaction (see Chapter 7: Execution). 6.3. Reinforcement layers (geosynthetic)
The Chelles experiment (2007) indicates that the state of stress above a granular transfer platform reinforced by geosynthetic layers differs depending on the type and number of layers in the configuration: Case of the load transfer platform reinforced by a layer of geotextile, i.e. composed of a rather deformable material: the geotextile deforms during embankment construction, and this deformation is concentrated around the inclusion heads; Case of the load transfer platform reinforced by a geogrid layer, i.e. composed of a less deformable material: the geogrid deforms in a uniform pattern during installation of the granular platform; afterwards, the deformation is also concentrated around the inclusion heads during embankment construction. The geogrid tends to prestress the load transfer platform prior to its loading by the embankment, which yields a certain amount of cohesion. The interpretations drawn from the Chelles full-scale experiments served to quantify this additional equivalent cohesion; The number of layers introduced is also a key factor in that it contributes to increasing transfer platform stiffness. 6.4. Settlement efficiency
The reinforcement by rigid inclusions significantly reduces settlement both at ground level and throughout the soil depth. In the Chelles instrumented test embankment, it has been observed that settlement occurs for the most part during the construction stage, which therefore makes it necessary to impose settlement criteria with reference to expected settlements after embankment construction and not before. The efficiency calculated for stresses at the level of inclusion heads is not always the most pertinent design parameter; instead, the rationale should target reducing settlements. As an illustration, in the case of the Chelles embankment, it can be remarked that a 20% stress efficiency has yielded a 60% settlement reduction! 7. SEISMIC LOADINGS
The objective of a reinforcement step using rigid inclusions is to introduce sufficient mechanical characteristics into the reinforced soil so as to allow building a shallow foundation (or perhaps a raft or ground slab) or an embankment under fully acceptable stability and settlement conditions.
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In the case where the reinforced soil is subjected to seismic loadings, two very distinct domains need to be distinguished (the AFPS Soil improvement and reinforcement processes under seismic action Technical Guide, 2011): Domain no. 1: Inclusions are necessary for structural stability and for load-bearing capacity, with verifications of the ultimate limit states (GEO). The next step requires guaranteeing the same level of inclusion strength during an earthquake as that taken into account in design calculations, thus justifying that these inclusions remain within the elastic domain (justifications comparable to current rules in effect for piles). Domain no. 2: The rigid inclusions are primarily intended to reduce settlements and are not required to justify the structural stability or load-bearing capacity. The absence of structural failure must then be justified when exposed to seismic action by neglecting either part or all of the inclusions, in a way that is not detrimental to human safety in the event of structural damage. Remark: The situation may be encountered where the Project Owner imposes that
the structure still be in working order after the earthquake, i.e. without any physical disorders and operational limitations appearing either during or after the earthquake [EN 1998-1 Standard, Section 2.1 (1) P]; in this case, the inclusions would enter into domain n° 1. The granular transfer platform must be able to perform the following functions: Facilitate energy dissipation by means of sliding in the granular medium. Accordingly, the load transfer platform plays the role of a fuse triggering a controllable sliding, rather than footing rotation via a loss of load-bearing capacity. A hierarchy in the strength of various system components is thus introduced, and this step naturally assumes the absence of a plastic zone outside of the transfer platform. This finding implies that rigid inclusions do not fail and therefore prove to be correctly designed or even overdesigned; Reduce loadings in the inclusions (decrease in both shear force at the inclusion head and lateral displacement of the soil over the upper part of the rigid inclusions); Perform a filtering effect by avoiding any seismic loading amplification, or even in some cases by reducing inertial forces. This reduction phenomenon is closely correlated with energy dissipation in the load transfer platform by friction. The intensity of this phenomenon depends on transfer platform thickness; Ultimately, increase soil load-bearing capacity. The load transfer platform may be sized to make the transition from domain no. 1 to domain n° 2. Both shear and normal stresses will develop in the rigid inclusions when exposed to kinematic and inertial effects. In domain no. 1, where inclusions are necessary for structural stability (and load-bearing capacity), it will be mandatory to verify that all inclusion sections remain compressed under the induced loadings and moreover that normal and shear stresses continue to be acceptable (refer to Chapter 5: Justifications). The earthquake resistance calculation for foundation soils reinforced by rigid inclusions is complicated by the very complex feature of the soil-inclusion-platform-foundationsuperstructure interaction under cyclic loading. Incident waves induce deformations in the soil, which then transmits these deformations to the foundations and subsequently to the structure. The interaction present is thus very strong and it decomposes into a kinematic interaction and an inertial interaction:
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The soil deformed by incident waves forces the foundations, and consequently the superstructure, to follow its movement (i.e. a kinematic interaction). Even in the absence of superstructure loads, foundations will exhibit different displacements than the free field soil displacements due to differences in stiffness between foundation and soil; The superstructure mobilized by the foundation movement will develop inertial forces that serve to induce soil-foundation system forces (i.e. an inertial interaction).
The two mechanisms occur simultaneously; the soil-foundation-structure (the soil-structure interaction) system response can be obtained by simply combining these mechanisms. The need to take into account a combination of both mechanisms depends on: the type of soil, the seismic zone, and the category of structure (as referred to in Section 5.3 of the AFPS Soil improvement and reinforcement processes under seismic action Technical Guide, 2011). In liquefiable zones, the liquefaction potential may be reduced by use of rigid inclusions under the eventually combined effect of the following actions: If inclusions are being used to increase density of the surrounding soil, e.g. by soil displacement and/or vibration, then the gain in density following treatment would need to be verified by in situ tests conducted between inclusions; Should inclusions be used to lower shear stress in the soil, then the design must be carried out according to Hashin s homogenization method (1983), as detailed in the AFPS Soil improvement and reinforcement processes under seismic action Technical Guide (2011). Any method that consists of increasing average shear strength of the treated mesh by incorporating inclusion strength would not be valid. This approach imposes verifying inclusion integrity (i.e. both normal and shear stresses must remain acceptable). The practical application of this design method typically only allows for a limited increase, on the order of 5% to 10%, in the safety factor relative to liquefaction. The AFPS Soil improvement and reinforcement processes under seismic action Technical Guide (2011) will be consulted for: A review of the appropriate analytical methods; Indications on the role played by a group of inclusions in a potential soil liquefaction.
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References Internal reports (ASIRI National Project)
Baudouin G. - Sols renforcés par inclusions rigides : modélisation physique en centrifugeuse de remblais et de dallage. Thèse de doctorat, université de Nantes, 27/10/2010. Briançon L. « art en France et à , 2002. Briançon L. - expérimentation de Saint-Ouen- ». Rapport 1-07-102 et annexes numériques, juillet 2007. Briançon L. - « ». Rapport 2-08-1-05, juillet 2008. Briançon L. « Complément benchmark tranche 1 ». Thèmes 1 et 4. Rapport 1-07-1 et 4-02, novembre 2007. Chakroun S., Simon B. - « Simulation du matériau Schneebeli dans Plaxis ». Rapport 1-06-402, décembre 2006. Chevalier B. - Études expérimentale et numérique des transferts de charge dans les matériaux granulaires. Application aux renforcements de sols par inclusions rigides. Thèse de doctorat, université Grenoble I Joseph-Fourier, 5/09/2008. http://tel.archivesouvertes.fr/docs/00/36/73/05/PDF/These_Bastien_Chevalier-version3.pdf. Chevalier B., Combe G., Villard P. - « Modélisation discrète : étude du report de charge ». Rapport 3-08-4-01, 2008. Chevalier B., Combe G., Fantino R., Grange S., Villard P. - « Étude des mécanismes de report de charge dans les matelas granulaires des remblais sur sol compressible renforcé par inclusions rigides ». Rapport 4-10-4-02, juillet 2010. Combarieu O. - « Remblais sur sol médiocre et inclusions rigides. Nouvelle approche du dimensionnement ». Rapport 1-07-5-01, 2007. Dinh A.Q. - Étude sur modèle physique des mécanismes de transfert de charge dans les sols renforcés par inclusions rigides. Application au dimensionnement . Thèse de doctorat, ENPC, 2009. IREX « Pôle Compétence Sols. Utilisation des inclusions rigides pour le renforcement des sols de fondation d », 2000. Jenck O. - Le renforcement des sols compressibles par inclusions rigides verticales. Modélisation physique et numérique. Thèse de doctorat, INSA Lyon, 29/11/2005. Jenck O., Dias D., Kastner R. - « Expérimentations sur modèle réduit bidimensionnel en laboratoire. Modélisation physique de la plate-forme de transfert de charge ». Rapport 106-3-01, octobre 2006. Jenck O., Dias D., Kastner R. - « Modélisation numérique bidimensionnelle du modèle de ». Rapport 1-06-4-01, octobre 2006. Jenck O., Dias D. - matelas de transfert de charge granulaire édifié sur inclusions rigides. Rapport 2-08-4-03, octobre 2007. Koscielny M., Briançon L., Dias D. « Synthèse benchmark tranche 1. Thèmes 1 et 4 ». Rapport 1-07-1 et 4-01, septembre 2007. Laurent Y. Renforcement des massifs de fondation par inclusions rigides verticales. Étude bibliographique et numérique. Mémoire de DEA, INSA Lyon, 17/09/2002.
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Le Hello B. - Renforcement par géosynthétiques des remblais sur inclusions rigides. Étude expérimentale en vraie grandeur et analyse numérique. Thèse de doctorat, université Grenoble I Joseph-Fourier, 26/06/2007. Okyay U.S. - Étude expérimentale et numérique des transferts de charge dans un massif renforcé par inclusions rigides. Application à des cas de chargements statiques et dynamiques. Thèse de doctorat, INSA Lyon, 24/11/2010. Rault G., Baudouin G., Thorel L. - « Essais centrifugeuse élémentaire (3*3 inclusions) : conception des montages (1) ». Rapport 2-07-3-05, décembre 2007. Rault G., Baudouin G., Thorel L. - « Essais centrifugeuse un groupe élémentaire (3*3 inclusions) : réalisation des montages (2) ». Rapport 2-08-3-06, mai 2008. Rault G., Thorel L. - « Étude du transfert de charge par cisaillement. Dispositif de plateau mobile. Essais de réception ». Rapport 3-09-3-14, octobre 2009. Thorel L., Rault G., Baudoin G. - « : ». Rapport 2-07-3-08 et annexes, novembre 200). External references (publications and standards)
AFPS « », 2011. Berthelot P., Besson C., Boucherie M., Carpinteiro L., Deryckere N., Frossard A., Glandy M., Pezot B., Poilpre C., Volcke J.-P. - « Recommandations sur la conception, le calcul, tassement ». Revue française de géotechnique n° 111, 2004, p. 3 à 16. British Standard BS 8006 - r ion on poor ground, 1995, p. 98-121. Cartier G. - Effet de groupe sur le frottement négatif (essais en centrifugeuse). Mémoire de DEA, LCPC Nantes, 11/07/1994. Chevalier B., Villard, P., Combe G. - Investigation of load transfer mechanisms in geotechnical earth structures with thin fill platforms reinforced by rigid inclusions. International Journal of Geomechanics, doi:10.1061/(ASCE) GM.1943 5622, 0000083, 2011. CLOUTERRE 1991 (+ Additif 2002) Recommandations pour la conception, le calcul, . Combarieu O. - « ». Bulletin de liaison des laboratoires des ponts et chaussées n° 71, mai-juin 1974, p. 93107. Combarieu O. - « Frottement négatif sur les pieux. » Rapport de recherche des Laboratoires des ponts et chaussées n° 136, octobre 1985, 151 p. Combarieu O. - Amélioration des sols par inclusions rigides verticales. Application à Revue française de géotechnique n° 44, 1988, p. 57-79. Combarieu O. « une fondation mixte ». C, 1988. Combarieu O. - « Fondations superficielles sur sol amélioré par inclusions rigides verticales ». Revue française de géotechnique n° 53, 1990, p. 33 à 44.
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Combarieu O. - « Estimation du frottement latéral sol-pieu à partir du pressiomètre et des caractéristiques de cisaillement ». Bulletin de liaison des laboratoires des ponts et chaussées n° 221, mai-juin 1999, p. 37-54. Combarieu O. « Remblais sur sol compressible et inclusions rigides. Amélioration de ». Revue française de géotechnique n° 122, 2008, p. 4554. DTU 13.2 - Fondations profondes pour le bâtiment. Norme AFNOR P11-212, 1992. EBGEO - Empfehlungen für Bewehrungen aus Geokunststoffen. Bewehrte Erdkörper auf punkt und linienförmigen Tragglieder. Abschnitt 6.9, Version du 15/11/2001, non publiée. (in Deutsch) Fascicule n° 62, Titre V - Règles techniques de conception et de calcul des fondations des ouvrages de génie civil. CCTG applicables aux marchés publics de travaux. Ministère de , 1993. FOREVER - Synthèse des résultats et recommandations du projet national sur les micropieux (1993-2001). Opération du RGC&U. Paris, Presses des Ponts, 2004. Frank R., Zhao S.R. - charge axiale de pieux forés dans des sols fins. Bulletin de liaison des laboratoires des ponts et chaussées n° 119 mai-juin 1982. Hashin Z. - Analysis of Composite Materials. A Survey Journal of Applied Mechanics, vol. 50, 1983, p. 481-505. Hewlett W.J., Randolph M.A. Analysis of piled embankments. Ground Engineering , April 1988, p. 12-18. Kempton G., Jones C.J.F.P. - The use of high strength link geotextiles over piles and voids. Earth reinforced, Ochiai, Hayashi and Otani (eds), Balkema, Rotterdam, 1992, p.613-618. Kempton G., Russell D., Pierpoint N., Jones C.J.F.P. Two and three dimensional numerical analysis of the performance of piled embankments. 6 th International Conference on Geosynthetics, 1998, p. 767-772. NF EN 1997-1, Eurocode 7 - Calcul géotechnique. Partie 1 : Règles générales. (indice de classement P 94-251-1) avec son annexe nationale (indice de classement P 94-251-2). NF EN 1997-2, Eurocode 7 - Calcul géotechnique. Partie 2 : Reconnaissance et essais géotechniques. NF EN 1998-1, Eurocode 8 - Conception et calcul des structures pour leur résistance aux séismes. Partie 1 : Règles générales, actions sismiques et règles pour les bâtiments. NF EN 1998-5, Eurocode 8 - Conception et calcul des structures pour leur résistance aux séismes. Partie 5 : Fondations, ouvrages de soutènement et aspects géotechniques. NF EN 1536 - Exécution des travaux géotechniques spéciaux - Pieux forés. (P94-310). NF EN 12699 - Exécution des travaux géotechniques spéciaux - Pieux avec déplacement de sol. (P94-311). NF EN 14199 - Exécution des travaux géotechniques spéciaux - Micropieux. (P94-313 ) NF P 94-262 - Justification des ouvrages géotechniques. de 7 - Fondations profondes. NF P 11-213, DTU 13.3 - Dallages - Conception, calcul et exécution, 2007. Okyay U.S., Dias D. - Use of lime and cement treated soils as Pile supported load transfer platform, Engineering Geology, vol. 114 (1-2), 2010, p 34-44. Plumelle C. - Revue française de géotechnique n° 30, 1985, p.47 à 57. SETRA Traitement des sols à la chaux et/ou aux liants hydrauliques (GTS). Application à la réalisation des remblais et des couches de forme. Guide technique, 2000. SETRA-LCPC Réalisation des remblais et des couches de forme (GTR). Guide technique, 1992. 88
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Simon B. - « ns rigides en déformation ». XV e Congrès international de mécanique des sols et fondations, Istanbul, vol. 2, 2000, p. 1007-1010. Simon B., Schlosser F. - Soil reinforcement by vertical stiff inclusions in France. Symposium Rigid inclusions ISSMGE TC36 , Sociedad Mexicana de Mecanica de Suelos, UNAM, Mexico, 2006. Swedish Geotechnical Society (SGS) Lime Cement columns. Guide for design, Zeevaert L. Discussion on negative friction and reduction of point bearing capacity . Proc.
4th.ICSMFE , 1957, vol. 3.
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CHAPTER 3
Design methods
1. NOTATIONS
The forces and loads considered in the design methods are shown in the reference diagram in Figure 3.1, where depths are measured from the inclusion head. The force-reduction elements in the cross-section of an inclusion, denoted respectively Q p (for axial force), T p (shear force) and M p (bending moment), can be identified by their respective values: Q p(z), T p(z), M p(z) in the cross-section of depth z below the head; Q p(0), T p(0), M p(0) at the level of the inclusion head; Q p(L), T p(L), M p(L)at the level of the inclusion base (length L). When the computational model includes a fictitious column overlying the inclusion on the height of the load transfer platform h R (or of the embankment), the forces applied at the top of the fictitious column are respectively Q p(-hR ), T p(-hR ) and M p(-hR ). When taken into consideration, the reduction elements applicable to a horizontal section of the volume of reinforced soil excluding the inclusions are designated using the same convention, by substituting the index s for p, i.e. Qs, Ts and Ms.
Figure 3.1: Reference diagram adopted for identifying the force reduction elements in the inclusion or soil.
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2. UNDERLYING PRINCIPLES
The design methods of a foundation on a soil reinforced by means of rigid inclusions are of three distinct types: Analytical models (Section 3); Numerical models in continuous medium using either finite elements or finite differences (Section 4); whose application remains complex and not yet widespread (Section 5). Each of these models may be used for both the ultimate limit state (ULS) and service limit state (SLS) verifications provided it is capable of taking into account: The behavior of an isolated inclusion loaded at the head, which is comparable to the behavior estimated by implementation of the w curves (curves linking the mobilized skin friction at a given depth with the corresponding axial displacement) and q w b curves (point pressure point displacement curve) proposed by Frank and Zhao (1982) as functions of the pressuremeter modulus E M, the pile diameter and the type of soil; The behavior of a structure, when applicable, in the absence of inclusions, in terms of both settlement and bearing capacity, with predictions based on classical methods such as: pressuremeter or penetrometer methods in the case of a shallow foundation; the oedometer method and bearing capacity and punching calculation in the case of an embankment, raft or pavement. Regardless of the method employed (analytical or numerical), the first step consists of evaluating the behavior of the structure without inclusions, which will allow determining the contribution of inclusions relative to the settlement and bearing capacity/punching. 3. ANALYTICAL METHODS
Three methods were selected within the scope of the ASIRI project; all three are simple to implement for solving some of the most common situations: grid of inclusions placed in the middle of the reinforced zone and subjected to uniform vertical loads. Their main intent is to calculate the average expected settlement after reinforcement and then estimate the maximum load applied to the inclusions. An extension to the case of vertically and horizontally-loaded footings was derived for each of these selected analytical methods. Such methods are not necessarily analytical in the strict sense of the term in that they typically do not lead to results in the form of explicit analytical formulas; they usually need to be solved numerically through the use, for example, of a spreadsheet or a solver. These methods however are capable of estimating the distribution of forces between soil and inclusions, settlements and horizontal displacements. They do not provide the possibility of incorporating any geotextile reinforcement in the load transfer platform.
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3.1. Vertical loads 3.1.1. Common elements to the methods
3.1.1.1. Behavior of the inclusion material
It is assumed that the material remains elastic. This behavior is characterized by a modulus of elasticity E and a design strength. 3.1.1.2. Soil compressibility
The Young s modulus of the load transfer platform depends on the degree of compaction and varies with both the stress state and stress path.
The apparent modulus of deformation to be used for compressible soil is an oedometric type modulus Eoed, calculated as a secant modulus between the initial and final stress states, taking into account the applied forces (see Chapter 6, Note 6). Remark: When
the pre-consolidation taken into account is linked to some earthworks (cut and fill operations), it is necessary to provide a detailed justification based on the duration of the various phases and their associated consolidation. 3.1.1.3. Soil/inclusion interaction force mobilization laws
From a general standpoint, the mobilization laws adopted are a function of the local relative displacement between soil and inclusion, with the difference between inclusion displacement and soil displacement being: w(z) = y P(z)-ys(z). This relationship applies to force mobilization at either the head or inclusion base as well as for side friction forces along the inclusion. a) Load at the inclusion base: For this case, Frank and Zhao s mobilization laws (1982) are typically adopted.
Figure 3.2: Semi-empirical mobilization curve of the resistance at tip of the inclusion (Frank and Zhao, 1982)
k q
m q E M
D P
(3.1)
where D p is the equivalent diameter of the inclusion tip. Design methods
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The values m q, which depend on both the type of soil and the method of installation, are listed in Table 3.1 below (Frank and Zhao, 1982). Table 3.1: Values of m q (Frank and Zhao, 1982).
Soil Silt, clay Sands, gravels Chalk Marly limestone Marl
Type of pile Driven, open 11 11 11 11 11
Driven, closed 11 14 4.8 4.8 4.8
Bored 11 4.8 11 11 11
b) Skin friction Skin friction mobilization is described at any depth by a transfer function, thus expressing the
The empirical curves established by Frank and Zhao (1982) for piles bored into fine-grained or granular soils, based on interpretations from a large sample of load tests, prove well suited for describing the interactions that develop along the full length of the inclusion. These relationships may be applicable as an absolute value, for positive as well as negative friction.
Figure 3.3: Semi-empirical mobilization curve of shaft friction (Frank and Zhao, 1982).
k
m E M
DS
(3.2)
where Ds is the equivalent diameter of the inclusion section. The values m , which also depend on the type of soil and method of installation, are provided in Table 3.2 (Frank and Zhao, 1982).
Table 3.2: Values of m (Frank and Zhao, 1982).
Soil Silt, clay Sands, gravels Chalk Marly limestone Marl
Driven, closed 2 3 0.8 0.8 0.8
Type of pile Driven, open 2 2 2 2 2
Bored 2 0.8 2 2 2
Other -w law expressions have been proposed by various authors. Combarieu (1988) offered an analytical expression of the Frank and Zhao laws. 94
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Figure 3.4: Adjusted friction law, according to Combarieu (1988).
Mobilization of the resistance at tip of the inclusion: w
D p q p mq E M
ln1
q
q p
(3.3)
(3.4)
Mobilization of skin friction: w
D s q s m E M
ln1
q s
Remark: In
the absence of pressuremeter values, the typical correlations for determining an equivalent pressuremeter modulus are to be used, although with caution (see Chapter 6).
c) Force at the inclusion head: The force at the inclusion head is calculated by considering the development of negative skin friction on a fictitious column that extends from the inclusion head, as highlighted in Chapter 2, Section 3.2.1. The mobilization law used for this friction may be assimilated with that described by Frank and Zhao for a granular soil by setting: The value m = 2; The threshold value q s = Ktan v = 1 and where v stress in the load transfer platform between inclusions.
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Figure 3.5: Development of shear along the fictitious column overlying the inclusion.
3.1.2. Common spacing
3.1.2.1. Principles
L subjected to uniform vertical loads. The unit cell is assimilated to a cylinder, with the main axis being that of the inclusion and a circular cross-section being an area equal to the grid area. Remark: In general, the model must be extended to layers located underneath the
base of inclusions. In an ideal approach, the model base is chosen at a depth where vertical stresses may be considered as uniform over the entire cross-section or, alternatively, at a depth below which settlements become negligible. As a consequence, both lateral deformations and shear stresses are equal to zero at the cylinder periphery, and moreover the total force applied by the structure is conserved at all levels, in each horizontal cross-section, with the addition of the overlying weight of the soil and the inclusion. It is assumed that at a given level, the settlement and vertical stress are uniform in the soil. 3.1.2.2. Differential equations
Equilibrium equations express the variation in forces with depth, as previously indicated, in any horizontal cross-section of the model, in the inclusion (Equation 3.5) and in the soil (Equation 3.6): dQ p ( z ) ( P p A p ) dz (3.5) (3.6) dQ s ( z ) ( P s A s ) dz where represents the shear developed at the inclusion/soil interface, s the unit weight of the soil at the indicated level (replaced by the submerged unit weight where appropriate), p the unit weight of the inclusion at the indicated level (also replaced by the submerged unit weight
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where appropriate), P the inclusion perimeter, and finally A p and As the respective crosssections of the inclusion and soil at the indicated level.
Figure 3.6: Model of the basic cell around the inclusion.
Both the inclusion settlement and average soil settlement satisfy the following equations: dy p ( z ) dy s ( z )
Q p ( z ) A p E p Q s ( z ) A s E s
dz
(3.7)
dz
(3.8)
where E p(z) is the Young s modulus of the inclusion material, and E s(z) the apparent modulus of deformation of the soil at the applied load level, to be evaluated based on an oedometric type of behavior (i.e. zero lateral deformation at the model s outer vertical boundaries and at the soil/inclusion interface, see Section 2.1.1.2 and Chapter 6, Note 6). Friction mobilization is described at the level of each layer by a transfer function (see Section on the relative displacement w(z), defined as the difference between inclusion displacement and soil displacement: y P(z)-ys(z): z ) f y p ( z ) y s ( z ) ( (3.9) 3.1.2.3. Solution
The nonlinear system composed of differential equations (3.5) through (3.9) requires, for its resolution, that the relevant boundary conditions be defined. Such conditions are partially of the stiffness type, i.e. fixed values of the load/displacement ratios at both the head and base. The resulting system can only be solved by means of iteration. The boundary conditions at the head of the model are as follows: Total load applied at the head of the model Q( hR ); The fraction of this load applied at the head of the model directly above the inclusion EQP = Q p( hR )/Q( hR ): - in the case of an embankment subjected to a uniform load at the head, the factor E QP constitutes the ratio of the inclusion section area to the grid area. - in the case of a slab on grade or raft, the value of the factor E QP is established by assuming that the surface settlements y p( hR ) and ys( hR ) are equal, which is justified by the fact that deformations of the structural surface element (concrete slab or raft) are negligible when compared to soil deformations. Design methods
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Figure 3.7: Boundary conditions at the top of an embankment or slab on grade model.
This calculation necessitates the update, at each iteration, of the average soil settlement profile y s(z) according to Equations (3.5) through (3.9). Moreover, it provides the distribution vs. depth of the settlement of the inclusion, the average soil settlement, the mobilized skin friction, the axial force in the inclusion, and the vertical stress in the soil. Figures 3.8 and 3.9 illustrate the application of this method to a slab on grade (or raft) and to an embankment over the same soil profile. The settlements calculated using the analytical method directly above the inclusion and in the surrounding soil are compared to those obtained from an axisymmetric finite element model. In the embankment case, it is observed that settlements become uniform in the embankment, at some height above the inclusion head.
Figure 3.8: Configurations analyzed.
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Figure 3.9: Settlement profiles calculated for a slab (left) and an embankment (right).
3.1.3. Footings
3.1.3.1. Specificities and references
In the case of spread footings placed on rigid inclusions, the limited number of inclusions no longer makes it possible to satisfy the hypothesis of a large number of adjacent identical grids.
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The interaction of the reinforced soil block below the footing with the surrounding nonreinforced soil domain must be taken into account. Few experiments involving spread footings on rigid inclusions have been reported in the technical literature. Nonetheless, two types of experiments will be cited herein, including a vertical loading of the targeted spread footings: Tests conducted in the CEBTP research facility's experimental tank specific to a spread footing lying, through a layer of sand or crusher run, on a loose sand reinforced by micropiles (Plumelle, 1985); Tests conducted in a geotechnical centrifuge on spread footings featuring varied geometry and lying, through a sandy layer, on sand reinforced by inclusions laid out in a very loose mesh pattern (Bigot et al., 1988). Lets also mention the lateral load tests on spread footings acting as a piled footing foundation, conducted in 1970 at Bucknell University (United States), as reported by Borel (2001). The ASIRI Projects experimental program was solely focused on the behavior of large structures: slabs on grade and embankments on rigid inclusions under vertical loading. No full-scale experimentation or centrifuge tests of a spread footing on rigid inclusions had been performed. ASIRI project data relative to these types of structures are input from the 3D numerical modeling of spread footings using models validated by comparison to simulations of large structures with experimental data collected on the same type of structures. These numerical models included the cases of vertical or inclined footing loading. The simplified models proposed could be evaluated by means of a comparison with 3D numerical modeling results (ASIRI National Project report, 2011); they cover: Simplified models MV1 through MV3 for a purely vertical loading of the footing; Simplified models MH1 through MH3, which take into account a lateral footing loading (inclined force or moment). The use of these simplified models requires consistency verifications specific to each model, thus making it possible to validate a posteriori whether or not the model is applicable to the given situation. Any model from the MV or MH series can be used interchangeably: They yield an increasing volume of information (soil settlement, inclusion settlement, soil stresses, loading inside the inclusion); They are based on an increasing number of computation steps; They require verification of a decreasing number of consistency tests, thus making it possible to verify a posteriori that the hypotheses intrinsic to the model are indeed acceptable. 3.1.3.2. Simplified models for a purely vertical loading
3.1.3.2.1. MV1 analytical model This model was first presented by Combarieu (1990). It allows estimating the limit load Q L and settlement y of the footing lying on rigid inclusions, under a centered vertical load, by interpolating between the case of the footing acting alone and the case of the footing acting as part of a composite foundation. 100
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foundation solutions: Rigid shallow foundation (1); Composite foundation, where the footing and piles both participate in carrying loads (3); Rigid spread footing foundation installed on top of inclusions (2). In series (1), (2) and (3), the load transfer layer was replaced by natural soil. The soil with a thickness of (H + h R ) is the natural in situ soil; it covers a much more resistant layer placed underneath the inclusions. The footing has a width of 2R.
Figure 3.10: Configurations associated with the three foundation solutions
Using pressuremeter tests, it becomes possible to calculate: For case (1), the limit load Q L1 and settlement under load, y 1; For case (3), the limit load Q L3 and settlement under load, y 3. For case (2), it may be considered that if h R , i.e. the distance between the bottom of the footing and the inclusion tips, exceeds 2R, then the inclusions do not improve the footing load-bearing capacity. It is proposed to calculate the load-bearing capacity as follows: if hr < 2R QL2 = QL1 + 1/4 (2 hR /R)2 (QL3 QL1) if hr > 2R QL2 = Q L1
(3.10) (3.11)
The transition from series (1), (2), (3) to series in situ soil thickness h R by a load transfer platform. According to this approach, it is considered that the extension of such a substitution is unlimited within a plane, which obviously constitutes an optimistic approximation.
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This substitution improves each of the Q L terms into QL terms. The improvement in footing load-bearing capacity due to the mere presence of the load transfer platform (LTP) however remains small as a result of the LTP s limited lateral extension. In most instances therefore, this improvement can be neglected for the purpose of justifying the load-bearing capacity. The results obtained using this calculation method are in agreement with the experimental findings of both Plumelle (1985) and Bigot and Canepa (1988). With respect to settlements, it is also well known how to calculate settlements corresponding
for the footing on inclusions, may be treated by introducing the notion of equivalent modulus over the height H + h R , thereby simplifying the settlement calculation to that of a shallow foundation on an equivalent multilayer. The estimated settlement y 2 (or y2 that of the footing on its own yet greater than that of the composite foundation, both of which can be calculated.
Figure 3.11: Principle of the equivalent modulus procedure.
Combarieus original method (1990) must be completed by two additional steps, intended to calculate loadings within the inclusions. Step 1
This first step consists of establishing the settlement profile y s(z) over the inclusion height, in association with the settlement value at the head y s( h R ). The applied load below the footing (width: 2R) yields the soil settlement under the footing y s(-hR ), by means of pressuremeter theory, and at every point y s(z) using the method suggested by Combarieu (1988). The principle here is to replace the pressuremeter modulus E M of each element layer of thickness R that enters into the settlement calculation, according to pressuremeter theory, by a very large value, which through the corresponding difference determines the contribution of this layer to total settlement. The composition of these element settlements is then used to draw the desired profile ys(z). Step 2
The loading curve of a single deep foundation element comprising the inclusion itself and the related load transfer platform prism on top of it, which is assumed to be embedded inside a soil block subjected to an imposed settlement y s(z) (as derived during Step 1 above), allows establishing the load Q p( hR ) to be applied at the head of this column in order to obtain a settlement equal to ys(-hr ). In this particular calculation, the shaft friction at any point along the inclusion (respectively the pressure under the tip) is correlated with the relative displacement w(z) = [y p(z) ys(z)] using Frank and Zhao s laws for friction mobilization 102
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(respectively, the point pressure). This calculation also determines the distribution of axial forces Q p(z) in the inclusion.
Figure 3.12: Calculation of inclusion loading in the soil block subjected to the imposed settlement profile y s(z)
In order to validate model consistency, it is necessary to verify that the stress found at the inclusion head is compatible with the following (see Chapter 5, Section 4.2): The shear strength characteristics of the load transfer platform; The ultimate stress value at the inclusion head; The load transfer platform geometry, taking into account edge effects as required. This consistency test is critical to the model validation step: When this test is not satisfactory, it becomes necessary to use a more detailed model; When this test is satisfied, the results obtained can be used to proceed with the set of STR and GEO verifications, as indicated in Chapter 5. Remark: This method neglects the settlement of the load transfer platform related
to stress concentration on the inclusion head. These settlements however may not necessarily be negligible. 3.1.3.2.2. MV2 analytical model This model was presented by Glandy and Frossard (2002). It is intended to study the behavior of a footing on inclusions subjected to a vertical load. This problem can be broken down into two distinct domains: 1) The pile domain, composed of the inclusions and soil volumes that extend the pile vertically until reaching the lower or upper model boundary. This domain comprises n identical elements, assumed to exhibit comparable behavior; 2) The soil domain, which serves to complement the above pile domain.
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Figure 3.13: Decomposition of the problem into two domains.
The interaction between the pile domain and the soil domain is assumed to be fully described by the shear stress that develops at their shared vertical boundary and by the vertical stress q at the base of the pile domain; it is assumed that these interactions can be described by the corresponding Frank and Zhao laws applied, considering the relative soilinclusion displacement at all points (instead of the absolute displacement for a pile).
Moreover, the method assumes that the settlement profile at the bottom of the footing is the same for both domains. This method requires an iterative computation in order to ensure the consistency of calculations carried out in each domain, from the standpoint of settlements as well as interaction forces. Moreover, it allows the estimation of a complete settlement profile along the inclusion axis (pile domain) and in the soil domain underneath the footing, given an initial hypothesis of total vertical load Q distribution between the soil domain (Q s fraction) and the pile domains (n Q p fraction).
Figure 3.14: Principle of the MV2 model's iterative computation.
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Based on the load Q s( h R ), which is assumed to be transmitted to the soil under the footing, the settlement profile ys (z) below the footing can be determined by associating the pressuremeter method with the method suggested by Combarieu (1988), as discussed in the previous section; this profile also provides the settlement of the soil domain at the level of the inclusion tip ys(L). Based on an assumed inclusion displacement relative to this settlement y s(L), the following can be calculated: End-bearing pressure mobilized at the tip, and for each successive slice along the entire pile domain height (i.e. inclusion plus volume of overlying load transfer platform): The amount of mobilized skin friction, taking into account the relative inclusion-soil displacement (or soil-soil displacement in the platform); The normal stress; The elastic compression of each slice and its cumulative settlement; The load Q p(-hR ) and the total settlement y p ( hR An iterative calculation of the assumed displacement at the tip needs to be performed in order to obtain the settlement compatibility at the top of both domains: y s ( hR ) = y p ( hR ). Iterative calculations of the ratio of the load assumed to be applied to the soil domain is also carried out so that this load gets summed with the n domain, yielding a value equal to the total load applied to the foundation: Q( hR ) = n * A p * Q p( hR ) + Q s( hR ) * (S n * A p) (3.12) where A p: area of the cross-section at the pile domain head; S: area of the footing. Figure 3.15 displays the application of the model to a simple case (Frossard, 2000), with the calculation highlighting the various points to be verified.
Figure 3.15: Example of results derived from the MV2 model (Glandy and Frossard, 2000).
In order to validate model consistency, it is necessary to verify that the stress obtained at the inclusion head is compatible with the load transfer platform shear strength characteristics and moreover that the mobilized skin friction above the neutral plane is indeed compatible with the limiting values of negative skin friction ( v This validation step requires that the vertical stress distribution in the soil domain be estimated as follows:
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For a relatively thin load transfer platform compared to the footing width, it can be assumed
that the total load at the bottom of the load transfer platform is equal to the load on the footing. According to this condition, it is possible to evaluate the stress in the soil domain at
This allows verifying that the stress obtained at the inclusion head is compatible with both the load transfer platform shear strength characteristics, i.e. ultimate stress at the inclusion head and the platform geometry; The edge effect (Chapter 5, Section 4.2); The consistency verification relative to the negative skin friction proves to be a difficult step as it depends on the vertical stress distribution in the soil domain, in alignment with the footing, which is not calculated in the model. All verifications with respect to negative skin friction thus impose adopting an additional hypothesis to allow the estimation of the vertical stresses at any point (e.g. diffusion of loads transmitted to the soil by the footing at a selected angle ). Such consistency tests are crucial to the validation of the model: When these tests are unsatisfactory, it becomes necessary to use a more detailed model. When these tests are satisfactory, the results obtained can be used to proceed with the set of STR and GEO verifications, as indicated in Chapter 5. Remarks: Friction
mobilization laws must incorporate the group effect between adjacent inclusions: for the same load at the head of the model, the shaft friction mobilized along an isolated inclusion is greater than that developed on one of the groups inclusions. To take into account this phenomenon, the friction mobilization curve in the MV2 model would need to be corrected by lowering, for example, the value of the coefficient m defined by the Frank and Zhao curves. This group effect is naturally modeled in the MV3 model (to be described below), which uses an axisymmetric model of the inclusion within a given group. Since the settlement profile generated around the inclusions does not include the influence of forces being transmitted to the soil below the neutral plane, this model may tend under certain conditions to underestimate the settlement of the structure (Fig. 3.16).
Figure 3.16: Loading of the soil block exposed to the action of positive skin friction mobilized under the neutral plane.
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3.1.3.2.3. MV3 analytical model (use of the monolithic approach) This model was presented by Simon (2010). The modeling process herein consists of the assimilation of the reinforced soil volume with inclusions under the footing to an equivalent homogeneous monolith. The following successive analyses are performed: The interaction between inclusions inside the reinforced volume, for the purpose of establishing the properties of this equivalent homogeneous monolith; Then the interaction of this monolith with the surrounding soil. The monolith studied herein is a prism circumscribed to the footing with main vertical axis and the same cross-sectional area: it includes the load transfer platform, the soil layer reinforced by inclusions and the upper part of the bearing layer where inclusions are embedded. This monolith represents the juxtaposition of several reinforced unit cells (inclusion and associated soil domain). The cell cross-section is equal to the area of influence of each inclusion under the footing. This approach entails 3 successive steps (Fig. 3.17), which are to be carried out using typical methods used for deep foundation design: Analytical methods for the study of an isolated pile or a pile located at the center of a reinforcement element mesh, under vertical loading, with the help of transfer functions characterizing shaft friction and end-bearing mobilization around the pile; Or axisymmetric finite element models.
Figure 3.17: Underlying principle of the MV3 model's three-step protocol.
Step 1
A study of the behavior, under distributed vertical load, of a basic unit cell without any interaction with the surrounding domain (i.e. case of a cell placed in the middle of a multiple network of identical cells) serves to establish the elevation of the horizontal plane underneath the inclusion tip where soil settlement is uniform (lower neutral plane). The average Design methods
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settlement derived between the upper cell face (below the footing), and this lower plane allows calculating the apparent equivalent modulus of deformation E * of the unit cell under vertical loading (Fig. 3.18).
Figure 3.18: a) Studied configuration; b) Step 1 of the calculation according to the MV3 model.
Step 2
A study of the vertical monolith with modulus E * assimilated to an isolated pile interacting with the surrounding (non-reinforced) soil domain, exposed to a vertical force Q, determines the profile ys(z) of the average monolith settlement, accounting for skin friction mobilization on the monolith perimeter. The settlement recorded at the top y s( h R ) remains less than the settlement of the cell studied during Step 1, as a result of the stress diffusion through shaft friction along the surrounding soil block (Fig. 3.19).
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Figure 3.19: Step 2 of the calculation according to the MV3 model.
Remark: The
friction taken into account at the monolith edge is a soil-soil type friction; it may be taken as the undrained cohesion c u in clayey layers. In sandy layers, the value adopted will be calculated from the values for p l the targeted layer. The models relevance depends on the limiting friction value considered along the monolith perimeter. It is recommended to calibrate the value of this limiting friction by applying a monolith model comparable to the footing loading case on the soil presumed to be non-reinforced in order to verify that the resulting settlement is in fact comparable to that obtained by pressuremeter theory a load ½kpl*. In this case, the monolith has the same height as that used with the inclusions and a modulus value equal to the modulus E of the soil and not the modulus E* determined during Step 1.
Step 3
The loading curve of an inclusion assumed to be isolated (including the load transfer platform prism displaying the same overlying cross-section) in a soil block subjected to an imposed settlement ys(z) makes it possible to establish the load Q p( hR ) applied at the head of this column in order to obtain a settlement equal to y s( hR ). According to this calculation, the shaft friction at any point of the inclusion is correlated to the relative displacement [y p(z) ys(z)] at the same depth. This load Q p( hR ) then determines the distribution of axial forces Q p(z) in the actual inclusion. The value at the inclusion head (i.e. depth h R under the base of the monolith studied during Step 2) is denoted Q p(0).
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Figure 3.20: Step 3 of the MV3 model calculation protocol.
To validate model consistency, it is necessary to verify that the stress calculated at the inclusion head is compatible with the load transfer platform shear strength characteristics and moreover that the friction mobilized above the neutral plane is compatible with the limiting values associated with the negative skin friction Ktan v Knowing the vertical stress at any depth in the monolith (Step 2) and the axial force in the pile domain (Step 3) enables the calculation at any point of the average stress in the soil domain and then the verification of the consistency of these results (load transfer platform and negative skin friction). Consistency tests are essential to validate this model: When these tests are unsatisfactory, it becomes necessary to use a more detailed model. When these tests are satisfactory, the results obtained can be used to proceed with the set of STR and GEO verifications, as indicated in Chapter 5. Remark: Group
effects relative to shaft friction are automatically taken into consideration by use of the axisymmetric model of an inclusion within a group, as introduced during Step 1.
3.2. Other loads 3.2.1. Horizontal load and moment on footings
The interaction between soil and inclusion is determined through the use of a set of simplified models identified below. These models are applied in accordance with the three methods developed subsequently.
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3.2.1.1. Common features of the simplified models that incorporate both a horizontal loading and a moment
The loading configuration considered herein has been presented in Figure 3.17; it includes a vertical force, a horizontal force and a moment. Lateral forces on the foundation cause shear to develop in both the soil and the inclusions: Shear generated in the soil introduces horizontal displacements of the soil block; The inclusions, which are also affected by a portion of the forces transmitted by the footing, interact with the soil subjected to this displacement field. The models must account for these interactions to evaluate the stress distribution within the inclusions. The horizontal force at the head of an inclusion T p(0) is bound by the following value since it can only be transmitted by friction between the load transfer platform and the inclusion head: Q p 0 (3.13) T p 0 min T ( h R ), Q p 0 tan Q( h R )
where: is the load transfer platform-inclusion angle of friction; Q p(0) the axial force transmitted to the top of the inclusion; Q( hR ) the vertical force applied to the footing; T( hR ) the horizontal force applied to the footing. Lets also observe that the force transmitted to the inclusion head can never induce a displacement of the inclusion head that exceeds the displacement of the surrounding soil. One acceptable approach for obtaining a loading envelope therefore consists of applying a shear force at the inclusion head that reduces the inclusion head displacement to a value equal to that of the surrounding soil, provided it remains less than the maximum value defined in Equation (3.13). Remark: The
numerical calculations performed within the scope of this project have demonstrated that the shear force actually acting at the inclusion head depends on the degree of shear strength mobilized in the load transfer platform. Since punching of the inclusion head into the load transfer platform mobilizes, under the vertical load component, a portion of this shear strength, the shear force capable of being mobilized at the head depends on the remaining amount of potentially mobilized strength. The mobilized shear force is small when the vertical force in the load transfer platform on the inclusion head is close to its ultimate value (see Chapter 5, Section 4.2.2: Calculation of the ultimate transfer of loads at the inclusion head). In all cases, the boundary conditions at the inclusion base are: T(L) = 0 and M(L) = 0. Loadings in the inclusions may be calculated via the coefficient of subgrade reaction method associated with the imposed lateral displacement field g(z) created in the soil due to the additional shear forces.
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These subgrade reaction coefficients are estimated in a manner similar to an isolated pile (see Appendix I of the NF P 94-262 Standard on deep foundations). The following analytical models present different ways of evaluating the imposed displacement field. Remarks: In general, the same rules as for shallow foundations are applied on the
unreinforced soil regarding the determination of passive pressure and side friction reactions on the lateral footing faces. When these reactions are neglected, the horizontal force at the bottom of the footing is equal to the horizontal force applied at the top of the footing. 3.2.1.2. Simplified models for horizontal loading and moment
3.2.1.2.1. MH1 analytical model The shear transmitted in the soil can be neglected by assuming g(z) = 0. The upper bound of the horizontal force potentially developed at the inclusion head is (see Section 3.2.1.1): Q p 0 (3.14) T p 0 min T ( h R ), Q p 0 tan Q( h R )
The inclusions are only taken into account if they are strictly located in the compressed zone, as shown in Figure 3.23. Remark: The
load transfer platform enables spreading shear forces generated by T with depth. This spreading can be neglected without jeopardizing safety.
Figure 3.21: Inclusions taken into account relative to the lateral loadings.
At this point, it is necessary to: Derive the vertical reaction distribution of both the soil and inclusions using a basic cell model subjected to vertical load; Convert these reactions into equivalent distributed spring stiffnesses for the soil and inclusions; Establish the vertical reaction distribution between the soil and the inclusions at the base of the load transfer platform that balances the load system [Q( hR ), M( hR )]. 112
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Remark: Neglecting, during this step, both the group effect (which would imply
lower subgrade reaction coefficients) and the soil displacement g(z) induced by Ti) is an acceptable simplification. the residual shear force (T 3.2.1.2.2. MH2 analytical model The horizontal force applied at the footing is used for the purpose of calculating the horizontal displacement of the footing v( h hR ) lying on an elastic mass. For this task, it is possible to use the foundation impedance formulas at the surface of a semiinfinite elastic mass. As an illustration, for a circular foundation of radius R at the surface of an isotropic homogeneous mass characterized by shear modulus G and Poisson s ratio , the stiffness K x = T/v with respect to a horizontal force is given by (Pecker, 1984): ) K x = 8 GR/(2 (3.15) Similar solutions for a two-layer system have been given by Gazetas (1990). Based on the shear stress applied to the soil at the level of the inclusion head, the shear stress (z) distribution at any depth could be calculated from a diffusion angle down to the bearing layer (where shear strains are considered to be negligible). Starting from the bearing substratum, the shear strain is integrated in order to derive the lateral displacement profile as follows: g(z) = z/G(z) dz (3.16) where G(z) is the shear modulus of the soil at depth z The parameter is calibrated to obtain a deformation at the top g(-h R ) equal to the value v(-hR ) determined previously. The resulting displacement profile is the targeted displacement field g(z). Remark: When the soil is homogeneous, the tri-linear profile proposed by Borel
(2001) for a piled-raft foundation can also be adopted. Table 3.3: Tri-linear 3.3: Tri-linear approximation of relative displacement in the center of a stiff rectangular footing L x B at the surface of a soil mass with height H (valid for H/B > 3).
Relative depth z/B Relative displacement g(z)/g(0)
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0 1
0.4 0.5
1 0.25
3 0
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Figure 3.22: Tri-linear 3.22: Tri-linear approximation of the g(z) profile (Borel, 2001).
The subgrade reaction calculation incorporates this displacement field g(z) and the following boundary conditions: at at the inclusion head: M p(0) = 0 (3.17) and T p(0) calculated in accordance with the recommendations set forth in Section 3.2.1.1. More specifically, a loading envelope is produced by selecting the value for T p(0) that yields a disp displa lace ceme ment nt of the the inclu inclusi sion on head head equa equall to g(0) g(0) i.e. i.e. equa equall to the the displ displac acem emen entt of the surrounding soil, provided T p(0) remains less than the maximum value defined in Equation (3.13); at at the inclusion tip: M p(L) = 0 (3.18) and T p(L) = 0 (3.19) 3.2.1.2.3. MH3 analytical model (monolithic method) The MH3 model, model, introdu introduce cedd in con conjun juncti ction on with the MV3 model, model, has has two succe successi ssive ve additional steps (Simon, 2010; Fig. 3.23). Remark: The considered monolith corresponds to only the compressed part under
the footing. This approach is similar to that employed to study an isolated pile subjected to transverse loading, as depicted by a force T and a bending moment M applied at the head and/or a displacement imposed on the surrounding soil g(z), on elastic-plastic springs (p = p(v) < p lim). The limited monolith length-to-width ratio and its orthotropic nature however require taking the shear deformations of the pile into account. The simple model of a thin beam, commonly used for piles, tends to be inappropriate in that case.
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Figure 3.23: Underlying 3.23: Underlying principle of Steps 4 and 5 in the MH3 model.
Step 4
The monolith with an equivalent modulus E *, which can ultimately be extended to the footing volume (modulus E b), is assimilated with a horizontally-loaded pile interacting with the exte extern rnal al soil soil bloc blockk via via elas elastic tic spri spring ngss p(v) p(v).. The The horiz horizon onta tall load load cons consid ider ered ed here herein in is characterized by the load system [T, M] applied to the footing. The calculation establishes a transverse displacement profile g(z) for the monolith, which is subjected to the loading action; it also determines the rotation ( h hR ) of the footing (Fig. 3.24).
Figure 3.24: Step 3.24: Step 4 of the calculation, according to the MH3 model, for the example shown in Figure 3.15a.
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Remarks: Since Since
the the mono monolit lithh unde underr cons consid ider erat atio ionn typic typical ally ly feat featur ures es a low low slenderness ratio, the shear deformations controlled by the G* 1 factor (with G* being the equivalent shear modulus of the monolith and 1 the reduced shear cross-section) cannot be neglected when compared with bending deformations controlled by the factor E*I (with E* being the equivalent deformation modulus of the the mono monolit lithh and and I the the cros crosss-se sect ctio ionn iner inertia tia of the the comp compre ress ssed ed zone zone of homogenized soil). The equivalent shear modulus G* may be assimilated with the shear modulus of the soil on its own (with the contribution of inclusions to shear strength remaining neg neglig ligible ible comp compar ared ed to that that of the the soil soil). ). This This G* valu valuee is thus thus equa equall to Esol/[2(1 + )], which is distinctly less than the value E*/[2(1 + )] that would have been obtained in a monolith made of isotropic material. This reasoning explains why deflections by shearing must not be neglected in comparison with those by bending (E sol denotes the deformation modulus of non-reinforced soil). Step 5
A subgrade reaction model, limited to the inclusion alone and assumed to be subjected to the previous displacement field g(z), is calculated assuming the following relevant boundary conditions: at at the inclusion head: M p(0) = 0 (3.20) and T p(0) evaluated in accordance with the recommendations set forth in Section 3.2.1.1. More specifically, a loading envelope is produced by selecting the value for T p(0) that gives a displacement of the inclusion head equal to g(0), i.e. equal to the displacement of the surrounding soil, provided T p(0) remains less than the maximum value defined in Equation (3.13); at at the inclusion tip: M p(L) = 0 (3.21) and T p(L) = 0 (3.22) This calculation in turn defines both the shear force distribution T p(z) and bending moment distribution M p(z) in the inclusion resulting from the loading [T, M] (Fig. 3.25).
Figure 3.25: Step 3.25: Step 5 of the calculation, according to the MH3 model, for the example shown in Figure 3.15a.
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Axial forces in the inclusions depend on the cell position with respect to the axis of rotation of the footing. The footing rotation (-hR ) (as calculated during Step 4) actually determines settlement along the axis of the cell placed a distance d from from the axis of rotation, as follows: y p(-hR ) = (-hR ).d (3.23) The associated axial forces in the inclusion placed at the center of this cell can then be estimated by assimilating them with the axial forces found under a uniform vertical loading of the cell that yields the same settlement y p(-hR ) = y s( h hR ). ). This step is performed by means of a specific calculation linking Steps 2 and 3. The forces Q p(z), T p(z) and M p(z) obtained according to the various load cases must be combined in order to verify the stresses in the inclusions. Remark: The
various inclusions placed beneath the footing are subjected to vertical forces that in theory differ from one another due to the footing rotation. The horizontal force applied at the top of each inclusion must remain compatible with the associated vertical force (according to the formula in 3.13).
3.2.2. Loadings under asymmetric conditions
Inclusions may be subjected to additional bending stresses under certain kinds of situations. These loads may be imposed on peripheral inclusions installed below embankment slopes, or on inclusions placed beneath a mechanically-stabilized embankment used as bridge abutment. They may also be those imposed by asymmetric load conditions on an industrial slab or during an earthquake. In the case of inclusions placed under an embankment slope, a g(z) type of approach proves possible. The maximum displacement displacement g max of the profile needs to be correlated with the maxim maximum um settl settlem emen entt ys(0) (0) in the the inte interm rmed edia iate te sect sectio ions ns foll follow owin ingg trea treatm tmen ent. t. The The proportionality factor = gmax/ys(0), as well as the shape of the g(z) curve, may be chosen following the observations recorded on instrumented embankments (see the NF P 94 262 Standard on deep foundation applications). The bending stresses inside the inclusions may be calculated similarly to piles placed in a soil subjected to a displacement g(z). Remark: Since
inclusions only typically represent a small volume of reinforced soil, it is permitted to consider that free displacement of the soil block between inclusions is not being modified by the inclusions.
In the case of earthquakes, the g(z) curve to be assessed is the one defined by the free field soil displacement, which depends on the shear wave velocity V s profile (AFPS, 2011). 4. NUMERICAL MODELS USING FINITE ELEMENTS OR FINITE DIFFERENCES
The finite element and finite difference methods are the most widespread for resolving mechanical equations involving continuous media. Both methods rely on a discretization of the model under study. Based on constitutive models of both soils and the various component materials found in this model, these methods allow Design methods
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simulating the behavior of the discretized medium in terms of stresses and strains under the effect of loads. The accuracy of a simulation depends on the relevance and quality of the soil constitutive models adopted and the discretization strategy selected for the studied soil block. Moreover, these types of methods lead to a verification of bearing capacity and stability criteria for the modeled zone. From the user s standpoint, no noteworthy differences distinguish the two methods. For For purpos purposes es of illustr illustrati ation, on, a 2D finite finite eleme element nt mesh mesh model model will will be prese presente ntedd below below (Fig. 3.26) along with a 3D model of a reinforced soil block beneath a footing (Fig. 3.27).
Figure 3.26: 2D 3.26: 2D computational model of an embankment overlying compressible soils.
Figure 3.27: Example 3.27: Example of 3D mesh for a footing supported by rigid inclusions.
The result obtained through these methods yields an approximated solution whose accuracy depends on: The The model constitutive laws of materials and interfaces; Discretization, resulting in a meshing pattern that must be finer where the strain field variations are greatest; The type of elements adopted (number of nodes) and interpolation laws incorporated into each element (linear vs. quadratic); The use of interfaces between structural elements and the soil in order to allow the integration of soil/structure interaction i nteraction phenomena; The The boundary conditions.
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4.1. Benefits of using these methods
These tools allow the geotechnical engineer to simulate complex structures (in terms of geometry and behavior); in addition, problems impossible to solve analytically can be solved in a complete manner. Compared to the simplified methods, numerical modeling in a continuous medium takes into account the entire configuration of the soil mass, the rigid inclusions and the interfaces between the various components. This type of modeling leads to the calculation of displacements, stresses and strains for each element and moreover enables considering the hydro-mechanical coupling whenever consolidation problems arise. The construction history of the particular structure, which includes for example the phasing of embankment installation, the placement of geo-synthetics or ground slab, and the lowering of the water table, can also be incorporated, thus making it possible to evaluate the impact of each phase of the works. Numerical modeling also allows performing the structural verification steps relative not only to displacements (in the service limit state SLS), but also regarding failure (ultimate limit state ULS). Calculations in small displacements on the initial geometry (common case) are typically performed. In some cases, when second-order effects can no longer be ignored, it becomes necessary to run the simulations with a large displacement assumption. This type of modeling allows updating the geometry of the mesh adopted during the loading sequence. This is necessary to correctly account for the influence of reinforcement layers that develop tensile forces, depending on the vertical displacements they undergo. These methods generate, from an extensive knowledge of the behavior of the different layers of soils as well as of the inclusions, the interactions between various components and the phasing of the construction of the structure, plus a set of relevant simulations of the overall performance of the structure. They are also beneficial for conducting parametric studies that demonstrate the sensitivity of a given parameter. 4.2. Limitations of two-dimensional modeling
Currently, 2D structural models are commonly used, either plane strain models or axisymmetric models. In the axisymmetric models, the grid of inclusions in the central part of the embankment is modeled by transforming the area of influence of the inclusion, whether rectangular or square, into a circle (Fig. 3.28). With this type of configuration, it is possible to only model a single unit cell located either close to the embankment axis or at the center of a slab on grade. In plane strain models, the complete response of the entire embankment or slab on grade on the soil reinforced by rigid inclusions can be obtained through broad simplifications relative to the rigid inclusion geometry. While the 2D hypothesis is valid for the embankment itself, it
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is no longer acceptable when adding the rigid inclusions. The 3D inclusion must then be transformed into an equivalent 2D plate (Fig. 3.29).
A slab on grade may also demonstrate a behavior closer to a 3D representation than a 2D behavior, in which case the model strays significantly from reality since the computational space remains two-dimensional.
Figure 3.28: Axisymmetric modeling of the central mesh (right)
Figure 3.29: Model of the embankment and soil reinforced by rigid inclusions in plane deformation.
4.2.1. Axisymmetric model
The axisymmetric analysis can only, strictly speaking, provide a model of the central mesh in the embankment axis, as the embankment itself is assumed to be symmetrical (Fig. 3.30). For a slab on grade, the interior of the slab far from the edges can be modeled, provided that the loading is uniform across the inclusion grid.
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Figure 3.30: Axisymmetric model representing a single mesh of a distributed load supported by a soil reinforced by rigid inclusions.
4.2.2. Plane strain model
In this type of configuration, the rows of inclusion are transform to the sectional plane of the model. In order to depict the entire embankment and rigid inclusion configuration in 2D, the rigid
relative to the normal force and an equivalent EI relative to the bending stiffness, while also verifying that the side friction developed against this plate and the forces transmitted at the head and base of the plate are comparable to the actual forces applied to the inclusions.
replacement ratio and thus correctly model the force at the head and base of the inclusion. Interface parameters must be set so as to replicate the force being mobilized by side friction. The plane strain model thus offers an acceptable approximation for the design of inclusions beneath embankments. In contrast, it is poorly adapted for the verification of the stresses developed in the load transfer platform at the top of the inclusions as well as stresses and moments in slabs on grade. Yet depending on the type of parameters (stresses, displacements), it is acceptable to choose to accurately model only a portion of the previously defined criteria. The validity of plane strain models should be verified by comparison with the results of an axisymmetric model. Design methods
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4.3. Modeling considerations 4.3.1. Geometric boundaries of these models
Model boundaries are chosen so as not to influence the calculation results. For an axisymmetric model, the vertical geometric boundaries are imposed by the model, which exhibits an oedometric behavior (Fig. 3.31). When a plane strain model is used, the model s vertical geometric boundaries must be placed at a distance such that the displacements and stresses contributed by the loads will remain negligible with respect to these boundaries. For a perfectly symmetric structure (from both a geometric and mechanical standpoint) with symmetric loadings as well, only half of the structure needs to be modeled (e.g. Fig. 3.28).
For these two models (axisymmetric and plane strain), horizontal geometric boundaries are chosen to take into account the geological profile in the case of a rigid substratum or a stiff shallow soil layer. In classical configurations, the rigid inclusions go through a layer of soft soil and are embedded into a much stiffer layer. Should this particular layer not be overlying a rigid substratum or a layer of very stiff soil, then it would be necessary to extend the model below the inclusion tip over a soil thickness sufficient to neglect the deformations due to stresses of the structure at depth as well as the stresses at the tip of the inclusions at depth. Special attention will be paid to the raft effect from groups of inclusions (Fig. 3.32). The load transmitted to the inclusions is subsequently transferred to the bearing layer. It is therefore critical to accurately model the thickness and characteristics of the underlying layers. Their compressibility could in fact cause additional non-negligible settlements.
Figure 3.31: Boundary conditions.
Figure 3.32: Raft effect and zone of influence.
It might be useful to test the sensitivity of the results by studying how they are affected by the choice of boundaries further away from the inclusions (larger model). 4.3.2. Boundary conditions
In an axisymmetric model, the horizontal displacement is by definition equal to zero on the model axis and the outer edge of the model.
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In the case of a plane strain model, more often than not, a zero horizontal displacement is imposed at the vertical boundaries of the model. When the problem is symmetrical (Fig. 3.31), e.g. in plane deformation, the horizontal displacement is by definition equal to zero on the vertical plane of symmetry. For both models, a zero vertical and horizontal displacement is imposed on the lower horizontal boundary. 4.3.3. Axisymmetric model of a unit cell
4.3.3.1. Embankment
Far from the toe of the embankment (Fig. 3.33), the following axisymmetric model may be considered (Fig. 3.34).
Figure 3.33: Sketch of in situ soil reinforcement by means of rigid inclusions ( embankment case).
Figure 3.34: Basic cell.
4.3.3.2. Slab on grade
An axisymmetric model can only represent the central mesh of a network of rigid inclusions; this model is specially adapted to uniform surface loads. The radius R of the equivalent model is chosen to represent the area of a unit cell, provided that this area's proportions are close to those of a square (i.e. b < 1.25 a): R
ab
(3.24)
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Figure 3.35: Sketch of in situ soil reinforcement by means of rigid inclusions (Slab on grade case).
Figure 3.36: Unit cell
4.3.4. Plane strain model
The requirements specific to this type of model are detailed in Section 4.2.2. Other geometry based requirements must also be taken into consideration. As a preliminary indication, the model dimensions are as follows: Width of the half-model such that L M - LR > 2 H; Depth of the model such that H M > 3LR (Fig. 3.37). Moreover, with respect to the influence of rigid inclusion tips, the following maximum values will be adopted beneath the tips: 10 times the tip diameter; 3 times the width of the raft equivalent to the group of inclusions. In all instances, it is necessary to verify that the results obtained are not influenced by the selected model dimensions. Quite often, the structure is symmetric from both a geometric and hydro-mechanical standpoint; under such conditions, which are indeed frequently encountered, this symmetry will be utilized to consider only half of the structure (Fig. 3.31).
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Figure 3.37: Geometry-based criteria for the plane model of an embankment over inclusions.
4.3.5. Volumetric or linear elements
Rigid inclusions may be represented by either volumetric or beam elements (Fig. 3.38). In soil reinforcement projects, it is preferable to model the rigid inclusions using volumetric elements in order to represent the interactions at the inclusion head and tip as well as along the shaft of the inclusion.
Figure 3.38: Model of inclusions using volumetric or linear elements.
Whenever an inclusion is represented by volumetric elements in linear elasticity, it is helpful to introduce a beam element with a very low stiffness EA into the inclusions so as to facilitate the analysis, by means of simple proportionality, of the forces in the inclusion. 4.3.6. Behavior of the soil mass below the reinforced volume
The axisymmetric model of a unit cell depicts the case of the uniform loading of a very large extended area. It is implicitly assumed that no load diffusion outside the volume of the model actually occurs. This model is representative over the inclusion length, since inclusions tend to attract the loads applied at the top of the model. A horizontal neutral plane where the stress distribution is uniform across the model should be located between the tip of the inclusion base and the base of the model (the lower neutral plane of equal settlement) (Fig. 3.39).
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Figure 3.39: Upper neutral planes of equal settlement, along with the intermediate and lower planes around an inclusion.
It is necessary to examine the amount of settlements caused by this uniform stress in the soil volume located below this neutral plane of equal settlement. If these settlements are non-negligible, their estimation may require a specific model distinct from the axisymmetric model of the unit cell: Simply extending the unit cell model is most definitely a pessimistic approach since no lateral diffusion of the load would be allowed to intervene. The resulting calculated settlement would thus be an upper bound of the total settlement under the structure (Fig. 3.40);
Figure 3.40: Extending the unit cell model downward in order to estimate settlements of the underlying soil layer.
One option consists of estimating the settlements of a fictitious foundation of the same
dimensions as the structure itself, which has been lowered to the level of the neutral plane positioned below the inclusion tips and loaded with the average stress of the structure. The total surface settlement is therefore the sum of the unit cell settlement (with the model limited to the neutral plane beneath the tip of the inclusion) plus the settlement of the lowered fictitious foundation (Fig. 3.41); 126
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A comprehensive global 2D model of the structure that incorporates its dimensions
(whether plane or axisymmetric), where the reinforced zone is modeled as a homogenized zone, gives a less pessimistic representation of load diffusion with depth. This model allows modeling the side interaction between the non-reinforced zone and surrounding soil block. The settlement calculated by the model thus represents an estimation of the total settlement of the structure (Fig. 3.42).
Figure 3.41: Fictitious footing loaded at the inclusion tip, for the purpose of estimating the settlement of the layer below the tip of the inclusions.
Figure 3.42: Homogenized equivalent volume interacting with the non-reinforced soil, for the purpose of estimating the settlements of the underlying bearing layer.
4.3.7. Use of 3D modeling
The primary advantage associated with three-dimensional modeling is the ability to represent the targeted problem in a comprehensive global manner. This type of simulation can be necessary in the case of a reinforced slope, a footing subjected to complex loading or a nonuniformly loaded slab on grade. All these models however lead to very high computational times. Design methods
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4.4. Constitutive models 4.4.1. Study of model parameters
Regardless of the type of model and computational tool, the modeling parameters must provide the opportunity for numerical models to replicate the actual behavior of the project as closely as possible. The parameter calibration phase needs to verify that the selected constitutive model, combined with the particular dataset of selected parameters, will yield representative results when applied to the simulation of the available test data. It is essential, during the preliminary phases, to calibrate the parameters described in the subsequent sections. Without any empirical field data, it is advised to select the least favorable hypotheses. In the absence of direct comparison with an in situ load test, it is recommended to verify the capacity of an appropriately-dimensioned model, using the selected constitutive models and parameters, in order to produce a loading curve at the head of an isolated inclusion comparable to the curve estimated according to the semi-empirical approach combining Frank and Zhao-type mobilization laws with ultimate values q s and q p relative to the type of inclusion considered. Similarly, underneath a footing, it is recommended to verify the capacity of an appropriatelysized model to yield a loading curve at the top of an isolated non-reinforced footing comparable to the curve estimated by implementing a semi-empirical pressuremeter or penetrometer type approach. 4.4.2. Mechanical characteristics of soils
The introduction of numerical models enables utilizing the best constitutive models adapted to each structure-soil combination. In other words, it is not necessary to solely use the socalled Mohr-Coulomb model (which is in fact a linear elastic-perfectly plastic model with a Mohr-Coulomb failure criterion), even though it is the most widely known and most widely used in the geotechnical community. The parameters selected for the materials in the calculation will thus depend on the selected constitutive model for a soil mass, structure or support.
4.4.2.1. Linear elastic-perfectly plastic model (Mohr-Coulomb)
This first-order model is the best known among geotechnical engineers; it can be used for stiff soils without any problem of consolidation. For a homogeneous and isotropic material, this model requires determining 5 parameters (as shown in Fig. 3.43).
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Figure 3.43: Elasto-plastic constitutive model.
In order to select the 5 relevant parameters (see Table 3.4), the most appropriate test is the triaxial test. Table 3.4: Mohr-Coulomb parameters .
Parameter E (Youngs modulus)
(angle of dilation)
Unit
Means of determination
kPa, MPa
Triaxial, pressuremeter (EM) 0.2 < Triaxial, correlations? Triaxial, correlations 30°
Degrees kPa Degrees
This model, which describes (using a limited number of parameters) the soil behavior up to failure, can still prove overly simplistic in some cases: For excavation during which the soil mass is unloaded; according to this model, the unload/reload modulus is equal to the loading virgin modulus, which is an unrealistic assumption, resulting in an excessive calculated heave at the bottom of the excavation when compared to experimental data; For slightly over-consolidated soft soils whose apparent deformation modulus depends on the stress increment. The initial stress state of the soil, which depends on both its geologic and anthropogenic history, must be specified by oedometer testing at various levels in order to determine the degree of over-consolidation (R OC) vs. depth. The stresses from the structure, the embankment, slab on grade loads, tanks and reservoirs, etc. will be used to determine the precise domain of stresses where the various layers will be loaded, i.e. normally consolidated domain vs. over-consolidated domain (Fig. 3.44). 0; the angle of friction will be set at the critical state NC = crit (on the yield surface) and will thus be identical to the peak friction
angle.
For soils with stresses in the over-consolidated domain, if the strain is limited and less than that of the elastic limit (i.e. below the yield surface), then the values will be set at the peak, where SC = peak SC peak . In the over-consolidated domain, stress paths end up on Design methods
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the limit state ellipse; the ends of these paths are therefore not aligned, though the curve is usually linearly interpolated in order to calculate peak peak . It can be noted on Figure 3.44 that the determination of peak peak requires experience and is less reliable than in the normally consolidated domain.
Figure 3.44: Determination of -consolidated domains (according to Josseaume and Azizi, 1991).
Sugg Chapter 6.
, based on correlations as a function of I p, are provided in
4.4.2.2. Elasto-plastic model with strain hardening (modified Cam-clay)
This model is well adapted for soils subjected to primary consolidation phenomena. The concepts of elastic limit state and critical state are introduced on the basis of: Isotropic consolidation tests that define the elastic limit points (Fig. 3.45); Triaxial tests that define the critical states and critical state line in the Cambridge q
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6 sin ' p ' 3 sin '
(3.25)
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Figure 3.45: Isotropic compression curve.
CVI: LEC: CEC: V: VA:
Figure 3.46: Stress and strain paths leading to critical state.
virgin isotropic compression curve critical state line critical state curve specific volume = (1 + e) initial specific volume average stress and deviatoric stress
So, in order to determine the 5 main parameters of the model, a series of oedometer tests and triaxial tests need to be conducted (see Table 3.5 for further details). The Soft Soil model has been derived from the modified Cam-clay model. Table 3.5: "Soft Soil" model parameters.
Parameter
*
*
(compression index) (decompression-recompression index)
(angle of dilation)
Units
Means of determination
Degrees kPa Degrees
Oedometer: Cc / 2.3 (1 + e) Oedometer: 2Cs / 2.3 (1 + e) Triaxial (or correlations?) Triaxial (or correlations?) 30°
4.4.2.3. Elasto-plastic model with strain hardening (modified Cam-clay) a nd creep
This model incorporates soil viscosity (Fig. 3.47) and is particularly applicable to soft organic clay and peat for which creep (secondary consolidation) cannot be neglected when compared to Terzaghi's primary consolidation.
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Figure 3.47: Creep curves.
C, the secondary consolidation rate, is defined as follows: H H0 C lg t lg t Using the void ratio, the creep index C e is expressed as: C e
e lg t
C
1 eo
(3.26)
(3.27)
where eo is the initial void ratio. With respect to the Soft Soil model, an additional parameter is thus required. Both short and long-term oedometer tests need to be conducted along with triaxial tests (Table 3.6). Table 3.6: Parameters used for the "Soft Soil Creep" model.
*
*
Parameter
(compression index) (decompression-recompression index) * (creep index) (angle of dilation)
Units
Degrees kPa Degrees
Means of determination
Oedometer: Cc/2.3 (1 + e) Oedometer: 2Cs/2.3 (1 + e) Long-term oedometer: Ce / 2.3 (1 + e) Triaxial (or correlations?) Triaxial (or correlations?) 30°
4.4.2.4. Hyperbolic model of the elasto-plastic type with strain hardening
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Second-order models are currently the most advanced for the purpose of simulating the behavior of both stiff and soft soils. As an example, let's describe the hyperbolic constitutive model which is an elasto-plastic type model with strain hardening (so-called Hardening Soil Model ); it features an initial nonlinear behavior, with a plastic threshold, an unloading modulus greater than the virgin loading modulus, and both compression and shear hardening (Fig. 3.48). This model also allows describing the dilatancy prior to failure.
The deviatoric curves q - axial strain 1 from the triaxial tests are approximated to hyperbolas, i.e.: q
1
1 E i
1
(3.28)
qa
with: Ei: tangent modulus of the virgin loading; qa: horizontal asymptote value of the deviatoric tensor.
Figure 3.48: Relation between stress q and strain 1 in the hyperbolic model.
The tangent modulus E i increases with stress 3:
' 3 p a
m
E i kp a
(3.29)
where k and m are parameters determined based on drained triaxial tests and p a is the reference pressure, typically taken as atmospheric pressure; k depends on the type of soil and its density. For sand material, m is on the order of 0.5, while for clay m is closer to 1. The failure threshold q f is determined from the Mohr-Coulomb criterion; the deviatorhyperbolic strain curve is truncated accordingly (Fig. 3.48). R f is the ratio of qf / qa ; its value generally lies between 0.8 and 0.9 and in the Plaxis software has been set by default at 0.9. In order to completely describe this model, a total of 10 parameters are necessary. A triaxial testing campaign should be conducted, in theory, with an unloading-reloading loop so as to measure Eur ref . Oedometric tests are also recommended. (Table 3.7).
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Table 3.7: The set of "Hardening Soil Model" parameters.
Parameter
E50ref Eoedref M Eur ref ur pref R f
Units
Means of determination
kPa kPa
Triaxial CD, with a V measurement Oedometer Triaxial, correlations? Triaxial, in unloading (3 E50ref ) Triaxial, in unloading (0.2) (100 kPa) Triaxial (0.9) Triaxial, correlations? Triaxial, correlations? 30°
kPa
kPa
(angle of dilation)
Degrees kPa Degrees
The soil parameter determination protocol is provided as part of Chapter 6, Soil Surveys. Remark: In
order to calibrate the parameters in this model, results from drained triaxial tests and/or oedometer tests are required.
4.4.3. Hydraulic characteristics of soils
The soil permeability values (both horizontal and vertical permeability) allow taking consolidation into account. The selection of these values requires that the evolution of the permeability with the load from the structure is known. Lets recall at this point the relationship between the coefficient of vertical consolidation c v and k v: cv
k v E oed
w
(3.30)
This formula can also be expressed as a function of C c, in the normally consolidated domain and, by extension, in the over-consolidated domain as a function of C s, for a given vertical stress k 1 e (3.31) in the elastic domain: p ' c v 2 .3 v C s
cv
2 .3
k v
w
1 e
C c
'
(3.32) in the plastic domain: p
w
The value of this coefficient depends on the vertical stress vertical permeability k v (expressed in m/s), and soil compressibility C c/(1 + e0). The variation in permeability k v is directly derived from variation of the void ratio e (Fig. 3.49) by the following relation: k e e0 lg v c k k v0
e c k lgk
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(3.33)
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Figure 3.49: Curve depicting the variation in coefficient of permeability k v vs. void ratio, thus enabling the determination of parameters c k and log kv0.
Benchmark values and correlations between these parameters are discussed in Chapter 6. 4.4.4. Characteristics of the inclusion/soil interfaces
These numerical calculation tools propose various types of interfaces for simulating the soil / inclusion interaction. The constitutive models typically used for interfaces are of the elasto plastic type. The elastic part allows modeling a gradual mobilization of shear with strain. As for the plastic part, two techniques are used: Either a reduction of Or a fictitious soil s, in compliance with the limiting values of shaft friction set forth by the French standard for deep foundations. Other means are also available to handle this phenomenon, for example by refining the mesh around the contact zone. In this approach, it is more difficult to incorporate the limiting shaft friction values qs, which also depend on the techniques of execution of the inclusions. In order to fully represent this interaction and define the set of model parameters, data from in situ axial load tests conducted on an isolated inclusion may also be used. 4.4.5. Characteristics of the rigid inclusions
A linear elastic model is typically adopted for the inclusions. The value of the long-term modulus is generally used in the design calculations. The shortterm modulus value is only used for short-term exceptional situations (shocks, impact loads or seismic actions). The Poisson's ratio value is typically set equal to = 0.2. The diameter of the inclusions in the model is the nominal diameter defined in Chapter 7, which depends on the execution technique, while the length selected is the theoretical value.
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4.4.6. Characteristics of the load transfer platform
The load transfer platform is composed of a granular material or else a material treated with a hydraulic binder. The characteristics of this layer can be determined from tests on the strength of these materials. The load transfer platform may at times be reinforced by geo-synthetics. A linear elastic model with a Mohr-Coulomb plasticity criterion may be adopted for cement or lime-treated materials. For granular soils whose behavior depends on the stress state, a more advanced constitutive model might prove more pertinent. The ASIRI National Project established the parameters of deformation and shear for a few representative materials (industrial gravel, lime and cementtreated silt) (Dupla et al., 2007; Okyay et al., 2010). 4.4.7. Characteristics of geo-synthetics
Geo-synthetics are usually characterized by a linear elastic constitutive model with a modulus value depending on the level of anticipated strain and the duration of application of the load al step in the design is to verify that the calculated tension is compatible with the material characteristics, as defined by the relevant regulations and codes. 4.4.8. Characteristics of the slab on grade or raft
A linear elastic constitutive model may be used. The Poisson's ratio value is set at = 0.2 for slabs on grade, in compliance with the DTU 13.3 Standard. To respect the settlement calculation that includes long-term deformations, it is recommended to adopt the long-term value for the slab or raft concrete modulus. Such an approach matches the DTU 13.3 specifications, which states in Article 6.3 that storage loads are to be considered as long-term loads. The short-term modulus value should therefore only be used for short duration loads (i.e. dynamic actions) and for exceptional / catastrophic events (shocks or seismic actions). 4.5. Construction phases
Generally speaking, the following phases are to be considered: Stress initialization: the initial stress state must comply with the over-consolidation ratio of each soil layer as well as the initial water table level; Construction conditions; - site re-grading (cut and fill), - installation of the inclusions, - installation of the transfer load transfer platform and geo-synthetics as required, - construction of the embankment or structure; Service situations (defined by associating a load system with an assumption regarding the drained vs. undrained behavior of soils); - accounting for variable loads, - calculation of both the consolidation and potential creep of the different soil layers, - various water table conditions. 136
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4.6. Calculation considerations
The constitutive laws selected for each layer are activated under the hypothesis of a drained vs. undrained behavior adapted to the various calculation phases. It is important to note that for the soils, the linear elastic, perfectly plastic model (Mohr-Coulomb) is not well suited to simulate undrained behavior. Calculations are performed assuming either small deformations (according to Euler's hypothesis) or large deformations (Lagrange s hypothesis). The large deformation calculation is critical in the presence of horizontal reinforcement layers acting as membranes (secondorder effect). 4.7. Analysis of the results
The analysis of the results shall validate the computational model, while verifying the various limit states and allowing the preparation of the design calculation report. 4.7.1. Validation of the results
The validation of the results needs to: Systematically verify all the geotechnical hypotheses made in the model; Check the relevance/adequacy of the choice of model boundaries as well as the selection of the grid of the inclusions to the most heavily loaded zones; Ensure that the adopted constitutive models and the selected modeling principles are capable of acceptably reproducing the behavior of an isolated inclusion loaded at the top or the behavior of a typical foundation representative of the structure; Verify the properties of interfaces are correct and that the interfaces are activated; Verify that convergence criteria have been met; Examine the results phase-by-phase (deformed mesh, displacement field, stress states, forces in structural elements, i.e. normal forces, shear forces, moments) on the appropriate type of output (maps and graphs with suitable scales, or tables) relative not only to the entire model, but also the more heavily loaded zones; Verify the consistency of the results with respect to skin friction (negative or positive) as well as the tip bearing pressure, as explained in Section 4.1 of Chapter 5; Ensure the consistency of lateral and frontal soil reactions on the foundation footing relative to the hypothesis to neglect or not these reactions. Remark: Consistency
with respect to load transfer platform behavior, as explained in Section 4.2 of Chapter 5, is automatically verified by the numerical models that incorporate the platform material strength criterion and that represent the inclusions individually (which is only the case for the 2D axisymmetric model of the unit cell or for any 3D model).
4.7.2. Verification of the various limit states
These verifications are detailed in Chapter 5. These steps must be presented in the design calculation report.
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4.7.3. Contents of the design calculation report
The design calculation report must contain the following elements: Input parameters for the constitutive models selected for: - in situ soils, - the load transfer platform, - embankments, if applicable, - the inclusions, - structural elements (slab on grade, footings, raft), - horizontal reinforcement layers; Description of the numerical model (software and version, types of elements); Geometry of the model and mesh; Details of the various calculation phases; Pertinent results in the form of tables and/or graphs adapted to the project configuration and - requirements, which may include: - displacement and/or stresses along the model's cross-sections, - position of the 3 neutral planes, if applicable (Fig. 3.39), - deformations / displacements at the surface (case of an embankment) (see Fig. 3.50),
Figure 3.50: Deformed mesh of the entire structure.
- normal stresses (or axial force) in selected inclusions, - bending moment and shear force in the same inclusions (if applicable), - stress field in the load transfer platform above the inclusions (Figs. 3.51 and 3.52), particularly the plot of the plastic zones, - loading in the structural elements (bending moment, shear force).
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Figure 3.51: Extension of the plastic zones under 1 m of embankment, revealing a failure mechanism above the inclusion head reaching the soil surface.
Figure Figure3.52: Extension 3.52: Extensionofofthe theplastic plasticzones zonesunder under7 m7ofmembankment, revealing a confined failure bulb of embankment, revealing a conned failure above thethe inclusion head. bulb above inclusion head.
5. HOMOGENIZATION-BASED METHODS 5.1. Simple homogenization method
One homogenization method applicable in cases when loads are exclusively vertical consists of modeling beforehand the behavior of a typical representative unit cell including a typical inclusion along with its associated soil and load transfer platform volumes. This unit cell is generally modeled using an axisymmetric model. The results of this model are then compared to those obtained with a second model featuring the same dimensions, where the soil and inclusion are replaced by a unique and homogeneous material, with characteristics chosen so as to yield results similar to the first model. This equivalence is typically achieved with regards to settlement, which allows defining the apparent modulus E* of the equivalent homogeneous material that provides an average equivalent settlement at the surface of the model. The properties derived may then be used in a more comprehensive model that encompasses some or all of the unit cells. This approach reduces the complexity of the model while describing the complete behavior of the structure. This approach is only valid for the specific modeled loading case. Let's point out that it is not possible for rigid inclusions to use the same homogenization procedure as that applied when designing stone column reinforcement projects, which states:
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E.A* = (E p A p + Es As) / A (3.34) E p and A p: modulus of deformation and cross-section of the inclusion, respectively. Es and As: modulus of deformation and area of the soil. The differential sliding at the soil/inclusion interface requires the introduction of a correction coefficient , i.e.: E.A* = (E p A p / + Es As) / A (3.35) Comparisons between the two methods have been performed and have demonstrated that this factor could easily exceed 10 in some cases. 5.2. Extended biphasic model 5.2.1. Modeling principle
With inspiration drawn from a homogenization approach, yet allowing for the limitations of the homogenization method to be corrected (i.e. failure to take into account the soil-rigid inclusion interactions, as well as bending and shearing of the inclusions), the biphasic model of a soil reinforced by rigid inclusions takes advantages of three characteristics of this reinforcement technique in the case of distributed loads (slabs on grade or embankments): Uniform grid of inclusions within the soil mass; The relative scale of the reinforcement (spacing between two consecutive inclusions), which is reasonably small compared to the overall dimensions of the inclusions; A reinforcement material (steel, concrete, etc.) with significantly better mechanical properties than the surrounding soil, but on the other hand with a fairly low volumetric proportion / replacement ratio (generally a few percent). A detailed presentation of this modeling approach is provided in Sudret and de Buhan (2001), Cartiaux et al. (2007) and Hassen et al. (2009), including its application to soils reinforced by rigid inclusions. This discussion will be limited to describing the underlying principle, as illustrated in Figure 3.53. The reinforced soil composite has been modeled at the macroscopic scale, not as a single equivalent medium as would be the case in a conventional homogenization approach, but instead by two continuous media, called phases, with mutual interaction.
Figure 3.53: Principle behind the biphasic modeling of a soil reinforced by rigid inclusions.
Such a modeling approach leads to a description of stresses (i.e. internal forces) relative to each of the phases assessed separately (Fig. 3.54): standard stresses for the matrix phase representing the soil; axial force, shear force and bending moment densities for the reinforcement phase, which is modeled as a continuous distribution of beams. 140
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Figure 3.54: Stresses and interaction forces relative to a biphasic model.
The interaction between phases is modeled using two types of forces: A volumetric density of interaction forces (denoted I) at any point in the reinforced zone which represents, at the macroscopic scale of the model, the forces applied by the surrounding soil along the length of the inclusions (so-called longitudinal interaction); A surface density (denoted p), which describes the forces applied by the surrounding soils at the extremities of the inclusions (head and tip). 5.2.2. Model implementation
Figure 3.55: Simplified biphasic model.
In the case of a soil layer reinforced by a uniform distribution of vertical rigid inclusions, subjected to a uniform and vertical load (Fig. 3.55), the biphasic model is equivalent to a simplified approach developed in the Taspie + computation software (Cuira and Simon, 2009). According to this configuration, forces inside the inclusions are actually simplified to the axial loading, whereas the interaction forces I and p are purely vertical. The interaction laws can thus be directly derived from the " -w" curves classically established for piles. Far from being limited to this unique situation, the biphasic model may in fact be easily integrated into a finite element computation code, and this software can solve a very broad array of situations. The main advantage of such a modeling technique, compared to a more conventional design method that models the soil and inclusions as two geometrically distinct elements, is twofold. With regards for example to a numerical simulation of the problem using either the finite element or finite difference technique, the conventional approach consists of separately discretizing the inclusions and soil, resulting in a mesh size significantly smaller than the size of the inclusions. Since the problem also happens to be threedimensional, such a numerical procedure requires considerable mesh preparation time and
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computation time and is therefore not compatible with the goal of a quick design of the solution. As an example of the superior performance of the biphasic model, Figure 3.56 shows the surface settlement profiles of a reinforced soil layer subjected to the weight of an embankment, as evaluated based on a 2D biphasic simulation and a comprehensive 3D numerical calculation whose implementation was far more complex than the 2D biphasic calculation (Hassen et al., 2009). The biphasic model was incorporated into the CESARLCPC software package (Bourgeois et al., 2006), with the constitutive laws of the individual phases, as well as the interaction laws, assumed to be elasto-plastic.
Figure 3.56: Comparison between a biphasic (2D) calculation and a 3D numerical simulation (extracted from Hassen et al., 2009).
5.2.3. Effects of shear and bending in the inclusions
In the cases where the soil reinforced by rigid inclusions is subjected not only to a vertical loading but also to a horizontal load (e.g. seismic event), it becomes impossible, given the inclusion cross-section, to neglect the bending and shear components of the interaction forces, which in this case can actually play the predominant role in support of the structure. The complete biphasic model, i.e. model that takes into account the bending and shear components, may be implemented numerically, i.e. using a numerical computation code (Thaï Son et al., 2009, 2010). Figure 3.57 below offers a stability calculation example of an embankment on a soil reinforced by rigid inclusions; this figure clearly shows the major role played by the resistance to bending of these inclusions.
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Figure 3.57: Stability computation for a seismically loaded structure according to the biphasic approach (Thaï Son et al., 2010).
References
AFPS - « Amélioration et renforcement des sols sous actions sismiques ». Groupe de travail, 2011. Bigot G., Canepa Y. - « Fondations de bâtiments. Utilisation des techniques de traitement et ». Rapport interne LPC, 1998, p. 37 - 41. Borel S. - Comportement et dimensionnement des fondations mixtes . Études et recherches LPC, GT 73, 2001. Bourgeois E., Rospars C., Humbert P., Buhan (de) P. - A multi-phase model for finite Proc. Num. Meth. Geotech. Eng ., Schweiger (ed.), Taylor & Francis Group, London,
2006, p. 341-346. BS8006 - Code of Practice for Strengthened/reinforced soils and other fills, Section 8, Design of embankments with reinforced soil foundations on poor ground Cartiaux F.-B., Gellee A., Buhan (de) P., Hassen G. « Modélisation multiphasique inclusions rigides ». Revue française de géotechnique, n° 118, 2007, p. 43-52. Combarieu O. - « ». Note dinformation technique LCPC, 1988, 15 p. Combarieu O. - « Fondations superficielles sur sol amélioré par inclusions rigides verticales ». Revue française de géotechnique, n° 53, 1990, p. 33-44. Cuira F., Simon B. - « renforcé par inclusions rigides ». Proc. 17th ICSMGE , Alexandrie, M. Hamza et al . (Eds.), IOS Press, 2009, p. 1163-1166. Dupla J.-C., Canou J., Dinh A.Q. - « Caractérisation des graves utilisées sur les plots expérimentaux de Saint-Ouen- ». Rapport ASIRI 1.07.3.02, 2007. Frank R., Zhao S.R. « sous charge axiale des pieux forés dans les sols fins ». Bulletin de liaison des laboratoires ponts et chaussées, n° 119, mai-juin 1982, p. 17-24.
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Gazetas G. - Foundation vibration . Foundation Engineering Handbook, chap. 15, Hsai-Yan Fang Eds, 2 nd Edition, 1990. Glandy M., Frossard A. - « ». , n° 1, 2002, p. 45-53. Hassen G., Dias D., Buhan (de) P. - Multiphase constitutive model for the design of piledembankments: comparison with three-dimensional numerical simulations . International Journal of Geomechanics, vol. 9, n° 6, 2009, p. 258-266. Hewlett W., Randolph M.A. Analysis of piled embankments . Ground Engineering , 21(3), 1988, p. 12-18. Josseaume H., Azizi F. - « Loi de comportement des sols raides. Détermination de la courbe ». Études et recherches des LPC, GT 33, 1988. Monnet A., Bernhardt V. (2000). Quelques propositions au sujet des fondations profondes, Revue française de géotechnique 90, p. 15-24. NF P 94-262 - Justification des ouvrages géotechniques. Normes d application nationale de lEurocode 7. Fondations profondes (à paraître). Okyay U.S., Dias D., David J.-P., Auriol J.-C. - « Essais de caractérisation du limon de Goderville traité ». Rapport ASIRI 3.09.03.10, 2009. Pecker A. - Dynamique des sols, Presses des Ponts, 1984. Plumelle C. « sions de micropieux ». Revue française de géotechnique n° 30, 1985, p. 47-57. Simon B. « déformation ». XV e ICSMGE , Istanbul, vol. 2, 2001, p. 1007-1010. Simon B. - « Une méthode simplifiée pour le calcul des semelles sur sol renforcé par inclusions rigides ». JNGG 2010, Grenoble, Tome 1, p. 529-536. Sudret B., Buhan (de) P. - Multiphase model for inclusion-reinforced geostructures. Applications to rock-bolted tunnels and piled raft foundations . International Journal for Numerical and Analytical Methods in Geomechanics, vol. 25, 2001, p. 155-182. Thai Son Q., Hassen G., Buhan (de) P. - « Dimensionnement sous sollicitation sismique de sols de fondations renforcés par inclusions rigides ». Proc. 17th ICSMGE , Alexandrie, M. Hamza et al . (Eds.), IOS Press, 2009, p. 606-609. Thai Son Q., Hassen G., Buhan (de) P. - Seismic stability analysis of piled embankments: a multiphase approach . International Journal for Analytical and Numerical Methods in Geomechanics, vol. 34, 2010, p. 91-110.
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Chapter 4
Design considerations
1. CHOICE OF IMPROVEMENT METHOD
The purpose of this chapter is to draw up an inventory of items that would justify choosing a rigid inclusion-based solution. The uniqueness of a reinforcement scheme using vertical rigid inclusions is for the soil, in relative proportion to its own strength, to bear a portion of the loads generated by the structure, with the bulk of these loads being transmitted by various mechanisms to the rigid inclusions. This process applies to foundations as well as to earthen structures. The basic criterion inherent in this set-up is the relative displacement of the inclusion with respect to the soil: for the system to operate optimally, soil settlement at the level of the inclusion head must be significantly greater than the displacement of the inclusion itself, with a granular load transfer layer intended to absorb the resulting differential movement. Generally speaking, the choice guiding a project towards a given type of soil improvement or reinforcement solution is, in most cases, based on an economic rationale taking into account traditional deep foundation solutions, associated with rigid and expensive structural designs (e.g. a solution of structural slab with a distributed load). This rationale generally comes first when designing the foundations for a heavily-loaded industrial slab on surface areas extending several thousand square meters. Various soil improvement and soil reinforcement processes may be considered for eventual selection within the scope of a slab-on-grade project featuring typical characteristics and/or a shallow type foundation system that meets both the absolute and differential settlement criteria. The choice of methodology is primarily dictated by the following criteria: Data concerning the soil, - type of compressible soil and its geomechanical characteristics, - thickness of the compressible layer, - presence of an aquifer; Data concerning the structure, - purpose and geometry of the intended structure (type and loading conditions), - operating constraints, - allowable residual strains and settlements; Data concerning works execution conditions, - environmental context, - interface with the various construction phases (earthworks, paving, structural frame, etc.), - works schedule.
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2. INPUT DATA
Depending on the set of criteria indicated above, it would be advised to specify the following items, above all else, in order to determine the "value" of a rigid inclusion solution. 2.1. Data relative to the soil
One or more standard lithostratigraphic cross-sections; Compressibility, eventual overconsolidation profile; these data must be used to derive an
estimated range of final total settlement without reinforcement; Water table elevation(s); Data relative to both the consolidation rate and permeability of the various layers; Soil strength profile: load-bearing capacity vs. foundation elevation; Compressible thickness heterogeneity; Lateral confinement capacity; Organic matter content; Presence of a creep-sensitive layer; Onsite seismic conditions. 2.2. Data relative to the structure and its operations
Layout plan and footprint of the project structure; Applied loads:
- permanent or temporary loads; - distributed or point loads; Eventual zoning considerations designating the extent of high-load areas and their intensity (whether maximum or minimum); Operating constraints; Displacement and strain criteria; Type of structure being supported; Technical guidelines to implement. 2.3. Data relative to works execution conditions
Works schedule and milestones; Eventual aggressiveness of the environment with respect to concrete; Presence of cobbles creating potential obstructions to penetration; Water table elevation (substitution method feasible or not ); Water table variations (seasonal, long-term); Type of excavated materials and conditions for reuse. 3. PROJECT-SPECIFIC CRITERIA
The project design necessitates that the deformation criteria to be met during serviceability limit state (SLS) verifications must have been defined and approved by the Project Owner, i.e.: absolute and/or differential settlements. Remark: The
criteria to be taken into account for ultimate limit state (ULS) verifications are listed in the most current rules and regulations as well as in the present recommendations. In the absence of prescriptions set forth by the Project Owner, it is possible to refer to one of the following documents: 146
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Annex H (informative) of Eurocode 7-1 (NF EN 1997-1 Standard), which gives the limiting values of structural deformation and foundation movement; Standard NF P 11.213 (DTU 13.3 reference), which indicates the limiting values of absolute and differential settlements for concrete ground slabs; Design of shallow and deep foundations (Frank, 1999), which provides a review of limiting values of settlements applicable to buildings and civil engineering structures; The RFF Railway Operator's Technical Guide; Technical guidelines specific to tanks and reservoirs; Guidelines relative to road pavements (surface evenness).
As a complement, a number of deformation-related consequences must also be taken into consideration with respect to: Maintaining the slopes for all utility networks; Operating criteria specific to some equipment (vibrating machines). In all cases, it is necessary to distinguish between: Cumulative settlements since the beginning of the building construction; Settlements occurring during the eventual proof loading test; Settlements undergone by services and equipment; Settlements recorded on the structure itself as well as those induced on neighboring structures. Experience has shown that a solution of reinforcement using rigid inclusions can lead to a reduction in settlements by a factor of between 2 and 10 compared to settlements of nonreinforced soil. 4. USE LIMITATIONS AND FIELDS OF APPLICATION
Any foundation project on soil reinforced by rigid inclusions must consider the full array of foundation components: inclusions, load transfer platform, and structural elements. The design must therefore focus on all of these components and cannot be broken down into several distinct functions that would successively treat each component individually. Herein lies a major characteristic of all foundation projects built on a soil that has been reinforced by rigid inclusions. As a result, the Engineer, who oversees and coordinates the design process and the execution of the works, plays a truly vital role in projects featuring a rigid inclusion solution. 4.1. Favorable factors
The factors that favor selecting a rigid inclusion strategy consist of: Projects with settlement criteria on finished structures that are not overly stringent; The following objectives: - reducing overall compressibility of the foundation soil, - increasing load-bearing capacity, - limiting interactions with neighboring structures, - allowing the use of a slab-on-grade instead of structural reinforced slabs, - shortening the construction schedule (given the fact that less of the load gets transferred to the soil, thus activating a more efficient consolidation phenomenon: reduced compressibility if remaining in the overconsolidated range, plus a higher consolidation coefficient for lower stress states), Design considerations
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- optimizing total cost of the resulting foundation, - preserving the natural seal between the various layers; the existence of a soil either with a limited lateral confinement capacity or capable of exhibiting creep; the ductile nature of the resulting foundation: - this characteristic proves favorable with regards to vertical loadings that can accommodate settlements over a larger extended range, as both soil and inclusions are mobilized; it is also favorable regarding seismic loadings by controlling the least favorable failure mode (translation) and by eliminating loadings at connections between the structure and its deep foundations. 4.2. Unfavorable factors
The following factors may produce unfavorable consequences: Projects whose criteria regarding acceptable settlement on the finished structure are especially stringent; The qualification required to perform structural design: the foundation system is a composite system that necessitates a comprehensive approach encompassing the design and execution phases (hence the importance of coordination among project actors in order to achieve an optimal design while preserving the integrity of all components during construction and until final acceptance of the works); More severe execution constraints (e.g. interfacing between three distinct contractors installing the inclusions, the load transfer platform and the slab). Many setbacks in a project actually arise from a lack of adequate coordination between these participants. Once again, the Engineer's key role in the design, choice of selected options, coordination, supervision and acceptance of the works needs to be stressed; The sensitivity of freshly-completed inclusions to asymmetric loadings that have negative and potentially destructive effects (simultaneous and successive execution of the inclusions, their eventual cutting-off and leveling of the load transfer platform layer); Horizontal forces and wide load differentials (deviatoric stresses); The requirement of a high-quality friction material for the load transfer platform layer which may prove to be detrimental in situations with limited mineral supply sources; The need for a working platform that guarantees stable conditions of the rigs. 5. OTHER SPECIFIC POINTS FOR CONSIDERATION 5.1. Load transfer at depths
Another important step is to verify the influence of transferring the loads from the structure to greater depths, especially with respect to the eventual settlement of deep compressible layers, by recognizing that the inclusions concentrate loads at their tip. 5.2. Edge effects
Edge effects are to be examined very carefully. Such an examination focuses on the inclusions placed beneath embankment slopes or else those placed at the periphery of slabson-grade and rafts or at the edge of spread footings. This consideration could lead to selecting one or more of the following measures: Reinforcing the inclusions with rebar at the edge; 148
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Allocating an over-width of the reinforced zone beyond the identified structural footprint; Inserting reinforcement layers (steel wire mesh or geogrid) immediately above the inclusion
heads.
Moreover, it is sometimes necessary to design a gradual transition zone placed between the treated and untreated zones (adaptation of the grid of installation and/or inclusion length between a reinforced and unreinforced platform zone, or between the embankment at the periphery of a bridge abutment and an intermediate embankment section). For some structures, edge effects might result in treating a larger footprint than the net footprint of the structure. 5.3. Special case of a very thick embankment installed on a consolidating soil
Caution must be exercised with respect to the initial state of consolidation of the in situ soils, especially when the site has been backfilled (whether recently or in the past) and the consolidation of lower layers is not yet complete: the settlements experienced by the structure will not exclusively depend on the structural loads, but also on a continuation of excess pore pressure dissipation. The underconsolidated nature of the layers can only be revealed through oedometric testing, piezocone tests or pore pressure cells. The case where the soil profile contains layers capable of exhibiting creep (peat or organic layers) falls in the same category as the previous case since creep settlement does not directly depend on loads applied at the surface. Another case would be one where project grading work requires a major preliminary backfilling process. Under these circumstances, it is preferable to install the inclusions prior to the embankment and then account for this load in the inclusion design. The introduction of reinforcement layers at the base of the embankment can, in some instances, offer a desirable option. 5.4. Choosing among the various rigid inclusion processes
During the preliminary project design stage, the type of inclusion (i.e. with or without soil displacement, driven, etc.) is typically not taken into consideration. An estimation of the load transmitted to the inclusion gives the order of magnitude of the targeted strength for a given diameter. 5.5. Impacts on Slab-on-grade design
The behavior of a foundation installed on reinforced soil constitutes a complex problem of soil-structure interaction between several localized elements with different characteristics and behavior (soil, concrete). The parameters involved in these interactions sometimes oppose one another on settlements or loadings in the structure: On the one hand, a stiffer load distribution platform induces smaller settlements, while generating stronger bending moment and shear force values within the slab;
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On the other hand, a more flexible load transfer platform creates larger settlements with less demand on the slab.
The mechanical characteristics of the load transfer platform layer (deformation modulus, angle of friction, cohesion) must be chosen so as to cover the expected dispersion in these values, by focusing on the high or low results, depending on the type of verifications where these values will be used. For the load transfer platform layer made of lime- or cement-treated soil, it is indeed necessary to take into account the eventual evolution in mechanical characteristics depending on the type of binder, its dosage and moisture variations. For these materials, the influence of loading type (e.g. cyclical nature) also needs to be incorporated. 6. DEVELOPMENT STEPS IN A CONSTRUCTION PROJECT
The design of a structure on a soil reinforced by rigid inclusions entails a step-by-step approach: preliminary design using simple methods, followed by the detailed project design and execution planning. This design process relies on a sequence of the following geotechnical engineering missions, as defined in the NF P 94-500 Standard: Preliminary site-specific geotechnical study (G11); Preliminary geotechnical design (G12); Detailed geotechnical project design (G2); Geotechnical design and monitoring of project execution (G3); Geotechnical supervision of the execution phase (G4). Remark: Two
documents (Syntec Ingénierie, 2009 and 2010) explain the links between the geotechnical engineering missions specified in the NF P 94-500 Standard and the Engineer s missions according to the MOP Law for constructing buildings or infrastructure. Another document, entitled Geotechnical considerations in the design and execution of concrete slabs and released in June 2011 by Syntec/Unesi/Coprec, emphasizes the importance of managing the interfaces among the various project contractors in reference to the NF P 94-500 Standard. 6.1. Preliminary site geotechnical study (mission G11)
This study is conducted prior to having a precise definition of the project. By referring to information contained on the geological map, risk prevention plans and data obtained from the BRGM Office (Geology and Mining) (particularly underground cavities, shrinkageswelling hazards of clays) and DRIRE Office (Environment) (mining, underground quarrying), the geotechnical engineer must indicate the major risks identified. He also establishes a program of geotechnical investigations for the purpose of quantifying these risks and, depending on their nature, recommends a set of feasible technical solutions. 6.2. Geotechnical study of the preliminary project design (mission G12)
Conducted in conjunction with the preliminary project design, this G12 mission is intended to mitigate the major geotechnical risks identified during the previous study. With respect to each of the risks encountered, the geotechnical engineer is to: 150
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Define one or more geotechnical models depending on the degree of homogeneity of the site and indicate, if possible at this stage, the depth at which the substratum may be considered non-deformable; these models are tied to the NGF ground level benchmark system; Use these models to examine the set of feasible solutions adapted to the design loads and estimate the resulting settlements; Indicate, should the settlements obtained not comply with serviceability criteria, the types of soil improvements potentially proposed by emphasizing the specificities of each improvement type (e.g. the hard point effect of rigid inclusions); Identify the measure(s) to adopt or consider adopting, especially in the presence of soils sensitive to shrinkage-swelling phenomena; Establish, if deemed necessary, a program of geotechnical investigations with the specific aim of determining a geotechnical model that either integrates in-plane heterogeneity or more narrowly targets the case of soils exhibiting complex behavior.
6.3. Services performed within the scope of the Engineer s mission 6.3.1. Geotechnical study of the detailed project design (mission G2)
This G2 geotechnical mission, assigned as part of the Engineer s scope of works, lays out a basic project solution encompassing the inclusions, the load transfer platform and the structure. This study, paid for by the Project Owner, is critical to defining the final structural design. This study is performed based on the Project Owner s set of specifications defining the design loads and acceptable values of deformations. The geotechnical model(s) derived must be developed to a sufficient level of detail. The soil deformation modulus values assigned to each layer are calculated as a function of: Duration of load application; Load intensity (stress-strain dependency); Water content variations, causing modifications in consistency and/or suction. The G2 geotechnical mission comprises: A design at both the serviceability limit state (SLS) and ultimate limit state (ULS) (including GEO and STR verifications) for the inclusions and load transfer platform; Based on the estimation of the settlement of the reinforced soil, definition of the equivalent homogenized soil profile; The means and methods to be used by the concrete slab contractor to incorporate eventual additional loadings due to the hard point effect of inclusions. Lastly, this mission is to indicate the construction steps to be implemented (particularly in the case of soils sensitive to desiccation phenomena) and, in the event of in-plane heterogeneities, it must define the appropriate geotechnical models taking these heterogeneities into consideration. This study also facilitates the preparation of the construction project bid documents.
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6.3.2. Geotechnical supervision of the construction phase (mission G4)
This mission falls within the scope of the Project Owner s responsibilities and comprises two phases: Supervision/management of the design documents submitted by each contractor responsible for each part of the final structure: - review of the geotechnical study of the detailed project design (G3), - review of the product fact sheets (e.g. GTR classification protocol for the materials to be used as sub-base ), - review of the inspection/quality control program (stripping of the inclusions, load testing on the inclusions, plate load testing, monitoring of pre-loading settlements, etc.) and their associated threshold values; Inspection and supervision of the works performed by the various contractors through onsite spot inspections: - review of the actual geotechnical context observed onsite and the potential need for additional construction plans (G3), - review of eventual adaptations proposed by the contractors, - review of the results generated from the quality control program.
6.4. Services provided within the scope of each contractor s contract
This mission, which encompasses the construction plans and works progress monitoring, is conducted for each structural element (platform, potential soil reinforcement, paving, foundation, etc.). Each individual contractor is responsible for fulfilling this mission. 6.4.1. Geotechnical evaluation of execution (Mission G3)
During the construction phase, the G3 mission (geotechnical evaluation of execution) pertaining to the inclusion component of the project may be performed either by the contractor responsible for soil improvement or else subcontracted to an outside entity. The G3 mission (inclusions) serves to validate the geotechnical model established during the project development phase, in addition to determining the size of the rigid inclusions and providing the elements required to complete the project's other components (load transfer layer and concrete slab). The geotechnical model, which covers a homogeneous zone, is intended to: Evaluate the deformations undergone by the reinforced soil; Perform all justifications within the geotechnical domain; Define the load distribution layer-related specifications necessary to the project; Provide all useful elements and parameters to the project design and the impact on the other structures. The earthworks contractor must determine both the means and methods required to meet the project specifications for the load transfer platform. The slab contractor then uses these data in its own construction plan; it refines the slab design by taking into account the various design and construction plans of the other works (material 152
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substitution, drainage, earthworks, soil improvements or reinforcements, base layer), as validated by the Engineer. This entire set of studies is then validated by the Engineer, advised by a geotechnical engineer as part of the G4 mission: Geotechnical supervision of the construction phase . 6.4.2. Geotechnical monitoring of project execution (mission G3)
The soil improvement contractor is responsible for handling, either on it is own or through a subcontractor, all internal and external quality control operations. The contractor responsible for installing the load transfer platform performs on its own or subcontracts internal and external quality control operations, and adopts all necessary measures to ensure preserving the integrity of all the installed inclusions, in particular during the earthworks, land leveling and compaction performed after the inclusions have been completed. As part of the ground slab works, any anomaly potentially detected by the slab contractor, as per the works acceptance reports received, is to be notified to the Engineer. 6.5. Services conducted as part of the technical inspection contract
Throughout the design phase, the technical inspector undertakes a critical examination of all of the project's technical specifications.
During the works execution period, the inspector also ensures, among other things, that the technical verifications under the responsibility of each contractor, as listed in Article 1792-1 of the Civil Code, are being performed in a satisfactory manner.
References
Frank R. - Calcul des fondations superficielles et profondes Ingénieur, Presses des Ponts, 1999. Loi MOP - Loi n° 85-704 du 12 juillet 1985 modifiée relative à la maîtrise d o uvrage publique et à ses rapports avec la maîtrise d , 1985. NF P 11-213 DTU 13.3 - Dallages - Conception, calcul et exécution , 2007. NF P 94-500 - Missions d i ngénierie géotechnique, Classification et spécifications, 2006. Syntec Ingénierie - Synchronisation des missions d i ngénierie géotechnique et de maîtrise d . Éditions Syntec-Ingénierie, 2009. Syntec Ingénierie - Synchronisation des missions d i ngénierie géotechnique et de maîtrise d d i nfrastructures. Éditions Syntec-Ingénierie, 2010. Syntec/Unesi/Coprec - La géotechnique dans la conception et la réalisation des dallages en béton, 2011.
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CHAPTER 5
Justifications
1. GENERAL FRAMEWORK FOR PRESENTING JUSTIFICATIONS
The justifications associated with structures built on soil reinforced by means of rigid inclusions are conducted in strict compliance with Eurocode 7. This step requires verifying both the serviceability limit states (SLS) and the ultimate limit states (ULS). The structures need to be differentiated depending on whether they are embankments, pavements and foundation of structures (slabs on grade, rafts, footings) supported on rigid inclusions. Such structures all share the characteristic of relying on the in situ soil for a portion of the support of the structural loads, with the bulk of this support being transmitted via various mechanisms to the rigid inclusions. In the case of foundations, the load transfer is produced by avoiding any direct contact between the structure and the inclusions thanks to the installation of a continuous load transfer platform. The present recommendations do not apply to footings that lie directly over the inclusions. In the remainder of this document, a distin 1 st domain corresponding to the case of inclusions required for stability of the structure and the 2nd domain corresponding to the case of inclusions not required to ensure the stability of the structure, but instead whose objective is primarily to reduce the settlements. 1.1. Serviceability limit states (SLS)
The limit states that need to be verified are related to either the vertical or horizontal movement. 1.1.1. Set-up
The behavior of structures lying on soil reinforced by rigid inclusions can only be fully understood with a detailed study of the interaction between the soil and the various structural elements (foundations, inclusions). This interaction entails considering the shear mechanisms at work within the load transfer platform, along the shaft and under the tip of the inclusion. In practice, the justification of these structures requires the implementation of a computational model capable of incorporating these various mechanisms as well as ensuring the compatibility of the deformations required to mobilize each individual mechanism. This step signifies that the justification systematically includes the calculation of displacements under service loadings. The verification with respect to serviceability limit states, to be emphasized herein, places the focus on deformations as described by Eurocode 7-1 in 2.4.8 (1): Ed < Cd (5.1) Ed: design value of the effect of actions; Cd: limiting design value of the effect of an action.
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1.1.2. Pertinent displacement or deformation criteria
The values of the effects of the actions to be considered may, depending on the Project s requirements, be included in the following list of parameters: Total/absolute settlement (maximum and/or average); Differential settlement; Rotation; Inclination; Deflection; Relative deflection; Relative rotation. The definitions of a number of terms relative to foundation movement and deformations are given in Figure 5.1: Settlement y, differential settlement y, rotation and angular deformation ; Deflection and relative deflection /L; Inclination and relative rotation (angular distortion) .
Figure 5.1: Definitions of foundation movements and deformations.
Note 1: The appearance and overall functionality of the structure may be altered whenever the calculated deflection ymax of a beam, slab or bracket subjected to quasi-permanent loads exceeds L/250, where L represents the span. Practically speaking, the deformation after construction y max is typically limited to L/500 for quasi permanent loads.
The foundation movement components that need to be considered are primarily the surface settlement values (average value yave or maximum value ymax) or relative settlement (or differential settlement: ymax - ymin), either with or without the ground slab, for comparison with allowable values. The pertinent settlement criteria are defined by the Project Owner in conjunction with the Engineer. Remark: Depending on the nature of the structure bearing on the ground (absence or not of a slab on grade, relative stiffness of this slab) and on the type and sensitivity of any surcharge (road, storage), there might be major differences in the allowable values.
These verifications are quite obviously complemented by verifying that the forces in the structural elements, most notably the inclusions, are compatible with the design resistance of the material of the different components. 156
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load transfer criterion is not included in the SLS computational model, it becomes necessary to verify after the fact the consistency of the calculated values of the vertical stresses between the soil and the inclusion heads relative to this shear strength. 1.1.3. Alternative SLS verification
1.1.3.1. Inclusions used to reduce settlement (Domain 2) The alternative verification with respect to the soil consists of the verification that a sufficiently low fraction of the ground strength has been mobilized to keep deformations within the required serviceability limits [EC7-1: 2.4.8 (4)]. Such verification is typically unnecessary whenever the inclusions strictly serve to reduce settlements, since the settlements are always calculated (as opposed to the procedure for deep foundations, for which the displacements are not systematically calculated and may be omitted). It is therefore unnecessary to verify the SLS forces within the inclusions relative to creep values. This is also true under the condition that the computational model is capable of accurately representing the gradual mobilization of both the shaft friction and point resistance along the entire inclusion, until a point close to failure. Numerical models in a continuous medium must include interfaces between the soil and the inclusions, with interaction laws matching collected experimental data (limiting value q s of the soil-inclusion friction in accordance with the type of soil and selected installation technique, gradual mobilization of friction with settlement of the element). One approach for verifying that this behavior is included in the model consists of modeling the case of a direct load at the top of an inclusion and then comparing the results obtained to the loaddisplacement curve determined using the -w law method proposed by Frank and Zhao (1982) or Combarieu (parabolic law, 1988). In the case of a simplified model, the relevance of the model must be verified with respect to: Load transfer platform shear and deformation characteristics; Vertical stress applied to the soil between inclusions. The model, applied to the case of loading of a rigid shallow foundation without an inclusion, must also yield results comparable with the settlement estimations obtained by the most appropriate method between the pressuremeter method or the oedometric method. 1.1.3.2. Inclusions required for the bearing capacity (Domain 1) When inclusions prove necessary to justify the ULS stability, the conditions set forth in the national Standards are applicable. It then becomes necessary to verify at SLS that: The maximum load in the inclusion does not exceed the design value of the critical creep load in compression R c,cr;d under the neutral plane (Article 14.2.1, NF P 94 262 Standard, Deep foundations); The stress applied on the soil at the level of inclusion heads (top of the inclusion) does not exceed the SLS limiting value (Chapter 13, NF P 94 261 Standard, Shallow foundations).
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1.2. Ultimate limit states (ULS)
For structures built on soil reinforced by rigid inclusions, only the STR and GEO ultimate limit states require verification in most instances (EC7-1: 2.4.7.3); they are correlated with: The internal failure or excessive deformation of the structural elements (inclusions, inclusion caps, reinforcement layers, footings, slabs on grade, rafts), in which the material strength (in compression, tension and shear) makes a significant contribution to the overall strength [STR]; The failure or excessive deformation of the ground in which the strength of soil is significant in providing resistance [GEO] (interaction of the inclusion with in situ soil, by means of friction and/or punching, and mobilization of the soil's intrinsic strength). Remark: The other limit states (EQU, UPL and HYD) tend not to be pertinent relative to inclusions, given that the inclusions are not connected to the structure.
It must now be verified that: Ed < R d Ed: design value of the effect of actions, R d: design value of the resistance to the actions.
(5.2)
1.2.1. General case (Design Approach 2)
According to the French national Appendix to EC7-1, the Design Approach 2 (DA2) must be selected for the general case. This approach uses a combination of the following partial factors for persistent and transient situations: According to this approach, the partial factors are applied to the actions or to the effects of actions and to the ground resistances, whereas partial factors M1 applicable to soil parameters ( u and ) are all set equal to 1. Based on the dataset A1, the permanent actions are weighted by G = 1.35 or 1.0, while the variable actions are weighted by Q = 1.5 or 0, in order to identify the least favorable case. The R2 partial strength factors are defined in the EC7 code solely for the following cases: Shallow foundations: - bearing resistance R;v = 1.4 - sliding resistance R;h = 1.1 Deep foundations: - base resistance b = 1.1 - shaft resistance (compression) s = 1.1 In the case of deep foundations, the NF P 94 262 application Standard (Appendices C and E) also introduces correlation factors 1 and 2, which depend on the number of load tests, or correlation factors 3 and 4, which depend on the number of soil tests and geotechnical investigation surfaces. Whenever inclusions are needed to justify ground bearing ): 158
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Incorporation of these coefficients 1, 2, 3 and 4 becomes necessary if the load-bearing capacity verification method; These coefficients are not applicable should the verification be conducted based on the method. These recommendations tend to favor the method. In Domain 2, since justification of the stability of the structure has been performed without taking inclusions into account, these coefficients are not used. Moreover, model coefficients R;d, defined in the national Application Standards for piles (NF P 94 262) and shallow foundations (NF P 94 261), must be acknowledged; these coefficients serve to define the characteristic resistance values of the ground R k based on either pressuremeter or penetrometer tests. Remarks: According to Design Approach 2, the choice of partial resistance factors is complicated by the fact that the assessed foundations cannot be considered in the category of either shallow foundations or deep foundations. Hence, Section 7 of the EC7 code which focuses on deep foundations, stipulates that the set of provisions it describes should not be applied to the design of piles that are intended for settlement reduction; such an indication directly targets the case of rigid inclusions placed beneath structural foundations when strictly used to reduce settlements. The distinction proposed in this document between Domain 1 (inclusions required for ground bearing stability) and Domain 2 (not required for ground bearing stability) addresses this specific observation. According to the national Appendix EC7-1, the Design Approach 3 (DA3) can also be adopted for the numerical analyses of soil-structure interaction. 1.2.2. Special case of embankments on rigid inclusions (Design Approach 3)
In the special case of embankments on rigid inclusions and for persistent and transient situations, Design Approach 3 should be selected for the overall or combined stability verification step, which is consistent with the choice made for reinforced soil structures (NF P 94 270 Application Standard). The combined stability verification of a reinforced soil structure must be carried out by considering a sufficient number of overall stability failure surfaces that intercept and/or run parallel to at least one of the reinforcing elements. The load transfer calculation considers the internal embankment equilibrium and therefore must be carried out with Design Approach 2. Design Approach 3 introduces the following combination for persistent and transient situations: The symbol * denotes actions from the structure; The symbol ^ denotes geotechnical actions. According to this approach, the partial factors are applied to actions or to the effects of actions from the structure and to ground strength parameters.
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All permanent actions (originating from the soil) are weighted by a factor G = 1.0, while the unfavorable variable actions (transmitted through the soil) are weighted by a factor Q = 1.3. The M2 partial factors are as follows: = = 1.25; cu = 1.4; = 1.0 The set of R3 partial resistance factors are all equal to1.0. 2. LIMIT STATE VERIFICATION MODELS
Experience has shown that for common structures, these verifications may be conducted using the simplified models described in Section 2.1. The more detailed models presented in Section 2.2 are typically only justified for exceptional structures. 2.1. Simplified models
models are intended to replace the more sophisticated models described below, in order to demonstrate that the fundamental relation Ed < R d is indeed satisfied. Simplified models lack the capacity to introduce more advanced laws (for soil and/or interfaces) or to establish relevant failure modes for the considered load case [e.g. difficulty in handling the failure of a footing exposed to loading (Q, T, M)]. These models are applicable to check both the SLS and ULS of footings, rafts, ground slabs, embankments or pavements. A fully elastic model without an interface is at first glance insufficient; at the very least, interface laws of the type Frank and Zhao would need to be introduced. 2.1.1. Simplified models for ULS verifications
Three approaches of increasing complexity are proposed herein in order to evaluate stability (Fig. 5.2). It is merely necessary to demonstrate that the stability criterion is satisfied with any one of the approaches. Remark: If the stability criterion can be verified using Approach (i), then it is necessarily verified with approaches of a higher level.
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Q: load applied to the footing, R v,d: design value of the ultimate ground bearing resistance over the footing surface, Q p (0): normal force at the inclusion head, Q p (I): normal force of the inclusion at the intersection with the failure surface.
Figure 5.2: Envelope models of increasing complexity (1) to (3).
2.1.1.1. Envelope model (1) This approach consists of demonstrating that the fundamental relation E d < R d is satisfied, even without having to take the inclusions into account. It applies to all situations in which inclusions primarily serve to reduce settlements and are not required for the stability of the structure (Domain 2). Slabs on grade are most often included in this category.
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The approach thus strictly consists of performing ULS (GEO and STR) structural verifications (on shallow foundations or embankments) while neglecting the presence of inclusions. Remark: The envelope model (1) is critical to identify which domain to associate with the inclusions: Domain 1: inclusions required for stability; Domain 2: inclusions used to reduce settlements and not required for stability.
For a shallow foundation (Fig. 5.3), these verifications are carried out according to Design Approach 2 by following the set of detailed conditions explained in the corresponding Application Standard (NF P 94 261, being drafted as of January 2011): Unfavorable permanent actions are weighted by G = 1.35, and unfavorable variable actions by Q = 1.5 (the alternative combination of 1.0 G + 0.0 Q tends not to be relevant); Bearing capacity is verified using the partial resistance factor R;v = 1.4; Sliding is verified by using the partial resistance factor R;h = 1.1; A model factor R;d is introduced into the computation of each of these resistances.
Figure 5.3: Envelope approach (1) applied to the case of a footing (i.e. with inclusions neglected in the computation).
For an embankment , the stability verifications are conducted by employing Design Approach 3. These verification steps are similar to the overall stability verification for reinforced soil structures described in the NF P 94 270 Standard. The computational models may be based on the Bish method or on the Yield design exterior approach: All permanent actions (originating from the soil) are weighted by a factor G = 1.0, and the unfavorable variable actions (transmitted through the soil) by a factor Q = 1.3; The following partial factors are used for the soil characteristics: = 1.25; cu = 1.4; = 1.0; All partial resistance factors are set equal to 1.0. The verification is satisfied if the safety coefficient F established by the computational model, neglecting the inclusions, is greater than or equal to 1 (Fig. 5.4).
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F = 1.00
Figure 5.4: Envelope approach (1) applied to the case of an embankment (with inclusions deactivated for this computation).
2.1.1.2. Envelope model (2) In this model, the contribution of the inclusions is taken into account by integrating the resisting force at the head of each inclusion, as calculated by the interaction calculation. For a footing , this envelope approach (2) may be directly applicable to loads with a resultant inclined at less than 10° off the vertical. For more pronounced inclinations, either an envelope model (3) or one of the detailed models described in Section 2.2 or 2.3 would need to be implemented. The bearing capacity verification is carried out at the level of the inclusion head over a footprint equal to the foundation area. At this stage, it is necessary to have calculated the action of the ULS design loads (Q d, Td, Md) applied at the base of the footing, the distribution of forces between the soil and each of the mobilized inclusions, according to the models presented in Chapter 3, and then have verified: The load transfer platform equilibrium conditions (GEO, Section 4.2), which define the domain of acceptable axial force values at the inclusion head Q p(0) (Fig. 5.54); this domain is built by integrating the limits relative to both the bearing capacity of the inclusion (GEO) and the allowable limit stresses of the material in the inclusion (STR, Section 3), as explained in Section 4.2.2.2; If the computational model is of the simplified type, then the forces transmitted at the inclusion head will satisfy the consistency conditions explained in Chapter 3, Section 2.2.4.2; The other model consistency conditions if they have not yet been considered in the above verification (e.g. negative friction). The forces at the inclusion head Q p(0) and T p(0) represent a global reaction (QR , T R , M R ):
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QR = Q p(0) TR = T p(0) MR = Q p(0) di where di is the lever arm of inclusion i relative to the center of the footing.
(5.3)
Figure 5.5: Envelope approach (2) applied to the case of a footing (inclusions taken into consideration when evaluating the load transmitted to the soil).
The load-bearing capacity verification E d < R d is performed: By adopting for E d the combination of the design loading (Q d, Td, Md) and of the reaction (QR , -T R , -M R ): (Qd - QR , T d - TR , Md + TR h R - MR ) (5.4) By setting for R d the design value of the ground bearing resistance below a shallow foundation with the same surface area as the footing, as evaluated using the NF P 94 261 Standard. The sliding verification takes place on the underside of the foundation, with (Q d, Td), and at the level of the inclusion head with (Q d - Q p(0), Td - T p(0)). Remark: Directly below the foundation, the design friction angle may be assumed equal to the effective critical state angle of critical friction angle crit of the load transfer platform material for cast-in-place concrete foundations and equal to 2/3 crit platform should be neglected. At the level of the inclusion head, the effective critical state angle of friction crit of the transfer platform should be considered if the inclusion actually penetrates into the platform; otherwise, the value adopted is weighted depending on the transfer of the loads at the inclusion head between the design value crit of the platform and the corresponding value of the supporting soil.
For an embankment , the stability verifications are performed as described in Section 0 according to Design Approach 3 and by means of a slice method or the Yield Design exterior approach: All permanent actions (originating from the soil) are weighted by a factor G = 1.0, and unfavorable variable actions (transmitted by the soil) by a factor Q = 1.3; The characteristic soil parameters are assigned the following partial factors: = 1.25; cu = 1.4; = 1.0 164
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All partial resistance factors are set equal to 1.0; For this calculation, each inclusion is replaced by an upward vertical force Q p(0); By analogy with the combined stability verification of reinforced soil structures (NF P 94 270 Standard), a model factor R;d must be introduced into this calculation. The value of this factor equals 1.1 when the structures are relatively insensitive to deformations, without otherwise influencing any of the other justifications required for serviceability limit states. It would be necessary to adopt higher values for structures that show great sensitivity to deformations. The verification step is satisfied provided the safety factor established by the computational model exceeds or is equal to 1 (Fig. 5.6).
Figure 5.6: Envelope approach (2) applied to the case of an embankment (inclusions deactivated and replaced b y an increasing vertical force).
2.1.1.3. Envelope model (3) 2.1.1.3.1. Underlying principle The bearing capacity verification herein is identical to the envelope approach (2), in substituting for terms Q p(0) and T p(0) (calculated at the level of the inclusion head) the terms Q p(I) and T p(I), which have been evaluated at the intersection of each inclusion with the failure surface. Remark: Subjected to the action of the ULS loads (Q d, Td, Md) applied at the base of the footing, the distribution of forces between the soil and each of the mobilized inclusions must have been previously calculated, according to the models presented in Chapter III, and then have been verified: the load transfer platform conditions of equilibrium (GEO, Section 4.2), which define the domain of acceptable axial force values at the inclusion head Q p(0) (Fig. 5.54); this domain is built by integrating the limits relative to both the load bearing capacity of the inclusion (GEO) and the structural resistance of the inclusion material (STR, Section 3), as explained in Section 4.2.2.2;
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if the computational model is of the simplified type, then the forces transmitted at the inclusion head will satisfy the consistency conditions explained in Chapter III, Section 2.2.4.2. The forces calculated in the inclusions Q p(I) and T p(I) represent a global reaction (QR , TR , MR ), evaluated similarly to the design loading (Q d, Hd, Md). QR = Q p(0) TR = T p(0) (5.5) MR = Q p(0) di + T p(0) hi di and hi are the vertical and horizontal distances between the point of intersection of the failure surface with inclusion i and the point where design loads (Qd, Hd, M d) are defined. The bearing capacity verification E d < R d is thus verified: By adopting for E d the combination of the design loading (Q d , T d , Md) and of the reaction (QR , -TR , M R ); By setting for R d the design value of the ground bearing resistance below a shallow foundation with the same surface area as the footing, as evaluated according to Standard NF P 94 261. This approach requires searching for the most critical failure surface as well as the contribution of the inclusions at the level of their intersection with this surface. Remarks: The verification against sliding failure is always performed in accordance with envelope model (2) procedures (i.e. by selecting for Q R and TR the values calculated at the inclusion head). In the case of a footing subject to a primarily vertical load on a homogeneous soil, it is acceptable to adopt the geometry of the Prandtl diagram as the critical failure surface.
Yield design theory (Salençon, 1983) offers the most comprehensive theoretical framework for evaluating the safety of structures lying on soil reinforced by rigid inclusions; this method is similar to the method used for soil nailed structures. For these structures, a more restricted part of the theory will be applied, by only considering: Its kinematic approach; The Mohr-Coulomb failure criterion; The motion of rigid blocks, as delimited by a succession of logarithmic spiral arcs with the same pole and with a parameter equal to the angle of friction of each layer. It is possible to take the bending strength of inclusions into consideration in addition to their compressive strength. Stability may then be evaluated by only considering the contribution of axial forces in the inclusions or else the combination of axial forces and shear forces. Practice has shown that a significant stability improvement is generally obtained with axial forces, whereas the additional benefit derived by adding shear forces is more limited: neglecting the shear contribution therefore does not exert much influence and remains a safe simplification. The set of multicriteria (Schlosser, 1983) establishes the domain of possible values for the force within each inclusion [Q P(I), T p(I)] (Fig. 5.7).
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Figure 5.7: Examples of the stability envelope domain [Q p(I), Tp(I)] of an inclusion depending on whether the shear force is taken into account or neglected.
The contribution of each inclusion (Q p(I), T p(I)) is determined by seeking the maximum participation to the resistant moment depending on the orientation of the rigid block displacement velocity vector (Fig. 5.8).
(V: velocity vector of the rigid block under consideration)
Figure 5.8: Determination of the maximum resistant contribution.
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2.1.1.3.2. Application to shallow foundations For footings, these calculations are carried out in accordance with Approach 2 of Eurocode 7 (see Section 1.2.1).
(Inclusions taken into account in the evaluation of load transmitted to the soil and by their interaction with the failure surface) Figure 5.9: Envelope approach 3 applied to the case of a footing
Remark: This approach is only strictly applicable to plane strain problems. It is still possible however to introduce shape coefficients comparable to those appearing in the bearing capacity formulation of square, rectangular or circular shallow footings in order to extend the results obtained to 3D situations.
Searching for the failure surface by associating two or more rigid blocks is also possible, as described in the NF P 94 270 Standard (for soil nailing structures): in a two-block approach, the resistant contribution of the soil block placed outside the footing is assimilated to the earth pressure at passive limit state on the vertical soil block boundary (Fig. 5.10). This strategy is applicable regardless of the type of loading (Q, T, M) being applied to the footing on the upstream block; this method includes two successive stages: Study of the passive limit state equilibrium within the soil volume outside the footing; Study of the active limit state equilibrium within the soil volume located underneath the footing subject to the action of load applied at the footing and the limit earth pressure over the boundary of both domains, as evaluated during the previous stage.
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Figure 5.10: Decomposition of the problem into two juxtaposed passive and active limit states of equilibrium.
2.1.1.3.3. Application to embankments For embankments, these calculations are carried out using Approach 3 (see Section 0), which relies on the Yield design exterior approach: All permanent actions (i.e. originating from the soil) are weighted by a factor G = 1.0, and unfavorable variable actions (transmitted by the soil) by a factor Q = 1.3; The characteristic soil parameters are assigned the following partial factors: = 1.25; cu = 1.4; = 1.0; By analogy with the combined stability verification of reinforced soil structures (NF P 94 270 Standard), a model partial factor R;d must be introduced into this calculation. The value of this factor is equal to 1.1 when the structures are relatively insensitive to deformations, without otherwise influencing any of the other justifications required for serviceability limit states. It would be necessary to adopt higher values for structures that show great sensitivity to deformations. The values for the contribution of each inclusion (Q P(I), TP(I)) are computed based on a strategy that relies on the specifications of Standard NF P 94 270 for nailed soils, as these structures had also been verified according to Approach 3: the coefficient of dataset M2 for the soil-inclusion interaction resistance is thus set at: M,f = 1.1. Compared to nailed soil structures, structures built on rigid inclusions also require taking into account the ultimate stresses at both the inclusion head and tip (these contributions are assumed to be zero in the case of nailed soils due to the small diameter of the nails). For the inclusions, these contributions are combined with the forces developed by shaft friction over either the inner part of the studied block or its outer part (Fig. 5.11). The same value of coefficient M,f of dataset M2 is adopted for the contributions at the head and at the tip. To ensure continuity with the NF P 94 262 Standard (for deep foundations), it is recommended to perform the calculations according to the " ground model " method, along with the application of the associated model factor R,d on the contribution of the inclusions (shaft friction, head and tip). The values of this factor depend on the inclusion installation
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method, as well as on the type and mode of interpretation of the geotechnical data (i.e. with or without statistical analysis). Remark: This is equivalent to applying a reduction coefficient M,f x R,d = 1.1 R,d on forces Q p(I), T p(I), M p(I).
The computation of forces mobilized in the inclusions must also take into account the limit design resistance of the inclusion material, as explained in Section 3.1 (concrete inclusions) or 3.2 (steel inclusions).
Figure 5.11: Application of the failure calculation to the case of an embankment built on rigid inclusions, for which only the axial contribution has been taken into account.
Remarks: In the example provided in Figure 5.11, where only the axial contribution of the inclusion has been taken into account, the inclusions placed to the left of the center of rotation contribute via a normal compressive force, while those placed to the right may be working in tension. This maximum resisting contribution in either compression or tension varies depending on the targeted failure surface, meaning that the contribution cannot therefore be chosen ahead of time; moreover, it must necessarily be established for each failure surface by applying the principle of maximum plastic work. Only the Yield Design approach allows applying this principle without any approximations. The design values of the forces in either tension or compression must be compatible with the STR verifications of the constitutive material of the inclusions. 2.1.2. Simplified models for SLS verifications
All the models described in Chapter III can also be used for SLS verifications. If some of the strength criteria have not been explicitly introduced in these models, they still need to be verified a posteriori. Depending on the specific models used, this verification may, for example, entail: Punching of the inclusion head into the load transfer platform; Vertical stress applied at the soil surface between the inclusions with regards to its allowable value for the specific situation considered The ratio of negative friction (/v) mobilized relative to the limit value Ktan, specific to each layer; Positive friction values relative to the limit friction value qs, associated with both the type of soil and inclusion installation technique;
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The value of the stress below the inclusion tip relative to the limit value q p, associated with both the type of soil and inclusion installation technique; Maximum stress values in the materials (inclusion, ground slab, reinforcement, etc.) relative to the allowable SLS values. 2.2. Detailed numerical models
The most comprehensive computational model is a 3D model using finite elements or finite differences in a continuous medium, through the use of advanced behavior constitutive laws for the various layers that take into account the range of soil-structure interactions via interface elements. These laws must be capable of describing the behavior in terms of stresses/strains until nearing failure. The introduction of interfaces between inclusions and the ground is essential for two reasons: It authorizes the sliding of soil against the inclusions; It allows defining a limit value for soil/inclusion friction in order to reflect the influence of the method of installation of the inclusions, which would have been neglected in the computational model (e.g. lateral displacement). The significant rotation of the principal stresses in the load transfer platform, coupled with the need to describe a nonlinear behavior highly dependent on the stress state, leads for the granular material typically used in the platform to the selection of an advanced behavior law (2nd-order model or nonlinear elasticity). The 1st-order model associating linear elasticity with the Mohr-Coulomb failure criterion might not be sufficient to assess ULS situations, even though it generally proves acceptable to check SLS situations. The (soil-inclusion) interface laws also need to introduce a failure criterion. It is preferable to introduce either a Cam-Clay or hardening soil type model (i.e. one that incorporates an isotropic strain hardening mechanism) for slightly overconsolidated compressible soils. Only these models are actually capable of reproducing the oedometric type behavior of soils while distinguishing deformations before and after the preconsolidation pressure. In the other cases, in particular for the bearing layer, the requirement or not of advanced laws must be examined on a case-by-case basis. For the inclusion component material, the adopted law must necessarily introduce the material-specific failure criterion (an elastic model without a failure criterion is unacceptable). The ability of the model to yield representative results up to near failure must be evaluated by assessing: The direct load case of an isolated inclusion, and then comparing this simulation: - to results of a direct load test, if available (with the failure load being set as the load yielding a settlement at the top equal to one-tenth of the diameter D/10); - otherwise, to the prediction obtained by using the Frank and Zhao type transfer curves; The loading of a rigid footing at the model surface (not reinforced by the inclusions) in order to compare:
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- under SLS loads, the calculated settlement with the settlement calculated using the most appropriate method (either the pressuremeter or oedometric method); - under larger loads, the values for bearing capacity or sliding resistance using conventional methods. Such models can obviously also be used for SLS verifications. 2.2.1. Detailed numerical models for ULS verifications
2.2.1.1. Case of foundations built on inclusions 2.2.1.1.1. Underlying principle If Design Approach 2 is selected, then the model allows establishing the applied load displacement curve of a characteristic point of the foundation, over an interval greatly beyond the service load. The shape of this theoretical load-displacement curve is examined to see if it reveals a limit value R c beyond which an increase in the ratio between displacements and applied forces is noticeable. In the event such a threshold is defined, the value of the design strength R d is: R d = R c/R (5.6) It is proposed herein to adopt the value R = 1.4 for the partial resistance factor. If the failure mechanism is associated with a sliding plane on the underside of the foundation, then the value R can be reduced to 1.1 in agreement with the conditions applicable to shallow foundations. Remark: Should the detailed models rely on a greater number of parameters, it is important to recall that the use of this method is acceptable only if the tests discussed in Section 2.2 have all been performed.
2.2.1.1.2. Application example An equivalent approach has been adopted to justify the ICEDA project, which was an exceptional structure subjected to some very specific requirements. This project was described in the historical review presented in Chapter 1 of this guide. A static load test area containing 9 inclusions has served to calibrate the constitutive laws of a numerical model representing the test section, using a 3D finite element model. A basic unit cell model using these constitutive laws was built in order to study the overall behavior of the foundation, with special emphasis on the settlement / applied load relation. A parametric study conducted on this model has enabled the determination of the sensitivity of the settlement to successive variations of practically all the parameters at increasing applied loads. Figure 5.12 illustrates one of the results obtained: it depicts the settlement vs. load behavior of a raft, for a given mesh and for the reference case (blue curve), as well as for the improved 172
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characteristics of compressible layer (red curve) and degraded characteristics of this layer (green curve). The settlement curve vs. loading indicates a change in behavior around an applied load of 360 kPa on the raft. In order to design the grid of inclusions for the ICEDA project under static loads, the forces in the inclusions corresponding to a load of 360 kPa on the raft were factored using the R coefficients of 1.0 at ULS and 1.4 at SLS, in order to define the maximum allowable forces.
Figure 5.12: Load-settlement curve established for the ICEDA project.
Once the ultimate value for the stress on the raft was defined, the grid of inclusions was designed with respect to the SLS such that: The calculated settlements remain less than the allowable settlement values; The integrity of the load transfer platform is verified: absence of zones where the shear strain (evaluated as the second invariant of the deviatoric strain tensor) would be greater than or equal to 5% and moreover would: - continuously connect the inclusion heads to the raft; - continuously connect the inclusion heads to the natural soil, at the periphery of the buildings; - continuously connect two contiguous inclusions. The structural integrity of the inclusions is verified, through the conventional methods described in the EC7 draft "Deep foundations" Standard. Remark: Calibration of the ultimate resistance value must be the same as for the case of the footing on non-reinforced soil.
2.2.1.2. Case of embankments built on rigid inclusions In this case, the verification step is carried out according to Approach 3.
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The ULS verification takes the form of a specific calculation during which the parameters for compared to their characteristic values applying the M2 set of partial factors: = 1.25 cu = 1.4 = 1.0 The M2 partial factors must be complemented by the factor applicable to the soil-inclusion lateral interaction strength M;f . As presented in Section 2.1.1.3.3 and in order to ensure continuity with Standard NF P 94 262 (deep foundations), it is proposed to adopt, for the factor M;f applicable to the shaft friction resistance, the composite value (1.1 R,d) where R,d is the partial factor associated with the "ground model" method in Standard NF P 94 262. The values of this factor depend on the inclusion installation technique, as well as on the type and mode of interpretation of the geotechnical data (with or without statistical analysis). As opposed to the shaft friction, the interaction at the head or base of the inclusion does not require, for this calculation, the introduction of a specific M2 coefficient. This interaction is correctly described by the input parameters for the soils provided that the inclusions are modeled as volume elements and not as "beam" elements (i.e. without thickness). Remark: It should be recalled that for the inclusion, the behavior law must necessarily introduce a failure criterion for the material in the inclusion (an elastic model without any failure criterion is unacceptable).
The ULS verification therefore requires a specific calculation step that consists of ensuring that an equilibrium has actually been reached when all M2 factors are applied to the soil parameters, inclusion material and shaft friction. The fact that the calculation performed using these new parameters actually converges on a solution provides the desired verification. Remark: It is to be noted that the displacements obtained have no physical significance. 2.2.2. Detailed numerical models for SLS verifications (settlements)
The purpose here is to verify that E d< Cd: E d and Cd are settlements (or deformations); C d is the allowable settlement (or deformation) defined by the Project Owner. This advanced model is employed without factoring the strengths. Since the model takes into account the full set of material failure criteria, the existence of localized plastic zones in the soil is acceptable as long as the SLS settlement criterion remains satisfied. Remark: In the case of the exceptional ICEDA structure, the previous criterion was supplemented by a criterion limiting the development of a free plastic flow zone: the absence of a continuous shear band (defined by a shear 1 above 5%) connecting either the inclusion heads to the raft, or the inclusion heads to the natural soil, at the periphery of buildings, or two contiguous inclusions. 1
Second invariant of the deviatoric strain tensor.
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2.3. Specific calculation models based on the Yield design theory for ULS verifications
These models apply the Yield Design theory (Salençon, 1983) within its general framework: Static and kinematic approaches; Displacement field not reduced to a field of rigid blocks. These models are capable of processing any type of loading cases (Q, T, M) by determining the associated failure mode. Remark: These models are to be used under exceptional circumstances and must be calibrated by comparison with other approaches, as illustrated in the following section. 2.3.1. Application example
This approach was applied to the exceptional structure of the foundations for the RionAntirion bridge, as described in Chapter 1 (Pecker, 1998). An upper bound on the foundation capacity was established using the Yield Design Kinematic approach by introducing the strength contribution of the inclusions into mechanisms such as the one presented in Figure 5.13. Given the foundation caisson dimensions (diameter: 90 m), this approach was developed exclusively in the form of a 2D plane strain model.
Figure 5.13: The studied failure mechanisms (case of a cohesive soil).
These mechanisms can be defined by 5 geometric parameters ( or , , and identified in Fig. 5.13). These mechanisms juxtapose the motions of rigid blocks and blocks under deformation fields compatible with the displacements of neighboring blocks. The minimization step over the space defined by these geometric parameters (representing all possible geometries of these various failure mechanisms) serves to establish the value of the smallest load capable of leading to failure. The theory indicates that this value constitutes an upper bound of the actual failure load: any load greater than or equal to this value necessarily causes the failure of the system.
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The set of ultimate values obtained allows defining a surface within the space (Q, T, M) that encompasses all loads that the system is able to withstand. Any loading represented by a point located outside this surface causes failure. A cross-section of this surface in a plane corresponding to a constant vertical force value Q gives the shape of this limit surface (Fig. 5.14). This example illustrates the increase in capacity obtained by installing inclusions compared to a situation with the same foundation on non-reinforced soil. The inclusions have served to raise the values of T max and Mmax that can be supported for a given Q value. The vertical part of the limit curve with inclusions represents the configurations in which failure occurs by sliding on the foundation's lower side.
Figure 5.14: Cross-section of the limit surface for reinforced soil.
The results from the Yield design calculations have proven to be consistent with those yielded by finite element numerical models as well as physical models tested in a centrifuge. In this special case, the general validation principle for detailed models presented in Section 2.2 has thus also been respected. 2.3.2. Verification principle
The formal inequality E d < R d therefore consists of verifying that the point representing the load Ed is within the volume R d delimited by the limit surface: Within this framework, Design Approach 2 consists of establishing the limit surface within the Q, T, M space based on non-weighted soil parameter values, then positioning the representative loading point obtained by applying factors G = 1.35 or 1.0 and Q = 1.5 or 0 to the characteristic values Q, T, M; Design Approach 3 consists of establishing the limit surface in the Q, T, M space based on the soil parameters modified using the set of M2 partial factors: = 1.25 cu = 1.4 = 1.0 and then locating the representative loading point (characteristic values Q, T, M assigned the A2 partial factors: G = 1.0 and Q = 1.3 or 0). The distance from the representative loading point to the domain boundary characterizes the .
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LIMIT STATES
The material strength limit states are relevant to the structure (footing, ground slab, raft), as well as to geotextiles, inclusion caps and the inclusion itself. Remark: Chapter 4: Design has focused the attention on the need to consider the sensitivity of the calculated loads on the choice of soil parameters. Whenever necessary, this parametric sensitivity study will be conducted by examining the dispersion observed on the measurements of the soil parameter relevant to the computational model. 3.1. Concrete or mortar inclusions
For rigid inclusions, the following limit states are to be verified: Strength relative to compression; Strength relative to bending; Strength relative to shear; Strength relative to buckling. These verifications are to be conducted by considering the following: Vertical loads of all types from the structure; Horizontal forces capable, in certain cases, of being transmitted to the inclusion head via the load transfer platform (industrial or commercial building footings, braking forces on a slab on grade, edge effects underneath an embankment or reservoir, or horizontal load behind an abutment); Loads potentially resulting from displacements imposed on the soil around the inclusions (asymmetric loading under the footprint of a reinforced zone, toe of an embankment, lateral soil displacement beneath a vertically-loaded footing); Loadings induced by an earthquake; Eventually, the forces experienced during construction (construction site vehicles circulating in the vicinity of the inclusion heads). 3.1.1. Compressive strength for axial loading
3.1.1.1. Definition of f cd When using concrete or grout, the computed value f cd s compressive strength for uniaxial load is defined according to either the Eurocode 7 National Application Standard (NFP 94 262 for Deep foundations) or the particular job specifications: f cd
f * Min cc k 3 ck ; cc C
f ck ( t )
C
; cc
C max
C
(5.7)
with:
cc: coefficient depending on the presence or absence of steel reinforcement (reinforced = 1, non-reinforced = 0.8); C: partial coefficient with a value equal to 1.5 at the fundamental ULS and 1.2 at the accidental ULS;
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f ck *: characteristic value of the compressive strength of the concrete, grout or mortar in the inclusion, as determined based on the following formula: 1 (5.8) f ck inf f ck (t ); Cmax ; f ck k1k 2 f ck : characteristic value of the compressive strength measured on cylinders at 28 days; f ck (t): characteristic value of the compressive strength measured on cylinders at time t ; Cmax: maximum compressive strength value taking into account the required consistency of the fresh concrete, grout or mortar, depending on the technique used, as shown in Table 5.1; k 1: value depending on both the drilling method and slenderness ratio, as listed in Table 5.1.
Table 5.1: Assigned values of C max and the coefficient k 1.
Case 1 2 3 4 5
Execution mode Drilled inclusions with soil extraction Drilled inclusions using a hollow auger with soil extraction Drilled inclusions using a hollow auger with soil displacement Inclusions either vibratory driven or cast in place Incorporation of a binder with the soil (treated soil columns, jet grouting, etc.)
Cmax (MPa)
k 1
35
1.3
30
1.4
35
1.3
35
1.3
(*)
(**)
(*) Value to be determined through field site testing. (**) columns of treated soil using a mechanical tool that guarantees the cross-section geometry: k 1 to be determined on a case-by-case basis with k 1 > 1.3.
For a soil treated by jet grouting or with a tool that does not guarantee a homogeneous section geometry, the k 1 value is to be determined on a case-by-case basis k 1 > 1.5. k 1 may be decreased by 0.1, only for drilled inclusions when the composition of the ground layers guarantees stability of the outer borehole walls or when the inclusion is cased and concreted in the dry (a guarantee of borehole wall stability must be demonstrated using the procedure outlined in the EN 1536 bored pile execution Standard): k 2 depends on the slenderness ratio: k 2 = 1.05 for inclusions whose ratio of smallest dimension d to length is less than 1/20; k 2 = 1.3-d/2 for inclusions whose smallest dimension is less than 0.60 m; k 2 = 1.35-d/2 for inclusions combining the two previous conditions. k 3 depends on the type of control performed, as specified in Table 5.2 below.
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Table 5.2: Values of k 3.
k 3 values Domain 1 (inclusions required for stability) Domain 2 (inclusions not required for stability)
Without test
With reflection or impedance tests (a)
With quality tests
With load bearing capacity tests
With reinforced control tests (b)
*
0.75
**
1.2
1.4
0.65
0.85
1.4
1.5
1.7
* In Domain 1, reflection or impedance tests are mandatory. ** In Domain 1, load tests are at least load-bearing capacity tests. (a) Only for small-sized projects (See Chapter 8, §2.2 and §4.1). (b)When reinforced control tests per Standard NF P 94 262 and with the required frequency are performed in addition to the load-bearing capacity tests.
The coefficients in Table 5.2 cannot be combined: for instance, when both load-bearing capacity tests and reflection or impedance tests are performed, the k 3 coefficient value equals 1.2 for Domain 1 and 1.5 for Domain 2. s
recall the following definitions (see Chapter 8: Controls): quality tests: static loading test conducted at the maximum value, as defined in Section 2.2.1.2 of Chapter 8; load-bearing capacity test: static loading test conducted at the maximum value, as defined in Section 2.2.1.3 of Chapter 8; reinforced control test: as intended in the Eurocode 7 National Application Standard NF P 94 262 for Deep foundations, whenever applicable. Example: small-sized project with 1500 ml inclusions and without any load-bearing test. Domain 1 inclusions will be controlled by reflection or impedance tests; they are assigned a coefficient k 3 = 0.75. Domain 2 inclusions receive a coefficient k 3 = 0.65 if not controlled by reflection or impedance tests and a coefficient k 3 = 0.85 otherwise.
3.1.1.2. ULS design compressive strength At the ULS, the maximum compressive stress is limited to the computed value f cd, while the average compressive stress on the compressed part of the cross-section is limited to a fixed value of 7 MPa. 3.1.1.3. SLS design compressive strength At the SLS, the maximum compressive stress in the concrete is limited to Min (0.6 k 3 f ck *, 0.6 f ck ) and the average compressive stress on the compressed part of the cross-section is limited to (0.3 k 3 f ck *). The value of k 3 is defined in Table 5.2.
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3.1.1.4. Calculation of the modulus of deformation For concrete: long-term modulus E = 3,700 f ck 1/3; For mortar: long-term modulus E = 2,700 f ck 1/3 (sand concrete, 1994). 3.1.2. Design strength for axial loading and bending
In Domain 1 (inclusions required for stability), the inclusions must be reinforced over the length where they are not fully compressed. In Domain 2 (inclusions not required for stability), it is proposed not to reinforce the inclusions, provided the maximum tensile stress in the concrete can be justified. In all cases, the maximum design compressive stress must comply with the criteria detailed in Sections 3.1.1.2 and 3.1.1.3. 3.1.3. Design strength relative to shear
The shear stresses are verified in accordance with Eurocode 2. Verify that cp < f cvd, with: cp = 1.5 V ed / Ac Ac: Area of the compressed section of the inclusion. 3.1.3.1. Case of a reinforced inclusion The verification steps are carried out in accordance with Eurocode 2, Section 6.2.3. 3.1.3.2.Case of a fully -compressed non-reinforced inclusion 3.1.3.2.1. Recall of the Eurocode 2 prescriptions. Verify that cp < f cvd, with: 0.5 clim = f cd - 2 (f ctd . (f ctd+f cd)) (Eurocode 2, Section 12.7) cp = N ed / Ac f ctm = 0.3 f ck *(2/3) f ctd = design tensile strength = 0.7 ct f ctm / c ct = 0.8 (Eurocode 2, Section 12.3.1) f cd = design compressive strength of the concrete f cvd = design shear and compressive strength of the concrete if cp < clim f cvd = (f ctd² + cp f ctd)0.5 if cp > clim f cvd = (f ctd² + cp f ctd - [(cp- clim)/2]²)0.5 3.1.3.2.2. Application to Domain 1 In Domain 1, the shear is verified in accordance with Section 12.6.3 of the NF EN 1992-1-1 Standard. As per Section 12.2.1(8) of Standard NF P 94 262 however, when the ULS design normal stress NEd/Ac exceeds 0.3f ck , it becomes necessary to verify that the shear stress cp does not exceed f cvd/10, as illustrated in Figure 5.15.
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Figure 5.15: Evolution of design shear strength vs. ULS normal compressive stress.
According to Section 12.2.1(8) of Standard NFP 94 262, in Domain 1, no shear is allowable as long as the inclusion diameter remains below 400 mm. Provided the transmission of horizontal forces has been calculated by using one of the three footing computation models described in Chapter 3 (i.e. MH1, MH2 or MH3), this threshold can be reduced to 300 mm. 3.1.3.2.3. Application to Domain 2 In Domain 2, a shear stress verification is not usually necessary, hence the condition on the inclusion diameter defined in Standard NFP 94 262 (Section 12.2.1(8)), is not applicable. 3.1.4. Buckling resistance
Buckling (or the amplification of bending loads) needs be verified, through conventional methods, provided the two following conditions have been satisfied: Pressuremeter modulus E M < 3 MPa, over a significant height (i.e. more than 5 diameters); Diameter inclusion D < 300 mm. The bending stiffness EI to be used in this analysis for non-reinforced inclusions must be justifiable up to the critical load. 3.2. Steel inclusions
All of the conditions described in Standard NF P 94 262 (Deep foundations) for steel elements are applicable. The maximum allowable stresses in the material are those listed in Eurocode 3. 3.3. Pile caps
Generally speaking, pile caps are considered to work as a cantilever on the inclusion head. Whenever pile caps or their equivalent are installed, their dimensions must be compliant with Eurocode specifications.
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3.4. Slabs on grade
In Standards NF P11-213-1 and NF P11-213-2 it is required to take into account the heterogeneity introduced by the improvement technique as part of the serviceability limit state verification. Remark: Standards NF P11-213-1 and NF P11-213-2 correspond respectively to Part Contract bill of technical clauses for paving in industrial or related uses Contract bill of technical clauses for paving in uses other than industrial or r from March 2005, with Amendment A1 adopted in May 2007. In the remainder of the present document, the term "DTU 13.3" will refer to these two documents. 3.4.1. Limit states requiring verification
According to DTU 13.3, the limit states requiring verification are relative to: Absolute and differential deformations of slabs on grade; Compressive strength of concrete in the case of a reinforced concrete slab on grade; Tensile strength in the case of a non-reinforced slab on grade. 3.4.1.1. Limit States for total and differential deformation of slabs on grade The total and differential vertical deformations must be compliant with the prescriptions set forth in DTU 13.3 (except for special specifications listed in Special Contract Clauses): Total settlement 1/2,000) in mm, where L1 is the smallest dimension of the rectangular envelope for the structure (expressed in mm); Differential settlement 2/2,000) in mm, between two points separated by L2 (expressed in mm). It should also be noted that this second criterion, which requires verification between a loaded zone and an unloaded zone is most often the limiting criterion. 3.4.1.2. Structural limit states The layout of rigid inclusions with respect to the applied loads and joints is taken into consideration in these verifications. 3.4.1.2.1. Compressive limit state of concrete in the case of a reinforced concrete slab on grade The compressive limit states of concrete are verified in the case of a reinforced concrete slab on grade in accordance with the set of design rules for reinforced concrete. A reinforced slab on grade must be used according to the DTU 13.3 whenever: The operating conditions defined in the Special Contractual Clauses require a limitation of the crack opening size; Joint spacing does not satisfy DTU 13.3, Section 5.6.6; The mechanical characteristics of the support, the actions or the construction method prohibit the design of a non-reinforced slab on grade;
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The slab on grade is intended to be covered with a skid resistant layer either directly on the slab or via a self-leveling product. According to the DTU 13.3 guidelines and in order to fulfill the non-brittle condition in tension, the minimum section area of steel reinforcement is 0.4% in each direction. 3.4.1.2.2. Tensile limit state for non-reinforced concrete in bending The calculated tensile stress in bending at the serviceability limit state under the most unfavorable action combinations listed in DTU 13.3 must verify the following condition for a non-reinforced slab on grade: SLS = 6.M/h² c28 (5.9) (M: moment per linear meter) As an example, for a concrete compressive strength fc 28 = 25 MPa, the limit tensile stress SLS = 1.8 MPa. It is also possible to refer to the limit splitting tensile strength value, f tsplitting28, at 28 days. In this case, the condition to be satisfied becomes: SLS = 6.M/h² tsplitting28 (5.10) For a given concrete strength class (e.g. C25/30), depending on the concrete mix design and the type of materials used, the characteristic splitting tensile strength can vary significantly, SLS varying between 1.8 and 2.7 MPa. Splitting tensile tests are required. Note: The initial approach stemming from compressive strength has a higher margin of safety since it takes into account the uncertainties between a concrete's compressive strength and its tensile strength. In reality, no mathematical relationship exists between these two magnitudes.
3.4.1.2.3. Bending tensile limit state of the concrete with metal fiber additives. Steel fiber-reinforced concrete slabs on grade are assimilated with non-reinforced slabs for the entire set of conditions listed in DTU 13.3. The specificities of these processes are governed by technical memoranda issued by the CSTB Building Research Center. The main exemptions are: the tensile stress strength of the composite concrete, concrete characteristics, distances between interruptions a slab on grade without sawed , or more commonly called ), and aspects of the construction method. The orders of magnitude of the limit tensile stresses evaluated by these technical memoranda, for fiber concentrations of between 20 and 40 kg/m 3, currently stand at: in the vicinity of joints (panel corner and edge): between 1.8 and 3.5 MPa; over the main part of the panel: between 2.5 and 5 MPa. s attention must be drawn to the fact that all technical assessments of fibers are based on the post-cracking behavior of the material; this behavior may lead to conflicts with the requirement for no cracking, hence making the slab unfit for its final purpose.
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3.4.2. Types of joints
In accordance with the DTU 13.3 guidelines, the slab on grade is split and isolated from the other structural elements using various types of joints. For all projects, prior to the execution phase, a slab layout will be prepared and will incorporate: Phasing of the pours; Construction layout; Special considerations at critical points: internal angles and circulation direction, presence of protuberances; Eventually, the position of static loads applied on the slab; Eventually, the inclusion mesh. Four types of joints exist, and each will be discussed in detail below. Remarks: In the event that the design explicitly takes into account the relative positions of the loads, joints and inclusions, then these hypotheses must be detailed in the project contract documents from the design phase; All of the contraction and construction joints (pour interruption, shrinkage, dilatation) solely transmit shear force and are to be modeled like hinges.
3.4.2.1. The pouring interruption joint (construction joint) This joint serves to delimit the daily casting phases and affects the entire ground slab thickness. It must be designed so as to prevent the relative vertical motion called "tinkling", while allowing for free horizontal, transverse or longitudinal movements and protecting the joint edge. Expansion joints are to be prohibited; only butt joints are authorized (Fig. 5.16).
Figure 5.16: Types of casting interruption joints.
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3.4.2.2. The shrinkage/contraction joint This joint is intended to control and position the cracking due to shrinkage. In most instances, it is constructed by sawing over a depth corresponding to one-third of the slab thickness. The continuity is ensured using welded wire mesh. For non-reinforced slabs with fiber concrete, the distances between shrinkage/contraction joints will not exceed 6 meters (except under special conditions). For slabs with fiber additives over 40 kg/m 3, or so- - and reinforced concrete slabs, saw-cut joints are not necessary; only the pour interruptions are to be installed based on the distance authorized by the method and by taking shrinkage into account in the design. 3.4.2.3. The expansion joint (for reference since it is rarely used on slabs on grade) This joint allows compensating for the expansion/contraction of a slab due to temperature variations; its use is not required inside buildings. 3.4.2.4. The separation or isolation joint This joint allows the decoupling of the slab from the influence of any obstacles or obstructions capable of interfering with its unrestricted motion. Such a joint lies within the expansion joint family. 3.4.3. Design considerations
Each load has an influence (of varying importance) on stresses in the slab depending on the zone considered (main part, edge or corner, near a joint) and must be taken into account. More specifically, for point loads, it is necessary to consider the least favorable configurations and combinations (Figs. 5.17 and 5.18). Remarks: The edge and boundary zones are sensitive areas; Layout of the rack bases is never known with certainty; This can lead to designs with higher safety factors.
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Figure 5.17: Examples of modeled situations in the main part of the zone for point loads.
Figure 5.18: Examples of modeled situations in the edge zone for point loads.
The slab on grade supported on soil reinforced by inclusions is a structure addressed in the DTU 13.3 document, yet its design over its main part requires incorporating the specific nature of a non-uniform distribution of reactions on the ground slab lower face. As such, the simplified method for evaluating deformations and loads, as explained in Appendices C3.1 and C4.1.4 to C4.1.7 of DTU 13.3, proves to be insufficient. The present recommendations propose two distinct methods based on an interpretation of the full-scale experiments and the analysis of a large number of detailed, three-dimensional computations (ASIRI, 2011): An envelope ; An alternative method based on differentiated subgrade reaction coefficients. Each of these methods serves to estimate the loadings of mechanical origin (related to loads). The effects of shrinkage and thermal gradient will then be added (along with the appropriate combination coefficients) to these loadings.
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3.4.3.1.
envelope
method
This method consists of defining the corrective terms due to the presence of inclusions, which are to be added, in the form of an envelope, to the bending moments in the slab calculated in accordance with Appendix C for the main part of the slab, the edges and corners of panels, on an equivalent homogenized soil. These two corrective terms are: One term representing the influence of the rigid inclusions on a continuous slab (no joint); Another term representing the interaction between rigid inclusions and joints. The determination of these corrective terms will be explained below, as well as the definition of the equivalent homogenized soil. Remarks: For all of the calculation methods presented below, it would be referable to select a sign convention and determine all of the bending moment values as algebraic values. The adopted sign convention will be specified by identifying on which fiber tension is being developed when the calculated moment is positive; When using the simplified method outlined in DTU 13.3, the approach assumes the use of butt joints capable of transmitting shear forces from one panel to the other.
3.4.3.1.1. Breakdown of the problem The results of the calculation for a slab on rigid inclusions can be broken down as the sum of , which represent respectively: : calculation of a slab on equivalent homogenized soil (Appendix C, DTU 13.3); : Influence of the rigid inclusions on a continuous slab without joints; : Interaction between rigid inclusions and joints. Each of these three terms may be evaluated separately. s now define the following notations: Results of the calculation = distribution of bending moment in any cross-section; S oed(SJ): results of the calculation for a continuous slab on an equivalent homogenized soil; S oed(JT): results of the calculation for a slab with joints on an equivalent homogenized soil; IR(SJ): results of the calculation of a continuous slab without joints on a network of rigid inclusions; IR(JT): results of the calculation of a slab with joints over a network of rigid inclusions. Regardless of the type of loading considered 1, the following equation can be written:
JT SJ Soed SJ IR JT Soed JT IR JT Soed IR IRSJ Soed SJ ma
1
mb
(5.11)
mc
Uniformly-distributed surcharge, alternating loaded and non-loaded bands, superposition of point loads, etc.
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3.4.3.1.2. mc term:
Results of calculation of a slab on an equivalent homogenized soil The soil reinforcement is represented by a homogenized soil profile, for which each layer is chara s modulus E S s ratio . This is the case adopted when designing an industrial slab in accordance with the method described in DTU 13.3 (Part 1, Appendix C), which allows taking into account the interaction between applied loads and joints, based on their respective positions. In this special case, during the design phase of the slab, it becomes necessary to perform the analysis at the panel edge and at the corner in systematically considering the case as well as the case where this curling effect is cancelled out by the subsequent to differential shrinkage attenuation (load Qs equals 0 in the Appendix C design method) because this last case may become the critical design case. It is therefore necessary to run two calculations in - the inclusions. Remark: In the case of a uniformly-distributed load, as per Article 5.1.1.1 of Part 1, DTU 13.3, an isolated concentrated load with an intensity equivalent to the distributed load value applied on a 1 m² total area (with an impact area corresponding to a 5 MPa pressure) must be considered in order to evaluate corner and edge zone loadings.
The homogenized soil profile is selected from the study of a basic unit cell (inclusion and the corresponding surrounding soil volume, load transfer platform and joint-free slab) subjected to an equivalent uniformly-distributed load q 0. This basic cell is modeled with a constrained condition at the edge (zero lateral deformation). Any of the methods described in Chapter 3 may be used here. The value of the load q 0 should be representative of the average load case for the condition being studied, on an area (see Fig. 5.19): Corresponding to several grids of inclusions, in order to ensure that the behavior of these inclusions is compatible with the zero lateral displacement boundary condition at the periphery of the model; In proportion with the reinforced soil thickness.
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Figure 5.19: Examples of an average load computation.
Settlement y at the model surface is used to define the equivalent oedometric modulus E oedo* over the total model height H: Eoedo* = q0 H/y (5.12) This oedometric modulus can be split into at least three moduli corresponding to a three-layer model bearing on a soil substratum assumed to be non-deformable: Load transfer platform: height H 1, modulus E oedo1; Reinforced soil: height H2, modulus Eoedo2; Soil layer underlying the reinforced soil: height H 3, modulus E oedo3. Since Eoedo1 and Eoedo3 are known values, the value E oedo2 can be calculated from the following formula: H/Eoedo* = H1/Eoedo1 + H2/Eoedo2 +H3/Eoedo3 (5.13)
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Remarks: H1 is the load transfer platform thickness (between the inclusion head and the bottom of the slab); H1 + H2 may be assimilated, indifferently, either as the sum of the load transfer platform thickness + inclusions length, or as the distance separating the bottom of the slab from the lower plane of equal settlement, located below the inclusion tip (Fig. 5.21); Selecting the thickness H2 as the compressible layer thickness, the inclusion length or the depth to the lower plane of equal settlement placed (located slightly below the tip of the inclusions) has no noticeable impact provided the value of the equivalent modulus Eoedo* over the total model height remains unchanged. This option however must be maintained for all of the calculations; The design according to Appendix C of DTU 13.3 implicitly assigns an infinite thickness to the deepest soil layer. Moreover, the geotechnical model typically assumes that an uncompressible substratum has been reached at a given depth. It is necessary to ensure the consistency of these two models, especially by verifying that the two profiles considered yield identical settlements. This step therefore leads to incorporating a layer with a very high modulus value into the computational model derived from DTU13.3 at the base of the model, which in turn simulates the incompressible substratum defined by the geotechnical engineer (Fig. 5.20).
Figure 5.20: Uncompressible substratum added to the "slab on grade" model.
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Figure 5.21: Example used to determine the H2, E oed2 couple.
For calculations that rely on Appendix C of DTU 13.3 and are performed in a conventional manner using the value = 0.35 for the soil, the equivalent oedometric moduli E oedo* are s moduli E*: E* = Eoedo* (1 + ) (1 - 2)/(1-) (5.14) Remark: The E* modulus corresponds to the E s modulus listed in Appendix C of DTU 13.3.
The equivalent modulus values to be used in the specific slab on grade calculations must be evaluated on the basis of residual settlements experienced from the construction of the slab. The goal here consists of defining these modulus values for consistency with the slab on grade, which only considers the loads directly applied to the slab. Example: Hypotheses: s take the example of an industrial slab on a fill layer with thickness h = 1.80 m and unit weight = 20 kN/m 3 and built on a soil previously reinforced by inclusions. The average surcharge load is 30 kPa (including the weight of the slab). If the analysis of in situ soil consolidation rate allows the estimation of the percentage of settlement reached under the embankment weight and prior to construction of the slab, then the equivalent modulus to enter into the ground slab design may be evaluated as follows. Results of the basic unit cell calculation: The calculation for a basic cell with inclusions incorporating all loads leads to the following results: 1) Total settlement under embankment weight q 1 = 1.8 20 = 36 kPa: h1 = 1.4 cm;
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2) Total settlement under operating load q 2 = 30 kPa: h2 = 1.2 cm. If the analysis of in situ soil consolidation rate allows estimating that the percentage of settlement reached under the embankment weight prior to slab execution is 40%, then the residual settlement of the slab (from the start of the construction of said slab) is therefore: hres 1 40%.h1 h2 2.0 cm As intended in DTU13.3, the slab is designed solely by considering the surcharge load q 2 (without taking into account the loading history: installation of the embankment and partial consolidation due to this load q 1). The homogeneous soil profile must therefore be adapted in order to derive the previously *
calculated total settlement hres ; the equivalent oedometric modulus E oedo over the total model height can thus be expressed as: q . H * E oedo 2 hres
(5.15)
The estimation of E oedo2 over the reinforced soil height remains in compliance with what had been previously defined (see Fig. V.21 above). Remarks: The model must be prepared in accordance with the phasing, in order to determine, among other things, whether or not the load transfer platform constitutes an additional load applied onto the soil compared to the initial conditions before construction; The homogeneous soil profile must be defined for each grid of inclusion and for each loading case. term:
Influence of rigid inclusions on a continuous slab without joints
Regardless of the loading type, term (influence relative to the rigid inclusion on the bending moment in a continuous slab without joints) may be evaluated by using the case of the basic unit cell subjected to a uniform load q 0 as defined in Section 3.4.3.1.2. Remark: The distribution of the radial moment M r in the axisymmetric model is u term, which is applied to both the distributions of the moment M x and the moment M y for the complete model of the slab.
This envelope is determined, as part of the analysis of a uniformly-loaded basic unit cell, using: The moment M upper (which creates tension in the upper fiber) equal to the radial moment obtained directly above the rigid inclusion M r (r = 0); The moment M lower (which creates tension in the lower fiber) equal to the radial moment obtained at the edge of the axisymmetric model M r (r = , where A is the mesh surface area).
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Figure 5.22: Definition of the M upper and Mlower moments calculated in a slab on grade on inclusions.
moments calculated from the homogenized model are therefore increased by Mupper when they result in tension on the upper fiber and by M lower when they result in tension in the lower fiber. Remarks: If for the same structure, several separate load cases exist, it would be necessary to conduct a basic unit cell calculation for each load case in order to determine the corresponding additional moments; For a load q 0 with a limited extent, it is also possible to consider that the moments Mupper and Mlower are proportional to the load, with all other parameters being held constant; The corr term is not applicable to moments calculated according to Sections C4.2.3 and C4.2.4 of Appendix C, DTU13.3 whenever the edge (or 5.23). The moments calculated with these methods only pertain to the raised part of the panel which is not influenced by the inclusions. Nevertheless, it may be necessary to study the influence of the load sharing between soil and inclusions on the determination of value q 0 used in the determination term.
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On the other hand, it is also necessary to study the case where this curling of the slab disappears subsequent to the attenuation of differential shrinkage (i.e. with load Qs equal to 0, as per Appendix C, DTU13.3), and in that case, the corrective term needs to be used.
Figure 5.23: . term:
Interaction between the rigid inclusions and the joints The presence of a joint in the slab produces the following effects: No bending moment at the location of the joint; The bending moment diagram is shifted in the vicinity of the joint. In practice, the set of studies carried out within the scope of the National Project have led to the conclusion that at the location of a joint and regardless of the type of loading, an upper term (i.e. specific to the interaction of the rigid inclusions with the joints) may be term, which was established from the basic unit cell calcu term (maximum moment offset) thus lies within the interval {-Mlower , -Mupper } (reminder: Mupper and M lower are both algebraic values). Between the joints, this interval decreases with the distance to the joints exclusively. It is equal to zero at a point on the ground slab sufficiently far from any joint. The overall shape is presented in Figure 5.24.
Figure 5.24: Example of the profile of corrective "mc" term values.
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Figure 5.25: Field of "mc" values calculated based on the moments M x
Figure 5.26: Field of "mc" values calculated based on the moments M y
In practice, three levels of complexity can be anticipated: 1) The relative position of inclusions with respect to the joints is known: the ) curve can then be built point by point using the basic shown in Fig. 5.24). 2) The relative position of inclusions with respect to the joints is not known, but the joint position is known: it is then necessary to use the upper bound and lower bound curves (continuous blue and red curves in Fig. 5.24). These curves only depend on the joint position, which is considered to be known; they span all inclusion positions relative to these joints. 3) In theory, the joint position remains unknown: with this level of complexity, it would be necessary to use the least favorable values over the interval, i.e. the upper bound ( M lower ) and lower bound ( M upper ) (parallel dashed lines in Fig. 5.24). These curves depend on neither the joint position nor the inclusion position; hence, they encompass all inclusion and joint positions. Remarks: term is not applicable to moments calculated according to Sections C4.2.3 and C4.2.4 of Appendix C, DTU13.3 whenever the edge (or
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5.23); the moments calculated with these methods only pertain to the raised part of the panel which is not influenced by the inclusions; On the other hand, it is also necessary to study the case where this curling of the slab disappears subsequent to the attenuation of differential shrinkage (i.e. with load Qs equal to 0, as per Appendix C, DTU13.3), and in that case, the corrective term needs to be used. The edges of the slab on grade (boundary of the structure) have a similar effect at term must therefore also be taken into account in term. Special case of continuous slabs - free slab on )
The design of slabs on grade with joints (typical spacing of 5 to 6 m between joints), which involves the combined use of the three terms , and , leads to an envelope of moment in all cases. The special case of a slab made of reinforced concrete or with the addition of steel fibers and without sawed joints (typical spacing of 25 to 35 m herein referred -free slab on ) can be desig term except in the vicinity of pouring joint interruptions and the edge of the structure. In this case, it has been observed in certain unique configurations (back-to-back racks and alternation of loaded and non-loaded bands) that the moment obtained, when solely focusing terms, might not constitute a strict upper bound of the calculated moment through a comprehensive 3D model. This is illustrated in Figures 5.27 and 5.28, which compare for the geometry displayed the values deduced from FLAC 3D calculations with the values of the moments M upper and Mlower calculated from the basic unit cell computation: In the case of loaded and non-loaded bands (Fig. values calculated by FLAC 3D in the longitudinal direction of the loaded strip exceed the negative moment M lower value at the intersection of the loaded zone axis and the inclusion axis; In the case of l values calculated in FLAC 3D in the rack direction exceed the Mlower value at location where the back-to-back racks are aligned with the inclusions. Consequently, it would be useful to apply a model coefficient R;d = 1.75 on the corrective term relative to the lower fiber over the typical part of the slab [M upper ; 1.75 M lower ] in all load cases (e.g. localized distributed loads, stationary or mobile point loads), with the exception of the uniformly-distributed load case.
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Figure 5.27: Comparison of "mb" values (along the Y direction) from FLAC 3D calculations with the M upper and Mlower values derived from a basic unit cell computation (succession of loaded/non-loaded bands).
Figure 5.28: Comparison of "mb" values (along the Y direction) deduced from FLAC 3D computations with the M upper and Mlower values derived from a basic cell computation (loading via the rack bases).
3.4.3.1.3. Summary A slab on grade supported by a network of rigid inclusions may be designed by adding the results of the following calculation cases: ma, which is the output from a model with joints lying on an equivalent homogenized soil; derived from the influence of rigid inclusions on the bending moment of a joint-free slab on grade, with this influence being bounded by [M upper ; Mlower ] (note: both M upper and Mlower are algebraic values); generated from the interaction between rigid inclusions and joints, bounded by [ M lower ; M upper ].
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In the general slab on grade case, the influence of the rigid inclusions interacting with the slab joints always remains bounded by: [Mupper - Mlower ; -(Mupper - Mlower )] terms are independent of the location of the load with respect to the joints, as opposed to term. With better knowledge of the relative positions of inclusions and joints, it is possible to refine the above interval (see Section 3.4.3.1.2 and Fig. 5.24). When the design explicitly takes into account the relative position of loads, joints and inclusions, these hypotheses must be listed in the contractual clauses in a detailed manner at the design stage. The design of slabs on grade with joints (typical spacing of 5 to 6 m between joints), which involves the combined use of the three term moment values in all cases. In the special case of a slab on grade without sawed joints (i.e. joint-free slab on grade), the term is equal to zero except in the vicinity of edges of the structure and pouring joints interruptions. It is then necessary to apply a model coeffic term for only the lower fiber of the slab [M upper ; 1.75 Mlower ] for all load cases, with the exception of the uniformly-distributed load case. 3.4.3.2. Alternative method: subgrade reaction coefficient According to this method, the ultimate objective is to define a computational model limited to the slab itself, the interaction of the slab and the foundation being modeled by springs with properties estimated for a given loading level. The first step is to study a basic unit cell of ground improvement under an equivalent uniform load of the same intensity as the load case being studied. Afterwards, a calibration step is performed on the previous results in order to determine a distribution of subgrade reaction coefficients. In a final step, these coefficients are incorporated into a model of a plate on elastic supports for the purpose of estimating the moments in the slab under the project loads (point and/or distributed loads).
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3.4.3.2.1. Analysis of the basic unit cell
Figure 5.29: The 5.29: The configuration configuration under study.
This This method method consists consists of studyi studying ng a basic basic unit unit cell subject subjected ed to an equiva equivalen lentt unifor uniformly mly-distributed load q 0 under the same conditions as those presented Fig. 5.29. The axisymmetric model of this basic cell has a radius R. This calculation gives the distribution of the vertical stress under the slab (Fig. 5.30) as well as the slab bending moment diagram.
Figure 5.30: Vertical 5.30: Vertical stress distribution characteristic directly under the slab.
3.4.3.2.2. Determination of subgrade reaction coefficients A simplified distribution of subgrade reaction coefficients k(r) = (r) / y(r) is defined in such a way that the bending moment distribution is similar to the bending moment diagram in the slab from the unit cell calculation. calculation.
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This simplified distribution is characterized by the following (see Fig. 5.31): Two Two values k i and k s; A A diffusion radius r k k underneath the ground slab. These parameters parameters as defined as follows. follows. 0 < r < r k k(r) = k i k r k k(r) = ks k < r < R
Figure 5.31: Simplified 5.31: Simplified subgrade reaction coefficient distribution.
It is recommended recommended to choose the values values k i, k s and r k k as follows: k s is calculated by considering both the minimum value of the stress s applied to the soil directly directly below the slab (Fig. 5.30) and the settlement settlement of the slab; For For a given value of r k k , chosen in the interval [r P, r P +H M], k i is calculated with the stress i, defined from the total load Q conservation equation applied to the mesh (Fig. 5.32), 2 2 2 i r k r k (5.16) k + s (R r k ) = Q and with the settlement calculated from the basic unit cell calculation; calculation; The The bending moment distribution for the uniformly distributed load Q is calculated for the circular plate of radius R on springs k i over the interval [0, r k k] and k s over the interval [r k k , R]; The The value for r k k is determined by iteration and is the value that gives the best agreement with the bending moment diagram established during Stage 1 (Section 3.4.3.2.1) with respect to the two values Mupper (directly above an inclusion) inclusion) and Mlower (at the edge of the model). This procedure has been illustrated by the example detailed in Figures 5.32 and 5.33, using an application to the case of a slab with thickness h = 0.17 m, a load transfer platform with thickn thickness ess HM = 0.5 0.5 m supp suppor orte ted d by a netw networ ork k of incl inclus usio ions ns (D = 0.42 0.42 m, and and mesh mesh a = 2.5 m): Figure Figure 5.32 shows the distributions k(r) obtained for various r k values in comparison with the value resulting from a FLAC 3D calculation; calculation; Figure 5.33 shows shows that that the maximum maximum moment moment obtained obtained in the plate plate direct directly ly above above an Figure inclu inclusio sion n decr decrea eases ses as the the valu valuee chos chosen en for for r k value rises rises.. In this this speci special al case case,, the the k(r) k(r) k value distribution defined by r k k = 0.5 m yields values for M upper and M lower , with good agreement
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with the corresponding FLAC 3D calculations; this r k value represents a diffusion cone with an approx. angle of 6h/10v from the top of each inclusion. inclusion.
Figure 5.32: Reaction 5.32: Reaction coefficient distributions for various r k values.
Figure 5.33: Influence 5.33: Influence of the parameter r k on the moments M upper and Mlower .
Remarks: The stiffness k i or k s cannot be correlated with the stiffness obtained by interpreting interpreting results from a plate load test. One method, which consists of selecting a set value for r k k and then calculating the values k i and k s based based on the average average stress stress (r) within each sector, sector, does not generally agree with the moment diagram from the basic unit cell and tends to underestimate the moment.
Seve Severa rall calcu calcula latio tions ns were were perfo perform rmed ed and and show showed ed that that the the choi choice ce of a fixed fixed valu valuee for for r k k corresponding to a 1h/5v diffusion on the load transfer platform height is acceptable (on the side of safety), provided that the design model satisfies all of the conditions explained in Chapter 3, Section 2.2.1.
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3.4.3.2.3. Focus on the slab on grade The The distrib distributi ution on of reactio reaction n coeffi coefficien cients ts define defined d by k i,i, k s and r k has been been exten extende ded d to a k has comple complex x slab-on slab-on-gr -grade ade model model (incor (incorpor poratin ating g joints joints), ), by reprod reproduci ucing ng the patter pattern, n, as many times as there are inclusions. In order to validate this extensive model, it is necessary to verify that when subjected to the same uniformly-distributed load as the model of the basic unit cell, the model leads more or less to the same moments as those established during Stage 1. Results may show sensitivity to choices made regarding both the design tools as well as the level of model discretization and the mesh. Remark: The three stages may be performed using different computation tools and software.
Such a comprehensive model makes it possible to treat all cases of distributed and/or point loads, provided the load resultant on a given mesh remains of the same order of magnitude as the uniform load set as the reference for the purpose of calibrating the k i and k s values. Remarks: It is necessary to verify that the springs are never mobilized in tension. Joints should be modeled as a hinge that allows for shear force transmission (with a zero moment imposed at the location location of the joint). Point loads may be modeled by taking into account the impact surface area (e.g. support bearing plate of a rack base) with a diffusion angle of 45° up to the neutral axis of the slab section. If the relative position of loads, joints and/or inclusions cannot be fixed, then it becomes necessary to perform a sensitivity analysis of the results for various configurations (Fig. 5.34).
Figure 5.34: Examples 5.34: Examples of unfavorable unfavorable configurations configurations for ground slab loadings.
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3.4.3.2.Comparative results of the two methods
The envelope method of additional moments by superimposing corrective terms is, by virtue of its envelope approach, relatively conservative; it allows the calculation of the moments at any point, including including at the edge of the structure. structure. Moreover, Moreover, it is well adapted to: The The sequencing of the design design stages; The The sequencing of work phases relative to the various various work phases; The The design approach described in DTU13.3 for non-reinforced soils; The level level of expert expertise ise of the variou variouss subcon subcontrac tractor torss (groun (ground d improv improveme ement, nt, earthwo earthworks rks,, industrial slab).
structure, far from the edges; it corresponds to an approach often adopted to link the study of soil-structure interaction and the detailed structural design. According to this approach, it is necessary to examine the least favorable configurations (Fig. 5.34).
The calculation of the subgrade reaction coefficients is especially sensitive to the type of loading and its special distribution (point loads, uniform loads). Remark: Ideally, the subgrade reaction coefficients should be calibrated for each load case, though they can only be calculated under a uniformly-distributed load for practical reasons. It is necessary to verify that the subgrade reaction coefficient values values determ determine ined d under under a unifor uniformly mly-di -distri stribut buted ed load load are still still accept acceptabl ablee in the case of point loads. This verification step may, for example, be completed through an iterative process using the stresses calculated directly under the slab for the least favorable favorable load (in terms of both intensity intensity and position). position).
This method does not allow for a simple estimation of forces and moments at the edge of the i and k s are selected at the edge of the structure, these forces and moments can be determined through the additional moment method. A comprehensive computational model that includes the inclusions, the foundation soil, the load transfer platform, platform, the slab on grade, grade, the location of the joints and distribution distribution of the loads may offer an alternative to these methods from the standpoint of refining the moments and forces in the slab. This model is necessarily a 3D finite element or finite difference model. This usually makes its creation and interpretation particularly complex.
Remarks: Tanks, reservoirs or structures built on rafts that are not addressed in DTU 13.3 may be design designed ed similar similarly ly using using the envelo envelope pe method method of additio additional nal moments by replacing the DTU13.3 type computations by raft type computations that that take take into into accou account nt the even eventua tuall exist existen ence ce of join joints ts (in (in whic which h case case spec specifi ificc models become necessary: 3D on equivalent homogenized soil, or comprehensive 3D on soil + inclusions, inclusions, or 2D axisymmetric axisymmetric with inclusions inclusions replaced replaced by equivalent equivalent cylinders).
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3.5. Footings and rafts 3.5.1. Rigid footings or rafts
The general calculation models for footings were detailed in Chapter 3. Our attention here is - platform thickness and the inclusion layout. l ayout. A design considering that the footing lies on isolated fixed supports directly located at the top of the inclusions will generate an envelope of forces and moments to be used for the footing design. 3.5.2. Flexible rafts
Flexible concrete rafts (e.g. reservoirs, tanks or basins), which work both in bending and shear, are subjected to a non-uniform reaction distribution similar to the slabs on grade. The verifications verifications can then be carried out by evaluating the forces and moments assuming the case of joint-free joint-free slabs on grade (Section 3.4.3). 3.4.3). The steel bottom floors of reservoirs and tanks are working in tension (via membrane effect) and may also contribute to a different distribution of the reactions directly above and in be be verific verificati ations ons must must be perform performed ed based based on forces forces and moments calculated using a relevant model. 3.6. Pavements The typical design of a pavement structure does not take into account the hard-point effects typica typically lly associat associated ed with with the presen presence ce of inclusi inclusions ons.. Under Under load, load, the risk risk of differ different ential ial settlements exists between the inclusion and the center of the grid of installation (Figs. 5.35 and 5.36).
Figure 5.35: Example 5.35: Example of an "egg box" type of deformation beneath a pavement.
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Figure 5.36: Deformation underneath a pavement.
It is therefore necessary to guarantee a sufficient distribution layer thickness H M between the pavement structure base and the inclusion head in order to ensure that the settlements at the pavement base remain acceptable. The following condition must then be verified: HM > 0.7 (s a) (5.17) A horizontal reinforcement (geosynthetics, welded wire mesh or slab) installed in the load transfer platform may help to reduce the thickness of this layer (see Section 3.7 of this Chapter).
Figure 5.37: Layers composing the pavement.
Point loads (i.e. loads due to traffic or storage) allow designing the pavement using properties obtained at the top of the subgrade layer (as determined by plate load tests). These characteristics depend on both the compaction and the thickness of the subgrade layer, but tend to be only slightly influenced by the presence of inclusions. In contrast, the pavement surface settlements must be calculated using a model that incorporates inclusions. Lawson (2000) proposed charts for designing the geosynthetic layer stiffness as a function of acceptable differential settlements at the embankment surface (Fig. 5.38). These results may be used for SLS situations, yet they cannot replace the settlement analysis performed using conventional methods.
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Figure 5.38: Charts for geosynthetic design based on allowable differential settlement (Lawson, 2000).
3.7. Load transfer platform reinforcement 3.7.1. Foreword
The ASIRI National Project studied the specific case of embankments on inclusions, with a load transfer platform reinforced by geosynthetics and geotextiles: full-scale experiment carried out on the Chelles site (Briançon, 2008), coupled with physical and numerical modeling work (Jenck, 2005; Chevallier, 2008). Reinforcements using welded wire steel mesh or a concrete slab were not mentioned by these authors. The justifications relative to geosynthetic layers (geotextiles, geogrids and composite products) might also rely on the experience acquired through both experiments and the construction of many structures in France and abroad. A number of national standards or recommendations have dealt with this specific topic: BS8006 (2010), EBGEO (2010), Nordic Handbook (2005), and CUR 159B (2010). The items presented in these Recommendations pertain solely to reinforcement using geosynthetic layers and rely on the referenced research examples. The use of welded wire steel mesh or a slab will need to be specifically studied. With regard to welded wire steel mesh, for which bending strength and stiffness will always be neglected, the verification may be performed comparably to the justifications proposed for geosynthetics (verifications of tension, anchorage in the transverse and longitudinal directions and non-sliding), but still meeting the NF P 94 270 Standard (for reinforced soils). As for slabs, the verifications must match the justifications proposed for slabs on grade in Chapter 5, Section 3.4. All of the methods discussed in detail in Chapter 3 can give the stress distribution in the horizontal plane located at the inclusion head; these methods specifically model the load transfer mechanism both by shear in the load transfer platform and friction along the inclusion in compressible soils. Therefore, these methods are different from the design methods used in standards and recommendations on the use of geosynthetics like the method initially proposed
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by Hewlett and Randolph (1988), and subsequently adopted in the BS8006 Standard (2010). The Hewlett-Randolph method will be presented herein for illustration purposes: it is limited to providing the stress distribution on the geosynthetics layer without taking into account either the settlements or the inclusion friction phenomena. In contrast, the method used to calculate the tension in the various layers, selected by these Recommendations, is based on the BS8006 Standard Method (2010). 3.7.2. Function of geosynthetic layers
The reinforcement by geosynthetics can have two distinct and complementary objectives: Ensuring the transmission of forces stemming from the weight of the embankment located outside of the diffusion cones towards the inclusion heads (so-called stress approach), which influences the optimal thickness of the load transfer platform; Absorbing These functions serve to determine the limit states needed to be verified. 3.7.3. Computational approach for the ULS verifications
Consistent with the EC7 NF P 94 270 Application Standard (2009) dedicated to reinforced embankments: Verifications pertaining to the geosynthetic reinforcement function at the base of the load transfer platform (i.e. soil support between inclusions, lateral thrust, anchorage) are conducted in accordance with the Design Approach 2 as intended in Eurocode 7; For the general stability study of an embankment installed on compressible soil, as performed with failure surfaces intercepting the geosynthetic reinforcement, the Design Approach 3 must be employed. 3.7. verification
The tension Td calculated in the horizontal geosynthetic reinforcements must be less than the computed long-term strength value R t;d. This tension is derived from the characteristic short-term strength value R t;k (as measured according to the NF EN ISO 10319 Standard), isochronous creep curves (established as per the NF EN 13431 Standard) and the appropriate partial coefficients that serve to take into account long-term product behavior: R Rt ;d t ;k geo
This verification must be carried out in a ULS situation and, if necessary, a SLS situation (see Section 3.7.5.4). The safety coefficient on the geosynthetic material geo can be expressed as: geo = M;t . creep . deg . dam M;t partial material factor set equal to 1.25 (as per the NF P 94 270 Standard). The values of creep , deg and dam are specific to each product and supplied by the individual producer. Default values have been proposed in the NF P 94 270 Standard:
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partial coefficient correlated with geosynthetic behavior vs. time. Application creep of this coefficient allows, over the entire structural use period, taking into consideration the influence of creep on the tensile strength of geosynthetic reinforcements as well as limiting structural deformations. creep =1/ creep, as defined in the NF P 94270 Standard, Appendix F.4.3. deg partial coefficient correlated with aging of the geosynthetic products, e.g. by means of hydrolysis or oxidation, given the product's environmental conditions. deg =1/ deg, as defined in the NF P 94270 Standard, Appendix F.4.4. dam partial coefficient corresponding to the geosynthetic reinforcement damage produced by their installation along with embankment compaction. dam =1/ dam, as defined in the NF P 94270 Standard, Appendix F.4.2. Remarks: The NF P 94270 Standard serves to define the partial coefficient creep for the SLS and ULS limit states, by taking into account both the creep failure criterion and allowable creep deformation criterion. The partial coefficient dam corresponding to damage may vary with respect to the deformation. At the SLS, the value corresponding to the geosynthetic service deformation would be a suitable choice. The other partial factors ( M;t and deg) are identical at both the SLS and ULS. 3.7.5. Tensile forces under vertical loading
3.7.5.1. Review of notations
Figure 5.39: Definition of the configuration geometry.
HM: s: a:
embankment height, center-to-center spacing between inclusion, inclusion head dimension (assuming a square inclusion head).
In the case of a circular inclusion head of diameter D, the equivalent square dimension is set such that: a
D 2
4
0.9 D
(5.18)
3.7.5.2. Computation of load transfer between soil and i nclusions All of the methods detailed in Chapter 3 allow deriving the stress distribution in the horizontal plane placed at the inclusion head, which serves to evaluate tension in the geosynthetic layers.
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These methods make it possible to calculate the average vertical stress v,geo applied to the soil between the inclusion heads. As an example of other potentially effective methods, Hewlett and Randolph's (1988) will now be presented.
Hewlett and Randolph method:
Figure 5.40: Schematic diagram of the Hewlett and Randolph method (extracted from BS8006-2010).
This method considers hemispherical domes for the purpose of calculating load transfer efficiency, by focusing on failure at the key of vaults or at the inclusion heads (Fig. 5.40). For thin embankments (relative to the inclusion spacing), stability at the keystone typically governs the mechanism, whereas for thicker embankments, stability at the inclusion head level becomes predominant. This method calculates the average vertical stress applied to the geosynthetic by evaluating the efficiency of load transfer towards the inclusions, in considering system failure either at the top of the arch (i.e. efficiency EV) or at the level of the inclusion heads (efficiency E T). The selected efficiency is the lower of the two, thus maximizing the load transferred to the geosynthetic reinforcement. Emin = Min (EV, ET) Efficiency EV: a 2 E v 1 1 A AB C (5.19) s
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2( K
1 )
a p A 1 s s 2 K p 2 B 2 H 2 K p 3 s a 2 K p 2 C 2 H 2 K p 3
(5.20)
(5.21)
(5.22)
(5.23)
Efficiency ET: E T
1
a K p a 1 K p 1 s K p 1 1 a s s 2 K p
(5.24)
The vertical load to be absorbed by the geosynthetic between two adjacent inclusions equals: (5.25) v, geo = s2/(s2 - a 2) v (1 - E min) with: v = r H + G g + Q q (5.26) HM: embankment height above the geosynthetic r : unit weight of the embankment g: permanent excess vertical load q: variable excess vertical load partial factor on the soil unit weight : G: partial factor on the permanent actions Q : partial factor on the variable actions 3.7.5.3. Tensile force T d;mesh in the geosynthetic The main principle of this method assumes that the entire vertical load acting between two inclusions is a , resulting in tension in the geosynthetic and in considering that no load is being transmitted to the soil between the inclusions. The BS8006:2010 Standard gives the relation between the tension in the geosynthetic T and both W T, the vertical load between two inclusions, and the geosynthetic deformation d: ( s a ) s v , geo ( s a) W T 1 1 1 1 = (force per linear meter) (5.27) T d ;mesh 2a 6 d 2a 6 d with: WT v, geo (force per linear meter) This equation with two unknowns Td;mesh and d can be solved either by using the forcedeformation law of geosynthetics (with introduction of the tensile stiffness of the geosynthetic) or by taking into account a maximum deformation criterion (called the reference deformation). 3.7.5.4. Reference deformation It is necessary to consider the deformation of the geosynthetic to calculate the mobilized tension T d;mesh.
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In a ULS situation, the reference geosynthetic deformation is the one selected by the BS8006 Standard (2010), i.e.: d = 6%. For a load transfer platform thickness H M > 0.7 (s-a), the reference deformation must not exceed this maximum long-term value of 6%. For thinner embankments (e.g. when the condition H M > 0.7 (s-a) has not been satisfied) and for which the load transfer is not guaranteed, this reference deformation must be lowered to values of less than 3% in order to reduce the risk of differential deformation at the load transfer platform surface. In this case, verification in an SLS situation becomes necessary to ensure that the differential deformation at the load transfer platform surface is acceptable. It must be noticed that the value of the partial coefficient the reference deformation.
creep also
depends on the choice of
The reference geosynthetic deformation must include the initial deformation as well as the creep deformation: the initial geosynthetic deformation is necessary to develop reaction forces. Moreover, the long-term deformation (due to creep) must be limited in order to ensure that localized, time-delayed deformations do not occur on the embankment surface. The post-construction creep deformation of the geosynthetic must be reduced to a minimum so as to prevent localized differential deformations at the embankment surface, while not exceeding 2% over the structural life cycle. This deformation is determined on the basis of indications provided in the ISO/TR 20432 guide. These two criteria would nee s isochronous load-deformation curves (Fig. 5.41).
Figure 5.41: Verification of deformation criteria and choice of partial factor creep on the geosynthetic isochronous load-deformation curves (according to the NF P 94 270 Standard).
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3.7.6. Tensile force when subjected to active slope forces
If horizontal forces caused by the active earth forces of an embankment are not fully dissipated, it is necessary to install a horizontal reinforcement at the embankment base. This reinforcement might also serve to limit lateral soil displacements and therefore any displacement of the inclusions. The maximum tensile force T d;thrust;max mobilized in the geosynthetic by the embankment lateral active forces is calculated below the embankment crest (Fig. 5.42): Td;thrust;max = 0.5 . K a ( . r . H R + 2 G . g + 2 Q q).H (5.28) with: HR : embankment height above the geosynthetic, K a: coefficient of active earth pressure of the embankment: K a tan
2
d ' 4 2
(5.29)
K a is calculated with the design value d (using the Design Approach 2, the value of equals 1 meaning that the design value d quals the characteristic value): unit weight of the embankment; r : g: permanent excess vertical load; q: variable excess load; partial factor on the soil unit weight; : G: partial factor on the permanent actions; Q : partial factor on the variable actions. Beneath the embankment slopes, the tensile force Td;thrust mobilized in the geosynthetic by the embankment lateral active pressure decreases with distance from the slope crest; this force may be calculated at any point based on the embankment slope and thickness above this given point.
Figure 5.42: Configuration examined at the edge of the embankment.
Remarks: The coefficient creep required to determine the design long-term strength R t;d is obtained by adopting the same reference deformation value as that used for vertical loads (Section 3.7.5.4). It is important to note that this configuration may also induce lateral displacements of the compressible soil capable of creating bending moments in the inclusions that also require verification. 212
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3.7.7. Determination of the geosynthetic(s)
s longitudinal direction, the geosynthetic must display an allowable strength R tL,d such that the following condition is met: Td;mesh < R tL;d (5.30) Td;mesh: tensile force mobilized in the geosynthetic subjected to the action of vertical loads applied to a unit cell (see Section 3.7.5.3). In the embankment's transverse direction, the geosynthetic must display an allowable strength R tT,d such that: Td;mesh + Td; thrust;max < R tT;d (5.31) Td;thrust;max: tensile force mobilized in the geosynthetic subjected to lateral active slope forces (Section 3.7.6). 3.7.7.1. Anchorage length computation In most instances, this verification is done in the transverse direction and may at times prove necessary in the longitudinal direction at the boundary of the treated zone. In all cases, the geosynthetic anchorage length is limited to the available footprint L ht, which depends on the embankment geometry (Fig. 5.42). In the specific case where the length L ht is not suitable for creating a sufficient one-layer anchorage, it would be necessary to introduce a trench-type or overlapping anchorage type construction (see Chapter 3: Execution Conditions). The length Lfr , which is measured from the crest of the slope, is the length required to mobilize by friction (on a single side) the strength relative to lateral forces (block thrust) (Fig. 5.42). This length is expressed as follows (BS8006, 2010):
L fr
T d ;thrust ;max
r h tan d '
with: Td;thrust;max: r : h: :
R;h R; f
(5.32)
tensile force in the geosynthetic due to lateral pressure on the embankment slope unit weight of the embankment; average embankment height in the anchorage zone (corresponding to L fr ); reduction coefficient of the soil-geosynthetic interface friction:
tan geo tan ' d
(5.33)
: design value of the angle of friction of the soil atop the reinforcement layer (according to the Design Approach 2, the value equals 1, and the design value d equals the characteristic value) : design value of the angle of friction of the soil-geosynthetic interface R,h : partial factor of the sliding resistance (equal to 1.1 with the Design Approach 2 as per EC7) R,f : partial factor of the soil-reinforcement bond resistance. It is proposed herein to adopt the value R,f = 1.35, in compliance with the NF P 94 270 Standard (Design Approach 2).
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s longitudinal direction, length L aL, as measured from the last inclusion needed for mobilization of anchorage forces by friction on both the upper and lower faces of the geosynthetic, is such that (BS8006, 2010): T d ;mesh R ;h R ; f LaL (5.34) ' '
r h 1 tan d 1 2 tan d 2
': ': h:
design value of the angle of friction of the soil above the geosynthetic reinforcement design value of the angle of friction of the soil below the geosynthetic reinforcement average height over length LaL.
In the s transverse direction, length LaT, as measured from the last inclusion (Fig. V.42) needed for mobilization of anchorage forces by friction on both the upper and lower faces, is such that (BS8006, 2010): T d ;mesh T d ;thrust R ;h R ; f LaT (5.35) ' '
r h 1 tan d 1 2 tan d 2
h: average embankment height over length L aT Td;thrust:tensile force in the geosynthetic due to active embankment pressure, evaluated in the plane of the outside edge of the last inclusion head. Remark: In the absence of a detailed calculation to derive the T d;thrust force value, it would be a safe assumption to adopt T d;thrust;max value when computing L aT (see Fig. 5.42).
3.7.7.2. Special case of reinforcement layer overlapping The length of overlapping can be justified from the previous equations by: Using the force corresponding to the direction of the overlap; Replacing the term (2tan'd2) by the geosynthetic-geosynthetic friction tangeo-geo. Remark: The angle of friction geo-geo is given by the manufacturer. 4. LIMIT STATE CONSISTENCY VERIFICATIONS 4.1. Inclusion behavior 4.1.1. Behavior at the tip
It must be verified that the force being mobilized does not exceed the limit value calculated in accordance with the principles set forth in both Eurocode 7 and the National Application Standard (NF P 94 262): Limit value of the tip resistance: (pressuremeter method) R b = k p . pl A (penetrometer method). R b = k c . qc A The values of k p or k c are those found in either Eurocode or any of the special specifications. Remarks: The conventionally-defined R b values refer to a settlement at the head equal to 10% of the inclusion diameter. In the case of inclusions beneath an embankment and even when they contribute towards bearing capacity and stability of the structure, this threshold proves 214
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irrelevant since settlement at the tip is not necessarily limited to 10%. In order to introduce other R b values than those calibrated on a 10% settlement, it is required to interpret the results of an instrumented load test on an inclusion of the same type as those actually installed. The k p or k c value depends on the relative embedment depth, according to the relationship given in the NF P 94 262 Standard. 4.1.2. Behavior along the shaft
4.1.2.1. Positive friction in the bearing layer and in the compressible soils below the neutral plane It must also be verified that the value of friction mobilized under the neutral plane does not exceed the limit value qs calculated in accordance with the principles set forth in both Eurocode 7 and the National Application Standard (NF P 94 262): The limit value of lateral friction q s is evaluated by either the penetrometer or pressuremeter method; The qs values are listed in the NF P 94 262 Standard or else in the specifications intended for the given technique; otherwise, experimental values established onsite are to be used. Remark: It is to be observed that friction mobilized in the vicinity of the neutral plane tends to be small, independently of the maximum friction at this elevation (Fig. V.43). In some cases, it may be preferable for the load-bearing capacity verification not to consider the total length below the neutral plane, but instead a reduced length from the tip.
Figure 5.43: Friction mobilized in the vicinity of the neutral plane.
3.7.7.2.Negative friction above the neutral plane It must be verified here that the friction neutral plane does not exceed the limit value v (where v calculated against the inclusion). Ktan is the empirical factor defined in Chapter 2.
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Remarks: The choice of the Ktan reference value must be made judiciously since this factor is pivotal to the overall design and influences to a different extent the maximum force in the inclusion and the resultant settlement. This verification is mandatory when introducing finite element modeling; it consists of verifying values of the ratio v at all points on the inclusion above the neutral plane.
4.2. Load transfer platform behavior
This verification consists of establishing, for the applied external loading, the maximum allowable stress value at the inclusion head that's compatible with both the load transfer platform material characteristics and the structural geometry. 4.2.1. Method justification
4.2.1.1. Experimental results Load
transfer mechanism on the inclusion head:
The mobile bottom tray tests in a centrifuge gave, for various geometric configurations, the maximum values reached at the inclusion head (Okyay, 2010). The results obtained with a granular load transfer platform placed beneath a loaded rigid plate (ground slab analogy) provide a very worthwhile set of results, as they correspond to a material whose shear characteristics were experimentally measured for different in situ densities of the material. These results were obtained for various area replacement ratios and load transfer platform thicknesses HM (with HM/D = 1.4 to 2, with D being the inclusion diameter). Figure 5.44 presents an example of the variation of the load transfer on an inclusion head in the case of a ground slab.
Figure 5.44: Load transfer ratio on an inclusion head vs. relative settlement y/D during a centrifuge test with a mobile bottom tray.
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Characterization of the load transfer platform material behavior:
The load transfer platform material, installed at 85% of the Relative Density Index value (I D), displays an angle of friction equal to 42°, in association with a peak phenomenon (Fig. 5.45). For ID = 60%, no peak was observed. The angle of friction obtained at the maximum load is equal to 38°; this value is representative of the critical state.
Figure 5.45: Characteristic curves of shear tests on the material composing the load transfer platform for moving bottom tray tests
4.2.1.2. Method evaluation based on the Prandtl failure diagram It is proposed here to calculate the limit value of the stress at the inclusion head based on the failure diagram developed by Prandtl (Fig. 5.46).
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Figure 5.46: Prandtl's failure diagram in the load transfer platform.
The relations expressing conservation of force q p+ + (1-) qs+ = q0 (5.36) and the local e s diagram q p+ = Nq q s+ (5.37) constitute a system of equations that allows the calculation of the maximum limit stress value q p+ at the inclusion head for a given situation (, q0), when the coefficient Nq is known. Remarks: Equation (5.37) neglects the surface term 0.5 B N whose contribution remains c, which is not applicable to a purely frictional material; Equation (5.37) is applicable to the axisymmetric problem of stresses around an inclusion head of diameter B, just as it applies to the plane strain problem around a continuous shear wall of width B. The shape factor s q associated with the coefficient Nq actually equals 1 in both cases, according to Terzaghi; The above remark, indicating a value of 1 assigned to the shape factor s q associated with the coefficient Nq, confirms that the axisymmetric problem may be treated like a plane strain problem, yet without requiring any corrective term. This point will be utilized in order to take edge effects into account.
The values of factor Nq are respectively Nq = 85.4 (for q = 48.9 (for Remark: As indicated in Section 4.2.1.1, the value of depends on its Relative Density Index value I D.
The values of the stress at the inclusion head, calculated using the N q values, were compared with the values measured in the tests and experiments presented in Section 4.2.1.1 (Fig. 5.47). It appears that with Nq(42°), the calculated design values overestimate the experimental values for the lowest area replacement ratio ( = 1.25%, purple triangles). The choice of Nq(38°) value leads to a much better agreement with experimental values. The magnitude of mobile bottom tray displacements (representing the effect of a settlement on the supporting soil) required to reach the limit values q p+ reflects a significant increase in the load transfer platform volume and, hence, a reduction of its compaction. The angle
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at constant volume) turns out to be better adapted to the final situation.
Figure 5.47: Comparison of calculated and measured values of limit stress on the inclusion head.
4.2.1.3. Conclusions The limit stress value at the head of inclusions placed at the center of a mesh may be determined on the basis of Equations 5.36 and 5.37, by adopting for the N q coefficient value the calculation result using the angle of friction at the critical state (i.e. shear at constant volume). This value is less than the peak friction value for materials with a Relative Density Index (ID) above 60%. It is suggested herein to introduce the N q coefficient in association with the shape factor value sq previously proposed by Terzaghi, which equals 1 regardless of the foundation shape. This choice has been adopted in order to compare the experimental results with theoretical values. The Nq value associated with the Prandtl mechanism is representative of situations in which the load transfer platform thickness exceeds the height H max for the full failure mechanism to develop. The ratio H max/D increases with the angle of friction, as illustrated in Table 5.3. For HM/D less than Hmax/D, the apparent load-bearing capacity coefficient Nq* would be more favorable than the coefficient derived by the Prandtl mechanism, and it remains a safe assumption to neglect this increase.
Figure 5.48: Geometric parameters describing the Prandtl failure diagram.
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Table 5.3: Characteristic values of Prandtl diagram parameters.
Nq Hmax/D Lmax/D L1/D
30 18.4 1.59 4.29 2.64
35 33.3 1.90 5.77 3.39
38 48.9 2.15 7.00 4.00
40 64.2 2.35 8.01 4.51
In a comparable manner, it may be noted that for a distance between inclusions of less than 2L1 (Fig. 5.48), the failure surfaces associated with two neighboring inclusions overlap. For meshes smaller than this threshold, the factor N q* is thus also higher and moreover neglecting this increase would not compromise safety. The width L1 is therefore the value to take into consideration when verifying the possible interference between inclusions, as illustrated in Figure 5.49 showing the results for a finite element model of an elementary unit cell modeling the mobile bottom tray system (Okyay, 2010). The domain of plastic points (shown in red) is actually very similar to Domain L1 of the Prandtl mechanism.
Figure 5.49: Numerical simulation of a moving plate test below a slab on grade, demonstrating the extent of the plastic zones.
4.2.2. Computation of limit transfer at the inclusion head over the general main section
4.2.2.1. Introduction In this section, let's consider a network of rigid inclusions with diameter D = 2.r p installed on a square mesh pattern of dimension s, covered by a load transfer platform of thickness H, defined by ) and exposed to a uniformly-distributed load q 0.
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Figure 5.50: Problem hypotheses and geometry.
Remark: The load from the load transfer platform weight .HM is separated here from the loading q 0 applied on the load transfer platform (eventually composed of both permanent loads and operating loads).
When the load is applied on the system and depending on the geometry and nature of this loading, two types of axisymmetric limit equilibrium can be generated between the applied stress q0, the stress at the inclusion head q p+ and the stress applied on the soil between inclusions qs+. s
diagram:
The first limit equilibrium diagram within the load transfer platform may be modeled by the Prandtl diagram, which associates a Rankine active limit state domain (I) above the inclusion head, with a domain delimited by a logarithmic spiral arc (II) and another Rankine passive limit state domain outside the inclusion head (III).
Figure 5.51: Prandtl failure diagram in the load transfer platform.
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Shear cone: The second limit equilibrium diagram within the load transfer platform can be modeled by a vertical cone section opening onto the load transfer platform surface, originating from the inclusion head and forming an angle ' with respect to the vertical plane equal to the angle of friction of the load transfer platform material.
Figure 5.52: Failure diagram in the load transfer platform using a shear cone type model.
For a given external load q0, these two types of limit equilibrium serve to define the maximum load that may be concentrated at the inclusion head q p+, i.e. the maximum system efficiency at the level of the inclusion head s note that an increase in load q 0 allows an increase in stress at the inclusion head q p+, and that the failure of the system will only occur when it no longer becomes possible to increase the applied load q 0. Remark: The tests and experiments conducted in the centrifuge and on discrete models have demonstrated that: The Prandtl model failure diagram is applicable when considering the material's critical angle (large deformations within a compacted material) (Section 4.2.1.2); The shear cone failure diagram is associated with the peak angle of the material (mobilized for small deformations).
limit states at the ULS This verification is performed by implementing Design Approach 2 from EC7, with the following combination of partial factor datasets: For the Prandtl diagram: According to Design Approach 2 from EC7 and based on Prandtl's diagram, the limit stress at the inclusion head q p+ can be determined from: the stress applied on the supporting soil q s+; ' and ; and the following formula: c' q p s q . N q q s s C . N c s . N .r p (5.38) c'
where: s, sc, s q are the inclusion head shape coefficients
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N q tan 2 4 '
'
N c N q 1 cot '
2 e
. tan ' '
'
N 2. N q 1 tan '
'
= = = 1 (set M1 as defined in EC7). Remarks: For a relatively thin load transfer platform, the platform weight is typically neglected and so are the term s .N.r p. . For granular load transfer platforms, the value of the shape coefficient s q will be set equal to 1 regardless of the foundation shape, in agreement with Terzaghi.
For the shear cone: According to Design Approach 2 from EC7 and from the shear cone diagram depiction, the limit stress at the inclusion head q p+ is determined using the applied external load q0, ' and in the following set of equations:
Figure 5.53: Technique with shear cone development.
If H M H C q p
R r p tan'
:
H M RC ² 1 RC RC ² q0 1 RC ² 1 c' 3 r p ² r p r p ² tan' r p ² c'
(5.39)
where :
' '
RC r H M tan
If H M H C q p
H c 3
R r p tan'
:
1 R² c' R² R R² R ² 1 1 H M H C q0 r p ² ² ² ' ² r r r tan r p p p c' p
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223
where: s R
= = = 1 (set M1 as defined in EC7). Remarks: For HR > HC, the shear cones of adjacent inclusions overlap, and the surface area of each inclusion's zone of influence remains equal to s2; In the case of an embankment supported by rigid inclusions, the height H R and load q0 to be used in these equations are respectively the total height of the embankment plus load transfer platform and the surcharge load applied at the top of the embankment. The limit stress q p+ defined by Equation 5.39 or 5.40, corresponding to a shear cone opening onto the load transfer platform surface only exists as a design parameter for thin load transfer platforms that are not covered by any rigid structural element such as a raft, a slab on grade or a footing. It is the case for example of a road embankment on which an operating load is being applied.
Moreover, the stress applied on the supporting soil q s+ is limited at the ULS by the allowable stress v,d referenced in the current standards (with set R2 defined in EC7), e.g. for the pressuremeter method: qs+ < v,d = k p.ple*/(R,v R;d) (5.41) where: R,v = 1.4 at the ULS (set R2 defined in EC7-1), combined with the appropriate model coefficient R;d defined in the National Application Standard NF P 94 261 (for shallow foundations). The value of v,d is derived from the geotechnical soil investigation. Remark: This value should be determined in a realistic manner since an overly conservative value (e.g. 0) would render any design of the load transfer platform impossible.
Finally, the stress applied at the inclusion head is limited by the load-bearing capacity of the inclusion as well as by the allowable stress in the inclusion material, i.e.:
Rb R ,d b R s R ,d s ; f cd 2 r p
q p+ < q p ,max Min
(5.42)
where, referencing the National Application Standard 94.262 and the " ground model " approach: R b is the ultimate soil resistance at the tip of the inclusions; R s is the ultimate shaft friction under the neutral point; b = s = 1.1 at the ULS (set R2 defined in EC7-1); R,d = 1.25 (model coefficient); f cd as defined in Section 3.1.1.
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Therefore, in the (q s+; q p+) plane and independently of the load level, the domain of allowable stresses at the ULS in the load transfer platform is determined by Equations 5.38, 5.41 and 5.42, which correspond respectively to curves 1a, 2 and 3 (shown in Fig. 5.54). Under certain conditions, this domain may also be partially limited by the curve (1b) associated with Equation 5.39 or 5.40 corresponding to a shear cone opening onto the load transfer platform surface. This additional limit only exists as a design parameter for thin load transfer platforms that are not topped by any rigid structural element such as a raft, a slab on grade or a footing.
Figure 5.54: Allowable domain of stresses at the load transfer platform base.
Remark: For illustration purposes, the curves in Figure 5.54 above (1b) associated with the Equation 5.39 or 5.40 correspond to the case of a thin embankment not covered by any rigid structural element, with the additional constraints: Load resulting exclusively from the weight of a load transfer platform with variable thickness (shown in red); The load transfer platform has a given thickness and an external load applied at the surface (blue).
4.2.2.3. Load conservation principle For a given load q (for which the partial factors of the set A1, as defined in EC7 have been applied), stresses q0, qs+ and q p+ are in equilibrium and required to satisfy the load conservation equation:
q 0 G . . H M s 2 q s s 2 .r p 2 q p .r p 2
(5.43)
The mobilized stress parameters (qs+, q p+) must simultaneously satisfy the load conservation equation (5.43) while falling within the allowable domain defined above in Figure 5.54. For a given load q 0, the allowable limit stress in the load transfer platform at the inclusion head q p;d+ is thus determined by solving the system of equations associated with the curves (1a), (1b), (2), (3) and (4). The principle is illustrated in Figure 5.55. For this load q 0, the allowable domain can be reduced to the intersection of segment (4) with the shaded surface (delimited by curves derived from Equations (1a), (1b), (2) and (3)). Justications
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+
Figure 5.55: Determination of q p;d (case where qpmax < sq.Nq.qsmax + sc.Nc)
The calculated design limit q p;d+ thus depends on the structural load q 0, but remains independent of the deformability of the various soil layers: this value solely depends on the applied load q0, system geometry (load transfer platform thickness H M, mesh size s , inclusion ) of the load transfer platform material. In contrast, the value (qs+; q p+) actually mobilized at the load transfer platform base lies inside the allowable domain, on segment (4) of the load conservation line, at a position that depends on the deformability of the various soil layers. This value turns out to be heavily dependent on the deformability of the soil layer located directly beneath the load transfer platform; the greater s compressibility, the closer the mobilized value moves towards the allowable limit value. 4.2.2.4. System efficiency and load -bearing capacity The system efficiency at the load transfer platform base is used to measure the proportion of total load in the inclusion; this efficiency is expressed as follows:
E
q p .r p
2
q0 . H M s 2
(5.44)
The maximum efficiency that can be mobilized by the soil reinforcement at the level of the load transfer platform base (eventually corresponding to the line in Equation (1), (3) or (1b)) decreases with the applied load, whereas the efficiency actually being mobilized during loading tends to increase with the applied load. A variation in external load q 0 moves the point representing the equilibrium in the plane (q s+; q p+) along a curve that, for high loads, tends towards the asymptotes of Equation (1), (1b) or (3). In other words, the increase in applied external load q 0 increases the efficiency towards its maximum value yet can never cause internal failure of the load transfer platform by intersecting with the equation (1) line (Fig. 5.56).
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+
+
Figure 5.56: Evolution of the equilibrium point (q p ;qs ) vs. applied load
The maximum allowable loading on the load transfer platform + reinforced soil system corresponds to the uniform stress qmax applicable to the system prior to its failure. This maximum load ( system load -bearing capacity) results from summing two terms: qmax s 2
v ,d s 2 .r 2 q p ;u .r 2
(5.45)
The potentially mobilized stress at the level of the inclusion head q p;u can then be determined by employing the following relation: q p ;u
c' Min s q . N q v ,d sC . N c s . N .r p ; q p max c'
(V5.46)
In the specific example illustrated in Figure 5.57, the maximum load corresponding to a uniform stress qmax on the mesh results in a stress v;d applied to the soil around the inclusion and the stress q p,max on the inclusion head.
Figure 5.57: Maximum stress q max on the load transfer platform + reinforced soil system. (Note: The case illustrated corresponds to one in which q p;u = qp max.)
4.2.2.5. Geometric considerations In the plane (O; x; y), the polar equation of the logarithmic spiral in the Prandtl scheme is set up as: r r 0 e Justications
tan ' 4 2
(5.47) 227
Depending on the intrinsic load transfer platform parameters, the main dimensions of this logarithmic spiral are as follows:
Figure 5.58: Main dimensions of the logarithmic spiral.
with: height of the Rankine active limit state domain: D h1 tan 4 ' 2 2 the extent of Rankine active limit state domain: r 0
D e
tan ' .
(5.48)
2
2 cos 4 ' 2
(5.49)
tan ' . cos 4 ' 2 2 e D cos 4 ' 2
L 2 r 0 cos 4 ' 2 h2 d 1
r 0 e r 0 e
' tan ' . max 4 2 ' tan ' . max 4 2
. sin max h1 . cos max
(5.50)
(5.51)
(5.52)
the angle at the top of the logarithmic spiral:
1 max tan 1 ' tan
(5.53)
Application example: With the following hypotheses: D = 0.30 m s = 1.75 m q0 = 50 kPa C = 0 kPa = 38° the following values are obtained: q p;d+ = 1,160 kPa
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h1 = 0.31 m h2 = 0.34 m L = 2.10 m d1 = 0.50 m In order to allow the logarithmic spiral to fully develop within the load transfer platform, the platform must have the following minimum dimensions: HM > h1 + h2 d>L Remarks: For the case of thin embankments not covered by a structural element (such as a footing, slab on grade, raft, etc.), then these criteria are used to determine a minimum thickness Hmin to optimize system efficiency. Otherwise, the load potentially mobilized at the inclusion head (i.e. efficiency) is reduced and failure occurs due to shear around a cone developing to the upper embankment surface. The limit load is controlled by the cone weight to which the double effect of cohesion and surface load must be added. Experiments have led to the conclusion that the cone angle is equal to the peak friction angle of the material. For thin load transfer platforms (H M < h1 + h2) under a structural element (e.g. a footing, slab on grade or raft), since in this case the failure mechanism can only develop over a reduced height, then the potentially mobilized load at the inclusion head is greater than the load obtained using the Prandtl diagram. Without a detailed study, the use of the value obtained with the Prandtl scheme for load transfer platform thicknesses of less than (h1 + h2) will lead to a safe design. 4.2.3. Calculation of the limit load transfer on the inclusions at the edge of the structure
4.2.3.1. Case of zero footing overhang 4.2.3.1.1. Presentation The configuration adopted herein is that depicted in Figure 5.59. The edge of the inclusion coincides with the edge of the footing. The load applied on the footing turns out to be nearly entirely retransmitted onto the inclusion head. The vertical stress applied on the soil at the level of the top of the inclusions is the stress H generated from the surrounding ground.
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Figure 5.59: Extreme case of an inclusion at the footing edge with an overhanging load transfer platform.
This value H only depends on the geometry and not on the footing load; it controls the failure mechanism capable of being developed from the top of the inclusion The limit value of the q p+/H ratio defines the coefficient Nq* associated with this case. 4.2.3.1.2. N q* evaluation method It is possible to determine the value of the coefficient Nq* simply by decomposing the mechanism into two juxtaposed failure mechanisms: an active limit state equilibrium (above the inclusion head), and a passive limit state equilibrium (elsewhere), as illustrated in Figure 5.60. Following the remark presented in Section 4.2.1.2, this analysis may be conducted as a plane strain problem.
Figure 5.60: Decomposition into an active limit state equilibrium and a passive limit state equilibrium.
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Since the equilibrium considered herein are those of a weightless medium, the intermediate stress q in the plane separating the two domains is uniform. This stress q represents respectively: Volume 1 (left side of the figure): active earth pressure at the angle p+ in the weightless medium: q = q p+ K q1 (5.54) Volume 2 (right side of the figure): passive earth pressure reaction at the angle stress H in the weightless medium: q = H K q2 (5.55) The coefficient K q1 (respectively K q2) is the surcharge pressure transmission coefficient in a weightless medium relative to the active limit state (respectively, passive limit state). Its analytical expression was established by Caquot and Kérisel (1966) in the most general case (Fig. 5.61). These expressions become simplified in the present case in recognizing that: 0 = = = 0. By applying Equations 5.55 and 5.56, it results that the ratio q p+/H is equal to K q2/K q1; this ratio is therefore similar to a load-bearing capacity factor Nq*. Remarks: This approach may be extended to the case of a material exhibiting cohesion the natural soils (and not the load transfer platform) may require introducing an additional cohesion term. Neglecting natural soil cohesion constitutes a safe assumption.
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Figure 5.61: Transmission of a surcharge pressure in a weightless medium (Caquot and Kérisel, 1966).
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4.2.3.1.3. Case of a zero footing overhang and an extended load transfer platform The failure mechanism develops within a homogeneous medium. The Prandtl solution therefore is directly applicable.
Figure 5.62: Configuration of the zero footing overhang and extended load transfer platform.
It is worthwhile however to compare the value N q(Prandtl) with the value obtained using the previous approach consisting of breaking down the problem into two juxtaposed states of equilibrium. The inclination of stress q in the vertical plane separating the two domains is chosen equal to the angle of friction Table 5.4 confirms that it is indeed acceptable to assimilate the term N q* = K q2/K q1 with Pr s load-bearing capacity factor. Table 5.4: Comparison of N q* values with Prandtl's load-bearing capacity factor Nq.
Nq (Prandtl)
1, Kq2( /-1) 5.804
18.43
1.00
Nq*= K q2/Kq1
Nq*/Nq
30
18.40
Kq1(1 /1 0.315
33
26.09
0.285
7.425
26.05
1.00
35
33.30
0.266
8.850
33.27
1.00
38
48.93
0.240
11.745
48.94
1.00
40
64.20
0.224
14.393
64.25
1.00
1
This observation shows that a decomposition of the bearing capacity problem into two juxtaposed active - passive limit states of equilibrium constitutes a valid approximation. It is proposed herein to extend this approximation to the case where the two domains are made of different materials.
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4.2.3.1.4. Case of a zero footing overhang and a platform limited to the footing footprint
Figure 5.63: Configuration of the zero footing overhang and a platform limited to the footing footprint.
In this situation, Volume 1 is characterized by the angle of friction of the granular platform (1 il (2 stress q in the vertical plane separating the two volumes must be set equal to the smallest angle of friction, which in theory would be the friction angle of the surrounding soil. This approach was applied combining a range of values for 1 - 40°] for the platform and another range of values 2 - 30°] for the surrounding soil. Table 5.5 summarizes the Nq* values over the two defined intervals. Figure 5.64 displays the same results graphically and then compares them to the N q values that would have been obtained with a load transfer platform extending beyond the limits of the structure. For a platform whose angle of friction is 1 q applicable to the main central portion of the structure, equal to 33.3, is divided for the extreme case of an inclusion placed at the edge of the structure by a factor of 2 or 3, depending on whether the angle of friction of the surrounding soil is 25° or just 20°.
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3 8 7 0 4 4 . 8 . 6 . 8 . 0 . 8 0 2 5 8 1 2 2 2 2
* q N
.
2
) 4 4 4 4 4 0 0 0 0 0 8 8 8 8 8
2
'
(
l i o S
)
1
5 1 ( 2 3 1 . q 0 / K 1
n o i t c i r f f o e l g n a ( n o i s n e t x e d e t i m i l f o m r o f t a l p r e f s n a r t d a o l a r o f r o t c a f * q N e h t f o s e u l a V
2
l i o S
'
(
. . . . . 4 4 4 4 4
K
)
1
6 0 ( 2 3 1 . q 0 K /
2
2 0 1 7 5 2 2 2 2 . . . 0 0 0
3 0 2 . 0
3 5 9 5 4 6 4 . 5 . 0 . 2 . . 0 3 4 9 1 1 1 1 1
* q N
) 2 2 2 2 2 7 7 7 7 7 8 . 8 . 8 . 8 . 8 . (
'
2 q
K
2 2 2 2 2
)
1
4 0 ( 2 3 1 . q 0 K / 1
° 5 1 =
0 9 0 1 7 4 2 0 2 . 2 . 2 . 2 . 0 0 0 0
8 6 2 8 4 5 9 . . 8 . 5 . 6 . 0 6 7 8 9 1
* q N
) 9 9 9 9 9 2 2 2 2 2 ( 1 1 1 1 1
2
l i o S
2 q
K
. . . . . 2 2 2 2 2
)
1
5 0 ( 2 3 1 . q 0 / K 1
1 ( q
N
r m e r d f o a s f 1 t o n L a a r t l p
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2 q
: 5 . 5 e l
b a T
7 0 2 . 0
) 2 2 2 2 2 0 0 0 0 0 0 0 0 0 0
1
l i o S
8 6 5 7 5 2 2 2 2 . . . 0 0 0
8 1 1 1 1 0 . 7 . 0 . 1 . 7 . 3 4 6 8 9 1 1 1 1 1
* q N
. . . . . 5 5 5 5 5
K
1
2 q
1 0 0 7 5 2 2 2 2 . . . 0 0 0
2 0 2 . 0
4 . 1 . 3 . 9 . 2 . 8 6 3 8 4 1 2 3 4 6
0 3 5 8 0 3 3 3 3 4
235
As a consequence, these values indicate that under the same load transfer platform conditions with 1 below the surface of the surrounding soil does not exceed 160 kPa (soil 2 115 kPa (for a soil with 2
Figure 5.64: Comparison of N q* values (case of a zero overhang platform) with N q values for a load transfer platform extending beyond the edge of the structure
4.2.2.6.Case of a footing overhang greater than L max
If the footing largely extends bey s mechanism may fully develop in the load transfer platform, but becomes controlled by the average stress q s+ applied to the soil between inclusions. The coefficient Nq, to be used in Equation 5.39, is the Prandtl value for angle 1 transfer platform. It may be considered herein that this condition is fulfilled when the footing extends beyond the edge of the inclusion by more than L max (Fig. 5.48). The limit stress value obtained at the inclusion head via the Prandtl mechanism will then be denoted q p+(P). In the special case of a purely frictional granular load transfer platform, Equations 5.38 and 5.43 allow establishing the following relationship q p+(P) function of the area replacement ratio : N q q 0 M H M (5.56) q p ( P ) ( N q 1 ) 1 where: HM: load transfer platform thickness between the inclusion head and the footing; angle of friction of the load transfer platform; M: unit weight of the load transfer platform.
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4.2.3.3. Case of an intermediate overhang between 0 and L max This case is illustrated in Figure 5.65. The failure mechanism in Volume 2 (passive limit state equilibrium) is controlled by both the stress q s+ and the stress H. The factor Nq* to be evaluated thus also depends on the ratio L/D (L: structural overhang, D: inclusion diameter). The transmission coefficient for passive surcharge pressure can no longer be expressed analytically. Its direct calculation can be performed by applying a Yield Design failure approach. This method for given values of q s+, H and L allows determining the passive limit state earth pressure in the vertical plane separating Volumes 1 and 2. These computations wer for several configurations. Several calculations were performed between the two extreme cases of a load transfer platform largely extending beyond the edge of the structure and the case where the load transfer platform was limited to the edge of the footing. In this case, the passive earth pressure reaction mechanism was actually developing in both the load transfer platform and surrounding soil.
Figure 5.65: Case of a foundation overhang less than Lmax.
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Figure 5.66 presents, for illustration purposes, the limit stress values q p+ derived by this approach for the two extreme situations of a load transfer platform largely extending beyond the footing and limited to the edge of the footing. This study demonstrates that the limit stress on the inclusion head varies rather linearly between the two values, associated respectively with: No overhang, i.e. load transfer platform limited to the edge of the footing: q p+(L = 0) = N q* H; An overhang of L, greater than L max, (load transfer platform extending well beyond the edge of the footing) for which the limit value is that produced by the Prandtl mechanism q p+(P), calculated with Equation 5.57 for a given load q 0 and an area replacement ratio .
Figure 5.66: Variation in limit stress on the inclusion head vs. extent of the load transfer platform beyond the footing edge.
Remark: The case studied herein is that of a load transfer platform with thickness HM = 30 cm, an inclusion of diameter D = 30 cm, angle of friction 1 platform and 2 ratio HM/D has not been neglected).
The limit stress on the considered footing for a given overhang L can thus be estimated using a linear interpolation between the two extreme values q p+(L = 0) and q p+(P) (Fig. 5.67): L (5.57) q p L q p L 0 q p P q p L 0 L max
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determine the threshold threshold stress on the inclusion head by interpolating interpolating Figure 5.67: Principle 5.67: Principle used to determine between the extreme values for an overhang greater than L max and a zero overhang.
4.2.3.4. Edge effect combination In the general case, where more than one inclusion is installed beneath the footing, the edge effect effect analyze analyzed d above above only applies applies to a fractio fraction n of the inclus inclusion ion.. This This fractio fraction n obviou obviously sly varies depending on whether the considered inclusion lies at a corner or on a side of the footing. The limit stress q p+(L) only only portion of the perimeter, whereas the limit value calculated with Prandtl's mechanism, q p+ portion portion of the inclusion. inclusion. The selected value must therefore be a weighted average of these two terms. By analogy with the distribution of negative friction within a group of piles, as defined in Appe Append ndix ix H of Stan Standa dard rd NF P 94-2 94-262 62 (for (for Deep Deep foun founda datio tions ns), ), it is propo propose sed d to use use the following weighting relationship in order to establish the limit stress values on the inclusion head q p+ applicable to the different locations of the inclusions under the footing:
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Single row of inclusions q p ,a
q p ,e
1 3
2 3
q p ( P )
q p ( P )
2 3
1 3
q p ( L )
(5.58)
q p ( L )
(5.59) Figure 5.68
Several rows of inclusions (i) interior q p ,i q p ( P )
(5.60)
(a) corner q p ,a
7 12
q p ( P )
5 12
q p ( L )
(5.61)
(e) exterior q p ,e
5 6
q p ( P )
Figure 5.69
1 6
q p ( L )
(5.62)
4.2.4. Summary
The limit stress value at the inclusion head for an inclusion placed at the center of a mesh may be determined based on Equations 5.38 and 5.43, by adopting for the coefficient N q the value associated with the Prandtl mechanism (Table 5.3), along with a shape coefficient s q equal to 1. The angle of friction is the one found at the critical state (i.e. shear at constant volume). It is safe to neglect the increase in Nq when the load transfer platform is of limited thickness relative relative to the inclusion inclusion diameter. In the case of peripheral inclusions, the limit stress at the top of the inclusion depends on the relative position of the edge of the outermost inclusion to the edge of the footing (overhang L). Results obtained confirm the validity of the assumption that this stress varies linearly with L over the interval [L = 0, L max] (Lmax: width of the Prandtl mechanism, see Fig. 5.58 and Table 5.3) between these two extreme values: For For an over overha hang ng L grea greater ter than L max, i.e. the value q p+(P) associat associated ed with with the Prandt Prandtll mechanism as calculated by Equation V.56 in the configuration of a basic unit cell subjected to a uniform load q 0. The coefficient Nq only depends on the load transfer platform angle of friction (Table 5.5); No No overhang, i.e. the value q p+(L = 0) = N q* H; this value depends on the vertical stress H applied outside the footing at the level of the inclusion head as well as on the coefficient N q*, calculated using the angles of friction of both the load transfer platform and surrounding soil (Table 5.3).
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The value q p+ (L) (L) is obta obtain ined ed by line linear ar inte interp rpol olat atio ion n betw etween een thes thesee two two valu values es (Equation 5.57). To determine the limit values for different inclusions at different locations under the footing, different combinations of the weighted values of q p+(L) and q p+(P) are used depending on the actual location location of the inclusion with respect to the footing footing edge. Application example:
Figure 5.70: Layout 5.70: Layout of the example under study.
Load transfer platform thickness HM = 0.3 m, and angle of friction 1 Inclusion diameter D = 0.4 m Area replacement replacement ratio in the central central mesh: mesh: = = 0.2 0.2 2/1.22 = 8.7% Surrounding soil: angle of friction friction 2 = 18 kN/m 3 Influence of the ratio HM/D neglected Design load on the footing Q d = 2.2 MN (representing an equivalent uniform stress q 0 ~ 300 kPa). 1 Nq (P) = 48.9 (Table 5.3) Lmax/B = 7.0 (Table.3) Lmax = 7.0 7.0 0.4 0.4 = 2.8 m + The value q p (P) applicable for an overhang of L greater than 2.8 m: Nq = Nq(P) = 48.9 = 0.087 q0 + + MHM ~ 300 kPa (platform weigh ight MHM neglected) q p+(P) = 2,839 kPa (Equation 5.56) + qs (P) = 2,839/48 2,839/48.9 .9 = 58 kPa + The value q p (L = 0) for a zero overhang Nq*( *(1 2 (Table 5.5) + q p (L = 0) =Nq* H H = 13.05 13.05 0.8 0.8 18 18 = 188 kPa + yielding: q p (L) = 188 + 0.3/2.8 (2,839 188) 188) = 472 kPa and the following limit values at the inclusion inclusion head for: an interior inclusion q p,i+ = 2,839 kPa a corner inclusion q p,a+ = 7/12 7/12 2,839 2,839 + 5/12 472 472 = 1,850 kPa
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Note: Note: The previous calculations were performed assuming that: The The stress qs+(P) obtained in the interior grid remains less than the calculated value of the limit stress at the soil surface v,d; The maximum load in inclusion Q p,max satisfies the strength criteria relative to both the soil The and native inclusion material. Remark: In the case of a thin load transfer platform located under a rigid structure (such as a footing, slab on grade or raft), at the edge of this structure and under certain certain geomet geometric ric condit condition ionss (distan (distance ce from from the inclus inclusion ion compare compared d with with the distance to the edge of the structure, platform thickness, etc.), two failure modes may coexist: one described with the Prandtl mechanism, and the other for a plastic flow starting from the inclusion head extending at the surface to the edge of the structu structural ral element. element. The constru constructio ction n specif specificat ication ionss adopte adopted d for purpos purposes es of this this document typically enable avoiding the generation of plastic flows up to the ground surface; as such, no special verification beyond the one presented above is required herein.
Figure 5.71: Development 5.71: Development of failure failure m echanisms echanisms according to the extent of foundation overhang.
4.2.5. Special case of materials treated with hydraulic binders
Materials Materials treated with hydraulic binders binders reach a non-neglig non-negligible ible tensile strength. This feature is taken into account in the design process for pavement pavement layers. The failure mechanism may be correlated with the first crack (failure by shear or tensile failure). The recomme recommenda ndatio tions ns current currently ly impleme implemente nted d in road road work work (SETRA (SETRA-GT -GTS S 2000 2000 and Road Road Standards) provide indications on expected strength levels for a given treatment as well as the design limit values to be taken into consideration.
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In ligh lightt of the the curr curren entt stat statee-of of-t -the he-a -art rt,, it is prop propos osed ed here herein in to adop adoptt the the same same set set of recommendati recommendations. ons. Close attention attention must be paid to adopting a failure criterion compatible compatible with this tensile strength.
References BS8006 Code Code of Practice for Strengthened/reinforced soils and other fills. fills. Section 8, Design of embankments with reinforced soil foundations on poor ground, 2010. on s de sable - e e du projet national Bét on Sablocrete. Presses des Ponts, 1994. Berthelot P., Durand F., Glandy M., Frossard A A « « Dallage et modules de déformation des couches de sols ; applications aux renforcements de sols par inclusions et analyse du comportement du matelas de répartition ». XIV ECSMGE 2007, 2007, Madrid, Spain. Briançon L. L. « « ». ». Rapport 2-08-1-05, juillet 2008. s, Gautier-Villars, 1966. Caquot A., Kerisel J. - T ra raité de mécanique de s s ol Chevalie Chevalierr B. Étude s expér iment ale a le et numér ique de s t ran ran s fer ts ts de charge dan s le s matér iau x granulaires. Application aux renforcements renforcements de sols par inclusions rigides. rigides. Thèse Thèse de doctor doctorat, at, université Grenoble I Joseph-Fourier, soutenue le 5 septembre 2008. CUR Design Design guideline for piled embankments embankments.. CUR 226, 2010. s EBGEO Empfehl ung f ür den E nt wurf und d ie Berechn ung von E rdk rdk örper mit Bewehr ungen al Geok un stst offen. te E rdk t- oder l inienf örmi gen offen. I n: n: Bewehr t rdk örper au f punk t gen T raggl raggl iedern. Deutsche f ür G echnik e.V., e.V., (German Geotechnical Society), Ernst & Sohn, (Kapitel 9), 2010. Ge sell schaf t t f Geot echn Glan Glandy dy M., M., Fros Frossa sard rd A. « ». ». , n° 1, 2002, p. 45-53. Hewlett W.J., Randolph M.A. Analysis Analysis of piled embankments embankments. Ground Engineering , April 1988, p. 12-18. ISO/TR ISO/TR 20432 20432 Li gne gne s d irect r ri ce s pour l a dét erm ermination de la r ésist ance ance à long t erme erme de s s, 2007. g éo s ynt hétique s pour le renforcemen renforcement de de s s ol Jenck O. Le renforcement de s sol g ide s ver ti od él is s compre ssible s par incl usi usion s r i g ticale s. M od isation physique et n numér ique. Thèse de Doctorat, INSA Lyon, 29 novembre 2005. Lawson Lawson C.R. Servicea Serviceability bility limits for low-height low-height reinforce reinforced d piled embankm embankments ents. Proceedings GeoEng 2000, 2000, Melbourne, Australia. Lancaster: Technomic Publishing Co. NF EN 1997-1, Eurocode 7 7 C alcul g éot echn echnique. Partie 1 : Règles générales. (indice de classement C alc P 94-251-1) avec son annexe nationale (indice de classement P 94-251-2). NF P 11-213, DTU 13.3 - Dallages - C oncep onception, calcul et ex exécution, on, 2007. NF P 94-262 Justificatio Justification n des ouvrage ouvrage s g éot echn echnique s - - Fondations profondes profondes.. NF P 94-270 94-270 Calculs Calculs géotechniques Ouvrages de soutènement, Remblais renforcés et massifs en sol cloué, 2009. Nordic handbook Guideli Guidelines nes for reinfo reinforce rced d soils soils and fills, fills, Nordi Nordicc geosy geosynth ntheti eticc group, group, rev. rev. B, october 2005. Étude expér iment ale ts de charge dan s u n ma ssi f Okyay U.S. Étu ale et n numér ique de s t ran ran s fer ts f renforcé par g ide s. A ppl ication à de s ca s de chargeme chargemen nts st atique s et dynamique s. Thès Thèsee de incl usi usion s r i g doctorat, INSA Lyon, 24 novembre 2010. Pecker A. Capacity Capacity design principles for shallow foundations in seismic areas. Keynote lecture, XIth lecture, XIth European conference conference on earthquake engineering engineering , Paris, 1998. Salençon J. J. C alcul à analy se l imit e. Presses des Ponts, 1983. C alc à la r u pture et analy Schlosser Schlosser F. « Analog Analogies ies et différ différenc ences es dans dans le compor comportem tement ent et le calcu calcull des ouvrag ouvrages es de soutènement en terre armée et par clouage des sols ». n° n° 418, 1983. SETRA T ra rait emen ement de s sol s à la chau x et /ou au x l iants hydraul ique s ( GTS GTS ). A ppl ication à la isation de s remblais et de r éal is de s couche s de forme. forme. Guide technique, 2000.
SETRA-LCPC SETRA-LCPC Réalisation Réalisation des remblais et des couches de forme (GTR). Guide technique, 1992 (révisé 2000). Justications
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CHAPTER 6
Geotechnical investigations
1. GEOTECHNICAL ENGINEERING MISSIONS MISSIONS DEDICATED DEDICATED TO REINFORCING COMPRESSIBLE SOILS SOILS BY MEANS MEANS OF RIGID INCLUSIONS
This document serves to define, with reference to the NF P94-500 Standard on geotechnical missions, the set of preliminary geotechnical designs (G1) and detailed designs (G2), with the objective objective of reinforcing reinforcing compressible compressible soils by means of rigid inclusions. inclusions. It details details the scope of geotechnical investigations required during the various study phases. Note: Throug Throughou houtt
this this chapte chapter, r, the notatio notations ns used to represe represent nt geotech geotechnic nical al parameters will be defined in the table included in the Appendix to the Recommendations section. 1.1. Geotechnical site feasibility study (G11)
This study is solely intended to broadly define the geological geological and geotechnical geotechnical characteristics characteristics of the project setting, typically without necessitating more in-depth geotechnical surveys. In general, such a study only includes an analysis of pertinent documentation, a non-exhaustive list of which is provided below: below: Geological Geological study; Hydrogeological Hydrogeological study; Geotechnical Geotechnical databases: geotechnical consulting engineers, Infoterre, archives, publications, etc.; Site inspection, survey of soils and neighboring zones; Site Natural Natural Risk Prevention Plan (French acronym: PPR); Documentary evaluations; Documentary Environmental Environmental constraints. The The repo report rt gene genera rated ted from from this this initi initial al study study defin defines es a draft draft preli prelimin minary ary geol geolog ogica icall and and geotechnical model that describes foundation soil compressibility. This model must expose the variou variouss risks risks inhere inherent nt in the predicted predicted settlem settlement entss of structu structures res in terms terms of execut execution ion difficulty, difficulty, costs and scheduling; scheduling; it must also propose propose a range of feasible feasible technical technical solutions. 1.2. Preliminary geotechnical design (G12)
The purpose of this preliminary geotechnical design is to provide the basis for a preliminary design of the structure by adopting the set of geotechnical hypotheses for consideration and identi identifyi fying ng the genera generall constru constructio ction n guide guidelin lines. es. In relying relying on the outcom outcomee of a technica technicalleconomic study, this stage provides a choice of solutions that address the constraints imposed by the Project Owner and Engineer, e.g. maximum settlements, differential settlements, construction schedule. Upon completion of this G12 study, the Project Owner and Architect select the approach that best satisfies their technical and economic constraints.
Geotechnical investigations
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This preliminary geotechnical design must also comprise the geotechnical surveys needed to specify the geotechnical data described in detail in Chapter 4; these investigations may include: Geophysical surveys; Geological boreholes with sample extraction; In-laboratory identification testing; Laboratory tests to determine mechanical parameter values; In situ testing campaigns; Hydrogeological investigations. The report produced on this preliminary design is to establish the definitive geological/hydrogeological/geotechnical model; moreover, it provides a series of dimensional sketches of the various solutions, with an emphasis on settlements. In some cases, this report may reach the conclusion that the project structure does not require any improvements or reinforcement, notably should the estimated site settlements remain compatible with the structures stability and serviceability. This G12 report is to set forth a schedule of additional surveys, depending on the potential feasible solutions, to be conducted during the detailed geotechnical design phase (G2). 1.3. Detailed geotechnical design (G2) specific to a rigid inclusion-based reinforcement project
From a general perspective, this detailed design offers an approximation of quantities / schedules/execution costs for the projects geotechnical structures, and a list of the consequences of residual geological risks incurred relative to each of the various feasible techniques, as input to the Project Owner s decision-making process. Keep in mind that the contents of this design, as described in the present section, are specific to reinforcement projects involving rigid inclusions . During the Design phase, this study must serve as the basis, depending on constraints imposed by the Project Owner and Engineer, for defining: Type of inclusions; Inclusion mesh pattern; Inclusion length; Thickness and implementation criteria relative to the transfer platform. Within this framework, a campaign of additional geotechnical investigations is planned for the purpose of determining the values of all parameters input into the design and dimensioning calculations for the reinforcement solution by rigid inclusions; this campaign features: Cone penetration tests, piezocone tests to complete the lithographic sections and determine the over-consolidated zones; Shear characteristics: cu Determination of cu using a vane test; Compressibility characteristics: p, ROC, e 0, Cc and C s, Cv, k v under various stress levels, ck , Ce; Testing: installation of piezometers and subsequent monitoring, in order to identify the amplitude of water table fluctuations over time.
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2. GENERAL RECOMMENDATIONS FOR ESTABLISHING THE GEOTECHNICAL SURVEY PROGRAM
The scope of application of this guide encompasses geotechnical surveys of relatively soft soils intended to resist loads caused by the surface foundations of buildings (ground slab, rafts and footings), reservoirs, embankments and linear structures, as well as the inclusion embedment layer. The first objective of these geotechnical investigations is to produce the entire set of calculation parameters to evaluate structural displacements (settlements and potential horizontal displacements) of the sites natural soils. These calculation results must then establish, depending on project constraints, the best suited reinforcement technique. In some cases, the conclusion may be drawn that it is not necessary to reinforce the soils. The second objective is to derive the values of parameters necessary to design the reinforcement elements, which in this case would be rigid inclusions. The geotechnical survey program must take into account the three following elements: The type of structure to be built: the type and characteristics of structures as well as all eventual project constraints (threshold settlement values, construction timeline, etc.) are to be defined in accordance with the NFP 94-500 Standard; the responsibility for furnishing these elements lies with both the Project Owner and Engineer; The geological, hydrogeological and geotechnical setting: a preliminary survey is required based on the available elements, namely: - site inspection: unbuilt land, existing structures, underground pipes, accessibility of the worksite for construction equipment; - a documentary search (e.g. geological maps, subsoil databases, relevant theses, natural risk prevention plans, previous studies); - land survey of parcels bordering the project; The Geotechnical Zone of Influence: zone of interaction with the project, presented both in plane view (existing structures) and in depth (pipelines, streets and utility lines, etc.). The results of surveying campaigns are presented in Tables 6.1 to 6.3, in accordance with the conditions stipulated in the Recommendations on the consistency of geotechnical surveys for building construction issued by the USG organization.
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h t t e s a f e o c r i t t y s h n t n e e s h i y i b t a s r b t r s a d t e r l t r u e c e f e e t c a c e h r t n h a d e t h e m f i v u o c o 3 l w f l t e , i r n p d t s s i c o a a s m n r e e i o j l b t e y o e y a e t h r e a p h A t l t r a b
h t p e D
. m a r g o r p y e v r u s l a c i n h c e t o e g I R I S A
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g n i d n u o s l a c i r t c e l e l a c i t r e v n r o o i t y c a a : r r s r f c a e i r s l y a c c i h i r p t m s o c e l e i e G e S
o t d e t d i n u s a y l l e h p w a r ) i 2 g a e t r t o t s : s N l i g e o s n e s i r ( d s f o n e s u l i o s n o s a o l h e t r b a , i a c o s i b l c i g i f o i d o l e s t t n o e e r o f G C o s d i
< a e n r r a e e t e e t r c a h a t s p : f s r 2 : g h g u s s n n e i a m i d r 0 n M d l i o 0 u F 5 . u B 2 o s
f o g n i d r o c e r h t i w : s s e g l n o i r h d s e e r n r g e o u u t a e b o s s e e u v m a i r v o t i a t u c p c i n u r u t t r t n s g n t s i o e i e p c d r o D b
l a n o i t r f i e d p o d a g t n 2 n e m e i n m 0 e o d n 0 r u c + o n 5 . s i 2
: s . e r w o u l t e c b u r 1 t s e r t o a e N n e i L e s
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f s o e c s v i l i f h t a o c c p i e a s j g l r n b l g i o e o i o s r t O o d h a t t e
e o i r c y a G m L t s e s l
r o f n n i o t i t c e a j o r m P
248
n a l p t t c e u j o o r y a P l
, s t s e t n o d n i t a a y r t h e p n a e r p i g t e a n r . o s ) c t 2 l : i s o e g s t n r o i o N d f n t e u n e s o s e ( n l m o e i a l c p i t a c n m i a o f i h c t c e a n e M s a d i
e 2 i . l h o I s V d T . s d n i n a x a a e 1 t e . i I s h t V e f s h t o e r n s u e g d i o i s F g n h . i s t d t o s n b e t e p e n d o d n a , s r s m e t g n 0 e i 5 m d n 2 0 u d 5 o s n a r o e 0 0 m 5 3 a s n e e e e m h o t w s t g e n b g i n i n e i n g a n t n u n a r r o c a s e s n . e i n i l h s e o y c e i l n m d w t e t c l s n i i u s s o o a n s b h s a o o l c t t l L n f e c i e o w j e o s n r e a o p u z l s f y i r a s o v x i t t e a a t n h t n e e s o m e t r m n e d n g h g e i t l l a w i p a a , d d L e a e t 4 h t e e g h b n t r a o o t g t n e d e l s e h t d t h a e t c e g o n n i i w l d e d i s n b e v a i t d h y s s t y e u i l b m m i b d s a o i t e e l z i n o r a i v n h t a l e n i r g e r o o o m b s o e n e t g h b i s l t e y , t a a e n l r m a u a e r t n g c s g t n u i i r n a t t i t p u s o p m c r a a a e c f o i n t a y e l d e l v y p a r e r u m s a o v F r u x e s . f h e y T n i t o : a l y 1 t i t c b e i a i s i t p r o e a n e N d v d
y e 3 . b h t I V d e e r s t e e n e h r u w i g m e l e F p s n c i m a o e n c h e t w o b i n h s y s a ; e e s m l o u h n c e a g r i b o a a p b f m d o a s c e r e o i g c r n i s e e y h e t h e v t r n , u o ) s U n e o T h t i t P , a r C e b r c i o l n a e e c r e y n f o e r b c s o z s l i e i i h t o p s ( n s e o u i c o v d i e r e s a a v d B e t n . h e t e l o y m r f e h i u e s r t a o n e e b d i m d o e e r t r o e u s s c l b e i r e p c s s n o e r p e r o t e p i f e e a r k s e a n a l m o l l e t l w i s a s w e l s a , t ) s a t T e n t P i n C a t o ( i n t g o n c a r i t l t e p s u n e u m p o c s e n n n o e . i o o t i c t c n C i a r a . f g s t i t s g a i s n s e i h t s v d i n n w a i e u l l o b d a a c s e i u p l n e p v i a h i t u v c r q e c t u e e f r o t s f e s i g e r o 5 l . l d e t e I A g V n m h : i n o 2 i r g e m t e u t o a o x n e r N e p h t
ASIRI National Project
Figure 6.1: General geotechnical surveying. (Design/execution of embankments on soft soils, SETRA/LCPC technical guide, 2000).
Figure 6.2: Detailed geotechnical surveying. (Design/execution of embankments on soft soils, SETRA/LCPC technical guide, 2000).
Figure 6.3: Soil identification abacus according to the cone penetration test (CPT). (Douglas and Olsen, 1981).
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Figure 6.4: Soil identification abacus according to both the CPT and CPTU tests (Robertson et al ., 1986).
Figure 6.5: Soil identification abacus according to the standardized CPT and CPTU parameters (Douglas and Olsen, 1981).
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d n a r h t e e t p . i , y a f e l b r a w s D t r d a r r e s e n s f e i t e u a p e u c o e r W d g q a e n o t s r c e l i l e a r t s t b c i e n i i e t s a e . r m s v m n e e o o k o e . o d z f h d p v y i p e c o k e i e v t s h y i o i l o o l T p z n t r t i a e o t g i , e b i d p i t n e n g r p a i o s a o e u r t ) e n s o I h e m i z u i l m a i t r l r t e s C P T D o b s C e ( a e h t m e p
. m a r g o r p y e v r u s l a c i n h c e t o e g I R I S A
: 2 . 6 e l
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e y r h o a e t t e v h r n e a r c e r t r d e a y e r t e t c o p a n m d a f p r y u r i , l e t t u s h e e 2 s t s s l n e o a e l y M m m c c i g o m z r 0 o e e 0 e o l i r r t o c o s p 0 , i i e 1 3 n m h g o r d y e H l
s n , o n i t o i a b i s a s o t r a r n r r v o i e o t t e c ) r a a l ( e i b r d w a y a t n l i v r a r a s s b e n e s e e l o t v e a i t b i t c t e a w e t r p c f c e n e r j o n e f b c t i x o E d a , e c O E r s / w o d , e c f s n e s y s a H r ) o y l e E l a t h n n , i 1 a n g B c e i o l e i i a v t i t h b i r E c r s o a i , : o e s e t t d s N w e s e a r i m o l r e e r g L v e H P W e s e l ( P g a
n o i t a m r o f n i t c e j o r P Geotechnical investigations
n a l p t u o y a l t c e j o r P
. n o i t a d i l o s n o c r e v o l i o s o t n o i t u b i r t n o c s t i r o f t n a t r o p m i s i g n i r e w o l d n a g n i s i a r e l b a t r e t a w f o e m i t r e v o n o i t a n i m r e t e d e h T : 1 e t o N
251
e s y i r r , r r o s e t e n f r t n n v o r e e i e e e t o p t i ( e m m o y e a t u s a s a s c h m i u i t t l r m l e d s e e d i d c r e e r n i h l t n n 7 u e i t o i e v b s c : s m e t s h o i s a . s n e t : e d s h s a r ) l r T t p e n m e v m r n p a o - o P e r h , r p w D o 0 k e 3 e C o T r o s c F m d l i e F 5 P . o t C b o a e b a h n b 0 c h t
. m a r g o r p y e v r u s l a c i n h c e t o e g I R I S A
: 3 . 6 e l
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e t e r s d t s o o e o n ) f n N a C 4 s ( N o , ) p t ( k d e c d s 2 t I . v c ) n o n e o , , k a z e t a 1 t c , s 1 ) e N s e ) e p C o S ( t 1 i B p 9 s s d N s s , e e e r ( V t t 0 t e n e d t s r a e o n p c s e t e o c t , s 0 a t i p s w r ) y y N R t , e n t y e ( l a C N n 1 T s t s t w e d o r e i s v e i l n , ) i m - . O C r e o ( t t a t e e 7 s n 3 o , , b o r f s i e ( l ) t ) d i f t t w e i s i N e 5 8 s e y m a o s s , t e o l - d ( n t e e s t c l e 6 t e f o i s a r r ) c e u t , ¸ N p y u i o s r p e C i u t s t t e ( e d n s a N i t e n n a n , ( m s n n s d e d p o u ) e d , O o - e g o a r r ) v n 1 N I C v P I M C ( e o ( 9 0 1 0 0 y 0 m l , r e s u a 0 g v c 1 m e i n i n f d e i n r < d r n s c o n e i h n s e a g n g t a a c p a e u e 2 n t m t n i e r i s r g t a o a d a i m n h d o p e s a d n i n e 0 e h u o t c d u c i s 0 o a t G e f m n o w a 5 s w u u s f r : r o 2 , e m e n s n . M s u 2 u e i e s m e e r n 0 m h i a m a w e n w : t r r o 0 f m t o 0 o t e 2 e 4 F 0 5 F b m 0 5 o b =
t f f o 1 o e s 1 r n e s r s P g f o e y e t o d s s o F p i e t e t s l e e i N s v s a l i s n : m i t p w n r o n 2 e a b c o c i i s k e t o s n s s x a i 9 c j i a i i t e k p s b i c a R f d e h e r e r e c T o e s t O f i i r t u p t r e t i f f i e u c G n s l m o t s m i e s a o a e r ; a s s s r e d 0 a r e P e F C a y l 0 R r I a l C 3 p h t p s e n t n i o h l i t g e a i e i m m h p t r t s u o t n n o r f d e n a a i t t o m i l s t c k c u e e e r n t e i c a c l j i s u o b v v d n r r m o r e e e P S E C S h
252
3 , 1 u + x s e U o t . C b o ) 5 r e N 1 o h t ( u e c D f , t o ) o C 2 N , n o 1 ( U i u t s c e U p t t u o e s : t c r a N d s s x t n e e a s t a p e , ) e p t l a a h 4 i r x t r 1 a a h a d e t i e h r i h n S T w s a
c s
f s o e e s t l l t : e n n c s b t a b a e e n m m t n w w e a i o o e l a l p l l t l l r t t e t t a a e s e c s s c e n m t m l a r l o a u a i t g c u e n u t u c n m m t n d i r i u c e i m i x x w e r t s e a a j l e e l o s f o M t t l f e M R r e i o h P s d f t
e n o z l a c i n h ) c e e t o c n e e u G ( l f n G I i Z f o ASIRI National Project Project
Note 1: The cone penetration and pressuremeter tests will serve to justify the load-bearing capacities of rigid inclusions. On the other hand, these tests cannot reliably estimate either the consolidation settlement or creep settlement of soft soils, and even less reliably the settlement dura duratio tions ns.. Use Use of a pressu pressure re meter meter may prov provee accep acceptab table le for for rela relativ tively ely inco incomp mpre ressi ssibl blee unsaturated soils, whose settlement periods may be considered of short duration. Note 2: The first identification testing campaign objective is to classify and then qualify the soils soils (high (highly ly plastic plastic clay, clay, peat, peat, etc.). etc.). The second second objecti objective ve consist consistss of correla correlatin ting g these these identif identifica ication tion parame parameters ters with with both both the shear shear and compre compressib ssibilit ility y paramet parameters, ers, in order order to complete the project database (wn, with Cc/(1 + e0), p). Note 3: Benchmark values for the physical parameters of compressible soils. Table 6.4: Benchmark 6.4: Benchmark values of compressible soils. d
(Mg/m )
(Mg/m3)
e
wn (%)
wL
I p
Soft clays
2.6-2.7
0.9-1.8
1.2-2
30-100
20-80
15-50
Muck
2.4-2.7
0.7-1.5
1.5-3
60-150
80-180
Peat
1.4-2
0.1-0.5
3-10
200-1,000
Designation
s
3
MO (%)
2-10 10-100
Note Note 4: Oedo Oedome metri tricc testi testing ng is crit critica icall for for estim estimat atin ing g prima primary ry and and seco second ndary ary (cree (creep) p) settlements settlements as well as their predicted durations. durations. Note 5: Preconsolidation pressure The determination determination of preconsolida preconsolidation tion pressure pressure ' p p is an essential, yet very delicate, step. An indica indication tion of the degree degree of over-c over-cons onsolid olidatio ation n (R OC may be obta obtain ined ed from from OC = p /v0) may soundings using the cone penetration and piezocone tests (Fig. 6.6). For a normally consolidated clay, the theoretical variation of q tvs. depth can be plotted, with adequate knowledge of the relation between c u and v0 or between c u and q t (see Note 13), and then compared to the q t values values record recorded ed by the cone cone penetra penetratio tion n or piezoc piezocone one.. This This comparison of the two values displays whether the soil is over-consolidated or instead nearer the normally consolidated state. Figure 6.6 provides an example for a homogeneous clay, which which is distinc distinctly tly over-co over-conso nsolid lidate ated d at the top and then then very very slightly slightly over-c over-cons onsoli olidat dated ed throughout its depth.
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Figure 6.6: Indication 6.6: Indication of the degree of over-consolidation based on q t vs. depth.
Note 6: Compressibility
Recompression index:
C S
Compression index:
C C
e
on the unloading-reloading cycle
lg V ' e
lg V '
Oedometric tangent modulus for a stress in the over-consolidated domain vs. C s):
v,
E oed v'
on the initial loading
in the normally consolidated domain, vs. C c (or 2.3 v '
C c or C s
1 e
Oedometric Oedometric secant modulus, modulus, E oed, over a stress interval v1, v divided divided by the volumetric variation variation over this same interval: interval: v ' 1 e1 E oed v' 1 , v' 2
v2,:
quotient of the variation in
e
Note 7: Correlations relative to compressibility Between compression index C c and liquid limit w L:
Tabl Tablee 6.5 6.5 prov provid ides es two two corr correl elati ation onss that that vary vary acco accord rding ing to the the sites sites wher wheree they they were were established. Table 6.5: Determination 6.5: Determination of C c on the basis of wl.
Site Clays with low or average sensitivity Marine Rio de Janeiro clay Between
254
Correlation
Reference
Cc = 0.009 (w L-10) -10)
Terz Terzag aghi hi and and Peck Peck (19 (1948) 48)
Cc = 0.013 (w L-18)
Ortigao (1975)
the compressibility factor Cc/(1 + e0) and natural water content w n (Fig. 6.7):
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Figure 6.7: Range of C c/(1 + e 0 ) values vs. wn for normally consolidated, non-organic clays (Lambe and Whitman 1969, western U.S. soils).
Between compression index C c and natural water content content wn (Fig. 6.8):
., 2009). Figure 6.8: Correlations 6.8: Correlations for Bordeaux clays- C c and Cs = f(wn) (A. Marache et al .,
Note 8: Benchmark values for compression index C c and compressibility factor Cc/(1 + e0). Table 6.6: Benchmark 6.6: Benchmark values for the compressibility parameters of compressible soils.
Type of soil
e0
Cc
Cc/(1 + e0)
Soft clays
1.2-2
0.3-1
0.15-0.3
Muck
1.5-3
0.7-1.6
0.25-0.4
Peat
3-10
2-10
0.4-0.8
Note 9: Consolidation coefficient Accord According ing to Terzag Terzaghi hi s theo theory ry of cons consol olid idati ation on,, the the vertic vertical al cons consol olid idat atio ion n coeff coeffici icien entt depends on both vertical permeability k v and the odometric modulus E oed, as related by the following expression:
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k v E oed
cv
w
This relation can also be written as a function of C c within the normally normally consolidated consolidated domain and, and, by extensi extension, on, within within the over-co over-conso nsolida lidated ted domain domain vs. C s for a stress possible to the t he stress st ress imposed on the soil by the structure to be built: in in the over-consolidated domain: p k 1 e ' cv 2.3 v
C s w
in in the normally consolidated domain: p
cv 2.3
k v 1 e ' C c w
This coefficient coefficient depends depends on the vertical vertical effective effective stress v (expressed (expressed in m/s), as well as on soil compressibility compressibility Cc/(1 + e). The variation in permeability k v is correlated with the variation in void ratio e (Fig. 6.9) by means of the following relation:
k v k v 0
lg
e e0 c k
e c k lgk
Figure 6.9: Permeability 6.9: Permeability coefficient k v variation curve vs. void index e. Determinati Determination on of both ck and lg k v0.
Note 10: Characterization of vertical creep C : Rate of secondary consolidation:
H C
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H 0 lg t lg t
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C e: Creep index:
C e
e lg t
C 1 eo
Benchmark values of the ratio C e/Cc. Note 11: Benchmark Table 6.7: Benchmark 6.7: Benchmark values for the creep parameters of compressible soils.
Type of soil
Ce /Cc 0.03-0.05 0.03-0.05 0.05-0.10
Soft clays Muck Peat
Note 12 Let us recall herein the principles of triaxial testing, as described in the NF P 94-070 and NF P 94-074 Standards issued in October 1994. For soils sheared in the normally consolidated domain 0; the angle of friction will be derived at the critical state NC = crit (on the load face) and will remain indistinguishable from the angle of friction friction at the peak (Fig. 6.10). For soils sheared in the over-consolidated domain, if the deformation is limited and less than that of the yield stress (beneath the yield surface), then the values will be set at the peak (Fig. 6.10), resulting in: SC = peak SC peak . In the over-conso over-consolidated lidated domain, domain, stress paths all lead onto the ellipse. The path ends are therefore not aligned; however, the curve will generally generally be lineari linearized zed in order order to calculat calculatee peak peak . It can can be obse observ rved ed in Figure 6.10 that the determination of peak peak requires considerable skill and is less reliable than the calculation performed in the normally consolidated domain.
overFigure 6.10: Example 6.10: Example of the determination of overconsolidate consolidated d domains for a Romainville Romainville green plastic clay (Josseaume (Josseaume and Azizi, 1991).
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Figure 6.11: Curves representing the deviator and excess pore pressure vs. axial strain during undrained tests conducted on normally consolidated and over-consolidated saturated clays.
For a given clay, the angle of friction drops with the plasticity index value. Several correlations can be identified, among which let us cite Fahri s (1970) corresponding to French clays: 8 tan ' 0.21 I p 6 Note 13: Correlations relative to the undrained cohesion c u Based on the standardized strength measured using the cone penetration test, q c or qt and cu (Eurocode EC7-2): Cone penetration cu = (qc v0)/Nk Nk must be determined at the project site. Generally, the value of Nk is set at: 15 < N k < 17. Piezocone cu = (qt v0)/Nkt Nkt must once again be determined at the project site. Its value typically lies between 15 < N kt< 20. Based on the
plasticity index, Ip: For normally consolidated clays: on any given site, Skempton proposed (Fig. 6.12): cu = (0.11 + 0.0037 I p) v0
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Figure 6.12: Values of the ratio c u/ v0vs. plasticity index I P.
Note 14: Classifications and benchmark values of c u, qc, E M and pl. According to Terzaghi (Table 6.8). Table 6.8: Values of c u vs. clay consistency.
Clay consistency Very soft Soft Firm Stiff
cu (kPa)) < 12 12-25 25-50 50-100
According to the Recommendations on gravel columns : highly compressible soils, organic soils: c u< 20 kPa or q c< 300 kPa. According to Houÿ 1986: see Table 6.9 below: Table 6.9: Values of pl and EM.
Type of soil
EM (MPa)
Muck Soft clay
0.2-1.5 0.5-3
pl (kPa) (using a probe with very low inertia) 20-150 50-300
Note 15: Increase in undrained cohesion by means of consolidation Structural calculation procedures should never introduce the parameters cu and ccu, which have absolutely no physical meaning; the only purpose of cu is to express the rise in c u vs. consolidation stress within the normally consolidated domain. cu is the cu gain factor as a function of the increase in consolidation stress. Its value is obtained directly in either the Lambe diagram (Fig. 6.13) or the Mohr diagram (Fig. 6.14): sin CU tan cu 1 sin CU
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Figure 6.13: Determination of cu in the Lambe diagram.
Figure 6.14: Determination of cu in the Mohr diagram.
For very recent soils, e.g. marine clay, for which it can generally be considered that the entire layer is normally consolidated, short-term cohesion cu rises linearly with depth beginning from zero at the surface (Fig. 6.15). For most soils, we obtain: c u = 0.25 to 0.35 v0 for clays, and c u = 0.5 v0 for peat. For over-consolidated soils at the surface (e.g. subsequent to water table level variations that over-consolidate, by means of suction, the soil slice through which the water table is fluctuating during drying-rewetting cycles), it can be concluded that cohesion exhibits a nearconstant value in the over-consolidated soil thickness, before increasing proportionally with z (Fig. 6.15).
Figure 6.15: Evolution of the value of c u vs. depth.
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References
Eurocode 7-1 - Calcul géotechnique. Partie 1, Règles générales, juin 2005. Eurocode 7-2 - Calcul géotechnique. Partie 2, Reconnaissance des terrains et essais. septembre 2007. Leroueil S., Magnan, J.-P., Tavenas F. - Remblais sur argiles molles . Lavoisier, 1985. Lunne T., Robertson P.K., Powell J.M. - Cone penetration testing in geotechnical practice. Blackie academic and professional, 1997. Marache A. et al . - Understanding subsurface geological and geotechnical complexity at various scales in urban soils using a 3D model. Université de Bordeaux, GHYMAC. Georisk 2009. NF P 11-213-1 - DTU Dallages 13.3 : Conception, calcul et exécution, mars 2005. NF P 11-300 (ou GTR 1992) - Guides techniques, fascicules 1 et 2. Réalisation des remblais et couches de forme. SETRA, LCPC, septembre 1992. NF P 94-500 - , décembre 2006. « Recommandations sur la consistance des investigations géotechniques pour la construction USG ». Le Moniteur (cahier détaché n° 2 du 16-12-2005, n° 5325). SETRA-LCPC - Études et réalisation des remblais sur sols compressibles. Guide technique, novembre 2000. SETRA-LCPC - Traitement des sols à la chaux et/ou aux liants hydrauliques, application à la réalisation des remblais et des couches de forme . Guide technique, janvier 2000.
Geotechnical investigations
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CHAPTER 7
Execution conditions
1. COORDINATION WITH GEOTECHNICAL ENGINEERING MISSIONS
To ensure high structural quality, the following steps are necessary and pertain to all elements of the rigid inclusion system: embankments, inclusions, capping layers or platforms, rebar, excavation pits, earthworks, foundations: Definition by the Prime Contractor of the various target objectives: maximum settlements, loading intensity, schedule restrictions, ground slab thickness, etc.; Completion by a certified Engineer of the geotechnical project design (type G2); Execution of the works by a Contractor assigned oversight of the execution plan and geotechnical monitoring (type G3); Completion by a qualified Structural Engineer of the geotechnical construction supervision task (type G4), for the purpose of managing all external controls, especially technical interfaces among the various works involved in the project; Assignment, through an organization certified by the competent administrative authority, of a technical control mission intended to provide risk prevention assistance. Prior to the involvement of the Contractor, either the Project Owner or Engineer will have completed all of the preliminary information requests regarding concessionary agreements. Moreover, the soil reinforcements, like any other technique related to geotechnical works, require supervising the works execution, in addition to monitoring and maintenance steps in accordance with the prescriptions set forth in Eurocode 7, Section 4. The purpose of this chapter is to define the execution steps and procedures relative to: The working platform; Rigid inclusions (inclusion layout, production, low cut-off); Pile caps or head extensions; Load transfer platforms (type, thickness, implementation); Eventual geosynthetic reinforcement included in the platforms. Lets point out that these various elements may in fact be installed by different contractors, a situation that necessitates excellent interface management. It should also be recalled that a series of execution designs are mandatory, in order to: Validate appropriateness of the technique given the type of soil and working environment; Verify the means and methods deployed in light of the targeted results, in terms of performance, output rate and schedule; Refine the design of the rigid inclusion solution selected during the project's geotechnical study phase, by taking into account the full set of execution parameters, including geometric and mechanical characteristics of the rigid inclusion, specific points implying adaptation of the inclusion grid pattern, characteristics of the load transfer platform (this study process must be conducted according to the principles outlined in Chapter 5); Develop a layout showing the location of inclusions based on the set of technical data validated by the Engineer; Execution conditions
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Adjust the works phasing plans according to the program of the other contractors; Propose technical solutions that allow managing environmental constraints, geotechnical hazards and execution-related risks (e.g. discovery during the execution phase of underground or buried structures not detected by previous investigation surveys); Present a method statement submittal for rigid inclusions, with their location, the different stages of the process and a quality control plan. 2. CONSTRUCTION OF THE WORKING PLATFORM 2.1. Role of the working platform
A working platform is typically constructed before the rigid inclusion works. This platform allows the transport of the rigid inclusion installation equipment during all weather conditions. The characteristics of such a platform must be adapted to actual execution conditions (type of equipment, ease of circulation on the site, etc.). Moreover, platform execution may give rise to an acceptance that guarantees the safety of onsite construction vehicles. This working platform can be part of the load transfer platform but must be controlled by specific tests described in this Chapter. In this case, the working platform must undergo an acceptance procedure to verify the achievement of the specified performances. Furthermore, upon completion of the rigid inclusions, this working platform is typically affected by subsequent jobsite operations, which may undermine the integrity of previously installed rigid inclusions (whether reinforced or not). 2.2. Works after rigid inclusion execution
Both during and after soil reinforcement measures, precautions need to be taken in order to avoid damage to the inclusions (which in general have not been steel reinforced) as well as of the capping layer. The risks of damage to the upper part of a rigid inclusion may appear in the following cases: Circulation of construction vehicles either directly above or in the vicinity of rigid inclusion heads; Insufficient platform bearing capacity with regards to the circulation of construction vehicles; Installation of utility lines (water, gas, electricity, etc.) either between or in alignment with the rigid inclusion mesh; Earthworks involved in excavating the footing pits; Restoration of the working platform subsequent to soil reinforcement works in order to proceed with localized material purging; Restoration of the working platform by running binder treatment equipment (using lime, cement); Second compaction of the working platform and installation of an additional capping layer extending to the underside of the structure.
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2.3. Construction principles
In the general case, any excavation pit or material excavation beneath the finished level of the unreinforced inclusion heads is not recommended. Should such excavations prove necessary for the project, e.g. in order to perform utility line purging or lay trenches, then it would be appropriate to establish a set of prescriptions aimed at reconstituting the initial mechanical performance and preserving the integrity of the inclusions. When the rigid inclusion heads are stopped at the platform surface level, a minimum amount of time to obtain sufficient strength, must be allotted between the production of inclusions and the earthworks stage. For columns with mortar, cement or grout, this period must be validated by testing on samples, relative to both the setting and strength increase of the inclusion material. Remark: This transition period can be as long as 1 week for inclusions produced in situ.
Whenever the working platform is incorporated into the load transfer platform, it is necessary to verify that the transfer platform has not been deteriorated or polluted. Remark: Given these constraints, it would be preferable to stop the inclusions slightly below the upper level of the working platform.
In pursuing with installation operations, a minimum thickness of 25 cm must be ensured between the rigid inclusion heads and the zone of re-compaction. The two following configurations then become feasible: The inclusion head is situated at the level of the working platform, in which case it is necessary to add material over 25 cm so as to isolate the inclusion heads prior to compaction; The inclusion head is positioned more than 25 cm below the stripped surface level of the working platform, then re-compaction can be initiated from the working platform. Whenever the rigid inclusions are not reinforced, the earthworks performed between inclusions must abide by the following precautions: Stable excavation pits over the short term without any contribution from the inclusions; - reminder: need for soil retaining system beyond an excavation pit vertical distance of 1.30 m if an individual needs to enter the excavation; under all circumstances, specific regulatory criteria must be respected for human safety. - in the case of a sloped embankment, the slope must not intercept the inclusions; Carefully completed earthworks around each inclusion prior to low cut-off. 3. EXECUTION PHASE FOR RIGID INCLUSIONS 3.1. Review of execution techniques
Rigid inclusions may be installed by means of either soil extraction or soil displacement techniques; these methods have been sorted into five main categories as follows: Bored rigid inclusions with soil extraction; Bored rigid inclusions with soil displacement; Cast-in-place vibro-driven or driven rigid inclusions; Prefabricated vibro-driven or driven rigid inclusions;
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Rigid inclusions installed by incorporating a binder with the soil (treated soil columns, jet grouting, etc.).
Moreover, rigid inclusions may be distinguished by their component material: mortar, concrete, grout, steel, or even wood. From a general standpoint, all pile and micropile execution methods would be applicable for installing rigid inclusions (see Appendix A: Standard NF P 94-262). The inclusions that mix a binder with the soil constitute a special subcategory of inclusions produced in situ, particularly as regards control procedures. For a detailed description of each of these implementation techniques, the interested reader is referred to: Standard NF EN 1536 for bored piles without soil displacement; Standard NF EN 12699 for piles with soil displacement; Standard NF EN 14199 for micropiles; Appendix A of Standard NF P 94-262 for pile and micropile-related techniques; Standard NF EN 12 716 for techniques on soil-cement columns derived by jet grouting; Standard NF EN 14 679 for the execution of treated soil columns. 3.2. Material-related requirements
The rigid inclusion component material exhibits a much higher deformation modulus than that of any soil layers and a specific strength independent of the level of confinement capable of being provided by the surrounding soil. In addition to the mechanical characteristics taken into consideration in the design calculations, requirements related to the following must also be verified: Execution: resistance to leaching, workability of these materials; Durability: corrosion, attacks from chemical and bacteriological agents. 3.3. Description of the execution methods
Among the aspects or criteria playing a role in the choice of execution method, let's cite the following (non-exhaustive list): Borehole stability; Risk of false-refusal; Stability of a column with fresh material; Creation or not of excavations; Vibrations and nuisances; Possibility of reinforcing the inclusion; Recording of execution parameters; Rate of output; Maximum lengths and diameters; Strength of the embedment layer; Aggressiveness of the soil and water; Site accessibility of the inclusion execution equipment; Local means; Phasing constraints related to the method employed (scheduling plan).
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3.3.1. Bored rigid inclusions with soil extraction
3.3.1.1. Simple bored, bored with casing or bored with slurry The process of simple bored inclusion can only be used in a soil that allows ensuring borehole stability, which in general refers to a cohesive soil that more often lies above the groundwater table. The drilled cased technique or slurry drilled is employed to produce an inclusion whenever borehole stability cannot be ensured. The concreting step must take place with protection from a casing or the tremie pipe; it is still necessary however to verify that the lateral soil pressure is sufficient to contain the weight of the column of fresh material following extraction of the temporary casing. 3.3.1.2. Installation by continuous flight hollow auger The technique involving a hollow auger allows for the pressurized injection, along the auger's central axis, of a material (mortar / concrete mix) in a continuous manner throughout the tool rise motion. This process could be effective when soil conditions are "unstable", including beneath the reinforcement layer. 3.3.1.3. Installation by micropile technique The micropile execution techniques may also be used to install rigid inclusions. 3.3.2. Bored rigid inclusions with soil displacement
This category of inclusions are introduced according to the boring with displacement processes, which moreover requires the use of specially designed tools for this purpose, i.e. auger or screw tools with a reverse pitch in the displacement part. The inclusions are installed practically without any excavation using a hollow tool that enables concreting the inclusions by their tip. The hydraulic composite (either concrete or mortar), introduced via the web of the screw, is set within the soil cavity throughout the tool rise; it must be easily pumped and is often added under slight pressure. In certain types of soils (e.g. loose soils), the displacement may also lead to ground compaction between the inclusions and moreover improve friction along the shaft. 3.3.3. Cast-in-place vibro-driven or driven rigid inclusions
3.3.3.1. Cast, driven or vibro-driven inclusions This process consists of lowering into the soil a hollow metal tube, closed at the tip by either a locking plate or a valve, by means of vibro-driving or pile-driving using a hydraulic or diesel gravity hammer. The tube is lowered until reaching a predetermined height or else a predefined refusal criterion. The concreting step takes place inside the tube, which is then extracted from the soil. This is a process of soil displacement without the need for excavation.
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Vibro
Concrete Column type inclusions
The Vibro Concrete Column (or VCC) type inclusions offer a specific execution process. The implementation protocol calls for introducing into the soil a vibrating needle along the lines of that used to create stone columns. The inclusion is then built by incorporating concrete or mortar as the tool rises.
In a cohesive soil, the characteristics of these inclusion types only differ slightly from the characteristics of bored inclusions with displacement. In fine-grained soils, the load-bearing capacity of the inclusion may be improved by means of soil compaction thanks to the vibrator set inside the instrument used to install the inclusion. 3.3.4. Prefabricated vibro-driven or driven rigid inclusions
Prefabricated inclusions may be driven into the soil by means of a vibrator or with the assistance of a pile driving hammer. 3.3.4.1. Wood inclusions Use of wood inclusions probably represents the oldest method for reinforcing foundation soils. In some countries and for special cases, this method is still being applied. Let's note a variation in the quality of inclusions in terms of both geometry and strength depending on the wood quality. In zones where the groundwater table is lowered, it must be ensured that the inclusions always remain completely submerged in order to avoid their deterioration. For smaller loads (less than 500 kN) and anchorage lengths limited to 12 m, this method can be used, albeit with certain precautions; its applications are mainly devoted to temporary reinforcement works. Inclusions are set into place by means of a pile-driving technique. In order to facilitate inclusion penetration and avoid their damage, special precautions must be taken: steel tip at the inclusion base, steel strip around the inclusion head, pre-boring step, etc. 3.3.4.2. Metal inclusions Prefabricated metal inclusions are typically H -shaped profile sections or tubes not filled with concrete.
Execution constraints must be taken into account during inclusion implementation, while corrosion-related risks are to be incorporated into the design. Metal inclusions are relatively robust and may be installed using machinery with a high embedding capacity. 3.3.4.3. Concrete inclusions Precast concrete inclusions can be used for a wide range of loads, with designs varying according to geometry and compressive strength of both the concrete and reinforcements. Concrete inclusions may or may not be reinforced and moreover are laid out either in a single length or in several jointed and welded segments.
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3.3.5. Inclusions produced by mixing a binder with the soil
Inclusions produced by mixing a binder with the soil yield columns of stabilized soil that, given the level of mechanical performance typically obtained, can resemble rigid inclusions. This mix may be derived by means of various techniques: mechanical, hydraulic, with or without air, etc. The primary techniques employed are as follows: Jet grouting; Soil mixing (via either a dry or wet process); Treated soil trench. The objective of these soil treatment methods is to mix hydraulic binders into the soil in order to improve its mechanical characteristics by generating rigid or semi-rigid columns. Both the modulus of elasticity and simple compressive strength depend heavily on the type of ground configuration and binder contents; they often amount to between 5 and 10 times less than their counterpart values for concrete. All soils may be treated; however, soil treatment using a high content of organic matter, sulfates or nitrates must undergo a preliminary study (see the Soil Treatment Reference Guide, Standard NF P 94 100). 3.4. Summary of the inclusion methods
Table 7.1 lists a sampling of characteristics from the main types of inclusions catalogued, whether they be of a technical (vibrations, noise, excavation) or mechanical nature. Table 7.1: Sample characteristics of the main types of inclusions catalogued. Type of inclusion
Prefabricated
Vibrations
Noise
Excavation
wood
yes
yes
no
Estimated long-term modulus (in MPa) 10,000-15,000
metal (steel)
yes
yes
no
210,000
concrete
yes
yes
no
10,000-20,000 ( 1) (2)
Driven, hammered Fabricated and bored in situ
Treated soil columns
Drilled by percussion Vibro-driven
yes
yes
no
yes
no
shallow
Simple bored
no
no
yes
Drilled cased or sludge drilled Bored with a continuous auger Bored with displacement Soil mixing
no
no
yes
no
no
yes
no
no
shallow
no
no
shallow
Variable: 250 - 9,000 (3)
Jet grouting
no
no
variable
500 - 1,000 * compressive strength
Mortar: 5,000 - 10,000 Concrete C15: 9,000 Concrete C25: 11,000
1
depends on the type of concrete and reinforcement; 2depends on the type of grout; 3depends on the type of binder and soil.
3.5. Description of the works
This description is produced by the Engineer within the scope of the contracts Special Technical Clauses, and then detailed by the Contractor as part of the technical specifications. These two documents must serve to define the following elements: Diameter of the rigid inclusions;
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Depth of the rigid inclusions or their embedment within a load-bearing layer, in compliance with the project design computations (the stop criterion must be subsequently defined at the time of calibrating the workshop when construction starts up); Maximum working stress of the rigid inclusions and compressive strength (fc28) of the material used in the case of a binder-containing material (concrete, mortar, grout, soil-binder mix, etc.); The inclusion mesh underneath the ground slab or embankment, and the thickness of both the working platform and capping layer forming the load transfer platform; The layout of inclusions underneath soil blocks and footings, and the layouts adopted at the soil block-inclusion interface in the case of moments or horizontal forces; The procedure of cutting the rigid inclusions underneath the soil blocks; Pile cap dimensions, if applicable; Characteristics and performance of the reinforcement layer, if applicable.
3.6. Means and methods
The Contractor describes within a technical execution procedure both the human resources and equipment scheduled for implementation in order to achieve the predefined objectives: Worksite supervision: composition of the worksite supervisory team, references of the site foreman; The execution team: composition of the team, which in general features 3 members for small jobs (1 site foreman, 1 drill operator, 1 pump operator); The execution method, as ultimately described in the previous section, in specifying the type and volume of excavation material to be removed; The number and type of production workshops, their power rating (torque for an auger, frequency and amplitude for a vibro-hammer, etc.), the maximum working depth, providing The possibility to justify the output rates relative to job scheduling; The resources selected for manufacturing and transporting the component material; Transport onto the worksite when introducing ready-mix materials; Onsite production in the case of installing an in situ mixing unit; Transport onto the worksite: concrete pump or loader when using dry concrete. The control plan appended to the execution procedure summarizes, for each implementation phase, the acceptance criteria, as well as the type, frequency, resources and manager of the corresponding control measures. 3.7. Inclusion execution drawings
When the inclusion design studies and execution drawings lie outside the Engineer s mission, these elements are typically established by the Contractor, in conjunction with the execution studies produced by other site actors and then validated by the Engineer and control bodies; they indicate: The layout of the inclusion grid pattern with dimension benchmarks; Distinctive signs of the various inclusions: reinforced or unreinforced, inclusions beneath the structure and beneath the ground slab; The cross-section view beneath the ground slab revealing: the working platform, the inclusion surface, details of the load transfer platform; A sketch of the cross-section view underneath the soil blocks, revealing: the lower block surface, and the load transfer platform dimensions.
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3.8. Site preparation
Prior to the Contractor's entry on the worksite to execute the inclusions, the Project Owner or Engineer will have ensured completion of: Access paths and tracks compatible with the vehicles proposed by the Contractor; The identification and eventual shutdown of both the aboveground and underground utility lines; The removal of eventual vestiges; A working platform according to the Contractor s specifications with 2 m of overhang compared to the inclusion footprint; Location of the primary structural axes projected using the offset chair technique, with the location of each inclusion remaining the Contractor s responsibility, as laid out in the execution plan. 3.9. Works execution
During execution of the works program, the site foreman is to collate the following information: Site location verification; Progress of the works; Quality of the materials delivered; Execution parameters. This set of information is typically transmitted on a weekly basis during jobsite meetings. 3.10. Construction specifications 3.10.1. Minimum diameter
For inclusions not reinforced, with mortar, grout or concrete and executed in situ without relying on a micropile type technique, the typical minimum diameter is equal to 250 mm. Smaller-diameter non-reinforced inclusions are only feasible following a detailed examination of consequences related to: inclusion slenderness, offset, verticality flaws, parasitic bending loads, risks of constriction, and difficulties in controlling integrity. 3.10.2. Theoretical cross-section and diameter
For inclusions bored with or without displacement, the nominal diameter is that of the boring tool. For inclusions driven with a lost plate, the nominal diameter would be the tube diameter and not the plate diameter. For inclusions driven with a valve, the cross-section and equivalent diameter must be selected to represent the footprint obtained after concreting without exceeding the tube dimensions. For other techniques (e.g. jet-grouting), the cross-section and equivalent diameter are verified following stripping or another specific control step. The cross-section of prefabricated inclusions is the one guaranteed by the supplier.
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3.10.3. Mesh configuration
3.10.3.1. Minimum mesh size The distance between inclusions must be established to avoid any impact on the diameter and integrity of the adjacent inclusions. In an extensive network, a minimum center-to-center distance of 3 (shaft) diameter lengths is recommended for inclusions executed in situ without soil displacement, and this distance increases to 4 diameters for inclusions executed with soil displacement. In such cases, no specific controls are typically practiced to ensure inclusion integrity. For a group of localized inclusions, the same minimum spacing is recommended. Should it prove impossible to respect these recommendations, it would be necessary to verify the integrity of inclusions already installed in the vicinity along with the absence of significant movement in both the soil and the fresh material composing these inclusions. Other values can also be adopted by altering the inclusion execution phasing (e.g. waiting for material setting before executing the adjacent inclusion) and/or in planning a specific control program (involving integrity, monitoring of the platform or inclusion head lifting). For some applications, these minimum spacing distances may be neglected if nondisplacement techniques are used to, for example, install secant inclusion walls by means of soil mixing, jet grouting or bored inclusion approaches, etc. Remark: This minimum spacing criterion may influence the footing size and therefore must be taken into account as of the design phase.
3.10.3.2. Maximum mesh size The maximum mesh size cannot exceed: For an inclusion head or pile cap diameter of less than 0.5 m: 3 m or a 9 m 2 cross-section; For any larger diameter: 6 times the inclusion head diameter. For the special case of inclusions underneath an embankment supporting a pavement, the clear span of pile caps or inclusion heads, as calculated along the diagonal for square or rectangular meshes, must not exceed twice the embankment height (Fig. 7.1).
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Figure 7.1: Platform thickness criterion vs. type of mesh.
Remark: This criterion may be extended to the case of medium to stiff soils (e.g. a total expected settlement on natural ground of less than 5% of the embankment height).
The use of reinforcements (geosynthetics, steel fabric mat) acting in tension may serve to increase this spacing or reduce the pile cap diameter, provided justification of the differential settlements. 3.10.4. Number, minimum distances and installation offset of inclusions
3.10.4.1. Inclusions underneath a ground slab or raft When placed under distributed loads, inclusions are installed at their theoretical axis. The tolerated axis offset is less than or equal to 20 cm in distance and 2% in inclination.
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At the border of the structure, it is necessary to lay out a row of inclusions around the edge of the ground slab if it has become separated from the peripheral grade beam. The axis of this row must remain at a distance from the ground slab edge of no more than one-fourth of the spacing. 3.10.4.2. Inclusions underneath footings 3.10.4.2.1. General principles As a general rule, it is imposed that inclusions are laid out on at least two parallel axes, i.e.: Along the x-axis once Mx/Q > B/6; Along the y-axis once My/Q > L/6.
Figure 7.2: Forces applied at the footing.
The minimum distance from the bare part of the inclusion (or pile cap, if present) to the edge of the footing equals 15 cm, when taking into account the execution tolerance. It is to be recalled that the design presented in Chapter 5, Section 4.2.3, entitled Calculation of the transfer limit on inclusions heads at the edge of the structure , accounts for the distance between the bare part of the inclusion and the edge of the footing. In the case of soils with especially low shear strength, in general it would be prudent to set an upper overhang at the minimum value of 15 cm, in order to ensure better platform confinement around the inclusions heads and thereby enhance inclusion efficiency. The execution tolerance in all directions must not exceed 10 cm. The inclination tolerance equals 2% in all cases. 3.10.4.2.2. Inclusions under isolated footings The number of inclusions under a given footing depends on both the allowable stress and settlement. Remark: Within a given structure, it is entirely realistic to find some footings with reinforced underlying soil while others resting on natural soil have been slightly loaded. For such a situation to be authorized, settlements must remain 274
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homogeneous (e.g. secondary frame support of sheathing on industrial hangar, studs). The minimum width of the isolated footings is set at: Min (60 cm; 15 cm + inclusion diameter + platform thickness) For footings installed on a single inclusion, the following additional conditions are imposed: Total vertical load on the support limited to 150 kN at the serviceability limit state (SLS) and to 200 kN at the ultimate limit state (ULS); Verification that the load applied onto the support may be fully absorbed by the isolated inclusion, assumed to be directly loaded at the head; Moments contributed by the structure less than the criteria announced in Section 3.10.4.2.1; An execution tolerance lowered to 5 cm; For an execution tolerance of between 5 and 10 cm, the offset of the reaction created by the inclusion relative to the downward loads must be compensated by an offset opposite the soil reaction under the footing. This step entails verifying that the stress being exerted on the soil due to this offset remains acceptable (Fig. 7.3).
Figure 7.3: Soil reaction compensating for the inclusion offset.
Remark: For soil blocks laying on a network of inclusions, the installation tolerances may be proposed and justified by the Contractor; they will then be submitted for approval to both the Inspection Office and Project Engineer.
3.10.4.2.3. Inclusions under strip footings The minimum width of continuous footings is set at: Min (60 cm; 15 cm + inclusion diameter + platform thickness) The layout pattern in staggered rows is recommended in order to avoid the consequences of an eventual offset correlated with the execution tolerances. 3.10.4.3. Inclusions crossing a thick layer of soft soils For all scenarios (ground slab, embankment, footings), a more extreme verticality tolerance than that for piles (2% for piles according to the application EC7 Standard) may be imposed
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upon completion of the design studies for a number of situations (longer inclusions with small diameters and placed in soft soils) relative to the parasitic bending capable of being caused, even under a vertical load. 4. PREPARATION OF THE INCLUSION HEAD 4.1. General principles 4.1.1. Cut-off of cement, mortar or grout inclusion
The cut-off operation refers to adjusting the level of the inclusion head. The heads of cement, mortar or grout columns have to be set to an appropriate elevation while the material is fresh. The inclusion head can stop on the surface of the working platform, but the elevation can also be located below the working platform (i.e. low cut-off). The leveling step may be performed in one of several ways, depending on an array of parameters (e.g. depths, tolerances required, type of soils, reinforcement layer elevation, inclusion diameter): Either by halting the casting operation; Or by manual or mechanical excavation (using valves) of inclusion material before setting; Or by mechanical excavation of the soil and inclusion material before setting until reaching the specified elevation (ditching bucket); Or by drilling in the fresh mortar until the specified elevation.
Figure 7.4: Manual adjustment of the inclusion head elevation in fresh concrete.
If possible, a cut-off of the inclusion head at the same elevation as the platform surface is preferred.
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Remark: Stopping the casting operation or excavating below the water table is strictly prohibited. 4.1.2. Cutting of inclusions
The cutting operation designates preparation of the inclusion head installed on the hardened material so as to reach the intact material at the required level. This cutting step must be carried out over at least 10 cm, in order to verify the quality of the inclusion head material. The earthworks contractor must exercise great vigilance when conducting works adjacent to the inclusions, both before and after this cutting step. Inclusion cutting typically entails: A hand-held jackhammer; Performing sawing; The assistance of concrete spreaders; Use of a chemical cutting system: after a wait time of at least 7 days to allow for setting, this process makes it possible to excavate all at once and then remove the pieces of extra inclusions without fearing a degradation of the inclusions already installed. Use of hydraulic rock breakers is strictly forbidden. It is not necessary to cut off the inclusion when the leveling technique employed yields highquality inclusion heads. In the case of a low level that lies beneath the footing, the inclusion is systematically cut over at least 10 cm as a means of verifying the quality of the material composing the head.
Figure 7.5: Chemical cut-off for the head inclusions below the raft level.
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Figure 7.6: Low head inclusion elevation due to a basement excavation.
4.2. Elevation tolerance
An execution tolerance must be defined according to the type of structure and production constraints. In the case where the lower inclusion levels are determined with the aim of incorporating all or part of the working platform into the load transfer platform, the following criteria must be satisfied (Fig. 7.7): It is not recommended to perform this leveling beyond a depth of 30 cm in order to allow for a high-quality compaction of the material located above the leveled surface; The cut-off inclusion level (including tolerance) must be positioned above the lower level of the working platform; It is necessary to cut the rigid inclusions if the inclusion head elevation exceeds by more than 5 cm the required horizontal plane, as per the design.
Figure 7.7: Execution tolerance to be taken into account on both sides of the required design elevation level.
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4.3. Execution of pile caps or expanded heads
Should the design call for using pile caps or expanded heads, it would be necessary to limit their equivalent diameter to three times the equivalent diameter of the inclusions. These elements can be either cast in place or prefabricated. Depending on their geometry and applied loads, they may or may not be reinforced with steel bars. When a cast-in-place option is selected, the inclusion execution procedure must incorporate this implementation step. 5. PLATFORM IMPLEMENTATION
In this section, the term load transfer platform refers to the embankment layer located between the inclusion head and the structure. The platform execution and control methodology differs depending on the type of implementation planned underneath large-sized foundations (raft, ground slab) or else in a localized manner under small-sized isolated foundations. It is also possible to incorporate all or part of the working platform into the load transfer platform under certain conditions. In all cases, the construction specifications must be established such that: The minimum characteristics provided in Section 6.4 above the inclusion head are obtained over its entire thickness; The introduction of compaction controls becomes feasible; Earthworks below the inclusion elevation are forbidden (given the major risk of shearing the inclusions).
Figure 7.8: Implementation of a granular platform at the base of the earthworks.
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5.1. Reconstitution of the working platform in the event of a low inclusion elevation 5.1.1. Untreated granular pad incorporated into the platform
The working platform must be closed above the inclusion heads by a sandy or sandy gravel and easily-compacted material, with a surplus volume. The shear strength characteristics of this material must be equivalent to those of the granular platform. The platform is then once again compacted to form the base of the load transfer platform. 5.1.2. Platform treated with hydraulic binders (cement or road binder)
Except when special measures are implemented, a working platform treated with hydraulic binders cannot be easily reworked once the inclusions have been installed; in this case, it is preferable to refrain from incorporation into the platform and instead cut-off the inclusion at this platform's upper level. 5.1.3. Lime-treated platform
A working platform treated with lime proves easier to rework once the inclusions have been executed (delayed material strength increase) and, hence, easier to integrate into the load transfer platform should its characteristics and homogeneity meet requirements. In this case, it is essential to ensure and verify the consistency of execution tolerances for the various operations: inclusion leveling elevation and thickness of the reprocessing step. 5.2. Location of a platform under large-sized foundations (ground slab or raft)
These construction specifications are inspired from the specifications issued for implementing the capping layer underneath the ground slab, as intended in the DTU Technical Guideline 13.3. It must be ensured that the platform has been well compacted and remains free from pollution (cuttings, equipment traffic on the platform) over its entire height, especially at the base where it is exposed to the heaviest loads above the inclusion heads. 5.3. Implementation of a platform underneath a small-sized foundation
Placement of a platform beneath a small-sized foundation is only possible provided the excavation pit walls are stable or retained and moreover at the time of its installation, the water table is below the earthworks base. For very deep excavation pits, special measures need to be designed to guarantee pit stability and human safety. This platform may be built before or after installation of the inclusions. In all cases, it would be necessary for the implementation methods to guarantee platform compaction quality over its entire thickness. The choice of a treated soil platform might, under certain conditions, lead to overcoming the set of compaction difficulties.
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The effective management of interfacing among the various project actors requires that all execution constraints be fully understood by the Engineer as of the design stage. Under certain conditions, it could be recommended to conduct a preliminary full-scale test. 5.3.1. Platform installation after inclusion execution
The inclusions may be installed from a high elevation platform with a low cut-off at the theoretical platform base. This installation consists of excavating down to the inclusion head, then installing and compacting the load transfer layer, before casting the footing (Fig. 7.9).
Figure 7.9: Platform executed after installation of the inclusions.
Figure 7.10: Preliminary mechanical earthworks.
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Figure 7.11: Final manual earthworks with eventual cuts.
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It sometimes proves necessary to excavate below the inclusion leveling elevation (e.g. as required by the design or when the low soil bearing capacity limits the densification of the load transfer layer (see Fig. 7.12)). In this case, it is necessary for the inclusions to be steel reinforced over a sufficient height, extending a minimum of 4 times the maximum inclusion diameter or exposed height.
Figure 7.12: Need for steel reinforcement of the upper part of the inclusion to allow for earthworks below the inclusion heads.
5.3.2. Platform installation prior to inclusion execution It is possible to create the excavation pit, fill it with platform material and compact the filled pit before installing the inclusions (Fig. 7.13). The cut-off is then conducted into fresh concrete at the required elevation. As a next step, excavation cuts are performed to a depth 30 cm above the leveling elevation. It is in fact not recommended to perform earthworks leveling beyond 30 cm above the point of inclusion leveling in order to ensure a high-quality compaction of both the material and the footprint. The earthwork leveling is once again compacted prior to implementation of the potential additional platform and concreting of the footing.
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Figure 7.13: Platform set-up prior to inclusion production.
5.4. Minimum characteristics of the material used as a platform 5.4.1. Untreated materials
Shear strength characteristics are critical in the presence of rigid inclusions. It is preferable to implement a high friction angle material. Shear strength characteristics are, in general, justified either by a testing campaign dedicated to the project or by tests reported on the product fact sheet or in reference to a database. Remark: The shear strength values to be taken into account are those corresponding to the level of compaction potentially obtained on the project site.
5.4.1.1. Underneath the ground slab, raft, embankment or pavement The following materials are eligible for use, according to the DTU Technical Guideline 13.3 on Ground slabs (Section A.2.2.1.1). Table 7.2: Materials eligible for use in capping layers (DTU Guideline 13.3).
Soil classification according to Standard NF P 11-300
Classification symbol according to the Technical guide for embankment and subgrade construction (GTR 92) B11, B31
Sandy and gravelly soils with non-clayey fines and coarse elements Soils containing non-clayey fines and C1B1, C1B3, C2B1, C2B3, C1B4, C2B4 coarse elements after elimination of the 0/d fine fraction Water-insensitive soils D1, D2, D3 (except for D32) Chalks R11 Miscellaneous limestone blocks R21, R22 Siliceous rocks R41, R42 Igneous and metamorphic rocks R61, R62
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Shear strength characteristics are determined by means of testing; otherwise, reference is made to Standard NF P 94 270 (Reinforced embankments and nailed soil walls), in which the friction angle varies between 30° and 36° depending on the particle size distribution criteria set forth in Standard NF EN 14475 ( Reinforced embankments execution standard). Moreover, higher shear strength values, identical to those of the platform under the footings, may be adopted provided they are associated with the material and degree of compaction defined in Section 6.4.1.2 for footings. The minimum characteristics and means of control are those listed in Table 7.3, which has been extracted from the Earthworks guide for building platforms and industrial facilities in the presence of water-sensitive soils (2009). Table 7.3: Minimum characteristics and means of control. Minimum required values (corresponding to a platform quality grade PF2)
Tests Static loading Plate Dyna-plate Dynamic Load-bearing loading capacity meter
Standards NF P 94-117.1 NF P 94-117.2
Static loading
NF P 94-117.3
Deflection under a 13ton axle
Westergaard
Benkelman Beam or deflectograph
NF P 98-200
Values
Reference
EV2
GTR Guide
Kw d 0 mm (granular subgrade layer) d (treated subgrade layer)
DTU 13.3
Catalogue of pavement structures
Remark: In the case of hydraulic binder-treated layers, the deflection measurement is more relevant than the plate test.
5.4.1.2. Underneath footings The materials available to compose the platform underneath a footing are the same for ground slab production, with the exclusion of chalk, the B11 materials and fine-grained materials treated exclusively with lime. The shear strength characteristics are justified by tests either specific to the project or reported in the product fact sheet or in reference to a database. In the absence of shearing tests, it may be possible to consider a 40° friction angle for crushed materials and 38° for rounded materials, provided the distribution layer is composed of a thickness well adapted to the supporting soil quality, with the following minimum characteristics: Class D1, D2, D3 or R (except for chalk), depending on the GTR92 guide (or NFP 11-300 standard); With LA < 35, MD < 30, and LA + MD < 60;
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Remark: LA: Los Angeles test, Standard NF EN 1097 2; MD: Micro-Deval test, Standard NF EN 1097 1
Compacted to at least 95% of the OMP (Optimum density of Modified Proctor compaction test).
In terms of compaction, a minimum of 95% OMP is recommended in all cases. 5.4.2. Treated materials
The strength of treated materials must be compatible with the loading transmitted in the platform. An assessment of the treatment ability must be conducted according to Standard NF P 94 100. Remark: The cohesion durability assumed in the design calculations must be guaranteed throughout the structural life cycle. 5.5. Minimum thickness
The minimum thickness is set equal to 40 cm under a raft or ground slab, and at 30 cm under a footing. This thickness must be raised should it fail to meet the compactness criteria sought at the layer bottom. 5.6. Platform overhang in the presence of footings
A minimum platform overhang relative to the space occupied by the footing is necessary in order to ensure platform compaction quality over its entire thickness underneath the footing. This overhang is greater than or equal to half the platform thickness, with a 30-cm minimum. 5.7. Eventual incorporation of a reinforcement layer 5.7.1. General remarks
The load transfer platform may be reinforced by installing one or more geosynthetic layers or a steel fabric mat. The reinforcement layers and their positioning must be chosen on the basis of the type of product, the component materials (i.e. type of polymers for geosynthetics), their mechanical or design characteristics, their evolution over time and the physicochemical aggressiveness of the contact soil or water. The set of specifications relative to the reinforcement layers are the same as those listed in Standard NF P 94 270: Retaining structures, reinforced embankments and nailed soil blocks, as complemented by the following considerations: The specifications focusing on geosynthetics and the interaction with embankments must be indicated in accordance with Standard NF EN 13251: Geotextiles and geotextile-related products-Characteristics required for use in earthworks, foundations and retaining structures;
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Within the scope of the EC Marking campaign, and in compliance with Standard NF EN 13251, the adopted characteristics must be expressed by the material producer in the form of an average value and the corresponding tolerance value(s) at the 95% confidence level. Durability-related information must be provided in accordance with the directives set forth in Appendix B (normative) of Standard NF EN 13251. 5.7.1.1. Types of geosynthetics The geosynthetics applied in these contexts may be: Reinforcement geotextiles, either woven or knitted, ideally placed at the base of the load transfer platform or embankment; Or reinforcement geogrids, preferably placed in the thickness of the load transfer platform granular layer. A reinforcement geogrid might also be installed on the load transfer platform base, at the interface with the supporting soil, yet it would be necessary to combine the eventual geogrid with a separation geotextile in order to avoid contaminating the granular layer by the finegrained soil. 5.7.1.2. Component material The component polymer must be compatible in durability terms with the embankment material. The polymers used to produce embankment reinforcements are mainly polyester (or polyethylene terephthalate, PET), polypropylene (PP), along with other polymers like polyaramide (pAR) and polyvinyl alcohol (PVA). These polymeric components are chosen depending on the chemical characteristics of the materials (pH, etc.) in contact with the reinforcement, including water when applicable. The minimum requirements have been defined in Standard NF EN 13251. 5.7.1.3. Required characteristics The design characteristics of geosynthetics for the purpose of reinforcement are as follows: Its long-term tensile strength, as determined based on short-term tensile strength (as per Standard NF EN ISO 10319, see Fig. 7.14) and on the isochronous creep curves (as per Standard NF EN 13431, Fig. V7.15); Its stiffness, which most often is expressed based on tensile strength at a given level of deformation (e.g. at 2%, 3%, 5% or 10%); Its interaction coefficients at the interfaces with materials in contact with the geosynthetic reinforcement layer.
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Figure 7.14: Curves derived from a tensile test conducted according to Standard NF EN ISO 10319.
Figure 7.15: Isochronous creep curves.
5.7.2. Layout drawings and installation guide
5.7.2.1. Installation and connection of the geosynthetic reinforcement layers The general guidelines, applicable to earthen structures reinforced by geosynthetic layers, give rise to a number of practical implementation rules, the most essential of which will be discussed below. These rules serve to complement those previously mentioned in Standard NF G 38060: General recommendations for the acceptance and implementation of geotextiles .
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The platforms receiving the reinforcement layers must be compacted, leveled and cleared of all angular elements or other component capable of damaging the layers (by either punching or tearing) during the steps of their spreading, positioning and pre-tensioning. The direct contact between the geosynthetics and inclusion heads must be avoided in order to minimize the risks of perforation and tearing along the edges and in the corners. A level of protection can be provided by a few-centimeter layer of fine-grained material (whether sand or gravel) or else a punching-resistant geosynthetic material. The reinforcement layers are spread on the platform, then cut along the length or ultimately deployed by means of prefabricated panels. The compliance of the layer's mechanical anisotropy with the direction of the forces the layer will be required to absorb in the structure, is to be verified in accordance with the indications included in the execution drawings.
Figure 7.16: Layout of geosynthetic layers displaying a mechanical anisotropy under an embankment.
The geosynthetic layers must be placed so as to prevent any folds while facilitating an initial pretensioning during embankment installation. The circulation of construction vehicles directly on top of the geosynthetics needs to be prohibited. An initial protective layer containing at least 20 cm of materials is necessary to allow for the circulation of construction site vehicles or equipment. 5.7.2.2. Longitudinal overlap and end protection of the rei nforcement layer To the extent possible, reinforcement overlap in the direction of the forces to be absorbed must be avoided. Otherwise, the layouts that ensure reinforcement continuity between adjacent layers are shown on the following drawings according to the justifications provided in the design calculation. In the case of reinforcement by two perpendicular layers on the same level, the longitudinal overlap between two adjacent layers must be at least 30 cm.
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Figure 7.17: Transverse and longitudinal overlap between geosynthetic layers under an embankment.
5.7.2.3. Anchorage elements To prevent geosynthetic layers from sliding, especially along the outer boundary of the rigid inclusion zone, an anchorage device should be assembled in order to absorb the forces calculated during the design stage. This anchorage may be produced in accordance with one of the following layouts: Simple anchorage (Fig. 7.18): the reinforcement layer is installed flat and extends beyond the footprint zone for inclusions with length L a, as calculated during the design stage. This length takes into account: the tensile force to be absorbed, the characteristics of materials in contact with the reinforcement layer, and the embankment thickness within the anchorage zone;
Figure 7.18: Simple anchorage of the geosynthetic layer.
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Anchorage with a trench cut and cover (Fig. 7.19): A trench is cut beyond the inclusion zone to allow anchoring the reinforcement layer with a cover;
Figure 7.19: Anchorage of the geosynthetic layer by means of a trench cut and cover method.
Anchorage with a geosynthetic layer wrapped around (Fig. 7.20).
Figure 7.20: Anchorage of the geosynthetic layer wrapped around.
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6. INTERACTION WITH THE OTHER PROJECT COMPONENTS (ROADS AND UTILITIES, STRUCTURAL WORKS)
It is incumbent upon the Project Engineer to develop a set of procedures and specific interface management phasing between the earthworks and rigid inclusion components, in order for the load transfer platform covering the rigid inclusions to be completed without damaging the inclusion heads while at the same time respecting the thickness and characteristics defined in the rigid inclusion design. In the case of in situ material treatment, the thicknesses of material layers are to be established so as to avoid deteriorating the heads of rigid inclusions as construction machinery rolls on top of these layers. In most cases, such coordination requires a certain waiting time between installation of the rigid inclusions in a given zone and platform availability for the other works components. A leveling operation should be required for the lower inclusion elevations under the working platform, and then the platform leveling operation using periodic fill and repeat compaction of the entire platform must be conducted separately from the additional platform construction. Special measures (undercutting, shoring, propping, inclusion integrity verifications) must be taken into account in the event of excavation work subsequent to the inclusion installation (passing utility lines, building pits or other works below grade).
References
FNTP, FFB, EGF-BTP, SBTF, USG, Syntec Ingénierie - Guide pour la réalisation des terrassements des plates- , décembre 2009. NF EN 1097 2 -Essais pour déterminer les caractéristiques mécaniques et physiques de granulats - Partie 2 : Méthodes pour la détermination de la résistance à la fragmentation, juin 2010. NF EN 1097 1 - Essais pour déterminer les caractéristiques mécaniques et physiques des granulats - -Deval), août 2011. NF EN 1536 - Exécution des travaux géotechniques spéciaux. Pieux forés, octobre 2010. NF EN ISO 10319 - Géosynthétiques. Essai de traction des bandes larges, août 2008. NF EN 12699 - Exécution de travaux géotechniques spéciaux. Pieux avec refoulement de sol, mars 2001. NF EN 12716 - Exécution des travaux géotechniques spéciaux. Colonnes, panneaux et structures de sol-ciment réalisés par jet, octobre 2001. NF EN 13251 - Géotextiles et produits apparentés. dans les travaux de terrassement, fondations et structures de soutènement, septembre 2001. NF EN 13431 - Géotextiles et produits apparentés. Détermination du comportement au fluage en traction et de la rupture au fluage en traction, novembre 2000. NF EN 14199 - Exécution des travaux géotechniques spéciaux. Micropieux, septembre 2005. NF EN 14475 - Exécution de travaux géotechniques spéciaux. Remblais renforcés, janvier 2007.
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NF EN 14679 - Exécution de travaux géotechniques spéciaux. Colonnes de sol traité. Version corrigée, septembre 2005. NF G 38060 - Textiles. Articles à usages industriels. géot cations. Contrôle des géotextiles et produits apparentés, juin 1994. NF P 11-300 - Exécution des terrassements. Classification des matériaux utilisables dans la , septembre 1992. NF P 94-100 - Sols : reconnaissance et essais. Matériaux traités à la chaux et/ou aux liants hydrauliques. , août 1999. NF P 94-262 - Justification des ouvrages géotechniques. onale de Eurocode 7. Fondations profondes, mai 2011. NF P 94-270 - Calcul géotechnique. Ouvrages de soutènement. Remblais renforcés et massifs en sol cloué, juillet 2009.
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CHAPTER 8
Controls and instrumentation
1. INTRODUCTION
In order to guarantee high structural quality, and in accordance with the NF P94-500 Standard on geotechnical project missions, it is necessary for all geotechnical structures (embankments, inclusions, load transfer platforms, reinforcement layers, earthworks, foundation structures, etc.) to respect the following steps: Definition by the prime contractor of project-specific criteria: allowable settlements, load intensity, task scheduling, etc.; Execution by a certified Engineer of the (G2) draft geotechnical design, and (G4) geotechnical works supervision; Achievement of the works by a qualified contractor, assigned the (G3) geotechnical works planning and monitoring; Execution of a technical control mission with the aim of contributing to risk prevention, assigned to a body certified by the competent administrative authority. Moreover, soil reinforcements, like any other technique related to geotechnical works, require effective works execution supervision, monitoring and maintenance according to the prescriptions set forth in Eurocode 7, Section 4. The tests and controls pertaining to soil reinforcement works through the introduction of rigid inclusions encompass all or some of the following tests: Static loading tests on an isolated inclusion, which may be either failure loading tests or load-bearing capacity and deformation tests; Static loading tests on a group of inclusions; Information tests; Shaft integrity controls; Implementation controls; Load transfer platform controls; Geotextile or geogrid controls. 2. STATIC LOADING TESTS ON AN ISOLATED INCLUSION IN COMPRESSION
These tests are to be conducted in accordance with the NF P 94-150 Standard, as complemented by the set of protocols defined hereafter. 2.1. Failure loading tests
This round of tests is not to be performed systematically. When run, these tests feature objectives in numbers that are: Either set by the Engineer, Or determined by the contractor. This type of test is intended to: Validate the set of design parameters that define the rupture load; Controls and instrumentation
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And ultimately optimize the project relative to: - actual soil characteristics, - and/or the specific technique employed.
Each of these tests is carried out on a single inclusion not incorporated into the structure: The number of tests is defined based on the various geotechnical zones previously identified on the given project; The minimum test load must be determined on the basis of both the assumed inclusion geometry (diameter, length, material strength) and geotechnical parameters; this load is derived from terms specific to the tip R b and the shaft friction R s, as evaluated depending on the use profile; The characteristic load-bearing values (R b;k and R s;k 1 and 2, as defined in Eurocode 7 with respect to the number of such tests; The material strength of these inclusions, which has been taken into account to determine the actual test load, must be high enough when conducting the test. Remark: Lets highlight that upon conducting these tests, no negative skin friction is mobilized. In some cases, it may be beneficial to distinguish the tip term R b from the shaft friction term R s. It then becomes necessary to either install dedicated inclusion instrumentation or else place several inclusions of various lengths (see Fig. 8.1).
Figure 8.1: Results of loading tests conducted on inclusions of various lengths (Chelles experiment).
2.2. Load-bearing and deformation control tests
This test is carried out on an inclusion that may be integrated into the structure. Such a test serves to identify both the settlement vs. load curve and the creep load of the inclusion. From a practical perspective, the machine producing the inclusions can also perform the function of reaction block. For project sites lasting no longer than 1 week, the inclusions intended for testing would need to be made from a material with admixtures that enable accelerating its strength.
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2.2.1. Test load value
2.2.1.1. Design load The design load Q max equals the maximum load inside the inclusion at the level of the neutral plane in a serviceability limit state (SLS) situation. This load is the sum of the head load Q and negative skin friction (F N) from the inclusion head to the neutral plane (Fig. 8.2).
Figure 8.2: Distribution of forces in the inclusion by taking into account the negative skin friction and neutral plane position.
2.2.1.2. Case where the inclusions only serve to reduce settl ement (Domain 2) Generally speaking, these cases pertain to ground slabs, rafts or embankments, or else to footings whose stability at the ultimate limit state (ULS) is provided without requiring an inclusion. The test load equals the design load Q max increased by the negative skin friction F N. A test conducted using this maximum load is called a quality test .
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2.2.1.3. Case where inclusions provide structural stability at the ULS (Domain 1) These cases generally pertain to footings whose stability at the ULS cannot be ensured without introducing an inclusion. The test load is equal to: q Q + 2 FN F N, where (with Q being the load at the inclusion head).
q
= 1.5 and
FN
= 1.5.
A test performed with this maximum load is called a load-bearing capacity test. 2.2.1.4. Value of F N F N is evaluated via the following relation: qs x inclusion perimeter x neutral plane depth. q s must be the highest value per layer from among: The maximum positive skin friction value expected for this type of inclusion depending on the type and composition of the soil being crossed; The maximum negative skin friction value output by the computation model; The value obtained by the test defined in Section 2.2.2. Remark: To interpret the value derived for F N, another solution consists of neutralizing the shaft friction above the neutral point during the test. 2.2.2. Estimation of friction in soft soil
A compression test on a short inclusion conducted over the height of the soft soil layer serves to estimate the skin friction value within this layer. Remark: The inclusion length is typically equal to the depth of the neutral point. According to this configuration, the contribution of the tip effect is small, which justifies the compression test for its ease of implementation. 2.2.3. Test frequency
Loading tests are mandatory. It is acceptable to opt not to conduct loading tests for small-sized projects (with a total cumulative length of less than 2,000 lm for instance). In this case, the geotechnical type verifications (GEO) are carried out with an additional reduction factor of 1.5. This factor is applied to the characteristic values of tip resistance and shaft friction below the neutral plane. This point addresses the verifications described in the following sections of Chapter 5: 1.1.3: Alternative verification of bearing capacity SLS; 1.2: Ultimate limit state ULS; 4.1: Inclusion behavior. Remark: A similar reduction factor of 1.5 related to material strength is already included in the k 3 coefficient values given in Table 5.2 when no static loading test is performed.
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The frequency of these tests is set according to the prescriptions listed in Table 8.1, with at least 2 tests per independent structure and/or per designated homogeneous geotechnical zone. Table 8.1: Testing frequency.
Number of inclusions
Frequency of tests on inclusions required for load-bearing capacity at the ULS (Domain 1)
Between 1 and 600 Between 601 and 2,000 Beyond inclusion number 2,001
1 per group of 75 1 per additional group of 150
Frequency of tests on inclusions not required for load-bearing capacity at the ULS (e.g. case of settlement reduction) (Domain 2) 1 per group of 150 1 per additional group of 300
1 per additional group of 250
1 per additional group of 500
Remark: Each individual group corresponds to a homogeneous geotechnical zone.
2.2.3.1.Example Below is an example of a structure containing 1,100 inclusions uniquely devoted to settlement reduction, with 800 inclusions required for the load-bearing capacity at the ULS: Domain 2: settlement reduction: 1,100 inclusions, 6 tests: 4 until reaching 600, then 2 from 601 to 2,000, i.e. for 6 tests in all; Domain 1: load-bearing capacity: 800 inclusions, 10 tests: 8 until reaching 600, then 2 from 601 to 800, i.e. for a total of 10 tests. 2.2.4. Test procedure
An initial loading cycle is introduced with a load equal to 10% of the test load and being maintained for a period of 15 minutes. After unloading, the maximum test load is reached by increments of 20%, thus proceeding in five steps. Settlements are measured using at least 3 measurement points, distributed evenly over the plate installed on the inclusion head, at the following times: t = 1, 2, 4, 8, 15, 30 and 60 min during the loading stages; t = 1, 2, 3, 4, and 5 min during the final unloading stages. Over the course of the loading stages, it is authorized to proceed to the next stage provided displacement remains less than 0.02 mm/min on at least two consecutive measurements, with a minimum 15-minute interval. Otherwise, the entire stage, i.e. 1 hour, must be allocated. A prediction of the loading curve is to be furnished as part of the execution study, using the same computation models as those applied to the project design, yet in accounting for positive skin friction (as estimated in Section 2.2.2) from the top of the inclusion and in considering the case of an isolated inclusion. The results of these tests must then be compared with this prediction: Test results are deemed satisfactory if the measured settlements do not exceed the theoretical settlement by more than 20%. Otherwise, the results would have to be examined in coordination with the Engineer s mission;
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If settlements are found to be significantly less, the eventual impact on structural design parameters should be assessed.
3. INFORMATION TESTS
Information tests are conducted before the general site production adjacent to representative boreholes of each zone considered to be homogeneous from a geomechanical perspective. These tests are to be completed and compared with results obtained from tests carried out when producing the inclusions. These information tests are intended to: Verify that the anticipated depths as well as the geometric characteristics are feasible using the designated equipment; Adjust inclusion length whenever possible to identify the anchorage layer; Control for material consistency (concrete or mortar), whether delivered or produced onsite. The inclusions developed during these tests become an integral part of the project soil improvement steps. With the project Engineer's approval, other information tests may be undertaken in order to establish correlations between the various project zones, should their importance be considered necessary. These tests are also intended to determine the execution and concreting parameters for inclusions, on an as needed basis. Information tests are to be customized for each individual mode of inclusion execution, which will be discussed in detail below. Remark: It is highly recommended to perform these tests in the presence of both the Engineer s representative and the soil engineering consultant. If such is not the case and should an anomaly appear when conducting these information tests (e.g. noncompliant soil strength values, inclusion either too short or too long relative to the boreholes, considerable loss of concrete), the Project Owner, Project Engineer and geotechnical specialist (soil engineering firm) must be immediately notified in order to issue a ruling on the adaptation or optimization of the geotechnical structure proposed by the developer. Moreover, these tests must be written up in a report by the project developer, with distribution to all project actors as expeditiously as possible. 3.1. Inclusion-driving method
This technique pertains to either metal or prefabricated concrete inclusions directly driven or to inclusions made of concrete cast inside a driven closed steel tube. During inclusion installation, a pile-driving test sheet is established, consisting of: Inclusion identification number and type; Date and time of the beginning and end of the driving operation; Type of drop hammer used (single-acting, double-acting, diesel, etc.); Weight of the striking mass and the mass being struck (e.g. rigid inclusion, follower pile, pile helmet), as well as the driving energy;
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The number of hammer strikes necessary in order for the inclusion to penetrate a given length, typically 10 cm. This reading is taken over the entire penetration length in the soil by indicating the height(s) the hammer drops or the driving energy; Elastic refusal at the end of the driving operation; Refusal during the final three rounds of 10 strikes of the drop hammer; Any incidents during the driving operation (obstacles interfering with penetration, displacements of neighboring inclusion heads, interruptions to the driving process, etc.); The concrete volumes ultimately introduced (for the inclusions cast in place).
From this test sheet, the driving plot can be derived as follows (Fig. 8.3).
Figure 8.3: Example of an inclusion-driving plot.
In the case of a driven tube, keep in mind that the tube's base is composed of either a lost plate or a valve. In the case of concrete inclusions implemented inside a casing, both the driving curve and concreting curve need to be provided for each test. Any eventual loss of concrete must be reported. The tube lifting (extraction) speed would also need to be indicated. 3.2. Boring with or without soil displacement
The boreholes are monitored and described in borehole data sheets. Whenever the drilling technique so allows, a detailed soil cross-section must be established by specifying, to the extent possible, the color, type texture, odor and humidity of the soil in order to verify whether the soils being crossed are in fact those described by the surveying campaign. Alternatively, a continuous parameter recording is produced so as to offer the opportunity to generate a summary geotechnical cross-section, in addition to ensuring that the required inclusion embedment is achieved. These parameters shall be displayed in real time during execution of the inclusion. Moreover, should drilling be of the simple type (see section on the modes of inclusion execution), then it would be necessary to ensure excavation wall stability prior to the concreting step.
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During concreting, the injection pressure (should the technique so allow), the volume of concrete set into place and the pumping rate need to be specified. Any overconsumption or under-consumption and eventual loss of concrete must also be notified. During execution of the borehole, an execution fact sheet is produced (Fig. 8.4), detailing: Identification number and type of pile; Date and time of the beginning and end of the drilling operation; Characteristics of the various boring tools employed (drill bit, valve, hammer grab, auger, etc.), along with the eventual associated casing; Drilling parameter recording curves, should the technique implemented yield such curves, which if available are to be completed with any observation entry aiding the step of identifying the crossed layers (i.e. indices collected during execution); Description of characteristic samples for each soil layer crossed, as the technique allows; Any boring-related incidents (rockslides, cavities, accidental loss of drilling fluid, water inflow/seepage, etc.); Concreting curve (Fig. 8.5) should the technique so allow, or else concreting parameter recordings.
Figure 8.4: Example of curves recording drilling and concreting parameters.
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Figure 8.5: Example of concreting curve (when the technique so allows).
3.3. Driven inclusions
The driving step may be carried out by either a jacking + rotation combination or else jacking + vibration. This step provides a series of driving parameters (penetration speed, pressure on the driving tool, turning torque or vibrational frequency) and concreting parameters (tube extraction speed, volume of concrete placed, pumping rate and diameter calculated based on incorporated volume). Any eventual anomaly in concrete consumption must be specified. During inclusion installation, an execution data sheet is established that features: Identification number and type of inclusion; Date and time of the beginning and end of the driving operation; Characteristics of the various tools used and the casings; Any drilling incidents (rockslides, cavities, accidental loss of drilling fluid, water inflow/seepage, etc.); The volumes of concrete placed. 3.4. Vibro-driven inclusions
The purpose is to output the set of vibro-driving parameters (penetration speed, pressure on the testing tool, vibrational frequency) and concreting parameters (speed of tube extraction, volume of concrete placed, pumping rate, diameter calculated based on incorporated volume). Any eventual anomaly in concrete consumption upon execution must be indicated, along with any eventual incidents on the fresh concrete of neighboring inclusions. During inclusion production, an execution fact sheet is generated, covering the following: Identification number and type of inclusion;
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Date and time of the beginning and end of the vibro-driving operation; Curves presenting recordings of vibro-driving parameters, as permitted by the technique. These curves are complemented by any observation aiding the identification of layers crossed (indices collected during execution), Characteristics of the various tools implemented and the casings; Any incidents (sinkholes, water inflow/seepage, premature refusal, etc.); The volume of concrete placed. 4. SHAFT CONTROL TESTS 4.1. Structural integrity
Verification of the structural integrity of a concrete inclusion consists of conducting a test involving reflection or impedance. These tests are mandatory. The only exception is dedicated to the Domain 2 inclusions on operations of more minor importance (e.g. threshold on the order of 2000 linear meters). These tests are conducted according to the NF P 94-160-2 Standard (reflection-based method) and the NF P 94-160-4 Standard (impedance method). Remark: These tests are not considered as reinforcement control from the standpoint of the National Application Standard of Eurocode 7 (NFP 94-262: Deep foundations). 4.2. Diameter (isolated inclusion / inclusion group)
Inclusion diameter verification, when the inclusion has been cast in place, must be systematically performed upon the initiation of each project at a rate of 1 inspection per group of 500 inclusions or 5,000 linear meters placed. The inclusion is executed in the immediate vicinity of the project footprint. Once the concrete has been set, the inclusion is released over its maximum possible height and then ultimately extracted over this same height. Its diameter or circumference is then measured and any variation in diameter or circumference requires a specific analysis. Remark: A variation in diameter or circumference may be due to: The execution method, causing excessive soil disturbance; A pumping pressure either too strong or too weak; A soil either too stiff or too soft; Hydrogeological conditions. Level by level, these variations in diameter or circumference must be taken into account in the design, for increases in excess of 30% or for any kind of decrease (Fig. 8.6).
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Figure 8.6: Incorporation of the variations observed in the measured diameter.
4.2.1. Inclusions with nominal diameter equal to that of the tool
Without controlling for the inclusion diameter, a reduction coefficient applied to the tool diameter equals 1.10. 4.2.2. Other cases
Under this heading would fall for example: inclusions executed using the footprint of a vibrator equipped with an airlock (stone column with grout injection, inclusion of the Vibro Concrete Column type), hammered inclusions, and/or jet grouting. Without controlling the diameter, the nominal diameter will be limited to the tool diameter increased by at most 10%, except in the case of jet grouting. In these cases of jet grouting, it is necessary to verify the actual diameters obtained. 4.3. Mechanical characteristics of the component material 4.3.1. Compressive strength tests
The mechanical characteristics of the component material of inclusions can be verified by compressive strength tests at both 7 and 28 days, with a minimum of: 1 sampling (6 specimens) every 100 m 3 of material placed; 1 sampling (6 specimens) every 3 days; 2 samplings (12 specimens) per jobsite. For some techniques (jet grouting, soil mixing), these samplings may be performed at the column head upon completion of the execution step.
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4.3.2. Material consistency tests
Concrete should be supplied by a truck mixer. The contractor would perform at least two fresh concrete slump tests on each delivery truck batch (one test prior to placement, a second one during the placement step). In the case of concrete supply using an onsite mixing plant, concrete slump tests will be conducted at a rate of one test per each batch of 10 m 3 produced. 4.3.3. Inclusion head quality
When the leveling technique employed allows guaranteeing a high-quality inclusion head along with an acceptable degree of precision, the cutting-off step is no longer necessary and a simple visual inspection proves sufficient. 5. CONTROL OVER INCLUSION IMPLEMENTATION AND ELEVATION (BOTH DURING AND AFTER EXECUTION)
The controls required during execution, as performed by the contractor as part of an internal control protocol, cover all inclusions on the project site. These controls pertain to inclusion implementation and give rise to a layout of executed inclusions to be transmitted to the Project Engineer. This layout document precisely indicates all inclusions deliberately executed beyond the allowed tolerances (due to encountering obstacles, added or removed inclusions).
For inclusions located under a structural footing, the systematic acceptance of both the number and position of these inclusions is carried out by the subsequent works specialty (earthworks and/or structural engineering) based on this layout of executed inclusions . The acceptance step is recorded in a report that must then be transmitted to the Project Engineer for validation.
As long as execution deviations remain less than the implementation tolerances defined in Chapter 7, then it shall be considered that these deviations exert no impact on the behavior of the structure lying on top of the inclusions. With regard to execution deviations exceeding implementation tolerances, it must be verified that the structure is able to absorb the additional induced forces. 5.1. Under a footing
For inclusions executed with a cutting-off, the upper leveling of the inclusions before cuttingoff must be systematically recorded so as to avoid breaking when conducting earthworks and, moreover, must at least reach the theoretical leveling elevation increased by 20 cm (to ensure material quality at the final cutting-off elevation). Remark: These upper leveling elevations before the cutting-off have been indicated on the as-built drawing forwarded to the Project Engineer for input into the subsequent earthworks design.
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The elevation readings after the cutting-off, along with inclusion implementation, must be systematically controlled. 5.2. Under the ground slab, raft and embankment
In the case of a low leveling elevation, the elevation readings following the ultimate cuttingoff step and inclusion implementation must also be systematically controlled. In these cases, it must be verified that the leveling surface does not extend below the base of the working platform. 6. QUALITY AND THICKNESS CONTROL OF THE LOAD TRANSFER PLATFORM 6.1. Thickness
Each of the contractors and subcontractors involved on a project site must provide a set of as built drawings with elevation readings for the project structures, in accordance with the firm's execution monitoring requirement. The reconciliation of these level recordings with the design parameters is performed by the Project Engineer as part of the assigned task of providing geotechnical supervision services for project execution. Total thickness must be verified at least by means of simple comparison between the leveling of the working platform performed after reprofiling (see Chapter 7) and the leveling introduced following execution of the transfer platform. To control the load transfer platform thickness above the inclusion heads, the leveling of inclusion heads after an eventual cuttingoff step must also be taken into account. The leveling measurement frequencies are defined in the works contract documents. As a default value, the following recommendations have been issued: For extended structures (e.g. raft, ground slab, embankment): - a minimum of 3 points, - a leveling point, at a rate of: - 1 every 400 m², until reaching a surface area of 2,000 m 2, - 1 every 1,000 m² beyond the 2,000 m² threshold; Under a footing: - 1 leveling point in alignment with each footing. Remark: In the case of inclusions executed by soil displacement within a saturated clayey soil with a dense mesh pattern, it would be necessary to control the eventual lifting of the working platform before building the load transfer platform. 6.2. Quality
Load transfer platform quality must be controlled in alignment with the inclusion as well as in between inclusions. The load transfer platform material must be the target of identification and compaction controls.
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6.2.1. Identification tests
The identification tests to be carried out pertain to the following parameters: Material origin; Material classification, as intended by the GTR92 guideline (NF P 11-300); Particle size distribution curve; Hardness characteristics: LA, MDE and LA+MDE; Shear strength tests (c, ). Remark: For the case of natural gravel of the D1, D2, D3 and R types, shearing strength tests may be waived, with values adopted from Section 6.4.1 of Chapter 7. 6.2.2. Compaction control
Road type tests are recommended; these feature: density measurements (to be compared with the Modified Proctor optimum density), plate bearing tests, CBR or IPI.
Remark: The minimum values (E V2 and/or density) targeted are those defined in the chapter on Execution (Chapter 7) or else those defined in the design, should they be more stringent.
Should the load transfer platform thickness exceed 80 cm, then the pressuremeter or static penetrometer may be used to control compaction. Both the type and number of tests must be set forth in the project contract. The contents of the subsequent sections are intended as an aid when drafting works contracts. 6.2.2.1. Under structures with distributed loads (slab, raft, embankment or pavement) LCPC type Plate bearing tests (Standard NF P 94 117-1 to -3) are preferred for this application. The number of such tests is specified in reference to the rules specific to the given structure (DTU 13.3, GTR documents). As a default frequency, the following value is recommended: the minimum number is set equal to 3 tests, plus 1 additional test for every 2,000 m 2. 6.2.2.2. Under the footing When access conditions on the upper part of the load transfer platform complicate running plate tests, then density tests are to be favored; testing frequency: 1 for every 10 footings (with a minimum of 5 per project site). These density tests must be correlated with the set of tests conducted in alignment with the plate tests.
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7. ADDITIVES FROM THE FAMILY OF GEOSYNTHETICS
A geosynthetic control needs to be undertaken in compliance with both the NF G 38060 Standard and the CEN/TR 15019 recommendation document entitled: Geotextiles and related products - Worksite controls. 7.1. General remarks
These controls must place priority attention on: Products delivered to the worksite; Assessment of the compliance of load transfer platform materials with standards adopted for the reinforcement design regarding the risks of geosynthetic damage and durability; Verification of handling and storage conditions, which must comply with supplier recommendations; Verification of reinforcement implementation. Product positioning must be compliant with the layout and supplier recommendations. More specifically, the orientation, direction of installation and overlaps or junctions must be verified along with the anchorage devices. 7.2. Control upon acceptance of the products delivered to the worksite
This control step is intended to verify the compliance of characteristics for delivered products with the set of detailed specifications. This step comprises a verification in comparison with the "product" fact sheet (control of labeling, reinforcement layer marking); this procedure applies to all batches delivered. Remark: The supplier must allow the user to identify geotextiles or related products and provide compliance with requirements set forth in the EN ISO 10320 Standard entitled: Geotextiles and related products - Onsite identification. 7.3. Control of product characteristics after implementation
Product characteristics following implementation can be controlled in the form of a test board, intended to determine actual damage subsequent to works execution (see the NF P 94-270 Standard). 8. ADDITIVES LIKE METAL LATTICEWORK
Metal latticework is controlled in accordance with the NF P 94-270 Standard relative to reinforced embankments. 9. INSTRUMENTATION
The results of monitoring measurements must always be evaluated and interpreted; moreover, such a step normally proceeds in quantitative terms. This section contains a few fundamental rules for instrumenting a structure on a soil reinforced by rigid inclusions. These rules are based on experience acquired during the instrumentation of two full-scale experimentations and several actual structures executed as part of the ASIRI national project (Fig. 8.7).
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The instrumentation-based control of a structure built on a soil reinforced by rigid inclusions may be performed prior to the actual structural works on a prebuilt block or else directly on the structure itself. The instruments must be adapted to the given structure, e.g. embankment or reservoir. Sensors are to be positioned in representative zones, e.g. under the core and at the foot of the slope for an embankment, under the center and periphery for a reservoir (Fig. 8.8).
Figure 8.7: Depiction of instrumented structures within the scope of the ASIRI national project.
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The type of sensors introduced must be adapted to the settlement being measured, which tends to be quite small. The sensors used to monitor embankment settlements on soft soils (settlement balls, settlement plates, etc.) may prove unsuitable due to both their level of accuracy and their size.
Figure 8.8: Example of sensor implementation.
For a preliminary test block, the number of rigid inclusions must be high enough to ensure that the measurement is not adversely affected by edge effects: In a rectangular mesh configuration for example, sixteen inclusions yield a measurement of the central mesh under satisfactory conditions (Fig. 8.9a); To measure the amount of load transferred onto an inclusion, a 9-inclusion test block would be sufficient (Fig. 8.9b).
Figure 8.9: Sensor implementation zone determined as a function of the intended result: a) mesh measurement; b) load transfer on an inclusion.
To ensure that the instrumentation remains efficient and accepted by the various project actors, it must be designed so as to impede construction phasing as little as possible. Along these lines, the settlement sensors embedded into the soil are preferred over settlement meter gauges crossing the structure and capable of either slowing construction progress or being damaged (Fig. 8.10).
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Figure 8.10: a) embedded settlement sensor; b) settlement meter gauges.
Sensor size and measurement range both need to be adapted to the target structure. The acquisition mode (automatic vs. manual) and frequency (greater over the construction phase than during service) must take into account the execution phasing. To protect the load transfer mechanisms from being disturbed by sensor installation, the setup step must be integrated within the scope of normal works phasing. Remark: The fact of installing the sensors afterwards (e.g. inside a ditch or excavation) may locally modify material layer properties while interfering with measurements.
Special attention must be paid to implementing the instrumentation and conducting earthworks in the vicinity of the sensors: In case of a binder-based treatment on the load transfer (mixing) platform; During compaction of the load transfer platform; During excavation of the pit or trenches. The instrumentation must at least enable measuring the structural settlement. Other measurements may prove pertinent as well, i.e.: Measurement of load transfer onto rigid inclusions; Pore pressure measurement in the soft soil; Rigid inclusion settlement measurement; Measurement of reinforcement layer deformation on the load transfer platform: geosynthetics, latticework; Ground slab deformation measurement; Measurement of both lateral displacements and rigid inclusion angles of inclination at the foot of the slope in the presence of an embankment or structural perimeter. 9.1. Settlement measurement
The settlement may be measured along the vertical and/or horizontal profiles. 9.1.1. Measurement along a vertical profile
In the case of an embankment on soft soil, it may be worthwhile to measure the vertical profile of the settlement beginning at the substratum layer and extending to the top of the embankment. Such a measurement may entail placing a borehole magnetic extensometer,
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though its use requires embankment implementation precautions that must be taken into consideration by the earthworks contractor. The settlement of soft soil can also be measured using a rod extensometer. This device offers the advantage of being buried and not interfering with implementation of the structure. For any instrument placed into vertical boreholes, every assurance must be made that the sealing grout exhibits a sufficiently low stiffness so as not to alter the measurements. Reference should be made to the recommendations issued by Peignaud and Chaput (1983). 9.1.2. Measurement along a horizontal profile
For measuring horizontal profiles, the sensors introduced should be equipped with an appropriate precision and measurement mode; moreover, they should be of a size that does not modify the behavior of the surrounding medium. It may be beneficial to measure horizontal profiles at the level of inclusion heads above the load transfer platform. Horizontal profiles can be measured either by sending probes into a casing installed ahead of time (hydrostatic profilometer, horizontal inclinometer) or by measuring the vertical displacement of isolated sensors laid out in a row (settlement meter gauges, pressure sensor for the liquid level measurement - called a transmitter , whose operating principle will be explained in Section 9.1.3 - and settlement meter cells).
The primary advantage of probe-based measurements is that only the casing is lost. On the other hand, the probe dimensions necessitate a measurement increment; the introduction of casings requires cutting trenches, to be filled by sand in the transfer platform, which then is capable of locally modifying the settlement. In the case of specific structures (e.g. reservoirs), the set-up may be directly inserted into the raft of the given structure. This type of measurement also imposes preparing two points to serve as references on both sides of the profile, whose monitoring must also be extended to the leveling. Lastly, the precision of both the measurement and its position within the tube is considered unsatisfactory whenever the expected settlements are small; in addition, the differential settlement needs to be clearly identified between rigid inclusions and soft soil. Remark: In light of these difficulties, the settlement measurement protocol laid out herein may prove complicate to perform. 9.1.3. Point-specific measurements
Settlement meter gauges are inexpensive; their use however causes structural implementation difficulties along with the need for external intervention in order to perform the measurements. The ball-type settlement meter cells are too cumbersome to produce a precise settlement measurement.
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Experience has shown that the use of transmitters for liquid level measurements (Fig. 8.11) is the best adapted in terms of precision, space requirements, installation and acquisition: These transmitters are connected in series by means of both a hydraulic line to a reservoir, filled with antifreeze and fastened onto a support outside the structural footprint, and an electrical line running to the recording box; The reservoir ensures that the system always remains saturated and at constant load; Each transmitter measures the pressure variation between its position and the reservoir level; A reference transmitter is fastened beneath the reservoir and serves to calculate the settlement of the other transmitters placed underneath the structure. Each transmitter is compensated in atmospheric pressure by a capillary running along the electrical cable.
Figure 8.11: Settlement meter cells of the "transmitter" type.
This technique requires taking great precaution both in localizing the benchmark and in installing the sensors. Figure 8.11 presents a basic configuration for measuring horizontal profiles at the inclusion head level and above the load transfer platform using transmitters. A two-reference solution is preferred should the project site provide a feasible layout. 9.2. Load transfer control
The load transfer operation may be measured through the use of earth pressure cells (sensors) installed either on the rigid inclusion head, within the rigid inclusion, on the soft soil, or above and inside the load transfer platform (Fig. 8.12). Nonetheless, installation on the rigid inclusion head is preferable to that on soft soil, as the pressure measurement proves to be more reliable when the sensor is placed on a rigid surface; in this case, it is more effective to use circular sensors of the same diameter as the rigid inclusion. The measurement range of sensors positioned on rigid inclusions must be selected under the hypothesis that the entire load of a mesh lies on top of the inclusion.
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Figure 8.12: Position of earth pressure cells used to indicate load transfer.
In the case of inclusions fitted with prefabricated reinforcement cages, it is commonplace to determine the load applied onto the inclusion indirectly by measuring deformation inside the inclusion using strain gauges fastened to these cages. On the other hand, in the case of non-reinforced rigid inclusion instrumentation, this measurement becomes complicated by the absence of reinforcements for sensor installation. In this latter case, stress determination within the inclusion requires knowledge of the modulus value reached by the inclusion material on each and every measurement date. Remark: This strategy may prove complex when the planned measurement period is long (with a large number of specimens to be tested over time and an extended specimen preservation mode). 9.3. Pore pressure measurement in soft soil
When this measurement is deemed pertinent, the changes in pore pressure during both the construction and service life of the structure may be monitored by means of pore pressure sensors introduced in the soft soil, under the water table and prior to rigid inclusion execution. Remark: Whenever sensors are installed before inclusion execution, a precise inclusion and sensor implementation plan is necessary in order to avoid sensor damage.
The water table level may be controlled outside the structural footprint using either pore pressure sensors or several piezometers. Remark: Water table level monitoring is recommended whenever settlement measurements are conducted. 9.4. Deformation of horizontal reinforcements 9.4.1. Geosynthetic layers
When the load transfer platform is reinforced by one or more geosynthetic layers, the layer deformation measurement can yield useful information on how these geosynthetics contribute to load transfer mechanisms. Conventional methods (deformation gauges, strain gauges) are difficult to apply here due to sensor encumbrance or connection between the sensor and geosynthetic layer.
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Fiber-optic sensors inserted into geosynthetic layers are capable of measuring the point deformations or else deformations all along the optical fiber. The use of optical fibers has yielded excellent results in terms of precision, durability and ease of implementation, provided a few precautions have been strictly followed during installation (ASIRI Report 2.07.1.01, 2007) (Fig. 8.13).
Figure 8.13: Geosynthetic layers equipped with optical fibers (Geodetect ®).
9.4.2. Metal latticework
As regards metal latticework, the deformation measurements derived using conventional deformation or strain gauge-type sensors remain well adapted, yet still require following precautions at the time of installation. 9.5. Lateral displacements and inclination of inclusions
Lateral displacements may be measured by installing vertical inclinometer boreholes in the soil or placing inclinometers directly into the inclusions. Inclinometer sensors are able to indicate any inclination variation in the rigid inclusions, localized at the foot of the slope or at the periphery of the structure.
Figure 8.14: Inclinometer casing positioned at the foot of the slope.
9.6. Measurement acquisition systems
The measurement acquisition system, regardless of its type, may be either automatic or manual depending on: measurement duration and frequency, types of sensors used, human resources, and accessibility conditions. In order to ensure measurement acquisition system durability, it is imperative to adopt a series of special precautions (e.g. anti-vandalism protection).
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References
ASIRI « Rapport davancement de Chelles », 2.07.1.03, 2007. G 38060 Textiles. Articles à usages industriels. Recommandations pour lemploi des et produits apparentés, juin 1994. NF P 94-500 - . NF EN 1997-1 (P 94-251-1) - Eurocode 7 Calcul géotechnique. Partie 1 : « Règles générales ». NF EN 1997-1/NA (P94-251-1/NA) - Eurocode 7 Calcul géotechnique. Partie 1 : « Règles générales ». Annexe nationale à la NF EN 1997-1, 2005. NF EN 1997-2 (P94-252) - Eurocode 7 Calcul géotechnique. Partie 2 : « Reconnaissance des terrains et essais ». NF P 94-150-1 - Sols : reconnaissance et essais. Essai statique de pieu sous effort axial . Partie 1 : « En compression ». NF P 94-150-2 - Sols : reconnaissance et essais. Essai statique de pieu sous un effort axial . Partie 2 : « En traction ». NF P 94-160-2 - ndation. Partie 2 : « Méthode par réflexion ». NF P 94-160-4 - . Partie 4 : « Méthode par impédanc »e. NF P94-262 (P94-262) - Calcul géotechnique. Fondations profondes. NF P 11-300 - Exécution des terrassements : classification des matériaux utilisables dans la . NF P 94 117-1 - Sols : reconnaissance et essais. Déformabilité des plates-formes. Partie 1 : « Module de déformation statique à la plaque ». NF P 94 117-2 - Sols : reconnaissance et essais. Portance des plates-formes. Partie 2 : « Module sous chargement dynamique ». NF P 94 117-3 - Sols : reconnaissance et essais. Portance des plates-formes. Partie 3 : « Coefficient de réaction de Westergaard sous chargement statique dune plaque ». NF P 94-078 - Sols : reconnaissance et essais. Indice CBR après immersion ; Indice CBR immédiat ; Indice portant immédiat. Mesure sur échantillon compacté dans le moule CBR. NF P 94-093 - Sols : reconnaissance et essais. Détermination des références de compactage atériau. Essai Proctor normal ; Essai Proctor modifié. NF P 11-213-1 (DTU 13-3) - Dallages. Conception, calcul et exécution. Partie 1 : « Cahier des clauses techniques des dallages à usage industriel ou assimilés ». Homologuée mars 2005. NF P11-213-1/A1 (DTU 13.3) - Dallages. Conception, calcul et exécution. Partie 1 : « Cahier des clauses techniques des dallages à usage industriel ou assimilés ». Amendement homologué mai 2007. NF P 11-213-2 (DTU 13-3) - Dallages. Conception, calcul et exécution. Partie 2 : « Cahier des clauses techniques des dallages à usage autre quindustriel ou assimilés ». Homologuée mars 2005. NF P 11-213-2/A1 (DTU 13-3) - Dallages. Conception, calcul et exécution. Partie 2 : « Cahier des clauses techniques des dallages à usage autre quindustriel ou assimilés ». Amendement homologué mai 2007. NF P 11-213-3 (DTU 13-3) - Dallages. Conception, calcul et exécution. Partie 3 : « Cahier des clauses techniques des dallages de maisons individuelles ». Homologuée mars 2005.
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