Soil-structure interaction c
ZACE Services Ltd August 2011
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Examples of soil-structure interaction
Sheet-pile walls Prestressed anchors Diapraghm walls Nailing Foundation rafts with piles Building-foundation In all the above problems strong displacement/pressure may appear → soil-structure interfaces play an N Prefacediscontinuity N N 2D problems important role
1.4
HOW TO RUN SHEET-PILE WALL PROBLEM
• Data file: tutorials/sheet-pile-wall.INP
• Description
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Generation of a complex geotechnical model of installation of an anchored sheet pile wall, followed then by an excavation is the goal of this tutorial. The geometry of the model Sheet-pile wall: example will evolve in time and some model components like wall, anchors or excavated soil layers will appear or disappear according to the assumed scenario. The geometry of the model is shown in the figure below. 12 m
18 m
6m
8m
3
3
Anchors
3
6m
3
2
Excavation zone-1
Medium sand
Excavation zone-2
Sheet pile wall
5
Clay
Sequence of all steps is shown in the following table.
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Sheet-pile wall: Modeling issues 2D/3D model? Ultimate limit state analysis (ULS) (M-C model is enough) Serviceability limit state (SLS) is (or not) main concern ? (if yes then M-C model is too poor and HS small strain model shall be used) Each construction step must be reproduced (if SLS is major concern and to avoid numerical problems witch convergence) Contact interfaces must be present Sheet-pile wall can be modeled using beam/shell elements or special continuum elements (Continuum for structures) (only elastic behavior is possible) Fixed anchor zones can be activated possibly with adhesive interface Prestress can be controlled in time 5 / 60
Sheet-pile wall: Constitutive aspects G - current secant shear modulus Go - shear modulus for very small strains
Atkinson 1991 If serviceability limit state is our major concern then we should use more sophisticated model for soils (HS with small strain) 6 / 60
Linear / nonlinear beams in plane strain
Plane strain continuum shell ribb system Interval between beams a = L Interval betweenPlane beamsstrain a = 1 discrete 2D domain:
L
Beam elements
User data: A, Iz ( data per beam ) (a)automatically A’=A/a I’=Iz/a Program Interval between beams a = L beams a computes =1 (A’, I’ – values per unit length ) Results are given per beam (!)
Interval between
2D domain:
2D domain:
Beam elements
Beam elements
User data: A, Iz ( data per beam ) Linear / nonlinear beams in plane strain (b) I’=Iz/a Program computes automatically A’=A/a (A’, I’ –Here values per(a) unitorlength Results are model given (!) 2D axisymmetric (b) is beam good enough Plane )strain continuum shell per Plane strain discrete ribb system 7 / 60
near beams in plane strain
ell
a=1
L
Sheet-pile wall: 2D/3D model ?
L
Sheet-pile wall: 2D/3D model ?
Plane strain discrete ribb system Interval between
Interval between beams a = L
beams a = 1
2D domain:
L Interval
Beam elements
User data: A, Iz ( data per beam ) Program computes automatically A’=A/a I’=Iz/a between(A’, beams a =per L unit length ) Results are given per beam (!) I’ – values
main: L
ements
am ) 1 Here 2D model may not be good enough..... cally A’=A/a I’=Iz/a Results beams(!)and in anchors (same definition for L) will be ) Results are2 given perinbeam output per beam/anchor (!) 8 / 60
8
the Problem type list. The predefined system Clay of units for both data preparation and visualization of results can be verified in menu Control/Units. 5
Sheet-pile wall: Construction steps Sequence of all steps is shown in the following table.
Initial state (t = 0)
Installation of sheet pile wall (t = 1) Excavation zone-1
Installation of first anchor (t = 2) Excavation zone-1
Installation of second anchor (t = 4)
• Drivers
Excavation of 1 sand layer (t = 3) Excavation zone-1
Excavation of 2 sand layer (t = 5)
Use June existence/unloading functions associated with elements 16, 2007 QuickHelp DataPrep Theory Benchmarks (continuum, beam, Z Soilr -3D-2PHASE v.7 etc..) plus time dependent drivers (driven TU–37 load/consolidation) 9 / 60
The whole computational process will consist of three drivers i.e. the Initial state which will yield the initial stress distribution (including user defined coefficient of in situ lateral pressure Ko = 0.8 in clay layer), Time dependent/Driven load to analyze all Sheet-pile wall: Drivers construction and excavation steps and at the end Stability (using c − tan(φ) reduction fromtomenu: Drivers algorithm)Accessible will be carried assessControl/Analysis the global safety & factor. The complete set of drivers is given in the following figure.
To learn on how to set up the drivers list watch the video
Set drivers 10 / 60
N Preface N N 2D problems
Sheet-pile wall: Existence functions
• Existence function Accessible from menu: Assembly/Existence functions
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Introduction of contact elements leads to discontinues mesh connectivity along the interface. For that reason before the sheet-pile wall is installed, full compatibility of the Sheet-pile Contact displacement field must wall: be preserved in theinterfaces interface. This effect can easily be achieved during generation of interface elements, where contact is defined in dual mode (full continuity first and then real interface behavior). Both modes are controlled by the two existence functions (in our case continuity is controlled by the existence function number 7 while real contact behavior by function number 6). It is strongly recommended to apply a distinct label to each existence function. To edit existence functions use menu Assembly/Existence function. To learn on how to enter existence functions watch the video singular point .
Edit existence functions
interface is defined on edges of continuum subdomains only; contact • Generation Contact of the model elements are created automatically once the virtual and then the real mesh is 1
created The computational model is built in the following steps and some of them are documented 2 Selected edges must be shared by the two subdomains in form of video films. 3 The interface can be created along continuum-continuum, continuum-beam, 1 Create a new project and continuum-truss interfaces continuum-membrane 4 Nonstandard situations like connection of the bottom point of the sheet-pile 2 Edit materials videos/tut2d-6/tut2d-6-materials.avi wall with soil ( by default beam is separated from the continuum at this point) 3 Edit must existence functions videos/tut2d-6/tut2d-6-exf.avi be handled at the FE model level 5 To connect/disconnect points use method Edit construction lines separated nodes at singular videos/tut2d-6/tut2d-6-constr4 Interface/Update/Link singular nodes/Interface/Update/Delete link lines.avi 6 Any mesh refinement in the adjacent continuum or structure automatically 5 Drawenforces macro-model videos/tut2d-6/tut2d-6-macromesh refinement in the contact interface 12 / 60 model.avi
Contact interface: Setting continuity/real contact mode
Contact interface may behave in a different manner in certain time periods Possible contact modes: 1
2 3
Full continuity of all degrees of freedom (DOF) (displacements, pressures, temperatures etc..) on both segments of the interface element Full continuity of all DOF except pressure field True contact behavior; in this case decision on how to handle non-kinematic DOF (pressure, temperature, humidity) in the interface can be set at the material level (switching ON/OFF and editing groups of parameters: Flow , Heat and Humidity ).
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Contact interface: Setting continuity/real contact mode A
B
Remarks 1
The three aforementioned contact type behaviors can be selected from combo-box (A)
2
For contact type: Continuity... only the existence function is meaningful
3
For contact type: Contact existence function, material number and unloading function are all meaningful
4
The existence function, unloading function and material ID can be set in the edit fields or selected from lists of predefined ones 14 / 60
Contact interface: mesh discontinuity
1
Here at the interface 3 nodal points are created to model strong discontinuoes motion of the neighbouring domains
2
In the initial state we want all these nodes to be compatible 15 / 60
Contact interface: Setting continuity/real contact mode A
B
Remarks 1
2
The Continuity for all inactive periods check-box set to ON will enforce automatic generation of contact elements with full continuity attribute in all inactive periods of true contact behavior The Automatic generation of continuity prior to first contact apparition option enforces automatic generation of contact elements with full continuity attribute only in the first inactive period for true contact behavior
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z’
Contact interface: Flow through... Fully permeable contact with compatible pressures on both faces
z’
x’
x’
0
0
Permeable contact kx = kx h kz = kz /h (h is a thin layer thickness)
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Contact interface: Effective vs total stress
For permeable interfaces effective stress mode is enforced For impermeable interfaces effective/total stress mode can be selected NB. Effective stress mode makes sense only when at least to one side of the interface a permeable continuum is adjacent 18 / 60
Contact interface: General remarks
singular point
Interface elements are treated as any other elements If we do not deactivate the interface during excavation the program will do it automatically If we do not assume an unloading function (0 index) then the interface will inherit it from the excavated adjacent continuum 19 / 60
Contact interface: Setting existence/unloading functions
singular point
Interface elements are treated as any other elements If we do not deactivate the interface during excavation the program will do it automatically If we do not assume an unloading function (0 index) then the interface will inherit it from the excavated adjacent continuum 20 / 60
Contact interface: Setting material data
Instead of generating several contact zones one may set only one contact material activating automatic inheritage of strength properties from adjacent continuum 21 / 60
Contact interface: Controling overpenetration Penalty approach kn
P
P
P
P
overlap
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Contact interface: Controling overpenetration
1
The overpenetration can be checked in the postprocessing (Element info for interface element)
2
If excessive overpenetration appears one may try to increase the kn multiplier (this must be made with care) or to activate Augmented Lagrangian option through menu Control/Contact algorithm
3
In case of convergence problems due to contact try to decrease slowly the kn multiplier 23 / 60
Contact interface: Augmented Lagrangian approach P
t=0
t=1
P
t=1 after augmentation
Contact force/stress is computed as N = No + kn gn (No is an estimate of a Lagrange multplier) P (a) Force P generates overpeneration gn = kn (b) Force in the interface will be equal to N = P (c) Update Lagrange multiplier No = N = P (d) Compute force in the interface N = No + kn gn = P + P = 2P while N should be equal to N = P hence gn = 0 24 / 60
Contact interface: Augmented Lagrangian approach Accessible from menu: Control/Contact algorithm
This algorithm in nonlinear applications must be used with care Excessive overpenetration leads to underestimation of internal forces in contacting bodies
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Modeling elastic structures with aid of continuum elements Standard continuum finite elements representing structures like beams/shells yield very poor results unless very fine mesh is used To remedy the problem a family of robust continuum elements was implemented to enhance bending/shear behavior These elements are generated exactly in the same manner as standard continuum but at the material level Continuum for structures instead of Continuum must be selected Elastic model is the only one allowed by Continuum for structures formulation Minimum 2 elements per thickness must be generated to recover properly bending moment
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Modeling elastic structures with aid of continuum ele... Example of cantilever beam (recovering of sectional forces) q=1 kN/m2
4m
Mz=7.33 kNm/m
Standard Q4 elements
Mz=7.95 kNm/m
Enhanced elements
NB. New stress recovery technique is used for postprocessing hence only results from the central point are stored 27 / 60
Prestressed anchors: General remarks
anchor anchor fixed zone
Anchor consists of two parts: active and fixed part Stiffness of both parts is assumed to be the same The active part joins the anchor head and fixed part Adhesive interface can be generated between soil and fixed part 28 / 60
Prestressed anchors: prestressing Prestress marker
Link marker
The anchor endpoint may be attached to the background continuum at any point Prestress can be controled via existence function and load time function
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Prestressed anchors: fixed zone anchor
Anchor fixed zone
The fixed part may can be created but exlusively in the direction indicated by the local X axis of the truss element The split value should be compatible with the mesh density of the background continuum Generation of fixed anchor zone interface is optional 30 / 60
Prestressed anchors: fixed zone interface
d
Same option option applies to nails 31 / 60
Diapraghm walls: Modeling issues 2D/3D model? Serviceability limit state (SLS) is the main concern → small strain stiffness must be considered Each construction step must be reproduced (if SLS is major concern and to avoid numerical problems witch convergence) Contact interfaces must be present Diapraghm wall can be modeled using beam/shell elements or special continuum elements (Continuum for structures) (only elastic behavior is possible) Fixed anchor zones can be activated possibly with adhesive interface Prestress in anchors can be controlled in time
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Diapraghm walls: 2D/3D model ?
photo from Master thesis by A. Burmer, Poland In the Milano method when floors are partially made the 3D is recommended In the 3D one may analyze full model including foundation raft, piles, floors In the 3D one may optimize the structure including ground supports 33 / 60
Diapraghm walls: 2D/3D model ?
photo from Master thesis by A. Burmer, Poland In the Milano method when floors are partially made the 3D is recommended In the 3D one may analyze full model including foundation raft, piles, floors In the 3D one may optimize the structure including ground supports 34 / 60
Diapraghm walls: Constitutive aspects G - current secant shear modulus Go - shear modulus for very small strains
Atkinson 1991 Here we are in the range of small strains in major part of the computational domain 35 / 60
Diapraghm walls: example of excavation in Berlin sand
(after Schweiger...) 36 / 60
Diapraghm walls: excavation in Berlin, sand FE model
(after Schweiger...) 37 / 60
Diapraghm walls: excavation in Berlin, results -600
-400
-200
0
200
-0.04
400 0
-0.03
-0.02
-0.01
0 0 -5
-5
-10
-10
-20
-15
Y [m]
Y [m[]
-15
HS HS-small MC
-20
-25
-25
-30
-30 -35
-35 Ux [m]
M [kNm/m] 0
0
0.01
0.02
HS-small HS MC Measurement
0.03
20
40
60
80
100
120
140
0.01
0.04
0 0.005
-10 -20
0
Y [m]
-40
HS HS-small MC
-50 -60
UY [m]
-30 HS HS-small MC
-0.005
-0.01
-70 -0.015
-80 -90
-0.02
-100 Uy [m]
X [m]
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Nailing: general remarks
40ft
120 ft
Excavated layers
120 ft 1 2 3 4 5 6 7 8
15o
ft
40ft
L=30
Contrary to some simple limit equilibrium methods finite element model requires a multi-step excavation and nail installation procedure to eliminate spurious forces in nails and potential numerical divergence problems Nails can be attached to the facing wall at any point not necesarilly at the node (important mainly in 3D) Nail core is modeled as beam element 39 / 60
Nailing: general remarks
d
Nail core=beam
Nail injection zone Nail interface
Nail consists of two material zones: core + interface Stiffness of the injection zone is neglected Adhesive interface can be generated between soil and injection zone 40 / 60
Nailing: automatic excavation front for soil layers 1
2
3
4
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Run method Macro model/Subdomain/Update/Define Nailing: automatic front for facing layers excavation front construction to set up existence functions for subsequent layers to be excavated 2 In the dialog box for the excavation front activate flag 1 1
Existence function [
] , set the label subsoil layers, select 2
first defined existence function (No 1) that will be applied to first row of excavated elements from the top, activate option } Edge 1-4 that indicates the direction of excavation front propagation and set value 1 to the edit field For every .... layers of elements... [ 3
1
2
]
The above setting will enforce application of existence function No 1 to the first top row of elements in the real mesh, No 2 to the second one etc... Run method Macro model/Subdomain/Update/Define excavation front to set up existence functions for subsequent facing layers that are to be constructed The above setting will enforce application of existence function No 11 to the first top row of facing elements (beams) in the real mesh, No 12 to the second one etc... 42 / 60
Nailing: generating nails
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Nailing: generating nails
Nail interface is optional (if not created then full displacement compatibility is enforced) Mesh density for the nail (defined as split parameter) should correspond to the one in the background continuum The material data for the interface is the same as for fixed anchor zones (see next slide) During stability analysis both soil and soil-nail interface strength parameters are reduced (unless it is redefined at the material level)
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Nailing: setting material properties
d
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Foundation rafts: Problem to be solved
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Foundation rafts: discretization problem If we have lot of piles it is almost impossible to 1 2 3
Create 3D compatible FE mesh for plate-piles-interfaces system Compute the problem on a PC platform Each redesign of piles generates new complex 3D mesh
Conclusion: we need absolutely a simplified treatment 47 / 60
Foundation raft: real FE vs simplified FE model
plate-pile connection
Shell Q4
beam elements
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Foundation rafts: Z Soil implementation Piles are modeled with aid of beam elements Beams are embedded in continuum without any restriction put on FE meshes Beam nodes can be connected to other elements like shells/beams/membranes/continuum not necessarily at element vertices Beam nodes can be connected to other elements via selected set of degrees of freedom The sliding interface between beam and continuum is created automatically The additional interface between bottom of the pile and subsoil can be optionally added Nodal forces can be applied at any point on the raft Penalty approach is not accepted (except for the frictional contact) 49 / 60
Nodal link option
4 3 A
1
Constraint equation(s): uA =
2
P4
i=1
Ni ui
Hence: stiffness, force vector from node A of a beam element is dispatched on shell degree of freedom DOF’s of node A are dependent on other DOF’s Attention: constraints cannot be nested (!)
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Nodal link: example of beam-beam connection
Link node to the selected element
Deformation
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Nodal link: example of beam-shell connection
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Foundation rafts: pile frictional interface
τ=σn tan φ+c
ft=0, fc< fcult
How to estimate σn ? NB. We can leave φ = 0 and make contact purely adhesive like in codes for pile design 53 / 60
Foundation rafts: σn estimation in pile interfaces xL
R = SQRT (A/π)
ΔLi
Pi
R
zL
yL
R σn =
L minR(σn i , 0)dl L dl
σni is computed by effective stress transformation from the continuum elements in which interface and beam is embedded 54 / 60
Foundation rafts: generating piles
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Foundation rafts: generating piles
1
Split parameter controls mesh density in pile macro-element; it is recommended to avoid too big differences in mesh densities between continuum and piles; such modeling may lead to axial force oscillations in the pile for high strength parameters of subsoil
2
To avoid instabilities due to rigid rotation of the pile along its axis the rotation along local pile axis is fixed internally by the preprocessor
3
Mesh refinement near the zone of the pile foot is recommended to avoid underestimation of settlements
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Foundation rafts: real life example
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Building-subsoil interaction: Examples
Example 1 At the material level in group Main
Frame structure (static/pushover/dynamic analysis
Next slide
Remark: Each member is discretized by one element (not necessarily for reinforced concrete because of different amount and position of the reinforcement)
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Building-subsoil interaction: Examples
Example 2
Frame structure resting on subsoil
At the material level in group Main
Next slide
Remark: Each member is discretized by one element (not necessarily for reinforced concrete because of different amount and position of the reinforcement)
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Flexibility vs displacement based beam formulation q=1.0 kN/m
Mz for 1 „flexibility based” beam 1.33
1.33 0.667
Mz for 4 „displ. based” beam 1.25
0.75
1.25
Gauss points Nodal points
Note that result for Flexibility based beam (one per member) is exact ! 60 / 60
