Soil Stiffness

Determination of Soil Stiffness Parameters Short Course on Computational Geotechnics + Dynamics Boulder, Colorado January 5-8, 2004 Stein Sture Professor of Civil Engineering University of Colorado at Boulder

Contents General concepts and stiffness of sand Hooke’s law E-moduli from triaxial testing E-moduli from oedometer testing

Examples on the estimation of E

Stiffness of clays Undrained clay behavior Drained clay behavior Examples on the estimation of E Computational Geotechnics

Determination of Soil Stiffness Parameters

Idealized and real stressstrain behavior of soils

Idealized types of stress-strain behaviors: (a) nonlinear elastic Model, (b) linear elastic model, and (c) elastoplastic model

Computational Geotechnics


Idealized and real stressstrain behavior of soils

Various types of elastoplastic behaviors: (a) strain hardening, (b) perfectly plastic, (c) strain softening, and (d) combination of a to c. Computational Geotechnics


Hooke’s Law of Isotropic Elasticity



Hooke’s Law of Isotropic Elasticity



Standard Drained Triaxial Test on Sand



Standard Drained Triaxial Test on Sand



Oedometer Test on Sand



Oedometer Test on Sand



Oedometer Test on Sand Hooke:

1  2 E (1  2 ) Eoed  Eoed 1  3

Loose:

E 2  150  ref p 3

Dense:


E 2  500  ref p 3

y p

ref

(  13 )



y p

ref


Oedometer Test on Sand  'y 

 'x K0

 2 'x

Loose:

x x E 2  150  2  150 p ref 3 p ref p ref

Dense:

x x E 2  500  2  500 ref ref ref p 3 p p



This implies: Computational Geotechnics

E  E 50 Determination of Soil Stiffness Parameters

Summary on Stiffness Parameters: Sand (Laboratory based experience) E  E 50 

Loose:

2 E oed 3

  13

E  150 ref p  p

' x ref

E  Dense:   500 ref p p

' x ref

pref  100kPa

 Computational Geotechnics

EE

ref

Loose: E 15MPa

 'x pref



Dense: E  50MPa

 'x pref

 'x pref

Unloading: About 4 times stiffer.  small  Determination of Soil Stiffness Parameters

Selection of Moduli for FEM-Computation Example 1 (loading):

Layer 1 (extremely loose sand Mohr-Coulomb model: / Layer 1:  y 0  70kPa 

Average

 Computational Geotechnics

 'y  95kPa

ref E 50 15MPa

 'y  50kPa

 'x  50kPa

 E 50  15000 0.5  10000 kPa Determination of Soil Stiffness Parameters

Selection of Moduli for FEM-Computation Example 2 (unloading):

Layer 1 (dense): E 50  45MPa ref

Unloading:

Layer 3 (medium):

Eurref  4 E50ref ,  0.15

for both layers

 Mohr-Coulomb model: Layer 1:

  2  1.5  55kPa ' y

E  4  45000



Layer 3:


 'x 10kPa

E 50ref  30MPa

'

27.5 100



 'x  27.5kPa

 95000 kPa

E  4  30000 0.10  38000 kPa




Eoed from Cone Penetration Test in Sands Cone Resistance:

qc

Correlation: E oed  qc

Literature  NC-Sand:  = 1 to 3

 Vermeer’s Experience:  = 3 Alternatively: Eoed  (30  10) qc p ref



Undrained Triaxial Test on Clay

15000 Cu Ip%

Normally consolidated clay:

E u50 

Cu = undrained shear strength (or Su)

E u50  3G50





Idealized and real stress-strain behavior of soils



Idealized and real stress-strain behavior of soils



Plate Loading Tests

Duncan & Buchignani (1976) Computational Geotechnics


Plate Loading Tests



Summary on Stiffness Parameters: Clay Undrained Conditions

Do not use empirical relationships only. Get good quality experimental data from lab tests, cone penetration tests and vane tests



Drained Behavior for Clays



Drained Behavior for Clays



Soil Stiffness

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