The document discusses methods for determining soil stiffness parameters from laboratory and in-situ tests. It provides equations to estimate the Young's modulus (E) of sand from triaxial compression tests, oedometer tests and cone penetration tests. It suggests values for E of 15 MPa for loose sand and 50 MPa for dense sand based on laboratory tests. For clays, it suggests estimating E from undrained shear strength (Cu) or 3 times the shear modulus (G). The document emphasizes that empirical relationships only provide estimates and that laboratory tests are needed to accurately determine soil stiffness.

1. 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

2. 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

3. Idealized and real stress-
strain behavior of soils
Idealized types of stress-strain behaviors: (a) nonlinear elastic
Model, (b) linear elastic model, and (c) elastoplastic model
Computational Geotechnics Determination of Soil Stiffness Parameters

4. Idealized and real stress-
strain 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 Determination of Soil Stiffness Parameters

5. Hooke’s Law of Isotropic
Elasticity
Computational Geotechnics Determination of Soil Stiffness Parameters

6. Hooke’s Law of Isotropic
Elasticity
Computational Geotechnics Determination of Soil Stiffness Parameters

7. Standard Drained Triaxial Test on
Sand
Computational Geotechnics Determination of Soil Stiffness Parameters

8. Standard Drained Triaxial Test on
Sand
Computational Geotechnics Determination of Soil Stiffness Parameters

9. Oedometer Test on Sand
Computational Geotechnics Determination of Soil Stiffness Parameters

10. Oedometer Test on Sand
Computational Geotechnics Determination of Soil Stiffness Parameters

11. Oedometer Test on Sand
Hooke:
Loose:
Dense:
oed
oed E
E
E
3
2
)
2
1
(
1
1




 



(  1
3 )
ref
y
ref
p
p
E
3
2
150



ref
y
ref
p
p
E
3
2
500



Computational Geotechnics Determination of Soil Stiffness Parameters

12. Oedometer Test on Sand

y
'

x
'
K0
 2x
'
ref
x
ref
x
ref
p
p
p
E
150
2
3
2
150





ref
x
ref
x
ref
p
p
p
E
500
2
3
2
500





E  E50
Loose:
Dense:
This implies:
Computational Geotechnics Determination of Soil Stiffness Parameters

13. Summary on Stiffness Parameters:
Sand
(Laboratory based experience)
E  E50 
2
3
Eoed

  1
3

E
pref
150
x
'
pref

E
pref
 500
x
'
pref


E  Eref x
'
pref

E 15MPa
x
'
pref

E  50MPa
x
'
pref
pref
100kPa
Loose:
Dense:
Loose:
Dense:
Unloading: About 4 times stiffer.  small
Computational Geotechnics Determination of Soil Stiffness Parameters

14. Selection of Moduli for FEM-Computation

E50
ref
15MPa

y0
/
 70kPa

y
'
 50kPa
y
'
 95kPa x
'
 50kPa
E50 15000 0.5 10000kPa
Layer 1 (extremely loose sand
Layer 1:
Average
Mohr-Coulomb model:
Example 1 (loading):
Computational Geotechnics Determination of Soil Stiffness Parameters

15. Selection of Moduli for FEM-Computation
Example 2 (unloading):

E50
ref
 45MPa

E50
ref
 30MPa
15
.
0
,
4 50 
 
ref
ref
ur E
E

y
'
 2 1.5'
 55kPa

x
'
 27.5kPa
E  4  45000 27.5
100  95000kPa
x
'
10kPa kPa
E 38000
10
.
0
30000
4 


Layer 1 (dense): Layer 3 (medium):
Unloading: for both layers
Mohr-Coulomb model:
Layer 1:
Layer 3:
Computational Geotechnics Determination of Soil Stiffness Parameters

16. Eoed from Cone Penetration Test in
Sands

qc

Eoed qc
 = 1 to 3
 = 3
ref
c
oed p
q
E )
10
30
( 

Cone Resistance:
Correlation:
Literature NC-Sand:
Vermeer’s Experience:
Alternatively:
Computational Geotechnics Determination of Soil Stiffness Parameters

17. Undrained Triaxial Test on
Clay

Eu
50

15000Cu
Ip%
Eu
50
 3G50
Normally consolidated clay:
Cu = undrained shear strength (or Su)
Computational Geotechnics Determination of Soil Stiffness Parameters

18. Idealized and real stress-strain
behavior of soils
Computational Geotechnics Determination of Soil Stiffness Parameters

19. Idealized and real stress-strain
behavior of soils
Computational Geotechnics Determination of Soil Stiffness Parameters

20. Plate Loading Tests
Duncan & Buchignani (1976)
Computational Geotechnics Determination of Soil Stiffness Parameters

21. Plate Loading Tests
Computational Geotechnics Determination of Soil Stiffness Parameters

22. 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
Computational Geotechnics Determination of Soil Stiffness Parameters

23. Drained Behavior for Clays
Computational Geotechnics Determination of Soil Stiffness Parameters

24. Drained Behavior for Clays
Computational Geotechnics Determination of Soil Stiffness Parameters