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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

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Contents

General concepts and stiffness of sandHooke’s law

E-moduli from triaxial testing

E-moduli from oedometer testing

Examples on the estimation of E

Stiffness of claysUndrained clay behavior

Drained clay behavior

Examples on the estimation of EComputational Geotechnics Determination of Soil Stiffness Parameters

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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

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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

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Hooke’s Law of Isotropic

Elasticity

Computational Geotechnics Determination of Soil Stiffness Parameters

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Hooke’s Law of Isotropic

Elasticity

Computational Geotechnics Determination of Soil Stiffness Parameters

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Standard Drained Triaxial Test on

Sand

Computational Geotechnics Determination of Soil Stiffness Parameters

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Standard Drained Triaxial Test on

Sand

Computational Geotechnics Determination of Soil Stiffness Parameters

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Oedometer Test on Sand

Computational Geotechnics Determination of Soil Stiffness Parameters

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Oedometer Test on Sand

Computational Geotechnics Determination of Soil Stiffness Parameters

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Oedometer Test on Sand

Hooke:

Loose:

Dense:

oed oed    E  E  E 3

2)21(

1

1

   

 

 

 

(     13

)

ref  

 y

ref    p p

 E  

3

2150

 

ref  

 y

ref    p p

 E  

3

2500

 

Computational Geotechnics Determination of Soil Stiffness Parameters

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Oedometer Test on Sand

  y'   x

'

 K 0 2  x

'

ref   x

ref   x

ref    p p p E 

 

150232150     

ref  

 x

ref  

 x

ref    p p p

 E   

50023

2500

    

 E   E 50

Loose:

Dense:

This implies:

Computational Geotechnics Determination of Soil Stiffness Parameters

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Summary on Stiffness Parameters:

Sand(Laboratory based experience)

 E    E 50  2

3 E oed 

 

    13

 

 E  pref  

 150     x'

 pref  

 

 E  pref  

  500     x'

 pref  

 

 E   E ref      x

'

 pref  

 

 E  15 MPa     x

'

 pref  

 

 E   50 MPa   

 x

'

 pref  

 pref  100kP 

Loose:

Dense:

Loose:

Dense:

Unloading: About 4 times stiffer.  smallComputational Geotechnics Determination of Soil Stiffness Parameters

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Selection of Moduli for FEM-Computation

 E 50

ref  15 MPa

 

  y0

/ 70kPa

 

  y' 50kPa

  y' 95kPa     x

' 50kPa

 E 50 15000 0.5 10000 kP 

Layer 1 (extremely loose sand

Layer 1:

Average

Mohr-Coulomb model:

Example 1 (loading): 

Computational Geotechnics Determination of Soil Stiffness Parameters

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Selection of Moduli for FEM-ComputationExample 2 (unloading):

 E 50

ref   45 MP 

 

 E 50

ref  30 MPa

15.0,4 50      ref  ref  

ur    E  E 

 

  y' 2   1.5  ' 55kPa

 

  x' 27.5kP 

 E    4 45000   27.5100  95000 kPa

  x'10kP    kPa E  3800010.0300004  

Layer 1 (dense):  Layer 3 (medium): 

Unloading:  for both layers 

Mohr-Coulomb model: Layer 1: 

Layer 3: 

Computational Geotechnics Determination of Soil Stiffness Parameters

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E oed 

 from Cone Penetration Test in

Sands

qc

 

 E oed   qc

 = 1 to 3

 = 3

ref  

coed    pq E  )1030(  

Cone Resistance: 

Correlation: 

Literature NC-Sand: 

Vermeer’s Experience: 

Alternatively: 

Computational Geotechnics Determination of Soil Stiffness Parameters

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Undrained Triaxial Test on

Clay

 E u50

15000 C u

 I  p%

 E u50 3G50

 Normally consolidated clay:

Cu = undrained shear strength (or Su)

Computational Geotechnics Determination of Soil Stiffness Parameters

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Idealized and real stress-strain

behavior of soils

Computational Geotechnics Determination of Soil Stiffness Parameters

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Idealized and real stress-strain

behavior of soils

Computational Geotechnics Determination of Soil Stiffness Parameters

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Plate Loading Tests

Duncan & Buchignani (1976)

Computational Geotechnics Determination of Soil Stiffness Parameters

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Plate Loading Tests

Computational Geotechnics Determination of Soil Stiffness Parameters

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Drained Behavior for Clays

Computational Geotechnics Determination of Soil Stiffness Parameters

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