Soil Parameters for Drained and Undrained Analysisand Undrained Analysis

Applied Theory

Dr Minna Karstunen

based on work by Dr H. Burd, University of Oxford

Introduction

• The aim is to discuss the choice of parameters for the Mohr-Coulomb model.

• More advanced soil models may have some advantages over the Mohr-Coulomb model (but require the specification of a larger number of parameters)

• Typical experimental methods currently used to measure • Typical experimental methods currently used to measure the soil parameters are briefly discussed.

• It is also useful, however, to estimate values of soil properties based on previous experience, and on correlations with other soil parameters.

Undrained and Drained Loading

• In carrying out any analysis in geotechnical engineering it is usually necessary to distinguish between drained and undrained loading. and undrained loading.

• The soil may also be partially drained which means that it lies between these two extremes.

Undrained and Drained Loading

• drained analysis appropriate when– permeability is high

– rate of loading is low

– short term behavior is not of interest for problem – short term behavior is not of interest for problem

considered

• undrained analysis appropriate when– permeability is low and rate of loading is high

– short term behavior has to be assessed

Undrained and Drained Loading

Suggestion by Vermeer & Meier (1998)

T < 0.10 (U < 10%) � undrained analysis

T > 0.40 (U > 70%) � drained analysis

tDγ

EkT

2

w

oed====

k = permeability

Eoed = stiffness in 1-d compression

γw = unit weight of water

D = drainage length

t = construction time

T = dimensionless time factor

U = degree of consolidation

Drained Analysis

Drained analysis may be carried out by

using a constitutive model based on

effective stresses in which the material model is specified in terms of drained model is specified in terms of drained parameters.

Modelling Undrained Behavior with

PLAXIS

Method A (analysis in terms of effective stresses):type of material behaviour: undrainedeffective strength parameters (MC: c', ϕ', ψ‘)effective stiffness parameters (MC: E50', ν‘)

Method B (analysis in terms of effective stresses):

Need to be

careful in case

of stiff OC

clays!

Method B (analysis in terms of effective stresses):type of material behaviour: undrainedtotal strength parameters c = cu, ϕ = 0, ψ = 0effective stiffness parameters E50', ν'

Method C (analysis in terms of total stresses):type of material behaviour: drainedtotal strength parameters c = cu, ϕ = 0, ψ = 0total stiffness parameters Eu, νu = 0.495

Mohr Coulomb Model for Drained

and Undrained Analysis

• For drained loading, a total of 5 parameters are

required to specify the Mohr-Coulomb model.

These are; two strength parameters (c' and φ' ),

a dilation angle (ψ) and two elastic parameters.

• For undrained calculations, a separate failure

model based on an undrained shear strength, cu,

is used. Note that cu is not a fundamental

property of the soil; it depends on the stress

level and also the stress history.

Mohr Coulomb Model for Drained

and Undrained Analysis

Drained or

Undrained

(Approach A)

Undrained

(Approach C)(Approach A)

(Approach C)

Mohr Coulomb Model for Drained

and Undrained Analysis

• To analyse a problem using the Mohr-Coulomb

model, appropriate values of the material

parameters must be selected to provide a good

match with the soil being modelled.

• The selection of these parameters is

complicated by the fact that real soil behaviour

often departs considerably from the fundamental

assumptions on which the Mohr-Coulomb model

is based.

The Mohr-Coulomb Model and

Real Soil Behavioura) Most real soils do not exhibit linear elastic behaviour

prior to failure

G/G

[-]

0

1 Retaining walls

Foundations

G/G

[-]

0

1 Retaining walls

Foundations

Shear strain [-]γ

Dynamic methods

Local gauges

Conventional soil testing

Sh

ear

mo

du

lus

G/

10-6

10-5

10-4

10-3

10-2

10-1

0

Tunnels

Foundations

Larger strains

Very

small

strains Small strains

Shear strain [-]γ

Dynamic methods

Local gauges

Conventional soil testing

Sh

ear

mo

du

lus

G/

10-6

10-5

10-4

10-3

10-2

10-1

0

Tunnels

Foundations

Larger strains

Very

small

strains Small strains

The Mohr-Coulomb Model and

Real Soil Behaviour

b) The stiffness of soil tends to increase with increasing stress level. In PLAXIS the stiffness can be specified to increase linearly with depth below

the soil surface.the soil surface.

c) Unloading stiffness differs from stiffness in primary loading

The Mohr-Coulomb Model and

Real Soil Behaviour

Triaxial compression test on a sample of Leighton Buzzard sand

The Mohr-Coulomb Model and

Real Soil Behaviour

d) The friction angle of a sand depends on its density and stress level. The stress level. The choice of φφφφ'

needs careful consideration of these factors.

The Mohr-Coulomb Model and

Real Soil Behaviour

Drained Triaxial Test

Undrained Triaxial Test

Pressuremeter Test

++=

u

uhoLc

GcP ln1σ

The undrained shear strength may be calculated from the limiting cavity

pressure PL (for details see Clarke (1995).

u

For penetration in clays, the

tip resistance qt is given by:

Cone Penetrometer Test

vouktt cNq σ+=

where σvo is the total vertical

stress in the soil at the level of

the cone and Nkt is an empirical

factor, typically in the range of 10

to 20. For further details, see

Lunne et al, (1997).

vouktt

Correlations for Undrained

Shear Strength (cu)Shear Strength (cu)

Undrained Shear Strength from

MC Parameters

++= '

2

1'cot''sin 0

vu

Kcc σφφ

Example: Undrained parameters

from MC

++= '

2

1'cot''sin 0

vu

Kcc σφφ

Example: Undrained parameters

from MC

In this example:

where cuo=4.698 kPa and ρ= 2.326 kPa/m.

zcc uou ρ+=

Example: Undrained parameters

from MC

Note that the correlation is unlikely to give an accurate

shear strength profile for an overconsolidated clay. A

better estimate is obtained with Critical State models.

For an incompressible material, the undrained For an incompressible material, the undrained

Poisson’s ratio would be 0.5 (Method C). However, this

value cannot be used for finite element calculations,

because it would result in an infinite value of bulk

modulus. A suitable value of undrained Poisson’s

ration for use in FE analyses is νu=0.495. In this case,

the appropriate value of undrained Young’s modulus

would be 5537 kPa.

Correlations for su based on

Cam ClayA useful correlation that is based on Cam Clay theory

(and confirmed by the results of laboratory testing) is:

( )µ

σσOCR

cc uu

=

''

where σ’vi is the vertical effective stress at the start of

undrained loading and OCR (the overconsolidation

ratio) is equal to σ’p/ σ’vi, where σ’p is the vertical

(effective) preconsolidation stress.

According to data collected by Muir Wood (1990) µ is

close to 0.8 and (cu/σ’vi)NC lies between 0.1 and 0.35.

σσNCvivi

''

Example

At an OC clay site, the

water table is at the ground

surface.

The preconsolidation

stresses correspond to the stresses correspond to the

application of a vertical

effective stress of 500 kPa

at the ground surface.

Take (cu/σ’vi)NC as 0.2, µ

as 0.8 and the submerged

unit weight of the soil as 8

kPa/m.

cu from Index Tests

PL

PL

ww

wwI

−

−=

)1(1002 LI

uc−

×=

NOTE: This is

remoulded strength

(intact strength can

be much higher)

cu of London Clay

cu of London Clay

Friction and Dilations Angles

for Sandfor Sand

Correlations for Friction Angle

Bolton (1986) proposes a relationship

ψφφ 8.0'' += cv

where φ’cv is the critical state friction angle and ψ is the angle of dilation.

Correlations for Friction Angle

A study by Bolton (1986 and 1987) onpublished sand test data, suggested that themaximum dilation rate of a sand depends ona relative density index IR:a relative density index IR:

kPapforp

II DR 150'1150

'ln5 >−

−=

kPapforII DR 150'15 <−=

minmax

max

ee

eeI D

−

−=

Correlations for Friction Angle

The following correlations were found byBolton to give a good fit to the availabledatabase of test results:

Rcvpeak I5'' =−φφ

Rcvpeak I3'' =−φφ

for plane strain

for triaxial test

For quartz sand, the critical state friction angle φ’cv is approximately 33 degrees.

Correlations for Friction Angle

Determining the relative density of a sand deposit is rather difficult. For

correlations that relate cone resistance to relative density are described in

Lunne et al. 1997.

Estimation of Stiffness

Stiffness of Clay

• Option 1 - Use E50. For problems here relatively large strains are expected (e.g. for foundation bearing capacity and studies of the deformation of soft soil beneath an embankment).

• Option 2 - Use a small strain Young's modulus. If the problem involves the calculation of deformations of stiff problem involves the calculation of deformations of stiff clay under working conditions (e.g. the analysis of the interaction between a tunnel liner and the surrounding ground)

• Option 3 - Use the unloading Young's modulus, Eur. If the problem is dominated by unloading (as may be the case, for example, in an excavation problem)

Measurement of Stiffness in the

Triaxial test

Not accurate for strains below 1%

Measurement of Stiffness in the

Triaxial test

Correlations for Stiffness

Jardine et al. (1984) conducted a series of triaxial tests on a range of soils, using local gauges to measure strains.

Correlations for Stiffness

Jardine et al. (1984)

Correlations for Stiffness

Plate loading tests

by Duncan & by Duncan &

Buchignani (1976).

Data correspond to

strain values of

about 0.1%

Correlations for Stiffness

Data from Termaat, Vermeer and Vergeer (1985) may be used to suggest the following correlation for normally consolidated (Dutch) clay:clay:

P

uu

I

cE

1500050 ≈

Case

Studies

Stiffness profile for

various London clay

site (Matthews et al,

2000, re-plotted by

Simon and Menzies

2000)

Case Studies

Scott et al. (1999)

Stiffness Anisotropy

• Recent studies on natural clays (normally consolidated and overconsolidated) suggest that their stiffness may be anisotropic. Typical data for London clay anisotropic. Typical data for London clay can be found e.g. in Gasparre et al. (2007)

Stiffness of Sands

• Based on data on undrained triaxial testing of sandfs at different densities by Tokheim (1976) and Leahy (1984)Loose sand

References:• Atkinson, J.H. (2000). Non-linear soil stiffness in routine design. Géotechnique 50(5), 487-508

• Atkinson, J.H., Richardson, D. and Stallebrass, S.E. (1990). Effect of recent stress history on the stiffness of overconsolidated soil. Géotechnique 40(4) 531-40.

• Bolton, M.D. (1986). The strength and dilatancy of sands. Géotechnique 36(1), 65-78

• Bolton, M.D. (1987). Discussion on the strength and dilatancy of sands. Géotechnique 37(2), 219-226.

• Burd, H.D. (2007). Soil parameters for drained and undrained analysis. Numerical Methods in Geotechnical Engineering, 12-14 June, 2007, Manchester.

• Burland, J.B. and Hancock, R.J.R. (1977). Underground car park at the House of Commons: geotechnical aspects. The Structural Engineer, 55(2), 87-100

• Burland, J.B. and Kalra, J.C. (1986). Queen Elizabeth II conference centre geotechnical aspects. Proc. ICE, Part 1,80.

• Clarke, B.G. (1995). Pressuremeters in geotechnical design. Blackie Academic.

• Clayton, C.R.I, and Khatrush, S.A. (1986) A new device for measuring local axial strains on triaxial specimens. Géotechnique 36(4) 593-598.

• Clayton, C.R.I., Edwards, A. and Webb, J. (1991). Displacements in London clay during construction. Proc. 10th Int. Conf. on Soil Mech and Fdn. Engng, Florence, 2, 791-796.

• Clayton, C.R.I., Matthews, M.C. and Simons, N.E. (1995). Site Investigation. Blackwell Science.

• Cole, K.W. and Burland, J.B. (1972). Observations of retaining wall movements associated with large excavation. Proc. 5th European Conf. on Soil Mechanics and Foundation Engineering, Madrid, 1,445-453.

• Duncan and Buchignani (1976).

• Gasparre, A., Nishimura, S., Minh, N.A., Coop, M.R. and Jardine, R.J (2007). The stiffness of natural London Clay. Géotechnique 57(1) 33-47 • Gasparre, A., Nishimura, S., Minh, N.A., Coop, M.R. and Jardine, R.J (2007). The stiffness of natural London Clay. Géotechnique 57(1) 33-47

• Gordon, M.A. (1997). Applications of field seismic geophysics to the measurement of geotechnical stiffness parameters. PhD Thesis, University of Surrey, Guildford

• Hope, V.S. (1993). Applications of seismic transmission tomography in civil engineering. PhD Thesis, University of Surrey, Guildford

• Jardine, R.J. , Symes, M.J. and Burland, J.B. (1984). The measurement of soil stiffness in the triaxial apparatus. Géotechnique 34(3) 323-340.

• Leahy, D. (1984). Deformation of dense sand, triaxial testing and modelling. PhD thesis, NTNU, Trondheim.

• Lunne, T., Robertson, P.K. and Powell, J.J.M. (1997) Cone Penetration Testing in Geotechnical Practice. Blackie Academic.

• Mair, R.J. (1993). Developments in geotechnical engineering research: applications to tunnels and deep excavations. Unwin memorial Lecture 1992. Proc. ICE, 3,27-41.

• Matthews, M.C., Clayton, C.R.I., and Own, Y. (2000). The use of field geophysical techniques to determine geotechnical stiffness parameters. Proc. ICE (Geotechnical Engineering),143, 31-42.

• Muir Wood, D.M. (1990). Soil Behaviour and Critical State Soil Mechanics. Cambridge University Press.

• Scott, P., Talby, R. and den Hartog, N. (1999). Queensbury House, London: a case study of the prediction and monitoring of settlements during the construction of a deep excavation. Proc. Int. Symp. Beyond 2000 in Computational Geomechanics, 163-176. A.A. Balkema.

• Simons, N. and Menzies, B. (2000). A short course in foundation engineering. Thomas Telford. 2nd Ed.

• Stevens A. et al. (1977) Barbican Arts Centre. The Structural Engineer, 55(11) 473-485.

• St. John, H.D., Potts, D.M., Jardine, R.J. and Higgins, K.G. (1993). Prediction and performance of ground response due to construction of a deep basement at 60 Victoria Embankment. Proceedings of the Wroth Memorial Symposium, Oxford, July 1992, 581-608. Thomas Telford.

• Termaat R.J., Vermeer P.A. and Vergeer G.J.H. (1985). Failure by large plastic deformation. Proc. ICSMFE, 4, 2045-2048.

• Tokheim, O. (1976). A model for soil behaviour. PhD thesis, NTNU, Trondheim.

• Wroth, C.P. (1984). The interpretation of in-situ soil tests. 24th Rankine Lecture, Géotechnique, 34(4), 449-89

• Wroth, C.P. (1988). Penetration testing - a more rigorous approach to interpretation. Proc. Of International Conf. on Penetration testing, ISOPT-1, Orlando, 1, 303-311.

Bibliography

• Further information on the topics discussed in this lecture can be found in the following books:

• Simons, N., Menzies, B. and Matthews, M. (2002). A short course in geotechnical site investigation. Thomas Telford investigation. Thomas Telford

• Potts, D.M. and Zdravkovic, L. (2001). Finite element analysis in geotechnical engineering. Application. Thomas Telford

• Loo, B. (2007). Handbook of Geotechnical Investigations and Design Tables. Taylor & Francis.