Soil Parameters for Drained and Undrained Analysis

Introduction • The aim is to discuss the choice of parameters for the MohrCoulomb model. • More advanced soil models may have some advantages over the MohrCoulomb model (but require the specification of a larger number of parameters) • 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.

Soil Parameters for Drained

and Undrained Analysis

Applied Theory

Dr Minna Karstunen

based on work by Dr H Burd, University of Oxford

specification of a larger number of parameters)

• 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

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

– permeability is high

– rate of loading is low

– short term behavior is not of interest for problem considered

– 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

t D

γ

E

k T

2 w

oed

=

k = permeability

E oed = stiffness in 1-d compression

γ w = 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

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: undrained

effective strength parameters (MC: c', ϕ', ψ‘)

effective stiffness parameters (MC: E 50 ', 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: undrained

total strength parameters c = c u , ϕ = 0, ψ = 0

effective stiffness parameters E 50 ', ν'

Method C (analysis in terms of total stresses):

type of material behaviour: drained

total strength parameters c = c u , ϕ = 0, ψ = 0

total stiffness parameters E u , ν u = 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 , c u ,

is used Note that c u 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 Behaviour

a) Most real soils do not exhibit linear elastic behaviour prior to failure

Tunnels Foundations

Larger strains

Very small strains Small strains

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.

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

The Mohr-Coulomb Model and

Real Soil Behaviour

Drained Triaxial Test

Undrained Triaxial Test

u

u ho

L

c

G c

The undrained shear strength may be calculated from the limiting cavity

pressure P L (for details see Clarke (1995).



  u 

For penetration in clays, the

tip resistance q t is given by:

Cone Penetrometer Test

vo u

kt

where σ vo is the total vertical

stress in the soil at the level of

the cone and N kt is an empirical

factor, typically in the range of 10

to 20 For further details, see

Lunne et al, (1997).

vo u

kt t

Correlations for Undrained

Shear Strength (c u ) Shear Strength (c u )

Undrained Shear Strength from

2

1 '

cot '

'

u

K c

Example: Undrained parameters

2

1 '

cot '

'

u

K c

Example: Undrained parameters

from MC

In this example:

where c uo =4.698 kPa and ρ = 2.326 kPa/m.

z c

c u = uo + 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

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 ν u =0.495 In this case, the appropriate value of undrained Young’s modulus would be 5537 kPa.

Correlations for s u based on

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 (c u / σ ’ vi ) NC lies between 0.1 and 0.35.

At an OC clay site, the

water table is at the ground surface

The preconsolidation

stresses correspond to the application of a vertical

effective stress of 500 kPa

at the ground surface.

Take (c u / σ ’ vi )NC as 0.2, µ

as 0.8 and the submerged unit weight of the soil as 8 kPa/m

c u from Index Tests

P L

P L

w w

w

w I

−

−

=

) 1

be much higher)

c u of London Clay

c u of London Clay

Friction and Dilations Angles

for Sand

Correlations for Friction Angle

Bolton (1986) proposes a relationship

ψ φ

φ ' = ' cv + 0 8

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) on published sand test data, suggested that the maximum dilation rate of a sand depends on

a relative density index I R :

a relative density index I R :

kPa p

for

p I

150

' ln

for I

I R = 5 D − 1 ' < 150

min max

max

e e

Correlations for Friction Angle

The following correlations were found by Bolton to give a good fit to the available database of test results:

R cv

peak ' 5 I

φ

R cv

peak ' 3 I

' − φ =

φ

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 E 50 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 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, E ur 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 &

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:

P

u u

I

c

E 50 ≈ 15000

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 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

• 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

• 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

• 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.