WEEK 12

Soil Behaviour at Large Strains: Part 2

18. Structure and anisotropy

Last week we had a look at experimental data on soil strength from various sources. There

was a common feature in the reported data; whether reconstituted clays or pluviated sands,

they were obtained for laboratory-made soils. Such artificially prepared soils are preferred

for fundamental studies, because their behaviour is repeatable and (rightly or wrongly)

considered more ‘general’. In natural soils, however, peculiar soil structure developed

during soils’ geological lifetime renders their behaviour somewhat distinct from that of

laboratory-prepared soils. This week we focus on strength characteristics of natural soils.

18-1. Soil structure and sensitivity

Sensitivity ratio, St, is defined as

where

r

u

i

utc

cS =

where

cui : Undrained shear strength of intact specimen from unconfined compression test

cur : Undrained shear strength of remoulded specimen from unconfined compression test

Normally St is larger than 1, meaning

that intact soils is stronger when

undisturbed. Part of the reason for this

is explained by change in p’ due

to disturbance (p.10-11, last week).

However, that is not the whole story.

There is certainly an irrecoverable

element of strength in natural soil.

For exploring this feature, uncon-

fined compression test is not very

helpful, as we cannot separate the

effect of p’ loss and the other factor:

a permanent loss of natural soil

structure.

1

(After Bjerrum, 1954)

18-2. Destructuration (destruction of structure)

In Week 7 we studied that natural soil structure permits extra strength against compression

for a given void ratio, and that the structure-permitted strength can be lost upon loading

beyond yield.

Yielding and destructuration in Bothkennar

p′

q

Pure

shearTriaxial

compression

Isotropic

compression

K0-consolidation

The same can be true for shear strength. In many natural soils, the intact peak strength is

larger than remoulded or reconstituted strength. So the effect of natural structure on the

peak shear strength can be evaluated by comparing:

Approach (i)

(A) Natural sample before applying extreme stress/strain

(B) Natural sample which is stressed or strained to a large degree

or,

Approach (ii)

(A) Natural sample before applying extreme stress/strain

(C) Reconstituted sample (i.e. completely decomposed and made again from slurry in

laboratory

2

Yielding and destructuration in Bothkennar

Clay in K0-consolidation (Smith et al., 1992)

Example of Approach (i):

Destructuration in Saint Alban Clay (Champlain Clay), reported by Leroueil et al. (1979)

The Saint Alban Clay is a soft Canadian

clay, with St measured as 14 by un-situ

vane tests in this example.

In the bottom-right diagram, ‘intact” means

that the samples were sheared from σv’ < σp’.‘Destructured’ means that samples were

sheared after consolidated to σv’ > σp and

swelled to smaller σv’.

The bottom diagram shows comparison

of the limit yield surfaces from the two conditions.

Clearly, the natural structure allows higher shear

strength. Once it is destroyed, the permitted area shrinks.

So some people call soil structure

a “paperwork tiger”.

vσ ′log

e Loading beyond

‘natural’ yield stress, σp’

pσ ′ vcσ ′

Reconstituted

3

(Leroueil et al., 1979)

Example of Approach (ii):

Structure in four stiff, over-consolidated clays, reported by Burland et al. (1996)

Here the t - s’ data are normalised by the ‘intrinsic’ equivalent stress, σve* ( Week 6).

This is to take account of difference in e between the two types of samples by using the

intrinsic (i.e. reconstituted) compression curve as reference.

vσ ′log

eReconstituted

(‘Intrinsic’)

*

veσ

4

Pietrafitta Clay Todi Clay

Vallericca Clay Corinth Marl

(All from Burland et al., 1996)

18-3. Anisotropy of peak shear strength

The topic discussed here is related to cross-anisotropy described in Section 13-1 and the

“principal stress rotation” described in Section 15-2. Soils which deposited in a K0-

conditions exhibit cross-anisotropy in their peak strength as well as small-strain stiffness.

Exploiting the isotropy in the horizontal plane, here we focus on the vertical (v) – horizontal

(h) plane.

Let α be the angle between σ1’ and the v-direction.

v

h 1σ ′

hσ ′

3σ ′ vσ ′vhτ

vhτhσσ ′=′3

vσσ ′=′1vσσ ′=′3

hσσ ′=′1

(i) α = 0o (ii) α = 45o (iii) α = 90o

Bedding

planes, etc.

As we studied in Week 1, the description by q and p’, which are stress invariants, considers

only the magnitudes of principal stresses but not their directions (same for t – s’). So the q –

p’ description cannot differentiate the above cases. So for anisotropic soils, the strength

envelope cannot be defined uniquely as long as stress invariants are used.

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σ

τ

1σ3σ

PD for α = 0o

PD for

α = 45o

PD for α = 90o

p′

q

q – p’ state for

all the three cases

Mohr’s stress circle identical for the three

cases; only PD or (PP) is different.

For anisotropic soil, peak

strength envelope depends on α,

if defined by stress invariants.

Measuring shear strength anisotropy:

The following are approaches to measuring shear strength anisotropy. They have each

own advantages and disadvantages.

v

h

1σ ′

3σ ′

Sampling at inclined angles Testing with fixed principal stress

directions (triaxial/unconfined comp. etc.)

v

h

1σ ′

3σ ′

6

hSampling at fixed angles Testing with controlled principal

stress directions (HCA test, etc.)

v

hSampling at fixed angles

Triaxial

compression

1σ ′

3σ ′

1σ ′

3σ ′

3σ ′

3σ ′1σ ′Triaxial

extension

Direct shear

Different testing techniques

Example of peak shear strength anisotropy, as measured in HCA tests:

Note the following:

- In the above case (HPF4 silt), the

undrained peak shear strength for α=0o

is more than twice as large as that for

α=90o.

- In the bottom case (Toyoura Sand),

the undrained φ’ does not seem to be

very different for different α. However,

the dilatancy characteristics differ very

much, and as a result, the stress-strain

curves are very much dependent on α.

σz

σθ

σr

z

θ

r

Innercellpres-sure

Outer cellpressure

Axial force

Torque τzθ

σ1

σ2 3 1 3= +b( - )σ σ σ

σ3

α

(a)

(b)

(c)

τθz

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HPF4 silt (Zdravkovic & Jardine, 2000)

Toyoura Sand (Yoshimine et al., 1998)

18-4. Significance of peak shear strength anisotropy in geotechnical problems

(i) ‘Undrained’ (total-stress) analysis of slope stability (Lo, 1965)

The smaller the value for k is, the smaller

the stability number N is (of course!).

1

2

c

ck =

Fc

HN

1

γ=

: Anisotropy ratio

icccci2

212 cos)( −+= : Anisotropy model

: Stability number

γ : Total unit weight of soil

: Factor of safetyF

H : Height of slope

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(ii) Bearing capacity for cohesionless soils (effective-stress analysis) (Meyerhof, 1978)

The smaller the value for m is, the smaller

12 /φφ=m : Anisotropy ratio

qt DNBNq γγ γ += 2/

o90/)( 211 βφφφφ −−=: Anisotropy model

γ : Unit weight of soil

: DepthD

B : Width of foundation

1φ: Angle to sand deposition

: for

β

2φ: for φ o0=βφ o90=β

qNN ,γ :Bearing capacity factors

The smaller the value for m is, the smaller

the bearing capacity factors are (again,

of course they are!).

For cohesive soils (i.e. total-stress

analysis), Davis and Christian (1971)

presented corresponding analysis.

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(iii) Stability of embankment (Slope stability + bearing capacity) (Zdravkovic et al., 2002)

The diagram shows a result of analysis run with an advanced constitutive model (MIT E-3

model; Whittle, 1993) that is capable of describing strength anisotropy. It shows the

mobilised strength along the slip surface as against the strength that is attainable for

different shear modes.

As briefly mentioned in Week 10, Bjerrum (1973) sketched out mobilisation of different

strength due to anisotropy under embankment. The numerical analysis by Zdravkovic et al.

(2002) quantitatively demonstrated the effect.

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1σ

2σ

3σ

02 =δε

1σ

2σ

3σ

02 =δε

1σ

2σ3σ 02 =δε

Plane-strain extension

(PSE)

Direct simple shear

(DSS)

Plane-strain compression

(PSC)

(Bjerrum,1973)

(Zdravkovic et al., 2002)

18-5. Numerical model to express strength anisotropy

Expressing soils’ strength anisotropy has been a big issue in constitutive modelling. A

variety of models adopting a variety of different approaches exist. Among them, one of the

simplest and most commonly used in practice in Japan is the Sekiguchi-Ohta Model

(Sekiguchi & Ohta, 1977), which is a simple extension of the original Cam Clay Model (note

that the ‘original’ Cam Clay Model has a pointy yield surface; see p.10, Week 5). MIT E-3

Model mentioned in the previous page adopts a similar approach in describing anisotropy.

K0-consolidation

line:

p′

2/ijs

iiijij ps δσ ′−′=

′−′

′−′

′−′

=

p

p

p

zyzzx

yzyxy

zxxyx

στττστττσ

0== yzxy ττ

(Deviatoric stress tensor)

vz σσ ′=′

Assume plane strain condition

vhτ(Cross-section)

ps ijij′= β0

11

0== yzxy ττ

hx σσ ′=′

2/)( hvy σσσ ′+′≈′

02 =δε

2/2/ 0

ijij ss −

vhzx ττ =

vh

( ) 2/hv σσ ′−′

K0-consolidation

line:

-1.5 -1 -0.5 0 0.5 1 1.5

(σz-σθ)/2Cu,α=0

0

0.5

1

1.5

τ zθ/C

u,α

=0 HK

KSS

HPF4

Boston Blue Clay (OCR=1)

Boston Blue Clay (OCR=4)

London Clay (Series AC)

London Clay (Series R)

b = 0.5 or plane strain

Experimental results

(Nishimura, 2006)

2

0

2

00 )(22

vhvhhvhv ττ

σσσσ−+

′−′−

′−′=

0

ijsDSS

PSCPSE

References

Bjerrum, L. (1954) “Geotechnical properties of Norwegian marine clays,” Geotechnique 4(2)

49-69.

Bjerrum, L. (1973) “Problems of soil mechanics and construction on soft clays and

structurally unstable soils (collapsible, expansive and others),” Proceedings of 8th

International Conference on Soil Mechanics and Foundation Engineering, Moscow, Vol.3,

111-159.

Burland, J.B., Rampello, V.N., Georgiannou, V.N. and Calabresi, G. (1996) “A laboratory

study of the strength of four stiff clays,” Geotechnique 46(3) 491-514.

Leroueil, S., Tavenas, F., Brucy, F., LaRochelle, P. and Roy, M. (1979) “Behaviour of de-

structured natural clays,” Journal of Geotechnical Engineering Division, ASCE 106(GT6)

759-778.

Lo, K.Y. (1965) “Stability of slopes in anisotropic soil,” Journal of Soil Mechanics and

Foundation Division, ASCE 91(SM4) pp.85-106.

Meyerhof, G.G. (1978) “Beating capacity of anisotropic cohesionless soils,” Canadian

Geotechnical Journal 15, 592-595.

Nishimura, S. (2006) “Laboratory study on anisotropy of natural London Clay,” PhD Thesis,

Imperial College London.

Sekiguchi, H. and Ohta, H. (1977) “Induced anisotropy and time dependency of clay,”

Proceedings of Special Session, the 9th International Conference on Soil Mechanics and

Foundation Engineering, Tokyo, 229-239.

Smith, P.R., Jardine, R.J. and Hight, D.W. (1992) “The yielding of Bothkennar clay,”

Geotechnique 42(2) 257-274.Geotechnique 42(2) 257-274.

Whittle, A.J. (1993) “Evaluation of a constitutive model for overconsolidated clays,”

Geotechnique 43(2) 289-313.

Yoshimine, M., Ishihara, K. and Vargas, W. (1998) “Effects of principal stress direction and

intermediate principal stress on undrained shear behavior of sand,” Soils and

Foundations 39(3) 179-188.

Zdravkovic, L. and Jardine, R.J. (2000) “Undrained anisotropy of K0-consolidated silt,”

Canadian Geotechnical Journal 37, 178-200.

Zdravkovic, L., Potts, D.M. and Hight, D.W. (2002) “The effect of strength anisotropy on the

behaviour of embankments on soft ground,” Geotechnique 52(6) 447-457.

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