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.
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(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
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(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.
5
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 ′
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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
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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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