WEEK 11

Soil Behaviour at Large Strains: Part 1

16. Overview: ‘The’ strength, or strength’s’?

What is soil strength? In usual contexts, it means the peak strength, or the maximum stress

(or stress ratio) that soil can bear, mobilised at large strains. However, soils’ stress-strain

relationships exhibit a variety of strain-hardening/softening types, particularly at large

strains, depending very much on soil types, density, drainage conditions, deformation

modes and other factors. It is difficult in quite a few situations to define a unique strength

(‘the’ strength) without considering relevance to a particular engineering problem in interest.

τ τPeak strength

Critical State?

Strain softening

Strain

hardening

1

γ γ

Residual strength

(see Week 12)

hardening

Over-consolidated and/or cemented clays Normally consolidated clays

Strain

hardening

Sand; undrained conditions

(Verdugo, 1992)

Sand: drained conditions

(Cole, 1967; reproduced from Oda, 1975)

17. Peak shear strength

17-1. Drained strength and undrained strength

First of all, make sure that you understand the relationship between total and effective

stress paths under drained and undrained conditions, discussed in Week 3.

Consider triaxial compression of soil obeying the Mohr-Coulomb failure criterion:

q

φ

φ

′−

′

sin3

sin6

1

( Week 4)

1

3 ( Week 1)

uu cq 2= u∆

u∆

Drained path

uu cq 2=

Half the maximum value of q (qu) is

the undrained shear strength, cu(see the right diagram for why it

should be half. Recently, it is

encouraged to express it as Su).

The strength defined in terms of

effective stress (the envelope) and

the undrained shear strength are

related via the pore water pressure

development, ∆u.

2

p′

Difference between the drained and undrained

paths are due to excess pore water pressure, ∆u

0p′Undrained path:

Moderately contractive

Very contractive

σ ′

τ

1σ ′3σ ′ q

2/qcu =

φ ′

Now imagine that isotropic pressure is applied to the soil, increasing the total stress by ∆p.

Long-term strength: The strength available after any change in the total stress is converted

into a change in the effective stress via consolidation and dissipation of

pore water pressure.

q

0p′

Undrained effective path

uu cq 2=

0p

p

p

∆+

0

p

p

∆+

′0

uu cq 2=

Drained effective path

Undrained total path

p’ and p0u∆ 0u∆

Drained total path

Short-term strength: The strength available before the change in the total stress is

converted into a change in the effective stress.

3

q

0p′ 0p

p

p

∆+

0

uu cq 2=

p’ and p

0u∆

0u∆

Because the effective stress does not change,

cu does not change. The cu value (only) appears

to be independent of the total stress.

Note the following:

- If you look at the short-term strength in terms of the total stress, the strength looks like

independent of the stress. That is why it is considered as ‘cohesion’ and the letter “c” was

assigned. However, it has nothing to do with the intersect of the failure envelope (called

“true cohesion”. That is why it is encouraged to use “S” for “S”trength, in place of c.

- In usual cases, the short-term strength is relevant to clays, while the long-term strength is

relevant to sands/gravels. This is simply because of the time required for consolidation and

transfer of ∆p to ∆p’. Sometimes clays are called ‘c-material’ or ‘cohesive material’, while

sands/gravels are called ‘φ-material’ or ‘frictional material’. If the behaviour is interpreted in

terms of effective stress, such a nomenclature does not make sense.

Cut slope in the London Clay: Why does it stand (Assignment 4)?

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I was working here!

(Diagram from Kovacevic et al., 2007)

17-2. Shear strength from direct shear test

A direct shear test (shear box test) has the following characteristics:

- Constant vertical stress tests or constant volume (corresponding to undrained conditions)

tests may be performed.

- The horizontal stress is not known.

Because we do not know the horizontal

vhτ

vσ

?:hσ

(Diagram from Potts & Zdravkovic, 2001)

Because we do not know the horizontal

stress, we cannot construct Mohr’s stress

circle as we did in triaxial tests. It means

that we can derive neither cu (i.e. the radius

of the circle) nor φ’ (the slope of a tangent

to the circle) in a rigorous way. It involves

some assumptions to derive these.

It is often assumed that the shear stress,

τvh, is at the crown of the Mohr’s stress

circle (assuming σv = σh). Hence,

Or, it is also often assumed that the

maximum stress ratio is mobilised along

the horizontal plane. Hence,

These two assumptions are not compatible

(think why), but both are often invoked.

5

σ ′

τ

1σ3σ

),( vhv τσ ′

)/(tan 1

vvh στφ ′=′ −

),( vhh τσ ′

φ’ from direct shear test

φ’ from triaxial test

=

?

=

?

=

?

cu from

triaxial test

cu from

direct shear

test

max)( vhuc τ=

17-3. Peak shear strength of soils: Drained conditions

Peak shear strength of soils are closely related to dilatancy characteristics. It is observed

better under drained conditions.

Experimental findings:

Higher density and lower confining

stress

Higher peak stress ratio and

more dilative behaviour

Below is an interpretation of how

dilatancy adds apparent frictional

strength.

τ

σ

δγ

δε−

6

Drained simple shear of Leighton Buzzard Sand

(Cole, 1967; reproduced from Oda, 1975)

Dilatancy of granular material

(Diagrams taken from Wood, 1990)

)( δεστδγδ −−=W

δγτδ fE =

The work done by external forces:

The energy dissipated internally

due to friction:

where is the internal friction stress.

From ,EW δδ =

fτ

τδγ

δεστ =−+ )(f

DilatancyObserved

in test

True

friction

stress

Do you remember the data from Assignment 2? They were from drained triaxial tests on

normally consolidated Soma Silica Sand. Here indeed you see an ‘apparent’ cohesion for

the denser condition, caused by dlatancy.

0 50 100 150 2000

100

200

300

400

Dr

50% 90%

p0' = 20 kPa

p0' = 40 kPa

p0' = 80 kPa

q [kP

a]

p' [kPa]

0 2 4 6 8 10 12 14 16 18 200

100

200

300

400

500 Dr

50% 90%

p0' = 20 kPa

p0' = 40 kPa

p0' = 80 kPa

q [kP

a]

εq [%]

στ ′−

στ ′−f

Corrected for

From drained

test, uncorrected

0

2

4

6

8 Dr

50% 90%

p0' = 20 kPa

p0' = 40 kPa

p0' = 80 kPa

7

σ ′

Corrected for

dilatancy, or from

undrained test

Peak strength envelope for

uncemented (no true cohesion) soils0 2 4 6 8 10 12 14 16 18 20

-12

-10

-8

-6

-4

-2

ε p [%

]

εq [%]

Bjerrum & Simons (1960) showed that

corrected φ’ from drained triaxial tests

and φ’ from undrained triaxial tests are

broadly identical (diagram reproduced

from Ishihara, 1988).

17-4. Peak shear strength under undrained conditions: Clays

Under undrained conditions, we do not have the problem of dilatancy’s influence on the

apparent friction, because the constant-volume condition prohibits dilatancy. However, the

suppressed dilatancy leads to changes in the effective stress.

So under undrained conditions, knowing strength comes down to knowing which direction

the undrained effective stress path goes, as well as knowing the location of the peak

strength envelope.

sp ′′,

tq,

00 , sp ′′

Contractive

Neither dilative

or contractive

Dilative

We have already studied a model (the Cam Clay Model) to interpret these effective stress

path behaviour in relation to overconsolidation. For heavily over-consolidated soils,

however, it is difficult to observe effective stress paths converging to the Critical State, as

the strain-softening leads to bifurcation (i.e. shear banding) phenomena in most testing

methods.

8

00 , sp ′′

Effective stress paths of reconstituted Todi Clay (Burland et al., 1996)

17-5. Peak shear strength under undrained conditions: Sands

Shown in the diagrams are undrained triaxial compression data of clean, Toyoura sand by

Verdugo (1992; reproduced from Yoshimine & Ishihara, 1998).

Note the following:

- Dense sand can exhibit extremely high

shear strength, while the opposite is

true for loose sand (static liquefaction, or

flow failure).

- Higher confining stress can work as if

equivalent to looser conditions.

The right diagram is an interpretation of

these observations. A “phase transformation”

(Ishihara et al., 1975) from contractive to

dilative behaviour is characteristic of granular

soils.

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p′log

e

High p’Low p’

High e

Low e

Ultimate state line

(Critical State Line)

17-6. Sampling, disturbance and laboratory strength

Knowing the effective stress path characteristics under undrained conditions helps

understand the disturbing mechanisms involved in sampling. Let us consider normally

consolidated clay as an example, in which shear (i.e. changes in q) causes a reduction in p’.

p′

q

“Perfect sampling”

p’ reduces due to q reduction

for normally consolidated soils

Various actions during handling

A: In-situ stress

Start of unconfined

compression test

Not-perfect sampling in reality:

sampler intrusion, sample extrusion,

etc. causes shear

In-situ qu

Lab qu

B

qu∆

10

samples (see the diagram next page).

p’ may increase or decrease

0u

0vσ

0hσ

3/)2( 000 hvp σσ +=

qupuu ∆+−= 00

0

0

0=p

000 upp −=′quupp ∆−−=′ 00

A: In-situ stress B: After perfect sampling

During sampling (which is considered to be an undrained process for clayey soils), the

release of p is compensated by a reduction of u. Any change in p’ is therefore ideally

due to plastic deformation by shearing.

The change in p’ is recoverable by re-consolidation in a laboratory triaxial (CU) test, while

this is not possible in unconfined compression or unconsolidated triaxial (UU) test.

However, sample disturbance may cause permanent changes in the failure envelope in

‘sensitive’ soils. This loss of structure is generally not recoverable, as we see next week.

p′

q

In-situ stress

Start of unconfined

compression or UU

triaxial test

In-situ qu

Lab quRe-consolidation in CU test

(anisotropic)

Re-consolidation in CU test

(isotropic)

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triaxial test

Factors affecting p’ during sampling

(Hight et al., 1992)

References

Bjerrum, L. and Simons, N.E. (1960) “Comparison of shear strength characteristics of

normally consolidated clays,” Proceedings of Research Conference on Shear Strength of

Cohesive Soils, ASCE, 711-726.

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.

Cole, E.R.L. (1967) “The behaviour of soils in the simple shear apparatus,” PhD Thesis,

University of Cambridge.

Hight, D. W., Bike, R., Butcher, A. P., Clayton, C. R. 1. and Smith, P. R. (1992)

“Disturbance of the Bothkennar clay prior to laboratory testing,” Geotechnique 42(2) 199-

217.

Ishihara, K. and Tatsuoka, F. and Yasuda, S. (1975): “Undrained deformation and

liquefaction of sand under cyclic stresses,” Soils and Foundations 15(1) 29-44.

Ishihara, K. (1988) “土質力学 (Soil mechanics),” Maruzen (in Japanese).

Kovacevic, N., Hight, D. W. and Potts, D. M. (2007) “Predicting the stand-up time of

temporary London Clay slopes at Terminal 5, Heathrow Airport,” Geotechnique 57(1) 63–

74.

Oda, M. (1975) “On stress-dilatancy relation of sand in simple shear test,” Soils and

Foundations 15(2) 17-29.

Potts, D.M. and Zdravkovic, L. (2001) “Finite element analysis in geotechnical engineering:

Application,” Thomas Telford, London.

Verdugo, R. (1992) “Characterization of sandy soil behavior under large deformation,” PhD

Thesis, University of Tokyo.Thesis, University of Tokyo.

Wood, D.M. (1990) “Soil Behaviour and Critical State Soil Mechanics,” Cambridge

University Press.

Yoshimine, M. and Ishihara, K. (1998) “Flow potential of sand during liquefaction,” Soils

and Foundations 38(3) 189-198.

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