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Shear Strength of Unsaturated Soil

Shear Strength Characterization

Requirements for Shear Strength

Cannot use saturated soil parameters c' and ' andeffective stresses because effective stresses areunknown.

To characterize the shear strength of unsaturated soil, it isnecessary to measure the three stresses , ua, and u w at failure to determine the stress state variables ( - u a)and (u a - uw) at failure.

Test Procedures

1) Specimen preparation:

- undisturbed specimens should be taken fromrepresentative samples where the soil properties(composition, moisture condition, and density) arethe same;

- disturbed samples are prepared by reconstitution of

soil from dry or saturated (slurry) state, or byrecompaction of soil samples;

- disturbed samples must be prepared at the samemoisture condition and density to be "identical".

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2) Sample "consolidation":

- stresses are applied and the soil is allowed to come to

equilibrium so that the initial stress state variableswill be known;

- the matric suction pressures can be achieved by:

a) directly measuring the pore water and air pressures of a specimen;

b) applying both air and water pressures keepingua > uw (axis-translation technique).

3) Load to failure:

- soil is tested under undrained conditions by

preventing movement of air and/or water from thesoil and measuring the changes in pressure;

- soil is tested under drained conditions by allowingmovement of air and water from the soil underregulated (constant) pressures.

- soil is loaded to failure using triaxial or direct shearapparatus (modified to control pressures), and theshear strength is given as half the deviator stress atfailure, ( 1 - 3)f / 2 or the applied shear stress atfailure, ff .

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Failure Criteria

Mohr's circles are plotted using 1 and

3 but, for soils

that undergo large strains, there is a question as towhen does failure occur.

Maximum deviator stress = ( 1 - 3)max

Maximum principal stress ratio =)

) (

(

3

max31

u w

For undrained tests, the denominator of the latterexpression varies so the maximum for the two criteriado not necessarily occur at the same value of strain.

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Test Results How can we determine the shear strength ofunsaturated soils?

The shear strength of soil is dependent on the net normalstress and the matric suction.

1) Drained triaxial shear tests:

a) Three-dimensional plots

( 3 u a)

(ua u w)

'

b

b ' Plane

c'

= c' + ( 3 u a) tan ' + (u a u w) tan b

= [c' + (u a u w) tan b] + ( 3 u a) tan '

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b) Two-dimensional plots

'

c'

b

c'

( 3 u a)

(ua u w)

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2) Undrained triaxial shear tests

- Linear and nonlinear behavior likely.

3) Drained direct shear tests

a) linear and nonlinear behavior reported for vs. ( f - u a)

b) nonlinear behavior for b vs. (u a - u w) and for

vs. (u a - u w)

4) Undrained direct shear tests

- Linear and nonlinear behavior likely

Required Results

Shear strength parameters that give the shear strength as afunction of the net normal stress and the matric suction

pressure for a particular soil for drained or undrainedconditions.

Stress-strain behavior or volumetric strain behavior.

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Shear Strength Equations For Linear Behavior

In terms of net normal stress, ( f - u

a):

ff a f w f bc u u = ' + ( ' + ( u f a) tan ) tan

or

ff a f c u = + ( 'f ) tan

where

c c u w f b ' + ( u a= ) tan

If one used the stress state variable ( f - u

w):

"tan)(u + tan)u-(+ aa f w f ff uc =

For zero matric suction, the pore air and pore water

pressure are equal. The third term in the equations iszero. Therefor the friction angle ' is the same.

Setting the two equations equal (for matric sunction > 0):

-uaf tan ' + (u a u w)f tan b = - u wf tan ' + (u a u w)f tan "

This simplifies to:

tan " = tan b - tan '

Since, tan b < tan ', " would have to be negative.

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Stress Point Envelopes (Stress Paths)

The top point of the Mohr circle (p f , qf ) is used to

represent failure where:

q = 1/2 ( 1 - 3)

p = 1/2 ( 1 + 3)

3f 1f

p f

qf

a

Comparing Mohr-Coulomb failure envelope with thestress point envelope, gives:

tan = sin '

a = c' cos 'Using q

f vs. p f to represent failure, a and can be

determine by linear regression (objectively) and then '

and c' can be computed.

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For unsaturated soil, the stresses are given in terms of thenet normal stress to give:

q = 1/2 ( 1 - 3)

p = 1/2 ( 1 + 3) - u a

f f bq r = d' + p ' +f tan tan

r f = (u a - u w)f

Comparing the extended Mohr-Coulomb failure envelope

with the stress point envelope, gives:

tan ' = sin 'd' = c' cos 'tan b = tan b cos '

Multistage Testing

Testing a single sample under increasing matric suctionusing cyclic loading or sustained loading procedure.

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Mechanics of Unsaturated Soils

Homework Assignment

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