Geo Lecture 7

8/12/2019 Geo Lecture 7

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CIVE 2004

Lecture 7 –

Shear Strength of Soils




• There is a need to define the point at which a soil ‘fails’.




• There is a need to define the point at which a soil ‘fails’. – Peak shear strength

– Ultimate shear strength

– Critical shear strength (may be taken as equal to

ultimate shear strength). After critical strength isattained, the volume of the soil remains constant as

shearing continues. The soil is in a critical state.

– Residual shear strength. It is the lowest strength which

is reached after very large displacements. For sands, theresidual strength is the same as the critical state

strength. For clays, the residual strength is about ½ the

critical state strength.



Shear Strength Tests

Consist of 3 main stages:

– Saturation stage (if required)

– Consolidation stage

– Shearing stage. Shearing can take place either under

undrained conditions (that is, no dissipation of

porewater pressure) or drained conditions (that is, with

complete dissipation of porewater pressure). Why?



Shear Strength Tests

Soil strength depends on drainage conditions:

• different strengths will be measured for a given soil

that

(a) deforms at constant volume (undrained) – total stress

conditions or

(b) deforms without developing excess pore pressures

(drained) – effective stress conditions



Stress – Strain Relationships:

Types of Test



Shear box test

Source: Craig (1992)

Main features:

• Known normal force is applied.

• Shear force T is measured as shear displacement

(Dl) is applied.

• Vertical displacement (Dh) is measured.



Shear box test

N

T

Dh

Dl



Shear box test

Limitations:

• Cannot control drainage or measure porewater pressure.

• Quick test gives undrained (total stress)

measurements.

• Slow test ensuring complete porewater pressure

dissipation gives drained (effective stress)

measurements.

• Soil is forced to shear on a predetermined plane which is

not necessarily the weakest one.

• The stresses over the shear plane is non-uniform. Stress is

higher at the edges than at the centre.



Shear box test

Dense sands

• High degree of interlocking between particles.

• Shearing starts with initial

expansion/dilation (increase in

volume).

• Shear stress reaches a peak value atrelatively low strain.

• As interlocking is progressively

overcome with strain, shear stress

decreases from the peak value and

reaches an ultimate value.





Shear box test

Behaviour of sands

For tests performed under the same

normal stress:

• Initially dense samples attain higher

peak stress. The peak stress is a

function of initial density state.

• Dense and loose samples approach

the same ultimate shear stress and

void ratio (critical state), irrespective

of the initial relative density.

• A sand more dense than the criticalstate dilates whereas a sand less

dense than the critical state contracts.





Triaxial test





Triaxial test





Triaxial test

Deviator stress



Triaxial test

• Porewater pressure can be measured.

• Drainage can be controlled from the top and bottom of the

specimen.



Triaxial test

There are 3 stages in a triaxial test:

Stage 1: Application of s3 undrained, that is without

dissipation of porewater pressure in all types of test

Stage 2: Consolidation stage at constant s3. This stage isomitted in UU tests

Stage 3: Shearing stage at constant s3.

– Undrained shearing in UU and CU tests

– Drained shearing in CD tests



Types of triaxial test

There are 3 types of triaxial test:

• Unconsolidated undrained (UU): No consolidation stage 2

and undrained shearing stage 3

• Consolidated drained (CD): Consolidation stage 2 and

drained shearing stage 3

• Consolidated undrained (CU): Consolidation stage 2 andundrained shearing stage 3 with porewater pressure

measurement



Types of triaxial test

To obtain shear strength parameters, tests are carried out at

3 different confining pressures so as to obtain 3 Mohr

circles.



Triaxial Test - Failure Criterion

Deviator

Stress

s1 - s3)

•A specimen is considered to have failed when the applied

deviator stress reaches its maximum value

Axial Strain e1

Max. s1 - s3)



UU triaxial test

• Volume of the specimen remains constant

• Area correction of specimen is required to calculate axial

stress during shearing stage (Eq 7.16)

• Test allows determination of total strength parameters, cu

and fu

o

o

l

l

A A

D-

1



UU triaxial test

• For saturated clays, fu = 0. Undrained shear strength, t = cu

• Unconfined compression test, that is a test in which

confining pressure is zero, can be used to determine

undrained shear strength of a saturated clay



CD triaxial test

• Volume change of the specimen during consolidation ismeasured from volume of porewater expelled from

specimen

• Area correction of specimen is required to calculate axialstress during shearing stage (Eq 7.15)

• Test allows direct determination of effective strength

parameters, c' and f'

o

oo

l

l

V V

A AD-

D-

1

1



CU triaxial test

• Volume change of the specimen during consolidation ismeasured from volume of porewater expelled from

specimen

• Area correction of specimen is required to calculate axial

stress during shearing stage (Eq 7.16)

Ao and lo are dimensions of specimen afterconsolidation stage

o

o

l

l

A A

D-

1





Triaxial test



Knowing u and total stresses at failure, effective circles can be

plotted

0

s (kPa)

t

(kPa)

A B

u1 (Test 1)

Effective Mohr Circle

Total Mohr Circle

u2 (Test 2)



0

s (kPa)

t

(kPa)

A B

cu

fu

c'

f'

Both total stress parameters cu and fu and

effective stress parametersc

' andf

' can be determined

Total and Effective Shear Strength Parameters



Triaxial test





Pore Pressure Coefficients A and B

• During undrained loading, changes in porewater pressureresulting from changes in cell pressure or axial stress, or

both, are predicted from the following equation (Whitlow,

Eq 4.11):

• Isotropic compression: B = Du/Ds3

• B = 1, in saturated soils.

Worked examples: 7.8(a), 7.9, 7.11, 7.12, 7.16, 7.17, 7.18 (a)

Do problems: 7.7(a), 7.8, 7.9, 7.13

( ) 313 s s s D-DDD A Bu



Stress Paths

• The behaviour of a soil depends on the route (stress path)taken between the initial state and the final state.

• The stress path method in laboratory testing allows the

actual field stress changes to be simulated more

realistically than by using conventional test proceduresalone.

• Stress path: a curve drawn through a series of points on a

plot of stresses.

• Stress point: a point on a plot of stresses representing the

selected components of stress at a particular instant.



Stress Paths

• Effective stress path (ESP): path plotted in terms of effective stresses.

• Total stress path (TSP): path plotted in terms of total

stresses.



Types of Stress Path Plot

• s1 v/s s3 space for total stresses• s1 v/s s3 space for effective stresses

• t v/s s or s' space (MIT)

– t = (s1 – s3)/2,

– s = (s1 + s3)/2, s' = (s1' + s3

')/2

– The stress point used is the maximum shear stress at

any stage, that is the topmost point of each Mohr circle.

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Geo Lecture 7