SHEAR STRENGTH

Shear strength of soil is its ability to resist sliding along internal surface within mass. The force

causing this type of sliding is called shear force and the resistance offered just before failure per

unit area is termed shear strength.

* Natural slopes of hillsides, slopes of earth dam, slopes of a cut and bearing capacity of soil depend

upon the shearing strength.

* Shear strength is mainly due to

1. Internal friction due to interlocking of particles and friction between individual particles of their

contact surfaces.

2. Cohesion, which is due to interparticle forces which tend to hold the particles in soil mass.

* Coulomb’s equation for shear strength is

t = c + s tan f

where s = Normal stress on the failure plane

c = Cohesion

f = Angle of internal friction

* Angle of internal friction depends upon

1. Shape of particles

2. Surface roughness

3. Type of interlocking

4. Lateral pressure

5. State of packing

The angle of internal friction is 25° to 30° for loose sand and 32° to 37° for dense sand.

Coulomb gave the above equation on the basis of total stress s which is the total load per unit area.

* Terzaghi modified Coulomb’s equation on the basis of effective stress. The effective stress is given

as the difference between the total stress and the pore water pressure. Thus

s¢ = s – u

where u is pore water pressure. The equation suggested is

T = c¢ + s¢ tan f¢

where c¢ = Effective cohesion

f¢ = Effective angle of friction

* In case of stresses in two-dimensional problems, principal planes (planes on which there is no

shear stress) can be found by the equations derived in strength of materials or by drawing Mohr’s

circle of stress.

* In case of three-dimensional problems, the equations suggested for two-dimensional problems may

be used, noting that,

s1 = maximum principal stress

s2 = minimum principal stress, normally referred as s3

.

Thus, Fig. 12.7 shows the Mohr’s circle of stress.

Fig. 12.7 Mohr’s circle of stress

Note

s1 = Maximum principal stress

s3 = Minimum principal stress

Radius of Mohr’s circle =

Centre of Mohr’s circle =

Any point D on the Mohr’s circle indicates the state of stress on a plane at q to maximum principal

plane.

Maximum stress = tmax =

Angle of obliquity with the normal of the plane b

 = tan

–1

\ sin bmax =

* The shear stress on the plane of maximum obliquity is less than the maximum shear stress.

* Drainage Conditions: Three types of shear tests have been developed based on drainage

conditions:

1. Undrained test: Drainage is not permitted during the test, i.e., no dissipation of pore pressure is

permitted.

2. Consolidated undrained test: Drainage is permitted initially till full primary consolidation takes

place. Later no drainage is permitted during subsequent application of either normal or shear

stresses.

3. Drained test: Drainage is permitted throughout the test so that full consolidation occurs and no

excess pore pressure is set up.

* The following types of tests are used to find the shear strength of soils:

Laboratory Tests

1. Direct shear test

2. Triaxial compression test

3. Unconfined compression test

4. Laboratory shear test

Field test: Vane shear test

Note the following:

1. Box shear test (direct shear stress) is suitable for clay samples. However, drained tests on sand

may be carried out.

2. In triaxial text vertical stress is the major principal stress (s1

). The other two stresses (s2 and s3

)

are both equal to the confining fluid pressure. In case of unconfined compression test cylindrical

specimen is failed under uniaxial stress only. In this case the cross-sectional area A at any stage of

loading may be computed on the assumption that the total volume of the sample remains the same:

Aoho = Ah

where Ao and ho are initial cross-sectional area and height of the sample respectively.

* The triaxial apparatus is well suited for carrying out all the three types of shear tests.

* Undrained shear strength of soft cohesive soil can be made by direct measurement by a shear vane

test. This test can be performed on a soil sample in a laboratory or on a undisturbed soil in situ at

the bottom of a bore hole.

* Ef ect of rate of strain: The shear strength of cohesive soil is affected by the rate of strain. Lower

the rate of strain, the lower is the shear strength.

1. Undrained strength of saturated cohesive soil for a test duration of 30 days is 40 to 80 per cent of

the strength of one minute test.

2. According to Skempton, if the variation of rate of strain is ± 5 times the normal rate of strain

makes hardly 5 to 10 per cent difference in the undrained strength.

3. If the shear strengths are compared on the effective stress basis, the changes in straining rate is

considerably less.

* Shear strength of cohesionless soils: Typical stress-strain curves for loose sand and dense sand are

as shown in Fig. 12.8.

Fig. 12.8 Axial strain

From the curve it may be noted that

1. Dense sand shows a relatively high initial tangent modulus and reaches peak value. Then stress

drops but strain increases.

2. Loose sand shows a relatively slower rate of increase of stress with strain.

3. The ultimate stress in both the cases is more or less the same.

* Sensitivity of clays: It is defined as the ratio of the shear strength of undisturbed clay to the shear

strength of remoulded clay in its undrained condition.

St =

Table 12.3 shows classification of clay according to its sensitivity.