Shear Strength of Soil - Civil Engineering SSC JE (Technical) - Civil Engineering

Shear strength

Shear strength of a soil is the capacity of the soil to resist shearing stress. It is defined as the maximum value of shear stress that can be mobilised within a soil mass.

• Plane a-a is the critical plane (plane on which failure is likely to occur).
• θ_c = Angle of the critical plane (a-a).
• σ₁ and σ₃ are the principal stresses acting on the given planes.

Relation between resultant, normal and shear stresses on the critical plane

In the figure above, β_max = Angle between resultant stress and normal stress on the critical plane. For many soils the maximum value of this angle corresponds to the internal friction angle φ.

For purely cohesive clays idealised as having no frictional resistance, φ = 0.

Common idealised cases of soil strength

(i)

Represents the case for non-cohesive soils (sands) where shear strength is mainly from friction - a φ-soil.

(ii)

Represents a combined C-φ soil where both cohesion (C) and friction (φ) contribute.

(iii)

Represents an idealised C-soil (purely cohesive clay) where shear strength is independent of normal stress.

(iv)

Another representation for C-φ soils (mixed behaviour).

(v)

Represents a purely φ (frictional) soil.

(vi)

For purely cohesive soils, at failure under uniaxial compression the major principal stress at failure satisfies:

σ₁ = 2C for an ideal C-soil.

Mohr-Coulomb theory

The Mohr-Coulomb failure criterion expresses shear strength as a linear function of normal effective stress. The commonly used form is:

τ = c′ + σ′ tan φ′

where τ = shear strength, c′ = effective cohesion, σ′ = effective normal stress, and φ′ = effective angle of internal friction.

In effective stress notation, the parameters are:

• c′ = Effective cohesion.
• σ′ = Effective normal stress (total stress minus pore pressure).
• φ′ = Effective friction angle.

Direct shear test

The direct shear test is a laboratory test to determine the shear strength parameters (c and φ) of a soil. A specimen is placed in a shear box split horizontally; a normal stress is applied and a horizontal force is imposed until the specimen fails along the split plane. The test gives a plot of shear stress versus normal stress; the failure envelope approximated by a straight line yields c and φ.

• Advantages: simple, quick, useful for granular materials and to obtain shear stress-displacement behaviour.
• Limitations: fixed failure plane, non-uniform stress distribution, sample disturbance, drainage conditions depend on specimen thickness.

Unconfined compression test

The unconfined compressive strength test is used for saturated cohesive soils (clays) to obtain a quick estimate of undrained shear strength.

q_u = (σ₁)_f

where q_u is the unconfined compressive strength and (σ₁)_f is the major principal stress at failure. In this test the minor principal stress σ₃ = 0 (no lateral confinement).

For an ideal purely cohesive soil under undrained conditions, the relation between q_u and cohesion is:

q_u = 2C

Vane shear test

The vane shear test is suitable for determining the undrained shear strength of soft, sensitive clays in the field and in the laboratory. A four-bladed vane is embedded into the soil and rotated; the torque required to cause failure is related to the shear strength.

Interpretation of vane shear results

Shear strength obtained from the vane test depends on whether both top and bottom of the vane participate in shearing or only one portion shears. Typical representations:

- When top and bottom of vanes both participate in shearing:

- When only bottom of vane participates in shearing:

The sensitivity of a soil is defined as the ratio of the undisturbed shear strength to the remoulded shear strength and is denoted S_f. Sensitive clays have high values of S_f.

Pore pressure parameters and pore pressure change

During shearing and loading, changes in pore water pressure occur. These changes affect effective stresses and therefore shear strength. Two commonly used pore pressure parameters are B and A, defined for different stress increments.

For change in pore pressure due to an increase in isotropic cell pressure (Δσ_c or Δσ₃):

• B = pore pressure parameter defined by ΔU_c = B · Δσ_c.
• Here ΔU_c = change in pore pressure due to increase in cell pressure and Δσ_c = Δσ₃ = change in cell pressure.
• Range: 0 ≤ B ≤ 1.
• B = 0 for dry soil.
• B = 1 for saturated soil when pore pressure change equals applied total stress change.

(ii)

For pore pressure change associated with deviatoric loading:

A = pore pressure parameter given by ΔU_d = A · Δσ_d.

where:

• ΔU_d = Change in pore pressure due to deviator stress.
• Δσ_d = Change in deviator stress.

(iii)

Overall pore pressure change:

ΔU = ΔU_c + ΔU_d

ΔU = total change in pore pressure (sum of isotropic and deviatoric contributions).

(iv)

Shear strength parameters and practical considerations

• Shear strength parameters are usually expressed as c (cohesion) and φ (angle of internal friction). For effective stress analyses they are written as c′ and φ′.
• Selection of parameters for design must consider drainage conditions: drained parameters for slow loading/drained conditions; undrained parameters (su or cu) for short-term undrained conditions.
• Factors affecting shear strength include soil type, density, confining stress, water content, sample disturbance, strain rate and structure.
• Common applications: slope stability, bearing capacity of foundations, earth pressure problems, design of retaining structures, and stability assessment of embankments and levees.

Summary

The shear strength of soil controls many geotechnical design problems. It is characterised by cohesion and friction components, and may be obtained from laboratory tests such as the direct shear, unconfined compression and vane shear tests. Effective stress concepts and pore pressure parameters are essential when interpreting strength under drained and undrained conditions. Appropriate selection and interpretation of shear strength parameters is critical for safe and economical geotechnical design.