Shear Strength of Soil

Shear strength governs bearing capacity, slope stability and earth pressure, so it is the most consequential soil property. The Mohr-Coulomb criterion τ = c + σ tan φ expresses strength as a cohesion intercept c plus a frictional part increasing with normal stress.

Because soil strength depends on effective stress, the effective form τ = c′ + σ′ tan φ′ (with σ′ = σ − u) is the fundamental relation; the total-stress parameters are only convenient for specific drainage conditions.

Strength is measured by direct shear, triaxial and unconfined compression tests, each simulating different drainage and confining conditions. Matching the test (drained/undrained, consolidated/unconsolidated) to the field situation is a key judgement examiners probe.

(total stress)

(effective stress; σ′ = σ − u)

(undrained clay)

Relation 1 —

(total stress)

Write this relation with symbols exactly as in Soil Mechanics & Foundations — BC Punmia before substituting numbers. Examiners award partial marks for a correct setup even when arithmetic slips.

Relation 2 —

(effective stress; σ′ = σ − u)

Write this relation with symbols exactly as in Soil Mechanics & Foundations — BC Punmia before substituting numbers. Examiners award partial marks for a correct setup even when arithmetic slips.

Relation 3 —

(undrained clay)

Write this relation with symbols exactly as in Soil Mechanics & Foundations — BC Punmia before substituting numbers. Examiners award partial marks for a correct setup even when arithmetic slips.

Relation 4 —

Write this relation with symbols exactly as in Soil Mechanics & Foundations — BC Punmia before substituting numbers. Examiners award partial marks for a correct setup even when arithmetic slips.

Terzaghi’s principle states that shear strength is controlled by effective stress σ′ = σ − u, the stress carried by the soil skeleton. When pore pressure rises (undrained loading), effective stress and hence strength can drop, which is why rapid loading of clays is critical.

The two strength parameters have distinct origins: cohesion c′ arises from cementation and electrochemical bonds and exists even at zero normal stress, while the friction angle φ′ reflects interparticle sliding and interlocking, contributing strength proportional to normal stress. Sands are largely frictional (c′ ≈ 0); clays can have significant cohesion.

For saturated clay under rapid (undrained) loading, a φ = 0 analysis with undrained shear strength c_u is used, and the unconfined compressive strength gives q_u = 2c_u directly. This short-term case often governs the stability of clay foundations and cuttings.

The triaxial test applies a confining pressure σ₃ and axial stress until failure, producing Mohr circles whose common tangent defines c and φ. Sensitivity, the ratio of undisturbed to remoulded strength, indicates how much a clay loses on disturbance — important for pile driving and excavation.

State assumptions explicitly before using any relation for shear strength of soil — steady state, uniform properties, linear elastic material, ideal gas, incompressible flow, etc., as applicable.

Wrong assumptions invalidate the entire solution even when the formula is correct. In Soil Mechanics viva and GATE descriptive questions, listing valid assumptions often earns separate marks.

1. Read the question and list given data with SI units (common in Soil Mechanics papers).
2. Draw a neat labelled diagram where applicable — examiners in Indian universities award diagram marks even when arithmetic slips.
3. Identify which relation from this topic applies to shear strength of soil.
4. Use equation 1: .
5. Use equation 2: .
6. Substitute values, compute, and verify units and sign (direction).
7. State conclusion in one line — e.g. safe/unsafe, stable/unstable, feasible/infeasible.

Shear Strength of Soil appears in foundation and earthwork design. In Indian civil curricula this topic is tested because it connects theory to engineering properties of soils.

GATE and semester exams often combine shear strength of soil with earlier units — revise prerequisites before attempting mixed problems.

Industry interview panels sometimes ask: "Where did you use shear strength of soil?" — answer with a lab, mini-project, or plant visit example if possible.

• Mixing total and effective stress parameters in one calculation.
• Forgetting to subtract pore pressure to get effective stress.
• Using drained parameters for a rapid (undrained) short-term loading of clay.
• Taking q_u = c_u instead of the correct q_u = 2c_u for unconfined compression.

Before attempting shear strength of soil problems, confirm you can:

1. Drained vs undrained tests match field drainage conditions
2.
3.

Revise the solved examples in Soil Mechanics & Foundations — BC Punmia and one previous-year GATE or university paper for this unit.