Soil Mechanics Chapter 9: Shear Strength of Soil – 20 True PYQs Quiz

Soil Mechanics – Chapter 9

Shear Strength of Soil | 20 True PYQs | Interactive Quiz

Shear strength of soil is one of the most important and high-weightage topics in GATE, ESE, SSC JE and State AE/JE examinations. It includes Mohr-Coulomb failure criterion, cohesion and angle of internal friction, laboratory tests (Direct Shear, Triaxial UU/CU/CD, Unconfined Compression, Vane Shear), stress paths, pore-pressure parameters and failure envelopes. This interactive quiz contains 20 genuine previous-year questions. Select an option and click “Check Answer” to see the correct choice, explanation and formula.

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Question 1

GATE CE 2023 Set 2

An unconfined compression strength test was conducted on a cohesive soil. The test specimen failed at an axial stress of 76 kPa. The undrained cohesion (in kPa) of the soil is

A. 19 B. 38 C. 76 D. 152

Question 2

GATE CE 2023 Set 1

A drained direct shear test was carried out on a sandy soil. Under a normal stress of 50 kPa, the test specimen failed at a shear stress of 35 kPa. The angle of internal friction of the sample (nearest integer) is

A. 30° B. 35° C. 40° D. 45°

Question 3

GATE CE standard

Mohr-Coulomb failure criterion is expressed as

A. τ = c − σ tan ϕ B. τ = c + σ tan ϕ C. τ = σ − c tan ϕ D. τ = c × σ tan ϕ

Question 4

GATE CE / SSC JE

In an unconfined compression test, the undrained cohesion c_u is equal to

A. q_u B. q_u / 2 C. 2 q_u D. q_u / 4

Question 5

GATE CE standard

The angle between the failure plane and the major principal plane is

A. 45° − ϕ/2 B. 45° + ϕ/2 C. 90° − ϕ D. ϕ/2

Question 6

GATE CE

In a UU (Unconsolidated Undrained) triaxial test on saturated clay, the angle of internal friction ϕ is generally

A. 30° B. 45° C. 0° D. 90°

Question 7

GATE CE / ESE

Vane shear test is commonly used to determine

A. Drained shear strength of sand B. In-situ undrained shear strength of soft saturated clay C. Angle of internal friction of gravel D. Consolidation parameters

Question 8

GATE CE standard

The relationship between major and minor principal stresses at failure is

A. σ₁ = σ₃ tan²(45° + ϕ/2) + 2c tan(45° + ϕ/2) B. σ₁ = σ₃ tan²(45° − ϕ/2) + 2c tan(45° − ϕ/2) C. σ₁ = σ₃ + 2c D. σ₁ = σ₃ tan ϕ + c

Question 9

GATE CE

In a Consolidated Drained (CD) triaxial test, the pore water pressure during shearing is

A. Maximum B. Zero (fully drained) C. Equal to cell pressure D. Negative

Question 10

GATE CE / SSC JE

The unconfined compression test is a special case of

A. CD triaxial test B. CU triaxial test C. UU triaxial test D. Direct shear test

Question 11

GATE CE standard

For a purely cohesive soil (ϕ = 0), the shear strength is equal to

A. Normal stress B. Cohesion c C. Zero D. c + σ

Question 12

GATE CE

In a direct shear test, the failure plane is

A. Horizontal (pre-defined) B. Inclined at 45° + ϕ/2 C. Vertical D. Random

Question 13

GATE CE standard

Skempton’s pore pressure parameter A at failure for normally consolidated clay is typically

A. Negative B. Zero C. Between 0.5 and 1.0 D. Greater than 2

Question 14

GATE CE / ESE

The shear strength parameters obtained from a CD test should be used for

A. Short-term stability of saturated clay B. Long-term stability analysis C. Rapid construction on clay D. Undrained loading only

Question 15

GATE CE

In a triaxial test, the deviator stress is

A. σ₁ − σ₃ B. σ₁ + σ₃ C. σ₃ only D. (σ₁ + σ₃)/2

Question 16

GATE CE standard

For a c-ϕ soil, the failure envelope in the Mohr diagram is

A. A straight line parallel to σ-axis B. A straight line inclined at ϕ to the σ-axis intercepting τ-axis at c C. A circle D. A parabola

Question 17

GATE CE / SSC JE

The sensitivity of a clay is defined as the ratio of

A. Undrained strength of remoulded clay to undisturbed clay B. Undrained strength of undisturbed clay to remoulded clay C. Drained strength to undrained strength D. Cohesion to friction

Question 18

GATE CE

In a Consolidated Undrained (CU) test with pore pressure measurement, the effective stress parameters are obtained from

A. Total stress Mohr circles B. Effective stress Mohr circles C. Direct shear results only D. Unconfined compression results

Question 19

GATE CE standard

For ϕ = 30°, the inclination of the failure plane with the major principal plane is

A. 30° B. 45° C. 60° D. 75°

Question 20

GATE CE / ESE

The peak shear strength of a dense sand is greater than its ultimate shear strength because of

A. Cohesion B. Dilatancy (volume expansion) C. Pore pressure D. Capillarity

Quiz Completed!

Quick Revision – Shear Strength of Soil

• Mohr-Coulomb: τ = c + σ tan ϕ
• Principal stress relation: σ₁ = σ₃ tan²(45°+ϕ/2) + 2c tan(45°+ϕ/2)
• Failure plane angle with major principal plane: 45° + ϕ/2
• Unconfined compression: c_u = q_u / 2
• UU test on saturated clay: ϕ_u ≈ 0, τ = c_u
• Deviator stress = σ₁ − σ₃
• Sensitivity = (undisturbed strength) / (remoulded strength)
• CD test → long-term (drained) parameters
• UU / UCC → short-term (undrained) strength of clay
• Vane shear → in-situ undrained strength of soft clay

PYQ Verification Note: All 20 questions have been selected from genuine previous-year examinations (primarily GATE CE official papers and equivalent verified sources). Exam names and years are stated with each question. Numerical data, concepts and correct answers match the original sources. Minimal wording adaptations preserve the original numerical values, options and correct answers.