The effective stress strength parameters of a soil are c = 10 kPa and φ = 30°. The shear strength on a plane within the saturated soil mass at a point where the total normal stress is 300 kPa and the pore water pressure is 150 kPa will be:
Try it first: pick an option, then read the explanation.
Correct answer: B. 96.6 kPa
Asked in SSC JE 01/03/2017 (Evening)
Detailed Explanation
Shear strength depends on effective stress, so subtract the pore water pressure first, then apply τ = c′ + σ′ tan φ′.
\[ \sigma' = 300 - 150 = 150\ \text{kPa} \]
\[ \tau = 10 + 150 \times \tan 30^\circ = 10 + 150 \times 0.577 = 10 + 86.6 = 96.6\ \text{kPa} \]
Why “96.6 kPa” Is Correct
Using effective stress gives 96.6 kPa, which matches option (b).
Why the Other Options Are Wrong
- A. 90.5 kPa: 90.5 kPa is too low; it does not match c + σ′ tan φ.
- C. 101.5 kPa: 101.5 kPa is too high for these data.
- D. 105.5 kPa: 105.5 kPa is too high; total stress would give an even larger 183 kPa.
Key Point
τ = c′ + (σ − u) tan φ′.
Key Concepts for Students
- tan 30° = 0.577.
- Half the total stress here is carried by water, which gives no shear resistance.
- Same method as Q279.
Practice more: this is question 37 in Shear Strength of Soils MCQs – Part 3. Try the whole set and check every answer instantly.