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GATE 2022 CE (CE2) – Question 41

Geotechnical Engineering · Effective stress principle and quicksand condition · 2 marks · Multiple choice

A saturated soil lies under water height h₁, with submerged unit weight γ′. A is its top, B is h₂ below A, C is h₃ below B. The valve is closed as shown. Find $\sigma_A^{\prime}+\sigma_B^{\prime}+\sigma_C^{\prime}$.

Saturated soil under standing water with points A,B,C, heights h1,h2,h3 and a closed valve. See the attached source image.
  1. $(2h_2+h_3)\gamma^{\prime}$
  2. $(h_1+h_2+h_3)\gamma^{\prime}$
  3. $(h_2+h_3)(\gamma_{sat}-\gamma_w)$
  4. $(h_1+h_2+h_3)\gamma_{sat}$

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Show answer and explanation

Correct answer: (A) $(2h_2+h_3)\gamma^{\prime}$

Explanation

The closed valve gives hydrostatic pore pressure, so water above the soil adds equally to total stress and pore pressure. Its contribution cancels from effective stress.

At A, B, C the effective stresses are 0, h₂γ′ and (h₂+h₃)γ′. Their sum is **(2h₂+h₃)γ′ (A)**.