The GATE Grind

GATE 2023 CE (CE1) – Question 57

Geotechnical Engineering · Earth pressure theories: Rankine and Coulomb, sheet piles · 2 marks · Numerical answer

A smooth vertical retaining wall supporting layered soils is shown in figure. According to Rankine's earth pressure theory, the lateral active earth pressure acting at the base of the wall is _____ kPa (round off to one decimal place).

a smooth wall with a surcharge $q = 20$ kPa. Layer 1 is 3 m thick (bulk unit weight 18 kN/m³, $\phi = 32°$, $c = 0$). Layer 2 is 4 m thick (19 kN/m³, $\phi = 25°$, $c = 20$ kPa).

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: 35.22 to 35.58

Explanation

The vertical stress at the base is $20 + 18 \times 3 + 19 \times 4 = 150$ kPa. The active coefficient of layer 2 is $K_a = \tan^2\left(45° - \frac{25°}{2}\right) = 0.4059$. The active pressure at the base, with the cohesion of layer 2, is $\sigma_a = K_a\sigma_v - 2c\sqrt{K_a} = 0.4059 \times 150 - 2 \times 20 \times 0.6371 = 60.9 - 25.5 = 35.4$ kPa. (The layer above only affects the vertical stress, which already includes it.)