A retaining wall of height 10 m with clay backfill is shown in the figure (not to scale). Weight of the retaining wall is 5000 kN per m acting at 3.3 m from the toe of the retaining wall. The interface friction angle between base of the retaining wall and the base soil is 20°. The depth of clay in front of the retaining wall is 2.0 m. The properties of the clay backfill and the clay placed in front of the retaining wall are the same. Assume that the tension crack is filled with water. Use Rankine's earth pressure theory. Take unit weight of water, γw = 9.81 kN/m3.

The factor of safety (round off to two decimal places) against sliding failure of the retaining wall after ignoring the passive earth pressure will be _______.

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GATE CE 2021 Official Paper: Shift 1

CT 1: Ratio and Proportion

2536

10 Questions
16 Marks
30 Mins

__Concept:__

Active earth pressure is given as:

Where, \({K_a} = \frac{{1 - \sin ϕ }}{{1 + \sin ϕ }}\)

Let Z_{c} = Depth of tension crack

∴ Depth of tension crack

At Z = Z_{c}, p_{a} = 0

For ϕ_{u} = 0, k_{a} = 1

∴ Depth of tension crack

__Calculation:__

Given;

ϕ = 0

c = 30 KN/m^{2}

γ = 17.2 KN/m^{3}

γ_{w} = 9.81 KN/m^{3}

W = 5000 KN

δ = 20°

H = 10 m

Total active thrust due to grain and water pressure;

= 424. 347 kN/m

Frictional resistance = **N tanδ = **W tanδ

= 5000 tan20°

= 1819.851 kN

= **4.29**