A vertical retaining wall of 5 {m} height has to support soil having unit weight of 18 {kN} {/} {m}^{3}, effective cohesion of 12 {kN}{/} {m}^{3}, and effective friction angle of 30^{\circ} . As per Rankine's carth pressure theory and assuming that a tension crack has occurred, the lateral active thrust on the wall per meter length (in {kN} \/ {m}, round off to two decimal places), is

GATE Civil Engineering (CE) 2020 Shift 1 Solved Paper

Question : 46 of 65

Marks: +1, -0

A vertical retaining wall of

5 {m}

height has to support soil having unit weight of

18 {kN} {/} {m}^{3}

, effective cohesion of

12 {kN}{/} {m}^{3}

, and effective friction angle of

30^{∘} .

As per Rankine's carth pressure theory and assuming that a tension crack has occurred, the lateral active thrust on the wall per meter length (in

{kN} \/ {m}

, round off to two decimal places), is

Solution:

{ka}=\;{1-\sin 30}/{1+\sin 30}=\;{1-.5}/{1+.5}=\;{.5}/{1.5}=1 / 3

Depth of tension crack

\;{2 c}/{γ √{ {ka}}}=\;{2 × 12}/{18 √{1 {/} 3}}=2.309

σ_{ {H}}= {ka} σ_{ {v}}-2 c √{ {ka}}

σ_{ {H}}=\;{1}/{3} × 18 × {z}-2 × 12 × √{1 {/} 3}

σ_{H}=6 z-13.856

σ_{H} A T

TOP

(z=0)=-13.856

σ_{ {H}}

AT BOTTOM

( {z}=5)=16.144

Net thurst

=[\;{0+16.144}/{2}] × 2.69 × 1

=21.72 {kw} {/} {m}

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