A 12 ft tall cantilever retaining wall supported on a 2 ft deep continuous footing will retain a sandy soil with c' = 0, Φ' = 35°, and γ = 124 lb/ft^3. The ground surface above the wall will be level (β = 0) and there will be no surcharge loads. Compute the active pressure and express it as the

Question

A 12 ft tall cantilever retaining wall supported on a 2 ft deep continuous footing will retain a sandy soil with [latex]c^{\prime } = 0[/latex], [latex]Φ^{\prime } = 35°[/latex], and [latex]γ = 124 lb/ft^{3}[/latex]. The ground surface above the wall will be level (β = 0) and there will be no surcharge loads. Compute the active pressure and express it as the equivalent fluid density, then compute the total force imposed by the backfill soils onto the wall and the back of the footing.

Accepted Answer

[latex]K_{a}= an ^{2}\left(45° - \Phi /2 ight) = an ^{2}\left(45° - 35°/2 ight) =0.271[/latex]

[latex]G_{h}=\gamma K_{a}=\left(124 lb/ft^{3} ight) \left(0.271 ight) =34 lb/ft^{3}[/latex]

Therefore, the retaining wall should be designed to retain a fluid that has a unit weight of [latex]34 lb/ft^{3}[/latex]. The active earth pressure acts on both the wall and its footing, so H = 14 ft.

[latex]P_{a}/b=\frac{G_{h}H^{2}}{2} =\frac{\left(34 lb/ft^{3} ight) \left(14 ft ight) ^{2}}{2} =3332 lb/ft[/latex]

Question 16.5: A 12 ft tall cantilever retaining wall supported on a 2 ft d...

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