A 6 m tall cantilever wall retains a soil that has the following properties: c' = 0, Φ' = 30°, and γ= 19.2 kN/m^3. The ground surface behind the wall is inclined at a slope of 3 horizontal to 1 vertical, and the wall has moved sufficiently to develop the active condition. Determine the normal and

Question

A 6 m tall cantilever wall retains a soil that has the following properties: [latex]c^{\prime } = 0[/latex], [latex]Φ^{\prime } = 30°[/latex], and [latex]γ= 19.2 kN/m^{3}[/latex]. The ground surface behind the wall is inclined at a slope of 3 horizontal to 1 vertical, and the wall has moved sufficiently to develop the active condition. Determine the normal and shear forces acting on the back of this wall using Rankine's theory.

Accepted Answer

[latex]\beta = an ^{-1} \left(1/3 ight) =18°[/latex]

[latex]K_{a}=\frac{\cos \beta - \sqrt{\cos ^{2}\beta - \cos ^{2}\Phi } }{\cos \beta + \sqrt{\cos ^{2}\beta - \cos ^{2}\Phi } } =\frac{\cos 18° - \sqrt{\cos ^{2}18° - \cos ^{2}30°} }{\cos 18° + \sqrt{\cos ^{2}18° - \cos ^{2}30°}} =0.415[/latex]

[latex]P_{a}/b=\frac{\gamma H^{2}K_{a}\cos \beta }{2} =\frac{\left(19.2 kN/m^{2} ight) \left(6 m^{2} ight) \left(0.415 ight) \cos 18°}{2} =[/latex] 136 kN/m

[latex]V_{a}/b=\frac{\gamma H^{2}K_{a}\sin \beta }{2} =\frac{\left(19.2 kN/m^{2} ight) \left(6 m^{2} ight) \left(0.415 ight) \sin 18°}{2} =[/latex] 44 kN/m

These results are shown in Figure 16.12.

Question 16.2: A 6 m tall cantilever wall retains a soil that has the follo...

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