Question

When the top tension portion of the wall in cohesive soil is neglected, the total lateral thrust is given by __________

(a) Pa=\(\frac{1}{2}\)Ka γH^2 cot^2 α-2c cot⁡α

(b) Pa=\(\frac{1}{2}\)Ka γH^2 cot^2 α-2c cot⁡α+\(\frac{2c^2}{γ}\)

(c) Pa=\(\frac{1}{2}\)Ka γH^2 cot^2 α-2c cot⁡α-\(\frac{2c^2}{γ}\)

(d) Pa=Ka H^2-2c cot⁡α

I have been asked this question in semester exam.

The above asked question is from Active Earth Pressure of Cohesive Soils in chapter Failure Envelopes & Earth Pressure of Geotechnical Engineering II

Answer 1

Right answer is (b) Pa=\(\frac{1}{2}\)Ka γH^2 cot^2 α-2c cot⁡α+\(\frac{2c^2}{γ}\)

The best I can explain: When the negative tensile portion is neglected, the total lateral thrust is given by,

\(P_a=\int_{z_0}^H p_a.dz = \int_{z_0}^H(γzcot^2 α-2c cot⁡α).dz\)

substituting for  \(z_0=\frac{2c tan⁡α}{γ},\)

∴ Pa=\(\frac{1}{2}\)Ka γH^2 cot^2 α-2c cot⁡α+\(\frac{2c^2}{γ}.\)