Question

For a cohesive backfill with surcharge q, when at depth z0, pa=0, then the depth z0 is ___________

(a) \(z_0=\frac{q-2c cot⁡α}{γ} \)

(b) \(z_0=\frac{2c tan⁡α}{γ}-\frac{q}{γ} \)

(c) \(z_0=\frac{2 cot⁡α}{γ}+\frac{q}{γ} \)

(d) \(z_0=\frac{cot⁡α}{γ}-\frac{q}{γ} \)

I have been asked this question by my school teacher while I was bunking the class.

My question comes from Active Earth Pressure of Cohesive Soils topic in chapter Failure Envelopes & Earth Pressure of Geotechnical Engineering II

Answer 1

Right option is (b) \(z_0=\frac{2c tan⁡α}{γ}-\frac{q}{γ} \)

Best explanation: Since the lateral pressure for cohesive backfill with surcharge q is given by,

pa=γzcot^2 α-2c cot⁡α+qcot^2 α,

when pa=0,

∴ \(z=z_0=\frac{2c tan⁡α}{γ}-\frac{q}{γ}. \)