Question

In case of cohesive backfill, the passive pressure intensity is given by _______

(a) pp=γz tan^2 α-2c tan⁡α

(b) pp=γz tan^2 α+2c tan⁡α

(c) pp=-2c tan⁡α

(d) pp=γz tan^2 α/2c tan⁡α

I have been asked this question in my homework.

This key question is from Passive Earth Pressure: Rankine’s Theory topic in chapter Failure Envelopes & Earth Pressure of Geotechnical Engineering II

Answer 1

The correct option is (b) pp=γz tan^2 α+2c tan⁡α

Explanation: Since the principal stress relationship on a failure plane is given by,

σ1=2c tan⁡α+σ3 tan^2 α,

 σ1=pp and σ3=γz,

∴ pp=2c tan⁡α+γztan^2 α

∴ pp=γz tan^2 α+2c tan⁡α.