Question

With respect to the flow value, the total passive pressure for cohesive backfill is _______

(a) Pp=\(\frac{1}{2}\) Nφ γH^2+2cH √Nφ

(b) Pp=γH^2+2c √Nφ

(c) Pp=Nφ γH^2-2c √Nφ

(d) Pp=Nφ H^2-2c √Nφ

I got this question during a job interview.

Origin of the question is Passive Earth Pressure: Rankine’s Theory in section Failure Envelopes & Earth Pressure of Geotechnical Engineering II

Answer 1

Right option is (a) Pp=\(\frac{1}{2}\) Nφ γH^2+2cH √Nφ

Easiest explanation: The flow value is given by,

Nφ= tan^2 α=Kp,

since the the total passive pressure for cohesive backfill is given by,

Pp=\(\frac{1}{2}\) Kp γH^2+2cH tanα,

therefore on substituting the value of Nφ in the equation, we get,

Pp=\(\frac{1}{2}\) Nφ γH^2+2cH √Nφ.