Question

The hydraulic gradient in terms of pore water pressure is given by _________

(a) \(i=\frac{γ_w \overline{u}∂h}{∂z} \)

(b) \(i=\frac{\overline{u}∂h}{γ_w ∂z} \)

(c) \(i=\frac{\overline{u}∂h}{∂z} \)

(d) \(i=\frac{1}{γ_w}\frac{∂\overline{u}}{∂z} \)

The question was posed to me by my school principal while I was bunking the class.

Asked question is from Stress Distribution topic in chapter Stress Distribution of Geotechnical Engineering I

Answer 1

The correct answer is (d) \(i=\frac{1}{γ_w}\frac{∂\overline{u}}{∂z} \)

Best explanation: The hydraulic gradient i is given by,

\(i=\frac{∂h}{∂z} \,where\, h=\frac{\overline{u}}{γ_w} \)

∴ from the two equations, we get,

\(i=\frac{1}{γ_w}\frac{∂\overline{u}}{∂z}.\)