Question

The Westergaard’s influence factor is given by _____________

(a) \(K_W=\frac{1}{π\left[1+2(\frac{r}{z})^2 \right]^\frac{3}{2}} \)

(b) \(K_W=\frac{Q}{z^2} \)

(c) \(K_W=\frac{1}{π\left[1+2(\frac{r}{z})^2 \right]^\frac{5}{2}} \frac{Q}{z^2} \)

(d) \(K_W=\frac{1}{π\left[1+2(\frac{r}{z})^2 \right]^3}\frac{Q}{z^2} \)

I got this question in exam.

Enquiry is from Stress Distribution in division Stress Distribution of Geotechnical Engineering I

Answer 1

Right option is (a) \(K_W=\frac{1}{π\left[1+2(\frac{r}{z})^2 \right]^\frac{3}{2}} \)

The best explanation: The Westergaard’s equation is given by,

\(σ_z=\frac{1}{\left[1+2(\frac{r}{z})^2 \right]^\frac{3}{2}} \frac{Q}{z^2}\)

∴ \(σ_z=K_W \frac{Q}{z^2}.\)

Where KW is the Westergaard’s influence factor given by,

\(K_W=\frac{1}{π\left[1+2(\frac{r}{z})^2\right]^\frac{3}{2}}. \)