Question

The maximum value of σz on vertical line is ____________

(a) \((σ_z)_{max}=\frac{0.0888Q}{r^2} \)

(b) \((σ_z)_{max}=\frac{0.0844Q}{z^4} \)

(c) \((σ_z)_{max}=\frac{0.2733Q}{z^3} \)

(d) \((σ_z)_{max}=\frac{0.4775Q}{z^3} \)

The question was posed to me at a job interview.

My query is from Stress Distribution topic in division Stress Distribution of Geotechnical Engineering I

Answer 1

Correct answer is (a) \((σ_z)_{max}=\frac{0.0888Q}{r^2} \)

The explanation is: The maximum value of σz on vertical line is obtained at the point of intersection of vertical plane with radial line at the angle of39°15’. The corresponding value of \(\frac{r}{z}\) is 0.817.

∴ \(z=\frac{r}{0.817}=1.225r \)

KB=0.1332

\(σ_z=K_B  \frac{Q}{z^2} \)

\(σ_z=0.1332 \frac{Q}{1.225r^2} \)

∴ \((σ_z)_{max}=\frac{0.0888Q}{r^2} \)