Effective Stress And Permeability – GATE CE Geotechnical Engineering Practice Questions & PYQs | BattleExam | BattleExam

Q3GATE 2023NAT

A vertical trench is excavated in a clayey soil deposit having a surcharge load of $30 \mathrm{kPa}$ . A fluid of unit weight $12 \mathrm{kN} / \mathrm{m}^{3}$ is poured in the trench to prevent collapse as the excavation proceeds. Assume that the fluid is not seeping through the soil deposit. If the undrained cohesion of the clay deposit is $20 \mathrm{kPa}$ and saturated unit weight is $18 \mathrm{kN} / \mathrm{m}^{3}$ , what is the maximum depth of unsupported excavation (in $\mathrm{m}$ , rounded off to two decimal places) ? ____

🚀 Solve in Practice Mode

📖 Explanation

We know, $\alpha=45+\frac{\mathrm{Q}}{2}$ here $\mathrm{Q}=0$ $\therefore$ Failure plane is at $45^{\circ}$ It is said that there is no seepage hence no flow of fluid. But considering the fluid is there in the pores. Also, considering given $\gamma_{\text {sat }}$ is the value for given fluid.

\begin{aligned} \therefore \quad \gamma_{\text {sub }} & =\gamma_{\text {sat }}-\gamma_{\text {fluid }} \\ & =18-12 \\ & =6 \mathrm{kN} / \mathrm{m}^{3} \end{aligned}

Now, equating the forces on the considered failure plane. As it is clay $\mathrm{Q}=0, \mathrm{~K}_{\mathrm{a}}=1$ . $\therefore \quad \frac{1}{2} \times x \times x \times 1 \times \gamma_{\text {sub }} \times \sin 45^{\circ}+30 \times x \sin 45^{\circ}$ $=C \times x \sqrt{2}$ $3 x=10$ $\therefore \quad x=3.33 \mathrm{~m}$ Solving with lateral earth pressure approach. $\mathrm{K}_{\mathrm{a}}=1$

\begin{aligned} & P=\sigma_{v} K_{a}-2 C \sqrt{K_{a}} \\ & P=\left(30+\gamma_{\text {sub }} z\right) \times 1-2 C \times \sqrt{1} \end{aligned}

When $\mathrm{P}=0$ , $30+6 z-2 \times 20=0$ $\therefore \quad 6 z=10$ $z=\frac{10}{6}$ $\therefore \quad$ Unsupported excavation $=2 \times \frac{10}{6}=3.33 \mathrm{~m}$

Explanation Figure 1

Explanation Figure 2

Explanation Figure 3