Question

A vertical cut is to be made in saturated clay with \( C = 15 \) kN/m\(^2\), \( \varphi = 0 \), and \( \gamma = 20 \) kN/m\(^3\). What is the theoretical depth to which the clay can be excavated without side collapse?

• A. 6 m
• B. 2 m
• C. 2.5 m
• D. 3 m

Hint:

- The critical height (\( H_c \)) determines the maximum depth that can be excavated without requiring side support. - If excavation exceeds \( H_c \), the clay may collapse due to shear failure.

Answer 1

The Correct Option is D

Step 1: Use the equation for the critical depth (\( H_c \)) in saturated clay: \[ H_c = \frac{4C}{\gamma} \] where, \( C = 15 \) kN/m\(^2\) (cohesion of clay), \( \gamma = 20 \) kN/m\(^3\) (unit weight of clay). Step 2: Compute the critical depth: \[ H_c = \frac{4 \times 15}{20} \] Step 3: Calculation: \[ H_c = \frac{60}{20} = 3 { m} \] Thus, the correct answer is (D) 3 m.