Question

The depth at which the tension is zero for cohesive soils with retaining wall in terms Ka is _____

(a) \(z_0=\frac{2cK_a}{γ} \)

(b) \(z_0=\frac{2c}{γ} \frac{1}{√K_a } \)

(c) \(z_0=\frac{2cK_a}{γ} \)

(d) \(z_0=\frac{2c}{γ}(\frac{1}{K_a}) \)

The question was asked in class test.

This intriguing question originated from Active Earth Pressure of Cohesive Soils in division Failure Envelopes & Earth Pressure of Geotechnical Engineering II

Answer 1

Right answer is (b) \(z_0=\frac{2c}{γ} \frac{1}{√K_a } \)

The explanation: The tension at the top level of retaining wall reduces to zero at a depth,

\(z_0=\frac{2c tan⁡α}{γ}, \)

Since, \(K_a=\frac{1}{tan^2 (45°+\frac{φ}{2})}, \)

∴ \(z_0=\frac{2c}{γ} \frac{1}{√K_a}. \)