Question

The cohesion (\( c \)), angle of internal friction (\( \phi \)) and unit weight (\( \gamma \)) of a soil are 15 kPa, 20°, and 17.5 kN/m\(^3\), respectively. The maximum depth of unsupported excavation in the soil (in m, rounded off to two decimal places) is \(\underline{\hspace{2cm}}\).

Hint:

The maximum depth of unsupported excavation is given by \( H_{\text{max}} = \frac{2c}{\gamma \sin(\phi)} \), where \( c \) is the cohesion, \( \gamma \) is the unit weight, and \( \phi \) is the angle of internal friction.

Answer 1

Correct Answer: 4.8

The maximum depth of unsupported excavation can be found using Terzaghi's formula: \[ H_{\text{max}} = \frac{2c}{\gamma \sin(\phi)}. \] Substituting the given values: \[ H_{\text{max}} = \frac{2 \times 15}{17.5 \times \sin(20^\circ)} \approx 4.8 \, \text{m}. \] Thus, the maximum depth of unsupported excavation is \( \boxed{4.80} \, \text{m} \).