Question

A vertical trench is excavated in a clayey soil deposit having a surcharge load of 30 kPa. A fluid of unit weight 12 kN/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 kPa and saturated unit weight is 18 kN/m$^3$, what is the maximum depth of unsupported excavation (in meters, rounded off to two decimal places)?

Hint:

In problems involving trench stability, always consider the effects of surcharge and fluid pressure along with the cohesive strength of the soil.

Answer 1

Correct Answer: 3.3

For vertical excavation in clayey soil with a surcharge load, we can use the following formula to estimate the maximum depth of unsupported excavation: \[ \text{Maximum depth of excavation} = \frac{C_u - \gamma_f h}{\gamma_s} \] Where: - \( C_u \) = Undrained cohesion of the clay deposit = 20 kPa - \( \gamma_f \) = Unit weight of the fluid = 12 kN/m³ - \( \gamma_s \) = Saturated unit weight of the soil = 18 kN/m³ - \( h \) = Depth of the unsupported excavation In equilibrium, the surcharge load \( S \) (30 kPa) and the fluid weight must balance the soil's resistance to collapse. So, applying the equilibrium condition for the maximum depth: \[ C_u + S = \gamma_s h + \gamma_f h \] \[ 20 + 30 = (18 + 12)h \] \[ 50 = 30h \] \[ h = \frac{50}{30} = 3.33 \, \text{m} \] \boxed{3.33\, \text{m}}