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A vertical cut is to be made in a soil mass having cohesion c, angle of internal friction φ, and unit weight γ. Considering Kₐ and Kₚ as the coefficients of active and passive earth pressures, respectively, the maximum depth of unsupported excavation is

1. 4c/(γ√Kₚ)
2. 2c√Kₚ/γ
3. 4c√Kₐ/γ
4. 4c/(γ√Kₐ)

Correct answer: 4c/(γ√Kₐ)

Solution

The correct option is derived from the relationship between soil cohesion, unit weight, and the coefficients of earth pressure. The formula 4c/(γ√Kₐ) reflects the maximum depth of unsupported excavation, taking into account the active earth pressure conditions that allow for greater stability in the excavation.

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