Question
In a clayey soil having $100 \text{ kN/m}^2$ as unit cohesion and $15 \text{kN/m}^3$ as unit weight, an excavation is made with a vertical face. Taking Taylor's stability number as 0.3, what is the maximum depth of excavation so that the vertical face remains stable ?
This question was previously asked in
CUET PG 2026 Agri-Business Management Question Paper (25-Mar-2026) (Shift 2)
The correct answer is
$22.22 \text{ m}$
Calculating Maximum Stable Excavation Depth in Clayey Soil
Problem Analysis
The question asks for the maximum permissible depth of a vertical excavation in clayey soil. We are given:
- Unit cohesion ($c$): $100 \text{ kN/m}^2$
- Unit weight ($\gamma$): $15 \text{ kN/m}^3$
- Taylor's stability number ($S_n$): $0.3$
The goal is to find the maximum depth ($H$) for stability.
Stability Formula
For a vertical cut in clayey soil, the relationship between cohesion, unit weight, depth, and stability number is given by:
$c = S_n \times \gamma \times H$Calculation of Maximum Depth (H)
To find the maximum depth ($H$), we rearrange the formula:
$H = \frac{c}{S_n \times \gamma}$Now, substitute the given values:
$H = \frac{100 \text{ kN/m}^2}{0.3 \times 15 \text{ kN/m}^3}$ $H = \frac{100}{4.5} \text{ m}$ $H \approx 22.22 \text{ m}$Conclusion
The maximum depth of excavation for the vertical face to remain stable is approximately $22.22 \text{ m}$.
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