Net Safe Bearing Capacity from Ultimate Bearing Capacity A shallow foundation bears on soil with ultimate bearing capacity qu = 300 kN/m^2. Depth of foundation Df = 1 m, unit weight of soil γ = 20 kN/m^3. Using a factor of safety FS = 2.5, compute the net safe bearing capacity.
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A100 kN/m^2
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B112 kN/m^2
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C800 kN/m^2
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D100.5 kN/m^2
Answer
Correct Answer: 112 kN/m^2
Explanation
Introduction / Context:Bearing capacity terms distinguish between gross and net values. Design often uses net safe bearing capacity (qns), which subtracts the overburden at foundation level and divides by a factor of safety to guard against shear failure.
Given Data / Assumptions:
- Ultimate bearing capacity (gross): qu = 300 kN/m^2.
- Depth Df = 1 m; unit weight γ = 20 kN/m^3.
- Factor of safety FS = 2.5.
Concept / Approach:
Net ultimate bearing capacity: qnu = qu − γ * Df. Net safe bearing capacity: qns = qnu / FS. This removes the contribution of overburden pressure and applies safety margin to the shear failure criterion.
Step-by-Step Solution:
Compute overburden at foundation level: γ * Df = 20 * 1 = 20 kN/m^2.Net ultimate: qnu = 300 − 20 = 280 kN/m^2.Net safe: qns = 280 / 2.5 = 112 kN/m^2.Verification / Alternative check:
Cross-check units and arithmetic; results are consistent with typical values for medium soil strengths.
Why Other Options Are Wrong:
- 100 and 100.5 kN/m^2: Do not match the net–ultimate then divide by FS sequence.
- 800 kN/m^2: Exceeds ultimate capacity; impossible.
Common Pitfalls:
Dividing gross ultimate by FS without subtracting overburden; confusing net safe with gross safe capacity.
Final Answer:
112 kN/m^2