Stability of masonry dam (sliding check): The force of friction at the base should be at least what multiple of the total horizontal water pressure per metre length to avoid sliding?

Introduction / Context:
For gravity and masonry dams, sliding stability is ensured by providing adequate frictional resistance at the dam–foundation interface against the horizontal water thrust. Design is often done with a prescribed factor of safety against sliding to account for uncertainties in loads, material properties, and uplift forces.

Given Data / Assumptions:

• Total horizontal water pressure per metre length is P_w.
• Resultant resisting friction is μ * W, where W is effective vertical force (including self-weight and considering uplift, if any).
• A standard factor of safety against sliding is adopted in preliminary design.

Concept / Approach:
The no-sliding condition requires μ * W ≥ P_w. For design safety, codes and classic practice adopt a factor of safety F_s, so μ * W ≥ F_s * P_w. A commonly used minimum F_s is about 1.5 for normal loading conditions, implying frictional resistance at least 1.5 times the driving water thrust.

Step-by-Step Solution:

Verification / Alternative check:
Some practices may adopt larger factors for unusual loads (e.g., earthquake, flood). For the baseline question with typical options, 1.5 is the accepted minimum.

Why Other Options Are Wrong:

• Equal to P_w gives F_s = 1.0 (no safety margin).
• Double or 2.5 times are conservative beyond the common minimum; not typically specified as the minimum.
• 0.5 times is unsafe (F_s < 1).

Common Pitfalls:
Ignoring uplift or sediment pressure; confusing overturning checks with sliding; using peak instead of long-term friction coefficients without safety factors.

Final Answer:
1.5 times the total water pressure