Question

For a rectangular masonry dam, the weight of dam, uplift pressure and horizontal force causing the sliding are 300 kN, 60 kN and 80 kN respectively. If the coefficient of friction between the dam base and soil is 0.5, then the factor of safety against sliding is

• A. 1.07
• B. 1.5
• C. 1.88
• D. 2.0

Hint:

The formula for FOS against sliding is a critical check in dam design.
FOS = $\frac{\mu (\Sigma V)}{\Sigma H}$.
Remember that uplift force reduces the net vertical force, which in turn reduces the frictional resistance.
Always use the net vertical force ($Weight - Uplift$) in the calculation.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
The question asks to calculate the factor of safety (FOS) against the sliding failure of a masonry dam, given all the relevant forces and the coefficient of friction.

Step 2: Key Formula or Approach:
The Factor of Safety against sliding is defined as the ratio of the total resisting forces to the total sliding (or driving) forces.
\[ \text{FOS}_{sliding} = \frac{\text{Resisting Forces}}{\text{Sliding Forces}} \] -

Sliding Force: This is the net horizontal force pushing the dam, given as 80 kN.
-

Resisting Force: This is the frictional force developed at the base of the dam. It is calculated as the coefficient of friction ($\mu$) multiplied by the net vertical force. The net vertical force is the weight of the dam minus the uplift force.
\[ \text{Resisting Force} = \mu \times (\text{Weight} - \text{Uplift Force}) \]

Step 3: Detailed Explanation:
We are given:
- Weight of the dam ($W$) = 300 kN
- Uplift force ($U$) = 60 kN
- Horizontal sliding force ($H$) = 80 kN
- Coefficient of friction ($\mu$) = 0.5
First, calculate the net vertical force:
\[ \Sigma V = W - U = 300 \text{ kN} - 60 \text{ kN} = 240 \text{ kN} \] Next, calculate the maximum resisting force (frictional force):
\[ F_{Resisting} = \mu \times \Sigma V = 0.5 \times 240 \text{ kN} = 120 \text{ kN} \] Now, calculate the Factor of Safety:
\[ \text{FOS}_{sliding} = \frac{F_{Resisting}}{F_{Sliding}} = \frac{120 \text{ kN}}{80 \text{ kN}} \] \[ \text{FOS}_{sliding} = \frac{12}{8} = \frac{3}{2} = 1.5 \]

Step 4: Final Answer:
The factor of safety against sliding is 1.5.