Q1: If W is weight of a retaining wall and P is the horizontal earth pressure, the factor of safety against sliding, is

ANS:C - 1.5

The factor of safety against sliding for a retaining wall can be calculated by comparing the resisting force (due to friction or other means) to the driving force (horizontal earth pressure). The factor of safety is defined as the ratio of the resisting force to the driving force. Let's denote:

• W as the weight of the retaining wall.
• P as the horizontal earth pressure.

Then, the factor of safety (FS) against sliding is given by: FS=Driving ForceResisting Force​ FS=W/P​ The higher the factor of safety, the more stable the retaining wall is against sliding. Now, looking at the options provided:

1. FS=W/P​ = 1.0: This implies that the resisting force is equal to the driving force, which means there is no safety margin against sliding. This option does not provide any safety against sliding.
2. FS=W/P​ = 1.25: This option indicates that the resisting force is 1.25 times greater than the driving force. It suggests a moderate safety margin against sliding.
3. FS=W/P​ = 1.5: This option implies that the resisting force is 1.5 times greater than the driving force. It indicates a reasonable safety margin against sliding.
4. FS=W/P​ = 2.0: This option indicates that the resisting force is 2 times greater than the driving force. It suggests a high safety margin against sliding.
5. FS=W/P​ = 2.5: This option indicates that the resisting force is 2.5 times greater than the driving force. It suggests a very high safety margin against sliding.

Therefore, the most appropriate option for a reasonable safety margin against sliding is: 1.5.