Answer:
To calculate the factor of safety against sliding, we need to consider the forces acting on the structure due to the soil and water. Given that the structure's height is the same on both sides, and assuming that the soil properties are consistent along the height of the structure, we can analyze the equilibrium of forces.
The forces acting on the structure due to the soil are the weight of the soil and the passive resistance. The passive resistance is the horizontal force developed at the soil-structure interface that resists sliding.
Given:
Unit weight of soil (γ) = 139 pcf
Soil friction angle (φ) = 30 degrees
Height of the structure (h) = same on both sides
Water table = Ground surface on the left, 9 ft above soil on the right
1. Calculate the weight of the soil on both sides:
Weight of soil on the left (W_left) = γ * h * 30 ft
Weight of soil on the right (W_right) = γ * (h + 9 ft) * 9 ft
2. Calculate the passive resistance on both sides using Rankine's Earth Pressure Theory:
Passive resistance on the left (R_left) = 0 (since the water table is at the surface)
Passive resistance on the right (R_right) = 2 * c * A
Where:
c = Cohesion of the soil
A = Area of the soil-structure interface
3. Calculate the net horizontal force on both sides:
Net horizontal force on the left (F_left) = W_left - R_left
Net horizontal force on the right (F_right) = W_right - R_right
4. Calculate the factor of safety (FS) against sliding:
FS = F_left / F_right
Remember that this calculation considers full passive resistance assuming no sliding along the bottom of the structure. If you have specific values for cohesion (c) and the dimensions of the structure's base, you can substitute those values into the calculations to obtain the factor of safety against sliding.