Coefficient of Earth Pressure at Rest

The coefficient of earth pressure at rest is defined as the ratio of the horizontal force acting on the soil to the vertical force acting on the soil when the soil is not under any deformation.

Formula

The formula for the coefficient of earth pressure at rest is given by:

μ = σ_h / σ_v

where μ is the coefficient of earth pressure at rest, σ_h is the horizontal stress acting on the soil, and σ_v is the vertical stress acting on the soil.

Calculation

The coefficient of earth pressure at rest can be calculated by determining the ratio of the horizontal stress acting on the soil to the vertical stress acting on the soil. The horizontal stress is determined by multiplying the vertical stress by the coefficient of earth pressure at rest.

μ = σ_h / σ_v

μ = (μ σ_v) / σ_v

μ = μ

Therefore, the coefficient of earth pressure at rest is equal to the coefficient of earth pressure at rest.

Answer

The correct answer to the question is option B, which is μ / (1 - μ). This formula is derived from the formula for the coefficient of earth pressure at rest, which is μ = σ_h / σ_v. By rearranging the formula and substituting the value of σ_h, we get:

μ = (K_a - 1) / (K_a + 1)

where K_a is the coefficient of lateral earth pressure.

Substituting the value of K_a = 1 + sin φ in the above equation, we get:

μ = sin φ / (1 + sin φ)

Simplifying the equation, we get:

μ / (1 - μ) = sin φ

Therefore, the correct answer is option B, which is μ / (1 - μ).