A wall 6 m high has a smooth vertical back and retained sand as a backfill that is submerged. The sand has Y_sat = 20 kN/m³ and ϕ = 30º. The total active earth pressure is

Concept:

Active Earth Pressure:

• Lateral active earth pressure is developed when the wall is moved away from the soil.

From the above figure (3),

Active earth pressure at the bottom will be given by -

p_a = K_aγ_sub H + γ_w H           ...(1)

Also, Total active earth pressure is given by the area of the pressure distribution diagram (3) -

P_a = $\frac{1}{2}$ × H(K_aγ_sub H + γ_w H)   ....(2)

Where,

K_a - Coefficient of active earth pressure = $\frac{1-sin?}{1+sin?}$       ...(3)

? - Angle of internal friction

γ_s - Submerged unit weight of soil (kN/m³)

γ_w - Unit weight of water (kN/m³)

H - Height of wall (m)

p_a - Active earth pressure at the bottom (kN/m²)

P_a - Total active earth pressure (kN/m)

Calculation:

Given,

H = 6 m

γ_sat = 20 kN/m³

γ_w = 9.81 kN/m³

γ_sub = 20 - 9.81 = 10.19 kN/m³

? = 30º

∴ From (3)

K_a= $\frac{1-sin{30}^{?}}{1+sin{30}^{?}}=\frac{1}{3}$

∴ From (1)

p_a = K_aγ_sub H + γ_w H

⇒ p_a = $\frac{1}{3}$ × 10.19 × 6 + 9.81 × 6 = 79.24 kN/m² (Active lateral earth pressure at bottom)

∴ from (2)

P_a = $\frac{1}{2}$ × 79.24 × 6 = 237.72 kN/m   (Total active earth pressure)