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Earth pressure coefficients and types

Short answer

Earth pressure coefficient K = σ′h/σ′v. At-rest K0 ≈ 1−sinφ (no movement). Active Ka = tan²(45°−φ/2) (wall moves away). Passive Kp = tan²(45°+φ/2) (wall moves into soil). Ka < K0 < Kp; for smooth vertical wall KaKp = 1. For φ=30°: Ka=0.33, K0=0.5, Kp=3.

Explain earth pressure coefficient and its types (relative wall movements and lateral earth pressure coefficients).

The earth pressure coefficient KK is the ratio of the horizontal effective stress to the vertical effective stress at a point in the soil:

K=σh′σv′K = \frac{\sigma_h'}{\sigma_v'}

Its value depends on the soil strength and on how much the wall moves.

TypeWall movementValue
At rest K0K_0No movement (rigid, fixed wall)K0≈1−sin⁡ϕ′K_0 \approx 1-\sin\phi' (normally consolidated); larger if over-consolidated
Active KaK_aWall moves away from soil (about 0.001-0.005 H)Ka=tan⁡2(45∘−ϕ/2)=1−sin⁡ϕ1+sin⁡ϕK_a = \tan^2(45^\circ-\phi/2) = \dfrac{1-\sin\phi}{1+\sin\phi}
Passive KpK_pWall moves toward soil (about 0.01-0.05 H)Kp=tan⁡2(45∘+ϕ/2)=1+sin⁡ϕ1−sin⁡ϕK_p = \tan^2(45^\circ+\phi/2) = \dfrac{1+\sin\phi}{1-\sin\phi}

Relation: Ka<K0<KpK_a < K_0 < K_p and KaKp=1K_a K_p = 1 (for horizontal backfill and smooth vertical wall). For example, for ϕ=30∘\phi = 30^\circ: Ka=0.333K_a = 0.333, K0=0.5K_0 = 0.5, Kp=3K_p = 3.

✓ Answer checked by Claude Sonnet 5.5

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