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Earth pressure on walls

The soil behind a retaining wall pushes on the wall. If the wall yields slightly, we get active earth pressure, the smallest. If the wall is pushed into the soil, we get passive earth pressure, which is much larger. The pressure increases linearly with depth.

K_a = \frac{1 - \sin\varphi}{1 + \sin\varphi}

active earth pressure coefficient

K_p = \frac{1}{K_a}

passive coefficient

P_a = \tfrac12 K_a\,\gamma\,H^2

active force per metre of wall

Symbols

$\varphi$	friction angle	°
$\gamma$	unit weight	kN/m³
$H$	wall height	m
$P_a$	active force	kN/m

Example

$\varphi = 30^\circ$ , $\gamma = 18$ kN/m³ and $H = 4$ m:

$K_a = 1/3$ and $P_a = 0.5\cdot\tfrac13\cdot 18\cdot 16 = 48$ kN/m.

Double the wall height gives four times the force, because H is squared.

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Part of Geotechnical Engineering: Earth pressure, bearing capacity and stability.