Active Earth Pressure Coefficient for Vertical Wall (Rankine)

The Active Earth Pressure Coefficient for a Vertical Wall  calculator computes the pressure (Rankine) coefficient for a vertical wall based on the angle of shearing resistance.

INSTRUCTIONS: Choose units and enter the following:

• (φ)  This is the angle of shear resistance

Active Earth Pressure Coefficient for a Vertical Wall (K_a):  The calculator returns the pressure.

The Math / Science

The Active Earth Pressure Coefficient for a Vertical Wall equation computes the active lateral earth pressure, the pressure that soil exerts in the horizontal direction on a wall, from the angle of shearing resistance, `phi`.  This equation assumes the wall is vertical. The coefficient of lateral earth pressure, K, is defined to be the ratio of the horizontal effective stress, `sigma'_h`, to the vertical effective stress, `sigma'_v`.

The formula for the active coefficient of horizontal soil pressure, `K_a`, is defined as:

           K_a = tan²(45-φ/2)

Shear resistance is an attribute applied to soil mechanics which results from the friction of interlocking particles that comprise the soil. There may also be bonding at the particle contacts that contributes to the overall shear resistance.

Shear strength is a term used often in soil mechanics to describe the amount of shear stress that a body or mass of soil can resist before it expands or contracts.  This shear resistance is due to interlocking of the soil particulate material and it resists expansion or contraction in volume due to shear strains. If soil expands its density will decrease along with it's shear strength. The soil state at which the shear stress and density remain constant while the shear strain increases is the "critical state" or " steady state".

Volume change behavior and inter-particle friction depend on multiple factors:

• the density of the soil particles
• the inter-granular contact forces
• the rate of shearing
• the direction of the shear stress
• and other factors

The average normal inter-granular contact force per unit area is called the effective stress.