Annex C

(informative)

# Sample procedures to determine limit values of earth pressures on vertical walls

## C.1 Limit values of earth pressure

(1) The limit values of earth pressure on a vertical wall, caused by weight density γ, uniform vertical surface load (*q*) and ground cohesion (*c*) should be calculated as follows:

- active limit state:

τ_{a}(*z*) = σ_{a} · tan δ + *a* (positive for downward movement of ground)

- passive limit state:

τ_{p}(*z*) = σ_{p} · tan δ + *a* (positive for upward movement of ground)

where:

*a* is the adhesion (between ground and wall)

*c* is the ground cohesion

*K*_{a} the coefficient of horizontal active earth pressure

*K*_{p} the coefficient of horizontal passive earth pressure

*q* the vertical surface load

*z* the distance down the face of the wall

β the slope angle of the ground behind the wall (upward positive)

δ the angle of shearing resistance between ground and wall

γ weight density of retained ground

σ_{a}(*z*) the stress normal to the wall at depth *z* (active limit state)

σ_{p}(*z*) the stress normal to the wall at depth *z* (passive limit state)

τ_{a}(*z*) the stress tangential to the wall at depth *z* (active limit state)

τ_{p}(*z*) the stress tangential to the wall at depth *z* (passive limit state)

(2) Equations (C.1) and (C.2) may be applied, either in terms of total or effective stress, as appropriate.

(3) Values of the earth pressure coefficients may be taken from figures C.1.1 to C.1.4 for *K*_{a} and C.2.1 to C.2.4 for *K*_{p}. They are approximately on the safe side.

(4) Alternatively, the numerical procedure described in C.2 may be used.

(5) In layered soils, the coefficients *K* should normally be determined by the shear strength parameters at depth *z* only, independent of the values at other depths.

(6) Intermediate values of active earth pressure between the rest state and the limit state may be obtained by linear interpolation.

(7) Intermediate values of passive earth pressure between the rest state and the limit state may be obtained by parabolic interpolation as shown in figure C.3.

*K*

_{a}of active earth pressure with horizontal retaining surface (β = 0)

*K*

_{a}of active earth pressure with inclined retaining surface (δ/φ’ = 0 and δ = 0)

*K*

_{a}of active earth pressure with inclined retaining surface (δ/φ’ = 0,66)

*K*

_{a}of active earth pressure with inclined retaining surface (δ/φ’ = 1)

*K*

_{p}of passive earth pressure: with horizontal retaining surface (β = 0)

*K*

_{p}of passive earth pressure: with inclined retaining surface (δ/φ’ = 0 and δ = 0)

*K*

_{p}of passive earth pressure: with inclined retaining surface (δ/φ’ = 0,66)

*K*

_{p}of passive earth pressure: with inclined retaining surface (δ/φ’ = 1)