Engineering and Construction

Retaining walls are sometimes constructed at the top of slopes. In this case, there is a descending ground surface in front of the retaining wall and Eq. 11.5 cannot be used to determine the passive earth pressure coefficient. For either a descending slope (−β) or ascending slope (+β ) in front of the retaining wall, the following equation can be used to determine the passive earth pressure coefficient kp:


where: f is the friction angle of the soil in front of the retaining wall (degrees) and b is the slope inclination measured from a horizontal plane, where a descending slope in front of the retaining wall has a negative b value (degrees).

Although not readily apparent, if β = 0, Eq. 11.10 will give exactly the same values of kp as Eq. 11.5. For example, substituting β = 0° and f = 30° into Eq. 11.10, kp = 3 which is exactly the value obtained from Eq. 11.5.

Suppose that a retaining wall is constructed at the top of a 2:1 (horizontal:vertical) slope. In this case, the slope inclination is β = -26.6°. Assuming f = 30° for the soil comprising the slope, then according to Eq. 11.10, the value of kp = 1.12. Thus for the case of a 2:1 descending slope in front of the retaining wall, the passive resistance will be significantly reduced (kp decreases from 3 to 1.12). Many retaining walls tilt or deform downslope because the condition of a sloping ground surface in front of the retaining wall significantly reduces the passive resistance for the wall foundation.

There can be additional factors that contribute to the failure of retaining walls constructed at the top of slopes. In some cases, there may be a low factor of safety of the entire slope that is exacerbated by the construction of a top of slope wall. In other cases, where the soil in front of the retaining wall is clayey, there can be slope creep that causes a soil gap to open up at the front of the retaining wall footing. In these cases of a descending clayey slope in front of the retaining wall, the depth of creep of the outer face of the slope must be estimated and then the passive pressure should only be utilized below the depth of surface slope creep.