RANKINE’S LATERAL EARTH PRESSURE FOR A SLOPING BACKFILL AND A SLOPING WALL FACE
Rankine (1857) established the principle of stress states or stress fi eld in solving stability problems in soil mechanics. We have used Rankine’s method in developing the lateral earth pressures for a vertical, frictionless wall supporting a dry, homogeneous soil with a horizontal surface. Rankine (1857) derived expressions for Ka and Kp for a soil mass with a sloping surface that were later extended to include a sloping wall face by Chu (1991). You can refer to Rankine’s paper and Chu’s paper for the mathematical details.
With reference to Figure , the lateral earth pressure coeffi cients according to Rankine’s analysis are
Retaining wall with
sloping soil surface, frictionless soil–wall
interface, and sloping back for use with
Rankine’s method.
where the subscript R denotes Rankine, and
The angles of the failure planes to the horizontal for active and passive states are
The sign conventions for h and b are shown in Figure; counterclockwise rotation is positive. The active and passive lateral earth forces at the limiting stress state are
These forces are inclined at
to the normal of the wall face. The angles ja and jp (reminder: the subscripts a and p denote active and passive) are not interface friction values.
In the case of a wall with a vertical face, h = 0, Equations reduce to
and the active and passive lateral earth forces act in a direction parallel to the soil surface, that is, they are inclined at an angle b to the horizontal. Thus,