In the classical Coulomb’s earth pressure theory

the failure surface in the backfilled cohesionless soil behind rigid retaining wall in slope engineering is assumed a plane. However

it has been proved by a number of laboratory and field tests that this failure surface is actually a curved surface. In this paper

based on the vertical differential element method and the variational principle with moveable boundary

a quadratic ordinary differential equation of the first order about the failure surface is deduced. Three cases of the equation are discussed: 1) without lateral shear force at the interface between two elements

and the back of the retaining wall is frictionless

the failure surface is a plane; 2) lateral shear force is a constant

and the back of the wall is rough

the failure surface is also a plane

the two cases above mentioned are identical to Coulomb’s theory; 3) lateral shear force increases linearly from the tip to the toe

the failure surface is a curved surface. Results show that the proposed approach can predict right failure pattern of the backfilled cohesionless soil

which is in good agreement with that of the laboratory and field tests.