On the basis of Coulomb’s concept that the active earth pressure against the back of a retaining wall is due to the thrust force exerted by a sliding wedge of soil between the back of the wall. Considering an inclined rough retaining wall under the general conditions such as curvilinear fill

cohesive soil and uneven surface load

the functional extreme-value isoperimetric model about active earth pressure is deduced based on the force equilibrium equations of the sliding mass. Then the problem of active earth pressure is transcribed as the functional extreme-value problem of two undetermined functions by means of Lagrange undetermined multiplier. According to Euler equations

linear sliding surface function and linear normal stress function are obtained. Combined with the boundary conditions and transversality conditions

the problem of active earth pressure turned to be the solution of a one-dimensional equation. The magnitude of active earth pressure calculated by variational method is the same as that of Coulomb’s theory; and the location of application point of earth pressure is not always at 1/3 height of the retaining wall by case studies. In addition

curvilinear fill and uneven surface load also have significant effect on the magnitude and the location of application point of active earth pressure.