Based on the force equilibrium equations of the sliding mass behind the flexible supporting structure

a functional extreme value isoperimetric model is developed for calculating the active earth pressure with considering the point of resultant force. The problem of concern is cast into a functional extreme-value problem of two undetermined functions by means of Lagrange undetermined multiplier. According to Euler equations

logarithmic spiral sliding surface and normal stress function along the sliding surface are obtained. With combining the boundary conditions and transversality conditions

the conditional functional extremum problem of active earth pressure is changed equivalently into the problem of searching the minimum of unconstrained optimizations of function with two unknown Lagrange multipliers. Two special cases in which the slip faces are plan and arc surface are discussed. For a general soil

the active earth pressure resultant force is minimal when the point of resultant force is on the low limit of location; it increases nonlinearly as the point of resultant force moves up

and the slip face is changed from plan to logarithmic spiral face accordingly. For a sandy soil

the upper limit of location factor increases and the active earth pressure increases as the internal friction angle increases. For a soft clay

the active earth pressure is maximum when the point of resultant force is on the lower limit of location; it decreases nonlinearly as the point of resultant force moves up

and the slip face is arc face and moves away from pit accordingly.