ACTIVE EARTH PRESSURE CALCULATION CONSIDERING FORCE POINT LOCATION

Considering an inclined rough retaining wall under general conditions such as curvilinear fill, cohesive soil, and uneven surface load, a functional extreme-value isoperimetric model about active earth pressure is deduced based on the force equilibrium equations of sliding mass. Then the problem of active earth pressure is transcribed as a functional extreme-value problem of two undetermined functions by means of a Lagrange undetermined multiplier. According to Euler equations, logarithmic spiral sliding surface and normal stress function along the sliding surface are obtained. Combined with the boundary conditions and transversality conditions, the conditional functional extremum problem of active earth pressure changed equivalently into the problem of searching the minimum of unconstrained optimizations of a function with two unknown Lagrange multipliers. For general soil, the active earth pressure resultant force is minimal when the point of a resultant force is on the low limit of location and it increases nonlinearly as the point of the resultant force moved up, the slip face is changed from a plan to a logarithmic spiral face accordingly. The active earth pressure resultant force is maximal when the point of the resultant force is on the high limit of location. The minimal and the maximal active earth pressure can be regarded as an interval estimation of active pressure, which comprises the earth pressures on the rigid retaining wall with any wall movement. The result shows that the design method of anti-overturning stability of retaining wall based on Coulomb's earth pressure theory maybe lead to a lower safety factor. It is a feasible method to guide the design based on the interval estimation of the active earth pressure and its action point.