Semianalytical Solution for General Active Earth Pressure Considering the Coupling and Dilatation

Abstract

Rankine pressure involves the special case of active earth pressure and merely considers the influence of the internal friction angle; however, the analytical solution for the general case involving a rough retaining wall, inclined boundary, and soil dilatation effects has not been investigated to date. This study developed a new slip line theory that considered the dilatation effect and then derived a general analytical solution, which considered the internal friction angle, dilatation angle, interface friction angle, and inclination angle of the boundary. The sliding surface and pressure coefficients were discussed in terms of the numerical method of slip line theory. The analytical solutions of the pressure coefficients related to the surcharge and cohesion were found to be identical to the numerical results. When one of the interface friction angles and the inclination angle did not equal zero, the total earth pressure could not be simply expressed as the linear superposition of the three terms like the Rankine expression, and the total result was related to the ratio (q+ccot⁡φ)/γ. When producing the earth pressure, this coupling effect between the surcharge, cohesion, and weight displayed regularity. The correction coefficient of the analytical solution for the pressure coefficient due to the weight was introduced and determined from the results of the numerical method, and a semianalytical solution was provided.