Sensitivity analysis of parameters of Rankine's earth pressure with inclined surface considering intermediate principal stress

Up to now the Rankine's earth pressure theory has not been widely used under the condition of inclined surface. Generally, the classical earth pressure theories are based on the Mohr-Coulomb criterion and the intermediate principal stress is not taken into account. First, a formula for Rankine's active and passive earth pressures with inclined surface as well as that for the intermediate principal stress in the plane strain assumption is derived. Then, the formula for shear strength parameters in the unified strength theory is derived based on the formula for the intermediate principal stress, so the shear strength parameters under the Mohr-Coulomb criterion can be transformed into the shear strength parameters under the unified strength theory. Finally, an example is given to carry out sensitivity analysis of six factors in terms of the design theory of orthogonal tests. The six influential factors are considered including the cohesion, internal friction angle, intermediate principal shear stress parameter, Poisson's ratio, angle of inclined surface and unit weight. It is shown that among the influential factors of Rankine's active earth pressure, the unit weight is the most important one, followed by the intermediate principal shear stress parameter, the cohesion, the internal friction angle, the angle of inclined surface and the Poisson's ratio; among those of Rankine's passive earth pressure, the internal friction angle is the most important one, followed by the intermediate principal shear stress parameter, the Poisson's ratio, the cohesion, the angle of inclined surface and the unit weight. So the effect of the intermediate principal stress on the calculated results of the Rankine's earth pressure is a critical factor.