Abstract:
To reasonably characterize the active earth pressure distribution on circular shafts with the depth of the inclined surface under steady-state seepage, the formulation of matric suction for unsaturated soils with an inclined surface under steady-state seepage was first derived using Darcy's law. The differential slip line equation of active earth pressure on shafts was then developed based on the suction stress theory of unsaturated soils. Furthermore, the active earth pressure solution of shafts under steady-state seepage was obtained by iteratively calculating the boundary problem. Finally, comparative verifications and parametric discussions of the obtained solution were carried out along with its application steps. The results show that the obtained slip line solution of active earth pressure on shafts in unsaturated soils under steady-state seepage comprehensively considers nonlinear profiles of suction stress, couplings of environmental factors, different types of soils, and the surface inclination. Meanwhile, the obtained solution can naturally degenerate into the iterative solution of active earth pressure for the shaft in saturated soils with an inclined surface as well as the shaft in unsaturated soils with a horizontal surface under nonlinear suction stress. The differential iteration method employed is straightforward, and the computational accuracy can be readily controlled. In addition, the correctness of the obtained solution is verified by comparing it with existing solutions of both the shaft in saturated soils with an inclined surface and the shaft in unsaturated soils with a horizontal surface reported in the literature. For different values of the steady-state seepage quantity or the saturated permeability coefficient, the active earth pressure on shafts in clays varies significantly, yet that in sands with high permeability and slight suction stress remains nearly constant. The active earth pressure on shafts in sands, silts and clays at great depths increases obviously with the increase of the inclined surface angle, particularly at the shaft bottom.