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稳态渗流下圆形竖井主动土压力的滑移线差分解

DIFFERENTIAL SLIP LINE SOLUTIONS OF ACTIVE EARTH PRESSURE ON CIRCULAR SHAFTS UNDER STEADY-STATE SEEPAGE

  • 摘要: 为合理描述稳态渗流下倾斜地表圆形竖井主动土压力沿深度的分布规律, 本文首先利用达西定律提出地表倾斜非饱和土的稳态渗流基质吸力公式, 并基于非饱和土的吸应力理论, 建立了有关竖井主动土压力的滑移线差分方程, 继而迭代求解边界问题得到稳态渗流下竖井的主动土压力解答, 最后结合解答应用步骤进行对比验证和因素影响分析. 研究结果表明: 所得稳态渗流下非饱和土圆形竖井主动土压力的滑移线解答综合考虑了吸应力非线性分布、环境因素耦合、土体类型不同与地表倾斜, 且能自然退化为倾斜地表饱和土竖井与非线性吸应力下水平地表非饱和土竖井的主动土压力迭代解; 差分迭代求解的思路清晰、精度易控, 所得解答的正确性得到文献倾斜地表饱和土竖井与水平地表非饱和土竖井解答的验证; 对于不同的稳态渗流量或饱和渗透系数, 黏土竖井的主动土压力变化显著, 而高渗透性与微弱吸应力砂土竖井的主动土压力几乎不变; 砂土、粉土与黏土竖井的深层主动土压力均随地表倾角增加而明显增大, 特别是在井底处.

     

    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.

     

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