为研究地表径流拖曳力对多层边坡稳定性的影响,建立了多层边坡渗流-径流耦合模型。该模型采用Navier–Stokes方程描述地表径流,用Brinkman-extended Darcy方程描述土层渗流,径流区和渗流区的流体运动均满足连续性方程,且在交界面处的流体满足流速相等和切应力连续双边界条件。根据上述条件推求出径流区和渗流区的流速分布,并引入Newton内摩擦定律求出坡面径流区与渗流区交界面处的水流拖曳力。基于每层土的受力特性,利用刚体极限平衡理论对径流状态下多层边坡的稳定性进行分析,得出每层土的稳定系数。并结合工程实例讨论径流水深、边坡坡度和上下部土层厚度分别对上下部土层稳定系数的影响。结果表明,考虑地表径流拖曳力效应时,上部土层的稳定系数为0.92,下部土层的稳定系数为1.18；当不考虑拖曳力效应时,上部土层的稳定系数为1.02,下部土层的稳定系数为1.23。上部土体的安全系数下降了9.95%,下部土体的安全系数下降了4.99%。因此,在进行多层边坡稳定性分析与计算中,应考虑地表径流拖曳力作用。
Abstract
In order to study the influence of surface runoff drag force on the stability of multi - layer slope, a multi - layer seepage - runoff coupling model was established. The Navier-Stokes equations are used to describe the surface runoff. The Brinkman-extended Darcy equation is used to describe the seepage of the soil. The fluid motion in the runoff and seepage regions satisfies the continuity equation, and the fluid at the interface satisfies the continuous and double shear boundary conditions. According to the above conditions, the velocity distribution of the runoff and seepage areas is deduced, and the Newton internal friction law is used to find the drag force of the flow at the interface between the runoff and the seepage. Based on the stress characteristics of each layer, the stability of multi - layer slope under runoff condition is analyzed by rigid body equilibrium equilibrium theory, and the stability coefficient of each layer is obtained. The effects of runoff depth, slope gradient and upper and lower soil thicknesses on the stability coefficient of upper and lower soil layers were discussed with engineering examples. The results show that the stability coefficient of the upper soil layer is 0.92 and the stability coefficient of the lower soil layer is 1.18 when considering the drag effect of the surface runoff. When the drag force effect is not taken into account, the stability coefficient of the upper soil layer is 1.02, The stability factor is 1.23. The safety factor of the upper soil decreased by 9.95%, and the safety factor of the lower soil decreased by 4.99%. Therefore, in the multi-layer slope stability analysis and calculation, should consider the role of surface runoff drag force.
关键词
多层边坡 /
径流-渗流耦合 /
拖曳力 /
刚体极限平衡理论
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Key words
Multi - layer slope /
coupling of runoff and seepage /
drag force /
the limit equilibrium theory of rigid body
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基金
: 国家自然科学基金项目( 41772321) ; 国家重点基础研究
发展规划( “973”计划) 项目( 2015CB057903) ; 中国地质
调查局基础地质调查项目( DD20160272) ; 四川省科技
支撑计划( 2014SS027) ; 四川省教育厅科自然科学重点
项目( JYTZD2016-001)
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