水流拖曳力对斜坡浅层土稳定性的影响分析

为研究强降雨条件下地表径流和裂隙水流的拖曳力作用对斜坡稳定性的影响，建立斜坡地表径流和地下水渗流耦合分析模型。采用Navier-Stokes方程描述地表径流和裂隙水流，Brinkman-extended Darcy方程描述土体和岩石中的渗流，并根据不同介质交界面处流速相等及剪应力连续的边界条件，推求各介质中的流速分布。应用Newton内摩擦定律求得水流对斜坡产生的拖曳力，进而将拖曳力嵌入刚体极限平衡理论对斜坡稳定性进行分析。典型斜坡实例计算结果表明，当未考虑拖曳力效应时，斜坡的安全系数为1.164，考虑水流对斜坡土体产生拖曳力效应时，斜坡的安全系数为1.089，斜坡安全系数降低了6.44%。这表明拖曳力作用对斜坡的稳定性存在不利影响，斜坡土体在近乎临界稳定状态下拖曳力将对斜坡失稳起到决定性作用。最后分别讨论了考虑拖曳力和不考虑拖曳力情况下斜坡的安全系数与径流水深、斜坡倾角、土层厚度之间的关系。分析表明，在其他条件相似的条件下，斜坡越陡，斜坡土体的安全系数下降越明显；斜坡安全系数随着斜坡倾角增加而不断降低，随着土层厚度的增加而不断降低。

Analysis for influence of water flow drag force on stability of slope shallow soil

The coupling analysis model of the surface runoff and water flow in fissures is established to study the effect of surface runoff and groundwater seepage on the stability of slope under heavy rainfall condition. The Navier–Stokes is used to describe the runoff and subsurface runoff, and the Brinkman-extended Darcy equation is used to describe the seepage in the soil and rock. Under the boundary conditions of the equal velocity and continuous shear stress at the interface of different media, we could inquire into the flow distribution of internal seepage and subsurface runoff. The drag force generated by water flow on the slope is obtained by applying the Newtonian friction law, and the drag force is embedded into the rigid body equilibrium theory to analyze the slope stability. The calculation results of the actual slope show that the safety coefficient of the slope is 1.164 when the effect of drag force is not considered. And the safety coefficient of the slope is 1.089 when the drag effect exerted by the water flow on the slope soil is taken into consideration, and the safety factor of the slope is decreased by 6.44%. It shows that the drag force effect has a great negative influence on the stability of the slope, and the drag force can play a decisive role in the critical steady state. Finally, the relationships between the safety coefficient of slope and runoff depth, soil thickness and slope inclination are discussed respectively considering drag force or not. The analysis shows that under similar conditions, the steeper the slope, the more obvious the decrease of the safety factor of the slope soil. The safety factor of the slope decreases with the increase of the slope inclination and the thickness of the soil layer.