基于有限元极限平衡法的三维边坡稳定性

提出了一种基于有限元弹塑性应力场和极限平衡状态的三维边坡稳定分析方法——三维有限元极限平衡法。首先，考虑三维空间中滑动方向，提出滑动面上一点在滑动方向上的极限平衡条件，并证明滑动面上土体整体达到极限平衡状态与滑动面上土体各处在滑动方向上处于极限平衡状态等价。再通过刚体极限平衡假定计算主滑方向和滑动面上各点滑动方向。最后，定义局部安全系数为抗剪强度与滑动方向上剪应力投影的比值，基于三维边坡整体极限平衡条件将局部安全系数通过积分中值定理转变为整体安全系数。该方法计算简单，消除了剪应力比形式定义安全系数滑动面形状限制，具备合理性与有效性。算例验证结果表明，该方法滑动方向假设合理，安全系数与严格三维极限平衡法结果一致。 

Three-dimensional slope stability based on the finite element limit equilibrium method

A finite element limit equilibrium method was proposed based on finite element stress analysis combined with a limit equilibrium condition to analyze the slope stability. The local safety factor defined in the form of shear strength and shear stress ratio in a three-dimensional (3D) space does not consider the sliding direction influence on the calculation results. In this paper, a 3D finite element limit equilibrium method that considers the sliding direction was proposed. This method was different from the limit equilibrium and strength reduction methods and analyzed slope stability through the “true” stress state without reducing the material strength parameters. First, considering the sliding direction in the 3D space, the limit equilibrium condition of a point was proposed on the slip surface in the sliding direction. An equivalent relationship was proved of the slip surface was in the limit equilibrium state, and each point of the slip surface was in the limit equilibrium state in the sliding direction. Then, the main sliding direction and the sliding direction of each point on the slip surface were calculated assuming the rigid body limit equilibrium. Finally, the local safety factor was defined as the ratio of the shear strength to the shear stress projection in the sliding direction. Based on the equivalent relationship of the limit equilibrium state of the 3D slope, the local safety factor was transformed into a global safety factor by applying the integral median theorem. The method is simple to calculate, eliminates the limitation of the slip surface shape of the safety factor defined by the shear stress ratio form, and is reasonable and effective. The verification result of the calculation example shows that the sliding direction assumption of the method is reasonable, and the safety factor is consistent with the result of the strict 3D limit equilibrium method.