《工程科学学报》录用稿，htps:/doi.org/10.13374/i,issn2095-9389.2021.04.29.002©北京科技大学2020 基于有限元极限平衡法的三维边坡稳定分析 苏振宁”，邵龙潭)回 1)大连理工大学，工业装备结构分析国家重点实验室，大连116024 ☒通信作者，E-mail:shaolt@dlut.edu.cn 摘要本文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一一三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乘 衡法结果一致。 关键词三维边坡稳定：有限元：极限平衡条件：安全系数：滑动方向 分类号TU473 finite element limit 0o3sad,。A Three-dimensional slope stability analysis equilibrium method SU Zhenning,SHAO Longtan Technology,Dalian,116024,China Corresponding author,E-mail:shaolt@dlut.edu.cn Abstract The finite element limit equilibrium method is a slope stability analysis method based on finite element stress analysis combined with limit equilibrium condition.The safety factor defined in the form of shear stress ratio in the three-dimensional space does not consider the influence of the sliding direction on the calculation results.In this paper,a three-dimensional finite element limit equilibrium method is proposed by considering the sliding direction.This method is different from the limit equilibrium method and the strength reduction method. This method analyzes the slope stability through the "true"stress state without reducing the material strength parameters.First,considering the sliding direction in the three-dimensional space,the limit equilibrium condition of a point on the slip surface in the sliding direction is proposed.An equivalent relationship is proved that the slip surface as a whole is in the limit equilibrium state and each points of the slip surface are 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 are calculated by the assumption of rigid body limit equilibrium.Finally,the local safety factor is defined as the ratio of the shear strength to the shear stress projection in the sliding direction.Based on the equivalent relationship of limitequilibrium condition of the three-dimensional slope,the local safety factor is transformed into the global safety factor through 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 three-dimensional limit equilibrium method. Key words three-dimensional slope stability;finite element method;limit equilibrium condition;safety factor;sliding direction 收离日期： 基金项目：国家自然科学基金资助(No.52079018)工业装备结构分析国家重点实验室自主课题基金(No.S14208)基于有限元极限平衡法的三维边坡稳定分析 苏振宁 1)，邵龙潭 1) 1 1) 大连理工大学，工业装备结构分析国家重点实验室，大连 116024  通信作者，E-mail: shaolt@dlut.edu.cn 摘 要 本文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。 关键词 三维边坡稳定；有限元；极限平衡条件；安全系数；滑动方向 分类号 TU473 Three-dimensional slope stability analysis based on finite element limit equilibrium method SU Zhenning1), SHAO Longtan1)  1) State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian, 116024, China  Corresponding author, E-mail: shaolt@dlut.edu.cn Abstract The finite element limit equilibrium method is a slope stability analysis method based on finite element stress analysis combined with limit equilibrium condition. The safety factor defined in the form of shear stress ratio in the three-dimensional space does not consider the influence of the sliding direction on the calculation results. In this paper, a three-dimensional finite element limit equilibrium method is proposed by considering the sliding direction. This method is different from the limit equilibrium method and the strength reduction method. This method analyzes the slope stability through the “true” stress state without reducing the material strength parameters. First, considering the sliding direction in the three-dimensional space, the limit equilibrium condition of a point on the slip surface in the sliding direction is proposed. An equivalent relationship is proved that the slip surface as a whole is in the limit equilibrium state and each points of the slip surface are 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 are calculated by the assumption of rigid body limit equilibrium. Finally, the local safety factor is defined as the ratio of the shear strength to the shear stress projection in the sliding direction. Based on the equivalent relationship of limit equilibrium condition of the three-dimensional slope, the local safety factor is transformed into the global safety factor through 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 three-dimensional limit equilibrium method. Key words three-dimensional slope stability; finite element method; limit equilibrium condition; safety factor; sliding direction 1收稿日期: 基金项目: 国家自然科学基金资助（No. 52079018）工业装备结构分析国家重点实验室自主课题基金（No. S14208） 《工程科学学报》录用稿，https://doi.org/10.13374/j.issn2095-9389.2021.04.29.002 ©北京科技大学 2020 录用稿件，非最终出版稿