基于矢量和的滑面应力抗滑稳定分析方法

矢量和抗滑稳定分析方法根据真实应力状态定义求解安全系数，物理意义明确，一批学者对其进行了研究。但是当合法向力矢量投影与合剪力矢量投影的符号相反且其绝对值大于合剪力矢量投影时，矢量和法计算出的安全系数可能为负值；另外，目前潜在滑移面上每点极限抗滑剪应力矢量的方向是根据潘家铮最大、最小原理确定的，将其定义为潜在滑移体滑动趋势方向在该点切平面上投影方向的反方向，但是潘家铮最大、最小原理描述的是滑移体力学系统抗滑能力最大，按照矢量和法的定义式，抗滑能力包括抗剪力和法向抗力两部分。基于矢量和思想与以上关于矢量和法的思考，提出一种滑面应力抗滑稳定分析方法，将潜在滑移面视为薄滑移带，以薄滑移带作为对象进行微元受力分析，每个微元的极限抗滑剪应力矢量方向取为该微元剪应力矢量的反向，所有微元的极限抗滑剪力矢量和的反向定义为潜在滑移体滑动趋势方向，最终将极限合抗滑剪力矢量在滑动趋势反方向的投影与合滑动剪力矢量在滑动趋势方向的投影的比值定义为安全系数。较极限平衡法，方法自动满足静力平衡、力矩平衡和变形协调条件，无需受力模式假设；较强度折减法，新方法基于真实应力，物理意义更加明确，安全系数以显式表达，无需迭代；通过经典二维静态边坡考题，验证此方法的可行性；将新方法应用到三维工程实例中，分析潜在滑移体在边坡开挖过程中安全系数的动态演化规律，证明方法的实用性。

Vector-sum-based slip surface stress method for analysing slip mass stability

The vector sum method (VSM) based on real stress state has been applied recently for analysing the slope stability, considering its clear physical meaning. However, the factor of safety (FoS) defined by VSM could be negative in the case where total normal force vector projection is negative, and its absolute value is larger than total shear force vector projection. Moreover, deduced by Pan’s Principle, the direction of shear resistance stress vector of every point on potential slip surface is currently defined to be opposite to that of the projection of the potential slip direction of the possible slip mass on the tangential surface through this point. However, according to the definition of VSM safety factor and Pan’s Principle, the direction of the projection of the potential slip direction on the tangential surface through this point is opposite to that of the total resistance stresses including shear and normal ones. In this study, a vector-sum-based slip surface stress method for analysing slip mass stability was proposed to overcome these two disadvantages above of VSM. The slip surface was treated as a thin slip band, and forces undertaken by an arbitrary element of the slip band was analysed. The direction of the limit resisting shear stress of an arbitrary element was defined as the opposite direction of the real shear stress, and the possible slip direction was defined as the opposite direction of the resultant limit resisting shear force. Finally, FoS was defined as the ratio of the projection of the limit resisting shear force vector sum in the opposite possible slip direction to that of real dynamic shear force vector sum in the possible slip direction. Compared with the limit equilibrium method, the proposed method satisfied the force and moment equilibrium equations and compatibility conditions without any assumption. Compared with the shear strength reduction method, the proposed method defined that the FoS was explicit form avoiding iteration. The classic two-dimension static slope case was used to verify the proposed method with comparisons among main methods for slope stability analysis, which indicated that the proposed method was feasible. Additionally, the proposed method was applied to a three-dimensional engineering case to study its stability during the excavation process, which showed the proposed method could be used for practical application.