滑面正应力近似方法对三维极限平衡法解的影响

采用楔形体与椭球滑面算例,研究了三维极限平衡法中滑面正应力近似方法对其计算结果的影响。使用线性插值近似滑面修正应力时,插值节点和网格数目的改变未对安全系数造成明显影响,但明显改变了修正应力的计算结果,网格交界处的修正应力易出现突变。采用移动最小二乘近似滑面修正应力后,安全系数基本不变,并且相对于线性插值,能在求解更少未知量的情况下获得更有规律的修正应力分布。算例表明,在采用线性插值和移动最小二乘近似计算滑面修正应力的情况下,安全系数基本不随滑面正应力的改变而变化,这与二维极限平衡法的相关研究结论基本相同,显示三维极限平衡法满足了平衡条件和合理性条件。

Impact of approximated normal stress on slip surface to three-dimensional limit equilibrium solution

The impact of approximation of the normal stress on slip surface to the three-dimensional limit equilibrium solution is studied using the sliding mass of the wedge and the sliding mass with an ellipsoid failure surface. When the modified normal stress on the slip surface is approximated with linear interpolation, the numbers of nodes and triangular meshes do not affect the values of the factor of safety, but can significantly affect the values of modified stress. It is easy to cause sudden change of modified stress at the boundaries of meshes. When the modified normal stress on the slip surface is approximated with moving least-squares, the factor of safety is almost unchanged, but a more regular distribution of the modified stress can be obtained with fewer unknowns in equations. The examples also show that, when using liner interpolation or moving least-squares to approximate the modified normal stress, different total normal stresses can lead to almost the same factor of safety. This result is similar to the conclusions obtained for two-dimensional limit equilibrium solution. So it is shown that the theory of three-dimension limit equilibrium satisfies all of the equilibrium conditions and reasonable conditions.