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.