The NMM (numerical manifold method) has shown its ability to solve continuum and discontinuum engineering problems in the same framework. In the present paper, the vector sum NMM (VSNMM) is proposed to investigate the stability of slopes. With the (vector sum numerical manifold method) VSNMM, the FOSs (factors of safety) of slopes are obtained using the real stress fields of the slopes. Compared with the limit equilibrium methods, the deformation and stress field of a slope can be obtained using the VSNMM. Besides, the computational cost of the VSNMM is much less than that of the strength reduction numerical manifold method (SRNMM), since only one elasto-plastic analysis is needed in the VSNMM, while a series of elasto-plastic analyses is needed in the SRNMM. Based on the VSNMM, the stability analyses of two slopes including a homogeneous slope and an inhomogeneous slope with three different materials are conducted. The numerical results based on the two slopes show that the VSNMM can accurately calculate the FOSs of the slopes.

NMM（数字流形方法）已显示出在同一框架中解决连续和不连续工程问题的能力。在本文中，提出了矢量和NMM（VSNMM）来研究边坡的稳定性。使用（矢量和数值流形方法）VSNMM，使用边坡的实际应力场获得边坡的FOS（安全系数）。与极限平衡法相比，利用VSNMM可以得到边坡的变形和应力场。此外，由于VSNMM仅需要一次弹塑性分析，而SRNMM却需要一系列弹塑性分析，因此VSNMM的计算成本比强度降低数字流形方法（SRNMM）的计算成本低得多。 。基于VSNMM，对包括三种不同材料的均质边坡和非均质边坡两个边坡进行了稳定性分析。基于两个斜率的数值结果表明，VSNMM可以准确计算斜率的FOS。