This study investigates the technique of variational calculus applied to estimate the slope stability considering the mechanism of planar failure. The critical plane failure surface should be determined because it theoretically indicates the most unfavorable plane to be considered when stabilizing a slope to rectify the instability generated by several statistically possible planes. This generates integrals that can be solved by numerical methods, such as the Newton Cotes and the finite differences methods. Additionally, a system of nonlinear equations is obtained and solved. The surface of the critical planar failure is determined by applying the condition of transversality in mobile boundaries, for which various examples are provided. The number of slices is varied in one of the examples, while the surface of the critical planar failure is determined in the others. Results are compared using analytical methods through axis rotations. All the results obtained by considering normal stress, safety factors, and critical planar failure are nearly the same; however, in this research, a study is carried out for “n” number of slices using programming methods. Sub-routines are important because they can be applied in slopes with different geometry, surcharge, interstitial pressure, and pseudo-static load.

这项研究研究了变分演算技术，该技术考虑了平面破坏的机理，用于估算边坡稳定性。应当确定临界平面破坏面，因为理论上它指示了在稳定斜坡以纠正由几个统计上可能的平面产生的不稳定性时要考虑的最不利平面。这将生成可以通过数值方法（例如牛顿科特斯和有限差分法）求解的积分。另外，获得并求解了非线性方程组。关键平面破坏的表面是通过应用移动边界中的横向条件确定的，为此提供了各种示例。在其中一个示例中，切片的数量有所不同，关键平面破坏的表面由其他因素决定。使用分析方法通过轴旋转比较结果。考虑法向应力，安全系数和临界平面破坏而获得的所有结果几乎相同；但是，在这项研究中，针对“n ”使用编程方法的切片数。子程序非常重要，因为它们可以应用于具有不同几何形状，附加力，间隙压力和拟静载荷的斜坡。