In this paper, a modified shear strength reduction method (MSSR) and its optimization variant (OPT-MSSR) are suggested. The idea of MSSR is to approximate the standard shear strength reduction to be more stable and rigorous from the numerical point of view. The MSSR method consists of a simplified associated elasto-plastic model completed by the strength reduction depending on the dilatancy angle. Three Davis' modifications suggested by Tschuchnigg et al. (2015) are interpreted as special cases of MSSR and their factors of safety are compared. The OPT-MSSR method is derived from MSSR on the basis of rigid plastic assumption, similarly as in limit analysis. Using the variational approach, the duality between the static and kinematic principles of OPT-MSSR is shown. The numerical solution of OPT-MSRR is obtained by performing a regularization method in combination with the finite element method, mesh adaptivity and a damped Newton method. In-house codes (Matlab) are used for the implementation of this solution concept. Finally, two slope stability problems are considered, one of which follows from analysis of a real slope. The softwares packages Plaxis and Comsol Multiphysics are used for comparison of the results.

中文翻译：

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抗剪强度折减法的优化和变分原理

在本文中，提出了一种改进的抗剪强度折减方法（MSSR）及其优化变体（OPT-MSSR）。MSSR 的思想是从数值的角度来近似标准的抗剪强度折减，使其更加稳定和严谨。MSSR 方法由一个简化的相关弹塑性模型组成，该模型通过根据剪胀角进行强度降低来完成。Tschuchnigg 等人建议的三个戴维斯修改。(2015) 被解释为 MSSR 的特殊情况，并比较了它们的安全因素。OPT-MSSR 方法是在刚性塑性假设的基础上从 MSSR 推导出来的，类似于极限分析。使用变分方法，显示了 OPT-MSSR 的静态和运动原理之间的对偶性。OPT-MSRR的数值解是通过结合有限元方法、网格自适应和阻尼牛顿法进行正则化方法获得的。内部代码 (Matlab) 用于实现此解决方案概念。最后，考虑了两个边坡稳定性问题，其中之一来自对实际边坡的分析。软件包 Plaxis 和 Comsol Multiphysics 用于比较结果。