中文摘要：

基于Dmcker-Prager屈服准则，推导了平面应变条件下材料不连续分叉条件的解析解，并在自主研发的弹粘塑性自适应有限元分析软件AFEAS中引入该不连续分义条什。给出了弹粘颦性本构关系和局部化求解流程，以追踪岩体中局部化区的出现和发展。边坡稳定在岩土工程中具有举足轻重的作用，研究边坡失稳机理具有重大理论与现实意义，根据分叉理论把边坡失稳作为一种分叉现象研究，与传统屈服破坏理论相比，分叉理论更具优越性，能够追踪局部化区的出现和发展过程，确定边坡极限承载能力，并能为边坡治理提供更明确的破坏范围。通过一个边坡失稳算例分析考核了该理论与软件的合理性。

英文摘要：

Based on Drucker-Prager yield criterion, analytical solution of discontinuous bifurcation of materials is formulated under plane strain condition, and the bifurcation condition is implemented in the self-developed elasto-viscoplastic adaptive finite element analysis software AFEAS. Elasto-viscoplastic constitutive relation and solution program of localization are given to trace inception and progression of localization zone of rock mass. Slope stability plays critical roles in many projects, studying failure mechanism of slopes has important significance of theory and application. According to Bifurcation theory, slope instability is studied as a bifurcation phenomenon. Compared with traditional yield damage theory, bifurcation theory has more advantages-process of inception and progression of localization zone can be traced, the collapse load-carrying capacity of the slope can be determined and more definite failure zone can be provided for slope stabilization. A numerical example of slope instability is studied and shows the rationality of the theory and software.