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上限定理是求解岩土工程问题的有效工具。以上限定理为理论基础,分析边坡的稳定性问题,并考虑了岩土材料破坏准则的非线性特性。在非线性Mohr-Coulomb破坏准则下,采用条分法与极限分析上限法相结合的方法,对边坡稳定性进行分析。通过切线法引入非线性强度参数ct、?t,推导了岩土材料在非线性破坏准则下的相关联流动法则,建立功能方程,推导了边坡直线滑裂面、折线滑裂面和光滑曲线滑裂面安全系数F的计算方程。采用数学规划法计算后与工程实际中常用的边坡稳定性分析方法进行对比,并获得安全系数F=1.0时的稳定性系数Ns。与已有的研究成果进行比较分析,结果表明了该方法的正确性及优越性。
The upper bound theorem is an effective tool to solve geotechnical engineering problems. The above limits serve as the theoretical basis to analyze the stability of slope and consider the nonlinear characteristics of the failure criterion of geomaterials. Under the condition of non-linear Mohr-Coulomb failure criterion, the stability of slope is analyzed by the combination of the upper and lower limit analysis methods. By introducing the nonlinear strength parameter ct, t by tangential method, the associated flow laws of geomaterials under nonlinear failure criterion are deduced. The functional equations are established and the slope linear slip surface, polyline slip surface and smooth curve are deduced Calculation equation of safety coefficient F of slip surface. Comparing with the method of slope stability analysis commonly used in engineering practice after mathematical programming, the stability coefficient Ns at safety factor F = 1.0 is obtained. Compared with the existing research results, the results show the correctness and superiority of this method.