扩展广义Drucker-Prager屈服准则在边坡稳定分析中的应用

对边坡稳定问题进行严格的理论分析通常采用极限分析上界法 ,此法认为土体的塑流遵守关联流动法则 (ψ =φ)并满足理想弹塑性条件 ,其局限性主要表现在 :求得的剪胀值远远超过实验测得的剪胀值。然而如果采用传统意义上的非关联流动法则(ψ =0 ) ,即完全不计体积变形 ,则剪胀对土工结构稳定性的重要影响又会被忽略。因此为了更好地描述土体的变形特性 ,应采用广义上的非关联流动法则 (ψ≠ φ)。基于有限元分析 ,推导了平面应变条件下基于非关联流动法则的Drucker Prager屈服准则 ,该准则与摩尔 -库仑屈服准则匹配 ,并能够考虑剪胀角的影响。算例分析表明 :基于文中D -P屈服准则的有限元分析与相同条件下塑性极限分析所得结果相近 ,误差在 3 %左右。由此不仅可以证明本文方法的正确性 ,且因采用了D -P准则表达形式 ,只需进行简单的参数转换 ,就可方便地引入现有有限元计算程序

Application of the extended general Drucker-Prager yield criterion to slope stability analysis

Rigorous theoretical analysis of slope stability problems is normally conducted by the upper bound method of plastic limit analysis,considering that the soil material is perfect plastic and obeys the associated flow rule. It's limitation lies in that the dilatancy obtained from this method exceeds that from experiments. However it will be shown that introduction of the classic non associated flow rule, namely neglecting the volumetric strain completely, neglects the important influence of dilatancy on stability of soil structure.Therefore the general non associated flow rule must be used in order to describe the soil deformation accurately.Based on the condition of plane strain, this paper deduces a D-P yield criterion matching the Mohr Coulomb criterion, which can deal with the effect of angle of dilatancy. The result of an example shows that the discrepancy between the results obtained by FEM based on D-P yield criterion and plastic limit analysis is 3% approximately.It proves that the method provided in this paper is not only reasonable but also can be introduced into current FEM program by transfering the parameter simplely because of the advantages of Drucker Prager criterion.