岩土材料极限分析上界法的讨论

Discussion on upper-bound method of limit analysis for geotechenical material

现行的极限分析上界法,尽管求解结果合理,但理论上却存在一些矛盾:如试验证明,关联流动法则不适用于岩土材料,而现行解法却采用了关联流动法则;传统分析中假设体积不变,但计算中却出现大于实际的体积剪胀变形;按关联流动法则,应力特征线与速度滑移线重合,但在分析中却采用速度方向与应力特征线方向成j角;实际土体破坏时,破坏面上同时存在着剪切力nt和正应力ns,但在计算中却反映不出摩擦功。近年在中国日益兴起的广义塑性力学理论为岩土材料的极限分析方法提供了科学的理论基础。作者提出了基于广义塑性力学的极限分析上界法,消除了上述矛盾,并获得了正确的计算结果。通过同经典算法的比较,证明了两种方法的计算结果几乎是一致的,但现行方法计算简便,因而,可作为一种实用的计算方法。论文还对上述两种算法作了系统的分析与比较,指出了它们求解的相同点与不同点。

The present upper-bound method of limit analysis has many self-contradictory conceptions in theory although its results are reasonable. For example, the associated flow rule is often used at present, but it is shown by experiments that it doesn抰 adapt to geotechnical materials; the volume deformation which is larger than real deformation is produced in calculating, but it is assumed to be constant in classical analyzing theory; the velocity slip line is the same as the stress characteristic line according to associated flow rule, but an angle j between the two lines is adopted in analyzing; the shear stress nt and normal stress ns exist simultaneously in every point of slip surface, but the friction work is not reflected in process of limit analysis. The scientific theory of the limit analysis method about the geotechnical materials is given by the generalized plastic mechanics theory, which thrives in China at the present years. The upper-bound method of limit analysis based on the generalized plastic theory is given in the paper, so these self-contradictory conceptions can be avoided completely and the right solutions are gained. To compare with the classical method, it is proved that the results of limit analysis solutions gained by two methods are nearly the same. The classical method can be used as a practical method since it is simple to solve questions. A systematic analysis and comparison of the above two limit analysis methods is given, and the sameness and un-sameness between them are clarified.