试论强度折减有限元法变形参数折减的必要性和相应判据

On the necessity of reducing deformation parameters for strength-reduction FEM and corresponding criteria

本文根据符合摩尔-库仑屈服准则的半无限域均质岩土体的应力场,用屈服准则公式推导的方法,探讨了在强度折减有限元法中,相关的变形参数是否应该折减的问题。推导出了在没有特定假设前提下的岩土体摩擦角与泊松比之间应满足的关系不等式,它包含了岩土体内聚力为零和岩土体深度为无穷大的两种特殊情况,更具有一般性。该关系不等式不仅说明了在强度折减有限元法中相关变形参数折减的必要性,同时也是对岩土体泊松比是否进行调整,调整多少的一个重要判据。通过计算与分析发现,如果在使用强度折减有限元法时,不遵守上述判据,在大多数情况下,仍然能获得与极限平衡法相同的安全系数,但是计算成果中将会出现大范围的并不存在的塑性区。鉴于有限元法在提出安全系数的同时,也要给出符合实际的应力、变形和塑性区信息,引入本文提出的判据,显然是有必要的。

Based on the yield criterion formula an improved inequality for expressing the necessary relationship between friction angle and Poisson＇ s ratio of geomaterial is suggested. This relationship is not only suitable for the special cases of without cohesion and infinite depth, but also for more general cases. According to this inequality the necessity of adjusting the Poisson＇ s ratio in FEM analysis can be determined. It is found that if the inequality criterion is not to be obeyed, the safety factor obtained will be the same as that calculated from limit equilibrium method but a plastic region will appear which not exist in reality. The necessity of reducing deformation parameters is illustrated by two examples.