基于不同客观本构关系的路基大变形固结分析

Large strain consolidation of roadbed based on various objective constitutive relations

针对路基大变形固结分析中常用的Jaumann率型本构关系不能考虑邻域变形之影响的缺点,将Truesdell率型本构关系引入到大变形固结理论。采用虚功原理和Galerkin加权残值法,推导了基于不同客观本构关系的大变形固结有限元方程。编制相应的平面应变有限元程序对路基大变形固结性状进行分析,主要讨论了Truesdell率型、Jaumann率型、简化Jaumann率型等3种大变形本构关系对路基固结性状的影响。算例分析结果表明:基于常用的Jaumann率型本构关系的大变形固结分析得到的路基沉降量、侧向位移和孔压等均偏大于基于Truesdell率型本构关系时的相应结果。小变形本构矩阵不能反映客观性要求,将导致计算结果产生较大偏差。对常见问题而言,Jaumann率型和Truesdell率型本构关系对计算结果的影响并不很大,传统分析方法在变形较小时仍具有较高精度。

In traditional large strain analysis of roadbed consolidation, the constitutive relation with Jaumann stress rate is used, which can not consider neighborhood-deformation. In this paper, Truesdell stress rate considering not only rigid-body motion but also neighborhood-deformation was introduced into large strain consolidation （LSC） theory. Using both virtual work principle and Galerkin＇s weighted residual method, the finite element formulations for LSC were derived, based on constitutive relations following objectivity principle, The corresponding plane-strain FEM programs were compiled and tested. The influences of Truesdell, Jaumann and simplified Jaumann stress rates on roadbed consolidation were mainly discussed. The results show that the settlement, lateral displacement and pore-water pressure calculated by traditional method are greater than those by the method based on the constitutive relation using Truesdell stress rate. The considerable magnitude of errors may occur for the case of using small-strain constitutive matrix, due to the dissatisfaction with objectivity principle. As far as common problems are concerned, the differences between the results by Jaumann or Truesdell stress rate could be neglected; and the traditional method is adequately accurate for the case of small deformation.