Finite Element Analysis of Strain Localizaion in ExcavationsResearch into Network Algorithms and Related Problems

本项目涉及对开挖和支撑开挖稳定性和变形行为的应变局部化研究。以往的研究已经证明了标准有限元方法在模拟连续开挖和施工过程中的有效性，特别是在土体均匀变形的情况下。然而，当土体内部形成一个狭窄的强烈剪切带时，标准的有限元插值就变得不够充分，因为它不能表示可能在有限元上形成的剪切带的影响。因此，在强烈剪切区，标准有限元方法将预测更刚的结构行为，即使分叉的反应已经是有序的。在支撑和捆绑开挖中，这意味着预测的移动和支撑载荷将较小，因此标准有限元解将偏向不安全的一侧。这项研究将通过将应变局部化建模为涉及位移场跳跃的强不连续问题来解决这一问题。土力学中的滑移线概念与这一分析是一致的。在有限元分析的背景下，涉及强不连续性的问题会导致完全独立于有限元网格的解，特别是即使在非结构化网格中也表现出对不连续性的精确分辨率。此外，这种方法允许使用传统的与速率无关的连续介质力学模型，即使是那些没有提供特征长度标度的模型，因为现在假设不连续点对应于数学意义上的测量零集。这项研究将使用基于乘性塑性的有限变形理论来研究排水和不排水行为，并将使用J2塑性和修正的Cam-Clay塑性模型。已知在连续开挖过程中形成应变局部化的现场案例有很多，这些将被用来检验所提出的分析方法的准确性。

This project involves the study of strain localization on the stability and deformation behavior of open and supported excavations. Previous studies have demonstrated the usefulness of the standard finite element (FE) method in modeling the process of sequential excavation and construction particularly when the soil mass is deforming homogeneously. However, when a narrow band of intense shearing forms within the soil, the standard FE interpolation becomes inadequate because it is incapable of representing the effect of shear bands which could form across the finite elements. Therefore, in the regime of intense shearing, the standard FE method would predict a stiffer structural behavior even though a bifurcated response is already in order. In braced and tied-back excavations, this implies that the predicted movements and support loads will be smaller, and so the standard FE solution will err on the unsafe side. This research will address this problem by modeling strain localization as a problem of strong discontinuity, which involves jumps in the displacement field. The idea of slip lines in soil mechanics is consistent with this analysis. Within the context of FE analysis, problems involving strong discontinuities result in solutions that are completely independent of the FE mesh, in particular showing a sharp resolution of the discontinuities even in unstructured meshes. Furthermore, this approach admits the use of traditional rate-independent models of continuum mechanics, even those which do not offer a characteristic length scale, since the discontinuities are now assumed to correspond to sets of measure zero in the mathematical sense. The investigation will cover drained and undrained behavior using a finite deformation theory based on multiplicative plasticity, and will involve the use of J2 plasticity and modified Cam-Clay plasticity models. There are numerous field cases where strain localizations are known to have formed during the process of sequential excavation, and these will be used to test the accuracy of the proposed analytical methodology.