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

该项目涉及到应变局部化对明挖和支护开挖的稳定性和变形行为的研究。 以往的研究已经证明了有用的标准有限元（FE）方法在模拟过程中的顺序开挖和施工，特别是当土体变形均匀。 然而，当一个狭窄的强烈剪切带的土壤中形成时，标准的有限元插值变得不够，因为它是无法代表剪切带的效果，可以形成跨越有限元。 因此，在强烈剪切状态下，即使分叉响应已经就绪，标准有限元方法也会预测更刚性的结构行为。 在支撑和回接开挖中，这意味着预测的移动和支撑载荷将较小，因此标准的有限元解将在不安全的一侧出错。 这项研究将解决这个问题，通过建模应变局部化的问题，强不连续性，其中涉及跳跃的位移场。 土力学中滑移线的概念与这种分析是一致的。 在有限元分析的背景下，涉及强不连续性的问题导致完全独立于有限元网格的解决方案，特别是即使在非结构化网格中也显示出对不连续性的尖锐分辨率。 此外，这种方法允许使用传统的率独立模型的连续介质力学，即使是那些不提供一个特征长度尺度，因为现在假设的不连续性对应于集的测量零在数学意义上。 调查将包括排水和不排水行为，使用有限变形理论的基础上倍增塑性，并将涉及使用J2塑性和修改剑桥塑性模型。 有许多现场的情况下，应变局部化是已知的顺序开挖过程中形成的，这些将被用来测试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.