Finite deformation geomechanics: developing a meshless scaled boundary method

土木工程师经常使用计算工具来预测他们想要建造的东西的行为，在施工之前。最流行的计算方法是有限元法（FEM），它通过将复杂结构（例如建筑物或基础）划分为更小的单元来工作。这些元素通过它们的角节点相互连接。每个元素都遵循一套规则，以确保满足平衡和兼容性定律（即元素不能重叠的事实）。将大量元素组合在一起，可以近似地（但可能高度精确地）模拟（复杂的）完整结构。有限元法得到了广泛的应用，但也存在一些不足；特别是，无限边界不能被建模。此外，当在三维空间中工作时，生成元素网格可能会有问题。对于有相当大的变形的情况，元件可以改变形状，使其精度下降。一个想要模拟大变形的例子是插入桩基础（本质上是一根钢管或混凝土管插入地下，后来支撑建筑物的一部分）。另一个例子是测定土壤刚度和强度的锥贯法测试。该项目将开发一种新的方法来对这些类型的问题进行建模，从而克服与FEs相关的许多困难。该方法是无网格法和尺度边界法的结合。无网格方法完全消除了生成单元网格的问题；一种方法只是在模型的边界内生成节点的分布。缩放边界技术允许精确建模无限边界（代表土壤垂直向下和横向延伸）。这个项目的一个关键部分是关注创建一个现实的模拟能力大（有限）变形的土壤。在传统的小变形理论中，我们假设我们可以在不改变其原始形状的基础上计算应力和应变。这种简化在许多情况下都很有效，但是当施加的载荷引起很大的变形时，除非我们跟踪问题形状的变化，否则就会出现错误。永久（大）位移将由一个新的公式表示，该公式考虑了不同方向（各向异性）的不同土壤压缩性。我们将把这个相当基础的工作与新的计算方法结合起来，创建一个通用的工具，可以处理地质力学中的许多问题（特别是那些对FEM构成真正困难的问题）。

Civil engineers make regular use of computational tools to predict the behaviour of the things they wish to build, prior to construction. The most popular computational method is the Finite Element Method (FEM) which works by dividing a complex structure (building or foundation, for example) into smaller elements. These elements are connected to each other by their corner nodes. Each element follows a set of rules that ensures the laws of equilibrium and compatibility (i.e. the fact that elements cannot overlap) are satisfied. Combining a large number of elements allows the (complicated) complete structure to be simulated in an approximate (but potentially highly accurate) sense.The FEM is widely used but has some disadvantages; in particular, infinite boundaries cannot be modelled. Furthermore, generating the mesh of elements can be problematic when working in three-dimensions. For cases where there is considerable deformation, the elements can change shape so much that their accuracy deteriorates. An example where one wishes to model large deformations is pushed-in pile foundations (essentially a tube of steel or concrete pushed into the ground, which later supports part of a building). Another example is a test known as the Cone Penetrometer test that determines the soil's stiffness and strength.This project will develop a new method for modelling these types of problem which overcomes many of the difficulties associated with FEs. The approach is a combination of a meshless method and a scaled boundary method. Meshless methods entriely remove the problem of generating the mesh of elements; one simply generates a distribution of nodes inside the boundaries of the model. The Scaled Boundary technique allows accurate modelling of the infinite boundaries (representing the soil extending vertically downwards and laterally). A key part of this project is concerned with creating a realistic simulation capability for large ( finite ) deformations in the soil. In conventional small deformation theory we assume that we can calculate stresses and strains on the basis that it has not changed its original shape. This simplification works well in many cases, but when the loads applied cause large deformations, errors appear unless we keep track of the changing shape of the problem. The permanent (large) displacements will be represented by a new formulation that takes account of the different soil compressibilities in different directions (anisotropy). We will combine this rather fundamental work with the new computational method to create a general tool that can handle many problems in geomechanics (particularly those that pose real difficulties for the FEM).