The numerical modeling of heterogeneities by the finite element method in 3D setting

Abstract

The paper proposes a variant of the algorithm for 3D numerical simulation of the rock mass stress-strain state in the vicinity of structural heterogeneities by the finite element method. Modeling of the stress-strain state is used, among other things, when analyzing the fractures in the rock mass, which can occur as a breakage or a shear along the weakening planes. The rock massif has a block structure, where the boundaries of various-scale blocks are structural disturbances of different orders. The surface planes of structural heterogeneities usually have complex geometry and spatial orientation, so the most adequate results can be obtained by 3D modeling of the disturbed rock mass. Besides, it is important to take into account the type of the stress-strain state, which can be not only gravitational, but also gravitational-tectonic, including horizontal loading of the rock mass. Accounting these features allows obtaining the most adequate geomechanical model of the studied object. For this purpose, the authors have studied and analyzed the existing approaches to modeling heterogeneities in the rock mass, including using the Goodman contact element, and developed its 3D modification. A mining engineer needs to have a handy tool that allows creating and editing a geomechanical model, taking into account mining plans and related sections. The model navigation, edition of its individual blocks to specify geology and creation of local sub-models make it necessary to use structured meshes of finite elements. Modification of the model with the introduction of contact elements entails the creation of an unstructured mesh, which complicates further manipulations with it. To solve this problem, a special zero element was developed, which allows saving a structured mesh format when implementing a contact element. This zero element, like the contact element, has zero thickness, and its nodes have averaged strength characteristics of adjacent blocks of the undisturbed rock mass. The result of these studies is a tool that allows creating 3D models of the rock mass stress-strain state, taking into account its structural heterogeneities and preserving the regular structure of the finite element mesh.