Modeling of Fracture Process under Water Pressure in Crack using XFEM

Abstract

The coupled hydro-mechanical process has played an important role in design and safety assessment in many engineering fields, such as dam engineering, geotechnical engineering and environmental engineering. Mathematical models for coupled hydro-mechanical process have been dominated by the finite element method (FEM) using equivalent continuum approaches. The aim of this paper is to present a new model to simulate the fracture process with hydro-mechanical interaction by the extended Finite Element Method (XFEM), which is a local partition of unity (PU) enrichment method. The proposed model includes: 1) the expression of the discontinuous displacement across the propagating crack; 2)the crack model for the mechanical behavior of cracking concrete; and 3) the description of the water flow in propagating crack.

In XFEM, problem-specific functions can be introduced to construct a proper approximation space. For example, the discontinuous displacement across the crack can be represented by enriching the Heaviside function to the nodes whose supports cut by the crack. The description of discontinuities is no longer dependent of mesh boundaries. So for simulation of moving discontinuities the re-meshing work can be avoided.

The cohesive crack model which originated from the fictitious crack model by Hillerborg et al is employed for the description of concrete cracking. In this model the deformation caused by cracking is assumed to concentrate into the discontinuity. The discrete approach is intuitively appealing for the crack is introduced explicitly. More importantly this direct reflection of the change in topology makes it possible to describe the water flow in cracks in a straightforward manner.

The modified cube’s law is used to compute the water flow state during the cracking process. Considering that the crack opening displacement (COD) changes during fracture process, the flow state will change with both time and solid boundary conditions. For convenience the computational fluid dynamics (CFD) solution is achieved by iteration. For the whole fluid-structure system, a loose-coupling technical is adopted in this paper. This approach solves the coupled system also using an iteration strategy, in which the loop of the CFD solution followed by computational structural dynamics (CSD) solution is repeated until convergence is achieved. So a dual-iteration system is included in the solve scheme.