A finite element mesh optimization method incorporating geologic features for stress analysis of underground excavations

Application of numerical modeling in civil and mining engineering projects not only increases the effectiveness of analysis but also improves the results of the analysis. However, due to complexity of model generation and analysis, it is still a time consuming process. The finite element method requires a discretization, or a mesh, to solve the partial differential equations representing a problem with essential boundary conditions. The finer and denser the mesh is, the more time and computer memory consuming is the analysis. Therefore, one of possible ways is to simplify the analysis by reducing the mesh density while maintaining the quality of solution. In the previous work carried out by Zsaki and Curran. (Int J Numer Anal Met 2005; 29(4): 369–393) a mesh optimization strategy was developed using a cost function by considering only the geometries of excavations. In this current work, the optimization strategy developed previously is improved by including the mechanical properties representing the geological features. Among different rock properties, Young’s modulus (E) and Poisson’s ratio (μ) were considered. The effect of each of these properties on the mesh optimization was investigated and it was concluded that E has the most significant effect on the results of stress analysis of dissimilar rocks. Subsequently, an expanded cost function incorporating E was formulated. Finally, an application of expanded cost function was demonstrated using a few representative case studies.

► Most finite element models contain more elements than warranted. ► Mesh optimization removes extra elements via simplifying boundary geometry based on material properties such as Young’s Modulus. ► The optimized models maintain solution quality at a region of interest. ► The solution times are reduced by three to four-fold for the optimized models.