Adaptive refinement of finite element meshes for geotechnical analyses

Ashraf El-Hamalawi, Cambridge University, Geotechnical Engineering Group


The popularity of the finite element method (FEM) stems from the ease with which engineering problems can be analysed. However, the approximations upon which the FEM is based, requires the identification of the various types of associated errors. This thesis is therefore concerned with minimising discretization errors, by developing a complete adaptive mesh refinement (AMR) system suitable for use in geotechnical engineering applications.

AMR comprises an error criterion to determine regions where discretization errors are high and when this is so, a refinement procedure may be implemented to produce a new mesh. A new error criterion was developed based on one of the superconvergent patch recovery methods, and pore pressures were incorporated as well. The newly developed criterion was found to be ultraconvergent, providing a convergence rate which is approximately two orders higher than the global rate.

For a given problem, a preliminary analysis was performed to establish the regions requiring refinement based on the error criterion. A newly developed enrichment algorithm was then used to generate the refined mesh, and the problem re-analysed until a prescribed tolerance was satisfied. Alternatively, an unstructured mesh generator using a modified form of the Delaunay triangulation algorithm was used to remesh the domain, creating a new optimal mesh. Remeshing was found to be more robust than enrichment. The mesh refinement system has been tested on several problems and has been found to improve results significantly. The Mandel consolidation problem was used to demonstrate the importance of including pore pressures in the a-posteriori error criterion, without which, regions of high pore pressures would have not been refined. AMR also played an important role in accurately predicting the bearing capacity factors of plane strain footings on single and multi-layered undrained Tresca soils. The improvement was less pronounced for the undrained axisymmetric case, where locking occurred, although to a lesser degree than would normally be expected.