Abstract
Abstract. The stress variation induced by aquifer overdraft in sedimentary basins with shallow bedrock may cause rupture in the form of pre-existing fault activation or earth fissure generation. The process is causing major detrimental effects on a many areas in China and Mexico. Ruptures yield discontinuity in both displacement and stress field that classic continuous finite element (FE) models cannot address. Interface finite elements (IE), typically used in contact mechanics, may be of great help and are implemented herein to simulate the fault geomechanical behaviour. Two main approaches, i.e. Penalty and Lagrangian, are developed to enforce the contact condition on the element interface. The incorporation of IE incorporation into a three-dimensional (3-D) FE geomechanical simulator shows that the Lagrangian approach is numerically more robust and stable than the Penalty, thus providing more reliable solutions. Furthermore, the use of a Newton-Raphson scheme to deal with the non-linear elasto-plastic fault behaviour allows for quadratic convergence. The FE – IE model is applied to investigate the likely ground rupture in realistic 3-D geologic settings. The case studies are representative of the City of Wuxi in the Jiangsu Province (China), and of the City of Queretaro, Mexico, where significant land subsidence has been accompanied by the generation of several earth fissures jeopardizing the stability and integrity of the overland structures and infrastructure.
Highlights
The exploitation of subsurface resources, including freshwater aquifers, involves various environmental problems
Attention has been directed to the activation of pre-existing regional faults, as well as the possible generation of new fractures, caused by groundwater withdrawals
The activation of faults can trigger or induce a seismic activity (González et al, 2012). Another problem related to the fault activation is the creation of preferential pathways for fluid leakage
Summary
The exploitation of subsurface resources, including freshwater aquifers, involves various environmental problems. From a mathematical point of view, this method is not exact, because the elastic springs have displacements for any non-zero stress value, while, in nature, in case of a closed fracture the relative displacements are exactly zero Numerically, this method causes a strong ill-conditioning of the stiffness matrix (Ferronato et al, 2012), because of the introduction of the penalty coefficients. A way to compute such an orientation is based on an application of the criterion of “Maximum Plastic Dissipation” (Wriggers, 2006), which uniquely provides the direction of the shear stress as a function of the relative displacement so as to maximize the friction work By implementing this criterion in the derivation of the variational formulation, we get a numerical scheme that converges quadratically
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