Coupling Between Weathering and Fracture: Finite Element Modeling of Granite Weathering Using Cohesive Elements

Abstract

ABSTRACT: This research examines the initiation of fracture propagation by weathering and explores how an escalation in fracture density accelerates weathering rates. By integrating cohesive zone elements into an ABAQUS FEM software through user-defined subroutines, we simulate arbitrary fracture paths and examine the effect of weathering on stress redistribution and fracture propagation in the bedrock. The weathering rate is scaled based on the magnitude of fracture opening displacements, which control fluid exchanges. Simulations in a topographical setting reveal that weathering significantly affects cohesive fracture propagation, particularly in the upper 30 meters where weathering accelerates both fracture propagation and the depletion of reactant mass, in particular unweathered biotite. These findings underscore the potential of the proposed methodology for predicting the interplay between weathering and fracture development, and thus explaining the formation of landscapes as a result of climatic events and ensued environmental processes. 1 INTRODUCTION Fractures play a crucial role in enhancing the connectivity of pore spaces, thereby significantly increasing rock permeability. This facilitation of fluid flow is instrumental in accelerating mineral dissolution processes, as evidenced by Hu et al. (2011). Fracture systems increase the specific surface of the bedrock, which escalates the likelihood of chemical reactions (St. Clair et al., 2015), thereby altering rock structure through the interplay of chemical, mechanical, and hydrological processes. Such transformations are pivotal in promoting further weathering, as was demonstrated in studies that document the coupling between bedrock weathering and fracture propagation (Navarre-Sitchler et al., 2015). Reversely, weathering enhances rock permeability (Worthington et al., 2016). A simplified homogenization model was recently introduced (Lebedeva and Brantley, 2023) to explain the impact of reactive flow in fractured rock. Despite these developments, the feedback mechanisms between weathering and bedrock porosity evolution via microcracks and metric fractures remain under-explored. In order to address this gap, Cohesive Zone (CZ) elements are inserted within the Finite Element Method (FEM) model initially developed by Xu et al. (2022). The fracture represented by the CZ elements, comparable in length to the volume elements, are significantly larger than the microcracks depicted in the damage variable of the homogenization model implemented in the Finite Elements (FEs), offering a novel approach to examining the intricate feedback effects between weathering and porosity evolution in bedrock. The homogenization approach is summarized in Section 2. The coupling between the CZ tractionseparation law and the continuum variables of the homogenization model is explained in Section 3. Numerical results are presented in Section 4, and conclusions are drawn in Section 5.