Fluid-filled Fracture Propagation with a Phase Field Approach in Subsurface by Employing Nonlinear Strain Limiting Models and Enriched Galerkin Methods

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The project aims to investigate the way in which pressurized and fluid-filled cracks or fractures spread through subsurface materials. In porous materials such as soils and rocks, the flow of the fluids through the material's pores can force significant deformations (such as cracks and fractures) to occur in the solid porous media. These poromechanical interactions are crucial to many important problems such as tunnel construction, subsidence, dam or levee failure, and CO2 sequestration. The classic mathematical model governing the spread of these deformations is formulated by coupling linear elasticity or poroelasticity with deformation systems. However, one of the major disadvantages of classical linear elasticity models is that strain values are linearly proportional to stress values. Thus, it contradicts the assumptions of the model, and it may not accurately predict realistic scenarios. This project focuses on establishing the nonlinear strain limiting model, a new class of theoretical model. The advantage of the nonlinear strain limiting models over classical linearized models is that strain remains bounded even if the stress tends to infinity, which is critical for fluid-filled fractures. The new model will be extended to consider poroelasticity. Next, the poroelasticity model will be coupled with a phase field approach to implement quasi-static fluid-filled fracture propagation. Moreover, the novel enriched Galerkin (EG) finite element approximations will be employed in the project to address several crucial issues for numerical discretization. It is well known that classical Galerkin finite element methods generally do not guarantee local mass conservation, which could lead to non-physical oscillation. EG methods will be investigated to overcome these challenges, and their stability and convergence for the poroelasticity system will be analyzed. The findings will then be used to develop a forecasting tool to predict the path of quasi-static fracture propagation and will be utilized to evaluate and validate the performance of these new models.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.