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Fluid-driven subsurface fractures interact with a variety of heterogeneous elements in the surrounding environment, including fluid-filled pores, material discontinuities, and other cracks and fissures. Their complex propagation is governed by fluid-solid interactions, characterized by nonlinear and coupled dynamics between the flow and the fracture. This thesis focuses on addressing a variety of such problems related to fluid-driven fractures or hydraulic fractures within increasingly realistic situations. Initially, we examine the post-shut-in behavior of a hydraulic fracture in the viscous regime, where viscous dissipation is the dominant form of energy dissipation. Subsequently, we investigate the propagation of a hydraulic fracture driven by displacement flows of two immiscible fluids and the propagation of a hydraulic fracture across a material discontinuity.When pressurized fluid is injected in a homogeneous infinite solid medium, a simple penny-shaped fracture forms and grows in the direction of the minimum confining stress. This type of fracture offers a representative focus for experimental investigations in a laboratory environment, serving as a powerful tool to understand the various physical mechanisms governing the growth of the fracture. Throughout the thesis, we vary different material properties of the solid media and fracturing fluids, including the Young's modulus of the solids, the viscosity of the fluids and, the flow rate of the injection. Gelatin serves as the clear brittle elastic solid medium, that allows us to observe and record the fracture growth because of its transparent nature. In the first study, we examine the post-shut-in behavior of a penny-shaped hydraulic fracture in the viscous regime. We measure both the fracture aperture and radius, noting that the fracture radius continues to grow slowly over time even after injection stops, until it reaches a saturation point.Next, we investigate the injection of an immiscible fluid at the center of a liquid-filled fracture. We study the displacement of the interface between the two fluids and its effect on fracture propagation. We conduct experiments and derive scales to predict the growth dynamics of the fracture. Finally, we present an experimental investigation into the propagation of hydraulic fractures in layered brittle media in the toughness regime, where the creation of new fracture surfaces is the dominant means of energy dissipation. We report that the relative stiffness of the initiating layer significantly influences fracture propagation: A fracture that forms in a soft layer remains trapped, whereas a fracture that originates in a stiffer layer experiences a rapid fluid transfer into the neighboring softer layer upon reaching the interface. Additionally, we present a quantitative model that captures the competing effects of elastic deformation and fracture propagation and report good agreement with experiments.

Scour of rock is a challenging and interesting problem that combines rock mechanicsand hydraulics of turbulent flow. On a practical level, rock erosion is a critical issue facingmany of the world’s dams at which excessive scour of the dam foundation or spillway cancompromise the stability of the dam resulting in significant remediation costs, if not directpersonal property damage or even loss of life. The most current example of this problem isOroville Dam in Northern California where massive scour damage to both the service andemergency spillways during the flood events of February 2017 led to the evacuation of morethan 188,000 people living downstream of the dam.This research is specifically aimed at developing the ability to numerically evaluate rock-water interaction, building upon the experimental and analytical work by George and Sitar. The focus is on producing simulation techniques capable of consid-ering the interaction between three-dimensional polyhedral rock blocks interacting with fluidsuch that the complex shape of the blocks is captured in both the fluid and solid numericalmodels. Accounting for the rock block geometry and orientations is essential in capturingthe correct kinematic response.To this end, a three-dimensional, open-source program to generate the fractured rockmass was developed based on a linear programming approach. The application runs onApache Spark which enables it to run locally, on a computer cluster or on the Cloud. Theprogram automatically maintains load balance among parallel processes and can be scaledup to meet computational demands without having to make any changes to the underlyingsource code. This enables the program to generate real-world scale block systems containingmillions of blocks in minutes.The second stage of this research effort focused on developing a new open-source DiscreteElement Method (DEM) program capable of analyzing the kinematic response of fracturedrock. The contact detection computations for DEM are also based on a linear programmingapproach such that similar logic and data structures can be used in both the block generationand DEM code, though the DEM code is written in C++. The program was validated against2analytical solutions as well as other numerical solutions and has been shown to accuratelycapture the kinematic response of three-dimensional polyhedral rock blocks.The DEM formulation was then extended to perform coupled fluid-solid interaction anal-yses by coupling it with the weakly compressible Lattice Boltzmann Method (LBM). Anew algorithm, which extends the partially saturated approach, was developed to considerthree-dimensional convex polyhedra moving through the fluid domain. The algorithm usesboth linear programming and simplex integration for the coupling process. The LBM codeand the new fluid-solid coupling algorithm were validated against experimental data andthe capabilities of the new coupled DEM-LBM implementation were explored by evaluatingthe performance of the program in simulating several different problems involving fluid-solidinteraction. The results show that the program is able to accurately capture the interactionbetween polyhedral rock blocks and fluid; however, further performance improvements arenecessary to simulate realistic, field scale problems. Particularly, adaptive mesh refinementand multigrid methods implemented in a parallel computing environment will be essentialfor capturing the highly computationally intensive and multiscale nature of rock-fluid inter-action.

Scour of rock is a challenging and interesting problem that combines rock mechanics and hydraulics of turbulent flow. On a practical level, rock erosion is a critical issue facing many of the world’s dams at which excessive scour of the dam foundation or spillway can compromise the stability of the dam resulting in significant remediation costs, if not direct personal property damage or even loss of life. This interaction between the blocky rock mass and water is analyzed by directly modeling the solid and fluid phases—the individual polyhedral blocks are modeled using the discrete element method (DEM) while water is modeled using the lattice Boltzmann method (LBM). The LBM mesh is entirely independent of the DEM discretization, making it possible to refine the LBM mesh such that transient and varied fluid pressures acting on the rock surfaces are directly modeled. This provides the capability to investigate the effect of water pressure inside the fractured rock mass, along potential sliding planes, and can be extended to rock falls and slides into standing bodies of water such as lakes and reservoirs. Results show that the coupled DEM–LBM implementation is able to accurately capture the interaction between polyhedral rock blocks and fluid by analytically solving for the solid volume fraction in the coupling computations using convex optimization and simplex integration; however, further performance improvements are necessary to simulate realistic, field-scale problems. Particularly, adaptive mesh refinement and multigrid methods implemented in a parallel computing environment will be essential for capturing the highly computationally intensive and multiscale nature of rock–fluid interaction.