Analysis of Fault Growth and Linkage Using Work Minimization

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To predict fault growth it is important to understand crack linkage under shear. If fault growth is governed by maximizing mechanical efficiency, a fault system will accommodate deformation either via slip on existing faults or via the growth of a new fault, depending on which is energetically easiest. Consequently, whether small flaws or cracks will link to form a larger crack depends on whether the energetic gain in efficient connection of cracks exceeds the work required to create the linking crack. Using the principle of work minimization, this research project numerically investigates how faults link and grow with two approaches: 1) parametric investigation of crack coalescence in order to test and calibrate the application of work minimization and 2) simulation of the evolution of the San Jacinto fault in southern California. The first approach uses mechanical models in a suite of parametric and stochastic investigations to evaluate the configuration of new fault growth that would both maximize efficiency of the system and are energetically favored to develop, i.e. the work cost is less than the efficiency gained. The stochastic models will incorporate different distributions of flaws in a sample under a variety of loading conditions to explore the effect of differing degrees of anisotropy. Furthermore, an investigation of the scaling of mechanical efficiency from the lab to regional scales will facilitate the second approach employed in the project. The second approach uses three-dimensional models to investigate the work associated with the evolution of a stepover between the Clark fault and the Coyote Creek fault, which are part of the San Jacinto fault in southern California. Numerical models will simulate several stages in the interpreted fault development at this stepover and assess the evolving mechanical efficiency. The study will (a) provide insight into the mechanical efficiency of fracture growth and coalescence, including the impact of anisotropy and the scale of the models; and (b) analyze the development of the San Jacinto fault through the growth and linkage of two fault segments based on the principle of work minimization.Tectonic plate boundaries in the Earth contain many active faults that slip in devastating earthquakes and contribute to building large mountain ranges. The size of potential earthquakes depends on the length of the fault; the larger the fault, the bigger the potential earthquakes. While the behavior of faults is understood, how they grow is not. Within the laboratory, scientists observed that within rocks, smaller cracks link to form fault surfaces. Since many rocks already have abundant small cracks but not all rocks contain faults, we need to understand the conditions that contribute to crack linkage and eventual fault development. This project examines how cracks link to form faults by applying the principle of work minimization. This principle implies that the Earth is lazy. Within a lazy Earth, cracks will only link up if the energetic cost of linking the cracks is less than the energetic benefit of having the cracks linked up. In the case of geologic faults, the benefit is that linked up cracks may more readily accommodate slip and the cost is the energy need to break the rock at the linkage. The project will develop tools to predict crack linkage that are based on work minimization. Once these tools are developed, they will be applied to the San Jacinto fault in southern California, which has a recent history of linkage of two segments. If the model predictions match the interpreted history of the San Jacinto fault then this tool may be of use for investigating other regions of the world and predicting future fault evolution.