Jessica McBeck

Growth by Optimization of Work (GROW)

Growth by Optimization of Work (GROW) is a new modeling tool that automates fracture initiation, propagation, interaction, and linkage. GROW predicts fracture growth by finding the propagation path and fracture geometry that optimizes the global external work of the system. This implementation of work optimization is able to simulate more complex paths of fracture growth than energy release rate methods. In addition, whereas a Coulomb stress analysis determines two conjugate planes of potential failure, GROW identifies a single failure surface for each increment of growth. GROW also eliminates ambiguity in determining whether shear or tensile failure will occur at a fracture tip by assessing both modes of failure by the same propagation criterion. Here we describe the underlying algorithm of the program and present GROW models of two propagating faults separated by a releasing step. The discretization error of these models demonstrates that GROW can predict fault propagation paths within the numerical uncertainty produced by discretization. Model element size moderately influences the propagation paths, however, the final fault geometry remains similar between models with significantly different element sizes. The propagation power of the fault system, calculated from the change in work due to fault propagation, indicates when model faults interact through both soft- and hard-linkage. First program to model fault growth through work optimization.Fault growth by work minimization as alternative to Coulomb failure planes.GROW models fault initiation, propagation and interactions.Work optimization detects soft- and hard-linkage.

Energy budget and propagation of faults via shearing and opening using work optimization

We present numerical models of faults propagating by work optimization in a homogeneous medium. These simulations allow quantification and comparison of the energy budgets of fault growth by shear versus tensile failure. The energy consumed by growth of a fault, Wgrow, propagating by in-line shearing is 76 % of the total energy associated with that growth, while 24 % is spent on frictional work during propagation. Wgrow for a fault propagating into intact rock by tensile failure, at an angle to the parent fault, consumes 60 % of the work budget, while only 6 % is consumed by frictional work associated with propagation. Following the conservation of energy, this leaves 34 % of the energy budget available for other activities and suggests that out-of-plane propagation of faults in Earths crust may release energy for other processes, such as permanent damage zone formation or rupture acceleration. Comparison of these estimates of Wgrow with estimates of the critical energy release rate and earthquake fracture energy at several scales underscores their theoretical similarities and their dependence on stress drop.

Work Optimization Predicts the Evolution of Extensional Step Overs Within Anisotropic Host Rock: Implications for the San Pablo Bay, CA

Recent geophysical imaging indicates that the Hayward Fault hard links to the Rodgers Creek Fault at 5m depth within the San Pablo Bay, CA, suggesting that earthquakes may be able to rupture continuously through the fault network. To investigate fault propagation, interaction, and linkage in segmented fault networks, including those within the San Pablo Bay, we simulate the development of two idealized, underlapping faults within an extensional step over at seismogenic depths using work optimization. We test the sensitivity of fault growth to strength anisotropy, material heterogeneities, and initial fault geometry. The optimal faults propagate toward each other until linking with the other fault at its tip and form a single hard-linked transverse fault. These faults propagate with relatively high propagation power or rate of efficiency gain. Less efficient faults form wider basins and develop with reduced propagation power. Models with initial fault geometries that more closely match the shallowly imaged Hayward and Rodgers Creek faults suggest that the faults link at seismogenic depths if a mapped segment of the Rodgers Creek that extends into the San Pablo Bay is currently inactive. Predictions of average slip rate, slip per earthquake, and earthquake magnitude from these models closely match paleoseismic estimates. The hard linkage of the Hayward and Rodgers Creek faults imaged in the near-surface, and predicted by these models, increases local seismic hazard by increasing the upper limit of throughgoing earthquakes to M 7.6.