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Contractional sandbox experiments that simulate crustal accretion and direct shear tests both provide direct data on the amount of work required to create faults (W prop) in granular materials. Measurements of force changes associated with faulting reveal the work consumed by fault growth, which can be used to predict fault growth path and timing. Within the contractional experiments, the sequence and style of early faulting is consistent for the range of sand pack thicknesses tested, from 12 to 30 mm. Contrary to expectations that W prop is only a material property, the experimental data show that for the same material, W prop increases with sand pack thickness. This normal stress dependence stems from the frictional nature of granular materials. With the same static and sliding friction values, incipient faults initiated deeper in the sand pack have larger shear stress drops, due to increased normal compression, σ n. For CV32 sand, the relationship between W prop and σ n, calculated from the force drop data as W prop (J/m 2) = 2.0x10-4 (m) σ n (Pa), is consistent with the relationship calculated from direct shear test data as W prop (J/m 2) = 2.4x10-4 (m) σ n (Pa). Testing of different materials within the contractional sandbox (fine sand and glass beads) shows the sensitivity of W prop to material properties. Both material properties and normal stress should be considered in calculations of the work consumed by fault growth in both analog experiments and crustal fault systems.

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We employ work optimization to predict the geometry of frontal thrusts at two stages of an evolving physical accretion experiment. Faults that produce the largest gains in efficiency, or change in external work per new fault area, ΔWext/ΔA, are considered most likely to develop. The predicted thrust geometry matches within 1 mm of the observed position and within a few degrees of the observed fault dip, for both the first forethrust and backthrust when the observed forethrust is active. The positions of the second backthrust and forethrust that produce >90% of the maximum ΔWext/ΔA also overlap the observed thrusts. The work optimal fault dips are within a few degrees of the fault dips that maximize the average Coulomb stress. Slip gradients along the detachment produce local elevated shear stresses and high strain energy density regions that promote thrust initiation near the detachment. The mechanical efficiency (Wext) of the system decreases at each of the two simulated stages of faulting and resembles the evolution of experimental force. The higher ΔWext/ΔA due to the development of the first pair relative to the second pair indicates that the development of new thrusts may lead to diminishing efficiency gains as the wedge evolves. The numerical estimates of work consumed by fault propagation overlap the range calculated from experimental force data and crustal faults. The integration of numerical and physical experiments provides a powerful approach that demonstrates the utility of work optimization to predict the development of faults.

Along the San Bernardino strand of the San Andreas fault (SAF) and across the eastern California shear zone (ECSZ), geologic slip rates differ from those inverted from geodetic measurements, which may partly be due to inaccurate fault connectivity within geodetic models. We employ three-dimensional models that are mechanically compatible with long-term plate motion to simulate both fault slip rates and interseismic surface deformation. We compare results from fault networks that follow mapped geologic traces and resemble those used in block model inversions, which connect the San Jacinto fault to the SAF near Cajon Pass and connect distinct faults within the ECSZ. The connection of the SAF with the San Jacinto fault decreases strike-slip rates along the SAF by up to 10% and increases strike-slip rates along the San Jacinto fault by up to 16%; however, slip rate changes are still within the large geologic ranges along the SAF. The insensitivity of interseismic surface velocities near Cajon Pass to fault connection suggests that inverse models may utilize both an incorrect fault geometry and slip rate and still provide an excellent fit to interseismic geodetic data. Similarly, connection of faults within the ECSZ produces 36% greater cumulative strike-slip rates but less than 17% increase in interseismic velocity. When using overconnected models to invert GPS for slip rates, the reduced off-fault deformation within the models can lead to overprediction of slip rates. While the nature of fault intersections at depth remains enigmatic, fault geometries should be chosen with caution in crustal deformation models.