We are undertaking a fundamental curiosity driven project that has immediate implications for public safety. The intellectual merit rests in development of an analytical technique to model laterally unconstrained shear displacement of a gravity loaded block. The public safety issue concerns safety of the Corps of Engineer's Folsom Dam. Completed in 1955, the structure is located just east of Folsom, California, and holds back over one million acre-feet of water. Between Folsom Dam and downtown Sacramento, the American River flows through one of the most densely populated regions in California. Recent calculations made with original surface topographic data have produced some unacceptably low factors of safety for seismic scenarios involving independent sliding of the monoliths, in which case there might be little or no lateral constraint on a given block. Co-P.I. Richard Goodman is a member of the Folsom Dam Outlets Modification Project external review panel, giving us unique access to existing topographic data on surface profiles beneath the Folsom monoliths. This enables us to approximately duplicate actual surface profiles in test samples, as well as to use the topographic data to analytically estimate the stability of the dam. There is currently no general analytical model for laterally unconstrained sliding, even if full topographic information is available for the entirety of both sliding surfaces (as in the case of Folsom Dam). We are developing a mathematical sliding model that takes into account the unconstrained boundary conditions, offering a prediction of the 3-D failure (dilation) route. We are utilizing the properties of functionals and examining relatively simple tests on rough surfaces to develop an analytic energy-based equation describing unconstrained sliding. Minimizing virtual work and setting constraints which reflect the interaction of the surfaces between which contact points are sliding allows the calculation of the lowest energy path of each sliding point along the surface. This methodology is being extended over the candidate set of likely contact points to describe the net motion of a rough block sliding over a rough surface, which is not a trivial problem because the contacting set of asperities changes with displacement. The equation will be empirically refined and extended to the semi-constrained case. Experimental verification of the proposed model is being carried out using a simple but entirely new device, which allows virtually unconstrained lateral motions in the principle directions. This device is being incorporated into the specialized acoustic emission (AE) shear testing facility built for a previous NSF grant. The upper loading platen for the normal load has embedded within 24 Glaser/NIST-type high-fidelity AE sensors which yields full quantitative time-domain waveforms from local movements on the sliding surfaces. The overdetermination of the present problem allows for extremely accurate source location in 3-D space and inversion for the detailed source kinematics expressed as a moment tensor. Besides the life safety issues, broader impacts include the furthering of our understanding of frictional behavior of unconstrained blocks. This will provide a tool for many other researchers in a variety of fields. Basic knowledge of the interaction and behaviors of interacting asperities will grow out of the inversion of AE data for source kinematics, which has important implications for fault rupture modeling and energy release estimates. This work is a direct outgrowth of the P.I.'s previous work. The P.I. works closely with Berkeley's Center for Underrepresented Engineering Students (CUES), in addition to the SUPERB and CAMP programs. We are presently using the Berkeley Edge to assist in finding qualified graduate students for the proposed project. The Berkeley Edge, partially funded by the National Science Foundation, is a recruitment, retention, and advancement program for traditionally underrepresented minority graduate students in science, mathematics, and engineering. In addition, the P.I. directly involves undergraduate students in all aspects of his research program (4 currently), and supervises students with backgrounds in electrical engineering, physics, and IEOR. This interdisciplinearity forces all the students to grow technically and to respect other disciplines and ways of approaching problems.
