Notes on Numerical Modeling in Geomechanics

William Pariseau obtained his B.S. degree in Mining Engineering at the University of Washington (Seattle) following the geological option and subsequently earned a Ph.D. in Mining Engineering at the University of Minnesota with emphasis on rock mechanics and with a minor in applied mathematics. Prior to his Ph.D., he obtained practical experience working for the City of Anchorage, the Alaska Department of Highways, the Mineral Resources Division of the U.S. Bureau of Mines (Spokane), the Anaconda Copper Co. in Butte, Montana, the New York-Alaska Gold Dredging Corp. in Nyac, Alaska. He served in the United States Marine Corps (1953-1956). He maintained a strong association with the former U.S. Bureau of Mines, first with the Pittsburgh Mining Research Center and later with the Spokane Mining Research Center. He is a registered professional engineer and has consulted for a number of commercial and government entities. Currently, he is a professor emeritus and former holder of the Malcolm McKinnon endowed chair in mining engineering at the University of Utah. He joined the Department in 1971 following academic appointments at the Montana College of Science and Technology and the Pennsylvania State University. He has been a visiting academic at Brown University, Imperial College, London, and at the Commonwealth Science and Industrial Research Organization (CSIRO), Australia. He and colleagues have received a number of rock mechanics awards; he was recognized as a distinguished university research professor at the University of Utah in 1991. In 2010, he was recognized for teaching in the College of Mines and Earth Sciences with the Outstanding Faculty Teaching Award. The same year, he was honored by the Old Timers Club with their prestigious Educator Award. He was honored as a Fellow of the American Rock Mechanics Association in 2015.

1. Introduction. 2. Interpolation Over a Triangle. 3. Derivatives of Interpolation Functions. 4. Linear Interpolation Over a Quadrilateral. 5. Derivatives for a Linear Displacement Quadrilateral. 6. Element Equilibrium and Stiffness. 7. Global Equilibrium and Global Stiffness. 8. Static Condensation and a 4CST Element. 9. Equation Solving. 10. Material Nonlinearity. 11. Time Integration. 12. Finite Element Seepage Formulation. 13. Hydro-mechanical Coupling. 14. Boundary Element Formulations. 15. Distinct Element Formulations. 16. Conclusion. Appendix A: Review of Fundamental Concepts. Appendix B: Study Questions. Appendix C: Question Replies.