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Based on a review of the literature, a numerical model of the chip formation process in laminated rock formations has been developed. The model uses a finite element approach to simulate the anisotropic behavior of laminated rock formations. The finite element program has been developed with the assumption of two-dimensional plane strain. Anisotropic elements and dynamic loading are used to represent the actual penetration process of a bit tooth. An iteration method, using an incremental approach, has been applied for the continuous tooth penetration process. Displacements and axial loads have been modified after each iteration. The program provides quantitative information on stresses and displacements during the penetration process. Furthermore, bit deviations in laminated formations can be inferred.. Different rock strength characteristics have been employed on each side of the bit Bit tooth-rock interaction for various formation dips (from ()O to 9(0) of the Berea sandstone have been simulated and compared with experimental results. / Master of Science

A Thesis presented to the Department of Geophysics of the University of the Witwatersrand, Johannesburg / Violent failure of the rock surrounding under ground excavations forms a major hazard and obstacle in deep-level mining. (Abbreviation abstract) / AC 2018

M.Sc. (Geology) / Please refer to full text to view abstract

Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Earth and Planetary Science, 1982. / Microfiche copy available in Archives and Science / Bibliography: leaves 42-44. / by Harvey Hartman Haines. / M.S.

Thesis. 1975. Ph.D.--Massachusetts Institute of Technology. Dept. of Earth and Planetary Sciences. / Bibliography: leaves 190-202. / by Kate Hadley. / Ph.D.

Quantifying the influence of pressure on the effective elastic rock properties is important for applications in rock physics and reservoir characterization. Here I investigate the relationship between effective pressure and seismic velocities by performing inversion on the laboratory-measured data from a suite of clastic, carbonate and igneous rocks, using different analytic and discrete inversion schemes. I explore the utility of a physical model that models a natural fracture as supported by asperities of varying heights, when an effective pressure deforms the tallest asperities, bringing the shorter ones into contact while increasing the overall fracture stiffness. Thus, the model is known as the ?asperity-deformation? (ADM) or ?bed-of-nails? (BNM) model. Existing analytic solutions include one that assumes the host rock is infinitely more rigid than the fractures, and one that takes the host-rock compliance into account. Inversion results indicate that although both solutions can fit the data to within first-order approximation, some systematic misfits exist as a result of using the rigid-host solution, whereas compliant-host inversion returns smaller and random misfits, yet out-of-range parameter estimates. These problems indicate the effects of nonlinear elastic deformation whose degree varies from rock to rock. Consequently, I extend the model to allow for the pressure dependence of the host rock, thereby physically interpreting the nonlinear behaviors of deformation. Furthermore, I apply a discrete grid-search inversion scheme that generalizes the distribution of asperity heights, thus accurately reproduces velocity profiles, significantly improves the fit and helps to visualize the distribution of asperities. I compare the analytic and numerical asperity-deformation models with the existing physical model of elliptical ?pennyshape? cracks with a pore-aspect-ratio (PAR) spectrum in terms of physical meaning and data-fitting ability. The comparison results provide a link and demonstrate the consistency between the use of the two physical models, making a better understanding of the microstructure as well as the contact mechanism and physical behaviors of rocks under pressure. ADM-based solutions, therefore, have the potential to facilitate modeling and interpretation of applications such as time-lapse seismic investigations of fractured reservoirs.