Fault slip in a mining context
Fowkes, N.D. and Mason, D.P. and Napier, J.A.L.
(2006)
Fault slip in a mining context.
Mathematics in Industry Study Groups in South Africa > MISGSA 2006: University of the Witwatersrand (23rd - 27th January 2006).
Full text available as: Abstract/SummaryRecent articles on the broad range of computational and analytic techniques currently used to investigate excavation collapse are reported. Advances in physical models are also described. Simple models for determining fault slip due to underground and surface excavations and structures are investigated. Problem Statement The violent failure of rock in deep-level mining operations has been an ongoing deterrent to the optimal extraction of valuable mineral resources in many countries. In South Africa this problem has plagued the gold mining industry for many years and has been the subject of extensive research efforts for at least four decades. Although production from South African gold mines has now decreased significantly, considerable economic interest is currently vested in the extraction of large-scale chrome and platinum reserves concentrated in the Bushveld Complex situated west and north of Pretoria in South Africa.
One of the pioneering efforts to explain the mechanics of rockbursts was made in the early 1960’s by N.G.W. Cook (Cook, 1965). He proposed a simple stability analysis in which the unstable region is considered to be coupled to an “external” loading region. By comparing the effective load-deformation response of the external region (loading “stiffness”) to the load-deformation characteristics of the “internal” region one can state whether the “system” will respond in a stable or an unstable manner. This approach is essentially a simplified form of more detailed analyses of stability examining changes in the structure of the partial differential equations of motion at a point of instability (for example, Rice, 1976, Vermeer, 1990, Gajo et al., 2004). Further elaborations of these concepts have been made by considering numerical models of fault slip and accompanying earthquake cycles that depend on the nature of the fault cohesion breakdown physics and on friction laws that are dependent on the rate of fault slip (Rice, 1993, Lapusta and Rice, 2003).
Other significant approaches to the problem of rapid rock failure and ongoing cycles of failure, associated with earthquakes or intermittent volcanic eruptions, have been numerous attempts to link these phenomena to theories of critical phenomena and the determination of critical exponents that are associated with first and second order phase transitions. This has been linked closely to the concept of “self-organized criticality” that can be used to explain the universality of power law statistics that apply to a wide variety of phenomena including the frequency-magnitude relationships associated with earthquakes and deep mine seismic activity (Bak et al., 1987, Tang and Bak, 1988, Anghel, 2004). A linked consideration is the predictability of earthquakes that might be related to “log-periodic” oscillations that are imposed on acoustic emission or seismic activity records prior to failure (Moura, 2005).
For the purposes of the study group, it is suggested that a review should be made of the intrinsic formulation of the equations of motion at a point of failure transition and that it should be assessed whether a Lie/ Symmetry analysis could be applied to these systems when the equation structure is in transition.
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