Based on cusp-type catastrophe theory, a sample rock–rock model for studying the pillar rockburst mechanism is presented in this paper. It is shown that the stiffness ratio, K, of the roof and floor to the pillar plays an important role in the outbreak of instability. Additionally, simple formulae for the deformation jump and the energy release are derived. Based on the assumption that there exists a proportional relationship between the number of microseismic events and microfractured elements, the theoretical microseismic event rate produced by the double rock sample, loaded in series under uniaxial compression, is obtained. Using a newly developed numerical code, RFPA2D, the progressive failure process and associated microseismic behavior of the twin rock samples are simulated, which shows that the spatial distribution of microseismic events develops progressively from disorder at the initial loading stage to order prior to the main shock. The numerically simulated results also confirm that a soft roof and floor promote an unstable failure or collapse of pillars, while a stiff roof and floor can lead to a stable failure of pillars. Additionally, the simulated results reproduce the deformation jump and the energy release that occur during a pillar rockburst. It is demonstrated that the proposed model properly simulates the pillar failure process.

Analytical and Numerical Study on the Pillar Rockbursts Mechanism

A cusp catastrophe model is developed for slip-buckling slope by catastrophe theory, and the formulations of the necessary and sufficient conditions for instability of the slope are presented. It is found that different regions (II, III and IV in Fig. 4) in the control space divided by the bifurcation set correspond well to the primary, secondary and tertiary creep phases. The corresponding discriminate expressions for the slope in each of these three creep phases are given. The applicability of the cusp catastrophe model is tested by applying the equations to the Bawang Mountain landslide, located 5 kilometers above the Ertan hydroelectric power station along Yalong River in China. The method gives reasonable results.

A cusp catastrophe model of instability of slip-buckling slope

Using catastrophe theory to describe railway system safety and discuss system risk concept

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Industrial mining heritage and the legacy of environmental pollution in the Derbyshire Derwent catchment: quantifying contamination at a regional scale and developing integrated strategies for management of the wider historic environment

Risk state changes analysis of railway dangerous goods transportation system: Based on the cusp catastrophe model

A brief introduction to catastrophe theory is presented, within the context of geological application, and a fundamental problem with a critical axiom of the theory noted. Implications for the application of this theory to modeling geological processes are noted and a solution to the problem proposed. The new approach is examined with reference to a model for sediment transport on the continental slope.

The geological implications of steady-state mechanisms in catastrophe theory

G-EXEC is a data-analysis and management system developed since 1972 by the Institute of Geological Sciences (IGS). System concepts incorporated in its design, including integration, modularity and generalization, enable the system to be (1) transported from computer to computer, (2) updated rapidly, (3) operated on any data set, and, of primary importance, (4) used by noncomputeroriented sedimentologists. Control of the system by the user proceeds through near-English commands which are translated into FORTRAN by the G-EXEC controller. The implementation of G-EXEC at the IGS enables the sedimentologist to employ programs for organization, manipulation, retrieval, statistical analysis and display of the data.

An analysis and management system suitable for sedimentological data

In an area of marginal farming, trace element distribution associated with lead, fluorite and baryte mineralization is important to the farmer because of the high infertility rate of the livestock and contamination of plant produce leading to the subsequent failure of the farming economy. Therefore sampling of superficial sediments was undertaken over the mineralized Carboniferous Limestone of North Derbyshire above the medieval lead and the modern fluorite workings. Twenty-seven elements were analyzed using emission spectrophotometry and subsequently compared with the geochemistry of the underlying bedrock. Discrepancies which occur are attributed to the glacial and periglacial action during the Wolstonian and Devensian glacial episodes.

John M. Cubitt

Papers

The geological implications of steady-state mechanisms in catastrophe theory

An analysis and management system suitable for sedimentological data

Trace element distribution in the superficial deposits of Northern Derbyshire, England

A classification study of shales in Kansas using electron-spin resonance spectroscopy

Data-base management software for computer applications on small computers