Time-dependent closure data in deep hard-rock mines appears to be a useful diagnostic measure of rock behaviour. Understanding this behaviour may lead to enhanced design criteria and modelling tools. In this paper we investigate the use of a time-dependent limit equilibrium model to simulate historical closure profiles collected in the South African mining industry. Earlier work indicated that a viscoelastic model is not suitable to replicate the spatial behaviour of the closure recorded underground. The time-dependent limit equilibrium model available in the TEXAN code appears to be a useful alternative as it can explicitly simulate the on-reef time-dependent failure of the reef. A key finding in this paper is that the model gives a much better qualitative agreement with the underground measurements. For both the model and actual data, the rate of time-dependent closure decreases into the back area. Calibration of the constitutive model nevertheless led to some unexpected difficulties, and the element size plays a significant role. It was also noted that the simulated closure is complex as it reflects the combined result of a number of elements failing at different times. The closure rate does not decay according to a simple exponential model. In conclusion, explicit simulation of the fracture zone in the face appears to be a better approach to simulate the time-dependent behaviour in deep hard-rock stopes. The calibration of the limit equilibrium model is very difficult, however, and further work is required.


Several research studies have been conducted to investigate the use of continuous stope closure as a diagnostic measure of rock mass behaviour in the deep gold mines of South Africa (e.g. Malan, 1995; Napier and Malan, 1997). The rock mass undergoes significant time-dependent deformation in some geotechnical areas, and the closure data is useful for identifying different geotechnical areas and areas prone to face-bursting (Malan et al., 2007). The value of continuous closure measurements was also demonstrated for the platinum industry. An example is shown in Figure 1 to illustrate the significant ‘creep’ component recorded in some of the areas. For the gold mines, it was proposed that the data may be useful to identify remnants that may be safely extracted. A difficulty faced in these early studies was that no numerical tool could simulate the time-dependent rock mass behaviour on a stope-wide scale. It was hypothesised that the time-dependent behaviour in the hard rock gold mines is caused by timedependent fracturing and other inelastic processes, such as gradual slip on parting planes. In the platinum mines, the face fracturing is less intense and the behaviour is most likely dominated by the time-dependent failure of the crush pillars. The commonly used elastic modelling programs cannot simulate this behaviour and the simulated convergence is simply a function of the mine geometry, depth, and elastic constants.

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