Abstract
The Mathews-Potvin stability method is widely used in the Canadian mining industry as a starting point to determine the maximum dimensions of mine stopes. However, it cannot be applied to inclined (more frequently encountered) mine stopes without conducting numerical modelling to obtain the stress factor A, defined as a function of the ratio of unconfined compressive strength of intact rock to the induced principal stress on the exposed stope walls. The need to conduct numerical modelling significantly limits the application of the Mathews-Potvin method. In addition, given its empirical nature and main application for preliminary design, it is deemed undesirable to conduct numerical modelling, especially elaborate modelling. Alternatively, theoretical methods can provide a much simpler and quicker way to estimate stresses around stopes and the corresponding stress factors. Over the years, a large number of studies have been conducted to estimate stresses around openings excavated with various cross-sections. However, theoretical or graphical solutions remain unavailable for mine stopes that typically consist of horizontal floor and roof, and two parallel inclined walls (hangingwall and footwall). To remedy this situation, a series of numerical simulations is first performed for openings with vertical and inclined walls, including typical stopes commonly encountered in underground mines. A group of empirical solutions is then formulated to estimate the induced principal stresses at the roof centre and mid-height of the stope walls. The validity and predictability of the proposed solution have been verified using additional numerical simulations. The proposed solution can thus be used to calculate stresses and the resultant stress factors A around typical mine stopes with any inclination angle and height to width ratio, under any in-situ stress state, without conducting numerical modelling.
Highlights
Ground stability is a challenging issue frequently faced by rock engineers
The results show that the proposed semi-empirical solution can be used to evaluate the induced principal stresses at the roof centre and mid-height of the wall around typical mine stopes
The well-known Mathews-Potvin method is an important design tool for mining engineers. The application of this method requires the determination of the induced stresses around inclined mine stopes using numerical modelling, as few graphical or theoretical solutions are available for such purposes
Summary
Ground stability is a challenging issue frequently faced by rock engineers. The trend towards larger and more powerful equipment to improve productivity requires larger underground openings. A second calibration of these four geometric functions by considering the wall inclination angle leads to the following equations: Equations [5] to [10] constitute the proposed solution for estimating the elastic stresses at the roof centre and midheight of the hangingwall and footwall around typical mine stopes These equations are independent of the stope depth and rock mass strength.
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