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ROCKENG09: Proceedings of the 3rd CANUS Rock Mechanics Symposium, Toronto, May 2009 (Ed: M.Diederichs and G.Grasselli)

Numerical Assessment of Factor B in Mathews’ Method for Open Stope Design
R.P. Bewick, P.Eng., M.A.Sc.
Golder Associates Ltd., Sudbury, ON, Canada

P.K. Kaiser, P.Eng., Ph.D.
Center for Excellence in Mining Innovation (CEMI), Sudbury, ON, Canada

ABSTRACT: A numerical modellingstudy was completed to derive the Factor B curves proposed by Mathews et al. (1980) & Potvin et al. (1988) to further understand the relationship between joint orientation and stope stability. A continuum finite element modelling approach which included joint elements was adopted to back-analyse and assess the influence of various joint properties and stress states on the shape of the Factor Bcurve. This paper provides insight into mechanisms affecting the shape of the Factor B curve. A better understanding of factors controlling the B-value potentially reduces some of the conservatism in the design of open stopes and other underground excavations.

1 INTRODUCTION The stability graph method developed by Mathews et al. (1980), later modified by Potvin et al. (1988), Clark (1998), Suorineni(1999a, 1999b, 2000), and Capes et al. (2005) amongst others, is an empirical approach that has been developed for open stope design based on the depth of mining, rock mass quality and stope span. The stability graph is a plot of stope hydraulic radius versus the modified stability number, N’, which is defined as:

N ' = Q ' xAxBxC

(1)

where Q’ = the modified Q rock mass classification (Bartonet al., 1974); A = the rock stress factor; B = the joint orientation adjustment factor – Factor B; and C = the gravity adjustment factor. The Factor B is used to account for the influence of the relative orientation of dominate jointing relative to the excavation surface (stope wall or back) being assessed. The relative angle is referred to as the angle β. It was included as a modifying factor inN’ because the influence of joint orientation relative to an excavation surface is not considered in the Q classification system (Suorineni, 1999a). The original Factor B proposed by Mathews et al. (1980) was based on expert discussion which considered change of behaviour based on the direction of loading with respect to the inclination of a plane of weakness (Figure 1). The revised Factor B curvewhich was based on a larger number of case histories after Potvin et al. (1988) is presented on Figure 2. The assumptions behind each of the curve’s respective shape are also presented in these figures.

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ROCKENG09: Proceedings of the 3rd CANUS Rock Mechanics Symposium, Toronto, May 2009 (Ed: M.Diederichs and G.Grasselli)

Figure 1: Factor B curve after Mathews et al. (1980) andunderlying assumptions regarding its shape.

Figure 2: Factor B curve after Potvin et al. (1988) and underlying assumptions regarding its shape.

The main difference between the curves proposed by Mathews et al. and Potvin et al. is between β angles of 0° and 45°. Mathews et al. (1980) assumed that there was a potential stability improvement as the dominant joint set becomes parallel to theexcavation boundary as a result of potential ‘beam’ behaviour. Potvin et al. (1988) observed that most structurally controlled failures occurred along joints having a shallow angle (0° to 30°) with respect to the exposed excavation boundaries. The interpretation by Potvin et al. was that the smaller the difference in the dip of the major critical joint set and the excavation boundary, the greater theprobability of having rock bridges fail and joints separate by blasting, stress/relaxation, or by other intersecting joint sets. Both the Factor B curves of Mathews et al. and Potvin et al. were scaled assuming that joints oriented at an angle of 90° to the stope boundary had no to little effect on stability as failure is difficult to mobilize (B = 1.0). Potvin et al. suggested an adjustment of 0.2...