Extending the Mathews stability graph for open–stope design

Abstract

The Mathews method of predicting open-stope stability was first proposed in 1980. The initial stability graph was based on a limited number of case studies, primarily from deep, North American, steeply dipping open stopes in strong rocks of medium to good quality. Since then new data have been added by various practitioners to modify, update and validate the method and support its use as a preliminary open-stope design tool.The original Mathews method has been extended with use of a significantly increased database of mining case histories. The format of the Mathews stability graph has been changed to reflect the broader range of stope geometries and rock mass conditions now captured within the database. The extended database now contains in excess of 400 case histories.Logistic regression has been performed on this larger database to delineate and optimize placement of the stability zones statistically. Isoprobability contours have been generated for all stability outcomes. The advantage of the logistic regression lies in its ability to minimize the uncertainties reflected in the method through the use of maximum likelihood estimates. The risks associated with use of the Mathews method can now be quantified and the true statistical significance of the stability zones understood.