A statistical model for assessing the risk of subsidence above abandoned mines.

Abstract

A statistical model for assessing the risk of subsidence in abandoned mines is presented. The model is based on the relationship that exists between the frequency and location of subsidence events and the physical conditions of the ground. These conditions are described by geological, mining, and physical variables. The model suggests the existence of regions in the multi-dimensional space of variables which can be associated with increases, or decreases, in the frequency of subsidence events. Regions associated with an increase in the frequency of subsidence events correspond to regions of higher risks, and vice versa. Risk is assessed by expressing the limits of these high and low risk regions in the space of variables, and by expressing the degree of membership of blocks of land within any of these regions. The theoretical framework for the model is extracted from discriminant analysis. The high and low risk regions are associated with two populations: (1) blocks which according to their ground properties are not likely to develop subsidence, and (2) blocks which are likely to develop subsidence. Risk is quantified by the probabilities of membership of blocks of land into any of these two populations. These membership probabilities are computed using discriminant functions which use geostatistical estimates of the ground's properties and the number of subsidence events registered in each of the blocks. Risk maps are produced by displaying membership probabilities contoured in appropriate levels. The model was applied in two urban areas: Penn Hills, near Pittsburgh, and Scranton/Wilkes-Barre in northeastern Pennsylvania. At Penn Hills, the risk maps generated were sensitive to the equal-covariance and multi-normality assumptions of the model. The risk map generated under a non-parametric approach resulted in closer agreement and comparable to an independently generated risk map. Both maps succeed in locating recent subsidence events inside medium and high risk zones in seven out of eight cases. In the Scranton/Wilkes-Barre area, the risk maps generated under the equal-covariance and the multi-normality assumptions, as well as that generated under the non-parametric approach, reproduce well the present degree of subsidence in the area.