Mapping the surface intensity of discontinuities in rock slopes using stochastic geometry

Slope stability in rock masses can be controlled by weak zones associated with discontinuities, their orientation, opening, persistence, spacing, and intensity. Since the intensity of discontinuities on rock slope surfaces can be complex to estimate, conventional methods of analysis assume homogeneous distributions by setting a constant value determined from compass and tape measurements in some sampled sectors of the slope. To account for the non-homogeneous nature of the rock mass on the entire slope surface, we propose to combine spatial statistics, data collection with short-range photogrammetry, and three-dimensional image analysis techniques to estimate and map discontinuity intensity. Thus, the novelty of this proposal is a different conceptualization of the phenomena, which in turn allows using new ideas and tools for its analysis. Given that it is not possible to predict where discontinuities occur, the discontinuities are formulated as geometric objects with random locations. Thus, they can be modelled through the stochastic geometry theoretical framework. It is assumed that the discontinuities are lines, and a sequence of points for representing each of them is used to make possible some computations. To accomplish this, each discontinuity set, defined as a set of lines, is represented by a spatial point pattern. Where the intensity function varies spatially, the non-parametric kernel is used to estimate the intensity, and the results are mapped for validation. The methodology is applied to two rock masses near Bogotá, Colombia, with promising results for discontinuity intensity slope zoning. These findings are relevant for application in road infrastructure and mining projects.