Rock fractures are of considerable engineering significance in fields such as hard rock tunneling and fractured rock hydrology. Fracture traces – the 2d manifestations of fractures at exposed rock surfaces – can provide valuable information about the rock mass. Of particular interest is estimating the distribution, or the mean and variance, of fracture size based on inevitably censored and biased field observations. This paper describes a novel and powerful tool – termed an image window – that can aid in the quantitative interpretation of fracture trace data. Image windows are used for the construction of subfields corresponding to regions of the rock mass that define the loci of fractures for certain types of intersection between fractures and the sampling window. Counts of the various types of fracture intersection on exposures can then be used to help infer the size characteristics of fractures in the rock mass in a meaningful way. The method can be applied in one or two dimensions towards estimating size characteristics of fractures traces, or, in three dimensions, to infer the size characteristics of fractures embedded in a 3-d rock mass and exposed at a 2-d sampling surface. We show how to construct image windows in one or two dimensions, and we introduce the construction of image windows in three dimensions.
Rock fractures are significant in several engineering fields, including hard rock tunneling and fractured rock hydrology; and fracture traces – the 2d manifestations of fractures at exposed rock surfaces - can provide useful information about the fractures in the rock mass. During site investigation or, e.g., tunnel excavation, the limited exposures of traces are used for estimation of the mean and variance of trace length, and other statistical information about the fracture and fracture trace populations. Such inferences must take into account unavoidable biases and censoring of the data obtained from the rock exposure [1–7].
This paper describes a novel and powerful approach to the interpretation of fracture trace data, using what the author terms image windows. The method automatically corrects for sampling biases and the effects of censoring. In addition to deriving information about the underlying population of fracture traces, we show how the technique can be used to derive information about the distributional parameters of fracture size in the 3d rock mass, not just the trace length.