Abstract

Campaigns to determine the state of in situ stress form an integral part of almost all underground rock engineering projects, but stress measurements obtained at different locations on a project site generally display spatial variability. However, there is no international consensus on techniques to objectively quantify such spatial variability, and the nebulous description of "stress heterogeneity" is often used. Our review shows that there are no consistent and universally agreed definitions for stress heterogeneity: the existing definitions are overly simplistic and lack a robust statistical treatment of variability in stress tensors. We demonstrate that stress data can be partitioned into homogeneous stress domains using the k-means algorithm in multivariate stress space, and the resulting clusters characterised using multivariate statistics. This allows us to propose a clear and unambiguous definition of stress heterogeneity. Our analyses also suggest that completely meaningful partitioning of stress data requires development of new algorithms and cluster validity indices.

Introduction

Campaigns to determine the state of in situ stress form an integral part of almost all underground rock engineering projects, and often comprise the application of relatively expensive measurement techniques such as hydraulic fracturing and borehole overcoring. The importance of such campaigns is heightened when designing critical infrastructure such as underground nuclear waste repositories, as these designs require high confidence in the stress state. When stress measurements are obtained at different locations on a project site, the results are generally found to display spatial variability. However, there is no international consensus on techniques to objectively quantify such spatial variability, and the nebulous description of "stress heterogeneity" is often used.

Although the term stress heterogeneity is commonly found in the civil, petroleum and mining related rock engineering literature on in situ stress, a consistent definition of it seems to be missing. Similarly, a formal means of characterising a stress field as either homogeneous or heterogeneous is also absent. For emphasis, we borrow the quote from the classical text The Logic of Chance, by John Venn: "What is meant by a homogeneous class? is a pertinent and significant enquiry, but applying this condition to any simple cases its meaning is readily stated" [1].

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