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This paper introduces a methodology to quantify the significance of changes in certain rock mass characteristics. The developed method can be applied to all data sets that consist of parameters classified into categories. The tools are developed from the principles of engineering geological rock mass characterisation and statistical theory. The basic approach is the construction of the so-called length matrix, which allows for the combination of observed changes in parameter categories and their change in lengths in a sequence of observations. The concept of the order of characteristic changes is introduced to construct the length matrix of two or more combined categories, which is essential to assess the significance of different rock mass characteristic categories, their consistency and persistence. By using the mathematical formulae introduced in this paper, four experimental models can be produced for engineering purposes. The first model is the frequency matrix, which gives the change length frequencies between different categories and is only valid in the range of observed data. The second model is the probability matrix, which describes the generic length probability of significant rock mass characteristic categories. The third model is the transition probability matrix, which predicts the generic change dependencies of significant categories. The last model, the model of multiple sequences, identifies probabilistically the two- or three-dimensional change consistencies of significant rock mass characteristic categories. The data sets of fracture intensity categories in the flat-lying limestone series of Birecik dam bedrock (Turkey) were used for verification and demonstration of applications. The first example shows the identification of the significant patterns of fracture intensity categories by applying the probability matrix. The model was verified in the second example and the patterns of fracture intensity categories were reliably predicted by applying a transition probability matrix. In the last example, the fracture intensity categories of dam bedrock were partitioned by applying the model of multiple sequences. |
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