Generation of random stress tensors

Abstract

To correctly incorporate stress variability in the increasingly widespread application of probabilistic‑related rock mechanics analyses, a robust approach for random stress tensor generation is essential. However, currently, the customary scalar/vector approaches to the generation of random stress tensors, which violate the tensorial nature of stress, together with other existing quasi‑tensorial applications that consider the tensor components as statistically independent variables, may yield biased results. Here, we propose a multivariate random vector generation approach for generating random stress tensor components that is based on tensorial techniques and which incorporates inter-component correlation. Differences between the proposed fully tensorial and existing quasi-tensorial approaches are demonstrated by examining the distributions of the tensors generated using both approaches, and the efficacy and transformational consistency of the proposed fully tensorial approach are investigated by generating random tensors in different coordinate systems. Our results suggest application of the existing quasi-tensorial approach (which ignores covariance) leads to greater scatter in generated tensors than does application of the proposed fully tensorial approach (which includes covariance). Additionally, the transformational consistency of the proposed fully tensorial approach allows generation of random tensors in any convenient coordinate system, while the existing quasi-tensorial approach only permits generation of random tensors in a particular coordinate system. The proposed fully tensorial approach provides a method that will assist with probabilistic-related analyses of rock engineering structures.