Multivariate distribution model for stress variability characterisation

Influence of water on deformation and failure of gypsum rock

“…Data on triaxially deformed gypsum are scarce and it was therefore interesting to compare our new results with existing data on Volterra gypsum. However, due to the strong impact of sample size on strength (Paterson and Wong, 2005, Bozorgzadeh et al, 2017, Gao et al, 2018, we were unable to perform this comparison using the results of Brantut et al (2011), despite the similarities with our data. We instead present in Figure 23 a comparison of the dry failure envelopes of branching selenite gypsum (from this study) and of Volterra gypsum based on the study of Olgaard et al (1995), who used a comparable sample size.…”

Correlation Between Fracture Network Properties and Stress Variability in Geological Media

“…It is worth emphasizing that we propose a novel tensor‐based framework, which processes stress data in an integrated form and does not violates their inherent tensorial nature (Gao & Harrison, , ), for characterizing stress variability in fractured rocks. This formalism aims to improve the conventional decoupled analysis, which customarily separates the information of stress magnitude/orientation and may lead to biased interpretations as also has been recognized by Hudson and Cooling ().…”

“…We obtain the stress field from the FEMDEM simulation in which all components of the second‐rank Cauchy stress tensor at each element node are determined. We analyze the stress data using the recently developed tensor‐based mathematical formulations (Gao, ; Gao & Harrison, , ), which overcome the drawbacks of conventional decoupled analysis of stress magnitude and orientation information (further discussions are in Text S2 and Figure S5).…”

“…The variability of stress tensor data can be adequately represented by the variability of their distinct tensor components in a multivariate statistics manner (Gao & Harrison, ). The overall dispersion of a stress field can thus be described by its effective variance—a widely used concept in the field of multivariate statistics for group variability comparison (Peña & Rodríguez, ).…”

Influence of boundary constraints on stress heterogeneity modelling

“…However, stress is tensor in nature formed by six distinct components. The conventional decoupled analysis of principal stress magnitude and orientation, which was usually adopted in the literature [38][39][40][41], may lead to biased assessment results [29,31,34,36,42,43].…”