Optimally Extracting the Asymptotic Features of Rock Fracture Process from Mode-I and Mixed-Mode Tests Under Three-Point Bending
Authors: Xiong Q. , Lin Q. , Gao Y. , Hampton J. C. 
Published: September 2022

ABSTRACT:
This paper consists of a series of attempts and discussions on the data analysis approaches to investigate and extract the asymptotic features in the rock fracture process. The rock fracture discussed here were under mode-I and mixed-mode loadings. We examine the process of creating the rock fracture from the artificial notch, as well as the following rock fracture propagation processes. The analysis consists of the spatial-sequential feature, and the topological triggering-triggered feature of the energy releases from the rock fracture process, as well as the change of data variance on the delineated rock fracture path through the DIC (digital image correlation) observation. The spatial-sequential feature shows a comparatively stable behavior during the rock fracture propagation stage. The growth of the rock fracture within this stable stage is produced from the naturally induced rock fracture; It can be fundamentally different from that induced from an artificial notch, especially in a mode-I test. The topological feature cross-validates this difference. The change of the data variance of the DIC delineated rock fracture path suggests similar conclusions, i.e., an erratic feature at the initial rock fracture path followed with stable propagation. The combination of the analyses may provide an approach to investigate the fracture toughness in rock materials more naturally/spontaneously, i.e., the influence of artificial notch is reasonably minimized or qualitatively characterized, and the rock fracture is induced from the preceding induced rock fracture.

1. INTRODUCTION
The behavior of rock mass under stress are of broad interesting for a variety of issues, for instance, the natural disasters like earthquake, tsunami, debris flows, and geological and civil engineering projects. As the rock mass behavior is strongly related to the natural discontinuities within, the theory of fracture mechanics has been extensively used for rock mechanics studies. Within fracture mechanics, the crack length and the fracture toughness are two key elements for the fracture propagation criterion, under the simplification of LEFM (linear elastic fracture mechanics (Asem et al., 2021)). The materialization of LEFM into the rock material requires the size-effect law so that the laboratory observations can be extrapolated to the prediction of large-scale structures. The laboratory observations of three-point bending tests on the beam samples with central or eccentric notch settings are usually used for measuring the parameter of fracture toughness. Such theoretical structure of LEFM requires as assumption that the non-linear region surrounding the crack tip, i.e., the rock fracture process zone (FPZ), to be small and surrounded by linear behavior. Many studies have reported the rock FPZ can be of non-negligible size (Nolen-Hoeksema and Gordon, 1987; Petit and Barquins, 1988; Wong and Xiong, 2018) and can show spatial temporal and evolution features (Xiong et al., 2021).