Combining Graphic Data Analysis and Mechanical-Statistical-Physical Models in Overcoming the Uncertainties of Laboratory Rock Mechanics Investigation
Authors: Xiong Q. , Lin Q. , Wu C. , Hampton J. C. 
Published: September 2023

ABSTRACT
The rock fracture process is related with an extensive list of natural and engineering disasters which produce detectable energy releases. The energy releases from the rock fracture process displays the scale-invariant features in its organization, providing the foundation of understanding the field-scale problems through laboratory work. Our recent studies investigate the energy release organization from the rock fracture process through the graphic perspective. The graph theory belongs to a sub-branch of artificial intelligence research, though draws limited attention within the rock mechanics community. The energy release organization incorporates a network format through a statistical-physical model. Such network acts as the bridge between the discrete essence of individual energy releases and the desire to understanding the continuous mechanical process in time and space. Our recent investigations discovered the phenomena of magnitude clustering escalation and the unexpected correlation of focal mechanism for the event pairs through the network connections. We inspect the alternative network of high-order connections to formalize the rejection of uncertainty influence on the new discoveries and conclusions. Inspection of such alternative networks also naturally rejects the criticism of experimental detection limit of observing the specific energy release organizations. Such application of the graph theory concept to the data investigation have combined the mechanical, statistical-physical, and experimental features.

INTRODUCTION
The rock fracture process is related with an extensive list of natural and engineering disasters, e.g., slope stability, dam failure, tunnel collapse, human-induced and natural earthquakes. The rock fracture process at a wide span of scales produces detectable energy releases. Much fundamentally, these energy releases from a variety of rock fracture processes display the scale-invariant features in its organization (Bares & Bonamy, 2018; Bares, Dubois, Hattali, Dalmas, & Bonamy, 2018; J. Davidsen, Stanchits, & Dresen, 2007; Xiong, Lin, Gao, & Hampton, 2022), providing the foundation of understanding the field-scale problems through laboratory work. Indeed, if the research investigation is about the certain type of energy release organization, the scale-invariant features can be more fundamentally used for addressing the concern of laboratory-and-field-scale analogue over other types of precepted analogue conditions created at laboratory-scale. Our recent study (Xiong, Brudzinski, Gossett, Lin, & Hampton, 2023) has investigated the magnitude clustering as a specific type of energy release organization from the rock fracture process crossing laboratory- to field- and tectonic-scales. The magnitude clustering phenomenon displays very special clustering signature escalation once we interrogate the interevent magnitude correlation via a graphic network of them. This graphic network is built up by the topological connections indicating non-trivial spatial-temporal correlation that is violating the null hypothesis of Gutenberg-Richter law (J. Davidsen et al., 2017; Xiong & Hampton, 2020). This method has been used for the investigation of a variety of phenomena, i.e., seismology, volcanic activity, hydraulic fracturing, and laboratory rock fracture process (Jörn Davidsen et al., 2021; Karimi & Davidsen, 2021; Li, Smith, & Ross, 2021; Ilya Zaliapin & Ben-Zion, 2013a, 2013b). The observation of magnitude clustering signature escalation provides indicative information on the mechanism causing the general magnitude clustering phenomenon.