A new mathematical tool for analyzing the fracturing process in rock: Partial symmetropy of microfracturing

5Citations
Citations of this article
4Readers
Mendeley users who have this article in their library.
Get full text

Abstract

We have shown that the symmetry of fracturing process in a macro-scale can be quantified by using the concept of symmetropy (an entropy-like measure of symmetry). Here we extend this approach to examining the symmetries in a range from small (partial) scales to larger (whole) scales: this approach is called partial symmetropy (PS). To check its applicability, we consider one illustrative example, the temporal change of the spatial patterns of acoustic-emission events in a well-documented rock fracture experiment. Our results are summarized as follows: (i) the PS enables us to distinguish the nucleation phases from the other phases such as the pre-nucleation and the propagation phases; (ii) the variation of the PS shows that the fracturing process is associated with a type of phase transitions from the subcritical state to the critical state; (iii) the scale dependence of the PS reveals the presence of the sandwich structure that consists of order and non-order in the evolution of the fracturing pattern; (iv) within the framework of non-extensive Tsallis entropy we develop the PS concept, and show that the degree of non-extensivity on a large scale increases immediately after the nucleation. The results shown in the present paper are not obtained by taking the traditional fractal approach, nor using only a simply symmetropy. We therefore propose that the PS is a useful tool to providing a strategy for describing qualitatively the phase changes in the observed fracturing process. © 2009 Elsevier B.V. All rights reserved.

Cite

CITATION STYLE

APA

Yamasaki, K., & Nanjo, K. Z. (2009). A new mathematical tool for analyzing the fracturing process in rock: Partial symmetropy of microfracturing. Physics of the Earth and Planetary Interiors, 173(3–4), 297–305. https://doi.org/10.1016/j.pepi.2009.01.010

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free