Fracture dynamics of solid materials: from particles to the globe

Abstract

Solid materials have been used extensively for various kinds of structural components in our surroundings. Stability of such solid structures, including not only machinery, architectural and civil structures but also our solid earth, is largely governed by fracture development in the solids. Especially, dynamic fracture, once occurring—quite often unexpectedly—evolves very rapidly and can lead to catastrophic structural failures and disasters like earthquakes. However, contrary to slowly enlarging fractures that can be recognized spatio-temporally in detail, it is extremely difficult to trace dynamically growing fractures even in controlled laboratory experimental conditions, and its physics still remains unexplored. This theme issue introduces and summarizes recent advancements in our understanding of the widespread topics of dynamic fracture of solids from well-assorted perspectives, involving laboratory experiments, simulations and analytical methods as well as field observations, with the common background of mechanics of fracture. Multi-scale subjects range from fracture of metals at atom or particle levels to disastrous rock bursts in deep gold mines and detection of unique signals before devastating fracture such as large, global-scale earthquakes. This article is part of the theme issue ‘Fracture dynamics of solid materials: from particles to the globe'.

A coupled finite difference‐spectral boundary integral method with applications to fluid diffusion in fault structures

“…We seek to re‐examine a prevailing assumption in the modeling of fluid migration within damage zones or the frictional interface of a fault. It is often assumed that the fluid in fault structures can be reduced to 1D flows along the fault given the greater permeability of the fault structure in comparison to the surrounding host rock 47 . Many studies addressing fluid‐induced seismicity have been based on this very presumption.…”

“…The inset of Figure 12A provides a schematic of the problem, where the injection line source is denoted by the red line and the gray magnitude represents the pressure gradient. According to the analytical solution given in Uenishi, 47 the pore pressure change along the fault is given by $$\Delta p(x,t) = q p_G(x, t)$$ with $$$$\begin{equation} p_G(x,t) = \frac{1}{\sqrt {2 \pi }} \frac{l_0(t)}{c \beta }{\left(e^{-{\left(\frac{|x|}{l_0(t)}\right)}^2} - \sqrt {\pi } \frac{|x|}{l_0(t)} \text{erfc}{\left(\frac{|x|}{l_0(t)}\right)}\right)}, \end{equation}$$$$where $$q$$ is the fixed volume rate during injection, $$l_0 = \sqrt {4 c t}$$ is the diffusion distance. We normalize the numerical solution by the maximum value of the analytical solution, that is, $$p_{\text{SBI-FD}}/\max (p_{\text{analytical}})$$.…”

“…It is often assumed that the fluid in fault structures can be reduced to 1D flows along the fault given the greater permeability of the fault structure in comparison to the surrounding host rock. 47 Many studies addressing fluidinduced seismicity have been based on this very presumption. (e.g., refs.…”

“…The inset of Figure 12A provides a schematic of the problem, where the injection line source is denoted by the red line and the gray magnitude represents the pressure gradient. According to the analytical solution given in Uenishi, 47 the pore pressure change along the fault is given by Δ𝑝(𝑥, 𝑡) = 𝑞𝑝 𝐺 (𝑥, 𝑡) with…”