Grain-Scale Subcritical Fracture in Rock: Statistical Mechanical Modeling and Discovery of Two Physically Distinct Subcritical Fracture Modes

Part I: An equilibrium statistical mechanics framework for investigating microfracture in rocks is proposed and tested. The framework consists of three elements: A) A simplified energy-based model describing atomic- to grain-scale mechanical and thermal rock fracture, B) A macroscopic, grain-scale statistical mechanics model that postulates existence of (thermomechanical) equilibrium, where (over appropriate timescales) rates of grain-scale microfracture (nominally) match rates of microfracture healing, and C) A resultant theoretical prediction connecting measurable fracture-induced acoustic emission (AE) with rock temperature. Comparisons of theoretical, temperature-dependent AE with AE observed during cyclic rock heating and cooling experiments support the validity of the model. Importantly, the results suggest that, for a given rock type - whether in pristine volumes devoid of grain-scale cracks or within volumes containing such cracks - the number of microfractures within the volume can be reasonably estimated as a calculable function of temperature and confining pressure, regardless of the rock's geological and weathering history.
PART II: The second part of the dissertation recasts traditional dimensional correlations between experimentally measured (tensile-driven) subcritical fracture speed, da / dt, and imposed stress intensity, KI, in dimensionless form. To the best of our knowledge, all existing correlations are well-described by the so-called (dimensional) Charles crack growth law: da / dt=AKIn where a, t, A, KI and n are, respectively, crack length, time, a rock-dependent (constant) prefactor, stress intensity, and subcritical crack growth index. Puzzlingly, however, in granite and similar fine-grained rock, experimentally determined n's are anomalously large, on the order of 40 to 150.
To tackle this puzzle, we apply dimensional analysis to existing (and difficult to obtain) Charles law correlations, recasting these in dimensionless form. While this practice is de rigueur in, e.g., fluid mechanics, physics, and heat transfer, it is new in the area of fracture mechanics. Importantly, recasting Charles' law in appropriate dimensionless form exposes two distinct regimes of subcritical fracture in rock: A) A slow growth regime, extant at stress intensities below a well-defined threshold, in which sub grain-scale cracks grow slowly along grain boundaries; and B) A fast subcritical growth regime, extant at stress intensities above the threshold, in which cracks grow intermittently across multiple grains. We show that each regime is well-captured by dimensionless Charles' law correlations, where slow regime n's are on the order of 1, and fast regime n's are clustered around approximately 4 to 6.
Crucially, these findings will allow development of improved, predictive crack growth models, suitable for predicting and interpreting geologically ubiquitous subcritical fracture in surface and near-surface rock, both on earth and on extraterrestrial bodies.