Crack growth and the thermoelastic behavior of rocks

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Abstract
The effect of cracks on the elastic moduli of rocks has received considerable attention in recent years; the role of crack growth in the brittle creep and dilatant deformation of rocks has also been extensively studied. However, less attention has been paid to the effects of cracks on other thermoelastic constants of rocks, such as their thermal expansion coefficients, and to the deformation resulting from the growth of cracks in rocks containing internal stresses. These effects have been studied experimentally and discussed in qualitative terms, but quantitative theories relating thermoelastic behavior to the presence or growth of cracks are lacking. A thermodynamic approach can be used to calculate changes in stress, pore volume, and thermoelastic properties for a sample of brittle rock containing open, growing cracks and subjected to changing temperature, pore pressure, and macroscopic strain. The analysis is based upon the relation between the flow of energy to an advancing crack edge and the crack tip stress intensity factors. The effect of cracks on the thermal expansion of aggregates is illustrated by applying the results of this analysis to a simple model of a monomineralic aggregate of uniaxial grains. Changes in the temperature of the aggregate from an initial stress‐free and crack‐free state lead to grain‐scale thermal stresses, which cause the growth of cracks. The resulting change in the linear thermal expansion of the material has the same sign as the temperature change; the magnitude of the change can be a significant fraction of the difference in linear thermal expansion between the a and c directions for the individual grains. These results, though not directly applicable to real rocks, indicate the importance of such effects in rocks and suggest the potential value of the thermal expansion properties of rocks as indicators of their history. Similar calculations show that the relaxation of internal stresses in rocks by crack growth can lead to strains comparable to those resulting from stress changes of tens to hundreds of bars, although the strain resulting from the growth of a single crack will not usually be resolvable. The common belief that the growth of cracks in internal stress fields cannot lead to a shortening or volume reduction may be incorrect in some cases, because of the grain‐scale elastic inhomogeneity and interactions between cracks and pores which are present in most rocks.

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