Theoretical models of acoustic emission in rocks with different heating regimes

Abstract

Mechanisms of the emergence of mechanical stresses in rocks with different regimes of their heating are studied. Theoretical models of acoustic emission induced by these stresses are justified and analyzed.Introduction. The reason for the emergence of acoustic emission (AE) in rocks is the formation of new cracks or the growth of already existing cracks under the action of mechanical stresses. If such stresses are induced by temperature effects, they are usually called the thermal stresses and the corresponding emission is called the thermoacoustic emission.One possible mechanism of the emergence of thermal stresses induced by a temperature gradient on the edges of cracks separating structural elements of the geomaterial was considered in [1]. That paper also justified the corresponding theoretical model of thermoacoustic emission (TAE) and the thermoemission memory effect arising in the course of cyclic heating of rocks with the maximum temperature being increased from one cycle to another [2]. That model, however, was not perfect because it could not give a clear explanation for the experimentally observed fact of higher values of TAE parameters in polymineral media than in monomineral media; moreover, the model did not explain the influence of the rate of the temperature increase in the sample on TAE parameters [2, 3].The present paper offers justification of TAE theoretical models whose specific feature is the allowance for thermal stresses induced by the difference in the thermal coefficients of volume expansion (TCVE) of individual mineral grains forming the rock and by the nonuniformity of the temperature field in the sample. Thermoacoustic Emission in a Uniform Temperature Field in the Examined Sample.If there are no temperature gradients in a geomaterial consisting of elements with different TCVEs, the only parameter determining TAE is the current temperature. The greater the difference between the current temperature and the initial temperature (at which the absence of mechanical stresses inside the mineral grains and on their boundaries is assumed), the greater the values of local stresses and the higher the probability of the growth of existing cracks and the formation of new cracks; as a consequence, the higher the degree of the acoustic emission. As the value of thermal stresses is proportional to the temperature difference, the derivatives of the total acoustic emission N Σ with respect to temperature can be assumed to have close values for different rates of temperature variation.If the rocks are considered as ideally elastic and brittle media and the redistribution of stresses due to the formation of microscopic defects is neglected, then the growth of the existing cracks and the formation of new cracks (accompanied by acoustic emission) during cyclic heating of the rocks occur only on exceeding the maximum temperature reached during the entire process, which determines the mechanism of the thermoemission memory effect.Model No. 1. To obtain a qualitative estimate of TAE, we consider a simple mod...

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