Thermodynamic-based constitutive model of hot dry rock after cooling

Abstract

The residual strength of hot dry rock (HDR) after thermal shock of cooling (TSC) is crucial for maintaining wellbore integrity in geothermal extraction. Notably, the residual strength of most HDR exhibits a non-monotonic variation as original temperature increasing. While damage mechanics can simulate the monotonic degradation of residual strength, accurately modeling this non-monotonic behavior remains challenging. To address this issue, this paper proposes a thermodynamic-based constitutive model that captures this non-monotonic behavior by considering the mutual influence between thermal and stress fields. By employing Onsager reciprocal relations, a constraint matrix for thermodynamic dissipation is established, providing a theoretical basis for constructing the thermodynamic constitutive model considering the mutual influence among physical fields. The model can not only simulate non-monotonic variations in residual strength but also monotonic. By adjusting the mutual influence coefficient of physical fields $\tilde{k}$, the model can simulate the transition from monotonic to non-monotonic behavior. This approach offers a new method for addressing more realistic and complex situations in practice engineering where both monotonic and non-monotonic behaviors coexist, overcoming limitations of assuming coexistence of "negative" and "positive" damage in traditional damage mechanics models. This model serves as a computational tool for wellbore stability analysis in geothermal extraction and provides different avenues for studying rock behavior in multi-physical fields.