A Modified Nonlinear Mohr–Coulomb Failure Criterion for Rocks Under High-Temperature and High-Pressure Conditions

In deep, geologically complex environments characterized by high in situ stress and elevated formation temperatures, the mechanical behavior of rocks often transitions from brittle to ductile, differing significantly from that of shallow formations. Traditional rock failure criteria frequently fail to accurately assess the strength of rocks under such deep conditions. To address this, a novel failure criterion suitable for high-temperature and high-pressure conditions has been developed by modifying the Mohr–Coulomb criterion. This criterion incorporates a quadratic function of confining pressure to account for the attenuation rate of strength increase under high confining pressure and a linear function of temperature to reflect the linear degradation of strength at elevated temperatures. This criterion has been used to predict the strength of granite, shale, and carbonate rocks, yielding results that align well with the experimental data. The average coefficient of determination (R2) reached 97.1%, and the mean relative error (MRE) was 5.25%. Compared with the Hoek–Brown and Bieniawski criteria, the criterion proposed in this study more accurately captures the strength characteristics of rocks under high-temperature and high-pressure conditions, with a prediction accuracy improvement of 1.70–4.09%, showing the best performance in the case of carbonate rock. A sensitivity analysis of the criterion parameters n and B revealed notable differences in how various rock types respond to these parameters. Among the three rock types studied, granite exhibited the lowest sensitivity to both parameters, indicating the highest stability in the prediction results. Additionally, the predictive outcomes were generally more sensitive to changes in parameter B than in n. These findings contribute to a deeper understanding of rock mechanical behavior under extreme conditions and offer valuable theoretical support for drilling, completion, and stimulation operations in deep hydrocarbon reservoirs.