Analysis of stress-strain relationship of brittle rock containing microcracks under water pressure

Brittle rock contains many microcracks under natural conditions. The theoretical models of brittle rock containing microcracks under the effect of water pressure, axial stress, and confining pressure have not yet been fully elucidated. Therefore, a new model based on a wing crack model and an improved Weibull model was established to analyse the effects of water on the progress of crack initiation, growth, and coalescence. In this improved wing crack model, the water pressure was introduced as a variable, and the analytical stress-crack relationship considering the water pressure was revealed. The relationship between the stress and strain was also obtained. The results revealed that the cracks more readily propagated and failure occurred under higher water pressure. The proposed theoretical curves agree with the experimental data obtained under various water pressures. The effects of water pressure with the change of the crack inclination angle, friction coefficient, crack initiation length, and wing crack length on the wedging force, internal stress, and stress-strain relationship were analysed. The analytical results were validated by experiments. The effect of water pressure on the stress-strain relationship was quantified using an analytical equation whereby the most disadvantageous angle cases, that is, cases wherein the wedging force was maximum, with zero friction were determined.