Ductile–brittle quantitative evaluation of rock based on post-peak properties under true triaxial stress

Abstract

To quantitatively evaluate the influence of high true three-dimensional stresses on the ductile–brittle behaviours of rock in deep underground engineering, a series of true triaxial compression tests with different stress levels were carried out on marble and four kinds of granite. The influences of true triaxial stress states (σ2, σ3) on the post-peak characteristics were analysed, and a new normalized ductile–brittle evaluation index was proposed based on post-peak energy conversion characteristics of rock under true triaxial stresses. The ductile–brittle behaviours of rock were divided into four qualitative levels, namely, ductile-brittleness, transitional, brittleness and super-brittleness, and the influences of true triaxial stress states on the ductile–brittle behaviours of rock were quantitatively investigated. The research shows that as σ2 increases or σ3 decreases (that is, the differential stress between σ2 and σ3 increases), the brittleness of rock increases, and its increase rate gradually decreases and tends to be stable, transforming from ductile-brittleness to transitional, brittleness and super-brittleness and resulting in super-brittleness being easily induced by low-σ3 and high-σ2 conditions. When the differential stress between σ2 and σ3 is small, the intrinsic characteristics of rock itself have an obvious influence on ductile–brittle behaviours. When the differential stress between σ2 and σ3 is large, all kinds of rocks can exhibit super-brittle behaviour. The change of stress controls the evolution of rock ductile–brittle behaviours, and high-stress controls rock brittleness. The rock brittleness under true triaxial stress is significantly higher than that under conventional triaxial stress at the same σ3. σ2 induces an increase in rock brittleness and causes the decay rate of brittleness to decrease with increasing σ3, and σ2 increases the upper limit of σ3 for brittle failure of rock. The enhancement effect of σ2 on rock brittleness must be considered when evaluating the brittle failure of deep surrounding rock under high-stress conditions; otherwise, the risk of brittle failure may be underestimated.

Evaluation Method for Determining Rock Brittleness in Consideration of Plastic Deformation in Pre-Peak and Failure Energy in Post-Peak

“…The results are shown in Figure 4. It can be observed that under natural conditions, the brittleness values of red-bed sandstone increased by 18 17.85% compared to the natural state. Therefore, both in the natural state and under saturated conditions, the brittleness index of red-bed sandstone decreases with increasing confining pressure, which is consistent with the trend of decreasing brittleness with increasing confining pressure in rock masses.…”

“…Based on the definitions provided by existing scholars, this study considers brittleness and ductility as opposing characteristics [17,18]. The strain occurring in the rock mass prior to failure can be divided into recoverable elastic strain and irrecoverable plastic strain induced by crack propagation.…”

“…By considering the strain at failure or the strain energy release, this approach provides insights into the rock's ability to undergo plastic deformation before failure. The advantage of strain-based definitions is their ability to capture the ductility or plasticity of rocks [17,18]. However, their drawback lies in the complexity of strain measurements and the need for advanced testing equipment.…”