Energy characteristics during the progressive shear failure of rock joints and brittleness evaluation

Abstract

The energy-driven progressive brittle shear failure of rock joints is a key mechanism behind deep engineering disasters such as joint-induced rockbursts and engineering earthquakes. To investigate the energy evolution mechanisms and disaster proneness, monotonic and stepwise loading-unloading tests were performed on regular dentate joints under constant normal stiffness boundary conditions. Results indicate a transition in damage mechanism from climbing wear of low-inclination asperities to brittle rupture of high-inclination ones, accompanied by a marked decrease in irreversible displacement. Energy analysis reveals a strong linear relationship between pre-peak elastic energy density and both input energy density and shear stress squared. The post-peak elastic energy release rate (g), and the self-sustaining instability coefficient (l) increase with joint undulation. A dimensionless brittleness index (BI) integrating the complete energy conversion and release process was proposed to quantify the energy balanced budget. The highly undulated joint R4 showed the most pronounced brittleness and instability intensity with the highest BI value of 0.697, along with g = 0.774 and l = 0.611. This study provides deeper insight into the understanding of the disaster-inducing proneness and stability assessment in jointed rock mass.

1. Introduction

Rock masses are distinguished from other engineering materials by the inherent presence of multi-scale joints, whose mechanical behavior governs their stability. In deep rock engineering, brittle failure such as joint-induced rockbursts and engineering earthquakes frequently originate from the shear-slip instability of these joints [1–5]. Statistical analyses reveal that a considerable proportion of rockburst events occur in joint-intensive zones. A notable example is the M3.4 rockburst in a deep South African gold mine, which Ortlepp attributed directly to fresh faults generated by shear rupture [6]. Similarly, rock joints were exposed during intense rockbursts at the Jinping II hydropower station and the Sichuan-Tibet railway [7]. Under high-stress conditions, jointed rock accumulates considerable deformation energy during excavation, with subsequent instability typically involving violent energy release and severe hazards. Such brittle failure is intrinsically associated with the interlocking condition and shear rupture of rock joints [8,9]. Consequently, the interaction between deep high-stress environments and inherent structures establishes essential preconditions for these hazards, where energy evolution fundamentally drives shear instability [10]. A comprehensive understanding of progressive joint damage combined with energy-based analysis of brittle failure is essential for stability evaluation and hazard prevention in deep rock engineering.

Rock joint shear instability results from asperity damage evolution under specific normal boundary conditions [11]. This process evolves through distinct stages, progressing from climbing wear under low normal stress to brittle rupture at elevated stresses. Direct shear test results have facilitated the development of numerous constitutive models to characterize this process. Li et al. [12] proposed a constitutive model that separately considers waviness and unevenness degradation to predict the shear behavior of rock joints based on wear process and dimensional analysis. Ban et al. [13] established the deterioration law of 3D roughness with shear displacement for the real contact joint surface, which effectively describes the post-peak softening behavior under low normal stress. Similarly, the multi-scale numeric...