Transmission of Seismic Waves With Tensile Components Across Cemented Rock Discontinuities Exhibiting Tension‐Softening Behavior

Experimental and Numerical Studies on Dynamic Response and Fracture Characteristic of Sandstone with Multiple Defects

Geological discontinuities (e.g., cracks, joints, faults, and cavities) fundamentally alter the integrity and mechanical behavior of rock masses. Under dynamic loading, such discontinuities induce stress concentration, disturb stress-wave propagation, and govern crack evolution, thereby acting as critical triggers for dynamic hazards in underground engineering. This study systematically investigates the dynamic response of sandstone containing multiple interacting defects, including intact, hole, flaw, intersected hole–flaw, and independent hole–flaw configurations. A combined experimental–numerical approach is employed, integrating triaxial Hopkinson bar (Tri-HB) expriment with quantitatively validated continuum-discrete coupling simulation. The results show that distinct dynamic stress–strain responses and fracture characteristics are governed by multiple interacting defects. Holes predominantly induce radial cracks and arching effects, while flaw tips cause strong directional stress concentration, with the inclination angle controlling crack propagation and seismic isolation. Hole–flaw intersected structures significantly accelerate crack coalescence, whereas hole–flaw independent structures exhibit pronounced energy dissipation and seismic isolation. At the mesoscale, failure evolution follows a sequence: shear triggering, tensile propagation, global instability. Force chain disturbance governs crack initiation direction, and local vortex-like velocity fields emerge near discontinuity intersections, promoting crack connectivity and dynamic instability. Energy partitioning analysis demonstrates that linear strain energy remains the dominant storage pathway, while complex discontinuities weaken storage capacity and markedly enhance frictional sliding, damping dissipation, and fragment motion, thereby enhancing energy dissipation and reducing energy storage capacity. These findings offer theoretical insights into the dynamic failure mechanisms of rock masses containing multiple discontinuities and guidance for hazard prevention in underground engineering.

On the Friction Between Soil and Steel With Extension to Soft Materials and Geological Faults

A unified constitutive model for friction is developed using a generalised power‐law framework that captures rate, load, temperature and state dependencies across granular, cohesive, soft‐material interfaces and geological faults. Grounded in an energy‐balance derivation and state‐evolution tribology, the model defines the interface velocity (strain‐rate) as the fundamental constitutive property. The inverted kinetic friction formulation utilises a power‐law representation, successfully reproducing static‐to‐dynamic transitions, direct velocity‐strengthening effects and evolutionary velocity‐weakening behaviours. Representative systems: rock penetration, cohesive soil sliding, high‐speed machining and fault friction are systematically mapped. The explicit incorporation of Arrhenius temperature kinetics corrected to couple the activation energy with the rate‐and‐state exponent () proves that the model captures macroscopic thermal weakening. Furthermore, numerical sensitivity analyses of the real area of contact evolution confirm sublinear growth under confining pressure, successfully predicting pressure‐induced friction drops. This robust formulation bridges classical empirical laws with modern rate‐and‐state mechanics. The framework is parsimonious, physically coherent and demonstrates powerful predictive capabilities across tribological and Earth science contexts.

Propagation and Fracture Mechanisms of One‐Dimensional Explosive Stress Waves Regulated by Cavity Structures

The propagation characteristics of explosive stress waves in rock masses are fundamentally influenced by the coupling conditions between the charge and the surrounding medium. This study systematically investigates the effect of annular cavity structures on one‐dimensional explosive stress wave propagation and rock fracture behavior through a custom‐built one‐dimensional loading experimental system. Eight groups of comparative tests were carried out with decoupling coefficients ranging from 0 to 0.875, and the time‐domain and frequency‐domain responses of rock specimens were obtained via ultra‐dynamic strain measurement, digital image correlation (DIC), and Hilbert–Huang transform (HHT). The results show that rock fracture patterns evolve through four stages with increasing decoupling coefficient, and a critical decoupling coefficient of 0.75 is identified, corresponding to the most significant asymmetric spalling effect. Frequency‐domain analysis indicates that the cavity structure acts as a mechanical filter, suppressing high‐frequency components (30–80 kHz) while enhancing low‐frequency energy (below 20 kHz), which transforms the loading regime from impulsive shock to combined impact‐quasi‐static gas expansion. This study establishes the correlation between spectral evolution and fracture mechanisms and provides theoretical support for the optimization of decoupled charge designs in rock blasting engineering.

Seismic Response and Failure Mechanisms of Tunnels Constructed Using the Pipe Roof Preconstruction Method

Deformation and Failure Characteristics of Three Sandstone Types Under True Triaxial Stress With a Fixed Lateral Stress Difference

This study conducts true triaxial compression tests on three types of sandstone under a constant intermediate principal stress of σ 2  = 28 MPa. The stresses applied to the X ‐direction surfaces are progressively increased while their difference remains fixed at Δ σ  = 3 MPa. Strength, deformation, failure mode, energy evolution, and plastic strain increment ratios (PSIRs) are analyzed. The results show that increasing the X ‐direction boundary‐stress level enhances rock strength and deformation capacity, although the magnitude of enhancement varies with lithology. Weak sandstone is predominantly characterized by tensile splitting; medium sandstone gradually evolves toward mixed tensile‐shear failure, and strong sandstone exhibits the clearest transition toward shear‐dominated failure. Acoustic emission distribution and energy evolution analyses indicate that enhanced lateral constraint suppresses crack opening, promotes shear‐related cracking, and increases elastic strain energy storage. The PSIRs results show that the anisotropy of macroscopic lateral plastic deformation decreases as the X ‐direction boundary stresses approach σ 2 .

Investigation of Compressive–Shear Fracture in Rock Considering Flaw Distribution and Interaction via an Improved Energy-Stress-Based Peridynamics Model

Predicting compressive–shear fracture in rock masses containing complex flaw distributions remains a major challenge in rock engineering. We propose an improved non-ordinary state-based peridynamics (NOSB-PD) model to simulate rock fracture behavior in this work. A stabilized NOSB-PD formulation is developed by incorporating a bond-level deformation gradient strategy to effectively suppress the zero-energy mode inherent in conventional NOSB-PD formulations, thereby ensuring deformation compatibility and numerical robustness. More importantly, the triple-shear energy criterion is introduced into the PD framework for the first time, enabling a more accurate characterization of shear fracture in rocks under complex stress states. The proposed NOSB-PD model is validated using two examples, demonstrating its excellent capability in suppressing the zero-energy mode and capturing fracture behavior in rock under compressive–shear conditions. Subsequently, the proposed model is used to systematically investigate the influence of flaw distribution on crack propagation and failure modes in rocks. The results indicate that variations in flaw distribution alter the local stress field, leading to a change in the rock fracture mode. Consequently, the rock bridge failure mode transitions from shear-dominated direct coalescence to mixed tensile-shear failure, and finally to tension-dominated indirect failure. The overall rock specimen is more prone to tensile–shear-mixed failure under conditions of shorter rock bridges with larger inclinations, or longer rock bridges with smaller inclinations. These findings provide new insights into the role of flaw distribution on rock fracture behavior.