This study investigated the evolution of mineral contacts and cracks in granite and sandstone subjected to high-temperature damage. To represent the heterogeneous strength distribution and random failure of rock micro-elements, a PFC damage contact model was developed by introducing a two-parameter Weibull strength distribution into particle contacts. A temperature-dependent damage coefficient was further incorporated into the failure criterion to describe the stress–strain response under coupled thermo-mechanical loading. The numerical results agree well with the experimental mechanical parameters, with errors in elastic modulus and peak strength below 5%. The proposed model effectively captures the elastic stage, peak response, post-peak softening behaviour, and damage evolution of the rocks, while the simulated failure modes are consistent with the observed damage characteristics. Statistical analysis of microcrack evolution and effective mineral contacts further explains the macroscopic failure mechanisms of feldspar-dominated granite and quartz-dominated sandstone. The results indicate that, under high temperatures up to 600 °C for sandstone and 400 °C for granite, sandstone cracks are mainly induced by thermal expansion, whereas granite cracks are related to reduced crystal spacing during cooling. Without lateral constraint, sandstone experiences relatively limited thermal damage, while granite develops more cracks due to thermal stress. Confining pressure improves sandstone strength but has limited influence on granite because inter-mineral microcracks are largely irreversible. At room temperature, mineral grain failure mainly occurs horizontally, whereas high temperature causes sandstone failure to shift obliquely. Granite develops multidirectional cracks due to local stress concentration.
Liquid nitrogen and microwave are emerging alternative methods for HDR reservoir fracturing, yet the combined application in rock fracture remains unclear. To investigate the combined effects, granite specimens with boreholes in the centre were cyclical treated by in-hole microwave irradiation (3 kW) and liquid nitrogen jet cooling. Physical and mechanical tests indicated that both P-wave velocity (Vp) and uniaxial compressive strength (UCS) of the specimens decreased with increasing irradiation time and cycles number. Compared to air-cooled specimens, liquid nitrogen cooling caused a greater reduction in Vp and UCS by 100.6% and 79.2%, respectively. Image analysis revealed that crack propagation length, fracture intensity (P21) and fractal dimension (Df) were directly proportional to both irradiation duration and number of cycles. Nuclear magnetic resonance (NMR) tests confirmed that the porosity of rock specimens increased from 13.8% to 39.8% after liquid nitrogen cooling, mainly due to the formation of micropores and mesopores. Additionally, a composite damage factor (DC) was proposed to better characterise thermal damage extent in granite. The present findings can serve as a reference for geothermal energy extraction from granite reservoirs.
This study investigates the roadway layout optimization of self-formed roadways without coal pillars (SFRCP) in close-distance coal seams. By integrating theoretical analysis, numerical simulation, and field application, the mining influence mechanism in close-distance coal seams was revealed, an optimal design scheme for the roadway layout was proposed, and its effectiveness was validated. First, based on the structural characteristics of the stope in close-distance coal seams, a mechanical model for mining stress transmission was established to elucidate the distribution of floor stress induced by the upper stope. Subsequently, the deformation and failure mechanisms of the surrounding rock for SFRCP were analyzed, identifying the key factors influencing roof deformation and coal rib failure depth. These findings formed the basis for proposing an optimal design scheme of roadway layout. Numerical simulations further compared the mine pressure evolution under different layouts, confirming the rationality of the proposed scheme. Finally, field engineering application based on the optimal roadway layout was conducted. Monitoring results confirmed that the surrounding rock deformation met the required safety standards, and the gob-side entry retaining performance was satisfactory. This research provides valuable insights for safe and efficient mining in close-distance coal seams.
Natural fractures in the Earth's crust provide important information on the stress field. However, stress inversion based on fracture characteristics remains challenging due to inherent data uncertainty and the limitations of deterministic interpretations. Existing approaches identify the feasibility of inverting crustal stress based on fracture hydraulic conductivity data and critical shear stress assumption. In that context, the fracture data is binarily treated, which is inconsistent with the continuous and stochastic nature of fracture characteristics of shear stress and fluid flow. This can lead to inversion instability and bias. To capture fracture criticality and the associated uncertainty, we develop a probabilistic stress inversion framework in which fracture criticality is quantified via a non-binary slip probability rather than a binary state. Stress inversion is formulated as an optimization problem that links fracture criticality probability and hydraulic conductivity, yielding estimates of stress orientation and relative magnitude. To systematically evaluate the impact of data uncertainty, synthetic datasets are generated using discrete fracture network models with varying fracture population, conductivity characteristics, and orientation diversity. The synthetic tests demonstrate that inversion performance is primarily governed by fracture orientation diversity, and the probabilistic formulation remains robust under some degree of misclassification and incomplete sampling. The method is further applied to four kilometer-scale scientific boreholes: Cajon Pass, Long Valley, Nevada Test Site, and KTB, where the inverted stress states are consistent with independent observations. These findings demonstrate that fracture diversity fundamentally controls the robustness and accuracy of kilometer-scale crustal stress inversion under geological uncertainty.
The complex water-induced deterioration of redbeds soft rocks poses a critical challenge in cross-scale disaster characterization, which is pivotal for mitigating geological hazards. Conventional experimental and numerical models mostly focus on a single scale, failing to capture the cross-scale evolution from meso-structural degradation to macro-hazard triggering, thus hindering disaster prevention and engineering safety. To address this gap, this study quantitatively bridges meso-scale deterioration mechanisms (pore evolution, mineralogical transformation, surface strain) with macro-scale disaster prediction. We conducted experiments on meso-structural deterioration under water action and explicitly linked the observations to a hydraulic-geotechnical coupling model based on Darcy’s law. Key findings reveal: (1) Porosity increased by 9.3% after 5 dry-wet cycles, with clay minerals (e.g., montmorillonite) decreasing by 47% due to dissolution and recrystallization. (2) The coupling model successfully predicted the transition from microcrack coalescence (0.016% strain threshold) to macroscopic shear failure, consistent with triaxial compression tests (peak strength reduction of 35% after 3 cycles). (3) Case studies of landslides in Zigui County showed that the model accurately simulated sliding displacements (91.3 m trailing edge vs. 373.1 m maximum) and accumulation patterns, validating the cross-scale mechanism linking mineral swelling, pore expansion, and slope instability. These results quantitatively bridge microstructural deterioration (e.g., Al/Mg leaching, quartz enrichment) with macro-disasters, providing a theoretical framework for predicting redbeds landslides and optimizing engineering interventions such as drainage systems and slope reinforcement.
Injection-induced seismicity during hydraulic fracturing of shale reservoirs poses a growing operational risk, yet the role of pore fluids in shaping failure precursors remains poorly resolved. This study applies critical slowing-down (CSD) theory to paired laboratory experiments on Longmaxi shale to identify how fluids alter the emergence of failure precursors and to elucidate the underlying mechanism. Pseudo-triaxial compression tests on one dry and one water-injected specimen, with real-time acoustic emission (AE) monitoring, were analyzed using the variance and autocorrelation of strain, AE count, and AE energy as CSD indicators tracking the transition from stable deformation to macroscopic failure. The results reveal a clear divergence in precursor timing: in the dry specimen, CSD indicators rose 1.7–4.9 s before the macroscopic stress drop, consistent with a true pre-failure precursor response; in the water-injected specimen, CSD indicators emerged 9.6–14.0 s after the initial stress drop, representing a post-onset lag rather than a pre-failure warning. This contrast is interpreted as a consequence of fluid-driven processes — chiefly lubrication, clay softening, and effective-stress reduction — that may shift the dominant macroscopic failure mode from brittle shear toward progressive tensile fracture, delaying cooperative instability. Together, the observations support a mechanistic hypothesis that pore fluids regulate the temporal position of CSD signals relative to macroscopic failure, and motivate a dual-regime monitoring framework in which pre-failure warning is appropriate for dry, brittle formations while post-onset hazard tracking is appropriate for fluid-saturated conditions.
During shield tunnelling in karst strata, cavities cause uneven excavation faces, leading to abnormal cutter wear or breakage and reduced efficiency. This study investigates the mechanical characteristics of shield disc cutter triggered by karst cavity, using full-scale linear cutting experiment on rock specimen containing cavities and collaborative cutters numerical simulation considering cavities size and position. Firstly, the linear cutting experiment investigates the process of cutting cavity boundaries with penetration depth and rock strength. As penetration depth increases, fragments at the cavity-boundary exit are larger than those at the entry side. With increasing rock strength, the peak normal force at the cavity boundary gradually exceeds the average force during continuous rock breaking. Numerical simulations show that cavity size and position strongly affect cutter force and cutterhead loads. When a cavity exists in the tunnelling face, cutters near the cavity show increased normal force, while distant cutters show decreased force. As the number of overhanging cutters increases, the force variation becomes more significant. The maximum variation rates of single-edge and double-edge cutters increase from 21.9% to 36.8% and from 23.8% to 33.7%, respectively. Compared with the no-cavity condition, cutterhead thrust and torque decrease, while the overturning moment increases. For twin cavities, the cutter force variation decreases with increasing cavity angle and increases with cavity eccentricity. This study provides a basis for optimizing tunnelling parameters in karst strata.
Effective seepage control in fractured rock masses is critical for underground engineering safety. This study investigated the permeability evolution of fractured granite before and after cement grouting, considering the effects of grout water-to-cement (W/C) ratio, fracture roughness, fracture inclination, confining pressure, and seepage pressure. A total of 25 specimen series, including fractured granite, cement paste, and rock-grout composites, were tested, yielding 225 permeability measurements. The results show that cement grouting reduced the permeability of fractured granite by approximately three orders of magnitude under the tested conditions, demonstrating its effectiveness in blocking fracture-controlled seepage pathways. The W/C ratio was the primary factor governing sealing performance: the 1:3 composites exhibited the lowest permeability, whereas the permeability increased by 25%-48% for the 1:2 composites and by a further 30%-35% for the 7:10 composites, mainly due to enhanced capillary-pore connectivity at higher W/C ratios. The rock-grout composites remained less permeable than fractured granite but more permeable than cement paste, indicating that residual interfacial gaps, shrinkage-induced microcracks, and local filling defects acted as preferential seepage paths. Unlike the fractured granite and cement paste, the composites exhibited an inverse permeability-seepage pressure response, attributed to particle migration and clogging, constrained cement paste deformation, and narrowing of interfacial channels. Fracture geometry further regulated permeability by altering rock-grout contact, flow-path tortuosity, particle retention, and effective seepage length. These findings suggest that the permeability of grouted fractured rock is jointly governed by grout matrix properties, interface integrity, and fracture geometry, providing guidance for grouting-based seepage control in fractured rock masses.
The length-to-diameter ratio (L/D ratio) effect is an important manifestation of the size effect in rock mechanics. Although this effect has been widely investigated under static and dynamic loading conditions, its influence under one-dimensional coupled static–dynamic loading remains insufficiently understood. In this study, coupled static–dynamic compression tests were conducted on red sandstone specimens using a modified split Hopkinson pressure bar (SHPB) system. The specimens had a fixed diameter of 50 mm and four different lengths of 25, 30, 40, and 50 mm, corresponding to L/D ratios of 0.5, 0.6, 0.8, and 1.0, respectively. The results show that the dynamic peak strength increases with strain rate for all L/D ratios, indicating a clear rate-dependent behavior. However, at a given strain rate, the dynamic peak strength decreases with increasing L/D ratio. This trend is consistent with that observed under static compression but differs from the commonly reported trend under purely dynamic loading. The peak strain also exhibits an L/D ratio effect, although its variation is more complex than that of peak strength. High-speed photography and digital image correlation (DIC) analysis reveal that specimens with larger L/D ratios are more prone to hoop cracking and axial segmentation, thereby reducing the specimen's equivalent stiffness and load-bearing capacity. In contrast, specimens with smaller L/D ratios mainly fail by axial splitting. These findings clarify the role of specimen geometry in rock failure under one-dimensional coupled static–dynamic loading and provide useful insights for evaluating the stability of rock structures subjected to dynamic disturbances.
Microbially induced carbonate precipitation (MICP) has shown great potential for repairing fractures and mitigating leakage risks. Nevertheless, the effects of temperature and pressure remain insufficiently understood. This study evaluated the effectiveness of MICP in shale fracture sealing, with a focus on the influence of aperture, temperature and pressure. The experimental findings indicate that temperature and pressure exerted dual effects on the MICP sealing process. On one hand, high temperature and high pressure (55 °C, 7.5 MPa) suppressed bacterial activity, thereby inhibiting calcium carbonate formation and resulting in a permeability reduction that was one order of magnitude less in Test HT compared to Test AT. On the other hand, calcium carbonate crystals formed under these conditions exhibited enhanced mechanical strength, which became particularly crucial when calcium carbonate content exceeded 40%. The results also showed that the permeability of the shale fracture samples decreased by one to three orders of magnitude after seven treatment cycles. This reduction was more pronounced in fractures with smaller apertures, especially those below 0.3 mm. For specimens with fracture apertures below 0.7 mm, the splitting tensile strength of the repaired samples ranged from 80 to 600 kPa, with corresponding breaking strains between 0.6% and 1.2%. A negative exponential relationship was observed between fracture aperture and splitting tensile strength. This study provides a systematic experimental evaluation of MICP-based shale fracture sealing under coupled temperature-pressure conditions, and reveals the dual role of high temperature and high pressure in inhibiting calcium carbonate precipitation while enhancing the mechanical contribution of the formed carbonate crystals.
High-temperature-induced thermal damage to rocks can significantly affect their physical properties and mechanical behaviour embedded at different depths due to microstructural changes. Although many studies have reported the high temperature effects on the microstructure changes and the corresponding mechanical responses, the coupled effects of thermally induced microstructure changes and confining pressure levels on the complete stress-strain behaviour and the relations between major and secondary failure planes in post-peak response remain poorly understood. In this study, three types of samples were extracted from the same intact block of Beijing dolomitic marble, exposed to different thermal treatments, and subjected to various test programs. Physical properties at particle scale (i.e. particle size distribution and micro-crack development) and element scale (i.e. colour parameter, ultrasonic wave velocity and open porosity), complete stress-strain behaviour at different confining pressures, and post-failure characteristics (i.e. failure pattern, stress-induced cracks and post-failure small particle distribution) were examined. Thermal damage led to the formation of inter- and intra-particle microcracks that increased discontinuities and small particle percentages, hence causing significant changes in the physico-mechanical properties of the marble. While higher temperatures reduced peak stress and Young’s modulus at zero confining pressure, the overall post-failure structural characteristics were found to be more affected by confining pressures, higher confining pressures simplified failure modes and reduced secondary crack formation. Although higher temperatures increased small particle generation, confining pressures notably diminished their quantity during shearing, highlighting the complex interactions between thermal and external stress conditions.
Deep underground engineering often subjects surrounding rock to complex conditions involving high in-situ stress, accumulated strain energy, and dynamic disturbances from activities such as mining. Understanding the damage and failure mechanisms under these coupled static-dynamic and energy-release conditions is crucial for predicting and preventing dynamic hazards like rockbursts. In this study, a series of experiments were conducted using a self-developed multi-strain-rate dynamic-static load superposition and energy release test system. This system simulated far-field strain energy accumulation and release through gas compression and expansion, while impact loads were applied by drop hammer. The damage process was characterized using mechanical parameters, fractal dimension analysis of fractures, and full-field strain measurement. The results indicate that the pre-peak mechanical behavior of rock is dominated by the superposition of static and dynamic loads, whereas the post-peak stage is governed by strain energy release. Strain energy release significantly amplifies the dynamic effects of rock failure, leading to more complex crack patterns (evolving from single shear to X-shaped conjugate and localized dispersed failures) and increased post-peak strain rates. Discrete element numerical simulations revealed that compressive stresses dominate the internal stress field, but tensile stresses control the instability-driven failure. Higher impact loads and strain energy magnitudes result in sparser contact force chains, non-uniform load transfer after local instability, and a rapid decline in bearing capacity. Furthermore, a quantitative relationship was established among input energy density, dissipated energy density, and fractal dimension, providing an index to evaluate rock fragmentation degree and dynamic effects under force-energy coupling.
Laser-assisted rock breaking is a promising technique for drilling, tunneling, and underground excavation. However, the thermo-mechanical damage mechanisms governing laser-induced rock weakening remain insufficiently understood, particularly at the mineral scale. In this study, nanoindentation tests were employed to quantify the thermo-mechanical degradation of individual minerals after laser irradiation, and the measured mineral properties were subsequently integrated into an accurate grain-based model (AGBM). This multiscale framework bridges laser-induced mineral-scale weakening and macroscopic rock damage evolution, providing new insights into the mechanisms governing laser-assisted rock breaking. Results show that biotite exhibits a reduction of up to 90% in elastic modulus within the heat-affected zone, whereas feldspar shows only minor changes and quartz retains relatively high rigidity, indicating that laser-induced damage extends beyond visible ablation pits and macroscopic cracks. The experimentally measured mineral-scale elastic properties were then incorporated into an AGBM framework to quantify the impact of mineral mechanical degradation on the macroscale strength of granite. The numerical results demonstrate significant reductions in elastic modulus and uniaxial compressive strength with increasing laser power. Analysis of stress, displacement, and damage evolution further shows that laser-induced mineral softening fundamentally alters internal stress redistribution, shifts damage initiation, and promotes microcrack coalescence into networks. These findings highlight the critical role of mineral-specific thermo-mechanical degradation in laser–rock interaction and offer a physically grounded basis for multiscale prediction of laser-induced rock damage.
Rock swelling induced by clay minerals causes volumetric expansion and triggers excessive floor heave, thereby compromising tunnel stability. Predicting long-term floor stability is challenging due to limited understanding of the time-dependent characteristics of rocks. Interactions between clay minerals and water further complicate floor heave mechanisms. This study develops a field-scale numerical model to investigate the time-dependent behaviour of swelling rocks. The model couples water diffusion with the mechanical deformation of the rock matrix and incorporates the viscoelastic properties of the rock. A material diffusivity constant is introduced to account for the influence of internal stress on the effective diffusion coefficient during water transport. Viscoelastic properties, including instantaneous elastic and creep responses, are captured using the Burgers model. The model is calibrated against field monitoring data and experimental observations. Sensitivity analyses are conducted to identify factors influencing the displacements of the roof, sidewall, and floor. Results reveal that the stiffness and the maximum swelling stress of the claystone floor have limited impacts on model displacements. The deformation behaviour is primarily governed by the viscosity properties defined in the creep model. Viscosity parameters related to the Maxwell dashpot dominate the long-term behaviour of the swelling rock. Model predictions indicate that higher viscosities delay strata deformation and prolong the time to stabilisation, potentially persisting beyond the service life of the tunnel. These findings are expected to provide insights into long-term stability analysis and to contribute to floor heave management.
This study investigates the reuse of mining waste tailings in geotechnical engineering as sustainable stabilizing materials when combined with cement. Two types of tailings—limestone and phosphate limestone—were mixed with different cement contents (0–6% by weight) and cured for 1–90 days to evaluate their effects on compaction properties. Modified Proctor compaction tests were performed to determine time-dependent maximum dry density (MDDt) and optimum water content (OWCt) for each mixture. Predictive models were developed using multivariable linear regression (LR) and artificial neural networks (ANN) with six input variables: cement content (C), ultrasonic pulse velocity (UPV), initial MDD, initial OWC, curing time (CT), and degree of saturation (SR). Because of the small dataset (n = 20 for each tailings type). To ensure generalizability and prevent overfitting within the small dataset (n=20 per tailings type), Leave-One-Out Cross-Validation (LOOCV) was applied. Both models achieved high predictive accuracy (R2 > 0.99), while the ANN slightly outperformed the LR model in capturing nonlinear relationships. Experimental results showed that increasing cement content and curing time increased MDDt and reduced OWCt, reflecting soil densification and reduced moisture demand due to cement hydration. Sensitivity analysis indicated that SR and UPV were the most influential factors affecting compaction behavior. The findings demonstrate that mining tailings combined with small amounts of cement can effectively enhance soil compaction. This approach promotes the recycling of mining residues and supports sustainable soil stabilization practices for road infrastructure within the framework of a circular economy.
Highways are critical transportation infrastructures that play a vital role in economic development and regional connectivity. However, frequent geological hazards pose significant threats to highway safety and resilience. With the rapid expansion of highway networks and the continuous accumulation of multi-source data, improving the efficiency and accuracy of hazard identification and prediction has become a major challenge in highway geological hazard prevention and mitigation. This paper systematically reviews the development of geological hazard assessment and prediction methods, recent advances in artificial intelligence (AI) application. Based on this review, an AI-enabled framework for highway geological hazard risk identification and control is proposed. The framework establishes a multi-source database by integrating engineering design documents and historical hazard information. AI models are then trained to learn from these data and identify potential hazard risks along highway, enabling risk identification from line-level to site-level. For the identified high-risk sites, Newton-force monitoring devices are deployed to provide sensitive detection of mechanical changes. Based on accurate forecasting results, proactive measures, including early warning, preventive reinforcement, and adaptive control, can then be implemented. The proposed framework combines the large-scale analytical capabilities of AI with the high sensitivity of physics-based monitoring. It can promote the transition of highway geological hazard management from reactive response to proactive prevention, providing a systematic solution for enhancing the safety and resilience of highway lifeline infrastructure.
Bench contour blasting is widely used in engineering construction to enhance excavation quality and minimize surrounding rock damage. However, traditional explosive charging often causes excessive overbreak and high vibration, affecting construction precision and safety. This study investigates the rock fracture behavior of the double base propellant charge through experiments, numerical simulations, and theoretical analysis, comparing it with the explosive charge in terms of overbreak, vibration, and surrounding rock damage. The results show that the charge of the double base propellant significantly reduces overbreak and vibration. At a 30 mm hole spacing, the overbreak depth decreases from 5.62 to 4.50 cm and the area from 15 to 5 cm2. At 40 mm, the depth of the overbreak drops from 10.59 to 7.65 cm and the area from 300 to 10 cm2. Vibration tests reveal a reduction in the resulting velocity from 26.629 cm/s to 13.582 cm/s (30 mm) and from 44.86 cm/s to 14.765 cm/s (40 mm). CT scans confirm that double-base propellant charging causes no surrounding rock damage, unlike explosive charging, which results in two distinct damage zones.Theoretical analysis using the Nobel-Abel and Lame equations suggests that the slower energy release of double-base propellant creates a quasi-static stress field, guiding crack propagation along the hole spacing line and reducing random damage. ANSYS/AUTODYN simulations further validate these findings, demonstrating that double-base propellant charging helps form a smoother excavation contour. This study provides theoretical and experimental support for its application in bench contour blasting.
Understanding the transition of rough rock fractures from a stable sliding state to a dynamically unstable state is crucial for the assessment of geological hazards. However, the relationship between macroscopic stress release and microscopic damage remains unclear. This study investigates the shear response of granite fractures using a grain-based model that combines acoustic emission (AE) analysis with moment tensor inversion. Direct shear simulations were performed for rock fractures with varying roughness (JRC = 0.42–18.96) under normal stresses ranging from 4 to 20 MPa. The results indicate that high confining pressure (particularly ≥ 15 MPa) inhibits crack opening and promotes brittle failure, abrupt stress release, and the enhancement of implosion sources associated with grain fragmentation and chipping. A dual-index criterion combining stress drop (Δτ) and AE b-value is further proposed to assess shear instability. The stable region (Δτ < 1.25 MPa, b > 1.0) is characterized by stable wear, distributed surface microdamage, low-amplitude acoustic emission activity, and a relatively small shear stress drop. The unstable region (Δτ ≥ 1.25 MPa, b ≤ 1.0) appears only in rough joint surfaces under high confining pressure conditions, particularly when JRC ≥ 11.12 and ≥ 15 MPa, reflecting rapid failure of the asperities and rapid crack propagation. Segmentation statistics further indicate that as roughness and normal stress increase, the proportion of the stable region decreases, while the proportion of the unstable region increases. These findings establish a directly measurable stress drop– AE b-value framework for assessing shear instability and slip risk in fractured rock masses.
This paper established a fully coupled bolt numerical model within the framework of two-dimensional disk DDA (DDDA) to simulate the mechanical interaction between negative Poisson’s ratio (NPR) material bolts and rock masses. Initially, the fundamental theory and algorithm of the bolt numerical model are described, including a bolt segmentation algorithm proposed to divide a bolt into sub-bolts, derivation of the sub-matrix for a sub-bolt that is superimposed into the DDDA simultaneous equilibrium equations, and establishment of the bolt mechanical constitutive model and failure criterion based on the elongation-tension relationship obtained from NPR bolt pullout physical tests. Subsequently, a series of verification numerical simulations are carried out. The simulation results are in excellent agreement with theoretical values or physical tests, demonstrating that the proposed bolt numerical model can accurately simulate the constant-resistance large-deformation energy absorption process of NPR bolts under tension and shear, as well as their strengthening effect on fractured rock masses. Lastly, an engineering application case is presented, showing that the proposed bolt numerical model can be used to reveal complex bolt-rock mass mechanical interactions and has broad practical application prospects in rock bolting for rock engineering.
