Wei-Tong Li , Qi-Zhi Zhu , Wei-Jian Li , Xing-Guang Zhao
{"title":"A microplane-enhanced quasi-bond method with a dual-mechanism fracture criterion for mixed-mode failure in rock-like materials","authors":"Wei-Tong Li , Qi-Zhi Zhu , Wei-Jian Li , Xing-Guang Zhao","doi":"10.1016/j.ijrmms.2025.106396","DOIUrl":"10.1016/j.ijrmms.2025.106396","url":null,"abstract":"<div><div>This paper presents an enhanced quasi-bond method for modeling mixed-mode fracture in rock-like materials. By integrating concepts from microplane theory, the proposed approach incorporates strain decomposition and projection onto bond directions, establishing bond-level stiffness through energy equivalence with classical elasticity. The formulation accommodates arbitrary Poisson’s ratios and preserves consistency across two-dimensional/three-dimensional settings. A novel dual-mechanism fracture criterion is introduced, incorporating both a bond-breakage rule based on energy thresholds and microstress states to differentiate tensile and shear cracks, and a complementary bond-level softening model that concurrently captures tensile and shear strength degradation. To improve numerical accuracy, a smoothed strain technique synchronizes strain updates with bond failure, and a hybrid finite element/quasi-bond coupling strategy enables efficient localized fracture resolution. Validations against notched beams and multi-flawed specimens under compression demonstrate the accuracy of the proposed model in solving mixed-mode fracture in rock-like materials. Engineering-scale extensions to jointed rock slopes reveal step-path fracture network evolution governed by flaw interaction-driven coalescence patterns, advancing geohazard predictions through explicit linkage between discrete fracturing and macro-scale instability.</div></div>","PeriodicalId":54941,"journal":{"name":"International Journal of Rock Mechanics and Mining Sciences","volume":"199 ","pages":"Article 106396"},"PeriodicalIF":7.5,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145956879","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Zhiqiang Yi , Yueping Yin , Zhihua Zhang , Luqi Wang , Xuebing Wang , Peng Zhao , Limei Zhang
{"title":"Deterioration and damage characteristics of rock masses within the fluctuating zone, Three Gorges Reservoir Area, China","authors":"Zhiqiang Yi , Yueping Yin , Zhihua Zhang , Luqi Wang , Xuebing Wang , Peng Zhao , Limei Zhang","doi":"10.1016/j.ijrmms.2026.106421","DOIUrl":"10.1016/j.ijrmms.2026.106421","url":null,"abstract":"<div><div>Since 2008, the water level in the Three Gorges Reservoir Area has fluctuated annually between 145 and 175 m. This fluctuation has caused significant deterioration and damage to the rock masses within the fluctuating zone. In this zone, the elevation difference can reach up to 30 m. This study uses the Longmen dangerous rock as a typical case to comprehensively reveal the deterioration and damage characteristics of rock masses through sonic CT (Computed Tomography) imaging. This is further supported by field geological surveys, drilling engineering, and underground television. The following findings were obtained: (1) The degree of deterioration and damage below the 175 m elevation decreases with depth. Specifically, the RQD (Rock Quality Designation) generally follows an exponential distribution function. (2) The development of fractures and fragmentation zones within the fluctuating zone is higher than in areas below the fluctuating zone. (3) The degree of deterioration and damage below the 175 m elevation is heterogeneous and exhibits surface to inside pattern. (4) The essential cause of deterioration and damage effects is the RWLF (Reservoir Water Level Fluctuation). Detailed, weakly alkaline erosive flowing water in the study area initiates chemical corrosion, leading to deterioration and damage effects on the rock masses. Under the influence of gravity from the overlying high and steep dangerous rocks, leading to the prominent manifestation of joint fissures. Furthermore, mechanical dynamic effects, such as scour, erosion, and washout, occur due to the RWLF and vessels. These effects cause small portions of the rock masses to gradually detach and be carried away into the water. As a result, phenomena such as corrosion and dissolution cavities are formed. The insights gained from this study are significant for understanding the instability mechanisms of high and steep dangerous submerged rocks.</div></div>","PeriodicalId":54941,"journal":{"name":"International Journal of Rock Mechanics and Mining Sciences","volume":"199 ","pages":"Article 106421"},"PeriodicalIF":7.5,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145980630","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Identification of elastic constants of transversely isotropic rocks using strain measurements from a single inclined specimen","authors":"Youn-Kyou Lee , S. Pietruszczak","doi":"10.1016/j.ijrmms.2026.106399","DOIUrl":"10.1016/j.ijrmms.2026.106399","url":null,"abstract":"<div><div>The elastic behavior of transversely isotropic rocks is governed by five independent constants. Conventional methods for measuring these elastic constants typically involve uniaxial compression tests on three specimens sampled at different inclinations with respect to the isotropy plane. However, this approach may introduce errors due to specimen heterogeneity. In this study, three sets of simple inversion formulas are derived to determine five elastic constants from strain data obtained during hydrostatic compression followed by an increment of axial stress applied to a single inclined specimen. Each of these three sets includes an identical equation for the shear modulus and a distinct matrix equation for the remaining four elastic constants. Although these matrix equations differ in appearance, they are mathematically equivalent and yield identical solutions. To facilitate coordinate transformation, the Mehrabadi-Cowin notation was employed, in which the strain and stress states are represented as first-order tensors in a six-dimensional space, and the corresponding compliance matrix is treated as a second-order tensor in the same space. The input data for the proposed inversion formulas consist of strain measurements taken in a coordinate system aligned with the strike and dip directions of the isotropy plane. If the orientation of the isotropy plane can be inferred from the strain data, then strain measurements obtained in an arbitrary coordinate system can also be used as input. Illustrative examples are provided to demonstrate the accuracy and practical relevance of the proposed approach.</div></div>","PeriodicalId":54941,"journal":{"name":"International Journal of Rock Mechanics and Mining Sciences","volume":"199 ","pages":"Article 106399"},"PeriodicalIF":7.5,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145908711","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Ali Aminzadeh , Prasanna Salasiya , Joseph F. Labuz , Mohammad Nooraiepour , Bojan B. Guzina
{"title":"Ultrasonic sensing of the mechanical fingerprint of reactive transport in rock","authors":"Ali Aminzadeh , Prasanna Salasiya , Joseph F. Labuz , Mohammad Nooraiepour , Bojan B. Guzina","doi":"10.1016/j.ijrmms.2026.106404","DOIUrl":"10.1016/j.ijrmms.2026.106404","url":null,"abstract":"<div><div>Mineral carbon storage in rock formations has gained significant interest in recent years. In principle, changes in mechanical rock properties driven by carbon mineralization could be quantified using seismic methods, opening the door toward field monitoring of carbon storage. However, these changes may vary spatially within a rock mass when reactive transport occurs. In this vein, full-field ultrasonic characterization of reacted specimens can help shed light on the process. We use a 3D Scanning Laser Doppler Vibrometer to perform full-field monitoring of one-dimensional (1D) ultrasonic waves in rod-shaped sandstone specimens exposed to NaCl-rich fluid. Our initial experiments were conducted on intact sandstone specimens with high aspect ratio (<span><math><mrow><mtext>length/diameter</mtext><mo>≃</mo><mn>15</mn></mrow></math></span>) to cater for 1D axial wave propagation. To investigate the evolution of the Young’s modulus and attenuation of rock due to reactive transport, we exposed the specimens to an under-saturated NaCl solution, achieving supersaturation – and so mineralization – through evaporation. The upward movement of the fluid, supplied at the bottom of each specimen, was achieved through capillary action. We deploy an elastography-type approach to back-analysis, known as modified-error-in-constitutive-relation (MECR) approach, to expose the spatially-heterogeneous evolution of mechanical rock properties due to reactive transport. Our results consistently demonstrate (i) an approximately 30% degradation of the Young’s modulus and (ii) 7-fold increase in ultrasonic attenuation due to mineralization. To better understand the root causes of these changes, we made use of the X-ray micro-computed tomography and scanning electron microscopy of selected cross-sections. The grain-scale information suggests that pore filling with powder-like participate is responsible for the increase in attenuation, while microcracking – observed by acoustic emission monitoring – is behind the observed damage of rock.</div></div>","PeriodicalId":54941,"journal":{"name":"International Journal of Rock Mechanics and Mining Sciences","volume":"199 ","pages":"Article 106404"},"PeriodicalIF":7.5,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145957139","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Multi-method constrained stress states in the Qiabuqia geothermal field, NW China: Insights from basin-basement contrasts","authors":"Zijuan Hu , Shengsheng Zhang , Chongyuan Zhang , Shian Zhang , Derek Elsworth , Wen Meng , Xianghui Qin","doi":"10.1016/j.ijrmms.2026.106422","DOIUrl":"10.1016/j.ijrmms.2026.106422","url":null,"abstract":"<div><div>We applied anelastic strain recovery (ASR), hydraulic fracturing (HF), and acoustic image logging to determine the full three-dimensional stress state in the Qiabuqia geothermal field, northeastern Tibetan Plateau. ASR measurements from twenty-five core samples across five boreholes in the geothermal field reveal a pronounced stress contrast between the sedimentary basin fill and the underlying granite basement. The sediments exhibit a normal faulting stress regime (S<sub>v</sub> > S<sub>Hmax</sub> > S<sub>hmin</sub>), primarily governed by gravitational loading. In contrast, the granite basement exhibits a strike-slip regime (S<sub>Hmax</sub> > S<sub>v</sub> > S<sub>hmin</sub>), indicating a dominant tectonic compression. Horizontal differential stress increases with depth in the sediments but decreases within the granite. We interpret these contrasts as resulting from variations in basement topography and mechanical properties between sedimentary and crystalline rocks. Acoustic image logs from borehole DR-8S indicate a mean S<sub>Hmax</sub> orientation of approximately N47° ± 21°E, aligning with regional stress indicators derived from focal mechanisms and GPS data. Weak alteration minerals on fractures and faults may facilitate reactivation, promoting stress release and local reorientation. Our results demonstrate that the present-day stress field is controlled by northeastward expansion of the Tibetan Plateau, with direct implications for the development and stability of the Qiabuqia geothermal reservoir.</div></div>","PeriodicalId":54941,"journal":{"name":"International Journal of Rock Mechanics and Mining Sciences","volume":"199 ","pages":"Article 106422"},"PeriodicalIF":7.5,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145961726","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Changhao Liu , Andrey Jivkov , Kiprian Berbatov , Majid Sedighi , Jiangfeng Liu , Hongyang Ni
{"title":"Microstructure-driven prediction of permeability and thermal conductivity in porous solids via a discrete multi-physics framework","authors":"Changhao Liu , Andrey Jivkov , Kiprian Berbatov , Majid Sedighi , Jiangfeng Liu , Hongyang Ni","doi":"10.1016/j.ijrmms.2026.106432","DOIUrl":"10.1016/j.ijrmms.2026.106432","url":null,"abstract":"<div><div>Accurate prediction of permeability and thermal conductivity of porous materials is essential for the design and optimisation of various engineering systems in energy, environmental and infrastructure applications. This study presents a discrete multi-physics modelling framework that enables direct prediction of these properties from microstructural information alone, without recourse to fitting against experimental data of fluid flow and heat transfer.</div><div>The method is based on combinatorial differential forms defined on a cell complex, allowing local conservation laws to be enforced while capturing material and interfacial non-linearities. Representative elementary volumes (REVs) were statistically reconstructed from high-resolution X-ray computed tomography (XCT) of two sandstone types, with mineralogical composition derived from X-ray diffraction (XRD) analysis. Local transport properties were assigned based on pore geometry and mineral-specific conductivities, incorporating realistic mixing rules at interfaces.</div><div>Simulations across 30 stochastic microstructural realisations per specimen of rock yielded permeability and thermal conductivity estimates that captured experimental trends and magnitudes without calibration. The results demonstrate the predictive capability and robustness of the approach, offering a viable pathway for microstructure-informed design and digital characterisation of porous and fractured geomaterials.</div><div>The central scientific contribution is a unified discrete operator formulation in which permeability and thermal conductivity emerge from the same mathematical structure, providing a physically consistent basis for modelling transport in heterogeneous and fractured rock materials.</div></div>","PeriodicalId":54941,"journal":{"name":"International Journal of Rock Mechanics and Mining Sciences","volume":"199 ","pages":"Article 106432"},"PeriodicalIF":7.5,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146033268","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Yang Xia , Yongtao Yang , Xuhai Tang , Hong Zheng , Changfu Wei , Zuliang Shao
{"title":"Investigation on artificial boundary problems in three-dimensional nodal-based continuous-discontinuous deformation analysis method for the seismic dynamic analyses of geotechnical structures","authors":"Yang Xia , Yongtao Yang , Xuhai Tang , Hong Zheng , Changfu Wei , Zuliang Shao","doi":"10.1016/j.ijrmms.2026.106420","DOIUrl":"10.1016/j.ijrmms.2026.106420","url":null,"abstract":"<div><div>To accurately simulate the seismic responses of geotechnical structures using the three-dimensional nodal-based continuous-discontinuous deformation analysis method (3D-NCDDAM), appropriate boundary conditions should be set at the artificial boundaries to avoid the generation of fictitious reflected waves. In this study, various boundary conditions are used to enhance the ability of 3D-NCDDAM for seismic response analyses of geotechnical structures: (1) a viscous boundary is incorporated to absorb wave energy; (2) a viscoelastic boundary is introduced, which not only absorbs wave energy but also captures the elastic recovery behavior of the geotechnical medium; (3) based on the seismic input boundary, seismic motion is accurately applied; (4) the free field boundary applied for wave propagation in the semi-infinite domain is extended to three-dimensional space. The generation algorithm of the free field model and its coupling calculation with the main computational domain are introduced in detail; (5) the static-dynamic unified boundary introduced into 3D-NCDDAM achieves the seamless transition of boundary conditions between the quasi-static and dynamic stages. The numerical results of several examples verify the accuracy of those boundary conditions, and the entire evolution process of the landslide trigged by earthquake is effectively simulated with the enriched 3D-NCDDAM.</div></div>","PeriodicalId":54941,"journal":{"name":"International Journal of Rock Mechanics and Mining Sciences","volume":"199 ","pages":"Article 106420"},"PeriodicalIF":7.5,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146006408","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Modeling the thermo-mechanical behavior of porous lava under reservoir conditions","authors":"Ghassan Shahin , Michael J. Heap , Marie Violay","doi":"10.1016/j.ijrmms.2025.106383","DOIUrl":"10.1016/j.ijrmms.2025.106383","url":null,"abstract":"<div><div>Harnessing geothermal energy and storing carbon dioxide in volcanic systems require reliable constitutive models to predict rock deformation and failure under extreme pressure and temperature. However, existing models are limited, especially when compared to the more advanced predictive tools available for sedimentary rocks. In this study, we integrate elastoplasticity, strain hardening, nonassociative plasticity, phenomenological thermomechanics, and bifurcation analysis to establish a novel constitutive model for porous lava. The model is calibrated against a unique dataset that provides the stress–strain and strain localization responses of porous andesite deformed at temperatures ranging from room temperature up to 800 °C and at effective confining pressures from room pressure to 50 MPa. These mechanical and thermal conditions are representative of deep geothermal reservoirs. Finite element simulations of laboratory experiments are used to demonstrate the model’s capabilities in terms of reproducing key mechanical characteristics, including the differential stress required for the first stress drop and deformation mechanisms, across varying pressure and temperature conditions. Further validation via full-field finite element computations, simulating borehole excavation in low- to high-temperature systems, underscores the model’s predictive capabilities. In particular, the field-scale simulations demonstrate the model’s efficacy in reproducing variable forms of deformation structures and deformation modes around boreholes with capabilities to provide more information about the displacement in the borehole walls. The proposed modeling framework can be integrated into commercial numerical tools and used to facilitate the engineering of safe and cost-effective geothermal energy production and carbon geostorage, as well as numerical models designed to better understand the stability and therefore the hazard potential of volcanic structures.</div></div>","PeriodicalId":54941,"journal":{"name":"International Journal of Rock Mechanics and Mining Sciences","volume":"199 ","pages":"Article 106383"},"PeriodicalIF":7.5,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145980631","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Capturing dynamic rockburst behaviors of deep rock masses with a novel nonlocal general particle dynamic method","authors":"Jin-Hu Pan , Xiao-Ping Zhou","doi":"10.1016/j.ijrmms.2026.106403","DOIUrl":"10.1016/j.ijrmms.2026.106403","url":null,"abstract":"<div><div>Understanding rockburst mechanism has always been a fundamental challenge in the field of geotechnical engineering. The nonlocal methods have excellent potential to simulate fragment problems such as rockburst. However, early researches employing nonlocal methods primarily focused on the static process of rockburst, their capabilities in simulating the full dynamic fracture propagation and fragment ejection processes remain to be further explored. To reproduce the dynamic rockburst process in deep tunnel, the present work proposes a novel nonlocal general particle dynamic method. Firstly, four types of contact behaviors in rockburst are identified and a contact model based on the theorem of momentum is proposed to determine the contact force. Secondly, we establish a joint model that distinguishes the tensile, compressive and shear deformation features of bonds to characterize the joints in rock masses. Thirdly, the Holmquist-Johnson-Cook constitutive model is modified to consider the features of high pressure and high strain rate in rockburst process and to simulate the damage evolution by incorporating the critical stretch criterion and critical equivalent strain criterion. The first three examples, oedometric test, block sliding on an inclined plane and wave propagation in a one-dimensional bar with a joint, are conducted to verify the proposed numerical framework. The final three examples simulate the rockburst phenomenon induced by excavation. The numerical results obtained by the developed approach are in high agreement with the experimental results and the field observations. The several typical features in rockburst, particle spalling, particle ejection and V-shaped rockburst pit, are successfully reproduced, which demonstrate that the proposed method possesses excellent ability to model the dynamic rockburst process and can provide a theoretical basis for hazard assessment and prevention strategies in deep underground engineering.</div></div>","PeriodicalId":54941,"journal":{"name":"International Journal of Rock Mechanics and Mining Sciences","volume":"199 ","pages":"Article 106403"},"PeriodicalIF":7.5,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145956889","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Numerical study on pillar stress distribution in room-and-pillar hard rock mines using stress concentration factor based on tributary area: Bridging to pressure arch effect","authors":"Dong-Ho Yoon , Jae-Joon Song","doi":"10.1016/j.ijrmms.2025.106198","DOIUrl":"10.1016/j.ijrmms.2025.106198","url":null,"abstract":"<div><div>This study analyzes how the stress distribution in panel pillars of room-and-pillar mining systems deviates from Tributary Area Theory (TAT) under changes in key design parameters, such as overburden height, pillar array size, opening width-to-pillar width ratio, and pillar width. The Stress Concentration Factor based on Tributary Area (SCF<sub>T</sub>) was employed to visualize the stress disturbance profile, known as the pressure arch effect, and provide a clearer understanding of load distribution while facilitating individual pillar stress calculations. Numerical analysis revealed that <span><math><mrow><msub><mrow><mi>S</mi><mi>C</mi><mi>F</mi></mrow><mi>T</mi></msub></mrow></math></span> profiles converge to stable shapes with increasing depth, and as panel width grows, central pillars exhibit <span><math><mrow><msub><mrow><mi>S</mi><mi>C</mi><mi>F</mi></mrow><mi>T</mi></msub></mrow></math></span> values closer to TAT predictions, while discrepancies persist at peripheral pillars. This observation suggests the possibility of controlled peripheral pillar trimming to enhance production without excessively increasing stress levels. Sensitivity analysis further indicated that the horizontal-to-vertical stress ratio (<em>k</em>) and pillar height, often overlooked, are critical factors for accurate stress estimation. These findings demonstrate the potential of <span><math><mrow><msub><mrow><mi>S</mi><mi>C</mi><mi>F</mi></mrow><mi>T</mi></msub></mrow></math></span> as a practical tool for realistic pillar stress estimation and its applicability for optimizing room-and-pillar mining system designs.</div></div>","PeriodicalId":54941,"journal":{"name":"International Journal of Rock Mechanics and Mining Sciences","volume":"199 ","pages":"Article 106198"},"PeriodicalIF":7.5,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145961727","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}