Theoretical and Applied Fracture Mechanics最新文献

{"title":"Development of a finite-strain phase-field formulation for thermo-mechanical brittle fracture in Total Lagrangian SPH and its comparative assessment with pseudo-spring model","authors":"Jerome Samuel Stephen ,&nbsp;Md Rushdie Ibne Islam","doi":"10.1016/j.tafmec.2026.105481","DOIUrl":"10.1016/j.tafmec.2026.105481","url":null,"abstract":"<div><div>This work presents the development of a finite-strain phase-field formulation for thermo-mechanical brittle fracture within the Total Lagrangian Smoothed Particle Hydrodynamics (TLSPH) framework and its comparative assessment with the pseudo-spring model. The proposed formulation extends TLSPH to coupled thermo-mechanical conditions through a multiplicative decomposition of the deformation gradient into elastic and thermal components, enabling consistent treatment of large deformations and temperature-dependent stresses. A hyperbolic regularization of the phase-field evolution equation is adopted to enhance stability and alleviate time-step restrictions inherent in parabolic formulations. Four representative problems are investigated: thermal cracking in a double-notched specimen, expansion-induced fracture in a two-layer cylindrical rock, dynamic crack branching in a notched plate under combined loading, and thermal-shock-induced fracture in ceramics. Results are validated against experimental and numerical data, with quantitative comparisons of crack paths, crack-tip velocity, branching angle, and strain–energy dissipation. The phase-field TLSPH formulation accurately captures continuous and parallel crack evolution under severe thermal gradients, whereas the pseudo-spring model efficiently reproduces multiple small radial cracks in heterogeneous media but exhibits spurious local damage under abrupt thermal shocks. The study establishes a robust particle-based framework for thermo-mechanical fracture and clarifies the relative strengths and limitations of continuum and discrete fracture representations within TLSPH.</div></div>","PeriodicalId":22879,"journal":{"name":"Theoretical and Applied Fracture Mechanics","volume":"143 ","pages":"Article 105481"},"PeriodicalIF":5.6,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146078525","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Peridynamic modeling of ballistic impact on metallic-ceramic functionally graded Sandwich plates","authors":"Ioannis Sioutis,&nbsp;Konstantinos Tserpes","doi":"10.1016/j.tafmec.2026.105435","DOIUrl":"10.1016/j.tafmec.2026.105435","url":null,"abstract":"<div><div>Functionally Graded Sandwich Plates (FGSP) composed of metallic-ceramic layers have been widely investigated for their superior ballistic performance. Their through-the-thickness variation in material properties significantly enhances energy dissipation and resistance to projectile penetration. While traditional numerical FEA tools such as LS-Dyna can simulate such phenomena with reasonable accuracy, the non-local method of peridynamics (PD) offers a promising alternative for capturing complex fracture and failure mechanisms, particularly under dynamic loading. To the authors' best knowledge, direct comparison of the two methods in computational terms on an actual case study has been lacking from literature. In the present article, the ballistic impact of a 0.30 caliber steel projectile to a 7-layer Al-SiC composite FGSP is numerically examined using a bond-based PD framework. Although LS-Dyna was initially selected for both FEA and PD simulations, limitations of the available PD implementation necessitated the adaptation of LAMMPS molecular dynamics simulator to accommodate a fully customized bond-based PD model. A comprehensive parametric study was performed, including variations in lattice discretization, horizon radius and material inhomogeneity, to assess the accuracy and robustness of the PD approach. Comparative analysis against conventional FEA results is presented, highlighting the strengths and limitations of each method in predicting impact response, failure modes and damage evolution. The results demonstrate that the PD method provides enhanced resolution of fracture phenomena, offering valuable insights into the design of advanced FGSPs in ballistic protection applications.</div></div>","PeriodicalId":22879,"journal":{"name":"Theoretical and Applied Fracture Mechanics","volume":"143 ","pages":"Article 105435"},"PeriodicalIF":5.6,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145940250","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Cross-scale crack evolution in pre-flawed sandstone under high temperature: Insights from a composition-aware thermal-mechanical grain-based model","authors":"Shi Liu ,&nbsp;Zhipeng Zhang ,&nbsp;Qixing Wu ,&nbsp;Chun Feng ,&nbsp;Chen Chen ,&nbsp;Xiasong Hu","doi":"10.1016/j.tafmec.2026.105450","DOIUrl":"10.1016/j.tafmec.2026.105450","url":null,"abstract":"<div><div>In deep energy extraction, thermal damage induced by high temperatures critically degrades the mechanical integrity of rock, posing substantial risks to engineering safety. To systematically clarify the damage mechanisms under coupled thermal-mechanical-fracture conditions, this study develops a novel Composition-Aware Thermal-Mechanical Grain-Based Model (CATM-GBM).This model explicitly integrates the rock's quantitative mineralogical composition and spatial heterogeneity, implementing a temperature-dependent thermal expansion function to capture differential mineral degradation and employing parallel bond model and smooth joint model to simulate intergranular tensile and intragranular shear failure modes. Results demonstrate pronounced mechanical degradation under high-temperature exposure, characterized by marked reductions in uniaxial compressive strength and elastic modulus, significant increases in peak axial strain, and a coherent transition from brittle to ductile post-peak behavior. Crack analysis reveals tensile-dominated failure throughout loading and identifies a critical transition near 500 °C: intergranular cracking prevails below this threshold, while intragranular cracking dominates above it due to intensified thermal mismatch stresses and micro-damage within mineral grains. Pre-existing flaws control macroscopic failure patterns, promoting through-going “X”-shaped conjugate shear bands in flawed specimens, in contrast to localized “V”-shaped failures in intact ones. Microscopically, deviatoric loading induces particle-scale anisotropy, triggering progressive grain rotation, slip, and contact network destabilization. Macroscopically, cracks initiate predominantly at flaw tips and propagate to form specimen-scale through-fractures. This research provides a systematic, multi-scale decoupling of thermal cracking evolution in fractured sandstone, establishing a robust predictive numerical framework for assessing thermomechanical stability in critical deep geological engineering applications, including enhanced geothermal systems and deep geological repositories for nuclear waste.</div></div>","PeriodicalId":22879,"journal":{"name":"Theoretical and Applied Fracture Mechanics","volume":"143 ","pages":"Article 105450"},"PeriodicalIF":5.6,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145940287","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A localizing gradient damage model for hydrogen-assisted cracking","authors":"Alok Negi ,&nbsp;Imad Barsoum","doi":"10.1016/j.tafmec.2025.105426","DOIUrl":"10.1016/j.tafmec.2025.105426","url":null,"abstract":"<div><div>Hydrogen-assisted cracking remains a critical threat to the durability and safety of metallic structures, arising from the interaction of diffusible hydrogen with the microstructure, which weakens interatomic cohesion and promotes premature fracture. This work presents a novel chemo-mechanical modeling framework that integrates material deformation, stress-assisted hydrogen diffusion, and hydrogen-induced degradation of mechanical properties. A localizing gradient damage enhancement is employed to regularize softening responses and produce sharply localized damage zones that correspond to macroscopic cracks, thereby eliminating the spurious effects typically observed in conventional gradient damage models. The approach delivers physically consistent, mesh-objective crack propagation and seamless integration into standard finite element workflows without requiring predefined crack paths or cohesive interfaces. The framework is implemented using a staggered solution strategy to ensure stable convergence even in nonlinear regimes and is validated through three representative case studies: a cracked plate under hydrogen charging, compact tension testing subjected to internal hydrogen-assisted cracking, and single-edge notch tension tests in sour environments. The simulations reproduce key experimental trends and accurately capture the interplay among hydrogen transport, stress fields, and damage localization. Owing to its predictive capability, numerical robustness, and ease of implementation, the proposed method provides a practical computational tool for assessing hydrogen-induced fracture and structural integrity in hydrogen-rich environments.</div></div>","PeriodicalId":22879,"journal":{"name":"Theoretical and Applied Fracture Mechanics","volume":"143 ","pages":"Article 105426"},"PeriodicalIF":5.6,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145940360","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Fracture behavior of compacted clay under mixed-mode I/II loading: Size effect analysis","authors":"Chuan Lv ,&nbsp;Junjie Wang ,&nbsp;Huikun Ling ,&nbsp;Mingdong Wei ,&nbsp;Hongzhi He ,&nbsp;Shiyuan Huang","doi":"10.1016/j.tafmec.2026.105509","DOIUrl":"10.1016/j.tafmec.2026.105509","url":null,"abstract":"<div><div>Compacted clay serves as a critical material for the core wall of earth-rockfill dams. The investigation into its fracture behavior is paramount for ensuring the operational safety and long-term stability of these structures. Pertaining to the size effect on soil fracture characteristics, prior investigations have predominantly focused on Mode I fracture. Conversely, research addressing the mixed-mode I/II fracture behavior, particularly concerning scale dependency, remains sparse. This study employs the cracked single-edge notched deep beam (CNDB) specimen configuration to execute mixed-mode I/II fracture tests on compacted clay. Macroscopic fracture characteristics, including the load-displacement curve, crack initiation angle, and critical stress intensity factors (<em>K</em>_If and <em>K</em>_IIf), were systemically characterized under the influence of the size effect. Furthermore, the Digital Image Correlation (DIC) technique was utilized to analyze the full-field displacement and strain fields, thereby quantifying the deformation state in the vicinity of the crack tip. The results demonstrated that the bearing capacity of the specimens exhibited an increasing trend with the enlargement of the specimen size. The size effect showed no statistically significant influence on the crack initiation angle. With the increase in the pre-fabricated crack inclination angle, <em>K</em>_If exhibited a decreasing trend, while <em>K</em>_IIf first increased and then decreased; both critical factors clearly manifested size dependency. Under pure Mode II loading, the failure mechanism of CNDB specimens was characterized as a tensile-shear fracture, primarily governed by the tensile stress component. The length of the fracture process zone (FPZ) was observed to increase with the pre-fabricated crack inclination angle, a trend further exacerbated by the enlargement of the specimen size. Finally, the Tangential Stress Contour (TSC) method was successfully validated for its accuracy in predicting the fracture load across different specimen dimensions.</div></div>","PeriodicalId":22879,"journal":{"name":"Theoretical and Applied Fracture Mechanics","volume":"143 ","pages":"Article 105509"},"PeriodicalIF":5.6,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146161695","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Phase-field modelling of mixed-mode fracture and coalescence in fissured rocks","authors":"Sheng Shi ,&nbsp;Yu Zhang ,&nbsp;Fengjin Zhu ,&nbsp;Anxin Meng","doi":"10.1016/j.tafmec.2026.105468","DOIUrl":"10.1016/j.tafmec.2026.105468","url":null,"abstract":"<div><div>The fracture behaviour of quasi-brittle rocks plays a decisive role in the safety and stability of rock mass engineering. The phase-field method offers significant advantages in modelling complex crack propagation. In this study, by introducing a parametric energy degradation function and a geometric crack function, a phase-field damage model is developed to accurately describe the processes of crack initiation, propagation, and coalescence in rocks. In terms of numerical implementation, a staggered iterative algorithm is employed to solve the coupled governing equations of the displacement and phase fields. The model systematically simulates the fracture process of rock specimens containing pre-existing cracks at various inclinations under uniaxial compression, successfully reproducing full-mode fracture behaviours ranging from pure Mode I to pure Mode II, as well as various typical coalescence patterns such as wing cracks and bridge cracks. Furthermore, by analysing the dynamic evolution of the maximum principal stress and the maximum shear stress, the mechanical mechanisms driving crack initiation, propagation, and coalescence under tensile–shear coupled stress fields are elucidated.</div></div>","PeriodicalId":22879,"journal":{"name":"Theoretical and Applied Fracture Mechanics","volume":"143 ","pages":"Article 105468"},"PeriodicalIF":5.6,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146038630","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Progressive damage in non-persistent fissured rock masses: Stress-strain analysis of inclination angle effects","authors":"Rui Yue ,&nbsp;Kegang Li ,&nbsp;Qingci Qin ,&nbsp;Mingliang Li ,&nbsp;Dong Tian ,&nbsp;Jianghu Ji ,&nbsp;Shiqian Yan","doi":"10.1016/j.tafmec.2026.105463","DOIUrl":"10.1016/j.tafmec.2026.105463","url":null,"abstract":"<div><div>Split Hopkinson Pressure Bar (SHPB) impact tests are performed to investigate the effect of fissure inclination on the dynamic mechanical properties of rocks. High-speed cameras recorded the complete rock fracture process. Combined with digital image correlation (DIC) and dynamic photoelastic experimentation, this study systematically investigated the dynamic fracture behavior and failure mechanisms of rocks containing non-persistent fissures at varying inclination angles, analyzing from the perspectives of strain fields and stress fields respectively. Experimental results revealed that the dynamic peak strength and energy utilization rate of sandstone with non-persistent fissure show a significant V-shaped change with the increase of fracture dip angle, and the effect of strength weakening and energy utilization efficiency reduction is the most prominent at 45° dip angle. The digital image correlation reveals that the failure mode evolves from shear failure → tensile-shear mixing failure → tensile failure with the increase of inclination angle. Following wing crack initiation, shear mechanisms are activated (with the exception of the 0° inclination case). The primary failure surface developed through the penetration of wing-shaped crack and far-field crack. Dynamic photoelasticity confirms that stress wave transmission-reflection effects at fissure interfaces are the root cause of the observed failure variations. Specifically, the tensile component of incident waves triggers the emergence of wing cracks and far-field cracks, while the shear component of reflected waves drives accelerated crack propagation and deflection. Isochromatic fringes can serve as an effective indicator of stress concentration characteristics, while crack propagation to follow the direction of maximum principal stress and the path of optimal energy release rate. This study establishes a coupled mechanism of fissure geometry characteristics – stress-strain field evolution – energy dissipation - crack propagation - macroscopic failure, providing a crucial theoretical foundation for stability assessment and dynamic hazard prevention in fissured rock masses within geotechnical engineering.</div></div>","PeriodicalId":22879,"journal":{"name":"Theoretical and Applied Fracture Mechanics","volume":"143 ","pages":"Article 105463"},"PeriodicalIF":5.6,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146038560","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A modified interaction integral approach for XFEM analysis of semipermeable cracks in piezoelectric materials","authors":"Kuldeep Sharma ,&nbsp;Rajalaxmi Rath ,&nbsp;Tinh Quoc Bui","doi":"10.1016/j.tafmec.2026.105477","DOIUrl":"10.1016/j.tafmec.2026.105477","url":null,"abstract":"<div><div>This study introduces a modified interaction integral (MII) approach within the extended finite element method (XFEM) framework to investigate semipermeable cracks in piezoelectric materials. An iterative technique, based on the iterative capacitor analogy (ICA), is developed to compute the semipermeable crack-face electric displacement condition (<span><math><msubsup><mrow><mi>D</mi></mrow><mrow><mi>y</mi></mrow><mrow><mi>c</mi></mrow></msubsup></math></span>). The proposed methodology is validated through three benchmark configurations: center crack, edge crack, and double-edge crack problems. The calculated intensity factors are compared with existing interaction integral methods reported in the literature. For all benchmark cases, the proposed approach demonstrates a notable reduction in percentage error under electro-mechanical loading, especially when the computed <span><math><msubsup><mrow><mi>D</mi></mrow><mrow><mi>y</mi></mrow><mrow><mi>c</mi></mrow></msubsup></math></span> is comparable to the applied electrical loading. In scenarios where <span><math><msubsup><mrow><mi>D</mi></mrow><mrow><mi>y</mi></mrow><mrow><mi>c</mi></mrow></msubsup></math></span> is relatively small (approximately <span><math><msup><mrow><mrow><mo>(</mo><mn>1</mn><mo>/</mo><mn>20</mn><mo>)</mo></mrow></mrow><mrow><mtext>th</mtext></mrow></msup></math></span> or less of the applied electrical loading), the variation in percentage error among the interaction integrals remains within 1%. Thus, in such cases, the standard interaction integral can be confidently employed for fracture mechanics analyses involving semipermeable crack-face conditions. To address inconsistencies in existing solutions for semipermeable edge and double-edge crack problems, new distributed dislocation method (DDM)-based solutions are also developed for comparison with XFEM results. Extensive numerical studies, considering variations in electrical and mechanical loads, polarization angles, and material constants, validate the robustness of the proposed approach in minimizing errors in the evaluation of electric displacement intensity factor (EDIF). Furthermore, the enhanced XFEM framework is employed to analyze macro–micro crack interactions and semipermeable crack-face electric displacement conditions in piezoelectric materials with a single edge-type macro-crack and various configurations of parallel micro-crack arrays.</div></div>","PeriodicalId":22879,"journal":{"name":"Theoretical and Applied Fracture Mechanics","volume":"143 ","pages":"Article 105477"},"PeriodicalIF":5.6,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146038557","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Influence of crack density on energy dissipation and damage evolution in rock–concrete composites under cyclic loading paths","authors":"Jiang Luo,&nbsp;Mingxuan Shen,&nbsp;Bin Du,&nbsp;JieWang,&nbsp;Haiyang Chen","doi":"10.1016/j.tafmec.2026.105474","DOIUrl":"10.1016/j.tafmec.2026.105474","url":null,"abstract":"<div><div>Rock-concrete composite structures are commonly encountered in engineering projects such as tunnels and dams, where pre-existing cracks significantly influence structural stability. Under engineering disturbances, their load-bearing mechanisms become more complex. This study conducted loading-unloading tests via Path I (constant lower limit with stepwise cyclic loading) and Path II (varying upper and lower limits with constant amplitude cycles), combined with acoustic emission monitoring. Based on the division of dissipated energy into damping energy and damage energy, a damage characterization model was established. Results indicate that the number of cracks is the dominant factor affecting macroscopic properties, as it accelerates microcrack coalescence through stress concentration at crack tips, significantly reducing peak strength and stiffness. Path II induced “interface hardening” in single-crack specimens but exacerbated damage in multi-crack specimens due to stress field superposition. The failure mode shifted from tensile failure to tensile-shear composite failure, with Path II being more prone to inducing shear cracks. Acoustic emission results showed a “silent-outburst” pattern in Path I, while damage accumulation was more uniform in Path II. The damage model revealed that when the number of cracks is ≥2, the damage rate under Path II is significantly higher than under Path I, owing to the synergistic effect of variable amplitude loading and stress fields. This study elucidates the coupled damage mechanism of cracks and loading paths, providing a theoretical basis for engineering stability assessment.</div></div>","PeriodicalId":22879,"journal":{"name":"Theoretical and Applied Fracture Mechanics","volume":"143 ","pages":"Article 105474"},"PeriodicalIF":5.6,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146189021","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Examination of the impact of elliptical cavities on the propagation law of stress waves within the tunnel surrounding rock","authors":"Jian Hua,&nbsp;Lei Zhou,&nbsp;Fukuan Nie,&nbsp;Hongdan Zhang,&nbsp;Yao Li,&nbsp;Meng Wang","doi":"10.1016/j.tafmec.2026.105491","DOIUrl":"10.1016/j.tafmec.2026.105491","url":null,"abstract":"<div><div>To examine the effects of elliptical cavities on the dynamic stability and failure patterns of straight-walled arched tunnels, this study utilizes a modified drop-weight impact test apparatus for dynamic experiments and performs numerical simulations via AUTODYN software. The research examines stress wave attenuation, energy dissipation, and the evolving characteristics of the stress field around the elliptical cavity through both experimental and numerical approaches. The findings reveal that elliptical cavities significantly obstruct stress wave propagation, resulting in considerable attenuation of peak stress amplitude and notable energy dissipation. The crack coalescence is observed between the tunnel crown and the rock bridge beneath the elliptical cavity, which leads to shifts in the stress field. Notably, the location of maximum circumferential stress deviates by approximately 10° for the inclination angle of θ = 45°. The results are indicative of the fact that the stability of the tunnel is highest under horizontal stress waves (θ = 90°) and lowest at θ = 45°, where damage initiation and stress concentration primarily occur at the haunches. Further, the dominant coalescence modes vary with cavity inclination: crown crack coalescence at θ = 0° and 15°, shoulder crack coalescence at θ = 30°, 45°, and 60°, and sidewall crack coalescence at θ = 75° and 90°. The tunnel shoulders and sidewalls represent the most vulnerable zones, exhibiting the highest susceptibility to failure.</div></div>","PeriodicalId":22879,"journal":{"name":"Theoretical and Applied Fracture Mechanics","volume":"143 ","pages":"Article 105491"},"PeriodicalIF":5.6,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146189020","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}