Theoretical and Applied Fracture Mechanics最新文献

{"title":"A k-elliptical local enrichment strategy with weighted-superposition shape functions for efficient modeling of interacting multiple crack tips","authors":"D.M. Li,&nbsp;Z.W. Wang,&nbsp;J.C. Wang,&nbsp;Q.D. Zhang","doi":"10.1016/j.tafmec.2026.105863","DOIUrl":"10.1016/j.tafmec.2026.105863","url":null,"abstract":"<div><div>The simulation of interacting multiple cracks in elastic solids remains a challenging problem in computational fracture mechanics, especially when crack tips are closely spaced. Continuum-based numerical methods often rely on global superposition or enrichment strategies that become computationally expensive for complex multi-crack configurations. This paper proposes a novel local enrichment approach that efficiently captures the overlapping crack-tip fields through weighted-superposition shape functions confined to <em>k</em>-elliptical domains around interacting tips. The method constructs the approximation by separately enriching for each tip within its local elliptical region and then applying a weighted superposition, thereby avoiding the cost of global nodal processing. The formulation is implemented within an element-free Galerkin framework and validated on several benchmark problems in isotropic and orthotropic media. Results show that the proposed technique accurately evaluates stress intensity factors for the investigated interacting-crack problems while exhibiting potential computational advantages compared with existing global superposition schemes. The strategy is general and can be readily integrated into other continuum-based discretization frameworks such as FEM, XFEM and IGA.</div></div>","PeriodicalId":22879,"journal":{"name":"Theoretical and Applied Fracture Mechanics","volume":"147 ","pages":"Article 105863"},"PeriodicalIF":6.0,"publicationDate":"2026-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148951297","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 alkali type and concentration on fracture parameters and brittleness of alkali-activated slag concrete by means of WFM, SEM and BEM methods: Experiments and predictions","authors":"Mohammad Hasan Khalilpasha,&nbsp;Alireza Mirzagoltabar Roshan","doi":"10.1016/j.tafmec.2026.105869","DOIUrl":"10.1016/j.tafmec.2026.105869","url":null,"abstract":"<div><div>This study introduces novelty through an extensive experimental analysis of how alkali type and concentration influence the fracture features of alkali-activated slag (AAS) concrete. Two alkali types, NaOH and KOH, were examined at four concentrations (4.5, 5.5, 6.5, and 7.5%). To this end, totally, 315 notched beams underwent three-point bending tests to assess the impact of alkali solution type and concentration on the fracture features and brittleness of AAS concrete. The fracture behavior was analyzed using three approaches: the work of fracture method (WFM), size effect method (SEM), and boundary effect method (BEM). Important fracture parameters, including fracture energy (<span><math><msub><mi>G</mi><mi>F</mi></msub></math></span>,<span><math><msub><mi>G</mi><mi>f</mi></msub></math></span>), fracture toughness (<span><math><msub><mi>K</mi><mi>IC</mi></msub></math></span>), characteristic length (<span><math><msub><mi>L</mi><mi>ch</mi></msub></math></span>), fracture process zone length (<span><math><msub><mi>C</mi><mi>f</mi></msub></math></span>), and reference crack length (<span><math><msubsup><mi>α</mi><mo>∞</mo><mo>∗</mo></msubsup></math></span>), were evaluated in conjunction with microscopic analysis and regression modeling. The outsomes indicate that increasing the alkali concentration from 4.5% to 6.5% resulted in higher <span><math><msub><mi>G</mi><mi>F</mi></msub></math></span> in WFM as well as increased <span><math><msub><mi>G</mi><mi>f</mi></msub></math></span> and <span><math><msub><mi>K</mi><mi>IC</mi></msub></math></span> in SEM and BEM. Conversely, <span><math><msub><mi>L</mi><mi>ch</mi></msub></math></span> in WFM, <span><math><msub><mi>C</mi><mi>f</mi></msub></math></span> in SEM, and <span><math><msubsup><mi>α</mi><mo>∞</mo><mo>∗</mo></msubsup></math></span> in BEM decreased over the same concentration range. However, when the alkali concentration increased from 6.5% to 7.5%, an opposite trend was observed in the fracture parameters. On average, the fracture energy attained from WFM was 2.17 and 2.46 times higher than the corresponding values obtained from SEM and BEM, respectively. In addition, at the same alkali concentration, NaOH-based AAS concrete exhibited superior fracture performance compared to KOH-based mixtures, although with lower ductility. Finally, multivariable predictive models were developed based on the experimental parameters, and comparisons were made with the results of this study and data from the literature. The findings provide mechanistic insight into the influence of alkali cation type on fracture process zone evolution through modifications in C-(A)-S-H gel structure and ITZ characteristics, offering useful guidance for the fracture-based design of alkali-activated concrete structures.</div></div>","PeriodicalId":22879,"journal":{"name":"Theoretical and Applied Fracture Mechanics","volume":"147 ","pages":"Article 105869"},"PeriodicalIF":6.0,"publicationDate":"2026-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148854193","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 mechanics assessment of bacterial self-healing concrete under pure and mixed-mode I/III loading","authors":"Mohammad Sadegh Karimi Doost,&nbsp;Mohammadreza Baradaran,&nbsp;Abolghasem Sayadi,&nbsp;Mohammad Hadi Fattahi","doi":"10.1016/j.tafmec.2026.105889","DOIUrl":"10.1016/j.tafmec.2026.105889","url":null,"abstract":"<div><div>This study investigates the mixed-mode fracture behavior of bacterial self-healing concrete (BSHC) incorporating Bacillus sp. (BS), Sporosarcina cascadiensis (SC), and <em>Staphylococcus aureus</em> (SAS) using the edge-notched disc bend (ENDB) method. Four bacterial concentrations of 10⁵, 10⁶, 10⁷, and 10⁸ cells/ml were examined under mode I, mixed-mode I/III, mixed-mode III/I, and pure mode III loading conditions. The results demonstrated that bacterial incorporation significantly improved fracture resistance and energy dissipation capacity compared with the control concrete (CC). Under tensile-dominated loading, the highest mode I fracture toughness (<em>K</em>_<em>Ic</em>) was achieved by the BS6 mixture, reaching 1.04 MPa·m^0.5, corresponding to a 50.72% improvement relative to the control specimen. Under shear-dominated loading, the SC7 mixture exhibited the highest mode III fracture toughness (<em>K</em>_{<em>IIIc</em>} <!-->), reaching 0.41 MPa·m^0.5, which represents an increase of approximately 51.85%. The Fracture energy (<em>G</em>_<em>f</em>) also increased considerably in the bacterial mixtures, particularly in SC6 and SC7, where the values under mixed-mode and shear-dominated loading exceeded twice those of the control concrete. The effective stress intensity factor (<em>K</em>_<em>eff</em>) revealed that the bacterial healing mechanisms were more efficient under mixed and shear-dominated loading conditions than under pure mode III loading. Scanning electron microscopy (SEM) and energy-dispersive spectroscopy (EDS) confirmed that microbially induced calcium carbonate precipitation (MICP) reduced porosity, densified the cementitious matrix, and improved the interfacial transition zone (ITZ) through localized pore-filling and calcite-precipitation mechanisms. Overall, the SC bacterial system exhibited the most stable and efficient enhancement in fracture performance under mixed-mode loading conditions.</div></div>","PeriodicalId":22879,"journal":{"name":"Theoretical and Applied Fracture Mechanics","volume":"147 ","pages":"Article 105889"},"PeriodicalIF":6.0,"publicationDate":"2026-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148854265","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":"Quantitative analysis of the effect of joint position on strain field evolution and fracture coalescence in rock-like specimens containing a circular hole","authors":"Fei Wang,&nbsp;Yufeng Cheng,&nbsp;Junlong Shang,&nbsp;Changtai Zhou,&nbsp;Shicheng Wei,&nbsp;Tao Dong","doi":"10.1016/j.tafmec.2026.105903","DOIUrl":"10.1016/j.tafmec.2026.105903","url":null,"abstract":"<div><div>In tunnel engineering, construction activities usually traverse natural rock masses containing joints. The positional relationship between joints and holes is a key factor controlling the mechanical properties and damage evolution of surrounding rock. To investigate the effects of the joint-hole positional relationship on strain field evolution, crack propagation, and coalescence behavior, uniaxial compression tests were conducted on rock-like specimens containing a single circular hole and a 45° inclined joint. A multi-field analysis framework integrating acoustic emission (AE), digital image correlation (DIC), the strain quantitative calculation model (SQCM), and COMSOL Multiphysics simulation was established. The results indicate that the peak strength of specimens is governed by the coupling of the boundary constraint effect and the stress superposition effect. When joints and holes are arranged at the central position, the mechanical properties and stress distribution are optimized, whereas proximity to the specimen boundary weakens the boundary constraint and intensifies stress concentration, thereby promoting premature failure. The relative spacing between joints and holes dominates the damage evolution by adjusting the superposition of compressive stress fields: a small spacing aggravates early damage and accelerates strain localization, while an increase in spacing weakens the stress superposition and gradually improves the peak strength. Mechanistically, the top and bottom of circular holes are high-tensile-stress zones, the horizontal sides are high-compressive-stress zones, and significant shear stress concentration occurs at joint tips. These spatially distinct stress characteristics lead to four representative crack coalescence modes, including tensile, compression–shear composite, shear-dominated, and multi-mechanism composite, each corresponding to a unique stress-driven failure path. Among them, the compression–shear composite mode exhibits the highest structural stability and residual load-bearing capacity. Furthermore, the damage variable derived from cumulative AE counts is spatiotemporally synchronized with the evolution of localized strain bands, and the sharp exponential rise in the proportion of high-strain pixels quantified via the SQCM serves as a reliable precursor to macro-instability. In summary, this study provides a comprehensive mechanistic understanding from mesoscopic damage accumulation to macroscopic instability, and lays a solid foundation for the stability assessment of jointed rock masses in tunnel engineering.</div></div>","PeriodicalId":22879,"journal":{"name":"Theoretical and Applied Fracture Mechanics","volume":"147 ","pages":"Article 105903"},"PeriodicalIF":6.0,"publicationDate":"2026-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148854127","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":"Mechanical and failure behaviors of nano-SiO2 modified 3D-printed sandstone with prefabricated flaws: A comparative study of experiment and DEM simulation","authors":"Yao Wang,&nbsp;Wenjie Zhang,&nbsp;Jinrong Xiao,&nbsp;Yonglin Dai,&nbsp;Min Qin,&nbsp;Rui Song,&nbsp;Jianjun Liu,&nbsp;Yuzhu Wang","doi":"10.1016/j.tafmec.2026.105874","DOIUrl":"10.1016/j.tafmec.2026.105874","url":null,"abstract":"<div><div>Discontinuous weak structural planes in rock masses, such as fractures and voids, profoundly affect their physico-mechanical properties and engineering stability. Three-dimensional printing (3DP) has recently gained attention in rock mechanics for its ability to fabricate analogs with complex geometries and controlled internal defects. In this study, sandstone analogs with pre-existing fractures at various inclination angles (0°–90°) were produced using binder jetting 3DP technology. The mechanical strength was enhanced via vacuum-assisted infiltration of nano-SiO₂ solution followed by thermal curing. The mechanical behavior, failure characteristics, and crack evolution mechanisms under uniaxial compression were systematically investigated through laboratory testing and discrete element method (DEM) simulations. A constitutive model for fractured rock masses was also established for supplementary analysis. Results show that vacuum infiltration effectively improves the strength of 3DP rock analogs. Prefabricated flaws reduce overall compressive strength, with uniaxial compressive strength (UCS) first decreasing then increasing as the fracture inclination angle increases. The maximum UCS (30.79 MPa) occurred at 90°, while the minimum (12.32 MPa) was at 30°. The inclination angle governs crack propagation paths and failure modes, resulting in a combined tensile-shear mechanism dominated by shear. DEM simulations on models with 30°, 45°, and 60° inclinations complemented the experiments, with failure processes analyzed from an energy perspective. The numerical results align well with experimental data, validating the approach's reliability. These findings offer new methodologies and insights for fractured rock mechanics and advance 3DP applications in rock engineering and related fields.</div></div>","PeriodicalId":22879,"journal":{"name":"Theoretical and Applied Fracture Mechanics","volume":"147 ","pages":"Article 105874"},"PeriodicalIF":6.0,"publicationDate":"2026-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148854266","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":"Uncertainty quantification of the Master Curve reference temperature and its application to fracture toughness characterization of reactor pressure vessel welded joints","authors":"Xin Zeng,&nbsp;Jianping Tan,&nbsp;Yupeng Cao,&nbsp;Taotao Cheng,&nbsp;Qianyi Ren,&nbsp;Bingxi Wang,&nbsp;Le Mei,&nbsp;Changjun Liu","doi":"10.1016/j.tafmec.2026.105912","DOIUrl":"10.1016/j.tafmec.2026.105912","url":null,"abstract":"<div><div>The reference temperature <em>T</em>₀ is a key parameter in the Master Curve approach for characterizing the fracture toughness of reactor pressure vessel steels. Due to the influence of test temperature, number of specimens, and statistical scatter in fracture toughness data, <em>T</em>₀ exhibits significant uncertainty. In this study, a synthetic <em>K</em>_Jc dataset was generated, and Monte Carlo simulations were performed to investigate the uncertainty of <em>T</em>₀ systematically. The effects of test temperature and the number of valid specimens on the mean value and standard deviation of <em>T</em>₀ were quantitatively characterized under different confidence levels. Subsequently, an improved standard deviation model for <em>T</em>₀ was developed and validated. In addition, fracture toughness tests were conducted on welded specimens of domestic SA-508 Gr.3 Cl.1 steel, including the base metal, weld, and heat affected zone. The results show that <em>T</em>₀ approximately follows a normal distribution, and the proposed standard deviation model exhibits good predictive performance for <em>T</em>₀ uncertainty. Among the tested welded joints, the base metal has the highest <em>T</em>₀ value, followed by the weld, while the heat affected zone has the lowest <em>T</em>₀ value. The conventional Master Curve approach was found to effectively characterize the <em>K</em>_Jc data of the different material regions. Moreover, the uncertainty-adjusted <em>K</em>_Jc(LB) curve demonstrates better overall performance than other deterministic lower-bound models. Furthermore, a probabilistic fracture toughness model incorporating <em>T</em>₀ uncertainty was established, which provides a more reasonable description of the scatter in the experimental data.</div></div>","PeriodicalId":22879,"journal":{"name":"Theoretical and Applied Fracture Mechanics","volume":"147 ","pages":"Article 105912"},"PeriodicalIF":6.0,"publicationDate":"2026-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148951173","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 energy dissipation and crack-arrest mechanisms in bolted pre-flawed granite under coupled static–dynamic loading","authors":"Yu Chen,&nbsp;Hui Liu,&nbsp;Linchong Huang,&nbsp;Yixian Wang,&nbsp;Bangbiao Wu,&nbsp;Xiang Li","doi":"10.1016/j.tafmec.2026.105886","DOIUrl":"10.1016/j.tafmec.2026.105886","url":null,"abstract":"<div><div>Pre-existing flaws in brittle rocks can rapidly evolve into unstable fractures under coupled static–dynamic loading, while bolting may modify the crack-driving force and fracture energy dissipation process. This study investigates the fracture energy dissipation and crack-arrest mechanisms of bolted pre-flawed granite through Split Hopkinson Pressure Bar tests, grain-based discrete-element simulations and analytical stress analysis. Granite specimens containing a 45° through-going flaw were tested in unbolted and bolted conditions under impact air pressures of 0.65–0.80 MPa and axial preloads of 0–30 MPa. The results show that bolting increased the dynamic compressive strength of pre-flawed granite by approximately 16% and reduced the peak strain rate by about 27%, indicating delayed impact-induced crack propagation. However, the crack-arrest efficiency was strongly dependent on axial preload. The strength enhancement decreased from about 18% without axial preload to 8.5% at 30 MPa, suggesting that excessive preload may weaken the incremental bolting effect through interface damage and shear–tension interaction. Fracture energy dissipation exhibited a non-monotonic dependence on axial preload and reached its optimum at 20 MPa, where flaw closure, interfacial frictional slip, localized plastic deformation and distributed microcracking were simultaneously activated. Grain-based simulations further revealed that bolting changed the dominant cracking mode from grain-boundary tensile cracking to intragranular shear-dominated fracture, thereby reducing breakage energy and suppressing post-peak kinetic energy release. The analytical stress model showed that bolting reduces the effective crack-driving intensity near flaw tips by redistributing the local stress field. These findings clarify how axial preload, interface response and grain-scale fracture transition jointly control crack arrest in bolted pre-flawed granite under coupled static–dynamic loading.</div></div>","PeriodicalId":22879,"journal":{"name":"Theoretical and Applied Fracture Mechanics","volume":"147 ","pages":"Article 105886"},"PeriodicalIF":6.0,"publicationDate":"2026-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148854125","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 phase-field model for dynamic fracture of micropolar media considering the tension-torsion coupling effect","authors":"Canjie Huang,&nbsp;Hongjun Yu,&nbsp;Yaode Yin,&nbsp;Yingbin Zhang,&nbsp;Shuai Zhu,&nbsp;Jianshan Wang","doi":"10.1016/j.tafmec.2026.105891","DOIUrl":"10.1016/j.tafmec.2026.105891","url":null,"abstract":"<div><div>This study incorporates the tension-torsion coupling (TTC) effect and micropolar rotational inertia to develop a dynamic micropolar phase-field framework applicable to micropolar media, particularly chiral materials with TTC behavior. A key feature of the proposed model is that the TTC effect changes the dispersion behavior of micropolar waves, leading to frequency-dependent wave propagation in micropolar media. Furthermore, the TTC coefficient affects the evolution of crack topology. The presence of TTC effect induces asymmetric microrotation fields, leading to a transition from symmetric to asymmetric crack propagation, which may be accompanied by secondary dynamic crack branching. The proposed model is validated against both static and dynamic benchmark tests, including the uniaxial tensile test of limpet tooth specimen, the Kalthoff–Winkler test, concrete three-point impact bending, and L-shaped concrete plate dynamic fracture tests. The proposed model shows good agreement with experimental observations of crack propagation patterns.</div></div>","PeriodicalId":22879,"journal":{"name":"Theoretical and Applied Fracture Mechanics","volume":"147 ","pages":"Article 105891"},"PeriodicalIF":6.0,"publicationDate":"2026-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148854126","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":"Through-thickness 3D-printed bio-inspired fibers to enhance mode I fracture resistance of composite bonded joints","authors":"Zhiyuan Xu,&nbsp;Ran Tao,&nbsp;Kunal Masania,&nbsp;Sofia Teixeira de Freitas","doi":"10.1016/j.tafmec.2026.105843","DOIUrl":"10.1016/j.tafmec.2026.105843","url":null,"abstract":"<div><div>Composite bonded joints are susceptible to sudden and brittle failure, especially under mode I opening loading conditions. To improve crack resistance under mode I, conventional solutions use through-thickness reinforcements, such as rivets, which is effective in delaying the crack growth but damage the performance of the composite. This study explores an alternative through-thickness reinforcement consisting of 3D-printed overlapping curl (OC) fibers with sacrificial bonds and hidden lengths (SBHL) to enhance fracture resistance under mode I of composite bonded joints. The OC fibers are embedded through the thickness of a structural epoxy, oriented perpendicular to the crack propagation direction, enabling effective activation of hidden length unfolding under mode I opening conditions. This through-thickness reinforcement fully exploits the SBHL toughening mechanism without introducing detrimental effects to the CFRP substrate, in contrast to conventional techniques such as Z-pinning or riveting. Double cantilever beam experiments demonstrate that the OC topology is essential for effective toughening, as it anchors the OCs within the adhesive and prevents pull-out, allowing hidden length unfolding that leads to extended crack bridging distance and increases the mode I energy release rate by up to 119<!--> <!-->%. Furthermore, numerical simulations are conducted to systematically explore the influence of OC mechanical parameters, providing design guidelines for improving the fracture performance of CFRP adhesively bonded joints.</div></div>","PeriodicalId":22879,"journal":{"name":"Theoretical and Applied Fracture Mechanics","volume":"147 ","pages":"Article 105843"},"PeriodicalIF":6.0,"publicationDate":"2026-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148854194","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Dynamic fracture coalescence across a finite rock bridge in shale containing opposing semi-penetrating flaws","authors":"Yucheng Wei,&nbsp;Ning Luo,&nbsp;Yabo Chai,&nbsp;Jianan Zhou,&nbsp;Hu Zhang,&nbsp;Chen Lin,&nbsp;Guangrui Ma,&nbsp;Guofeng Liang,&nbsp;Tangwen Zhong","doi":"10.1016/j.tafmec.2026.105892","DOIUrl":"10.1016/j.tafmec.2026.105892","url":null,"abstract":"&lt;div&gt;&lt;ul&gt;&lt;li&gt;&lt;span&gt;•&lt;/span&gt;&lt;span&gt;&lt;div&gt;Opposing semi-penetrating flaws define a finite 3D rock-bridge problem.&lt;/div&gt;&lt;/span&gt;&lt;/li&gt;&lt;li&gt;&lt;span&gt;•&lt;/span&gt;&lt;span&gt;&lt;div&gt;A configuration-specific index describes apparent rock-bridge resistance.&lt;/div&gt;&lt;/span&gt;&lt;/li&gt;&lt;li&gt;&lt;span&gt;•&lt;/span&gt;&lt;span&gt;&lt;div&gt;Matrix damage dominates, while bedding redirects and connects fracture paths.&lt;/div&gt;&lt;/span&gt;&lt;/li&gt;&lt;li&gt;&lt;span&gt;•&lt;/span&gt;&lt;span&gt;&lt;div&gt;Measured-wave diagnostics reveal mixed flaw-tip motion and energy transfer.&lt;/div&gt;&lt;/span&gt;&lt;/li&gt;&lt;/ul&gt;&lt;/div&gt;&lt;div&gt;&lt;div&gt;Transient disturbances induced by deep excavation and reservoir stimulation can activate and interconnect non-persistent discontinuities in bedded shale, where finite rock bridges govern the transition from localized damage to macroscopic failure. Nevertheless, it remains unclear how bedding orientation affects the dynamic coalescence of opposing semi-penetrating flaws across a finite three-dimensional rock bridge and how matrix and bedding interfaces contribute to this process. In this study, quasi-static compression and split Hopkinson pressure bar (SHPB) tests were conducted on cylindrical shale specimens with two opposing semi-penetrating flaws separated by a finite rock bridge. Quasi-static results were used to constrain orientation-dependent PFC3D models. A bedding-modified finite-element correction defined a configuration-specific apparent bridge-zone resistance index, while measured stress waves drove a coupled FLAC3D–PFC3D model to examine damage localization, flaw-tip kinematics, and energy transfer. Dynamic tests compared bedding orientations under a common nominal apparatus setting, and a supplementary fixed-orientation series evaluated loading-intensity sensitivity. After experiment-constrained dynamic adjustment, the coupled model matched the principal macroscopic responses and coalescence morphologies under the tested conditions. Peak response, apparent rock-bridge resistance, and coalescence trajectory vary non-monotonically with bedding orientation, reflecting competition between matrix-crossing and bedding-guided paths. Most modeled bond-breakage events occur in matrix contacts, whereas activated bedding interfaces redirect and connect dispersed damage, indicating matrix-dominated damage accumulation but bedding-regulated path development. Flaw-tip deformation involves mixed opening–sliding behavior rather than idealized single-mode fracture. Increased loading intensity raises peak capacity and accelerates post-peak bridge degradation without substantially changing the primary coalescence path. These findings clarify coalescence of opposing flaws across finite rock bridges in anisotropic shale.&lt;/div&gt;&lt;/div&gt;&lt;div&gt;Transient disturbances induced by deep excavation and reservoir stimulation can activate and interconnect non-persistent discontinuities in bedded shale, where finite rock bridges govern the transition from localized damage to macroscopic failure. Nevertheless, it remains unclear how bedding orientation affects the dyn","PeriodicalId":22879,"journal":{"name":"Theoretical and Applied Fracture Mechanics","volume":"147 ","pages":"Article 105892"},"PeriodicalIF":6.0,"publicationDate":"2026-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148854382","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}