Multiscale Fracture Mechanisms in Granite with Pre- existing Cracks: Experimental Characterization and Grain- Based Numerical Modeling

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This study systematically investigates the deformation and failure mechanisms of granite containing single and double pre-existing fractures through integrated mechanical testing, acoustic emission (AE) monitoring, and multiscale numerical simulations. Key findings reveal: (1) Fracture geometry controls strength: Uniaxial compressive strength (UCS) increases with fracture inclination angle, while elastic modulus remains stable. For double-fractured specimens, strength peaks at a rock bridge angle of 60°, where collinear crack alignment induces weakest resistance; (2) Three-stage evolution: AE activity transitions sequentially from initial compaction (minor events), peak activity (crack coalescence), to post-failure stabilization; (3) Contrasting failure modes: Single fractures exhibit progressive tensile-dominated failure with localized shear, whereas double fractures trigger abrupt tensile-shear hybrid failure; (4) Multiscale crack propagation: Under uniaxial compression, microcracks initiate at inter-mineral boundaries, propagate along intra-mineral interfaces, and culminate in rapid intra-crystalline crack coalescence, forming macroscopic fracture surfaces. These findings provide critical insights into fracture-driven rock failure, bridging microscale damage mechanisms to macroscale engineering behavior. Earth and environmental sciences/Natural hazards Earth and environmental sciences/Solid earth sciences/Sedimentology Pre-existing fractures Rock strength Crack propagation Failure mode Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 Figure 12 1 Introduction Rock masses, as primary constituents of the Earth's lithosphere, inherently contain defects such as fractures, joints, and voids due to long-term geological processes and anthropogenic activities [ 1 – 5 ]. Moreover, when these defects are subjected to further action, new cracks will sprout, resulting in damage expansion and penetration [ 6 – 9 ]. As the main material of roads, bridges, hydropower, mines and other projects, understanding fracture-driven rock behavior is thus critical for ensuring geotechnical safety and optimizing design strategies [ 10 – 11 ]. Extensive studies have explored the mechanical response of fractured rocks[ 12 – 15 ]. Early experimental work by Bobet & Einstein [ 16 ] revealed crack coalescence patterns in biaxially compressed specimens, while Prudencio et al. [ 17 ] classified four failure modes of jointed rock masses. For dual fractures, Chen et al. [ 18 – 19 ] demonstrated that joint connectivity governs strength anisotropy, and Cho et al. [ 20 ] linked fracture geometry to macroscopic deformation. With the development of numerical simulation, grain-based models (GBM) have emerged as powerful tools to simulate crystalline rock fracturing [ 21 – 22 ]. Potyondy & Cundall [ 23 ] pioneered bonded-particle GBMs, yet traditional smooth-joint (SJ) models oversimplify inter-grain mechanics, failing to capture realistic crack paths [ 24 – 25 ]. Recent studies by Liu et al. [ 26 ] and Wang et al. [ 27 ] improved boundary modeling but lacked multiscale validation against experimental data. Despite these advances, two critical gaps remain: (1) Cross-scale linkage: Most studies focus either on macro-scale experiments or micro-scale simulations, neglecting integrated analyses bridging crack initiation (mineral boundaries) to macro-fracture formation. (2) Model limitations: Existing GBMs inadequately simulate intra-crystalline cracking and multi-mineral interactions, limiting their predictive accuracy. To address these gaps, this study combines multiscale experiments (mechanical testing, acoustic emission monitoring) with an innovative Multilevel Parallel Bonded-GBM (Multi Pb-GBM). Using granite from the Jiaodong Group, we systematically investigate how fracture geometry (angle, rock bridge configuration) controls strength and failure modes, the evolution of micro-to-macro crack networks under uniaxial compression, and the role of mineral heterogeneity in fracture propagation. The research findings provided a database for in-depth study on mechanical properties of rock materials. 2 Mechanical experiment 2.1 Test scheme Rock samples in the following tests were granite taken from Jiaodong Group, and the sample heights were 100 mm × 50 mm × 30 mm (length × height × thickness) [ 28 ]. A cutting machine was used to predict cracks in the specimens. The length of the fractures was 15 mm, and the width was 1 mm. The crack distributions of rock samples were divided into 2 types, including single crack and double cracks, as shown in Fig. 1 . The dip angle of rock sample cracks was set as 0°, 30°, 60° and 90°. In order to avoid the influence of accidental errors, 3 identical samples were made for each group, and repeated experiments were carried out. A uniaxial compressive test was conducted on the WES-2000 digital hydraulic servo testing machine, and the uniaxial compressive strength (UCS) was recorded. The loading speed was set as 0.02 kN/s, and the loading was applied until the sample was destroyed. A PCI-2 acoustic emission system was used to collect the acoustic emission data [ 29 ]. In order to not affect the crack development observation, acoustic emission sensors were attached to the two sides of the model. The boundary conditions of the model samples are shown in Fig. 2 . 2.2 Failure mode Figure 3 showed the single crack test sample and failure results. During the loading process, the crack tip was the first area where the stress was concentrated. The failure of the sample with a crack angle of 0° started from the end of the horizontal crack and extended to the sample boundary from the upper right side and the lower left side, respectively. As a hard brittle rock mass, the macroscopic fracture of granite was instantaneous, so no new fracture point was observed during the experiment. In the sample with a crack angle of 30°, wing-like cracks were first generated at the crack tip, which expanded along the direction perpendicular to the prefabricated crack, and then developed in the direction of the maximum compressive stress. Secondary cracks gathered in large numbers at the lower end of the primary crack, and then a third main crack appeared on the lower right side, extending through the entire rock mass. No obvious sliding shear plane was generated in this process. The failure mode of specimens with 60° fracture angle was similar to that of 30° specimen, and the reverse wing fracture was obvious. When the dip angle increased to 90°, the end crack only expanded in a small amplitude after initiation, and multiple points in the specimen appeared cracks simultaneously. The main crack generated by the splitting failure extended along the loading direction and finally directly penetrated to the surface of the loading plate. In order to study the compressive strength characteristics and crack propagation laws of intermittently fractured rock, uniaxial compression tests were conducted on double primary fracture samples, and the test results were shown in Fig. 4 . When the rock bridge angle was 0°, shear-splitting failure occurred at the tips of the two prefabricated cracks. After penetrating the primary fissures, the two split cracks extended towards the loading plate, and shear cracks developed between the prefabricated cracks. When the rock bridge angle was 30°, minor secondary cracks appeared at the tip of the prefabricated crack, and then winglike cracks began to gather near the left primary fissures, resulting in the main fracture zone, which may be caused by the uneven force of the sample during loading. The rock bridge specimens with 60° and 90° rock bridge inclination angle maintained good integrity during loading, and the double joints of the specimens with 60° were almost collinear, and the prefabricated cracks above the rock bridge angle started to produce a wing-like fracture, forming a 60°damage surface. On the other hand, the rock bridge dip angle of 90° was affected by the boundary effect, and the splitting failure occurred directly next to the precast fissure, and the lateral expansion deformation was obvious. 2.3 Stress-strain law The stress-strain curve was recorded during the test. As can be seen from Fig. 5 , samples with different crack inclination angles had a compaction stage in the initial loading stage, and then the rock entered into a linear elastic stage, and the axial stress increased linearly with the increase of strain. With the progress of loading, invisible micro-cracks appeared inside the rock, and the failure entered into plastic deformation stage, and unrecoverable deformation developed. The stress load continued to increase until the peak strength was reached, the specimen entered into failure stage, the stress-strain curve dropped rapidly, and the brittle rock had no obvious residual strength. The peak uniaxial compressive strength of single-fracture rock with different angles was 104.76, 112.82, 120.54 and 134.98MPa, respectively. With the increasing of fracture inclination angle, the uniaxial compressive strength increased, while the elastic modulus was basically the same. With the increasing of rock bridge angle, the strength of rock with intermittent double fracture had compressive strength of 109.88, 124.10, 51.68 and 116.98MPa, respectively. Rock was most prone to failure when the rock bridge inclination angle was 60°, because the fracture inclination angle selected by the intermittent double joint test was also 60°, and when the rock bridge was in line with the primary cracks, the compressive strength of rock mass was reduced. 2.4 AE characteristics Acoustic emission refers to a phenomenon that occurs when the external load exceeds a certain critical value, micro-yielding or deformation occurs in the internal defect region of a solid, and excess energy is released instantaneously in the form of elastic waves [ 7 , 12 ]. The ringing count in acoustic emission monitoring represents the number of cracks in the specimen. The acoustic emission characteristics of rock samples are obviously different due to the different fracture results. The acoustic emission monitoring results of single fracture specimens were shown in Figure. 6. As the stress increased, the impact count and cumulative energy of 30°, 60° and 90° joint specimens increased slowly. When the stress reached the peak strength, the impact number increased sharply and attained the maximum value. The 0° fracture sample exhibited two concentrated periods of microcrack formation, which were the two main fracture surfaces that developed at the upper and lower ends of the pre-existing fissure. As shown in Figure. 7, the acoustic emission results of the interrupted double-fractured rock mass showed that when the rock bridge inclination angle was 60°, a large number of acoustic emission signals appeared, and the number of ringing had been at a higher level since 15 seconds of the test, the sample was prone to failure and the stress-strain curve was smoother. By comparing the deformation failure process characteristics of fractured rock mass, the AE process can be divided into three stages, including initial compaction and rising stage, peak stage and stable stage. First of all, under axial stress loading, micro-cracks and pores in fractured rock mass were compressed and closed. At this time, there were only a few acoustic emission events and a slight increasing trend. In the peak zone, cracks inside the specimen were connected to form a large fracture surface, and acoustic emission events increased sharply. In the stable zone, the number of cracks did not change after macroscopic failure, and the cumulative ringing number became stable. 3 Numerical simulations Through physical simulation testing, comprehensive conclusions of fracture initiation and propagation, stress-strain relationship and failure modes of fractured rock mass can be obtained. However, a large number of experiments demonstrate that granite fracture occurs not only around mineral boundaries but also inside minerals [ 24 – 25 ]. It is difficult to directly observe the process of microscopic damage and crystal scale fracture order in rock mass during physical tests, but numerical simulation technology is a reasonable and effective way to simulate rock mechanics issues [ 26 – 27 ]. 3.1 Multilevel Parallel bonded -Grain Based Modeling The GBM model has a powerful ability to simulate the fracture behavior of crystalline rock and is suitable for granite simulation. Potyondy and Cundall introduced GBM into PFCS to simulate the microstructure of crystalline rocks [ 30 – 31 ]. Each crystal consists of several bonded particles and the crystal is allowed to deform and break. The GBM model in PFC2D can not only simulate the initiation of microcracks and the interaction with the crystal boundary, but also captures the cracking behavior inside the crystal structure [ 25 – 26 , 32 ]. The traditional GBM method uses polygons to simulate crystals in granite samples, bonded by a parallel bond model, with smooth joint (SJ) being used to simulate the grain boundaries, because these boundaries are easily generated. However, the SJ model has obvious shortcomings: 1. crystal boundaries are treated as cracks with bond strength and do not produce local geometric expansion effects, resulting in a loss of the ability to force particles to roll against each other; 2. contact ignores the initial cohesion around the boundary and the rotational resistance between particles is absent; 3. under large strains, the SJ model only works when the surface clearance is negative [ 25 , 28 , 33 ]. In order to overcome these shortcomings a multi-Pb-GBM model is proposed to simulate the microstructure of crystalline granite. The parallel contact model is used to describe the crystal boundary instead of the traditional SJ model. The parallel contact model can be divided into three types: intra-crystal contact, intra-crystal boundary contact of the same mineral and boundary contact of different mineral species, as shown in Fig. 8 . The detailed modeling principles and optimization process can be found in the literature [ 29 ]. 3.2 Micro parameters calibration For the calibration experiment model, length is 100 mm and width is 50 mm, assembled of 14558 particles with a radius from 0.1 to 0.155 mm. The mineral crystal sizes are set to 3.3, 3.8, 2.8, 2.2 mm for K-feldspar, plagioclase, quartz and biotite respectively [ 28 – 29 ]. Different types of minerals are arrangement inside the numerical model randomly, and the volume fraction are 40%, 20%, 30% and 10%. The calibration models were shown in Figure. 9. Parameters put into the calculation model must be calibrated to the results of UCS and UTS tests. By adjusting the microscopic parameters, the stress-strain curve of the numerical experiment is basically consistent with the physical experiments (Figure.10). The calibrated micro-parameters and the experiment results were shown in Table 1 . The results indicate that the simulation was reasonable. Table 1 Microscopic parameters of the numerical simulation Microparameters K-feldspar Plagioclase Quartz Biotite Particle parameters Minimum particle radius R min (mm) 0.15 0.15 0.15 0.15 Particle size ratio R max /R min 1.52 1.52 1.52 1.52 Size of the crystal types (mm) 2.80 3.30 2.30 1.70 Particle density \(\:\rho\:\) (kg/m 3 ) 2600 2630 2650 2850 Friction coefficient of the particle \(\:\mu\:\) 0.80 0.80 0.80 0.80 Parallel bond model parameters Young's modulus \(\:\stackrel{̄}{E}c\) (GPa) 85 81 100 65 Normal/shear stiffness \(\:{K}_{n}/{K}_{s}\) 2.5 2.5 2.5 2.5 Tensile strength \(\:{\stackrel{̄}{\sigma\:}}_{t}\) (MPa) 60 55 65 45 Cohesive force \(\:\stackrel{̄}{c}\) (MPa) 85 95 115 55 Friction angle \(\:\beta\:\) ( o ) 40 41 42 38 Friction coefficient 0.5 0.5 0.5 0.5 3.3 Simulation results The calculation results of the 60° specimen that was most prone to failure were taken as an example to discuss the fracture characteristics of the rock material at the microscopic scale, as shown in Figure. 11. Four characteristic time points had been selected: Ⅰ was the crack initiation point at the tip of the prefabricated fissure; Ⅱ was the expansion and bending of the wing-shaped crack and the germination point of micro-cracks; Ⅲ was the peak strength point where a large number of internal micro-fractures gathered; Ⅳ was the point of overall failure of the specimen. The fracture development of the single fissure specimen at these four time points was shown in Fig. 11 (a). The thickness of the line segments reflected the number of micro-cracks within those areas, offering a more detailed account of the fracture evolution process of the fissured rock mass during the experiment. Figure 11 (b) depicted the stress-strain curve corresponding to the number of cracks. And Fig. 11 (c) showed the sequence of multi-level crack generation at the same time step, which helped us clearly understand the process of fracturing within the crystal during the uniaxial compression process, including the internal contact of crystals, contact at the boundaries of the same type of mineral crystals, and contact at the boundaries of different types of mineral crystals. During the loading process, stress concentration zones first emerged at the tips of the fissures. For the 60° specimen, wing-shaped cracks initiated earliest at the tip of the prefabricated fissure and began to expand perpendicular to the direction of the pre-existing fissure. Subsequently, the upper end of the prefabricated fissure propagated downward, and the lower end propagated upward, both curving to develop in the direction of maximum compressive stress. Secondary fractures accumulated extensively at the ends of the prefabricated fissures, followed by the generation of two additional collinear joints along the plane of the prefabricated fissure, which inclined the specimen as a whole towards shear failure, revealing a macroscopic shear surface. Eventually, the wing-shaped crack that first formed at the upper end turned towards the direction of maximum compressive stress, communicating with the lower boundary and forming the rock mass failure plane with the collinear joints, transforming local shear fractures into local splitting fractures. The rock mass underwent overall fragmentation, and the stress-strain curve decreased. Figure 12 presented the numerical experiment results of double fracture with 60° fracture and 30° rock bridge, showing the fracture conditions of the specimen at four characteristic points, as well as the corresponding types and quantities of fractures. From the figure, it was observed that secondary fractures first occurred at the tips of the two prefabricated fissures, and both extended along the direction of the principal compressive stress. Subsequently, the upper prefabricated fissure began to bifurcate at its tip, giving rise to several secondary wing-shaped fractures. Following this, the upper extension of the upper prefabricated fissure and the lower extension of the lower prefabricated fissure started to accumulate micro-cracks, resulting in two distinct bands of micro-cracks. Upon further loading, the fracture band on the upper left side expanded to the specimen's boundary, causing the specimen to undergo macroscopic shear failure in that area. It was evident that micro-cracks first appeared at the grain boundaries of different minerals, followed by fractures occurring at the grain boundaries within the same mineral, and finally, the number of internal contact fractures within the crystals rapidly increased to form a macroscopic fracture surface. 4 Conclusions The inclination angle of pre-existing fractures exerts a significant influence on the mechanical properties of granite. Experimental results demonstrate that uniaxial compressive strength (UCS) increases systematically with fracture inclination angle, while the elastic modulus remains nearly constant across all tested configurations. For double-fractured specimens, the rock bridge angle plays a critical role: strength peaks at 60°, where collinear alignment of fractures and rock bridge amplifies stress localization, leading to reduced load-bearing capacity. This geometric dependency underscores the importance of fracture orientation in predicting rock mass stability. Acoustic emission monitoring reveals a triphasic failure process in fractured granite. During initial loading, microcrack closure induces sparse AE activity (compaction phase). As stress escalates, rapid crack coalescence triggers an abrupt surge in AE signals (peak phase), correlating with macroscopic fracture formation. Post-failure, AE activity stabilizes as crack networks reach equilibrium (stable phase). This temporal pattern provides a diagnostic framework for real-time monitoring of fracture-driven instability. Single-fractured specimens exhibit progressive tensile-dominated failure, with minor shear components localized near fracture tips, preserving partial structural integrity. In contrast, double-fractured specimens undergo sudden tensile-shear hybrid failure due to stress interference between fractures, resulting in complete disintegration. The dominance of tensile behavior in double fractures highlights the synergistic effects of multiple defects on catastrophic failure. The Multilevel Parallel Bonded-GBM (Multi Pb-GBM) successfully replicates fracture evolution from mineral-scale initiation to macroscopic rupture. Simulations confirm that microcracks first nucleate at inter-mineral boundaries, propagate along intra-mineral interfaces, and culminate in intra-crystalline coalescence. Tensile cracks dominate, while shear cracks concentrate near mineral boundaries. This model bridges microscale heterogeneity to macroscale nonlinear behavior, offering a predictive tool for assessing brittle fractures in engineering contexts such as underground excavations and slope stability. Declarations Conflicts of Interest The authors declared that they have no conflict of interest regarding this study. We declare that we do not have any commercial or associative interests that represent a conflict of interest in connection with the paper submitted. Funding statement declaration Funding : National Science Foundation of China (Grant Nos. 42072305) and the Second Tibetan Plateau Scientific Expedition and Research Program (Grant no. 2019QZKK0904). Author Contribution Jie Guo and Guang Li wrote the main manuscript text, and Fengshan Ma prepared figures in the manuscript. All authors have read and agreed to the published version of the manuscript. Acknowledgments This research was supported by the National Science Foundation of China (Grant Nos. 42072305) and the Second Tibetan Plateau Scientific Expedition and Research Program (Grant no. 2019QZKK0904). Data Availability Data is provided within the manuscript. References Sajid, M. et al. Petrographic features as an effective indicator for the variation in strength of granites. Eng. Geol. 202 , 44–54 (2016). Li, G. et al. Damage evolution mechanism and deformation failure properties of a roadway in deep inclined rock strata. Eng. Fail. Anal. 143 , 106820 (2023). Yilmaz, N. G. et al. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-6926683","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":476011012,"identity":"77301e77-e86e-4178-b5b9-2544e42994bf","order_by":0,"name":"Jie Guo","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA/0lEQVRIie3RMUvEMBTA8VcCNwm3KoL5CukoSD+H4PJK4CYjgssN59GptxRdO+lX8L7Bk0BdxK6BW+ri7Bj0EF+V4pTD2wTzhwyB9+OlFCAW+6MphCMAIQrALciESbIF4SwfJr9KHms676btyXjBpHu7lONrSl49ZGchkroJKnxcmdoyya8e0tqh2KtAXwRJfapUXq5M8UWqBsEB7ANQHnrnN/l4MrcDkS2J901E7vakIHPXE/QzVISjjVvUzgt/S6PNkgmPUbp0eXlYKR3estBN6meZuWnt/bNfz+VBa63z0yy8hWCkhgsl5fCDVGC+31KA6H6u63l4NBaLxf5tn4HBYV4OQXE+AAAAAElFTkSuQmCC","orcid":"","institution":"Chinese Academy of Sciences","correspondingAuthor":true,"prefix":"","firstName":"Jie","middleName":"","lastName":"Guo","suffix":""},{"id":476011013,"identity":"eed7486c-6a51-4cd3-938b-79d91d70de0b","order_by":1,"name":"Guang Li","email":"","orcid":"","institution":"Chinese Academy of Sciences","correspondingAuthor":false,"prefix":"","firstName":"Guang","middleName":"","lastName":"Li","suffix":""},{"id":476011015,"identity":"e378b2fa-f1c5-44f7-88dc-77127f944073","order_by":2,"name":"Fengshan Ma","email":"","orcid":"","institution":"Chinese Academy of Sciences","correspondingAuthor":false,"prefix":"","firstName":"Fengshan","middleName":"","lastName":"Ma","suffix":""}],"badges":[],"createdAt":"2025-06-19 02:23:05","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6926683/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6926683/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1038/s41598-025-12159-4","type":"published","date":"2025-07-19T15:57:13+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":85565869,"identity":"9c7979e4-73c4-40d5-9723-93dd822a3a14","added_by":"auto","created_at":"2025-06-27 14:31:24","extension":"jpeg","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":81134,"visible":true,"origin":"","legend":"\u003cp\u003eRock specimens: (a) single crack; (b) double cracks.\u003c/p\u003e","description":"","filename":"image1.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-6926683/v1/f106d4cd8ef2df1012eb6bf3.jpeg"},{"id":85565871,"identity":"26d0aab3-52d8-4240-8363-c1f6f625ce86","added_by":"auto","created_at":"2025-06-27 14:31:24","extension":"jpeg","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":24615,"visible":true,"origin":"","legend":"\u003cp\u003eThe boundary conditions of the model.\u003c/p\u003e","description":"","filename":"image2.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-6926683/v1/286eefd0ddcbbcac9e34cde4.jpeg"},{"id":85565870,"identity":"c6815395-8a0b-450f-8822-b1427063f75e","added_by":"auto","created_at":"2025-06-27 14:31:24","extension":"jpeg","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":258960,"visible":true,"origin":"","legend":"\u003cp\u003eFailure mode of single crack samples: (a) 0°; (b) 30°; (c) 60°; (d) 90°.\u003c/p\u003e","description":"","filename":"image3.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-6926683/v1/54c2e427ada0458ad533667b.jpeg"},{"id":85565873,"identity":"71099a6e-4ec0-428e-884a-192577eaba9a","added_by":"auto","created_at":"2025-06-27 14:31:24","extension":"jpeg","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":240731,"visible":true,"origin":"","legend":"\u003cp\u003eFailure mode of double crack samples: (a) 0°; (b) 30°; (c) 60°; (d) 90°.\u003c/p\u003e","description":"","filename":"image4.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-6926683/v1/69f0586404a89ee127a5725c.jpeg"},{"id":85565877,"identity":"3ed5163d-7a8c-4948-b31d-67e94a89c20a","added_by":"auto","created_at":"2025-06-27 14:31:25","extension":"jpeg","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":90858,"visible":true,"origin":"","legend":"\u003cp\u003eStress-strain relationship in uniaxial compression test:\u003c/p\u003e\n\u003cp\u003e(a) single crack; (b) double cracks.\u003c/p\u003e","description":"","filename":"image5.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-6926683/v1/49f875faa9630dccd66206a1.jpeg"},{"id":85566585,"identity":"0f606e38-1d77-44fa-a9e5-e0b22756be80","added_by":"auto","created_at":"2025-06-27 14:39:25","extension":"jpeg","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":154983,"visible":true,"origin":"","legend":"\u003cp\u003eResults of acoustic emission ringing in single fractured rock samples:\u003c/p\u003e\n\u003cp\u003e(a) 0°; (b) 30°;(c) 60°;(d) 90°.\u003c/p\u003e","description":"","filename":"image6.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-6926683/v1/810b5561d0c94db2f458383a.jpeg"},{"id":85566584,"identity":"1702cfe3-dc07-466b-8b85-7e1dde332e5d","added_by":"auto","created_at":"2025-06-27 14:39:24","extension":"jpeg","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":163524,"visible":true,"origin":"","legend":"\u003cp\u003eResults of acoustic emission ringing in double fractured rock samples:\u003c/p\u003e\n\u003cp\u003e(a) 0°; (b) 30°;(c) 60°;(d) 90°.\u003c/p\u003e","description":"","filename":"image7.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-6926683/v1/97fa657b2597e5c1fd111bae.jpeg"},{"id":85565881,"identity":"f962ea5b-f383-4037-90c3-4e3f5984198d","added_by":"auto","created_at":"2025-06-27 14:31:25","extension":"jpeg","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":334650,"visible":true,"origin":"","legend":"\u003cp\u003eMultistage PBM import GBM. (a) Grain-based model; (b) a parallel bonded model; (c) classification of the three Pb-GBM.\u003c/p\u003e","description":"","filename":"image8.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-6926683/v1/dc460b0909407498b0c919fe.jpeg"},{"id":85565892,"identity":"85fa28db-141c-4f13-a16f-74a829f714af","added_by":"auto","created_at":"2025-06-27 14:31:25","extension":"jpeg","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":242189,"visible":true,"origin":"","legend":"\u003cp\u003eCalibration model and microcrack distributions in numerical tests:\u003c/p\u003e\n\u003cp\u003e(a) UCS tests; (b) UTS tests.\u003c/p\u003e","description":"","filename":"image9.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-6926683/v1/03688514c3d1da12026087a9.jpeg"},{"id":85566797,"identity":"0606f027-c777-4e01-873d-573e9e2d351f","added_by":"auto","created_at":"2025-06-27 14:47:25","extension":"png","order_by":10,"title":"Figure 10","display":"","copyAsset":false,"role":"figure","size":5713,"visible":true,"origin":"","legend":"\u003cp\u003eThe stress–strain curves: (a) UCS tests; (b) UTS tests.\u003c/p\u003e","description":"","filename":"placeholderimage.png","url":"https://assets-eu.researchsquare.com/files/rs-6926683/v1/84ad1f597eb5ce793bb2469b.png"},{"id":85566798,"identity":"6ff52820-69ca-41c4-b5ac-05376be304aa","added_by":"auto","created_at":"2025-06-27 14:47:25","extension":"jpeg","order_by":11,"title":"Figure 11","display":"","copyAsset":false,"role":"figure","size":172695,"visible":true,"origin":"","legend":"\u003cp\u003eAnalysis of damage characteristics of single fractured rock mass: (a) fracture\u003c/p\u003e","description":"","filename":"image10.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-6926683/v1/f4543a452ba8853d848750d3.jpeg"},{"id":85565884,"identity":"3eba44ab-7026-4694-9870-54fa13b1376b","added_by":"auto","created_at":"2025-06-27 14:31:25","extension":"jpeg","order_by":12,"title":"Figure 12","display":"","copyAsset":false,"role":"figure","size":174773,"visible":true,"origin":"","legend":"\u003cp\u003eAnalysis of damage characteristics of double fractured rock mass: (a) fracture development; (b) stress-strain curve and crack count; (c) sequence of multi-level crack generation.\u003c/p\u003e","description":"","filename":"image11.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-6926683/v1/34446d8953c6f9eb846b4e52.jpeg"},{"id":88506047,"identity":"67e8c8bf-cfdc-429b-9e4b-349c952a2448","added_by":"auto","created_at":"2025-08-07 07:29:56","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2576623,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6926683/v1/7899c6ce-a702-4da9-8920-70d5892f496e.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Multiscale Fracture Mechanisms in Granite with Pre- existing Cracks: Experimental Characterization and Grain- Based Numerical Modeling","fulltext":[{"header":"1 Introduction","content":"\u003cp\u003eRock masses, as primary constituents of the Earth's lithosphere, inherently contain defects such as fractures, joints, and voids due to long-term geological processes and anthropogenic activities [\u003cspan additionalcitationids=\"CR2 CR3 CR4\" citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e]. Moreover, when these defects are subjected to further action, new cracks will sprout, resulting in damage expansion and penetration [\u003cspan additionalcitationids=\"CR7 CR8\" citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e]. As the main material of roads, bridges, hydropower, mines and other projects, understanding fracture-driven rock behavior is thus critical for ensuring geotechnical safety and optimizing design strategies [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eExtensive studies have explored the mechanical response of fractured rocks[\u003cspan additionalcitationids=\"CR13 CR14\" citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e]. Early experimental work by Bobet \u0026amp; Einstein [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e] revealed crack coalescence patterns in biaxially compressed specimens, while Prudencio et al. [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e] classified four failure modes of jointed rock masses. For dual fractures, Chen et al. [\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e] demonstrated that joint connectivity governs strength anisotropy, and Cho et al. [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e] linked fracture geometry to macroscopic deformation. With the development of numerical simulation, grain-based models (GBM) have emerged as powerful tools to simulate crystalline rock fracturing [\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e]. Potyondy \u0026amp; Cundall [\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e] pioneered bonded-particle GBMs, yet traditional smooth-joint (SJ) models oversimplify inter-grain mechanics, failing to capture realistic crack paths [\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e]. Recent studies by Liu et al. [\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e] and Wang et al. [\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e] improved boundary modeling but lacked multiscale validation against experimental data.\u003c/p\u003e \u003cp\u003eDespite these advances, two critical gaps remain: (1) Cross-scale linkage: Most studies focus either on macro-scale experiments or micro-scale simulations, neglecting integrated analyses bridging crack initiation (mineral boundaries) to macro-fracture formation. (2) Model limitations: Existing GBMs inadequately simulate intra-crystalline cracking and multi-mineral interactions, limiting their predictive accuracy.\u003c/p\u003e \u003cp\u003eTo address these gaps, this study combines multiscale experiments (mechanical testing, acoustic emission monitoring) with an innovative Multilevel Parallel Bonded-GBM (Multi Pb-GBM). Using granite from the Jiaodong Group, we systematically investigate how fracture geometry (angle, rock bridge configuration) controls strength and failure modes, the evolution of micro-to-macro crack networks under uniaxial compression, and the role of mineral heterogeneity in fracture propagation. The research findings provided a database for in-depth study on mechanical properties of rock materials.\u003c/p\u003e"},{"header":"2 Mechanical experiment","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e\n\u003ch2\u003e2.1 Test scheme\u003c/h2\u003e\n\u003cp\u003eRock samples in the following tests were granite taken from Jiaodong Group, and the sample heights were 100 mm \u0026times; 50 mm \u0026times; 30 mm (length \u0026times; height \u0026times; thickness) [\u003cspan class=\"CitationRef\"\u003e28\u003c/span\u003e]. A cutting machine was used to predict cracks in the specimens. The length of the fractures was 15 mm, and the width was 1 mm. The crack distributions of rock samples were divided into 2 types, including single crack and double cracks, as shown in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e. The dip angle of rock sample cracks was set as 0\u0026deg;, 30\u0026deg;, 60\u0026deg; and 90\u0026deg;. In order to avoid the influence of accidental errors, 3 identical samples were made for each group, and repeated experiments were carried out.\u003c/p\u003e\n\u003cp\u003eA uniaxial compressive test was conducted on the WES-2000 digital hydraulic servo testing machine, and the uniaxial compressive strength (UCS) was recorded. The loading speed was set as 0.02 kN/s, and the loading was applied until the sample was destroyed. A PCI-2 acoustic emission system was used to collect the acoustic emission data [\u003cspan class=\"CitationRef\"\u003e29\u003c/span\u003e]. In order to not affect the crack development observation, acoustic emission sensors were attached to the two sides of the model. The boundary conditions of the model samples are shown in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec4\" class=\"Section2\"\u003e\n\u003ch2\u003e2.2 Failure mode\u003c/h2\u003e\n\u003cp\u003eFigure\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003e showed the single crack test sample and failure results. During the loading process, the crack tip was the first area where the stress was concentrated. The failure of the sample with a crack angle of 0\u0026deg; started from the end of the horizontal crack and extended to the sample boundary from the upper right side and the lower left side, respectively. As a hard brittle rock mass, the macroscopic fracture of granite was instantaneous, so no new fracture point was observed during the experiment. In the sample with a crack angle of 30\u0026deg;, wing-like cracks were first generated at the crack tip, which expanded along the direction perpendicular to the prefabricated crack, and then developed in the direction of the maximum compressive stress. Secondary cracks gathered in large numbers at the lower end of the primary crack, and then a third main crack appeared on the lower right side, extending through the entire rock mass. No obvious sliding shear plane was generated in this process. The failure mode of specimens with 60\u0026deg; fracture angle was similar to that of 30\u0026deg; specimen, and the reverse wing fracture was obvious. When the dip angle increased to 90\u0026deg;, the end crack only expanded in a small amplitude after initiation, and multiple points in the specimen appeared cracks simultaneously. The main crack generated by the splitting failure extended along the loading direction and finally directly penetrated to the surface of the loading plate.\u003c/p\u003e\n\u003cp\u003eIn order to study the compressive strength characteristics and crack propagation laws of intermittently fractured rock, uniaxial compression tests were conducted on double primary fracture samples, and the test results were shown in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003e. When the rock bridge angle was 0\u0026deg;, shear-splitting failure occurred at the tips of the two prefabricated cracks. After penetrating the primary fissures, the two split cracks extended towards the loading plate, and shear cracks developed between the prefabricated cracks. When the rock bridge angle was 30\u0026deg;, minor secondary cracks appeared at the tip of the prefabricated crack, and then winglike cracks began to gather near the left primary fissures, resulting in the main fracture zone, which may be caused by the uneven force of the sample during loading. The rock bridge specimens with 60\u0026deg; and 90\u0026deg; rock bridge inclination angle maintained good integrity during loading, and the double joints of the specimens with 60\u0026deg; were almost collinear, and the prefabricated cracks above the rock bridge angle started to produce a wing-like fracture, forming a 60\u0026deg;damage surface. On the other hand, the rock bridge dip angle of 90\u0026deg; was affected by the boundary effect, and the splitting failure occurred directly next to the precast fissure, and the lateral expansion deformation was obvious.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec5\" class=\"Section2\"\u003e\n\u003ch2\u003e2.3 Stress-strain law\u003c/h2\u003e\n\u003cp\u003eThe stress-strain curve was recorded during the test. As can be seen from Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003e, samples with different crack inclination angles had a compaction stage in the initial loading stage, and then the rock entered into a linear elastic stage, and the axial stress increased linearly with the increase of strain. With the progress of loading, invisible micro-cracks appeared inside the rock, and the failure entered into plastic deformation stage, and unrecoverable deformation developed. The stress load continued to increase until the peak strength was reached, the specimen entered into failure stage, the stress-strain curve dropped rapidly, and the brittle rock had no obvious residual strength. The peak uniaxial compressive strength of single-fracture rock with different angles was 104.76, 112.82, 120.54 and 134.98MPa, respectively. With the increasing of fracture inclination angle, the uniaxial compressive strength increased, while the elastic modulus was basically the same. With the increasing of rock bridge angle, the strength of rock with intermittent double fracture had compressive strength of 109.88, 124.10, 51.68 and 116.98MPa, respectively. Rock was most prone to failure when the rock bridge inclination angle was 60\u0026deg;, because the fracture inclination angle selected by the intermittent double joint test was also 60\u0026deg;, and when the rock bridge was in line with the primary cracks, the compressive strength of rock mass was reduced.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec6\" class=\"Section2\"\u003e\n\u003ch2\u003e2.4 AE characteristics\u003c/h2\u003e\n\u003cp\u003eAcoustic emission refers to a phenomenon that occurs when the external load exceeds a certain critical value, micro-yielding or deformation occurs in the internal defect region of a solid, and excess energy is released instantaneously in the form of elastic waves [\u003cspan class=\"CitationRef\"\u003e7\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e12\u003c/span\u003e]. The ringing count in acoustic emission monitoring represents the number of cracks in the specimen. The acoustic emission characteristics of rock samples are obviously different due to the different fracture results.\u003c/p\u003e\n\u003cp\u003eThe acoustic emission monitoring results of single fracture specimens were shown in Figure. 6. As the stress increased, the impact count and cumulative energy of 30\u0026deg;, 60\u0026deg; and 90\u0026deg; joint specimens increased slowly. When the stress reached the peak strength, the impact number increased sharply and attained the maximum value. The 0\u0026deg; fracture sample exhibited two concentrated periods of microcrack formation, which were the two main fracture surfaces that developed at the upper and lower ends of the pre-existing fissure.\u003c/p\u003e\n\u003cp\u003eAs shown in Figure. 7, the acoustic emission results of the interrupted double-fractured rock mass showed that when the rock bridge inclination angle was 60\u0026deg;, a large number of acoustic emission signals appeared, and the number of ringing had been at a higher level since 15 seconds of the test, the sample was prone to failure and the stress-strain curve was smoother. By comparing the deformation failure process characteristics of fractured rock mass, the AE process can be divided into three stages, including initial compaction and rising stage, peak stage and stable stage. First of all, under axial stress loading, micro-cracks and pores in fractured rock mass were compressed and closed. At this time, there were only a few acoustic emission events and a slight increasing trend. In the peak zone, cracks inside the specimen were connected to form a large fracture surface, and acoustic emission events increased sharply. In the stable zone, the number of cracks did not change after macroscopic failure, and the cumulative ringing number became stable.\u003c/p\u003e\n\u003c/div\u003e"},{"header":"3 Numerical simulations","content":"\u003cp\u003eThrough physical simulation testing, comprehensive conclusions of fracture initiation and propagation, stress-strain relationship and failure modes of fractured rock mass can be obtained. However, a large number of experiments demonstrate that granite fracture occurs not only around mineral boundaries but also inside minerals [\u003cspan class=\"CitationRef\"\u003e24\u003c/span\u003e\u0026ndash;\u003cspan class=\"CitationRef\"\u003e25\u003c/span\u003e]. It is difficult to directly observe the process of microscopic damage and crystal scale fracture order in rock mass during physical tests, but numerical simulation technology is a reasonable and effective way to simulate rock mechanics issues [\u003cspan class=\"CitationRef\"\u003e26\u003c/span\u003e\u0026ndash;\u003cspan class=\"CitationRef\"\u003e27\u003c/span\u003e].\u003c/p\u003e\n\u003cdiv id=\"Sec8\" class=\"Section2\"\u003e\n \u003ch2\u003e3.1 Multilevel Parallel bonded -Grain Based Modeling\u003c/h2\u003e\n \u003cp\u003eThe GBM model has a powerful ability to simulate the fracture behavior of crystalline rock and is suitable for granite simulation. Potyondy and Cundall introduced GBM into PFCS to simulate the microstructure of crystalline rocks [\u003cspan class=\"CitationRef\"\u003e30\u003c/span\u003e\u0026ndash;\u003cspan class=\"CitationRef\"\u003e31\u003c/span\u003e]. Each crystal consists of several bonded particles and the crystal is allowed to deform and break. The GBM model in PFC2D can not only simulate the initiation of microcracks and the interaction with the crystal boundary, but also captures the cracking behavior inside the crystal structure [\u003cspan class=\"CitationRef\"\u003e25\u003c/span\u003e\u0026ndash;\u003cspan class=\"CitationRef\"\u003e26\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e32\u003c/span\u003e].\u003c/p\u003e\n \u003cp\u003eThe traditional GBM method uses polygons to simulate crystals in granite samples, bonded by a parallel bond model, with smooth joint (SJ) being used to simulate the grain boundaries, because these boundaries are easily generated. However, the SJ model has obvious shortcomings: 1. crystal boundaries are treated as cracks with bond strength and do not produce local geometric expansion effects, resulting in a loss of the ability to force particles to roll against each other; 2. contact ignores the initial cohesion around the boundary and the rotational resistance between particles is absent; 3. under large strains, the SJ model only works when the surface clearance is negative [\u003cspan class=\"CitationRef\"\u003e25\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e28\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e33\u003c/span\u003e].\u003c/p\u003e\n \u003cp\u003eIn order to overcome these shortcomings a multi-Pb-GBM model is proposed to simulate the microstructure of crystalline granite. The parallel contact model is used to describe the crystal boundary instead of the traditional SJ model. The parallel contact model can be divided into three types: intra-crystal contact, intra-crystal boundary contact of the same mineral and boundary contact of different mineral species, as shown in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e8\u003c/span\u003e. The detailed modeling principles and optimization process can be found in the literature [\u003cspan class=\"CitationRef\"\u003e29\u003c/span\u003e].\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec9\" class=\"Section2\"\u003e\n \u003ch2\u003e3.2 Micro parameters calibration\u003c/h2\u003e\n \u003cp\u003eFor the calibration experiment model, length is 100 mm and width is 50 mm, assembled of 14558 particles with a radius from 0.1 to 0.155 mm. The mineral crystal sizes are set to 3.3, 3.8, 2.8, 2.2 mm for K-feldspar, plagioclase, quartz and biotite respectively [\u003cspan class=\"CitationRef\"\u003e28\u003c/span\u003e\u0026ndash;\u003cspan class=\"CitationRef\"\u003e29\u003c/span\u003e]. Different types of minerals are arrangement inside the numerical model randomly, and the volume fraction are 40%, 20%, 30% and 10%. The calibration models were shown in Figure. 9. Parameters put into the calculation model must be calibrated to the results of UCS and UTS tests. By adjusting the microscopic parameters, the stress-strain curve of the numerical experiment is basically consistent with the physical experiments (Figure.10). The calibrated micro-parameters and the experiment results were shown in Table \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e. The results indicate that the simulation was reasonable.\u003c/p\u003e\n \u003cdiv class=\"gridtable\"\u003e\n \u003ctable id=\"Tab1\" border=\"1\"\u003e\n \u003ccaption\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eMicroscopic parameters of the numerical simulation\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eMicroparameters\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eK-feldspar\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003ePlagioclase\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eQuartz\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eBiotite\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eParticle parameters\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eMinimum particle radius \u003cem\u003eR\u003c/em\u003e\u003csub\u003emin\u003c/sub\u003e (mm)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.15\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.15\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.15\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.15\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eParticle size ratio \u003cem\u003eR\u003c/em\u003e\u003csub\u003emax\u003c/sub\u003e\u003cem\u003e/R\u003c/em\u003e\u003csub\u003emin\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.52\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.52\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.52\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.52\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eSize of the crystal types (mm)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.80\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3.30\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.30\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.70\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eParticle density \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\rho\\:\\)\u003c/span\u003e\u003c/span\u003e (kg/m\u003csup\u003e3\u003c/sup\u003e)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2600\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2630\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2650\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2850\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eFriction coefficient of the particle \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\mu\\:\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.80\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.80\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.80\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.80\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eParallel bond model parameters\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eYoung\u0026apos;s modulus \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\stackrel{̄}{E}c\\)\u003c/span\u003e\u003c/span\u003e (GPa)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e85\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e81\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e100\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e65\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eNormal/shear stiffness \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{K}_{n}/{K}_{s}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.5\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eTensile strength \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\stackrel{̄}{\\sigma\\:}}_{t}\\)\u003c/span\u003e\u003c/span\u003e (MPa)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e60\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e55\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e65\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e45\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eCohesive force \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\stackrel{̄}{c}\\)\u003c/span\u003e\u003c/span\u003e (MPa)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e85\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e95\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e115\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e55\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eFriction angle \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\beta\\:\\)\u003c/span\u003e\u003c/span\u003e (\u003csup\u003eo\u003c/sup\u003e)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e40\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e41\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e42\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e38\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eFriction coefficient\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.5\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n \u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec10\" class=\"Section2\"\u003e\n \u003ch2\u003e3.3 Simulation results\u003c/h2\u003e\n \u003cp\u003eThe calculation results of the 60\u0026deg; specimen that was most prone to failure were taken as an example to discuss the fracture characteristics of the rock material at the microscopic scale, as shown in Figure. 11. Four characteristic time points had been selected: Ⅰ was the crack initiation point at the tip of the prefabricated fissure; Ⅱ was the expansion and bending of the wing-shaped crack and the germination point of micro-cracks; Ⅲ was the peak strength point where a large number of internal micro-fractures gathered; Ⅳ was the point of overall failure of the specimen. The fracture development of the single fissure specimen at these four time points was shown in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e11\u003c/span\u003e (a). The thickness of the line segments reflected the number of micro-cracks within those areas, offering a more detailed account of the fracture evolution process of the fissured rock mass during the experiment. Figure\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e11\u003c/span\u003e (b) depicted the stress-strain curve corresponding to the number of cracks. And Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e11\u003c/span\u003e (c) showed the sequence of multi-level crack generation at the same time step, which helped us clearly understand the process of fracturing within the crystal during the uniaxial compression process, including the internal contact of crystals, contact at the boundaries of the same type of mineral crystals, and contact at the boundaries of different types of mineral crystals.\u003c/p\u003e\n \u003cp\u003eDuring the loading process, stress concentration zones first emerged at the tips of the fissures. For the 60\u0026deg; specimen, wing-shaped cracks initiated earliest at the tip of the prefabricated fissure and began to expand perpendicular to the direction of the pre-existing fissure. Subsequently, the upper end of the prefabricated fissure propagated downward, and the lower end propagated upward, both curving to develop in the direction of maximum compressive stress. Secondary fractures accumulated extensively at the ends of the prefabricated fissures, followed by the generation of two additional collinear joints along the plane of the prefabricated fissure, which inclined the specimen as a whole towards shear failure, revealing a macroscopic shear surface. Eventually, the wing-shaped crack that first formed at the upper end turned towards the direction of maximum compressive stress, communicating with the lower boundary and forming the rock mass failure plane with the collinear joints, transforming local shear fractures into local splitting fractures. The rock mass underwent overall fragmentation, and the stress-strain curve decreased.\u003c/p\u003e\n \u003cp\u003eFigure \u003cspan class=\"InternalRef\"\u003e12\u003c/span\u003e presented the numerical experiment results of double fracture with 60\u0026deg; fracture and 30\u0026deg; rock bridge, showing the fracture conditions of the specimen at four characteristic points, as well as the corresponding types and quantities of fractures. From the figure, it was observed that secondary fractures first occurred at the tips of the two prefabricated fissures, and both extended along the direction of the principal compressive stress. Subsequently, the upper prefabricated fissure began to bifurcate at its tip, giving rise to several secondary wing-shaped fractures. Following this, the upper extension of the upper prefabricated fissure and the lower extension of the lower prefabricated fissure started to accumulate micro-cracks, resulting in two distinct bands of micro-cracks. Upon further loading, the fracture band on the upper left side expanded to the specimen\u0026apos;s boundary, causing the specimen to undergo macroscopic shear failure in that area. It was evident that micro-cracks first appeared at the grain boundaries of different minerals, followed by fractures occurring at the grain boundaries within the same mineral, and finally, the number of internal contact fractures within the crystals rapidly increased to form a macroscopic fracture surface.\u003c/p\u003e\n\u003c/div\u003e"},{"header":"4 Conclusions","content":"\u003col\u003e\n\u003cli\u003e\n\u003cp\u003eThe inclination angle of pre-existing fractures exerts a significant influence on the mechanical properties of granite. Experimental results demonstrate that uniaxial compressive strength (UCS) increases systematically with fracture inclination angle, while the elastic modulus remains nearly constant across all tested configurations. For double-fractured specimens, the rock bridge angle plays a critical role: strength peaks at 60\u0026deg;, where collinear alignment of fractures and rock bridge amplifies stress localization, leading to reduced load-bearing capacity. This geometric dependency underscores the importance of fracture orientation in predicting rock mass stability.\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003eAcoustic emission monitoring reveals a triphasic failure process in fractured granite. During initial loading, microcrack closure induces sparse AE activity (compaction phase). As stress escalates, rapid crack coalescence triggers an abrupt surge in AE signals (peak phase), correlating with macroscopic fracture formation. Post-failure, AE activity stabilizes as crack networks reach equilibrium (stable phase). This temporal pattern provides a diagnostic framework for real-time monitoring of fracture-driven instability.\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003eSingle-fractured specimens exhibit progressive tensile-dominated failure, with minor shear components localized near fracture tips, preserving partial structural integrity. In contrast, double-fractured specimens undergo sudden tensile-shear hybrid failure due to stress interference between fractures, resulting in complete disintegration. The dominance of tensile behavior in double fractures highlights the synergistic effects of multiple defects on catastrophic failure.\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003eThe Multilevel Parallel Bonded-GBM (Multi Pb-GBM) successfully replicates fracture evolution from mineral-scale initiation to macroscopic rupture. Simulations confirm that microcracks first nucleate at inter-mineral boundaries, propagate along intra-mineral interfaces, and culminate in intra-crystalline coalescence. Tensile cracks dominate, while shear cracks concentrate near mineral boundaries. This model bridges microscale heterogeneity to macroscale nonlinear behavior, offering a predictive tool for assessing brittle fractures in engineering contexts such as underground excavations and slope stability.\u003c/p\u003e\n\u003c/li\u003e\n\u003c/ol\u003e"},{"header":"Declarations","content":"\u003cp\u003e \u003ch2\u003eConflicts of Interest\u003c/h2\u003e \u003cp\u003eThe authors declared that they have no conflict of interest regarding this study. We declare that we do not have any commercial or associative interests that represent a conflict of interest in connection with the paper submitted.\u003c/p\u003e \u003c/p\u003e\u003ch2\u003eFunding statement\u003c/h2\u003e \u003cp\u003edeclaration\u003c/p\u003e \u003cp\u003eFunding : National Science Foundation of China (Grant Nos. 42072305) and the Second Tibetan Plateau Scientific Expedition and Research Program (Grant no. 2019QZKK0904).\u003c/p\u003e\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eJie Guo and Guang Li wrote the main manuscript text, and Fengshan Ma prepared figures in the manuscript. All authors have read and agreed to the published version of the manuscript.\u003c/p\u003e\u003ch2\u003eAcknowledgments\u003c/h2\u003e \u003cp\u003eThis research was supported by the National Science Foundation of China (Grant Nos. 42072305) and the Second Tibetan Plateau Scientific Expedition and Research Program (Grant no. 2019QZKK0904).\u003c/p\u003e\u003ch2\u003eData Availability\u003c/h2\u003e\u003cp\u003eData is provided within the manuscript.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eSajid, M. et al. Petrographic features as an effective indicator for the variation in strength of granites. \u003cem\u003eEng. Geol.\u003c/em\u003e \u003cb\u003e202\u003c/b\u003e, 44\u0026ndash;54 (2016).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eLi, G. et al. Damage evolution mechanism and deformation failure properties of a roadway in deep inclined rock strata. \u003cem\u003eEng. Fail. 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Discussion: A discrete numerical model for granular assemblies. \u003cem\u003eG\u0026eacute;otechnique\u003c/em\u003e \u003cb\u003e30\u003c/b\u003e (3), 331\u0026ndash;336 (1980).\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"Pre-existing fractures, Rock strength, Crack propagation, Failure mode","lastPublishedDoi":"10.21203/rs.3.rs-6926683/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6926683/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe mechanical behavior of pre-fractured granite is critically influenced by primary fractures, where macro-crack evolution originates from micro-crack accumulation. This study systematically investigates the deformation and failure mechanisms of granite containing single and double pre-existing fractures through integrated mechanical testing, acoustic emission (AE) monitoring, and multiscale numerical simulations. Key findings reveal: (1) Fracture geometry controls strength: Uniaxial compressive strength (UCS) increases with fracture inclination angle, while elastic modulus remains stable. For double-fractured specimens, strength peaks at a rock bridge angle of 60\u0026deg;, where collinear crack alignment induces weakest resistance; (2) Three-stage evolution: AE activity transitions sequentially from initial compaction (minor events), peak activity (crack coalescence), to post-failure stabilization; (3) Contrasting failure modes: Single fractures exhibit progressive tensile-dominated failure with localized shear, whereas double fractures trigger abrupt tensile-shear hybrid failure; (4) Multiscale crack propagation: Under uniaxial compression, microcracks initiate at inter-mineral boundaries, propagate along intra-mineral interfaces, and culminate in rapid intra-crystalline crack coalescence, forming macroscopic fracture surfaces. These findings provide critical insights into fracture-driven rock failure, bridging microscale damage mechanisms to macroscale engineering behavior.\u003c/p\u003e","manuscriptTitle":"Multiscale Fracture Mechanisms in Granite with Pre- existing Cracks: Experimental Characterization and Grain- Based Numerical Modeling","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-06-27 14:31:20","doi":"10.21203/rs.3.rs-6926683/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2025-07-02T06:16:50+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-07-01T15:30:02+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"133266107753846213078538823913074793296","date":"2025-07-01T01:52:15+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-06-30T04:00:49+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"303992811982349773924590087341157678555","date":"2025-06-25T01:41:02+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-06-25T01:25:40+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-06-25T00:34:17+00:00","index":"","fulltext":""},{"type":"editorInvited","content":"","date":"2025-06-24T12:57:43+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-06-23T09:09:47+00:00","index":"","fulltext":""},{"type":"submitted","content":"Scientific Reports","date":"2025-06-23T09:06:33+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"7960dade-bd47-4c79-bf38-adc0353778e0","owner":[],"postedDate":"June 27th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[{"id":50546204,"name":"Earth and environmental sciences/Natural hazards"},{"id":50546205,"name":"Earth and environmental sciences/Solid earth sciences/Sedimentology"}],"tags":[],"updatedAt":"2025-08-07T07:11:31+00:00","versionOfRecord":{"articleIdentity":"rs-6926683","link":"https://doi.org/10.1038/s41598-025-12159-4","journal":{"identity":"scientific-reports","isVorOnly":false,"title":"Scientific Reports"},"publishedOn":"2025-07-19 15:57:13","publishedOnDateReadable":"July 19th, 2025"},"versionCreatedAt":"2025-06-27 14:31:20","video":"","vorDoi":"10.1038/s41598-025-12159-4","vorDoiUrl":"https://doi.org/10.1038/s41598-025-12159-4","workflowStages":[]},"version":"v1","identity":"rs-6926683","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-6926683","identity":"rs-6926683","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}