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Keywords = initiation and propagation of multiple fractures

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22 pages, 13031 KB  
Article
Saturated Volume Fracturing Technology for Horizontal Well Groups in Coal Seam Roof and Application in the Huainan Mining Area
by Huazhong Ding, Shiliang Zhu, Lei Su, Haozhe Li, Jianjian Qi, Siqing Sun and Benliang Chen
Energies 2026, 19(12), 2903; https://doi.org/10.3390/en19122903 (registering DOI) - 18 Jun 2026
Viewed by 214
Abstract
The Huainan Mining Area features extensively developed, fragmented-soft and low-permeability coal seams, characterized by low porosity and permeability, complex geological structures, and significant difficulty in coalbed methane (CBM) drainage. Horizontal wells with staged fracturing in the coal seam roof have become a key [...] Read more.
The Huainan Mining Area features extensively developed, fragmented-soft and low-permeability coal seams, characterized by low porosity and permeability, complex geological structures, and significant difficulty in coalbed methane (CBM) drainage. Horizontal wells with staged fracturing in the coal seam roof have become a key method for regional gas control. To further enhance the volume fracturing stimulation effect and single-well gas production, this study targets the horizontal well group in the roof of the No. 8 coal seam in the Huainan Mining Area as the research object. A saturated volume fracturing technology for horizontal wells in the coal seam roof, centered on the concept of a high pump rate (18–20 m3/min) and a high proppant volume (>250 m3/stage), is proposed. This study investigates the fracture propagation mechanisms and fracturing parameter optimization of this technology, and conducts engineering application to verify its stimulation effect. Increasing the fracturing pump rate improves the proppant-carrying capacity of the fracturing fluid, successfully enabling high-rate and high-volume proppant placement. Optimization of the perforation parameters—12 holes per m per cluster and a cluster spacing of 15–25 m—utilizes high perforation friction and moderate stress interference to promote balanced initiation and propagation of multiple fractures within a stage. The optimized ‘saturated’ injection mode, with a single-stage fluid volume exceeding 2400 m3, a single-stage proppant volume exceeding 250 m3, and a maximum sand ratio exceeding 20%, combined with a multi-size proppant mixture, enables full propping of both main and branch fractures. Microseismic monitoring shows that the hydraulic fracture extension length increased by approximately 50% compared to conventional wells, significantly enlarging the stimulated reservoir volume (SRV). Saturated fracturing achieved stable gas production of 2000 to 3000 m3/d, with average production ramp-up rates of 21.47–26.40 m3/d (five times higher than the 5.34 m3/d of the conventional well), and the stable plateau period was notably extended from 36 days to over 150 days. The saturated volume fracturing technology proposed in this study provides an important reference for efficient CBM extraction and surface gas control in mining areas with similar geological conditions. Full article
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35 pages, 10085 KB  
Article
Mathematical Evaluation of Hydraulic Fracture Complexity Based on Digital Rock Modeling and Fractal Geometry
by Xin Liu, Tianjiao Li, Bin Gong, Zhengzhao Liang, Siwei Meng and Na Wu
Mathematics 2026, 14(12), 2153; https://doi.org/10.3390/math14122153 - 16 Jun 2026
Viewed by 208
Abstract
The fractal natural microstructure of shale reservoirs significantly influences hydraulic fracture propagation and reservoir stimulation. However, there is a lack of quantitative mathematical descriptions for the coupled regulation of micropores, natural fractures, and injection rates. This study develops a mathematical evaluation method for [...] Read more.
The fractal natural microstructure of shale reservoirs significantly influences hydraulic fracture propagation and reservoir stimulation. However, there is a lack of quantitative mathematical descriptions for the coupled regulation of micropores, natural fractures, and injection rates. This study develops a mathematical evaluation method for hydraulic fracture evolution in complex microstructured reservoirs using digital core technology, fractal geometry and a hydraulic–mechanical–damage coupling algorithm. High-resolution SEM images were used to reconstruct the microscopic fractal features. Integrated digital image processing and fractal analysis, along with geometric indices such as fractal dimension, fracture coverage, and stimulated area, and statistical measures including directional entropy, variance, and the Pearson correlation coefficient, were employed to systematically quantify fracture network evolution and complexity under different injection rates. Results show that fracture morphology, spatial complexity, and mineral damage mechanisms are jointly controlled by microstructure and injection rate. In particular, the directional distribution of pores and natural fractures is found to exert a dominant control on the propagation paths and branching behavior of hydraulic fractures, revealing a strong coupling between microstructural anisotropy and fracture directionality. Increased injection rates enhance fracture complexity and stimulation range, with varying effects from different microstructures. At low rates, fracture propagation is mainly determined by the initial microstructure, whereas at high rates, fractures tend to develop multiple pathways. Natural fracture structures contribute more to fracture complexity at high rates. The proposed comprehensive fracturability index (FI)-based fracturability evaluation model provides a systematic, quantitative approach to optimizing fracturing processes. Full article
(This article belongs to the Special Issue Advances in Finite Element Methods and Boundary Value Problems)
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38 pages, 7947 KB  
Article
Interpretable Prediction of Hydraulic Fracture Asymmetry in Shale Reservoirs Under Small-Sample Conditions
by Hanke Zuo and Yanhong Peng
Processes 2026, 14(12), 1900; https://doi.org/10.3390/pr14121900 - 11 Jun 2026
Viewed by 233
Abstract
To address the issues of strong inter-well interference during multi-well fracturing in shale reservoirs, low efficiency of conventional numerical simulation, and the tendency of machine learning models to overfit and lack interpretability under small-sample conditions, this paper constructs an explainable ensemble learning framework [...] Read more.
To address the issues of strong inter-well interference during multi-well fracturing in shale reservoirs, low efficiency of conventional numerical simulation, and the tendency of machine learning models to overfit and lack interpretability under small-sample conditions, this paper constructs an explainable ensemble learning framework for predicting hydraulic fracture asymmetry. A geology–engineering integrated numerical simulation is adopted to quantify the fracture asymmetry index η as an interference metric, and an initial dataset is constructed comprising natural fracture orientation, well spacing, and injection rate. Subsequently, Jensen–Shannon (JS) divergence-constrained Gaussian data augmentation and second-order interaction features are introduced, and the GBRT model parameters are optimized using particle swarm optimization (PSO). Furthermore, random forest and ridge regression are incorporated, and ensemble weights are determined via cross-validation to build a weighted ensemble prediction model. The results show that the proposed model achieves good predictive performance in repeated validation, with an average coefficient of determination R2 of 0.8484 and a 95% confidence interval of 0.8179–0.8790, while also demonstrating favorable overall accuracy in multiple baseline model comparisons and regularization-controlled experiments. Through leave-one-simulation-scenario validation, prediction interval analysis, and interpretability robustness testing, the model’s generalization boundary, prediction uncertainty, and explanation reliability under small-sample conditions are further evaluated. SHAP analysis and grouped permutation importance results indicate that the natural fracture angle is the dominant factor controlling asymmetric fracture response, while the interaction between well spacing and the natural fracture angle also significantly affects the predictions, suggesting that asymmetric fracture propagation is primarily governed by the combined effects of natural fracture steering and inter-well stress interference. The proposed framework can serve as a fast surrogate model for evaluating inter-well interference and screening fracturing designs within a given simulation parameter space, providing an interpretable data-driven approach for fracturing design optimization in shale reservoirs under small-sample conditions. Full article
(This article belongs to the Section Petroleum and Low-Carbon Energy Process Engineering)
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27 pages, 9477 KB  
Article
Low-Cycle Fatigue Behavior and Microstructural Damage Mechanisms of 316L Austenitic Stainless Steel in Cryogenic Environments
by Sujuan Guo, Guolong Zhang, Junnan Chen, Lei Li, Hui Zhang, Qicong Li and Jian Zhao
Materials 2026, 19(12), 2494; https://doi.org/10.3390/ma19122494 - 10 Jun 2026
Viewed by 274
Abstract
This study focuses on the low-cycle fatigue behavior and microstructural damage mechanisms of 316L austenitic stainless steel in cryogenic environments to enhance understanding of its fatigue performance and failure mechanisms over a wide temperature range. Uniaxial tensile and strain-controlled low-cycle fatigue tests were [...] Read more.
This study focuses on the low-cycle fatigue behavior and microstructural damage mechanisms of 316L austenitic stainless steel in cryogenic environments to enhance understanding of its fatigue performance and failure mechanisms over a wide temperature range. Uniaxial tensile and strain-controlled low-cycle fatigue tests were performed at 293 K, 173 K, and 77 K; microstructural evolution and damage mechanisms were explored via interrupted tests combined with multiple microscopic techniques and quantitative martensite analysis. The results show that the room temperature fatigue stress response has three stages, while low temperatures induce continuous cyclic hardening that stabilizes quickly; fatigue life increases with lower temperature and strain amplitude, more notably at high strains. Low temperatures enhance strength, increase hardness, slightly reduce plasticity, but maintain good toughness, suppressing crack initiation and propagation with ductile fracture. The findings clarify cryogenic fatigue damage mechanisms, providing experimental and theoretical support for cryogenic pressure-bearing component design and safety assessment. Full article
(This article belongs to the Section Mechanics of Materials)
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23 pages, 5490 KB  
Article
Effect of Tooth Count and Rim Thickness on the Operational Durability of Cylindrical Involute Gears
by Milan Perkušić, Stipe Pleština, Vjekoslav Tvrdić and Karlo Dvornik
Appl. Mech. 2026, 7(2), 45; https://doi.org/10.3390/applmech7020045 - 21 May 2026
Viewed by 468
Abstract
This paper presents a numerical assessment of bending-fatigue durability in the tooth root region of cylindrical involute gears. Multiple gear pairs were modelled with different numbers of teeth and varying gear rim thicknesses. The generated geometry was implemented in the ANSYS 2025 R2 [...] Read more.
This paper presents a numerical assessment of bending-fatigue durability in the tooth root region of cylindrical involute gears. Multiple gear pairs were modelled with different numbers of teeth and varying gear rim thicknesses. The generated geometry was implemented in the ANSYS 2025 R2 software suite, where the maximum normal stresses at critical locations in the tooth root region were determined through numerical simulation. A deformation-based method derived from Socie’s models was applied to estimate the duration of the phase leading up to fatigue crack formation in terms of load cycle accumulation. The gear geometry, together with the generated finite element mesh, was transferred to the FRANC2D/L version 4 software suite, where fatigue crack propagation was numerically simulated. Numerical analysis provided effective stress intensity factors, which then enabled an estimation of the number of load cycles required for an initiated crack to grow to the critical length associated with tooth failure. The total fatigue life in the tooth root region was evaluated as the sum of load cycles in the crack initiation phase and the crack propagation phase up to the critical crack length. The results show that all analysed factors exhibit very high resistance to fatigue fractures in the tooth root region. Furthermore, for gears with a rim thickness ratio greater than 0.7, the fatigue crack propagates through the tooth and reaches the fracture toughness limit of the material (KIc), whereas for lower rim thickness ratios, crack propagation occurs through the gear rim itself. Full article
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24 pages, 12607 KB  
Article
Experimental Validation of 2D Skeletal Point Method for Creep-Fatigue-Interaction Life Assessment in Perforated Plate Specimens Under Uniaxial Load
by Shouliang Xiang, Duoqi Shi, Nina Li, Tianxiao Sui, Ya Zhao and Xiaoguang Yang
Aerospace 2026, 13(5), 409; https://doi.org/10.3390/aerospace13050409 - 28 Apr 2026
Viewed by 344
Abstract
Geometric discontinuities in aero-engine turbine blades generate multiple stress concentrations along the airfoil, rendering life prediction exceptionally challenging. While conventional skeletal point method (SPM) offers reasonable accuracy in predicting creep-fatigue-interaction (CFI) life for simple structural specimens, they prove inadequate for geometries with poor [...] Read more.
Geometric discontinuities in aero-engine turbine blades generate multiple stress concentrations along the airfoil, rendering life prediction exceptionally challenging. While conventional skeletal point method (SPM) offers reasonable accuracy in predicting creep-fatigue-interaction (CFI) life for simple structural specimens, they prove inadequate for geometries with poor symmetry. This study introduces a novel two-dimensional skeletal point method (2D SPM) to analyze stress evolution characteristics, identify representative stresses, and predict CFI life in complex structures. Leveraging the film-cooling hole (FCH) features of a representative turbine blade, three perforated plate specimens were designed, manufactured, and subjected to CFI testing. Failure analysis confirmed crack initiation at hole-edge stress concentration zones, followed by inward propagation. Specimen fracture surfaces exhibited predominantly ductile dimpling features, with multi-origin fatigue characteristics observed only near hole-edges, collectively indicating creep-damage-dominated failure mechanisms. Five life prediction methodologies were comparatively evaluated. The results demonstrate that the 2D-SPM achieved the highest accuracy (all predictions within twofold scatter bands), followed by the conventional SPM (also within twofold scatter bands). The nominal stress method showed moderate accuracy (within fivefold scatter bands), while both hot point method and TCD methods proved unsuitable for creep-fatigue scenarios with significant stress evolution. Full article
(This article belongs to the Section Aeronautics)
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20 pages, 6028 KB  
Article
Grain-Scale Heterogeneity, Fracture Competition, and Non-Planar Propagation in Crystalline Rocks: Insights from a Hydro-Mechanical Phase-Field Model
by Gen Zhang, Cheng Zhao, Zejun Tian, Jinquan Xing, Jialun Niu, Zhaosen Wang and Wenkang Yu
Minerals 2026, 16(3), 339; https://doi.org/10.3390/min16030339 - 23 Mar 2026
Viewed by 459
Abstract
Grain-scale heterogeneity strongly influences hydraulic fracture initiation and trajectory in crystalline rocks, yet its contributions to non-planar growth and the interaction of multiple nearby cracks remain insufficiently quantified. To address this gap, we perform numerical experiments on a model containing two parallel pre-existing [...] Read more.
Grain-scale heterogeneity strongly influences hydraulic fracture initiation and trajectory in crystalline rocks, yet its contributions to non-planar growth and the interaction of multiple nearby cracks remain insufficiently quantified. To address this gap, we perform numerical experiments on a model containing two parallel pre-existing cracks using a hydro-mechanical phase-field framework, systematically quantifying how mineral distribution and axial compression govern non-planar hydraulic fracture growth and inter-fracture competition. The results demonstrate that mineral distribution is the primary driver of fracture complexity. Even within the same Voronoi tessellation, redistributing minerals alone yields markedly different trajectories, deflections, branching patterns, and final morphologies. Furthermore, non-planar growth follows a stepwise, energy-threshold-driven mechanism. When cracks penetrate strong grains or undergo large-angle deflections, propagation is impeded, and injection pressure builds up. Once a critical energy threshold is reached, accumulated energy is rapidly released along the path of minimum incremental energy, manifested as abrupt pressure drops and rapid crack advance. Additionally, the two nearby fractures exhibit strong mechanical competition. Despite negligible hydraulic interference in low-permeability granite, early growth of one fracture redistributes stresses and suppresses the driving force of the other, resulting in asymmetric development. Finally, axial compression primarily governs the overall propagation orientation and influences local failure modes but has a limited effect on peak pressure relative to mineral distribution. Full article
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23 pages, 3325 KB  
Article
Numerical Simulation Study on Fracture Propagation Mechanisms in Terrestrial Shale Reservoirs
by Xiaofei Sang, Juhua Li, Junlong Wu, Abubakar Mustafa Zubeir, Zhanquan Cheng, Sunyi Li, Yuan Hu and Haoran Gou
Energies 2026, 19(4), 922; https://doi.org/10.3390/en19040922 - 10 Feb 2026
Viewed by 523
Abstract
This study constructs a hydraulic-coupled phase-field fracture model based on the phase-field method, employing a granular random distribution model combined with a fractability evaluation index to comprehensively analyze the influence of multiple factors, including the brittleness index, stress difference, and natural fractures, on [...] Read more.
This study constructs a hydraulic-coupled phase-field fracture model based on the phase-field method, employing a granular random distribution model combined with a fractability evaluation index to comprehensively analyze the influence of multiple factors, including the brittleness index, stress difference, and natural fractures, on fracture propagation. The results indicate that fractures in Type I reservoirs with a high proportion of brittle components are more likely to initiate and exhibit extensive damage zones, with fracture propagation following a pattern of avoiding hard regions and favoring soft regions. The horizontal stress difference shows a significant negative correlation with the initiation pressure. Under conditions of small stress differences, mineral heterogeneity dominates the fracture morphology, while under large stress differences, stress orientation plays a predominant role. Additionally, the presence of natural fractures alters the stress field distribution and flow paths, highlighting the importance of accurately predicting the distribution and angular state of natural fractures for forecasting fracture propagation patterns. Finally, a comprehensive fractability evaluation index is established, and reservoir conditions and in situ stress parameters are categorized into three reservoir types for simulation. This study systematically elucidates the multi-factor synergistic mechanism of “brittleness-dominated initiation, stress difference-guided propagation, and natural fracture-disturbed paths.” The findings provide a novel and robust theoretical foundation for optimizing hydraulic fracturing designs and offer significant guidance for the efficient development of unconventional oil and gas resources. Full article
(This article belongs to the Section H1: Petroleum Engineering)
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22 pages, 42131 KB  
Article
Effect of Weld Surface Quality on the Fatigue Performance of Q420 Steel Used in Offshore Wind Tower Tube
by Jun Cao, Wubin Ren, Guodong Zhang, Shubiao Yin, Zhongzhu Liu and Xinjun Sun
Metals 2026, 16(2), 148; https://doi.org/10.3390/met16020148 - 25 Jan 2026
Cited by 2 | Viewed by 589
Abstract
The size of offshore wind turbine towers is increasing, and they are subjected to larger and more complex loads, which imposes more stringent requirements on the fatigue performance of welded plates in new offshore wind turbine towers. This study investigated the axial fatigue [...] Read more.
The size of offshore wind turbine towers is increasing, and they are subjected to larger and more complex loads, which imposes more stringent requirements on the fatigue performance of welded plates in new offshore wind turbine towers. This study investigated the axial fatigue performance of 25 mm thick welded plates made of the new Q420 steel grade. Fractures in the Q420 welded plates occurred at the junction of the coarse-grained zone of the filler metal and the heat-affected zone. By analyzing the fatigue striation spacing across multiple regions, it was found that the proportion of cycles in the crack propagation stage within the total fatigue life did not exceed 11%, indicating that the crack initiation stage is the decisive factor in the fatigue life of the specimens. Removing surface quality defects at the weld toe significantly increased both the fatigue life and the fatigue strength limit of the Q420 welded plates. Full article
(This article belongs to the Special Issue Feature Papers in Metal Failure Analysis)
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27 pages, 17457 KB  
Article
Experimental Investigation on the Mechanisms of Fiber Bragg Gratings to Monitor the Failure Processes of Pre-Cracked Sandstone Specimens
by Zesheng Zhang, Shiming Wei and Hua Nan
Appl. Sci. 2025, 15(22), 12266; https://doi.org/10.3390/app152212266 - 19 Nov 2025
Cited by 1 | Viewed by 719
Abstract
Real-time monitoring of internal fracture evolution in fractured rock masses using fiber Bragg grating (FBG) technology can help mitigate geotechnical hazards. This study employed FBG, acoustic emission (AE), and digital image correlation (DIC) to analyze pre-cracked sandstone under uniaxial compression. During the failure [...] Read more.
Real-time monitoring of internal fracture evolution in fractured rock masses using fiber Bragg grating (FBG) technology can help mitigate geotechnical hazards. This study employed FBG, acoustic emission (AE), and digital image correlation (DIC) to analyze pre-cracked sandstone under uniaxial compression. During the failure of the pre-cracked specimens, the FBGs experienced non-uniform stresses. In the initial loading phase, the stress concentrations at the crack tips and the wing-crack development were dominated by tensile stresses, and the maximum tensile strain was 1.01%. After the initial yield strength was reached, the crack-propagation process transitioned to shear-stress dominance, and a maximum shear strain of 6.45% was exhibited. During multiple stress decreases (180–250 s), the FBG-measured local shear and tensile strains reflected stress variations that were associated with shear-locking effects and failure stages. Before the tensile-crack initiation, the FBG-detected principal-strain concentration zones exhibited prolonged incubation periods, whereas the shear-crack initiation was preceded by shorter incubation periods. The evolution curves of the damage variable, which was defined by the FBG coupling strength, could be categorized into three distinct stages: initial damage accumulation, damage acceleration, and final damage. When the initial yield strength was reached, the damage variable rapidly increased, particularly during the two stress decreases. Full article
(This article belongs to the Special Issue Novel Insights into Rock Mechanics and Geotechnical Engineering)
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20 pages, 5389 KB  
Article
Diffusion Behavior of Polyurethane Slurry for Simultaneous Enhancement of Reservoir Strength and Permeability Through Splitting Grouting Technology
by Xiangzeng Wang, Fengsan Zhang, Jinqiao Wu, Siqi Qiang, Bing Li and Guobiao Zhang
Polymers 2025, 17(18), 2513; https://doi.org/10.3390/polym17182513 - 17 Sep 2025
Cited by 4 | Viewed by 816
Abstract
A polyurethane slurry was developed to simultaneously enhance the strength and permeability of geological formations, differing from the conventional fracture grouting used for soft-soil reinforcement. Injected via splitting grouting, the slurry cures to form high-strength, highly permeable channels that increase reservoir permeability while [...] Read more.
A polyurethane slurry was developed to simultaneously enhance the strength and permeability of geological formations, differing from the conventional fracture grouting used for soft-soil reinforcement. Injected via splitting grouting, the slurry cures to form high-strength, highly permeable channels that increase reservoir permeability while improving mechanical stability (dual-enhanced stimulation). To quantify its diffusion behavior and guide field application, we built a splitting-grouting model using the finite–discrete element method (FDEM), parameterized with the reservoir properties of coalbed methane (CBM) formations in the Ordos Basin and the slurry’s measured rheology and filtration characteristics. Considering the stratified structures within coal rock formed by geological deposition, this study utilizes Python code interacting with Abaqus to divide the coal seam into coal rock and natural bedding. We analyzed the effects of engineering parameters, geological factors, and bedding characteristics on slurry–vein propagation patterns, the stimulation extent, and fracturing pressure. The findings reveal that increasing the grouting rate from 1.2 to 3.6 m3/min enlarges the stimulated volume and the maximum fracture width and raises the fracturing pressure from 26.28 to 31.44 MPa. A lower slurry viscosity of 100 mPa·s promotes the propagation of slurry veins, making it easier to develop multiple veins. The bedding-to-coal rock strength ratio controls crossing versus layer-parallel growth: at 0.3, veins more readily penetrate bedding planes, whereas at 0.1 they preferentially spread along them. Raising the lateral pressure coefficient from 0.6 to 0.8 increases the likelihood of the slurry expanding along the beddings. Natural bedding structures guide directional flow; a higher bedding density (225 lines per 10,000 m3) yields greater directional deflection and a more intricate fracture network. As the angle of bedding increases from 10° to 60°, the slurry veins are more susceptible to directional changes. Throughout the grouting process, the slurry veins can undergo varying degrees of directional alteration. Under the studied conditions, both fracturing and compaction grouting modes are present, with fracturing grouting dominating in the initial stages, while compaction grouting becomes more prominent later on. These results provide quantitative guidance for designing dual-enhanced stimulation to jointly improve permeability and mechanical stability. Full article
(This article belongs to the Special Issue Polymer Fluids in Geology and Geotechnical Engineering)
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23 pages, 7438 KB  
Article
Numerical Simulation on Multi-Fractures Propagation Behavior Based on Hybrid Finite-Discrete Method in Deep Shale Formation
by Bin Wang, Jingfeng Dong, Peiyao Zhou and Kaixin Liu
Processes 2025, 13(9), 2944; https://doi.org/10.3390/pr13092944 - 15 Sep 2025
Viewed by 890
Abstract
Hydraulic fracturing technology serves as the primary method for efficiently developing deep shale resources. During hydraulic fracturing, the thermal stress caused by the injection of fracturing fluid, which has low temperature, has a significant effect on the propagation of multiple hydraulic fractures in [...] Read more.
Hydraulic fracturing technology serves as the primary method for efficiently developing deep shale resources. During hydraulic fracturing, the thermal stress caused by the injection of fracturing fluid, which has low temperature, has a significant effect on the propagation of multiple hydraulic fractures in deep shale reservoirs. Due to the unclear mechanisms governing multi-fracture propagation in deep shale reservoirs, this study proposed a hydraulic fracturing model for multi-fracture propagation based on the principles of linear elastic fracture mechanics. The model was employed to investigate how formation properties and operational parameters influenced the expansion of multiple hydraulic fractures. The findings revealed that thermal stress fracturing caused by low-temperature fluid injection significantly affected the rock breakdown pressure and fracture initiation timing. Specifically, when the reservoir temperature exceeded 180 °C, the breakdown pressure decreased substantially, and the fracture initiation occurred much earlier. Moreover, an increase in rock thermal conductivity further reduced both the breakdown pressure and the propagation pressure, alleviating the “stress shadow” effect on intermediate fractures and promoting more uniform fracture growth. Furthermore, when the reservoir temperature surpassed 180 °C and the thermal conductivity exceeded 1.3 W/(m K), the influence of horizontal stress difference and cluster spacing on multi-fracture propagation diminished sharply—by more than 40%. This condition facilitated tight containment of the deep shale reservoir and significantly expanded the stimulated reservoir volume. These findings not only enriched and refined the theoretical understanding of hydraulic fracturing in deep shale reservoirs but also provided a valuable reference for optimizing fracturing parameters in the development of deep oil and gas reservoirs. Full article
(This article belongs to the Special Issue Advanced Technology in Unconventional Resource Development)
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27 pages, 11253 KB  
Article
Failure Mechanism of Progressive Collapse Induced by Hanger Fracture in Through Tied-Arch Bridge: A Comparative Analysis
by Bing-Hui Fan, Qi Sun, Qiang Chen, Bin-Bin Zhou, Zhi-Jiang Wu and Jin-Qi Zou
Buildings 2025, 15(16), 2810; https://doi.org/10.3390/buildings15162810 - 8 Aug 2025
Viewed by 2516
Abstract
Although through tied-arch bridges exhibit strong structural robustness, collapse incidents triggered by the progressive failure of hangers still occasionally occur. Given that such bridges are unlikely to collapse due to the damage of a single or multiple hangers under the serviceability limit state, [...] Read more.
Although through tied-arch bridges exhibit strong structural robustness, collapse incidents triggered by the progressive failure of hangers still occasionally occur. Given that such bridges are unlikely to collapse due to the damage of a single or multiple hangers under the serviceability limit state, this study focuses on the failure safety limit state. Using the Nanfang’ao Bridge with inclined hangers and the Liujiang Bridge with vertical hangers as case studies, this paper investigates the dynamic response and failure modes of the residual structures when single or multiple hangers fail and initiate progressive collapse of all hangers. The results demonstrate that the configuration of hangers significantly influences the distribution of structural importance coefficients and the load transmission paths. Under identical failure scenarios, the Nanfang’ao Bridge with inclined hangers remains stable after the failure of four hangers without experiencing progressive collapse, whereas the Liujiang Bridge with vertical hangers undergoes progressive failure following the loss of only three hangers, which indicates that inclined hanger configurations offer superior resistance to progressive collapse. Based on the aforementioned analysis, the LS-DYNA Simple–Johnson–Cook damage model was employed to simulate the collapse process. The extent of damage and ultimate failure modes of the two bridges differ significantly. In the case of the Nanfang’ao Bridge, following the progressive failure of the hangers, the bridge deck system lost lateral support, leading to excessive downward deflection. The deck subsequently fractured at the mid-span (1/2 position) and collapsed in an inverted “V” shape. This failure then propagated to the tie bar, inducing outward compression at the arch feet and tensile stress in the arch ribs. Stress concentration at the connection between the arch columns and arch rings ultimately triggered global collapse. For the Liujiang Bridge, failure initiated with localized concrete cracking, which propagated to reinforcing bar yielding, resulting in localized damage within the bridge deck system. These observations indicate that progressive stay cable failure serves as the common initial triggering mechanism for both bridges. However, differences in the structural configuration of the bridge deck systems, the geometry of the arch ribs, and the constraint effects of the tie bar result in distinct failure progression patterns and ultimate collapse behaviors between the two structures. Thereby, design recommendations are proposed for through tied-arch bridges, from the aspects of the hanger, arch rib, bridge deck system, and tie bar, to enhance the resistance to progressive collapse. Full article
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17 pages, 8153 KB  
Article
Numerical Simulation of Freezing-Induced Crack Propagation in Fractured Rock Masses Under Water–Ice Phase Change Using Discrete Element Method
by Hesi Xu, Brian Putsikai, Shuyang Yu, Jun Yu, Yifei Li and Pingping Gu
Buildings 2025, 15(12), 2055; https://doi.org/10.3390/buildings15122055 - 15 Jun 2025
Cited by 6 | Viewed by 1874
Abstract
In cold-region rock engineering, freeze–thaw cycle-induced crack propagation in fractured rock masses serves as a major cause of disasters such as slope instability. Existing studies primarily focus on the influence of individual fissure parameters, yet lack a systematic analysis of the crack propagation [...] Read more.
In cold-region rock engineering, freeze–thaw cycle-induced crack propagation in fractured rock masses serves as a major cause of disasters such as slope instability. Existing studies primarily focus on the influence of individual fissure parameters, yet lack a systematic analysis of the crack propagation mechanisms under the coupled action of multiple parameters. To address this, we establish three groups of slope models with different rock bridge distances (d), rock bridge angles (α), and fissure angles (β) based on the PFC2D discrete element method. Frost heave loads are simulated by incorporating the volumetric expansion during water–ice phase change. The Parallel Bond Model (PBM) is used to capture the mechanical behavior between particles and the bond fracture process. This reveals the crack evolution laws under freeze–thaw cycles. The results show that, at a short rock bridge distance of d = 60 m, stress concentrates in the fracture zone. This easily leads to the rapid penetration of main cracks and triggers sudden instability. At a long rock bridge distance where d ≥ 100 m, the degree of stress concentration decreases. Meanwhile, the stress distribution range expands, promoting multiple crack initiation points and the development of branch cracks. The number of cracks increases as the rock bridge distance grows. In cases where the rock bridge angle is α ≤ 60°, stress is more likely to concentrate in the fracture zone. The crack propagation exhibits strong synergy, easily forming a penetration surface. When α = 75°, the stress concentration areas become dispersed and their distribution range expands. Cracks initiate earliest at this angle, with the largest number of cracks forming. Cumulative damage is significant under this condition. When the fissure angle is β = 60°, stress concentration areas gather around the fissures. Their distribution range expands, making cracks easier to propagate. Crack propagation becomes more dispersed in this case. When β = 30°, the main crack rapidly penetrates due to stress concentration, inhibiting the development of branch cracks, and the number of cracks is the smallest after freeze–thaw cycles. When β = 75°, the freeze–thaw stress dispersion leads to insufficient driving force, and the number of cracks is 623. The research findings provide a theoretical foundation for assessing freeze–thaw damage in fractured rock masses of cold regions and for guiding engineering stability control from a multi-parameter perspective. Full article
(This article belongs to the Special Issue Low Carbon and Green Materials in Construction—3rd Edition)
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13 pages, 2195 KB  
Article
Experimental Study on the Acid Fracturing Fracture Propagation Law of a Fractured Carbonate Reservoir in the Majiagou Formation
by Yongchun Zhang, Jianchao Kuang, Hao Zhang, Ying Zhong and Shijie Dong
Processes 2025, 13(3), 695; https://doi.org/10.3390/pr13030695 - 28 Feb 2025
Cited by 3 | Viewed by 2108
Abstract
Acid fracturing is a crucial method for reservoir reconstruction in carbonate reservoirs, and the propagation pattern of acid-etched fractures plays a key role in determining the scope of reservoir enhancement and post-fracturing productivity. However, large-scale physical simulations directly using acid solutions in fracturing [...] Read more.
Acid fracturing is a crucial method for reservoir reconstruction in carbonate reservoirs, and the propagation pattern of acid-etched fractures plays a key role in determining the scope of reservoir enhancement and post-fracturing productivity. However, large-scale physical simulations directly using acid solutions in fracturing experiments are limited, and the fracture propagation patterns under acid fracturing remain unclear. To address this gap, in this study, we collected carbonate rock samples from the Majiagou Formation in the Daniudi area, preparing large-scale fracturing specimens with side lengths of 30 cm. The propagation of acid fracturing fractures was investigated using self-developed true-triaxial acid fracturing equipment. Based on post-fracturing fracture morphology and pressure curves, the effects of fracturing fluid type, injection rate, injection mode, and natural fractures (NFs) on acid fracturing fracture propagation were analyzed. The experimental results showed that the acid solution effectively weakens the mechanical properties of the open-hole section, creating multiple mechanical weak points and promoting the initiation of fractures. Pre-fracturing treatment with low-viscosity acid can significantly enhance fracture complexity near the wellbore and expand the near-well stimulation zone. Lowering the injection rate increases the acid solution’s filtration loss into natural fractures, weakening the cementation strength of these fractures and encouraging the formation of complex fracture networks. Furthermore, employing a multi-stage alternating injection of high-viscosity and low-viscosity acids can reduce fracture temperature and acid filtration loss while also enhancing differential etching through viscous fingering. This approach improves the conductivity and conductivity retention of the acid-etched fractures. The results of this study can provide a reference for the acid fracturing stimulation of fractured carbonate reservoirs. Full article
(This article belongs to the Special Issue Recent Advances in Hydrocarbon Production Processes from Geoenergy)
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