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Keywords = discrete element models

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17 pages, 1490 KB  
Article
3D Reconstruction and Discrete Element Modeling of Wheat Kernels for Numerical Simulation of Grain-Storage Behavior
by Ziqing Zhang, Qirui Wang, Chao Zhao, Kaixu Bai, Qikeng Xu, Peifang Xin, Chunqi Bai and Hao Zhang
Appl. Sci. 2026, 16(6), 2915; https://doi.org/10.3390/app16062915 - 18 Mar 2026
Abstract
The physical structure formed during the packing of granular grain constitutes a fundamental ecological factor within the grain bulk ecosystem. Accurate simulations of grain-packing behavior help to deepen our understanding of this ecosystem. In this study, a white hard wheat was selected as [...] Read more.
The physical structure formed during the packing of granular grain constitutes a fundamental ecological factor within the grain bulk ecosystem. Accurate simulations of grain-packing behavior help to deepen our understanding of this ecosystem. In this study, a white hard wheat was selected as the test material, and a high-fidelity multi-sphere discrete element model of wheat kernels was constructed using three-dimensional laser scanning. Physical experiments were conducted to determine the basic physical properties of the kernels, including true density and bulk density. Using the angle of repose as the calibration parameter, the wheat-packing process was investigated with the discrete element method (DEM). The results indicated that the coefficients of static and rolling friction between particles were highly significant factors governing the angle of repose. The optimal parameter combination consisted of a particle–particle coefficient of restitution of 0.500, a coefficient of static friction of 0.388, and a coefficient of rolling friction of 0.054. The mean angle of repose obtained from the DEM packing simulation was 28.46°, corresponding to a relative error of 3.16% compared with the physical experiment. This calibrated parameter set is therefore considered accurate and reliable, and it provides baseline data for DEM simulations of wheat grain bulks. Full article
(This article belongs to the Special Issue Sustainable and Smart Agriculture)
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23 pages, 18768 KB  
Article
Deflection Analysis of Steel Truss Web–Concrete Composite Beams Based on Zigzag Beam Theory
by Ningning Zhou, Feng Gao, Rongqiao Xu and Yang Zhao
Buildings 2026, 16(6), 1183; https://doi.org/10.3390/buildings16061183 - 17 Mar 2026
Abstract
To address the inherent inaccuracies of the classical beam theory (which overestimates the flexural stiffness) and the “quasi-plane section method” (which neglects the shear deformation) in the deflection analysis of steel truss web–concrete composite beams, this study homogenizes discrete steel truss web members [...] Read more.
To address the inherent inaccuracies of the classical beam theory (which overestimates the flexural stiffness) and the “quasi-plane section method” (which neglects the shear deformation) in the deflection analysis of steel truss web–concrete composite beams, this study homogenizes discrete steel truss web members into a continuous steel web with equivalent thickness based on the strain energy equivalence principle. This homogenization is conducted under the assumption of fixed-end constraints for web members, thus establishing a sandwich laminated beam model. Incorporating the assumptions of zigzag axial displacement and layer-wise quadratic parabolic transverse shear stress, this study adopts the governing equations for static bending of composite beams derived via Hamilton’s mixed energy variational principle—this theory eliminates the need for an artificial shear correction factor, as the transverse shear stress naturally satisfies the zero boundary conditions at the upper and lower surfaces and the continuity condition at the interlayers. Analytical solutions for bending deflection under uniformly distributed loads are derived and validated against three-dimensional (3D) finite element (FE) models. The analysis results of a 45-meter-span beam demonstrate that the relative error in the maximum deflection of both simply supported beams and cantilever beams calculated by the proposed method is approximately 5%, which is significantly superior to the classical beam theory; the deflection induced by the zigzag effect at the mid-span of simply supported beams accounts for 15% of the total deflection, making it an indispensable key component in structural design. This method enables accurate deflection prediction and provides reliable technical guidance for the preliminary design of steel truss web–concrete composite beam bridges. Full article
(This article belongs to the Section Building Structures)
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24 pages, 3686 KB  
Article
Rock Burst Risk Assessment for Coal Mining in Coal Pillars Under Complex Geological Conditions
by Xingyu Jiang, Chi Liu, Haitao Li, Tuan He, Pengyu Mu, Huaguang Liu, Yiqin Liu and Zhihan Li
Sustainability 2026, 18(6), 2939; https://doi.org/10.3390/su18062939 - 17 Mar 2026
Abstract
To address the rock burst safety hazards encountered during coal seam mining in coal pillar areas under complex geological conditions and ensure sustainable and stable mine production, this study investigates the coal pillar area of a ventilation shaft in a mining area. Through [...] Read more.
To address the rock burst safety hazards encountered during coal seam mining in coal pillar areas under complex geological conditions and ensure sustainable and stable mine production, this study investigates the coal pillar area of a ventilation shaft in a mining area. Through an integrated approach incorporating field investigation, laboratory testing, numerical simulation, and engineering analogy, systematic research was conducted on rock burst mechanisms, geological modeling, and risk assessment. The results indicate that rock bursts in this coal pillar area represent tectonic-type disasters dominated by tectonic stress and induced by multi-factor coupling, with the coal seam exhibiting weak burst proneness. Based on a refined three-dimensional geological model constructed from borehole data, combined with mesh optimization and FDEM (Finite-Discrete Element Method) numerical simulations, precise delineation of rock burst hazard zones was achieved. These findings provide theoretical foundations and technical paradigms for safe mining operations in coal pillar area as under similar complex geological conditions, contributing to the sustainable development of coal resources through enhanced safety, extended mine service life, and optimized resource utilization. Full article
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15 pages, 4064 KB  
Article
Study on the Interlayer Contact Mechanism of Foamed Cold-Recycled Asphalt Mixture Under Static Loads
by Han Zhao, Jiangyu Liu and Junyan Yi
Coatings 2026, 16(3), 378; https://doi.org/10.3390/coatings16030378 - 17 Mar 2026
Abstract
To investigate the interlayer contact mechanism of foamed cold-recycled asphalt mixture under static loads, a three-layer asphalt pavement discrete element model (DEM) was established, with the surface layer composed of asphalt concrete-13 (AC-13), asphalt concrete-20 (AC-20) and asphalt-treated base-25 (ATB-25) foamed cold-recycled asphalt [...] Read more.
To investigate the interlayer contact mechanism of foamed cold-recycled asphalt mixture under static loads, a three-layer asphalt pavement discrete element model (DEM) was established, with the surface layer composed of asphalt concrete-13 (AC-13), asphalt concrete-20 (AC-20) and asphalt-treated base-25 (ATB-25) foamed cold-recycled asphalt mixture and cement-stabilized macadam as the base. Based on mortar theory, the pavement was divided into coarse aggregate, asphalt mastic and air void phases, and the Burgers Model, Linear Parallel Bond Model and Linear Model were adopted to characterize the bonding of asphalt-aggregate, cement contact interface and subgrade-surface layer, respectively. Static loads of 0.7 MPa, 1.1 MPa, 1.5 MPa and 1.9 MPa were applied to analyze the mechanical responses of asphalt-based and cement-based pavement systems from tensile strain, vertical compressive stress and vertical displacement. Results showed that mechanical indices of the pavement increase monotonically with static load and present obvious layered distribution. The cement-stabilized macadam base provides rigid support, significantly reducing tensile strain (TS) and vertical displacement (VD) of asphalt layers, while the asphalt-based system has flexible stress transfer and superior stress dissipation in the bottom layer. The two systems exhibit respective structural advantages, with the cement-based system outstanding in deformation control and the asphalt-based system suitable for flexible stress adaptation working conditions. Full article
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23 pages, 9128 KB  
Article
Mineral-Scale Mechanical Properties of Carbonate Rocks Based on Nanoindentation
by Zechen Guo, Dongjin Xu, Haijun Mao, Bao Li and Baoan Zhang
Appl. Sci. 2026, 16(6), 2874; https://doi.org/10.3390/app16062874 - 17 Mar 2026
Abstract
Carbonate reservoirs in the Shunbei area develop pronounced fracture networks after acidized hydraulic fracturing and thus have the potential to be repurposed as underground gas storage (UGS) after hydrocarbon depletion. Characterizing their mechanical behavior is essential for safe UGS operation; however, deep to [...] Read more.
Carbonate reservoirs in the Shunbei area develop pronounced fracture networks after acidized hydraulic fracturing and thus have the potential to be repurposed as underground gas storage (UGS) after hydrocarbon depletion. Characterizing their mechanical behavior is essential for safe UGS operation; however, deep to ultra-deep natural cores are difficult to obtain, and conventional macroscopic tests often cannot provide parameters that meet engineering requirements. To address this issue, nanoindentation combined with QEMSCAN (Quantitative Evaluation of Minerals by Scanning Electron Microscopy) was employed to quantify microscale mineral distributions and the mechanical properties of the major constituents. The investigated rock is calcite-dominated (89.62%), with minor quartz (9.89%) and trace feldspar-group minerals (1.89%). Minerals are randomly embedded, and soft–hard phase boundaries are widely distributed. A finite–discrete element method (FDEM) model was then constructed and calibrated in ABAQUS. The discrepancies in uniaxial compressive strength and elastic modulus relative to laboratory results were 6.51% and 9.91%, respectively, indicating good agreement in both mechanical response and failure mode. Parametric analyses using three additional models with different mineral proportions show that damage preferentially initiates at mineral phase boundaries and stress concentration zones induced by end constraints. Microcracks then propagate and coalesce into a dominant compressive–shear band, and final failure is mainly governed by slip along the shear band with localized tensile cracking. With increasing quartz and feldspar contents, enhanced heterogeneity and a higher density of phase boundaries lead to a higher density of crack nucleation sites and increased crack branching, and the failure pattern transitions from a single shear-band–controlled mode to a more network-like fracture system. Moreover, macroscopic strength is not determined solely by the intrinsic strength of individual minerals; heterogeneity and phase-boundary characteristics strongly govern microcrack behavior, such that higher hard-phase contents may result in a lower peak strength. Full article
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28 pages, 6829 KB  
Article
Numerical Simulation of Particle Deposition on Superhydrophobic Surfaces with Randomly Distributed Roughness—A Coupled LBM-IMBM-DEM Method
by Wenjun Zhao and Hao Lu
Coatings 2026, 16(3), 377; https://doi.org/10.3390/coatings16030377 - 17 Mar 2026
Abstract
Dust pollution has emerged as a critical issue in a wide range of industrial applications, creating an urgent demand for effective strategies to mitigate particle deposition. Recent experimental studies have demonstrated that superhydrophobic coatings represent a promising class of self-cleaning materials, primarily attributed [...] Read more.
Dust pollution has emerged as a critical issue in a wide range of industrial applications, creating an urgent demand for effective strategies to mitigate particle deposition. Recent experimental studies have demonstrated that superhydrophobic coatings represent a promising class of self-cleaning materials, primarily attributed to their hierarchical rough structures and intrinsically low surface energy. Nevertheless, the underlying self-cleaning mechanisms of superhydrophobic surfaces have not yet been fully elucidated. This work examines particle deposition on superhydrophobic surfaces featuring stochastic roughness distributions through computational modeling. Surface topographies were generated using Fast Fourier Transform techniques. An integrated lattice Boltzmann–discrete element method (LBM–DEM) framework simulated particle transport in superhydrophobic-coated channels. Particle–fluid coupling was achieved via the immersed moving boundary approach, while particle–surface interactions employed a modified Johnson–Kendall–Roberts (JKR) adhesion model. Parametric studies quantified effects of particle size, interfacial energy, flow Reynolds number, and topographical statistics on deposition dynamics. Experimental validation demonstrates good agreement between numerical predictions and measurements. Smaller particles exhibit a lower tendency to deposit on superhydrophobic surfaces, whereas increasing surface energy significantly enhances particle deposition due to stronger adhesion forces and the suppression of particle resuspension. In addition, higher Reynolds numbers effectively reduce particle deposition. The revealed self-cleaning mechanisms provide theoretical guidance for the design of high-performance self-cleaning coatings, and the identified effects of particle and surface parameters offer practical insights for anti-pollution engineering applications. Full article
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24 pages, 8260 KB  
Article
Numerical Investigation of the Seismic Performance of FRP-Reinforced Tunnel Linings Under Dynamic Excitation
by Qiwei Lin, Yujing Jiang and Satoshi Sugimoto
Infrastructures 2026, 11(3), 100; https://doi.org/10.3390/infrastructures11030100 - 17 Mar 2026
Abstract
Tunnel linings are critical structural components of underground infrastructure, and their seismic performance plays a decisive role in maintaining the serviceability and safety of tunnels. Under dynamic loading, excessive deformation and damage of the lining may reduce the effective cross-sectional capacity and threaten [...] Read more.
Tunnel linings are critical structural components of underground infrastructure, and their seismic performance plays a decisive role in maintaining the serviceability and safety of tunnels. Under dynamic loading, excessive deformation and damage of the lining may reduce the effective cross-sectional capacity and threaten the minimum safety clearance required for tunnel operation. Therefore, it is essential to investigate the deformation behavior and failure mechanisms of tunnel linings subjected to seismic excitation and to evaluate the effectiveness of reinforcement measures. In this study, a coupled numerical framework combining the finite difference method (FLAC3D) and the discrete element method (PFC3D) is developed to analyze the dynamic response of tunnel lining systems. The surrounding rock mass is modeled in FLAC3D to simulate stress wave propagation and global deformation, while the tunnel lining is represented in PFC3D using bonded particles to capture crack initiation, propagation, and post-peak failure behavior. The proposed FLAC3D–PFC3D coupled approach provides an effective tool for evaluating the seismic performance of reinforced tunnel linings and offers a practical basis for the design and assessment of seismic strengthening measures in underground engineering. Full article
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28 pages, 2545 KB  
Article
Modeling Rank Distribution and the Relative Importance Factor Index in Discrete Power-Law Models: Application to Social Resilience Using the Scopus Database
by Brian Llinas, Jose Padilla, Humberto Llinas, Erika Frydenlund and Katherine Palacio
Mathematics 2026, 14(6), 966; https://doi.org/10.3390/math14060966 - 12 Mar 2026
Viewed by 147
Abstract
Prior research on power-law distributions has primarily focused on modeling frequency patterns, with less attention given to rank distributions and how ranked positions reflect relative importance among elements. In discrete power-law distributions, frequency-based metrics often provide limited discrimination in the tail, where elements [...] Read more.
Prior research on power-law distributions has primarily focused on modeling frequency patterns, with less attention given to rank distributions and how ranked positions reflect relative importance among elements. In discrete power-law distributions, frequency-based metrics often provide limited discrimination in the tail, where elements may exhibit similar counts but differ in relative dominance. These patterns are especially evident, for instance, in academic publishing, where keywords, affiliations, and citations commonly exhibit power-law behavior. To address this limitation, we introduce the Relative Importance Factor (RIF) Index, a statistical measure derived from the estimated discrete power-law rank distribution rather than an additional independent parameter. The RIF Index compares the probability of an element at a given rank with its probabilities at lower ranks, enabling explicit pairwise statistical comparison, particularly within the tail. We formalize the mathematical framework for discrete rank modeling and apply RIF to synthetic data and a Scopus dataset on social resilience. Our results show that RIF clarifies dominance relationships among ranked elements, providing stronger discrimination in the tail than frequency-based measures alone. We further introduce the RIF matrix and RIF network to represent these pairwise relationships structurally, supporting interpretation of prominence patterns. Although demonstrated in academic publishing, the method generalizes to domains where categorical variables follow discrete power-law behavior under appropriate model-fit validation. Full article
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20 pages, 5917 KB  
Article
Seismic Performance and Parameter Optimization of Traditional Chinese Timber Structure Reinforced with Friction Dampers
by Meng Xiang, Yanping Niu, Leilei Liu, Xicheng Zhang, Maozhe Nie and Yao Cui
CivilEng 2026, 7(1), 17; https://doi.org/10.3390/civileng7010017 - 11 Mar 2026
Viewed by 123
Abstract
To effectively enhance the seismic performance of traditional Chinese timber structures, this study proposes a reinforcement method utilizing friction dampers. Based on the working mechanism of friction dampers and the extended discrete element theory, an analytical model for timber structures equipped with these [...] Read more.
To effectively enhance the seismic performance of traditional Chinese timber structures, this study proposes a reinforcement method utilizing friction dampers. Based on the working mechanism of friction dampers and the extended discrete element theory, an analytical model for timber structures equipped with these dampers was developed and validated through shake table tests. Subsequently, dynamic analyses were conducted to systematically evaluate the enhanced seismic energy dissipation capacity of the ancient timber structures by the reinforcement of friction dampers. The friction coefficient (μ), bolt pre-tension strain (ε), and action distance (l) were selected as key parameters. A multi-objective optimization function was constructed using the weighted sum method, enabling a multi-objective parameter optimization analysis for the friction dampers to identify the optimal parameter combination under specific conditions. The results indicate that the established extended discrete element model effectively simulates the dynamic characteristics of the structure. The installation of friction dampers significantly enhanced the structure’s energy dissipation capacity and substantially reduced the peak displacement. However, due to the initial stiffness introduced by the dampers, the lateral stiffness of the column frame increased markedly, leading to a significant amplification of the acceleration response, with a maximum increase in peak acceleration reaching 77%. The multi-objective optimization analysis revealed that with weighting coefficients λa = λb = 0.5, the optimal damper parameter combination is μ = 0.36, ε = 102 με, and l = 268 mm. Under these conditions, the structural displacement response decreased by 38.5%, while the acceleration response increased by 93.7%. It is noted that the derived optimal design solutions are pertinent to the specific structural typology and ground motions considered. Full article
(This article belongs to the Section Structural and Earthquake Engineering)
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17 pages, 2957 KB  
Article
Cracking Mechanisms of Mesoscale Concrete Models Containing Single and Double Fissures Based on DEM
by Jinfang Zhang, Yi Sun, Gongye Sun, Yifei Li and Shuyang Yu
Materials 2026, 19(6), 1071; https://doi.org/10.3390/ma19061071 - 11 Mar 2026
Viewed by 93
Abstract
Existing theories leave gaps in explaining the mechanism of concrete cracking. To explain the mechanism of concrete cracking, after considering various methods, this paper finally selects the Particle Flow Code (PFC) based on the discrete element method (DEM) for the research. We selected [...] Read more.
Existing theories leave gaps in explaining the mechanism of concrete cracking. To explain the mechanism of concrete cracking, after considering various methods, this paper finally selects the Particle Flow Code (PFC) based on the discrete element method (DEM) for the research. We selected concrete with single cracks and double cracks as the research object, and constructed a mesoscale model in PFC based on the parameters of the concrete. The model was verified by uniaxial compression tests and published experimental data, with simulated results matching experimental data within an acceptable error range. Simulate the situation of concrete cracking, plot the data into images, and analyze the patterns of the development of concrete cracks. During this process, we set the angle of crack formation and the number of cracks as variables. By analyzing the load–displacement curves and the crack evolution curves, we found that the mode of crack propagation changed from a linear extension to a branched expansion. It is also worth noting that when the inclination angle is 90 degrees, the bearing capacity of the specimen is the best, with its peak strength over 40% higher than that at 0° for single-fissure specimens and over 35% higher for double-fissure specimens, and the initial stiffness also reaches the maximum at this angle. Furthermore, throughout the entire testing process, the PFC based on the discrete element method was able to accurately capture the development process of concrete cracks. This study innovatively quantifies the evolution of tensile and shear cracks with inclination angle, clarifies the nonlinear correlation between peak strength and crack angle, and reveals the unique cracking behavior induced by double fissures, which is insufficiently studied in existing continuum simulations. The above findings not only enhance our understanding of the mechanism of concrete cracks, but also provide a reference for improving the strength of concrete. This study is limited to 2D uniaxial compression simulation, with the concrete microstructure idealized in the numerical model. Full article
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13 pages, 4313 KB  
Article
Numerical Simulation and Response Surface Optimization of Sliding-Cutting Digging Shovel for Two-Row Ridge Peanut Planting
by Qiantao Sun, Huan Qin, Jibang Hu, Huaigang Guo, Dongwei Wang and Wenxi Sun
AgriEngineering 2026, 8(3), 107; https://doi.org/10.3390/agriengineering8030107 - 11 Mar 2026
Viewed by 126
Abstract
To optimize the structural parameters of a peanut digging shovel and enhance its operational performance, the forces exerted on the digging shovel were examined through a graphical mechanics approach. This analysis identified the primary structural and operational parameters of the shovel’s design. A [...] Read more.
To optimize the structural parameters of a peanut digging shovel and enhance its operational performance, the forces exerted on the digging shovel were examined through a graphical mechanics approach. This analysis identified the primary structural and operational parameters of the shovel’s design. A numerical simulation model for the working resistance of the shovel was established adopting EDEM (2018) discrete element analysis software and subsequently validated through comparative analysis with field experiment results. Employing the Box–Behnken response surface method, quadratic regression models were constructed with digging resistance and soil non-breakage ratio as the response variables, while forward speed, soil entry angle, and blade tilt angle were taken as the influencing factors. Optimization analysis of these parameters was conducted. The optimization results indicate that with a forward speed of 0.8 m/s, a soil entry angle of 20°, and a blade tilt angle of 40°, the working resistance of the shovel is 1667 N, and the soil non-breakage ratio is 20.56%. The error between the field test results and the predictions from the optimized model was less than 2%, illustrating the feasibility of the model and the optimization outcomes. This study offers a technical reference for future simulation-based optimization of peanut digging shovels. Full article
(This article belongs to the Section Agricultural Mechanization and Machinery)
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15 pages, 3853 KB  
Article
Simulation and Monitoring of Interfacial Microcracks Between Ultra-Weak Fiber Bragg Grating Sensor and Asphalt Mixture
by Zengqing Hua, Yuxuan Li, Dongya Duan, Xiuying Luo and Yanshun Jia
Coatings 2026, 16(3), 349; https://doi.org/10.3390/coatings16030349 - 11 Mar 2026
Viewed by 132
Abstract
The precision of data gathered from Ultra-Weak Fiber Bragg Grating (UWFBG) sensing technology is limited when measuring strain within asphalt pavements. To better understand its measurement mechanism and correct possible errors, this study examines the synergy deformation behavior between UWFBG and asphalt mixtures [...] Read more.
The precision of data gathered from Ultra-Weak Fiber Bragg Grating (UWFBG) sensing technology is limited when measuring strain within asphalt pavements. To better understand its measurement mechanism and correct possible errors, this study examines the synergy deformation behavior between UWFBG and asphalt mixtures under loads. Initially, the mesoscopic model of asphalt mixture containing UWFBG was constructed using a discrete element model, followed by the validation of the model. Then, the propagation of microcracks at the interface between the asphalt mixture and UWFBG was analyzed, revealing damage characteristics of this material under various loading stages. Additionally, a quantitative relationship between the crack width and the monitoring strain was identified. The significant effect of introducing the sensor on crack propagation and interface debonding in strain response was also highlighted. The results indicate that when displacement exceeds 1.4 mm during a bending test, the number of both damage and microcracks increases markedly, with cracks progressively developing. Especially at the UWFBG interface subjected to a tensile load, microcrack growth rises sharply, leading to the failure of the interface. The mor-UWFBG interface is not the main damage location, but it is the most vulnerable location to damage and may be the one affecting the monitoring of UWFBG. Without sensors, a consistent linear relationship between monitoring strain and crack width is observed within the asphalt mixture. After introducing the UWFBG sensor, the strain-crack response of the asphalt mixture is divided into three stages: crack initiation, crack propagation, and interface debonding. When the crack width surpasses 0.03 mm, interface debonding significantly influences the strain growth rate, indicating the necessity of correcting the synergy deformation. Full article
(This article belongs to the Section Environmental Aspects in Colloid and Interface Science)
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23 pages, 16317 KB  
Article
Evolution and Prediction of Deep Coal–Rock Fracture Conductivity with Energy-Based Breakage Criterion of Proppant
by Pengyin Yan and Zhiming Wang
Processes 2026, 14(5), 866; https://doi.org/10.3390/pr14050866 - 8 Mar 2026
Viewed by 195
Abstract
It is of great significance to clarify the evolution law and control mechanism of fracture conductivity in different production stages for the efficient development of coalbed methane. However, research on fracture conductivity in coal–rock remains limited, and the existing models are inadequate for [...] Read more.
It is of great significance to clarify the evolution law and control mechanism of fracture conductivity in different production stages for the efficient development of coalbed methane. However, research on fracture conductivity in coal–rock remains limited, and the existing models are inadequate for predicting fracture conductivity with a consideration of staged proppant crushing. To address this gap, long-term conductivity tests were conducted on deep coal–rock under varying closure pressures and proppant gradation ratios. Within a coupled computational fluid dynamics and discrete element method (CFD-DEM) framework, a particle substitution scheme was integrated with the energy-based breakage model (Tavares breakage model) to develop a fracture conductivity predictor that incorporates proppant crushing and captures the time-dependent kinetics of proppant breakage during fracture conductivity evaluation. The model’s predictions align well with the experimental data, with an average error of less than 5%. The results indicate that fracture conductivity evolution can be delineated into three stages according to particle-breakage characteristics, (i) proppant pack compaction, (ii) the primary crushing of coarse proppant grains, and (iii) the secondary crushing of proppant fines, and the contributions of these three stages to the total conductivity loss are approximately 60%, 30%, and 10%, respectively. At a low closure pressure, fracture conductivity varies markedly among proppant packs with different particle sizes; once the closure pressure exceeds 40 MPa, the proppant pack enters the fines-breakage stage, and the conductivity differences among various particle size blends become marginal. Furthermore, a semi-empirical prediction model incorporating a composite crushing factor (CCF) was developed based on the Kozeny–Carman relationship, enabling a rapid evaluation of fracture conductivity in deep coal–rock fractures. Overall, these results provide a practical basis for fracture conductivity prediction and hydraulic fracturing parameter optimization in coal–rock reservoirs. Full article
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25 pages, 5611 KB  
Article
Static Ditching Performance Analysis and Experiment of Horizontal Ditching Device for Salix Psammophila Sand Barriers
by Feixu Zhang, Fei Liu, Xuan Zhao, Hongbin Bai, Wenxue Dong, Rifeng Guo, Haoran Jiang, Qihao Wan, Yunong Ma and Yarong Zhang
Agriculture 2026, 16(5), 617; https://doi.org/10.3390/agriculture16050617 - 7 Mar 2026
Viewed by 201
Abstract
To address the complex dynamic mechanisms and lack of static operation data in trench-digging for transverse planting of Salix psammophila sand barriers, a transverse trench-digging device was designed. Based on the discrete element method, the Hertz–Mindlin with JKR Cohesion model was used to [...] Read more.
To address the complex dynamic mechanisms and lack of static operation data in trench-digging for transverse planting of Salix psammophila sand barriers, a transverse trench-digging device was designed. Based on the discrete element method, the Hertz–Mindlin with JKR Cohesion model was used to simulate sandy soil. The Box–Behnken experiment was adopted to optimize the single auger structure with helix angle and soil-cutting angle as factors and trench depth and working torque as indices, yielding the optimal parameters of 30° soil-cutting angle and 20.37° helix angle (5.52 cm trench depth, 2.6 N·m maximum torque). The optimized auger was integrated into the device, and a further Box–Behnken experiment was conducted under a 20 cm fixed descending depth of the lifting platform. With auger rotation speed, shaft spacing and lifting speed as factors, and trench depth, soil compaction and Salix psammophila insertion depth as indices, the optimal operating parameters were determined as 257.25 r/min, 7 cm and 9 cm/s, corresponding to 6.7 cm trench depth, 33.37 kPa soil compaction and 14.87 cm insertion depth. This study clarifies the effects of auger and operation parameters on trench-digging quality, provides a basis for the design and parameter matching of dynamic continuous operation equipment, and offers a reference for the R&D of mechanized transverse planting equipment for Salix psammophila sand barriers, which is of practical value for reducing sand control costs and improving efficiency. Full article
(This article belongs to the Topic Ecological Protection and Modern Agricultural Development)
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24 pages, 4228 KB  
Article
From Layout to Data: AI-Driven Route Matrix Generation for Logistics Optimization
by Ádám Francuz and Tamás Bányai
Mathematics 2026, 14(5), 910; https://doi.org/10.3390/math14050910 - 7 Mar 2026
Viewed by 254
Abstract
This study proposes an end-to-end mathematical framework to automatically transform warehouse layout images into optimization-ready route matrices. The objective is to convert visual spatial information into a discrete, graph-based representation suitable for combinatorial route optimization. The problem is formulated as a mapping from [...] Read more.
This study proposes an end-to-end mathematical framework to automatically transform warehouse layout images into optimization-ready route matrices. The objective is to convert visual spatial information into a discrete, graph-based representation suitable for combinatorial route optimization. The problem is formulated as a mapping from continuous image space to a structured grid representation, integrating image segmentation, graph construction, and Traveling Salesman Problem (TSP)-based routing. Synthetic warehouse layouts were generated to create labeled training data, and a U-Net convolutional neural network was trained to perform multi-class segmentation of warehouse elements. The predicted grid representation was then converted into a graph structure, where feasible cells define vertices and adjacency defines edges. Shortest path distances were computed using Breadth-First Search, and the resulting distance matrix was used to solve a TSP instance. The segmentation model achieved approximately 98% training accuracy and 95–97% validation accuracy. The generated route matrices enabled successful construction of feasible and optimal round-trip routes in all tested scenarios. The proposed framework demonstrates that warehouse layouts can be automatically transformed into discrete mathematical representations suitable for logistics optimization, reducing manual preprocessing and enabling scalable integration into digital logistics systems. Full article
(This article belongs to the Special Issue Soft Computing in Computational Intelligence and Machine Learning)
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