Discrete-element method (DEM) simulation of rock direct shear resolves grain-scale cracking, but records it only as a list of broken bonds: a sparse binary point set that describes the three-dimensional crack field only implicitly. This work proposes a multi-modal neural operator that reconstructs, in one forward pass, the full crack field and the macroscopic response of a direct-shear specimen from a coarse-grained snapshot of its particle state at that instant. Bond-breakage events are recast into a continuous damage density field by Gaussian-kernel accumulation; density, initial-position and displacement fields enter a Transformer encoder as independent modalities, fused by cross-modal attention and decoded by two heads into three macroscopic scalars and a 643 damage field. Against a binary target trained with an imbalance-aware loss, that recasting buys learnability and costs positional fidelity, the two cancelling at native readout density. On a released benchmark of 1275 PFC3D cases and 26,872 frames, scored against eight baselines on a held-out split, it is statistically indistinguishable from the strongest on shear displacement, while convolutional baselines keep an edge on voxel-level crack overlap—the families are complementary rather than substitutable. These figures are stated against the DEM reference, itself anchored to laboratory direct shear over σn=10–60 MPa (calibration experiments at R2=0.941, an independent shale dataset at R2=0.953); the benchmark’s 1 and 5 MPa levels fall below it and mark the applicability boundary. The reconstructions stay physically consistent: cumulative input work explains crack accumulation at a pooled R2=0.907, against 0.845 for the DEM ground truth. Beyond rock direct shear, it is a route to full-field damage reconstruction from discrete simulations.
The macroscopic behavior of granular materials emerges from micromechanical interactions within particle assemblies, where fabric anisotropy serves as a key descriptor of particle rearrangements and microstructural evolution. Although the evolution of fabric anisotropy has been extensively investigated through X-ray tomography and Discrete Element Method (DEM) simulations, the influence of particle breakage under high stress remains insufficiently explored. In this study, DEM simulations with crushable particles are conducted to quantify how particle breakage modifies key fabric metrics, including coordination number and fabric anisotropy, under undrained triaxial compression across various confining pressures. A mass- and volume-conserving fragment replacement scheme is implemented to isolate the causal role of particle breakage. The evolving particle size distribution is tracked through a scalar breakage index. The results show that particle breakage suppresses strength and dilatancy, while the critical-state stress ratio remains largely unchanged within the investigated material and stress range. The all-contact coordination number decreases markedly with increasing breakage, whereas the mechanical coordination number is only slightly affected. Fabric anisotropy diminishes with increasing breakage severity, whereas its normalized form exhibits a slight increase. Based on these observations, a rate-form evolution law for fabric anisotropy that explicitly accounts for particle breakage is proposed, providing new insight into the coupling between microstructural degradation and macroscopic behavior of crushable granular materials.
The geological conditions and mining practices of a mine are used as the engineering backdrop to analyze the fracture features of overburden structure and the development law of surface fissures in shallow buried coal seam group mining. In the process of coal seam group mining, the fracture characteristics of the overburden structure and the mine pressure law are primarily studied using theoretical analysis, numerical modeling, and field measurement. Surface movement and deformation are affected by overburdened structural fracture, and this information may be utilized to address the issue of surface subsidence brought on by shallow buried coal seam group mining. The findings demonstrate that the key stratum often lies in the fracture zone during coal seam group mining, where it fractures to create the masonry beam structure. The masonry beam construction is vulnerable to sliding instability due to the ongoing mining of the lower coal seam, which causes secondary failure and surface deformation. It offers a foundation for surface prevention and control by understanding the contributing causes of masonry beam construction instability. Using numerical simulation, it has been shown that mining the coal seam group causes secondary damage to the key stratum of the upper coal seam, which causes the surface to be destroyed again. It offers a foundation for the mine to use when planning efficient preventative and control measures by simulating the morphological characteristics of the underlying stratum movement and surface subsidence of the 3# coal seam. Also, it reduces the economic loss brought on by surface sinking to the associated structures on the ground and successfully prevents secondary surface damage brought on by lower coal seam mining.
In simulations involving substantial domain evolution, the Particle Finite Element Method (PFEM) avoids mesh distortion by reconstructing the mesh from the current node cloud. However, unconstrained re-meshing in PFEM may introduce elements outside the physical domain, requiring filtering. The commonly used α-shape method, a purely geometric criterion, removes such elements using a user-defined threshold but often causes significant volume variation. To reduce this variation, this work proposes new techniques across the PFEM pipeline. First, for filtering new mesh elements, an efficient indicator-function-based filtering strategy retains elements only if their centroids lie within the previous physical domain. Second, to improve mesh-surface representation, dent-like artefacts in concave regions are corrected using a targeted boundary-node insertion routine, thereby reducing volume loss. Third, to limit volume increase, small elements are selectively removed after mesh-quality optimisation. Finally, to avoid volume variation associated with fluid–wall interaction, a barrier contact model is adopted. The examples demonstrate computationally efficient filtering performance and significantly reduced volume variation enabled by the proposed PFEM pipeline.
This study investigates the effects of k-shaped fissure inclination angle and confining stress on the fracture mechanisms of brittle building material specimens through experimental testing and particle-based numerical simulation. Physical specimens containing k-shaped fissures were prepared using gypsum as a representative brittle building material and subjected to uniaxial compressive loading at various inclination angles, while corresponding numerical models were analyzed using the discrete element method via PFC (Particle Flow Code) software under both confined and unconfined conditions. The results reveal that the ligaments confined between steeply inclined fissures fail first, after which tensile–shear bands propagate from the fissure tips toward the lateral boundaries of the specimen. As the fissure inclination angle decreases, fewer tensile–shear bands are observed. Crack initiation rate, propagation velocity, and coalescence activity are most pronounced at intermediate inclination angles. Steeply inclined fissure configurations exhibit delayed failure behavior, whereas moderately inclined configurations tend toward instantaneous brittle failure. The close correspondence between the particle-based computational outputs and the empirically obtained data serves as a strong confirmation of the reliability of the chosen simulation framework.
To comprehensively analyze the proppant transport behavior under reservoir conditions, the Darcy–Forchheimer equation is employed to describe the flow resistance in the reservoir. A complete numerical model of the reservoir–interlayer–artificial fracture system is established based on the CFD-DEM method. By calculating the forces acting on the proppant particles, the mechanical mechanism governing the formation of the sand bank is investigated. The differences in sand bank morphology between the present model and the conventional single-fracture model are analyzed. Emphasis is placed on analyzing the effects of viscous resistance coefficient, pumping rate, interlayer position, and fracture penetration ratio on sand bank morphology. Computational results reveal that drag force and pressure gradient force exert a dominant influence on proppant transport. Considering the fluid mobility in reservoir, fracturing fluid loss and flow resistance at the fracture tip lead to a shorter and higher sand bank, and enhance the pressure gradient force acting on surface particles of the sand bank, which increases the advancing angle and causes a “blunted tip” phenomenon. With the decrease in the permeability of the reservoir, the translational velocity of proppant particles within the fracture increases, which prolongs the particle migration distance and the sand bank length. When the fracture penetrates the lower interlayer, particles achieve a higher translational velocity and a lower settling velocity, resulting in a longer sand bank and a smaller dynamic advancing angle. In order to extend the effective propped fracture length, a penetration ratio in the range of 0.25–0.5 is recommended to allow the fracture to penetrate the lower interlayer. The model and computational findings facilitate the analysis of sand bank morphology under formation factors.
Smoothed Particle Hydrodynamics (SPH) is the standard tool for simulating high-velocity bird ingestion in aeroengines, yet LS-DYNA offers fifteen SPH formulations whose relative suitability for multi-stage ingestion has never been systematically assessed. This work presents a comprehensive evaluation of all fifteen formulations, combining (i) a physically representative single-impact benchmark, (ii) a sensitivity analysis of the governing numerical parameters, (iii) a double-impact configuration representative of sequential soft-body loading, and (iv) a validation against experimental data. The single-impact benchmark eliminates five formulations — symmetric (2, 3), adaptive SPH (9, 10), and moving least squares SPH (12) — due to unrealistic deformation, non-physical energy behavior, or core instability, narrowing the field to six candidates: default (0, 1), fluid particle (5, 6), and enhanced fluid (15, 16). Under double-impact loading, only the enhanced fluid formulations, which incorporate density filtering, retain stable shock propagation, coherent deformation, and accurate momentum partitioning; the remaining candidates suffer from either tensile-driven particle blow-up or unphysical clustering. Experimental validation against gelatin bird-surrogate impact tests confirms the predictive accuracy of the enhanced fluid formulations, with the renormalized variant (16) achieving the lowest displacement error and remaining numerically stable over extended computational domains where the standard renormalized formulation becomes computationally intractable. Formulation 16 is identified as the most robust and accurate SPH option for industrial bird-ingestion simulations in LS-DYNA, with formulation 15 offering a lower-cost alternative when computational efficiency outweighs the need for maximal accuracy.
Predicting shear-behavior transitions in block-in-matrix rocks (bimrocks) requires a descriptor that links mesoscale localization to macroscopic strength mobilization. Volumetric block proportion (VBP) specifies composition, whereas conventional interpretations based on peak friction-angle increments do not directly quantify the geometry of the active shear path. Here, equivalent shear-slip roughness is defined from the statistical centerline of a displacement-gradient-derived slip field and used to characterize the VBP-dependent transition. A three-dimensional Voronoi-expansion method and a heterogeneous discrete-element model are used to resolve stress-displacement responses, crack evolution, contact-force networks, and slip fields for VBP = 10-70%. Increasing VBP changes the response from localized matrix-through fracture with post-peak softening to distributed interface-guided shearing and stable frictional/block-rearrangement bearing. Concurrently, the residual equivalent slip path becomes progressively more tortuous, while load transfer evolves from matrix cohesion to frictional contact and block interlocking. The proposed roughness therefore complements VBP by quantifying how the imposed block proportion is expressed in the evolved localization geometry. Although evaluated from the post-deformation field, the residual numerical roughness converges toward the first-order theoretical estimate, indicating that the fully mobilized slip state is consistent with the model assumptions across the investigated VBP range. These results provide a measurable structure-mechanics link and support future roughness-informed strength formulations. Block morphology, orientation, gradation, anisotropy, and scale can be incorporated as refinements in broader validation.
This study develops a multi-patch B-spline-based MPM capable of handling Dirichlet boundary conditions along boundaries conforming with element edges while maintaining higher-order continuity within each patch. By inserting internal knots to decompose the parametric domain into multiple patches, we reduce inter-patch continuity to C0 and enforce the Kronecker delta property at adjacent patch interfaces to achieve strong coupling. This measure enables the analysis of localized phenomena around thin structures, such as sheet piles, while B-spline basis functions effectively mitigate numerical instabilities—specifically “cell-crossing errors.” The main contributions are the introduction of a multi-patch B-spline approximation into the shared background mesh of the hybrid MPM–FEM framework, its use for a non-cuboidal domain involving internal Dirichlet boundaries, and its application to the simulation of piping failure around a sheet pile. Numerical examples, including a cantilever beam and piping around a sheet pile, demonstrate that the proposed method suppresses cell-crossing errors and qualitatively reproduces the successive phases of piping failure — subsidence, uplifting, piping, and sedimentation — while strictly enforcing boundary conditions on the embedded structure.
Cardiovascular diseases remain a major global health burden, with calcific aortic valve disease (CAVD) constituting one of the most prevalent and debilitating conditions. Progressive leaflet stiffening due to calcific deposition alters valve kinematics, disrupts haemodynamics, and increases the risk of adverse events. Numerical modelling has emerged as a powerful tool for investigating these mechanisms, particularly for estimating quantities such as wall shear stress that are difficult to measure in vivo. However, traditional Eulerian-based fluid–structure interaction (FSI) methods rely on dynamic mesh deformation and remeshing, which can compromise numerical stability and accuracy when simulating the large deformations characteristic of calcified valves. The presents study proposes a fully coupled FSI framework for a native aortic valve using a purely Smoothed Particle Hydrodynamics (SPH) approach. The Lagrangian formulation of SPH eliminates mesh-related constraints, enabling robust representation distorted leaflet geometries and their interaction with pulsatile blood flow. Three calcification scenarios — healthy, moderately calcified, and partially calcified — are analysed to quantify their influence on valve dynamics and downstream haemodynamics. The model captures key pathological features, including asymmetric valve opening, altered leaflet motion, and the emergence of high-shear recirculating regions associated with thrombogenic risk. Quantitative comparisons with echocardiographic measurements and established finite-volume simulations demonstrate strong agreement, validating the predictive capability of the framework. Overall, the findings highlight the potential of SPH-based FSI modelling as a versatile and accurate approach for in-silico investigation of valvular pathophysiology and provide a foundation for future patient-specific assessment and cardiovascular device evaluation.
To address the challenges of complex strata pressure behavior and frequent roof disasters in fully mechanized top-coal caving faces with hard roofs, this study takes the working face 61617 as the engineering background. By integrating theoretical analysis, numerical simulation, and field monitoring, the formation mechanism of strong strata pressure in a hard-roof fully mechanized top-coal caving face is investigated. The stress evolution path, deformation and failure characteristics, and energy accumulation and release mechanisms of the hard roof during mining are analyzed. On this basis, the energy-concentrated blasting roof cutting technology based on "key stratum energy control" is proposed, achieving a full-process investigation from key stratum identification to energy regulation. The results indicate that strong strata pressure can be categorized into two main types: the long-span suspended roof fracture type and the advanced fracture rotation type. Based on the calculation of roof fracture spacing, the 11.25 m thick coarse sandstone is identified as the main key stratum, and the 7.4 m thick coarse sandstone as the subkey stratum. As the working face advances, strata pressure behavior is concentrated in the area ahead of the coal wall and the suspended roof above the goaf, exhibiting periodic patterns. The energy evolution follows a dynamic process of "accumulation-release-transfer," and the sudden release of energy upon reaching the storage limit of the key stratum constitutes the dynamic essence of strong strata pressure. Accordingly, a shaped charge pipe blasting for roof cutting scheme is proposed. By optimizing the borehole layout and blasting parameters, directional presplitting cutting is achieved. Field monitoring shows that this technology significantly improves roof caving conditions, reduces roadway deformation rates by 40%-55%, and results in a more uniform distribution of support loads, effectively controlling strata pressure. This provides a reliable technical approach for safe and efficient mining under the conditions of thick coal seams with hard roofs.
Most existing multiscale coupling models combining the discrete element method (DEM) with finite element method (FEM) or finite difference method (FDM) mainly focus on simulating subgrade surface stress responses, while the deformation mechanism associated with ballast penetration into fine grained subgrade soil remains insufficiently investigated. To address this gap, this study develops a coupled DEM-FDM model of the sleeper-ballast bed-subgrade that is capable of simulating ballast penetration into the subgrade. Comparative analysis with a conventional FDM model shows that the DEM-FDM model more realistically captures heterogeneous stress transfer at the ballast-subgrade interface, where multiple stress concentration channels are formed on the subgrade surface. The effects of subgrade grid size and soil elastic modulus on local stress and deformation at the ballast-subgrade interface were systematically analyzed. Results demonstrate that subgrade modulus is one of the dominant factors controlling whether ballast penetrates into the subgrade soil: when greater than 60 MPa, deformation is mainly settlement, whereas modulus values below 40 MPa lead to ballast penetration and local uplift of subgrade. Grid size is another critical factor, with smaller grids enhancing stress concentration capture and amplifying ballast penetration into subgrade. Field and laboratory tests further indicate that subgrade stiffness is highly sensitive to water content, with saturation reducing elastic modulus by over 80% despite adequate compaction, creating weak zones. Observed field defects such as ballast penetration and hidden voids arise from the combined effects of insufficient stiffness and stress concentration. These findings provide theoretical support for drainage improvement and interface reinforcement to ensure the long-term stability of heavy-haul railway subgrades.
Steady flows of dry granular materials impacting a rigid wall down a rough incline are investigated by simulations based on the discrete element method (DEM). This granular flow-obstacle setup, where quasi-static, dense inertial and dilute flow states co-exist, is used as a stringent test to cross-compare standard DEM using YADE and non-smooth DEM using SICONOS. Identical post-processing procedures, including coarse-graining and temporal averaging, are applied to assess the consequences of the different DEM implementations. Kinematic variables and stress fields obtained with both methods are compared at three different locations: the flow input at the exit of the feeding tank, the undisturbed region, and the vicinity of the obstacle. At the macroscopic scale, the two methods show good overall agreement. In particular, similar trends in terms of the mu(I) rheology are recovered, as well as comparable impact forces on the rigid wall. However, pronounced differences emerge at the contact scale, leading to different energy dissipation in the two simulations. Local discrepancies are observed near the boundaries both at the bottom and against the wall, where differences in contact force implementations are most pronounced and thus result in differences in basal slip velocities and stress distributions.
Understanding and controlling the viscosity of suspensions has contributed to the development of functional suspensions in diverse fields such as medicine, civil engineering, and industry. Numerous studies have been conducted to investigate the relationship between microscopic particle characteristics and macroscopic viscosity to find various functional suspensions. However, while many studies have reported spatial variations in relative viscosity, few have focused on unsteady relative viscosity. Unsteady viscosity refers to the time-dependent variation in viscosity, and is expected to represent an additional functional characteristic of suspensions. In this study, we investigated unsteady relative viscosity associated with the rotational motion of nonspherical particles. To understand the fundamental relationship between particle shape factors and relative viscosity, we performed a two-dimensional analysis of flow between parallel plates containing rectangular particles using the lattice Boltzmann method and the virtual flux method. The results indicated that the rotational motion of rectangular particles leads to unsteady variation of relative viscosity. Furthermore, we found that the variation of relative viscosity is amplified by changes in particle shape and mechanical conditions. This behavior is attributed to periodic variations in distance between the particle and the channel wall caused by particle rotation. In addition, we observed more pronounced unsteadiness in relative viscosity with a reduced inertial force and an increased ratio of particle diameter to channel diameter. These results suggest that the microscopic shape of particles and the inertial force of rectangular particles are important factors contributing to the macroscopic nonstationarity of relative viscosity.
Particle breakage governs the degradation of railway ballast under repeated loading; however, the influence of fracture configuration in the Bonded Particle Model (BPM) on macro-micro responses remain insufficiently understood. This study compares three BPM configurations-Uniform Bond Breakage Model (UBBM), Corner Bond Breakage Model (CBBM), and Diverse Bond Breakage Model (DBBM)-using coupled Finite Difference Method (FDM)- Discrete Element Method (DEM) triaxial simulations with a flexible membrane boundary. The results show that all breakable models exhibit similar responses at the lowest confining pressure of 60 kPa, whereas clear divergence emerges at higher confinement (90-240 kPa). Compared with the rigid model, the breakable specimen under a confining pressure of 60 kPa exhibits an approximately 50% reduction in peak deviatoric stress. Particle breakage also suppresses dilatancy, and this suppression becomes more pronounced under higher confining pressures. At the microscale, breakage promotes fragment redistribution and drives the transition of force chain structures from anisotropic to more isotropic patterns. Gradation analysis indicates that fragmentation is localized within the shear zone and intensifies with increasing confining pressure and axial strain. Overall, the results demonstrate that bond strength heterogeneity and fracture topology jointly govern the mechanical response and structural evolution of ballast. Among the examined configurations, the DBBM provides more consistent agreement with experimental observations, highlighting the importance of incorporating non-uniform bond structures in DEM simulations.
Aiming at insufficient discharge particle size uniformity and low qualified aggregate yield of the PF1315 impact crusher, this paper optimizes stone particle size ratio by combining crushing statistics principle and discrete element simulation technology. The Tavares breakage model in DEM is a particle breakage model based on energy threshold and damage accumulation, which enables direct visualization of the product particle size distribution. A DEM simulation model of the crusher and feldspar sandstone particles was established with reasonable physical and geometric parameters to realize high-precision crushing simulation. We systematically analyzed key indicators—particle trajectories, size distribution after crushing, and mass fractions of different size classes—to explore how operating parameters affect crushing performance. Special focus was placed on the mechanism of three key parameters—rotor speed, discharge port gap, and feeding rate—on crushing performance. Results show that finished aggregate uniformity and qualification rate present a nonlinear trend of first rising and then falling with increased rotor speed, with an optimal speed range existing. Discharge port gap and feeding rate significantly regulate finished product gradation; the mapping relationship between these two parameters and aggregate particle size ratio was established via quantitative analysis. The identified optimal parameter ranges (rotor speed 400–550 rpm, feeding rate 60–120 t/h) offer quantitative guidance for improving efficiency and reducing costs in industrial operation.
In order to achieve the accurate and stable simulation of fluid-structure interactions (FSI), the development of an entirely Lagrangian meshfree FSI solver is desirable, as this method can accurately impose fluid-structure interface boundary conditions. However, the existing methods are prone to numerical noise in the results without an additional artificial stabilisation, leading to unphysical or unstable pressure fields around the interface. In this study, a Riemann-based fluidstructure acceleration scheme is proposed for discretising the fluid-to-structure acceleration term, in the framework of Incompressible SPH (ISPH)-Total Lagrangian SPH (TLSPH) FSI solvers. This scheme improves the momentum transfer from the fluid to the structure, resulting in more accurate structural kinematics and enhanced kinematic boundary conditions for the fluid solver. Thus, the proposed scheme is designed to mitigate the instabilities at the fluid-structure interface induced by the kinematic discontinuities and to enhance a physically consistent transfer of momentum between fluid and structure. Three FSI benchmark tests are considered to validate the proposed scheme. These three tests include a hydrostatic water column on an elastic base plate, rotational sloshing with an elastic baffle, and dam break flow impacting an elastic plate. Through these typical and challenging FSI simulations involving 2-D inviscid single-phase fluid, the implementation of the proposed interaction scheme demonstrates that a more accurate fluidstructure interface motion is ensured, bringing a smooth and stable pressure field around the interface. Therefore, this study has established a foundation for an accurate and stable fully particle-based FSI solver.
Internal channels in soils can impair soil integrity and influence seepage erosion in complex ways. Meanwhile, seepage erosion may promote channel expansion, thereby threatening the safety of hydraulic structures such as embankments. This study uses the computational fluid dynamics-discrete element method (CFD-DEM) to develop idealized gap-graded soil models with different channel locations and intrusion degrees, and to investigate macro-and meso-scale responses during seepage erosion. Macroscopic behavior is characterized by the eroded fines ratio, local particle loss, permeability, and flow velocity. Mesoscopic evolution is described using coordination number, connectivity, and contact force chains. The results show a clear asymmetric effect of channel position on seepage erosion. An outlet-side channel intensifies fines migration and increases permeability, while an inlet-side channel reduces particle loss by suppressing boundary bypass flow. During seepage, particle detachment leads to significant channel enlargement (diameter increase > 52.5%) and elongation, indicating strong morphological feedback. In addition, internal channels alter contact force transmission, leading to more fine particles being incorporated into the load-bearing force chain network. Subsequent fines loss triggers a reorganization of force transmission networks. This reorganization induces more intense contact force redistribution in soils with internal channels, which may increase the severity of damage caused by seepage erosion. This work improves the understanding of seepage erosion in gap-graded soils with internal channels and provides a reference for engineering risk assessment and mitigation.
This study evaluated the performance of a pneumatic collection system designed to reduce losses of nutrient-rich alfalfa leaf fractions during harvesting. The system consisted of a suction unit integrated with a cyclone separator. A coupled computational fluid dynamics-discrete element method (CFD-DEM) framework was employed to systematically investigate the effects of key operating parameters, including airflow velocity (9, 13.5, and 18 m s-1), machine forward speed (2, 3, and 4 km h-1), and soil particle diameter (0.2, 1.0, and 2.4 mm). Additional simulations were conducted to assess the impact of cyclone design modifications, including a twofold increase in suction pipe radius, a 50% reduction in cyclone diameter, and the incorporation of a vortex finder. The results showed that an airflow velocity of 9 m s- 1 resulted in the accumulation of soil particles and alfalfa leaves at the cyclone inlet, causing partial blockage of the suction pipe. Increasing the airflow velocity substantially improved leaf collection and separation efficiency; however, it also promoted greater soil entrainment, thereby decreasing the purity of the collected material. Higher machine forward speeds reduced leaf collection efficiency because the shorter residence time of leaves within the suction zone limited their entrainment into the airflow stream. Reducing the suction pipe cross-sectional area effectively prevented inlet blockages and enhanced overall system performance without increasing fan power requirements. Although the inclusion of a vortex finder improved leaf-soil separation, complete separation was not achieved due to the similar terminal velocities of small alfalfa leaves and fine soil particles. Consequently, a fraction of the material remained suspended or retained within the cyclone, reducing separation effectiveness.
Understanding the dynamic motion and flooding behavior of damaged ships in wave environments is essential for assessing their survivability. This study conducts a numerical investigation using Weakly Compressible Smoothed Particle Hydrodynamics (WCSPH) method to simulate the response of damaged vessels under various regular wave conditions. The analysis begins with the simulation of a damaged cabin subjected to waves, and the numerical results are validated against experimental data to confirm the reliability of SPH framework. Subsequently, the motion and flooding behavior of a damaged International Towing Tank Conference (ITTC) barge-featuring one or two openings-is examined while the barge is freely floating. The investigation is further extended to KVLCC2 model to explore the influence of wave length, wave height, and wave direction on ship response. Detailed analyses focus on heave and roll motions under damage scenarios. The findings demonstrate that SPH method is capable of accurately reproducing both the flooding process and the hydrodynamic responses of damaged ships, offering practical insight for future research and design considerations related to maritime damage assessment.
