For moving-load problems that are approximately invariant in geometry and material properties along the traveling direction, 2.5D analysis preserves all three displacement components while reducing computational cost relative to full three-dimensional discretization. This paper develops a 2.5D Non-Uniform Rational B-spline (NURBS)-trace infinite-element method (NBIEM) for wave propagation in linear viscoelastic semi-infinite geotechnical media within a coupled finite/infinite-element framework. The bounded near field is discretized by isogeometric analysis, whereas the exterior is represented by tensor products of the boundary NURBS basis and admissible outgoing or evanescent exponential radial functions. The two subdomains share the same discrete NURBS trace space and boundary control-point degrees of freedom, enforcing displacement continuity without projection or mortar variables. For the selected radial functions, the far-field stiffness and mass contributions are evaluated from closed-form radial moments, avoiding a finite radial cutoff and radial quadrature. Comparisons with closed-form half-space solutions verify the computed displacement responses in the sub-Rayleigh and super-compressional regimes and the stress responses in the intermediate super-shear but sub-compressional regime. Low-frequency studies assess the sensitivity of the selected exterior setting to radial parameters and artificial-boundary placement. Additional tests characterize complex-valued response accuracy, phase fidelity, computational cost, and the frequency-dependent working range of the default S-wave-informed exterior realization. Applications to layered media, track–subgrade systems, and buried structures demonstrate the method’s ability to handle heterogeneous materials, multi-patch configurations, curved interfaces, and cover-depth-dependent geotechnical responses. The resulting framework provides a geometrically consistent and computationally efficient treatment of moving-load wave propagation and soil–structure interaction in semi-infinite domains.

This paper aims to develop a mixed finite element method for the three-dimensional quad-curl problem with low-order terms. We prove the regularity estimates on the solution to the primal weak problem under the assumption that the domain is a convex polyhedron. Subsequently, we introduce an auxiliary variable to reformulate the original problem as a mixed problem that consists of two curl-curl equations. Based on the regularity estimates, we establish the equivalence between the primal and mixed formulations. In this mixed finite element method, the primal and auxiliary variables are discretized by the N & eacute;d & eacute;lec's edge elements. We first derive the suboptimal error estimates for the mixed finite element method. In order to prove the optimal convergence, we construct a special projection with some good properties by using the Maxwell equation under the natural boundary condition. Then, by the duality argument, we prove the optimal error estimates for the approximation to the primal solution in the quad-curl equation. The numerical results illustrate the viability and optimal convergence of this method.

The dynamic confluence of self-expanding polymer grout during multi-source injection remains insufficiently quantified for pavement sub-slab void remediation. This study combines visualized horizontal-void experiments with Volume-of-Fluid (VOF) simulations to investigate the effects of injection mass, source spacing, void condition, borehole layout, and injection sequence on grout diffusion and confluence. The overlap width increased with injection mass and decreased with source spacing. Water-filled conditions slightly reduced the overlap width and increased the variability of cured density, but their independent effect remained limited within the tested range. An empirical power-law model was established for intersected grout bodies, achieving an in-sample coefficient of determination of 0.899. Under smooth horizontal-void conditions, the equilateral triangular layout produced a larger equivalent diffusion radius, higher spatial coverage ratio, and more balanced morphology than the linear layouts. The VOF model reasonably reproduced the observed diffusion morphologies in selected cases. Pressure–velocity analysis indicates that grout confluence is a stage-dependent hydraulic process involving independent expansion, pressure accumulation before contact, flow-path reconstruction in the confluence zone, and pressure relaxation after merging. Water mainly altered transient pressure and velocity responses by increasing local displacement resistance near the advancing front, without changing the overall diffusion pattern governed by injection mass and borehole spacing. These findings provide a basis for selecting injection parameters and optimizing borehole layouts in pavement sub-slab void repair.

Gassy clay is a composite material consisting of saturated soil with entrapped gas bubbles, typically encountered in deep, soft coastal clay deposits. These offshore fine-grained soils are often overconsolidated and contain gas bubbles. Most existing constitutive models focus primarily on normally consolidated clay and fail to accurately capture key features of overconsolidated gassy clay, such as its peak strength, strain softening, and critical state behavior. Based on thermodynamic principles and bounding surface theory, this study proposes an improved dilatancy equation that incorporates a shape adjustable yield surface. A new bounding surface model is developed to characterize the elastoplastic behavior of overconsolidated gassy clay, accounting for its composite structure and the effect of bubble flooding. The shear strength and stiffness of gassy clay are influenced by two competing mechanisms: gas cavities weaken the soil matrix, while bubble flooding facilitates partial drainage, resulting in strengthening under undrained conditions. The proposed model is validated through simulations of undrained triaxial compression tests on gassy Malaysian Kaolin and Speciwhite Kaolin clays under a range of overconsolidation ratios.

The interface bonding of polyurethane-concrete composites is critical for trenchless pavement rehabilitation, particularly in seasonally frozen regions where low temperatures compromise repair efficacy. This study investigates interfacial bonding under sub-zero conditions (-20 degrees C to 0 degrees C) via multi-scale characterization, mechanical testing, and theoretical modeling. The effects of temperature, grouting density, and crack width on interfacial strength, deformation capacity, and failure modes were systematically analyzed. A distinct failure mode divergence was discovered, primarily driven by density and modulated by temperature and crack width: increasing density shifts pull-off loading from cohesive to interfacial failure, whereas shear loading exhibits the opposite trend. Increasing temperature and crack width further promote this divergence. This trend can be quantitatively described by a dimensionless thickness ratio (lambda = tI/tII) between two interfacial zones, with critical transition thresholds converging at lambda approximate to 2.1 for both loading modes. Microscopic analysis attributes this to a temperature-gradient-driven zonal microstructure, comprising a dense matrix layer (Area I) formed by retarded reaction kinetics and a transitional layer (Area II) containing orthotropic ellipsoidal pores. These pores induce loading-direction-dependent mechanical effects, acting as stress-concentration sites under tension while contributing to shear resistance through their elongated morphology under shear. A semi-empirical model linking process parameters, microstructure, and macroscopic strength was established. Sensitivity analysis reveals pronounced asymmetry: under the same temperature and crack-width conditions, increasing the polyurethane density from 0.2 to 0.4 g/cm3 increases pull-off strength by 20.0-25.0%, whereas shear strength increases by 110.0-293.0%. Accordingly, differentiated engineering strategies "Temperature Priority" for tensile distress and "Density Priority" for shear distress are proposed.

Polyurethane polymer grouting materials with rapid expansion and solidification characteristics have been widely applied for infrastructure repair and reinforcement. An accurate characterization of the chemical reaction process of the slurry is essential for investigating its grouting mechanism. However, the high concentration of isocyanate groups in such polymer systems causes a “flat-top phenomenon” in Fourier transform infrared (FTIR) spectroscopy, rendering it difficult to accurately determine the conversion rate. To address this issue, a real-time method for measuring the reaction conversion rates of slurry components was proposed. The polyol conversion rate was obtained by tracking the integral area changes of the C—O bond peak in the carbamate product relative to the internal standard. The total slurry volume was determined at different time intervals using light detection and ranging (LiDAR)-based point cloud scanning, from which the gas volume was estimated. Combined with the solubility curve of the physical blowing agent and ideal gas law, the conversion rate of the chemical blowing agent was calculated. The isocyanate conversion rate was indirectly inferred based on the measured polyol and chemical blowing agent conversions. This method was applied to a polyurethane grouting material used in an engineering project, and the time-resolved conversion curves of all components throughout the reaction were obtained. The results revealed a three-stage evolution: a slow initial increase, a rapid rise in the middle stage, and a gradual deceleration in the later stage. The foaming reaction proceeded consistently faster than the gelation reaction did. These findings provide a foundation for further research on the diffusion mechanisms of polyurethane polymer slurries.

In this paper, we introduce a new framework for designing stabilization-free virtual element methods (VEMs) based on an finite element interpolation-based strategy, where we can simultaneously eliminate the stabilization terms in the discretizations of diffusion and reaction terms. The core idea is to construct a computable, polynomial-preserving, and norm-equivalent interpolation operator from the virtual element space to a (local) finite element space. Leveraging the properties of this operator, we design two types of stabilization-free schemes. The first scheme requires the interpolation to preserve the polynomial consistency related to the bilinear forms, thereby maintaining both consistency and stability as in the standard VEM. The second scheme relaxes this consistency requirement. While it may not satisfy the standard polynomial consistency, the second scheme retains optimal convergence with simpler construction, fewer degrees of freedom and, more importantly, applicable to more complex problems such as those involving nonlinearities or variable coefficients. We construct concrete interpolation operators for both conforming and nonconforming virtual elements in two and three dimensions. These operators are then employed to realize stabilization-free schemes for conforming and nonconforming VEMs. Numerical experiments confirm the optimal convergence rates of the proposed methods. The presented framework can be extended to design stabilization-free schemes for other polytopal discretization methods, such as the hybrid high-order method and the weak Galerkin method.

The dielectric properties of cement-based composites (CBC) are highly sensitive to environmental humidity, which seriously restricts the quantitative interpretation accuracy of ground-penetrating radar (GPR) in the non-destructive testing of cement concrete pavement. In view of the lack of targeted prediction models due to the unclear mechanism of humidity influence in existing research, the core innovations of this study are: (1) the synergistic mechanism of water vapor dipole polarization and adsorbed water multi-layer polarization is clarified, revealing the intrinsic reason for the accelerated growth of permittivity in the high humidity range; (2) the constructed four-component dielectric model of "cement mortar-aggregate-water vapor-adsorbed water" achieves high-precision prediction within the range of 50~100% RH (R2 > 0.94, relative error < 5%), and shows good predictive ability within the test scope of this study; (3) a GPR humidity correction protocol based on the model is proposed, which can effectively improve the accuracy of nondestructive testing of cement concrete structures. In this study, CBC samples with water-cement ratios of 0.4~0.6 were prepared using P.O 32.5/P.O 42.5 cement and limestone aggregate. Under the conditions of 20 ± 0.5 °C, relative humidity (RH) of 50~100%, and 2 GHz (common GPR frequency), the permittivity was measured using an Agilent P5001A network analyzer to verify the model. The results show that the permittivity increases monotonically with humidity, and the growth rate in the high humidity range (70~100%) is 2.2 times that of the low humidity range (50~70%); The higher the water-cement ratio, the shorter the age, and the lower the cement strength grade, the stronger the humidity sensitivity of CBC dielectric properties. This model provides a reliable humidity correction tool for GPR detection, and significantly improves the accuracy of nondestructive evaluation of cement concrete structures.

Polyurethane grouting materials are vital for repairing airport pavement slabs. However, the mechanisms controlling their impact fatigue damage under different temperature conditions remain inadequately understood. This study establishes a predictive model for temperature-dependent impact performance by integrating modified shock wave theory with an enhanced Lemaitre-Chaboche damage evolution framework. Validated by drop-hammer impact tests across densities (200-600 kg/m3) and temperatures (253-293 K), the model achieved over 91% accuracy in predicting damage evolution and fatigue life. Results show that impact-induced damage exhibits continuous accumulation without distinct stages, unlike low-strain-rate loading. Damage accumulation accelerates with increasing impact load and density but decelerates as temperature rises. Impact fatigue life decreases with higher density but increases with elevated temperatures. Maximum energy absorption occurs at 265 K and 400 kg/m3 density. Sensitivity analysis confirms temperature as the dominant factor influencing both fatigue life and energy absorption. Microstructural analysis reveals failure mode transitions from ductile cell-wall buckling at low densities to brittle fracture at high densities. Material selection guidelines are proposed: low-density grouts for cold regions and high-density grouts for warm climates. For variable climatic conditions, an optimal density range of 350-400 kg/m3 is recommended.

Fine grained sediments in coastal environments often form a composite structure with discrete gas bubbles embedded within a saturated soil matrix, posing unique challenges to the stability of transportation infrastructure. While gas cavities weaken the soil matrix by disrupting its structure, bubble flooding enhances strength by inducing local drainage and increasing the mean effective stress. However, most existing constitutive models focus on normally consolidated gassy clay and cannot fully describe the complex response of overconsolidated gassy clay. To address these features, a unified elastoplastic constitutive model for gassy clay is proposed based on the Unified Hardening framework. Specifically, a single novel parameter is introduced to model the detrimental effect of gas bubbles on plastic hardening. This formulation allows the model to explicitly capture the coupled influence of the overconsolidation ratio and gas bubbles on soil behavior. The proposed model is validated through simulations of undrained triaxial compression tests on gassy Malaysian Kaolin and Speciwhite Kaolin clays under a range of overconsolidation ratios. The results demonstrate that the model can effectively characterize the complex mechanical performance of gas-charged soft deposits, thereby providing a reliable theoretical basis for evaluating the stability and deformation of overlying transportation infrastructure.

Low-exothermic polymer grouting materials are classified as early-strength repair materials, and are used widely in road repair in seasonal frozen regions. Roads in these regions frequently are affected by snow-melting salt. Snow-melting salt can directly affect the mechanical properties and durability of road materials. In this study, salt-immersion (S-I) and salt-freeze-thaw (S-F-T) cycles were used to study the effects of snow-melting salts on low-exothermic polymer grouting materials with different densities. Subsequently, tests for water absorption, uniaxial compression, uniaxial tension, and scanning electron microscopy were carried out to study the changes in water absorption, mass, compressive strength and tensile strength of the materials under different immersion times and different numbers of S-F-T cycles. Ultimately, the mechanism of material mass loss and strength loss was determined from a microscopic perspective. The results indicate that during the S-I process, the water absorption of materials in salt solution is lower than that in water. However, the S-I process has minimal impact on the mechanical properties of the materials. The S-F-T cycles process exhibits a more pronounced detrimental effect on the materials, which originates from the breakage and deformation in their cell structure. As the number of S-F-T cycles increases, the cell structure of the materials gradually is damaged, leading to an initial increase in water absorption followed by a stabilization trend. Following immersion in liquid, the freeze-thaw damage is exacerbated further, resulting in a reduction of mass, compressive strength, and tensile strength of the materials. During the S-F-T process, the mass loss rate of the materials in CaCl2 solution was the highest, approximately 1.4 times that in CH3COOK solution and 2 times that in water. Simultaneously, the compressive strength loss rate of materials after 200 S-F-T cycles was the highest in CaCl2 solution, followed by CH3COOK solution, and it was lowest in water. Furthermore, materials with higher density had lower loss rates in terms of compressive strength, tensile strength, and mass, indicating enhanced resistance to freeze-thaw damage. The research findings provide a crucial basis for evaluating the application and durability of low-exothermic polymer grouting materials in seasonal frozen regions.

To address poor rheology, pumping challenges, and interfacial instability during pipe-jacking through sandy-spoil, this study develops a sodium polyacrylate (PAA)-modified bentonite slurry and establishes an integrated macro-micro-nano multiscale analytical framework. At the macroscopic level, an orthogonal design systematically evaluates fluid loss, Su's funnel viscosity, bleeding rate, and friction coefficient; the results indicate that 12-14% bentonite with 0.3-0.4% PAA simultaneously achieves low fluid loss, near-zero bleeding, and pronounced friction reduction while keeping viscosity within the pumpable range. At the microscopic level, TEM reveals a transition from a dense, agglomerated state to a flexible, lubricated state; PAA forms a coating layer and lubricating film that enhance particle dispersion and flow, strengthen thixotropic recovery, and thereby optimize structural stability and rheological performance. At the nanoscale, MD elucidates a cooperative interfacial mechanism: PAA and water assemble on mineral surfaces into a stable hydrated/lubricating layer, where weak interactions strengthen particle-water-polymer coupling, accounting for the macroscopic improvements in friction reduction and stability. Overall, PAA modification enables coordinated "lubrication-water retention-interface stabilization," providing experimental evidence and mechanistic support for optimizing pipe-jacking slurry formulations.

In this study, chitosan-sodium caseinate composite films loaded with ginger essential oil (GEO) nanoemulsions with antimicrobial and preservation functions were developed. The enhancement of film properties by tannic acid cross-linking and the application of composite films in cherry tomato preservation were investigated. Tannic acid cross-linking enhances the mechanical properties, barrier properties, ultraviolet resistance and thermal stability of the film. Analysis of the physicochemical and microbiological properties of cherry tomatoes during 15 days of storage showed that the film coating containing 20 % GEO nanoemulsion extended the shelf-life of the cherry tomatoes by approximately 6 days, and no fungal growth was observed during the 15-day period. At the same time, the film helped the cherry tomatoes to maintain the lowest weight loss (3.49 %) as well as the highest hardness (14.08 N), titratable acidity (21.99 g/kg) and soluble solids content (6.73 %). The spoilage fungus, identified as Fusarium oxysporum, was isolated from the spoilage site of the cherry tomatoes, and the composite film containing 20 % GEO nanoemulsion inhibited its mycelial growth to an area of 50.27 mm2. The results of this study provide new ideas for the development of new antimicrobial composite films for fruit preservation.

With the continuous impact of the greenhouse effect and energy crisis, the environmental assessment of asphalt mixtures is prosperous. Cold-mixed asphalt mixture is paid more attention as a greener and cleaner pavement material. However, the study on the environmental impact of cold-mixed asphalt mixture is lacking. In this study, the greenhouse gas (GHG) emissions and energy consumption of the composite cold-mixed asphalt mixture (CCMA) have been quantified from cradle to grave by the life cycle assessment, and compared with the counterparts of hot-mixed asphalt mixture (HMA). The crucial stages are identified based on their contribution to life cycle GHG emissions and energy consumption. Three alternatives are considered, and their potential for GHG emissions reduction and energy sustainability are discussed. The results show that the GHG emissions and energy consumption of CCMA are respectively 13.56 kg carbon dioxide equivalent and 4.61 kg coal equivalent over the life cycle. In comparison with HMA, the GHG emissions of CCMA are reduced by 74.3 % and the energy consumption by 41.6 %. The materials production stage is crucial, accounting for approximately 57.2 % of emissions and 48.4 % of energy demand over the entire life cycle. Optimizing mixing temperature, using recycled asphalt pavement and promoting electricity can achieve different scales of energy saving and emission reduction.

To investigate the shear bond performance of the polymer-concrete interface in crack-repaired concrete pavements under low-temperature conditions and extend pavement service life, theoretical analyses on the influence behaviors of crack width, grouting density, and ambient temperature are carried out based on interface shear tests. This study further explored the degree of influence of each factor on the mechanical properties of the polymer-concrete interface and developed a three-dimensional model of the concrete matrix-polymer interlayer system. The results show that under the action of shear stress, the failure mode of the polymer-concrete interface is mostly brittle fracture. Crack width, grouting density, and ambient temperature have significant effects on the shear strength of the polymer-concrete interface. The shear strength of the polymer-concrete interface is negatively correlated with ambient temperature, and positively correlated with crack width and grouting density. Among these three influencing factors, the sensitivities of crack width, grouting density, and ambient temperature to shear strength are 0.6569, 0.7587, and 0.5563, respectively; grouting density has the greatest influence on shear strength, while ambient temperature has the least significant influence. When the composite structure system is subjected to tangential shear force, interface damage first occurs on the upper side of the interface; subsequently, a strip-shaped transverse damage zone is formed and migrates along the depth of the bonded interface until complete failure of the interface. The research results can provide important guidance for evaluating the load-bearing capacity of pavements and the service life of roads after crack repair, particularly under similar low-temperature conditions as investigated in this study.

Loose defects in semi‐rigid base layers can critically compromise the structural performance and long‐term serviceability of asphalt pavements. However, accurate identification and quantitative assessment of such defects remain challenging due to the lack of reliable ground‐penetrating radar (GPR) data sets and the limitations of existing detection methods. This paper presents an integrated framework that combines data simulation, deep learning–based segmentation, and 3D reconstruction to address these challenges. First, a high‐fidelity synthetic data set was generated using a random medium‐based forward modeling approach to represent varying looseness depths and configurations. Second, a modified YOLOv8‐seg architecture was proposed, featuring a novel multi‐scale feature fusion module (DN module) and a Weighted Intersection over Union (WIoU) loss function to enhance segmentation precision under noisy and complex GPR conditions. It achieved a mean average precision (mAP) of 97.25% and a real‐time inference speed of 32.05 frames per second (FPS). Third, a 3D point cloud reconstruction approach based on inverse distance weighted (IDW) interpolation was introduced to restore the spatial morphology of the detected defect regions. Delaunay triangulation was then used to estimate the volumetric extent of the defects, achieving an overall estimation accuracy of 78.07%. Finally, the proposed framework was validated on a full‐scale pavement model, confirming its effectiveness in defect detection, morphological recovery, and quantitative assessment. The findings provide a reliable computational tool for pavement condition evaluation and maintenance planning.

A key challenge in highway reconstruction and expansion projects is to reduce longitudinal cracking at the junction of old and new roadbeds, which is a critical issue in the maintenance of transportation infrastructure. Polymer grouting technology, a non-excavation method for hidden subgrade defects, leverages material self-expansion properties to fill voids, enhance load-bearing capacity, and bond structural layers while providing seepage control-enabling rapid repair of longitudinal pavement joints. This study investigates the seepage characteristics of polymer-grouted longitudinal joints in reconstructed pavements by simulating post-repair infiltration behavior under rainfall conditions. The results elucidate the anti-seepage efficacy of polymer grouting, offering theoretical and practical insights for efficient longitudinal joint treatment in highway expansion projects.

An effective and reliable dielectric model for accurately calculating the dielectric constant of asphalt mastic can establish theoretical foundation for efficiently characterizing the dielectric constant of asphalt mixtures and back-calculating road quality indicators such as asphalt content using ground-penetrating radar (GPR). Based on the actual structural composition of asphalt mastic, this study first developed a dielectric model (CBM model) considering the influence of mesoscopic background media (BM). Subsequently, an interfacial transition zone (ITZ) at the microscale is incorporated to improve the CBM model, yielding a model integrating mesomicrostructural features (MCBM model). Finally, dielectric constant tests of asphalt mastic under temperature and ultraviolet (UV) light effects were conducted, leading to the development of the Rm-MCBM model (accounting for temperature effects) and the Km-T-MCBM model (considering temperature-UV light coupling effects) based on the MCBM model. The results show that the calculation accuracy of the CBM model is 2.33 % higher on average than that of model neglecting BM effects. The MCBM model further improves the average calculation accuracy by 2.89 % compared to the CBM model, with an average calculation error of 2.92 %. The average calculation errors of the Rm-MCBM and Km-T-MCBM models are 3.13 % and 3.26 %, respectively, representing only minor fluctuations of 0.21 % and 0.34 % compared to the MCBM model without environmental considerations. This small variation demonstrates the excellent stability of the MCBM model. Notably, all models exhibit errors below 5 %, indicating satisfactory accuracy. The dielectric model system developed in this study deeply integrates the meso-microstructural characteristics of asphalt mastic and fully accounts for environmental conditions. It not only establishes a theoretical framework for accurately predicting the dielectric behavior of asphalt mastic but also opens new avenues for exploring the intrinsic correlations between performance index variations and dielectric constant changes in asphalt mastic under environmental influences.

Accurate measurement and calculation of the dielectric constant of asphalt mixture serve as fundamental steps for enhancing the precision of ground-penetrating radar (GPR) in asphalt pavement quality inspection. To establish a dielectric model that precisely captures the structural characteristics of asphalt mixtures, mesostructure and microstructure analyses of the asphalt mixture are conducted based on a multiscale analysis approach; the results are then correlated with the macroscopic dielectric properties of the materials. Leveraging principles from dielectric physics, particularly the spherical polarization theory, a dielectric model for the mesostructure of the hybrid medium is developed (referred to as the improved model). Building upon the improved model, an asphalt mixture dielectric model that considers the microscale interface effect is constructed using the composite sphere combination method (referred to as the presented model). The results demonstrate that the improved model enhances the precision of calculating the dielectric constant of asphalt mastic and mixture by an average of 1.53% and 2.94%, respectively, compared to the original classical model. Moreover, the presented model shows further enhancement in accuracy compared to the improved model. Specifically, the overall average improvement of the presented model over the improved and original classical models is 2.86% and 5.8%, respectively. Notably, the presented model exhibits significantly higher accuracy compared to other classical models (such as the S-K, Looyenga, and Brown models). The research models align more closely with the actual composition of asphalt mixture, resulting in more precise calculation of the dielectric constant. This study offers guidance for enhancing the accuracy of GPR road quality detection and for the application of dielectric properties in the field of intelligent transportation.

This paper proposes an isogeometric boundary element method (IGABEM) to solve the nonlinear liquid sloshing problem in a rectangular container subjected to oscillatory excitation. Based on the semi-Lagrange approach, a fixed global coordinate system and a local Cartesian coordinate system that moves synchronously with the container are defined. Starting from the Laplace equation, the boundary integral equations for the liquid sloshing problem are derived using Gauss's divergence theorem and the integration by parts technique, while incorporating nonlinear kinematic and dynamic boundary conditions of the free surface. The corresponding boundary element solution system is then formulated. Non-Uniform Rational B-Splines (NURBS) are employed as shape functions to accurately describe the geometric boundaries and approximate the unknown physical fields. This method ultimately produces the discrete equations governing nonlinear liquid sloshing problem in an oscillating container. Compared with traditional polynomial interpolation shape functions, NURBS provide improved continuity both within elements and across element interfaces as well as local support. These properties make them particularly suitable for satisfying the continuity requirements of the liquid surface. For time integration, a second-order Runge-Kutta algorithm is employed for time-stepping to solve the IGABEM system equations, compute variable gradients at each time step, and update the computational grid in real-time. A series of numerical examples are presented, the results are compared with analytical solutions, experimental data, and alternative numerical methods for free and forced liquid sloshing, free surface fluctuations and internal pressures. These comparisons validate the accuracy and robustness of the proposed method. The numerical examples further investigate the effects of external excitation frequency, excitation amplitude, rotation center position, and bottom obstacle height on liquid sloshing responses in the rectangular container. The results indicate that changes in excitation frequency, vertical eccentricity of the rotation center, and obstacle height significantly influence the liquid sloshing behavior.