Search Results (57)

Traditional pipe roof support design methods generally assume horizontal ground conditions and treat the pipe roof as a monolithic beam, thereby neglecting the differential stress distribution among individual steel pipes under unsymmetrical loading. To address this gap, this paper presents two main contributions: a low-carbon cement-based grouting material suitable for pipe roof reinforcement, and a new mechanical model that simultaneously accounts for biased pressure conditions and the inter-pipe micro-arch effect. First, the working performance of limestone calcined clay cement (LC³) grout was systematically tested at a water–cement ratio of 1:1, and the optimal mix ratio was determined. Grout–soil reinforcement tests on weathered granite show that, for grout-to-soil volume ratios between 0.2 and 0.8, the compressive strength of the reinforced material exceeds 10 MPa and the elastic modulus exceeds 600 MPa. Second, a mechanical model for the pipe roof was established based on the Pasternak two-parameter foundation theory, incorporating both biased pressure conditions and the inter-pipe micro-arch effect. The model predictions were compared with existing field monitoring data in the literature, showing consistent trends and good agreement in peak deflection values. Parametric analysis reveals that under horizontal ground conditions, the pipe roof response is symmetric, with the vault as the most critical area. As the bias angle increases, the maximum response shifts toward the higher side of the terrain, and the stress difference between pipes on both sides increases significantly. Theoretical analysis of the low-carbon grouting material shows that pipe roof deflection is moderately reduced compared to traditional grouting materials, but at the cost of increasing bending moment and shear force within the steel pipes. The proposed low-carbon grouting material and the validated mechanical model provide theoretical support for the design optimization of pipe roof support in shallow unsymmetrical loading tunnels. Full article

This study presents an analytical investigation of the dynamic behavior of concrete beams reinforced with different types of nano-clay (NC) particles and resting on a Winkler–Pasternak elastic foundation. The equivalent elastic properties of the nanocomposite were determined using an Eshelby-based homogenization model. An improved quasi-three-dimensional beam theory was applied to formulate the governing equations of motion, which were subsequently then analytically solved using Navier’s method. The analysis shows that NC reinforcement systematically elevates the natural frequencies of the beam, with the magnitude of improvement varying by particle type and concentration. Increasing the NC volume fraction to 30% leads to a significant rise in the fundamental frequency, reaching about 30% for hectorite (SHca-1) compared with the unreinforced beam, whereas montmorillonite (SWy-1) produces a more moderate increase of approximately 13%. This reinforcing effect remains consistent across different span-to-depth ratios, indicating that the influence of nano-clay content on the dynamic response is largely independent of beam slenderness. Furthermore, increasing the Winkler foundation stiffness results in an almost linear rise in frequency of approximately 18–22%, whereas the Pasternak shear parameter produces a stronger effect, reaching around 25% enhancement depending on the reinforcement type. These results indicate that incorporating nano-clay platelets can be an effective strategy for enhancing the vibrational stiffness of concrete beams and improving their dynamic performance when interacting with supporting soil media. Full article

This study presents an analytical investigation into the free vibration behavior of perforated nanobeams resting on a Kerr-type elastic foundation within the framework of Eringen’s nonlocal elasticity theory. Specifically, Eringen’s nonlocal elasticity theory is employed to inherently capture small-scale effects, while the three-parameter Kerr model is utilized to provide a mathematically consistent representation of shear continuity and realistic surface interactions. In this context, the governing equations of motion for a perforated Euler–Bernoulli nanobeam are derived using Hamilton’s principle, incorporating both the nonlocal parameter and perforation geometric factors, namely, the filling ratio and the number of holes. The resulting equations are solved analytically via the Navier method for simply supported boundary conditions. The results indicate that the Kerr foundation model exhibits an intermediate behavior between the Winkler and Pasternak models, owing to the stiffness-reducing effect of its upper spring layer connected in series. A key finding is the “masking effect,” where high foundation stiffness significantly suppresses the frequency reduction caused by nonlocal small-scale effects. Furthermore, it is observed that in the absence of foundation support, the vibration behavior is governed by the competition between mass reduction and stiffness loss depending on the number of holes; however, foundation dominance stabilizes the system regardless of perforation geometry. Full article

The integration of silica nanoparticles (NS) into cementitious composites has emerged as a promising strategy to refine the microstructure and enhance concrete performance. Beyond their chemical role in accelerating hydration and promoting additional C–S–H gel formation, silica nanoparticles act as physical fillers, reducing porosity and improving interfacial bonding within the matrix. These dual effects result in a denser and more resilient composite, whose mechanical and dynamic responses differ from those of conventional concrete. However, studies addressing the vibrational and modal behavior of nano-reinforced concretes, particularly under elastic and viscoelastic foundation conditions, remain limited. This study investigates the dynamic response of NS-reinforced concrete slabs using a refined quasi-3D plate deformation theory with five (05) unknowns. Different foundation configurations are considered to represent various soil interactions and assess structural integrity under diverse supports. The effective elastic properties of the nanocomposite are obtained through Eshelby’s homogenization model, while Hamilton’s principle is used to derive the governing equations of motion. Navier’s analytical solutions are applied to simply supported slabs. Quantitative results show that adding 30 wt% NS increases the Young’s modulus of concrete by about 26% with only ~1% change in density; for simply supported slender slabs, this results in geometry-dependent increases of up to 18% in the fundamental natural frequency. While the Winkler and Pasternak foundation parameters reduce this frequency, the damping parameter of the viscoelastic foundation enhances the dynamic response, yielding frequency increases of up to 28%, depending on slab geometry. Full article

The present study models the deflection of nonlinear waves over a Kirchhoff plate underlying a Pasternak-like elastic foundation. A promising version of the tanh expansion analytical method has been deployed for the construction of regular exact solutions for the model, including the application of certain ansatz functions for validations and yet construction of more solutions. The resulting frequency equation and the modulation instability spectrum have been obtained for the linearized model, including the expressions for the related phase and group velocities. In addition, the study examines the equilibrium status of the resulting dynamical system with the help of the bifurcation analysis. Numerically, nonlinear deflection and dispersion of waves have been simulated through the acquired expressions and equations. Notably, the study notes that increasing both the Pasternak-like nonlinear parameter $\eta$ and time variation (for $x>0$) decreases the nonlinear deflection in the plate, while increasing the stiffness of the Winkler foundation increases deflection in the medium. In addition, the study establishes, concerning the determined frequency equation, that increasing the Winkler foundation stiffness increases the dispersion of nonlinear waves in the medium, while an opposite trend has been noted concerning the imposed Pasternak-like nonlinear foundation. In addition, both phase and group velocities, the gain function for modulation instability, and the resulting dynamical system have been noted to be greatly affected by the variation of the imposed foundational parameters. Lastly, this study has potential applications in various engineering fields while modeling and analysis of mechanical structures supported by additional structures. Full article

This paper addresses the issue of stress redistribution in surrounding soil during the construction of shallow-buried, large-section loess tunnels. Using the Luochuan Tunnel as a case study, we employ the FLAC 3D numerical simulation method to investigate the effects of advanced pipe roof support on the stability of the surrounding soil. The results demonstrate that advanced pipe umbrella reduces the stress release amplitude at the vault by 50% compared to the unsupported condition, due to a “pre-support-load bearing mechanism”, while promoting orderly stress recovery. The “longitudinal beam effect” and “transverse arch effect” of soils effectively suppress the plastic zone area of the surrounding soil from 413.3 m² (unsupported) to 95.0 m², achieving a reduction exceeding 77%. Furthermore, the pipe umbrella support facilitates the formation of a more efficient “active soil arch”, which exhibits distinct symmetrical characteristics. The arch’s stress distribution and spatial structure both follow symmetrical patterns, significantly enhancing the self-stabilizing capacity of the surrounding soil. As a result, the height of the stress release zone at the tunnel excavation face and the surrounding soil stability areas is reduced by 45.9% and 63.3%, respectively, compared to the unsupported condition. This study also establishes a Pasternak elastic foundation beam model that accounts for the spatiotemporal effects of support, elucidating the mechanism of pipe umbrella support and providing a theoretical foundation for the design and construction risk control of shallow large-section loess tunnels. Full article

Environmental conditions at shallow-buried tunnel portals often cause stratum moisture content variations, where pipe roof support is commonly used for pre-reinforcement. While studies show water content significantly affects soil strength, its impact on pipe roof behavior remains largely unexplored. This study develops a theoretical model for pipe roof longitudinal internal forces and deformations using Pasternak two-parameter foundation theory, incorporating subgrade reaction and shear moduli expressions that vary with saturation. Validation against field measurements shows good agreement with peak values, confirming model reliability. Parametric analysis reveals that increasing water content markedly amplifies pipe roof deformation: in unsaturated ground, deflection and rotation increase significantly with water content, while peak bending moment and shear force near the tunnel face slightly decrease. Under saturated conditions, the increases in deflection and rotation become substantially greater. The model quantitatively evaluates water content’s influence on pipe roof mechanical behavior, providing a theoretical basis for optimizing support systems in water-rich strata. Full article

The dynamic model and nonlinear forced vibration of a laminated beam with magnetostrictive layers, embedded on a nonlinear elastic Winkler–Pasternak foundation, in the presence of an electromagnetic actuator, mechanical impact, dry friction, a longitudinal magnetic field, and van der Waals force is investigated in the present work. The dynamic equations of this complex system are established based on von Karman theory and Hamilton’s principle. Then, by means of the Galerkin–Bubnov procedure, the partial differential equations are transformed into ordinary differential equations. The Optimal Auxiliary Functions Method (OAFM) is applied to solve the nonlinear differential equation. The results obtained are validated by comparisons with numerical results given by the Runge–Kutta procedure. Local stability in the neighborhood of the primary resonance is examined by means of the homotopy perturbation method, the Jacobian matrix, and the Routh–Hurwitz criteria. Global stability is studied by introducing the control law input function and using the approximate solution obtained by the OAFM in the construction of the Lyapunov function. La Salle’s invariance principle and Potryagin’s principle complete our study. The effects of some parameters are graphically presented. Our paper reveals the immense potential of the OAFM in the study of complex nonlinear dynamical systems. Full article

This study presents an analytical investigation of the thermomechanical stability of hyperbolic doubly curved shells reinforced with graphene origami auxetic metamaterials (GOAMs) and resting on a Pasternak elastic foundation. The proposed model integrates shell geometry, thermal–mechanical loading, and architected auxetic reinforcement to capture their coupled influence on buckling behavior. Stability equations are derived using the First-Order Shear Deformation Theory (FSDT) and the principle of virtual work, while the effective thermoelastic properties of the GOAM phase are obtained through micromechanical homogenization as functions of folding angle, mass fraction, and spatial distribution. Closed-form eigenvalue solutions are achieved with Navier’s method for simply supported boundaries. The results reveal that GOAM reinforcement enhances the critical buckling load at low folding angles, whereas higher folding induces compliance that diminishes stability. The Pasternak shear layer significantly improves buckling resistance up to about 46% with pronounced effects in asymmetrically graded configurations. Compared with conventional composite shells, the proposed GOAM-reinforced shells exhibit tunable, folding-dependent stability responses. These findings highlight the potential of origami-inspired graphene metamaterials for designing lightweight, thermally stable thin-walled structures in aerospace morphing skins and multifunctional mechanical systems. Full article

For tunnels constructed in a single direction, the pipe roof at the tunnel exit portal can be installed either as Outside-to-Inside advanced support arrangements (Out–In ASA) or Inside-to-Outside advanced support arrangements (In–Out ASA). To investigate the pipe roof’s mechanical behavior and deformation characteristics under two excavation methods, this study establishes Pasternak two-parameter elastic foundation beam models for the pipe roof. Corresponding boundary conditions are proposed for each support configuration, and the governing differential equation for pipe roof deflection is derived and solved. The Hanjiashan Tunnel is used as an engineering case study to validate the theoretical results by comparing them with field monitoring data. A comparative analysis and parametric sensitivity study are then conducted for the two construction methods. The results show that theoretical predictions align well with the field measurements, confirming the validity of the proposed model. This study proposed calculation parameters for the Hanjiashan Tunnel. Under this circumstance, the method of Out–In ASA has been proven to offer improved structural performance and safety when the tunnel face is close to the portal. Moreover, the timely installation of the initial support and the strong bearing capacity of the surrounding rock can further reduce pipe roof deformation near the tunnel exit. Therefore, the Out–In ASA method is recommended for single-direction tunnel excavation. If the method of Out–In ASA is not feasible due to site constraints, the method of In–Out ASA can be adopted, while early support and effective grouting should be guaranteed to ensure control of excessive deformation. The findings of this study can provide a theoretical reference for the construction of tunnel portals in single-direction excavation. Full article

The present research analyzed the nonlinear vibration of a CNTRC embedded in a nonlinear Winkler–Pasternak foundation in the presence of an electromagnetic actuator and mechanical impact. A higher-order shear deformation beam theory was applied to various models, as well as Euler–Bernoulli, Timoshenko, Reddy, and other beams, using a unified NSGT. The governing equations were obtained based on the extended shear and normal strain component of the von Karman theory and a Hamilton principle. The system was discretized by means of the Galerkin–Bubnov procedure, and the OAFM was applied to solve a complex nonlinear problem. The buckling and bending problems were studied analytically by using the HPM, the Galerkin method in combination with the weighted residual method, and finally, by the optimization of results for a simply supported composite beam. These results were validated by comparing our results for the linear problem with those available in literature, and a good agreement was proved. The influence of some parameters was examined. The results obtained for the extended models of the Euler–Bernoulli and Timoshenko beams were almost the same for the linear cases, but the results of the nonlinear cases were substantially different in comparison with the results obtained for the linear cases. Full article

In practical engineering, it is often necessary to constructed deep pits next to tunnels. So it is crucial to evaluate surrounding tunnels deformation and stress to ensure their safe operation. Pasternak soil model that considers soil nonlinear is adopted to solve tunnel beam’s differential equation to obtain longitudinal tunnel deformation and stress. The rationality of considering soil nonlinear methods was verified by contrasting measured with calculated results. On this basis, a comparative study was conducted on the calculation and analysis of various influencing factors based on engineering examples. It shows that the longitudinal tunnel deformation reduces with increase of soil modulus, tunnel axis and pit long side angle, tunnel stiffness reduction coefficient, tunnel axis and pit center horizontal distance. When discrete length of tunnel is less than 5 m, calculated value of longitudinal tunnel deformation changes little with discrete length. When pit depth increases, maximum longitudinal tunnel deformation also increases gradually. When tunnel buried depth gradually increases in the range of 1.5~3.9 times pit depth, maximum longitudinal tunnel deformation reduction rate becomes small. Similar pro-jects construction methods can refer to the results, and it have certain practical application value of engineering. Full article

This study numerically investigated free vibration characteristics of functionally graded material (FGM) beams on Winkler–Pasternak three-parameter elastic foundations using the modified generalized differential quadrature (MGDQ) method. To compare the effects of different beam theories on the predicted frequency responses, an nth order generalized beam theory was employed to establish the governing equations of the system’s dynamic model within the Hamilton framework. As a pioneering effort, a MATLAB (version 2021a) computational program implementing the MGDQ method was developed to obtain the free vibration responses of foundation-supported FGM beams. Parametric analyses were conducted through numerical simulations to systematically examine the influences of various factors, including beam theories, damping coefficients, foundation stiffness parameters, boundary conditions, gradient indices, and span-to-thickness ratios, on the natural frequencies and damping ratios of FGM beams. The findings provide an essential theoretical foundation for dynamic characteristic analysis and functional design of foundation-supported FGM beam structures. Full article

This study aims to investigate the behavior of viscoelastic materials exhibiting complex mechanical behavior characterized by both elastic and viscous properties. They are widely used in various engineering applications, such as structural components, transportation systems, energy storage devices, microelectromechanical systems (MEMS), and earthquake research and detection. Accurate modeling of viscoelastic behavior is crucial for predicting its performance under dynamic loading conditions. In this study, we modify the equations governing the thermoelastic resistance to describe the thermal variables of a thermoelastic micro-beam supported by a two-parameter Pasternak viscoelastic foundation by using a fractional Moore–Gibson–Thompson (MGT) model in the context of non-locality. The temperature, bending displacement, and moment were computed and graphically displayed using the Laplace transform method. Different theoretical approaches have been compared in order to explain how the phase delay affects physical phenomena. Numerical results show that the wave fluctuations of variables in thermoelastic micro-beams are slightly smaller for the studied model and that the speed of these plane waves depends on fractional and non-local parameters. Full article

To create a discretized prediction model for the deformation of an adjacent pipeline, the pipeline structure is discretized, the differential equations governing the longitudinal deformation of the pipeline are inferred, and the displacement expressions and the solution methods of the virtual nodes of each unit are provided after discretization. This approach is based on the Pasternak foundation beam theory. It aims to address the issue of the difficulty in predicting the deformation of the adjacent pipeline caused by shield tunneling in a saturated soft ground layer in the Yangtze River Delta. The deformation pattern of the surrounding soil is determined and confirmed through additional numerical simulation, and the discretized prediction model is contrasted with the conventional Winkler foundation beam model and the Pasternak foundation beam model. The findings demonstrate that the discrete prediction model is simpler to solve and more accurately describes the deformation characteristics of the adjacent pipeline as well as the deformation distribution law. The calculated deformation characteristics primarily appear as the adjacent pipeline’s deformation due to the double tunnel boring exhibiting a “mono-peak shape” with a large middle and small ends, which is consistent with the actual situation. The two main factors influencing the pipeline deformation are the shield tunneling distance and pipeline spacing; the former has a negative correlation with the pipeline deformation, while the latter has a positive correlation. This work can offer a straightforward deformation prediction technique for shield tunneling in the Yangtze River Delta’s saturated soft ground next to existing pipelines. Full article