Numerical analysis of geosynthetic-reinforced embankment performance under moving loads

The performance of geosynthetic-reinforced embankments under traffic moving loads is always a hotspot in the geotechnical engineering field.A three-dimensional(3D)model of a geosynthetic-reinforced embankment without drainage consolidation was established using the finite element software ABAQUS.In this model,the traffic loads were simulated by two moving loads of rectangular pattern,and their amplitude,range,and moving speed were realized by a Fortran subroutine.The embankment fill was simulated by an equivalent linear viscoelastic model,which can reflect its viscoelasticity.The geogrid was simulated by the truss element,and the geocell was simulated by the membrane element.Infinite elements were utilized to weaken the boundary effect caused by the model geometry at the boundaries.Validation of the established numerical model was conducted by comparing the predicted deformations in the cross-section of the geosynthetic-reinforced embankment with those from the existing literature.On this basis,the dynamic stress and strain distribution in the pavement structure layer of the geosynthetic-reinforced embankment under a moving load was also analyzed.Finally,a parametric study was conducted to examine the influences of the different types of reinforcement,overload,and the moving load velocity on the geosynthetic-reinforced embankment.

Random vibration analysis of FGM plates subjected to moving load using a refined stochastic finite element method

The article introduces a finite element procedure using the bilinear quadrilateral element or four-node rectangular element(namely Q4 element) based on a refined first-order shear deformation theory(rFSDT) and Monte Carlo simulation(MCS), so-called refined stochastic finite element method to investigate the random vibration of functionally graded material(FGM) plates subjected to the moving load.The advantage of the proposed method is to use r-FSDT to improve the accuracy of classical FSDT, satisfy the stress-free condition at the plate boundaries, and combine with MCS to analyze the vibration of the FGM plate when the parameter inputs are random quantities following a normal distribution. The obtained results show that the distribution characteristics of the vibration response of the FGM plate depend on the standard deviation of the input parameters and the velocity of the moving load.Furthermore, the numerical results in this study are expected to contribute to improving the understanding of FGM plates subjected to moving loads with uncertain input parameters.

Evaluation of vertical impact factor coefficients for continuous and integral railway bridges under high-speed moving loads

In the railway bridge analysis and design method,dynamic train loads are regarded as static loads enhanced by an impact factor(IF).The IF coefficients for various railway bridges have been reported as a function of span length or frequency of the bridges in Eurocode(2003).However,these IF coefficient values neglect the effects of very high speeds(>200 km/h)and soil-structure interaction(SSI).In this work,a comprehensive study to assess the impact factor coefficients of mid-span vertical displacements for continuous and integral railway bridges subjected to high-speed moving loads is reported.Three different configurations,each for the three-dimensional(3D)continuous and integral bridge,are considered.Also,single-track(1-T)and two-track(2-T)“real train”loading cases for both these bridge types are considered.Subsequently,finite element analysis of the full-scale 3D bridge models,to identify their IF values,considering the effects of SSI for three different soil conditions,is conducted.The IF values obtained from the study for both bridge types are comparable and are greater than the values recommended by Eurocode(2003).The results reveal that with a loss of soil stiffness,the IF value reduces;thus,it confirms the importance of SSI analysis.

Dynamic response analysis of a multiple-beam structure subjected to a moving load

In this study,the dynamic response of an elastically connected multi-beam structure subjected to a moving load with elastic boundary conditions is investigated.The boundary conditions and properties of each beam vary,and the difficulty of solving the motion equation is reduced by using a Fourier series plus three special transformations.By examining a high-speed railway(HSR)with mixed boundary conditions,the rationality for the newly proposed method is verified,the difference in simulated multiple-beam models with different beam numbers is explored,and the influence of material parameters and load speed on the dynamic response of multiple-beam structures is examined.Results suggest that the number of beams in the model should be as close to the actual beam number as possible.Models with an appropriate beam number can be used to describe in detail the dynamic response of the structure.Neglecting the track-structure can overestimate the resonant speed of a high-speed railway,simply-supported beam bridge.The effective interval of foundation stiffness(EIFS)can provide a reference for future engineering designs.

Ground vibration analysis due to a high-speed moving load in a tunnel

The surface response of an infinite viscous-elastic half-space due to a moving load in the tunnel is analyzed.The tunnel is modeled as an infinite long Euler-Bernoulli beam without thickness and the concept of the equivalent stiffness is introduced to simulate the half-space.The inverse Fourier transformation and the relative coordinate transform are utilized to transfer a double infinite integral to a double definite integral,which improves the operational efficiency.Then,the analytic solution of the surface response of a half-space due to a moving load in the tunnel is obtained.Finally,the laws of ground vibration responses induced by moving loads in the tunnel are analyzed,considering different tunnel embedded depths and different moving speeds.Results show that the displacement distortion can be obtained by at some special velocities.A theoretical explaination of this phenomenon is provided as well.

Numerical analysis of moving train induced vibrations on tunnel,surrounding ground and structure

This study is focused on the effect of vibration induced by moving trains in tunnels on the surrounding ground and structures.A three-dimensional finite element model is established for a one-track railway tunnel and an adjacent twelve-storey building frame by using commercial software Midas GTS-NX(2019)and Midas Gen.This study considered the moving load effect of a complete train,which varies with space as well as with time.The effect of factors such as train speed,overburden pressure on the tunnel and variation in soil properties are studied in the time domain.As a result,the variations in horizontal and vertical acceleration for two different sites,i.e.,the free ground surface(without structure)and the area containing the structure,are compared.Also,the displacement pattern of the raft foundation is plotted for different train velocities.At lower speeds,the heaving phenomenon is negligible,but as the speed increases,both the heaving and differential settlement increase in the foundation.This study demonstrates that the effect of moving train vibrations should be considered in the design of new nearby structures and proper ground improvement should be considered for existing structures.

Dynamics of the Moving Ring Load Acting in the System“Hollow Cylinder+Surrounding Medium”with Inhomogeneous Initial Stresses

This paper studies the influence of the inhomogeneous initial stress state in the system consisting of a hollow cylinder and surrounding elastic medium on the dynamics of the moving ring load acting in the interior of the cylinder.It is assumed that in the initial state the system is compressed by uniformly distributed normal forces acting at infinity in the radial inward direction and as a result of this compression the inhomogeneous initial stresses appear in the system.After appearance of the initial stresses,the interior of the hollow cylinder is loaded by the moving ring load and so it is required to study the influence of the indicated inhomogeneous initial stresses on the dynamics of this moving load.This influence is studied with utilizing the so-called threedimensional linearized theory of elastic waves in elastic bodies with initial stresses.For solution of the corresponding mathematical problems,the discrete-analytical solution method is employed and the approximate analytical solution of these equations is achieved.Numerical results obtained within this method and related to the influence of the inhomogeneous initial stresses on the critical velocity of the moving load and on the response of the interface stresses to this load are presented and discussed.In particular,it is established that the initial inhomogeneous initial stresses appearing as a result of the action of the aforementioned compressional forces cause to increase the values of the critical velocity of the moving load.

Key Technology of Cutting and Moving Large Spherical Tank

This paper mainly introduces the scientific cutting and hoisting construction technology before the large spherical tank(hereinafter referred to as spherical tank)moving and loading,so as to better ensure the construction quality of field assembly and welding in the process of spherical tank moving and loading.

A frequency and velocity-dependent impedance method for prediction of rail/foundation dynamics

This paper presents an efficient numerical tool for the prediction of railway dynamic response.A behavior calibration of the infinite Euler-Bernoulli beam resting on continuous viscoelastic foundation is proposed.Constitutive laws of the discrete elements are determined for a rectilinear ballasted track.A three-dimensional model coupled with an adaptive meshing scheme is employed to calibrate the beam model impedances by finding the similarity between the output signals using the genetic algorithm.The model shows an important performance with significant reduction in computational effort.This study emphasizes the major impact of the excitation characteristics on the parameters of the discrete models.

Numerical modelling of vibration response in loess hills due to a high-speed train on railway viaduct

In order to accurately analyze vibration characteristics and site effects of loess hills under moving load of a highspeed train,four types of loess hill models under railway viaduct was established by ABAQUS of finite element analysis software by field test.The dynamic response and stability of loess hills under two different vibration sources under high-speed train load were studied by using two-dimensional equivalent linear response timehistory analysis,and the influence of the mechanical parameters of loess on the vibration of different types of loess hill was analyzed.Results show that there are obvious differences between peak displacement cloud maps of loess hills under the railway viaduct under gravity and train load action.We analyzed the influence of the change of elastic modulus on vibration propagation of soil of foundation and loess knoll,and found that the change of elastic modulus of soil in different position of foundation has more effect on vibration propagation than that of loess knoll soil.At the same time,the vertical acceleration cloud maps of the four types of loess hills are obviously different.

A substructure approach for analyzing pile foundation and soil vibrations due to train running over viaduct and its validation

An efficient computational approach based on substructure methodology is proposed to analyze the viaduct-pile foundation-soil dynamic interaction under train loads.Thetrain-viaductsubsystemissolvedusingthe dynamic stiffness integration method,and its accuracy is verified by the existing analytical solution for a moving vehicle on a simply supported beam.For the pile foundation-soil subsystem,the geometric and material properties of piles and soils are assumed to be invariable along the azimuth direction.By introducing the equivalent stiffness of grouped piles,the governing equations of pile foundation-soil interaction are simplified based on Fourier decomposition method,so the three-dimensional problem is decomposedintoseveraltwo-dimensionalaxisymmetricfinite element models.The pile foundation-soil interaction model is verified by field measurements due to shaker loading at pile foundation top.In addition,these two substructures are coupled with the displacement compatibility condition at interface of pier bottom and pile foundation top.Finally,the proposed train-viaduct-pile foundation-soil interaction model was validated by field tests.The results show that the proposed model can predict vibrations of pile foundation and soil accurately,thereby providing a basis for the prediction of pile-soil foundation settlement.The frequency spectra of the vibration in Beijing-Tianjin high-speed railway demonstrated that the main frequencies of the pier top and ground surface are below 100 and 30 Hz,respectively.

3D seismic response of a 2D hill-valley staggered topography modeled by a 2.5D multi-domain IBEM

A two and a half dimensional(2.5D)multi-domain indirect boundary element method(IBEM)is developed to study the wave scattering of obliquely incident P-,SV-and SH-waves by a hill-valley staggered topography in a multi-layered half-space.The IBEM algorithm includes using 2.5D full-space and half-space Green’s functions to construct scattered fields in decomposed closed and opened half-space regions,respectively,and using the dynamic stiffness method to solve the free fields.All regions are finally integrated by introducing the compatibility conditions to obtain the total wave fields.The proposed 2.5D IBEM has the flexibility in dealing with complex boundaries by directly applying the fictitious loads on the regions’boundaries,with a less storage requirement compared to the full 3D models.Besides,by combining the specific advantages of the two kinds of Green’s functions,the method is well suitable for handling coupled topographies with high accuracy.The method is validated by comparison with published results for a single valley as well as a single hill topography.The effects of height-to-width ratio of hill and layering on dynamic responses are further parametrically investigated by numerical implementations in frequency domain.Results show that the interaction between valley and hills can lead to a more significant amplification within the valley region,and dynamic responses are deeply influenced by the height-to-width of hill,simultaneously depending on incident angle and frequency.Besides,the site effects become more complex when the stratification feature is taken into account.

Multi-harmonic forced vibration and resonance of simple beams to moving vehicles

This study modeled the moving-vehicle-induced forcing excitation on a single-span prismatic bridge as a multiple frequency-multiplication harmonic load on the modal coordinates of a linear elastic simple Euler–Bernoulli beam,and investigated the forced modal oscillation and resonance behavior of this type of dynamic system.The forced modal responses consist of multiple frequency-multiplication steady-state harmonics and one damped mono-frequency complementary harmonic.The analysis revealed that a moving load induces high-harmonic forced resonance amplification when the moving speed is low.To verify the occurrence of high-harmonic forced resonance,numerical tests were conducted on single-span simple beams based on structural modeling using the finite element method(FEM)and a moving sprung-mass oscillator vehicle model.The forced resonance amplification characteristics of the fundamental mode for beam response estimation are presented with consideration to different end restraint conditions.The results reveal that the high-harmonic forced resonance may be significant for the investigated beams subjected to vehicle loads moving at specific low speeds.For the investigated single-span simple beams,the moving vehicle carriage heaving oscillation modulates the beam modal frequency,but does not induce notable variation of the modal oscillation harmonic structure for the cases that vehicle of small mass moves in low speed.

A complex solution on the dynamic response of sandwich graphene-reinforced aluminum-based composite beams with copper face sheets under two moving constant loads on an elastic foundation

An analytical solution was used to investigate the elastic response of a sandwich beam with a graphene-reinforced aluminum-based composite(GRAC)on an elastic foundation using copper as the face layer of the functionally graded composite beam and a simply supported boundary condition.Mantari's higher-order shear deformation theory was utilized to derive the equations,which were solved in Laplace space and then converted into space–time using Laplace inversion.The exact response of the GRAC sandwich beam was obtained by considering the displacement at the mid-span of the sandwich beam.Two moving loads with different speed ratios were applied at a single point,and the effect of various parameters,including the spring constant,the speed ratio,the percentage of graphene,the moving load speed,and the distribution pattern,was investigated.This study aimed to eliminate any overlap and improve the accuracy of the results.The exact solving method presented has not been reported in other articles so far.Additionally,due to the difficulty of solving mathematical equations,this method is only applicable to simple boundary conditions.

Dynamic Loadings Induced Vibration of Third Order Shear Deformable FG-CNTRC Beams:Gram-Schmidt-Ritz Method

This research work deals with a study on dynamic behavior of functionally graded carbon nanotube-reinforced composite(FG-CNTRC)beams under various types of dynamic loads.Carbon nanotubes(CNTs)are used as the reinforcing materials that distribute continuously across the beam thickness.By using third order shear deformable theory(TSDT)in this current study,the straightness and normality of the transverse normal after deformation are unconstrained.The equations of motion based on TSDT are solved by Gram-Schmidt-Ritz method in which the displacement functions are generated via Gram-Schmidt procedure.Additionally,the time-integration of Newmark is also employed to carry out dynamic response of the beams under dynamic loads.Several effects such as material distributions,types of dynamic loads,boundary conditions and so on are taken into account.According to numerical results,it can be revealed that adding small amount of CNTs can reduce considerably the dynamic amplitude of FG-CNTRC beams.Moreover,the dynamic analysis of beam-like structures plays an important role in structural design because mass inertia matrix of the beam being involved in the equations of motion,which yields much larger deflection than that predicted by simple static analysis.