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.

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.

Numerical Simulation-Based Analysis of the Impact of Overloading on Segmentally Assembled Bridges

Segmentally assembled bridges are increasinglyfinding engineering applications in recent years due to their unique advantages,especially as urban viaducts.Vehicle loads are one of the most important variable loads acting on bridge structures.Accordingly,the influence of overloaded vehicles on existing assembled bridge structures is an urgent concern at present.This paper establishes thefinite element model of the segmentally assembled bridge based on ABAQUS software and analyzes the influence of vehicle overload on an assembled girder bridge struc-ture.First,afinite element model corresponding to the target bridge is established based on ABAQUS software,and the load is controlled to simulate vehicle movement in each area of the traveling zone at different times.Sec-ond,the key cross-sections of segmental girder bridges are monitored in real time based on the force character-istics of continuous girder bridges,and they are compared with the simulation results.Finally,a material damage ontology model is introduced,and the structural damage caused by different overloading rates is compared and analyzed.Results show that thefinite element modeling method is accurate by comparing with on-site measured data,and it is suitable for the numerical simulation of segmental girder bridges;Dynamic sensors installed at 1/4L,1/2L,and 3/4L of the segmental girder main beams could be used to identify the dynamic response of segmental girder bridges;The bottom plate of the segmental girder bridge is mostly damaged at the position where the length of the precast beam section changes and the midspan position.With the increase in load,damage in the direction of the bridge develops faster than that in the direction of the transverse bridge.Thefindings of this study can guide maintenance departments in the management and maintenance of bridges and vehicles.

Dynamic response of multi-scale structure in flexible pavement to moving load

In order to study the dynamic responses in the microstructures of the pavement structure, the multi-scale modeling subjected to moving load is analyzed using the discrete element method （DEM）. The macro-scale discrete element model of the flexible pavement structure is established. The stress and strain at the bottom of the asphalt concrete layer under moving load are calculated. The DEM model is validated through comparison between DEM predictions and the results from the classical program. Based on the validated macro-scale DEM model, the distribution and the volumetric fraction of coarse aggregate, mastics and air voids at the bottom of the asphalt layer are modeled, and then the multi-scale model is constructed. The dynamic response in the microstructures of the multi-scale model are calculated and compared with the results from the macro model. The influence of mastic stiffness on the distribution of dynamic response in the microstructures is also analyzed. Results show that the average values and the variation coefficient of the tensile stress at the aggregate-mastic interface are far more than those within the mastics. The dynamic response including stress and strain distributes non-uniformly in both mastics and the interface. An increase in mastic stiffness tends to a uniform distribution of tensile stress in asphalt concrete.

Dynamic Analysis of A Pontoon-Separated Floating Bridge Subjected to A Moving Load

For the design and operation of a floating bridge, the understanding of its dynamic behavior under a moving load is of great importance. The purpose of this paper is to investigate the dynamic performances of a new type floating bridge, the pontoon-separated floating bridge, under the effect of a moving load. In the paper, a brief summary of the dynamic analysis of the floating bridge is first introduced. The motion equations for a pontoon-separated floating bridge, considering the nonlinear properties of connectors and vehicles＇ inertia effects, are proposed. The super-element method is applied to reduce the numerical analysis scale to solve the reduced equations. Based on the static analysis, the dynamic features of the new type floating bridge subjected to a moving load are investigated. It is found that the dynamie behavior of the pontoon-separated floating bridge is superior to that of the ribbon bridge by taking the nonlinearity of eonneetors into account.

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.

High-precision solution to the moving load problem using an improved spectral element method

In this paper, the spectral element method(SEM)is improved to solve the moving load problem. In this method, a structure with uniform geometry and material properties is considered as a spectral element, which means that the element number and the degree of freedom can be reduced significantly. Based on the variational method and the Laplace transform theory, the spectral stiffness matrix and the equivalent nodal force of the beam-column element are established. The static Green function is employed to deduce the improved function. The proposed method is applied to two typical engineering practices—the one-span bridge and the horizontal jib of the tower crane. The results have revealed the following. First, the new method can yield extremely high-precision results of the dynamic deflection, the bending moment and the shear force in the moving load problem.In most cases, the relative errors are smaller than 1%. Second, by comparing with the finite element method, one can obtain the highly accurate results using the improved SEM with smaller element numbers. Moreover, the method can be widely used for statically determinate as well as statically indeterminate structures. Third, the dynamic deflection of the twin-lift jib decreases with the increase in the moving load speed, whereas the curvature of the deflection increases.Finally, the dynamic deflection, the bending moment and the shear force of the jib will all increase as the magnitude of the moving load increases.

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.

Dynamic response of a beam on a Pasternak foundation and under a moving load

The dynamic response of an infinite beam placed on a Pasternak foundation when the system was subjected to a moving load was investigated.We used the double Fourier transform and its inversion to solve the formulations of the problem.A closed form analytic solution of the beam was obtained by the theorem of residues.We selected a numerical example to illustrate the dynamic response of the beam on Pasternak and Winkler foundations,respectively.We discuss the effect of the moving load velocity on the dynamic displacement response of the beam.The maximum deflection of the beam increases slightly with increased load velocity but increases significantly with reduced shear modulus of subgrade at a given velocity.The maximum deflection of a beam resting on a Pasternak foundation is much smaller than that of a beam on a Winkler foundation.

STEADY-STATE RESPONSE OF A TIMOSHENKO BEAM ON AN ELASTIC HALF-SPACE UNDER A MOVING LOAD

By introducing the equivalent stiffness of an elastic half-space interacting with a Timoshenko beam, the displacement solution of the beam resting on an elastic half-space subjected to a moving load is presented. Based on the relative relation of wave velocities of the half-space and the beam, four cases with the combination of different parameters of the half-space and the beam, the system of soft beam and hard half-space, the system of sub-soft beam and hard half- space, the system of sub-hard beam and soft half-space, and the system of hard beam and soft half-space are considered. The critical velocities of the moving load are studied using dispersion curves. It is found that critical velocities of the moving load on the Timoshenko beam depend on the relative relation of wave velocities of the half-space and the beam. The Rayleigh wave velocity in the half-space is always a critical velocity and the response of the system will be infinite when the load velocity reaches it. For the system of soft beam and hard half-space, wave velocities of the beam are also critical velocities. Besides the shear wave velocity of the beam, there is an additional minimum critical velocity for the system of sub-soft beam and hard half-space. While for systems of （sub-） hard beams and soft half-space, wave velocities of the beam are no longer critical ones. Comparison with the Euler-Bernoulli beam shows that the critical velocities and response of the two types of beams are much different for the system of （sub-） soft beam and hard half-space but are similar to each other for the system of （sub-） hard beam and soft half space. The largest displacement of the beam is almost at the location of the load and the displacement along the beam is almost symmetrical if the load velocity is smaller than the minimum critical velocity （the shear wave velocity of the beam for the system of soft beam and hard half-space）. The largest displacement of the beam shifts behind the load and the asymmetry of the displacement along the beam increases with the increase of the load velocity due to the damping and wave racliation. The displacement of the beam at the front of the load is very small if the load velocity is larger than the largest wave velocity of the beam and the half space. The results of the present study provide attractive theoretical and practical references for the analysis of ground vibration induced by the high-speed train.

An explicit time domain solution for ground stratum response to harmonic moving load

Based on the thin layer method originally proposed in frequency domain, an explicit time domain semi-analytical solution has been developed for simulating three-dimensional layered ground responses to harmonic moving loads. The Fourier-Laplace transforms were applied to derive the transformed solution that satisfied the boundary conditions of horizontal infinities. The eigenvalue decomposition was performed with respect to Laplace parameter to express the ground motion corresponding to the eigenmodes. The formulation for each eigenmode incorporating the moving load expression was transformed back into time domain analytically, and the global system responses were given by means of the general mode superposition method. The proposed explicit time domain solution is suitable for studying various types of moving load acting on or inside the ground. In this paper a moving harmonic load with rectangular distribution was adopted to demonstrate the ground response simulation. Two illustrative examples for moving load with speeds below or above the ground Rayleigh wave velocity were presented to test the computational accuracy and efficiency of the proposed approach. A parametric study was also performed to investigate the influences of soil properties on the ground responses.

Two-dimensional interactions due to moving load in generalized thermoelastic solid with diffusion

The present paper is concerned with the investigation of disturbances in＇a homogeneous, isotropic elastic medium with generalized thermoelastic diffusion, when a moving source is acting along one of the co-ordinate axis on the boundary of the medium. Eigen value approach is applied to study the disturbance in Laplace-Fourier transform domain for a two dimensional problem. The analytical expressions for displacement components, stresses, temperature field, concentration and chemical potential are obtained in the physical domain by using a numerical technique for the inversion of Laplace transform based on Fourier expansion techniques. These expressions are calculated numerically for a copper like material and depicted graphically. As special cases, the results in generalized thermoelastic and elastic media are obtained. Effect of presence of diffusion is analyzed theoretically and numerically.

Codimension-two bifurcation of axial loaded beam bridge subjected to an infinite series of moving loads

A novel model is proposed which comprises of a beam bridge subjected to an axial load and an infinite series of moving loads. The moving loads, whose distance between the neighbouring ones is the length of the beam bridge, coupled with the axial force can lead the vibration of the beam bridge to codimension-two bifurcation. Of particular concern is a parameter regime where non-persistence set regions undergo a transition to persistence regions. The boundary of each stripe represents a bifurcation which can drive the system off a kind of dynamics and jump to another one, causing damage due to the resulting amplitude jumps. The Galerkin method, averaging method, invertible linear transformation, and near identity nonlinear transformations are used to obtain the universal unfolding for the codimension-two bifurcation of the mid-span deflection. The efficiency of the theoretical analysis obtained in this paper is verified via numerical simulations.

New Damage-locating Method for Bridges Subjected to a Moving Load

A new damage-locating method for bridges subjected to a moving load is presented, and a new ‘moving load dam- age-locating indicator’ (MLDI) is introduced. A vehicle is modeled as a moving load, the bridge is simplified as an Euler-Bernoulli beam, and the damage is simulated by a reduction of stiffness properties of the elements. The curvature and MLDI values at each node of the baseline model (undamaged) and the damage model are computed respectively. Then the damage or damages can be located from a sudden change of the MLDI value. The feasibility and effectiveness of the proposed method are validated by nu- merical simulation. The results indicate that the method is effective, being able to not only locate a single damage accurately, but also locate multiple damages in simply-supported bridges, including multiple damages in continuous bridges. The results also indicate that the MLDI can accurately locate damages under 5% measurement noise.

MOVING INCLINED LOAD AT BOUNDARY SURFACE

The analytic expressions for the displacement components and stresses at a point of an orthotropic micropolar elastic medium with an overlying elastic half space as a result of moving inclined load of arbitrary orientation were obtained. The inclined load was assumed to be a linear combination of a normal load and a tangential load. The eigen value approach using Fourier transforms was employed and the transform was inverted by using a numerical technique.The numerical results were illustrated graphically for aluminium epoxy composite.

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.

A dynamic problem on the edges of a mode Ι crack subjected to moving unit-step loads

By the theory of complex functions, a dynamic problem on the edges of a mode I crack subjected to moving unit-step loads are investigated. The Riemann-Hilbert problem is easily formulated by the ways of self-similar functions. The analytical solution obtained is rather simple and concise. After the solution was utilized by superposition theorem, the relevant solution on the case of arbitrary loading can be obtained.

Vibration characteristics of frozen soil under moving track loads

Vibration due to moving traffic loads is an important factor which induces frozen soil damage; this paper analyzed these vibration characteristics of frozen soil foundation under track loads. Firstly, seismic observation array （SOA） technology was applied to monitor the three dimensional dynamic characteristics of frozen soil under movable track load in a per- mafrost region and seasonal frozen soil area. Secondly, a numerical simulation for the response of frozen soil under movable track load was performed based on finite element analysis （FEA）, The results show that dynamic characteristics of frozen soil in perpendicular and parallel direction of the track are obviously different. In the direction perpendicular to the track, the vertical acceleration amplitude had an abrupt increase in the 9-10 m from the track line. In the direction parallel to the track, the acceleration in vertical and horizontal direction had a quick attenuation compared to the other direction. Lastly, various parameters were analyzed for the purpose of controlling the dynamic response of frozen soil and the vibration attenuation in frozen soil layer.

Three Dimension Finite Element Analysis of the Influence Factors of Stress Responses in the Roadbed and Ground under a Moving Load

Focusing on the vibration of the roadbed and ground induced by high-speed train load, a three dimensional finite element model which includes the roadbed and horizontal layered site is established to study how the site conditions, the load moving speed and the depth of the soil element influence the soil element stress response. Based on a track-subsoil analytical model in which the rail is simulated as an Euler-Bernoulli beam resting on Winkler foundation in the vertical plane, the reaction force between the sleeper and roadbed excited by a single axle is presented, and then that is exerted on relevant elements to simulate the moving load. The dynamic response in the roadbed and subsoil excited by a single axle moving load is computed based on the parallel computing platform of the ABAQUS finite element software, and the stress time-history, stress path and curves of the principal stress axes rotation of the soil element under the track are presented. The results show that： the soil element stress path is an apple-shaped curve in the horizontal shear stress τd versus the stress difference （σsh - σch ）/2 coordinate system; the principal stress axes rotate 180° for the soil element under the load moving line during the load running, and the stress state changes from the pure shear to triaxial shear and then back to the pure shear again. The element dynamic stress increases as the moving load speed increases, which increases sharply when the load speed approaches the Rayleigh wave velocity of soil layer; the site conditions and the soil element depth affect the soil element stress path significantly.