Field Testing and Numerical Simulation of the Dynamic Response of Loess Hill Site under High-Speed Train Load

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Introduction
Tere are various complex topographical features along the high-speed railroad line, and the dynamic response of different topographical features under the high-speed train load is not the same.In recent years, with the growth of the urban population and people's travelling needs are also getting bigger and bigger, so that the contradiction between the production and life of people and the increasing demand for transport is becoming more and more prominent.On the one hand, due to the factors of safety, economy, and comfort of high-speed train operation, it becomes the primary tool for people to travel; on the other hand, the vibration problem caused by high-speed trains is becoming more and more serious, causing the vibration of buildings along the line and generating a lot of noise, which seriously afects the normal life of residents along the line.In addition, the environmental vibration caused by high-speed trains is closely related to the nature of the soil of the site, the form of the railroad section, the running speed of the train, and the grouping of the train.
During the past decades, many researches have been carried out to unravel the vibration problems.Tese studies mainly can be divided into three categories: theoretical analysis [1][2][3][4][5][6], numerical simulation, and feld test.However, feld test and numerical calculation are the most common and important methods to study vibration.Regarding the numerical simulation, the fnite element (FE) numerical simulation is a very efective method to predict and analyze the track-subgrade behavior and the ground vibration induced by train loads.Xia et al. [7] studied the vibration of ground and buildings caused by train operation under elevated bridges through feld tests and found that the vibration intensity had a signifcant relationship with the train speed, and the ground vibration was amplifed in a certain range.Gao et al. [8] studied the vibration of the ground along the Qin-Shen railroad using feld testing techniques and discussed the efect of train grouping and speed on vibration.Chen et al. [9] tested and studied the vibration characteristics of the ground in a section of the Beijing-Guangzhou railway and its attenuation law.Guoyuan et al. [10,11] analyzed the vibration characteristics and found that the graded gravel section could signifcantly reduce the settlement based on the vibration and settlement feld test results of railroad road bridges and road culverts.Zhang [12] tested the vibration caused by the train operation under the viaduct and analyzed the vibration isolation efect of the barrier.Xiao et al. [13] tested and analyzed the vibration caused by train operation in the tunnel in three directions and found that the vibration in the vertical direction is smaller than that in the circular and radial directions, and there is a vibration amplifcation zone within a certain distance from the center of the tunnel.Zhang [14] and Gong-qi [15] studied the vibration generated by train operation in the embankment section using feld measurements and numerical simulations.Xiang-Lian and Zhou [16] studied the vibration of the site during the passage of trains along the West-Bao railroad through feld actual measurements and found that the vibration in each direction of vibration increases with the increase of train speed and axle weight, and there is a vibration amplifcation in a certain range.Wu et al. [17,18] studied the vibration characteristics of the permafrost area under train load and the deformation characteristics of the soil under repeated train load and found that the vibration would attenuate substantially when passing through the embankment, and the deformation of the soil would reach the maximum in the frst year of train operation and fnally stabilize.Wang et al. [19] tested the vibration caused by train operation in diferent seasons of the roadbed section in the seasonal permafrost area, and found that the vibration of the site in winter is due to the soil is in the frozen state, the modulus of elasticity of the soil increases, and the damping ratio decreases, and the peak vibration acceleration of each component is larger, but in the spring thawing season, the soil contains a large amount of water, which results in the vibration acceleration of the peak of the vibration in all directions is a phenomenon of decreasing.Te peak acceleration in the horizontal direction is slightly enhanced.Chen and Zhou [20] established the 3D FEM of the vehicle-track-subgrade coupling systems to study the diferent stifness efects of the subgrade surface layer, bottom layer, embankment, foundation, and fastener by analyzing the vertical displacement of the track-subgrade.Connolly et al. [21,22] established a three-dimensional numerical model to study the vibration characteristics of embankment in the soft soil regions under train loads.Degrande et al. [23] presented a three-dimensional FEM of tunnel soil to predict the vibrations in the free feld from excitation.Andersen and Jones [24] compared the 2D and 3D FEM of railway tunnels.Tese results showed that the 2D soil-tunnel FEM could efectively calculate the dynamic response of soil and tunnels.Lyratzakis et al. [25] established a 3D FEM to analyze the infuence of HST-induced vibration on the adjacent buildings and applied the efcient measure to minimize the vibration.Bian et al. [26] calculated the dynamic response of soil-induced train loads by using 2.5D FEM and analyzed the efects of track irregularity on ground vibration.Alves Costa et al. [27,28] established a 2.5D FEM-BEM model of roadbed-soil structure, considering the train-track dynamic interaction, and validated the correctness of the model by the feld vibration tests.Villalba Sanchis et al. [29] studied the dynamic responses of a dual gauge track induced by the train passage by experimental and numerical investigations.In order to accurately analyze vibration characteristics and site efects of loess hills under the moving load of a high-speed train, Yan et al. [30] established four types of loess hill models under railway viaduct by the fnite element analysis software by feld test, the dynamic response and stability of loess hills under two diferent vibration sources under high-speed train load were studied by using two-dimensional equivalent linear response time history analysis, and the infuence of the mechanical parameters of loess on the vibration of diferent types of loess hill was analyzed.
From the above studies, it can be seen that the research on vibration caused by train operation is mainly focused on fat sites in soft soil, permafrost, and loess areas, and there is less research on the vibration characteristics of complex terrain landforms along railroad lines.Te role of topography has been considered by scholars in the feld of earthquake engineering [31,32], and it is found that topography makes the vibration propagation characteristics signifcantly diferent from those of a fat site.However, there are signifcant diferences between the characteristics of vibrations caused by high-speed trains and ground vibrations in the time and frequency domains.Te Bao-Lan high-speed railway is the main component of the "eight horizontal and eight vertical" high-speed passenger transportation network in China, and one-third of the total length of the railroad is located in the Tianli basin, where the loess layer thickness is large, the wetness level is high, and there are complex topographical features such as tableland, beam, and hill [33].
Due to the very complex geomorphology of the Loess Plateau, there are not only roadbeds but also a large number of bridges and tunnels along the railroad line.Meanwhile, quite a number of previous studies did not consider the efects of diferent sites and landforms on vibration propagation.In order to accurately analyze the vibration characteristics of loess hilly sites under high-speed train operating loads and their site efects, a series of feld vibration tests were conducted in this work based on the site test profles, and a fnite element (FE) model of loess hilly sites under high-speed railroad viaducts was established.Te two-dimensional equivalent linear response time dynamic analysis method is used to study and analyze the dynamic response of the loess hilly site under the vibration source of the train operating load and its stability under the high-speed train load.Te vibration propagation characteristics, attenuation law, and spectral characteristics of the loess hilly site from the feld test and numerical simulation are compared and analyzed, and the vibration characteristics of the bridge piers and surrounding sites along the Baolan high-speed railroad are studied.Te study is of great help to the stability and safety prediction of railroad projects in loess areas.

Field Testing
2.1.Testing Instruments.Te ground vibration test instrument used is an 891-II type vibration meter (Figure 1), which is developed by the Institute of Engineering Mechanics of China Earthquake Bureau and can be used to test ground vibration, pulsation or vibration of building structures, and engineering vibration.Te vibrometer is mainly composed of a geophone and a SysCom data acquisition system, which mainly includes amplifers, recorders, flters, and data acquisition instruments.Tis instrument has the characteristics of small size, lightweight, easy to carry and use, and large test range.Te acceleration test range of this instrument is 0∼2.0 g, the sampling interval is 0.005 s, and the recording length of this instrument is 5 s before the excitation and 35 s after the excitation.
In this test, the X direction is specifed as the direction of train operation, the Y direction is perpendicular to the line direction, and the Z direction is the direction of gravity.

Loess Hill Site Environment and Measurement Point
Layout.Te test site is located under an elevated bridge of Qin'an-Tongwei on the Baolan passenger dedicated line, with a bridge height of about 20 m.One side of the bridge is a fat terrain, while the other side is a typical rectangular loess hill terrain.In the vertical direction of the high-speed railway bridge at a distance of 41 m on the side of the rectangular loess hills were arranged with a total of six measurement points, of which measurement point 1 was arranged at a distance of 2 m from the bridge abutment, measurement point 2 was arranged at a distance of 9 m from the bridge abutment, measurement point 3 was arranged at a distance of 18 m from the bridge abutment, measurement point 4 was arranged at a distance of 27 m from the bridge abutment, and measurement points 5 and 6 were arranged on the loess hill site, which was 30 m and 41 m away from the bridge abutment, respectively.Te width of the loess hill site was 11 m.Te height was 4.5 m.Te measurement point layout and the shape of loess hill are shown in Figure 2.

Numerical Simulation Methods: Finite Element and
Infnite Element Coupled Analysis Methods

Finite Element Analysis Methods.
Te fnite element unit method is an essential tool for engineering structural analysis and large-scale numerical calculations, and the emergence of the fnite element method is an important breakthrough in the feld of numerical calculations.Te basic method is to divide the fnite area into a fnite number of units, establish algebraic control equations on each unit and solve them, and then connect these divided units in a certain way, and the format of the divided units can be various shapes, so it can be used to solve the calculation of complex models.Dynamic analysis is diferent from statics, when the building structure receives a load, and the magnitude and direction of the load are related to time, which requires that not only the magnitude of the inertia force but also the infuence of damping should be considered in the dynamic analysis.At present, two methods can be used for solving dynamics problems, which are explicit and implicit solutions.
In order to understand the dynamic characteristics of a structure, such as a building, during the whole vibration process, it is necessary to use the time course analysis method to solve the problem.Te time course analysis method is used to solve the diferential equations of motion of the object by numerical methods of stepwise integration and fnally to fnd out the motion of the structure and building during the whole vibration process.

Infnite Element Analysis Method.
In geotechnical engineering, the community foundation is actually a semiinfnite space structure, which should be considered as infnite when calculating and analyzing.However, in the dynamic analysis of geotechnical engineering, it is generally only concerned with the vibration in and around the building structures and does not need to be considered infnitely far away, so it is reduced to a near-feld fuctuation problem.
In the numerical calculation model, it is impossible to build the foundation as an infnite area, and it is necessary to truncate it, but on the truncated boundary, the vibration wave will have an obvious bouncing efect, which is obviously not consistent with the actual situation, resulting in errors in the results of numerical calculation.In order to solve this problem, ABAQUS provides a new method, namely, infnite elements to meet the needs of the calculation.Te defnition of an infnite element in ABAQUS can only be rewritten by inp fle, and the unit name of the infnite element contains "IN."

Site Model and Soil Parameters of Loess Hill Site under
Viaduct of High-Speed Railroad.In order to study the infuence of rectangular loess hill site and soil mechanical parameters on vibration propagation under the elevated bridge, and the vibration characteristics of diferent forms of loess hill site, a rectangular loess hill model consistent with the site was established according to the feld measurement profle: the length of the rectangular loess hill is 11 m.
Te length of the rectangular loess hill is 11 m, and the width is 4.5 m, as shown in Figure 3. Te model is divided into two parts, the frst part is the bridge pier and pile Shock and Vibration foundation, the pier height is 20 m, the width is 4 m, using bored piles and two pile foundations, and pile length is 8 m, using C30 concrete; the second part is the loess body because the acceleration and displacement of the foundation vibration caused by the train are usually small, the soil body is considered elastic, its physical and mechanical parameters are shown in Table 1 [34], and the thickness of the loess is 40 m.Te left and right boundaries of loess body model are used as infnite element boundaries in order to prevent the refection efect of waves.
In order to compare with the feld test data, a total of six measurement points are arranged on the side of the rectangular loess hill under the bridge of the model structure, all of which are consistent with the location of the feld test points: measurement point 1 is arranged 2 m from the bottom of the bridge pier, measurement point 2 is 9 m from the bottom of the bridge pier, measurement point 3 is 18 m from the bottom of the bridge pier, measurement point 4 is 27 m from the bottom of the bridge pier, measurement point 5 is arranged on the left side of the rectangular loess hill, and the horizontal distance of measurement point 4 is 3 m.Te width of the loess hill is 11 m, the height is 4.5 m, and the measurement point 6 is arranged on the right side of the rectangular loess hill, which is 41 m from the bottom of the bridge pier, as shown in Figure 3. Te fnite element grid cell size is 1 m × 0.5 m, total of 7639 grids.Before application, high-pass fltering and baseline correction were performed by Seismosignal software to flter out the components of seismic waves with frequencies less than 0.1 Hz.Te vibration duration used for the calculation is 10.00 s, and the maximum peak acceleration is 51.27 cm 2 /s. Figure 4(b) shows the vibration Fourier spectrum characteristics, and the vibration duration applied for the calculation is dominated by the medium and high-frequency components, and the excellence frequency is 15 Hz. Figure 4(c) shows the vibration energy spectrum curve with a remarkable frequency of 15 Hz.

Stability Analysis of the Rectangular Loess Hill
Site under the Viaduct.Since the loess hill site and its surrounding sites are mainly subject to the action of gravity under natural conditions, their stability is mainly controlled by gravity, while the construction of the railroad viaduct in its vicinity is subject to the coupled action of gravity and train load due to the infuence of train operation.Terefore, in order to further analyze the characteristics of the loess hill site elevated under the coupling action of train load and gravity, the maximum vertical displacement clouds under the action of train load and gravity, and the Mises stress clouds under the coupling action of train load and gravity were compared and analyzed, as shown in Figures 5 and 6.
As can be seen from Figure 5, the vertical maximum displacement clouds under gravity load are signifcantly diferent from those under train load.Under gravity, the vertical displacement under the viaduct is larger, and the maximum vertical displacement decreases with the increase of depth and distance from the bottom of the bridge pier; while the vertical displacement of the loess hill is the largest, and again, the maximum vertical displacement is decaying with the increase of depth and distance from the loess hill.Also, under the action of train load, the vertical displacement only occurs around the bridge pier and has no efect on the vertical displacement of the loess hill basically.
As can be seen from Figure 6, there is basically no diference between the Mises stress clouds under gravity and under the coupling of train load and gravity, except that under the coupling of train load and gravity, there is a signifcant increase in the Mises stress applied to the pile foundation and its bottom soil.and 8 show the vibration acceleration clouds of the loess site under the same viaduct at diferent moments, respectively.From the fgures, it can be seen that the vibration acceleration distribution clouds of the loess hill site at different moments (6.68 s and 6.89 s) are similar, and the vibration acceleration all gradually decreases with the increase of the vibration source distance, but the acceleration all shows a signifcant increase on the loess hill site.

Comparison Analysis of Field Test and Numerical Simulation Results
4.1.Acceleration Time Range. Figure 9 shows the vertical (zcomponent) vibration acceleration time course of each observation point 1 to 6 in the loess site under the viaduct during the passage of a 16-section train with a speed of 242 km/h of the high-speed railroad, and it can be seen that the ground vibration acceleration waveform of each observation point in the loess site has similarity, and there is good symmetry above and below the vibration acceleration time course curve of each measurement point, and there are obvious periodic peaks, and the vibration in the loess hill.Te amplifcation efect is very obvious.
As can be seen from the fgure, the peak vibration accelerations of measurement points 1 to 6 recorded in the feld test are 18.74 cm/s 2 , 12.24 cm/s 2 , 9.67 cm/s 2 , 8.56 cm/s 2 , 11.26 cm/s 2 , and 12.81 cm/s 2 , respectively, and the peak vibration accelerations of measurement points 1 to 6 recorded in the numerical simulation are 19.49cm/s 2 , 15.46 cm/s 2 , 15.73 cm/s 2 , 10.94 cm/s 2 , 13.03 cm/s 2 , and 14.89 cm/s 2 , respectively, and it is obvious that the peak vibration acceleration of measurement points 1∼4 decays with distance as they are farther away from the bridge pier, while on the rectangular loess hill due to the infuence of site conditions, which makes the peak vibration acceleration of measurement point 5 and measurement point 6 appear "rebound increase", the data recorded in the feld test are 1.32 times and 1.49 times magnifed, respectively, compared to measurement point 4, and the data recorded in the numerical simulation are 1.19 times and 1.36 times magnifed, respectively, compared to measurement point 4. At the same time, the vibration durations of measurement points 1 to 4 recorded in the feld test were all 7.5 s, while the vibration durations of measurement points 5 and 6 were both 8.81 s.Both showed an increase in vibration duration, which were amplifed by 1.17 times compared with the frst four measurement points.
Figure 10 shows the peak vertical (z-component) vibration acceleration curves, amplifcation coefcients, and a Simulated− max /a Observated− max values for each observation point 1 to 6 at the loess site under the viaduct during highspeed railroad train operation recorded by feld tests and numerical simulations.From the fgure, it can be seen that the peak vibration acceleration of measurement points 1 to 4 recorded by both feld test and numerical simulation decayed linearly with distance, while measurement point 5 and measurement point 6 showed amplifcation phenomenon, and the overall peak value of numerical simulation was larger than that of feld test (Figure 10(a)).Figure10(b) shows the amplifcation factor obtained from the ratio of the peak acceleration at each measurement point to the peak acceleration at measurement point 1 in the feld test.Figure 10(b) shows the amplifcation coefcient of the peak acceleration of each measurement point and the amplifcation coefcient of the peak acceleration of measurement point 1, a Simulated− max /a Observated− max values range from 1.04 to 1.63, with the largest dispersion at measurement point 3, and a Simulated− max /a Observated− max values at the other fve measurement points range from 1.04 to 1.28.Tis indicates that there is still some error between the numerically simulated soil parameters and the real soil parameters.

Spectrum Analysis Method of Strong Vibration.
Spectral analysis of data from strong vibration observations is actually a process of Fourier transform and Fourier inverse transform.Te value of N (even) of the time function at equal time interval points x m (m � 0,1,2, ..., N − 1): where x m is denoted as a fnite trigonometric function with A k and B k as coefcients. ( Considering that this function is nothing but an approximation of the metric function x t .

􏽥 x(t) �
( Equation ( 3) is a fnite Fourier approximation of the function x t .Te coefcients A k and B k in equation ( 1) are of fnite Fourier coefcients.Te calculation of equation ( 1) is called the Fourier transform of the discrete value x m , and the calculation of equation ( 2) is called the Fourier inverse transform.
Here, the introduction of the complex Fourier coefcients

Shock and Vibration
In a more concise way, it can be expressed as the following equation, called the fnite complex Fourier series, x m e − i(2πkm/N) k � 0,1,2, . . ., N − 1. ( Equation ( 4) is the Fourier transform, and equation ( 5) is the inverse Fourier transform.Using the above calculation method, the observed data can be subjected to spectral analysis.

Fourier Spectrum.
From Figure 11, it can be seen that the Fourier spectrum waveforms of each measurement point recorded by numerical simulation and feld test have similarity and have obvious periodic peaks, the amplifcation of vibration in the loess hill is very obvious, and the overall amplitude and peak acceleration are similar to the linear decay with distance, and the amplifcation phenomenon is presented at measurement point 5 and measurement point 6.Te Fourier spectrum frequencies recorded by numerical simulation and feld test are mainly concentrated in 1∼40 Hz when the train with the speed of 240 km/h passes by, but the diference between the main frequencies recorded by the two is large, and the main frequency of Fourier spectrum vibration recorded by numerical simulation is around 15 Hz, which is the same as the main frequency of Fourier spectrum vibration of the input vibration wave, while the main frequency of Fourier spectrum vibration recorded by feld test is around 25 Hz.Te Fourier spectrum amplitude recorded by numerical simulation of the same measurement point is larger than the amplitude recorded by the feld test, and the Fourier spectrum frequency range of measurement points 3∼6 recorded by the feld test is larger between 1 and 45 Hz, while the Fourier spectrum frequency range of measurement points 3∼6 recorded by numerical simulation is between 1 and 25 Hz.
From Figure 12, it can be seen that the Fourier spectrum amplitudes of measurement points 1 to 6 recorded in the feld test are 11.95 cm/s 2 , 7.68 cm/s 2 , 6.23 cm/s 2 , 6.75 cm/s 2 , 8.45 cm/s 2 , and 9.62 cm/s 2 , respectively, and the Fourier spectrum amplitudes of measurement points 1 to 6 recorded in the numerical simulation are 13.82 cm/s 2 , 20.53 cm/s 2 , 22.64 cm/s 2 , 13.95 cm/s 2 , 16.53 cm/s 2 , and 16.83 cm/s 2 , respectively, and it is obvious that the Fourier spectrum

Energy Spectrum.
Te vibration acceleration energy spectrum refects the distribution of vibration acceleration energy at individual frequencies, and the relationship between the acceleration energy spectrum function G(ω) and the spectrum function f(jω) can be expressed as follows [35]: In order to further analyze the relationship between the vibration characteristics of each measurement point and the distance from the vibration source, the vibration acceleration signals of each measurement point recorded by numerical simulation and feld test were analyzed by energy spectrum, as shown in Figures 13 and 14.
From Figure 13, it can be seen that the energy spectrum waveforms of each measurement point recorded by numerical simulation and feld test have similarities and have obvious periodic peaks.When a train with an hourly speed of 240 km/h passes by, the frequencies of the energy spectrum recorded by the numerical simulation and the feld test are mainly concentrated in the range of 1∼40 Hz, but the diference between the main frequencies recorded by the two is large.Te amplitude of the energy spectrum recorded by the numerical simulation is larger than that recorded by the feld test, and the frequency range of the energy spectrum of measurement points 3∼6 recorded by the feld test is larger between 1 and 30 Hz, while the frequency range of the Fourier spectrum of measurement points 3∼6 recorded by the numerical simulation is between 1 and 20 Hz.
As can be seen from Figure 14, the energy spectrum amplitudes of measurement points 1 to 6 recorded in the feld test are 0.17 cm 2 /s 3 , 0.26 cm 2 /s 3 , 0.18 cm 2 /s 3 , 0.19 cm 2 / s 3 , 0.19 cm 2 /s 3 , and 0.21 cm 2 /s 3 , respectively, and the energy spectrum amplitudes of measurement points 1 to 6 recorded in the numerical simulation is 0.22 cm 2 /s 3 , 0.54 cm 2 /s 3 , 0.63 cm 2 /s 3 , 0.55 cm 2 /s 3 , 0.45 cm 2 /s 3 , and 0.58 cm 2 /s 3 , and the energy of measurement point 1 are the smallest, the data recorded in the feld test are 1.11 times larger than that of measurement point 4, and the data recorded in the numerical simulation are 1.05 times larger than that of measurement point 4.

Conclusion
Trough the feld vibration test and numerical simulation of the loess hill site during the passage of the train of the Baolan high-speed railway, the following conclusions were obtained based on the comparative analysis and research in both time and frequency domains: (1) Te vertical maximum displacement clouds under the action of gravity load and train load are obviously diferent.Under the action of gravity, the vertical displacement under the elevated bridge is larger, and the maximum vertical displacement decreases with the increase of depth and distance from the bottom of the bridge pier while the vertical displacement of the loess hill is the largest, and again, the maximum vertical displacement is decaying with the increase of depth and distance from the loess hill.Also, under the action of train load, the vertical displacement only occurs around the bridge pier and has no efect on the vertical displacement of the loess hill basically.
Tere is basically no diference between the Mises stress clouds under gravity and the coupled train load and gravity, except that the Mises stress on the pile foundation and its bottom soil increases signifcantly under the coupled train load and gravity.
(2) Te vibration acceleration distribution clouds of the loess hill site at diferent moments are similar, and the vibration acceleration all gradually decreases with the increasing distance of the vibration source, but the acceleration on the loess hill all shows a signifcant increase.Te waveform of ground vibration acceleration at each observation point of the loess site has similarity, and there is good symmetry above and below the time course curve of vibration acceleration at each measurement point, there is an obvious periodic peak, and the vibration amplifcation in the loess hill is very obvious, and the ratio of peak acceleration at each measurement point is recorded by numerical simulation and feld test, the a Simulated− max /a Observated− max values range from 1.04 to 1.63, with the largest dispersion at measurement point 3, and the a Simulated− max /a Observated− max values at the other fve measurement points range from 1.04 to 1.28, generally showing that the peak acceleration recorded by the numerical simulation is larger than that of the feld test.Te vibration durations of measurement points 1 to 4 recorded in the feld test were all 7.5 s, while the vibration durations of measurement point 5 and measurement point 6 at the location of the loess hill site were both 8.81 s.
Both showed an increase in vibration duration, which was 1.17 times larger than the previous four measurement points, respectively.(3) When a high-speed train with a speed of 240 km/h passes through, the Fourier spectrum frequencies recorded by numerical simulation and feld test are concentrated between 1 and 40 Hz, but the diference of the main frequency between the two records is large, the main frequency of Fourier spectrum vibration recorded by numerical simulation is 15 Hz, which is the same as that of the input vibration waveform, but the main frequency of Fourier spectrum vibration recorded by feld test is 25 Hz; as the distance from the bridge abutment gets farther and farther away, the Fourier spectrum amplitude of the loess fat site in the non-loess hills gradually decays with the distance, whereas the Fourier spectrum amplitude is amplifed in the loess hill site due to the site condition.(4) When the train with the speed of 240 km/h passes by, the energy spectrum frequencies recorded by numerical simulation and feld test are mainly concentrated in 1∼40 Hz, but the diference between the main frequencies recorded by the two is large, the main frequency of energy spectrum vibration recorded by numerical simulation is around 15 Hz, which is the same as the main frequency of energy spectrum vibration of the input vibration wave, while the main frequency of energy spectrum vibration recorded by feld test is around 25 Hz.Te energy spectrum of measurement point 1 is the smallest, and the energy spectrum of measurement points 2∼5 decays with distance as the distance from the bridge pier gets farther, but the energy spectrum of measurement point 6 has a "rebound increase," and the data recorded in the feld test are 1.11 times larger than that of measurement point 4, and the data recorded in the numerical simulation are 1.05 times larger than that of measurement point 4. (5) Trough the comparative analysis of the results of the feld vibration test and numerical calculation of the Baolan high-speed railway, it is found that the results obtained from the feld vibration test and numerical calculation of the high-speed railway have high similarity, which can provide the corresponding basis for the theoretical analysis of the vibration efect of the loess site of train vibration, verify the Shock and Vibration correctness and applicability of the theoretical model and numerical analysis model, and can evaluate the environmental vibration caused by the train and predict the train vibration.It can also provide a basis for the assessment of train-induced environmental vibration and the prediction of train vibration.

Figure 2 :
Figure 2: Schematic diagram of site and measuring points of rectangular loess hill site under the railway viaduct.(a) Field layout of vibration measuring points at the loess hill site under the railway viaduct.(b) Layout diagram of vibration measuring points at the loess hill site under the railway viaduct.

Figure 3 :
Figure 3: Model of loess hill site.

Table 1 :Figure 4 :Figure 5 :
Figure 4: Numerical calculation of the input vibration acceleration time range and its spectrum curve.

Figure 6 :
Figure 6: Mises comparison of stress clouds.(a) Mises stress clouds of the rectangular loess hill site under the viaduct under gravity load.(b) Mises stress clouds of the rectangular loess hill site under the viaduct with coupled gravity and train loads.

Figure 7 :Figure 8 :
Figure 7: Acceleration clouds of the loess site under the viaduct at t � 6.68 s.

Figure 10 :
Figure 10: Comparison of acceleration peak at each measurement point between feld test and numerical simulation.

Figure 14 :
Figure 14: Comparison of energy spectrum amplitude at each measurement point between feld test and numerical simulation.