Research Article  Open Access
Yefei Zhou, Gang Wang, Shuyi Yang, Niu Liu, "NearFault Ground Motion Impacts on HighSpeed Rail LargeSpan Continuous Girder Bridge considering PileSoil Interaction", Advances in Civil Engineering, vol. 2022, Article ID 7554440, 9 pages, 2022. https://doi.org/10.1155/2022/7554440
NearFault Ground Motion Impacts on HighSpeed Rail LargeSpan Continuous Girder Bridge considering PileSoil Interaction
Abstract
This paper examines and discusses the dynamic response of a highspeed trainbridgesoilpile foundation system to nearfault earthquakes. A 72 + 120 + 72 m continuous girder bridge of a highspeed railroad was selected as the model for calculation. Based on the py model for simulating pilesoil interaction, the momentcurvature analysis program XTRACT is used to calculate the moment and curvature of bridge piers and pile foundation sections, and the finite element (FE) software is used to establish two nonlinear global bridge models under seismic effects in the highintensity zone, one considering pilesoil interaction and one without considering pilesoil interaction. The Ap/Vp parameter, the ratio of peak acceleration to peak velocity of transverse ground shaking, is used to reflect the impulse characteristics of earthquakes and the effect of the Ap/Vp parameter on the dynamic response of bridges to earthquakes was studied. The elasticplastic response of the bridge system was calculated under lateral and vertical nearfault (NF) impulse/NF nonimpulse/farfield (FF) ground motions (GMs). The study shows that the structural displacement increases, and the internal force decreases after considering the pilesoil interaction. The results show that the bridge piers enter the elastoplastic phase under rare earthquakes. The NF ground shaking couples with the bridge into the elastoplastic phase with a more significant impulse period than the FF ground shaking intensifies the dynamic response of the bridge structure.
1. Introduction
A highspeed railroad has the advantages of high speed, high density, allweather, large capacity, comfort, safety, and reliability compared with other means of transport. It has become the trend of railroad development in the world. It is considering that the construction of railroads will inevitably pass through some densely populated urban areas and soft soil areas in the plains or other geological conditions. Therefore, ensuring the overall safety of the bridge structure and the safety of the trains on the bridge has become an urgent problem for the bridge designers to solve, which is because highspeed railroad bridges are subjected to forced vibration due to the powerful impact of the upper highspeed trains and structural fatigue under the longterm, highdensity effect of this power, which reduces the stability and strength. This vibration of the bridge structure, in turn, affects the safety and smoothness of the running vehicles on the bridge. Therefore, the study must consider the dynamic response of the vehiclebridge coupling.
Pile foundations are widely used for their high bearing capacity, good stability, low settlement, and ability to adapt to various geological conditions and loading situations. Due to multiple factors such as superstructure, overlying infinite foundation, and farfield ground motion, the pilesoilstructure dynamic interaction is one of the most complex topics in structural dynamics and soil dynamics and has received wide attention.
Erhan and Dicleli [1] developed a soilbridge nonlinear model considering SSI and calculated the seismic response of bridges under different earthquake intensities and found the influence of SSI on the seismic response of bridges under design. Khoshnoudian et al. [2] established SSI by building a simplified vertebral soil model and studying impulsive earthquakes' effect on dynamic structural stability. For SSI can cause lateral displacement of the structure, Khoshnoudian and Ahmadi [3] investigated the impact of the impulsive earthquake on the displacement ratio of the structure and pointed out that a smaller structural length to slenderness ratio as Timoshenko type piers may offset part of the lateral displacement response. Wang et al. [4] and Chotesuwan et al. [5] investigated the effect of SSI on the seismic response of bridges based on experiments. Moghaddasi et al. [6] investigated the effect of bending properties of pile foundations on the seismic response of structures by using a robust Monte Carlo method to develop an equivalent linear model of soilpile foundationbridge. Xie et al. [7] studied the SSI effect on the seismic response of a typical bridge in California. Durucan and Dicleli M [8] and Liu and Zhang [9] investigated the impact of Ap/Vp parameters on the seismic response of seismically isolated structures.
The study by Wang et al. [10] analyzed the effect of soilstructure interaction SSI (SSI) on the seismic response of bridges due to vertical earthquakes, including liquefaction potential. The study results indicate that the SSI effect tends to reduce the amount of response to certain ground motions and increase the demand for other ground motions relative to the fixed base case. This phenomenon can be explained by the frequency components of ground motions, the drift of the vertical selfoscillation period, and the generalization of the vertical spectral acceleration for higher modes. In addition, the liquefaction mechanism of nonliquefied soils is isolated concerning the SSI effect, revealing the impact of liquefaction on the bridge response. Li et al. [11] developed a threedimensional nonlinear vibration isolation finite element model of a prototype California HighSpeed Rail (CHSR) bridge under NF earthquakes by considering soilstructure and trackstructure interactions and calculating the seismic response of the bridge. The study did not compare the seismic response of the bridge before and after considering SSI. Galvín et al. [12] proposed a method for calculating the dynamic response of railroad bridges considering soilstructure interactions. The technique uses the substructure method to decompose the problem into two coupled interactions: the soilfoundation and the soilfoundationbridge systems. The foundation and surrounding soil are discretized using the finite element method and filled with perfectly matched layers to avoid boundary reflections. The benefit of the technique is that as the complexity of the problem increases, the technique allows access to specialized analysis tools to deal with both the soilfoundation and superstructure domains. Bhure et al. [13] studied the dynamic response of a subway bridge under moving loads. Track unevenness and train inertia effects were not considered. Moving load analysis was performed for the fixed foundation and the full pile models. It was shown that the resonance phenomenon of the full pile model was lower than that of the fixed foundation model in both loading cases.
Through the investigation and comparison of different research results at home and abroad, it can be found that the study of the vehiclebridge coupling dynamics of highspeed railroad continuous girder bridges under the action of earthquakes is of great significance to the design of both highspeed railroad bridges and highspeed trains in the future, so this research topic has gradually received extensive attention from various researchers. However, the existing research still has many shortcomings, mainly in the following points.
Firstly, the continuous girder bridges have received wide attention for their structural stiffness, small deformation, good dynamic performance, and benefits to highspeed traffic. So far, the leading research at home and abroad has been limited to simply supported girder bridges, and the vibration response of continuous girder bridges lacks systematic analysis. Therefore, the seismic response of largespan continuous girder bridges for highspeed railroads needs to be studied in depth.
Secondly, the existing domestic studies on the elasticplastic seismic response analysis of highspeed railroad continuous girder bridges are few and limited to the elasticplastic analysis of supported girder bridges. Still, the dynamic characteristics of the two are different. Therefore, the elasticplastic seismic response analysis of highspeed railroad continuous girder bridges is needed.
Again, most of the studies at this stage only establish the trainbridge model and ignore or simplify other system elements, such as not considering the influence of the soil on the structure. Therefore, a more detailed model to analyze the pilesoilstructure interaction should be established.
This paper selects the research object of a 72 + 120 + 72 m continuous girder bridge of highspeed railroad. The nonlinear model of the soilpile foundation is established with the SHAKE91 program. Py curve, tz curve, and qz curve and the hysteresis characteristics of bridge piers and pile foundation are simulated with the bilinear model to establish the dynamic responses railroad bridgesoilpile foundation continuous girder bridge system in the wrong geological development area. The dynamic calculation of the train largespan bridge system under velocity impulse NF earthquake is carried out. The study analyzes the elasticplastic seismic response of the bridge pile foundation system under NF earthquakes. It reveals the dynamic performance of railroad bridges in poorly developed geological areas under multidimensional seismic action. The research aims to promote the preliminary research results to the application by solving the core scientific problems behind the technical bottlenecks.
2. Power py (tz and qz) Curve Method
In recent years, the simulation of soil confining action around piles under intense earthquake action has been a complex problem and a hot research topic. Due to the complexity of pilesoil interaction, in this paper, based on the Winkler foundation assumption that the response of each soil layer is independent of the adjacent soil layers, an analytical model with dynamic py (tz and qz) curves is shown in Figure 2(e), which consists of three main parts: freefield soil, structural, and pile units. Among them, the pile is simulated with a beam unit. The nonlinear soil is simulated with three indifferent dynamic units: the active py unit acts as the horizontal resistance of the Earth, the dynamic tz unit simulates the vertical frictional force of the soil, and the dynamic qz unit simulates the vertical support of the ground, and the free field is part of the pilesoil interaction, and the springs used are not one, but multiple springs in series.
The load transfer (TZ) method models the pile as a series of cells supported by discrete nonlinear springs representing the frictional resistance at the soil surface (TZ springs) and nonlinear springs at the pile ends, meaning the endbearing springs (QZ springs). The soil spring is a nonlinear representation of the soil reaction force T (or Q at the pile end) versus the displacement Z, as shown in Figure 2(e). With known TZ and QZ curves, the axial loadsettlement response can be obtained using the computer program.
Appropriate TZ and QZ curves are necessary to obtain reliable settlement and axial monopile load transfer calculations. Such load transfer curves were initially obtained empirically. Coyle and Sulaiman [14] received TZ curves based on models and experience with fullsize sand pile loading tests. Vijayvergiya [15] and API [16], based on this work and other empirical results, made general recommendations for estimating TZ and QZ curves for sandy soils. The load transfer curves can also be satisfactorily constructed using theoretical methods related to the shear stiffness of the soil around the pile [17, 18].
The dynamic py (tz and qz) curve approach is a nonlinear foundation response method that takes into consideration soil nonlinearity, soil stratification, soil type, load type, soil interface slip and detachment, and farfield soil radiation damping, among other factors. It overcomes the shortcomings of the single parameter method (such as the 6spring method) for calculating the deflection, angle of rotation, and maximum bending moment of the pile by horizontal loadbearing pile, which cannot be wellmatched with the actual measured data and boundary conditions at the same time, and resolves the issue that the linear soil pressure and displacement solution method is not applicable to the actual soil nonlinear reaction when large deformation occurs.
3. Ground Vibration Selection
In this paper, based on PEER strong seismic records, concerning the recommendations of FEMAP695 Quantification of Performance and Response Parameters for Building Systems (ATC63 Project) [19], and according to the USGS code, according to the difference of the average shear wave velocity (Vs30) within 30 m below the ground surface, the average shear wave velocity of 360 m/s was used as the boundary.
The type of site ground shaking with shear wave velocity more significant than 360 m/s was selected. The ground vibrations were chosen from six groups of the nearfault (NF) impulse ground motions (GMs), six NF nonimpulse GMs, and six farfield (FF) GMs, each group including one horizontal ground vibration and one vertical ground vibration. Figure 1 depicts the timehistory curves of selected ground movements, such as the Loma Prieta earthquake that struck STG000, the Kocaeli earthquake that struck Yarimca, and the Hector Mine earthquake that struck BRS090. Data on the characteristics of each ground vibration may be found in Tables 1 through 3.
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4. Vibration Analysis of Railroad Bridges under near (Span) Fault Seismic Action
4.1. Project Overview
This paper uses a section of 48 m + 80 m + 48 m stubblefree castinplace prestressed concrete continuous girder bridge (double line) on the highspeed rail as the research background. Among them, the bridge structure schematic diagram is shown in Figure 2.
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The girder adopts the form of a singlebox singlecell section with variable cross section, and the bottom curve of the beam varies in a quadratic curve; the height of the cross section girder varies from 3.85 m to 6.65 m in the middle of the span; the thickness of the web differs from 0.6 m to 0.9 m; the thickness of the top plate varies from 0.4 m to 0.65 m; the thickness curve of the bottom plate varies from 0.4 m to 0.9 m; the typical cross section of the bridge is shown in Figure 2(b). The concrete material used in the girder is C40. The bridge pier is around an endshaped hollow pier with variable cross sections. The pier abutment is made of C35 concrete, and the pile foundation is made of concrete (C25) infill pile with 1 m diameter and 26 m pile length, and the foundation bearing is rigid and does not contact the soil. Standard reinforcement adopts HPB235 and HRB335 steel bars.
4.2. MomentCurvature Analysis of Bridge Pier Section
In this paper, XTRACT software is applied to perform the section bendingcurvature analysis, and the bridge pier section is discretized into various fiber unit models. Then the section momentcurvature calculation is performed. The specific implementation process is as follows: after defining the ground vibration input, the plastic hinge is formed through the centralized plastic model for nonlinear timehistory analysis. Using the FE program to calculate the average axial pressure at the bottom of the pier when the train crosses the bridge, according to the actual cutoff and size, the arrangement position of various types of reinforcement, based on the Mander restrained concrete stressstrain relationship, the section fiber unit is established. Calculate the yield curvature and yield bending moment, ultimate curvature, and ultimate bending moment of the pier section under the action of axial force. Table 4 shows the values of the characteristic points of the equivalent bifurcation momentcurvature relationship of the cross section.

In order to realize the nonlinear analysis of piers and piles, firstly, the parameters of mass density, axial strain, momentcurvature, and torsional and shear modulus of piers and piles are defined, and the above parameters can realize the nonlinearity of piers; when the moment response of piers and piles cross section exceeds the yield moment of cross section, the turning spring will be activated. The nonlinear properties, such as the abovementioned momentcurvature relationship, are assigned to the bridge pier and pile units, and the bending moment and turning angle of each element of the bridge pier are calculated.
4.3. Dynamic Response of the Bridge
The combination of horizontal and vertical earthquake highlevel seismic action is taken following the bridge design instructions and the site classification on which the bridge is built. The peak acceleration of ground vibration is considered to be 0.4 g following GB50112006 “Code for Seismic Design of Railway Engineering” [20]. All earthquakes are specified in the calculation to the fortification earthquake level. The train passes at 350 kilometers per hour across the bridge structure. The peak elasticplastic seismic response of two models of highspeed railroad reinforced concrete continuous girder bridges with and without pilesoil is computed in this article after lengthy computations.
Under rare earthquakes, the dynamic response of the bridge should be calculated by the nonlinear timeresponse analysis method, and the train travels over the bridge structure at 350 km/h. The peak elasticplastic seismic response of two models of highspeed railroad reinforced concrete continuous girder bridge considering pilesoil and not considering pilesoil is calculated, which is shown in Table 5, with the NF impulse/NF nonimpulse/FF typical earthquake Loma Prieta 1989 earthquake, Hector Mine 1999, and Kocaeli Turkey 1999 as examples, and the corresponding timehistory curves for the comparison of the two models considering pilesoil and not considering pile are shown in Figure 3.

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As shown in Table 5 and the timehistory curves in Figure 3, the midspan horizontal and vertical displacements and vertical bending moment response of the bridge under NF ground shaking are more significant than those under FF ground were shaking, which is due to the high amplitude effect of NF ground shaking. Thus the increased energy demand of the bridge under the impact of NF ground shaking should be considered.
4.4. Effect of Ap/Vp on Seismic Response
AP/VP is the ratio of peak lateral acceleration to peak lateral velocity (see equation (1)), whose value has a strong connection with the seismic dynamic response of the structure.where Ap and Vp are the peak lateral acceleration and the velocity, respectively; T_{g} is the remarkable period of ground shaking.
It is shown in Figure 4 that the AP/VP values and dynamic seismic reaction are linked. The dynamic response values of the two bridge structural models that include pilesoil and do not consider pilesoil are decreasing under the action of NF impulsetype ground shaking, NF noimpulse ground shaking, and FF ground shaking, as can be seen from the scattering trend.
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According to the calculated value of the momentcurvature skeleton curve response of the pier, as shown in Figure 5, the top moment of the first unit of the pier bottom is 7.65 × 10^{5} kN m at 350 km/h, which is larger than the yield moment and beyond the yield moment into the elasticplastic phase. The moment of the third element of the pier bottom is 6.38 × 10^{4} kN m, which is smaller than the yield moment; the element is in an elastic state. The study shows that the pier needs more excellent ductility and reinforcement under impulsetype NF earthquakes.
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From the momentangle relationship of the pier bottom unit in the above figure, it can be seen that the pier bottom is in the elasticplastic stage under the action of NF impulsive ground shaking, NF nonimpulsive ground shaking, and farfault ground shaking, and the bridge structure has different responses under different ground shaking excitation. In the case of pulsed NF ground shaking, the moment response of the pier bottom unit under the action of pulsed NF earthquake is larger than the other two types of earthquakes because of its longheld high amplitude pulsed action characteristics.
5. Conclusion
An earthquakeinduced model of the dynamic interaction between trains and bridges is presented in this work. The highspeed trainbridge model is chosen. The finite element software is used to study the continuous girder bridge's selfvibration characteristics, which are then used to conduct the dynamic analysis of the bridge. This model was used to determine the elasticplastic response of the bridge piers to transverse and vertical seismic stresses. That is evident from the findings.(1)Based on the finite element software, two nonlinear analytical models of a largespan continuous girder bridge for highspeed railroad without considering pilesoil interaction (i.e., pier bottom consolidation) and considering pilesoil interaction are established, and the bridge response corresponding to ground shaking is obtained by inputting eighteen groups of ground shaking effects. The structural displacement increases, and the internal force decreases after considering the pilesoil interaction. Hence, the internal structural force decreases, but the extended period will lead to a more significant structural displacement.(2)With the increase of Ap/Vp, the dynamic response values of the two bridge structure models, considering pilesoil and not considering pilesoil, under the action of NF impulsive ground shaking, NF nonimpulsive ground shaking, and FF ground shaking, all show a decreasing trend in the eight taken in this paper. For the 18 ground vibrations studied in this paper, the most pronounced structural response is found for Ap/Vp between 0 and 10.(3)Due to the brief duration of high amplitude pulsed action during pulsed NF ground shaking, substantial displacements of the bridge structure and the bottom unit of the piling are caused. This indicates that structural requirements are increased during pulsed NF seismic activity.
Data Availability
The data used to support the findings of this study are available from the corresponding author upon request.
Conflicts of Interest
The authors declare that there are no conflicts of interest regarding the publication of this paper.
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Copyright © 2022 Yefei Zhou et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.