Research ArticleNumerical Investigation on Dynamic Performance of aBridge-Tunnel Transition Section with a Deep BuriedPile-Plank Structure

Shuanglong Li 1 Limin Wei 12 Xiaobin Chen12 and Qun He12

1School of Civil Engineering Central South University Changsha Hunan 410075 China2National Engineering Laboratory for High Speed Railway Construction Central South University ChangshaHunan 410075 China

Correspondence should be addressed to Limin Wei lmweicsueducn

Received 15 June 2020 Revised 3 September 2020 Accepted 18 September 2020 Published 30 September 2020

Academic Editor Giovanni Garcea

Copyright copy 2020 Shuanglong Li et al)is is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

To address the track irregularity at transition zones between subgrade and rigid structures (bridge tunnel etc) some commontransition approaches such as trapezoid subgrade were adopted in many engineering areas However in regard to a mountainousarea the common transition approaches may not be practicable anymore due to the limitation of the length between subgrade andrigid structures In this paper a new type of bridge-tunnel transition section with a deeply buried pile-plank structure (DBPPS) forshort-distance transition is introduced A three-dimensional finite element model that considers vehicle-track-subgrade couplingvibration is proposed to study the dynamic performances of a DBPPS transition section in the ShanghaindashKunming high-speedrailway With this model that has been validated with measured responses from field tests the dynamic responses and thesmoothness in track stiffness along the transition zone are analyzed In addition the influences of train speed axle load and traindirection on dynamic responses are investigated and the influences of two optimization strategies including varying-length pilesand constant-length piles on the stiffness smoothness of the DBPPS transition section are discussed Results show that thevibration level of the DBPPS transition section is lower than that of the abutment and the tunnel and the additional load caused byvertical track stiffness difference aggravates the vibration at the connections between the DBPPS transition section and theabutment (or tunnel) Furthermore the smoothness in stiffness along the transition zone can be significantly improved by theimprovement strategy with varying-length piles

1 Introduction

Because of twomain factors [1ndash3] such as (i) vertical stiffnessdifference caused by different support conditions (ii) set-tlement deformation difference between subgrade and rigidstructures the subgrade and track components in thetransition zone showed higher degradation rates resulting inmore maintenance costs and worse passenger comfort [4]Canada China and Europe [5ndash8] have published corre-sponding technical specifications to address this problem soas to alleviate the degradation rates of the subgrade and trackcomponents Meanwhile many scholars have studied thedynamic performances of transition sections for differentforms such as subgrade-bridge transitions [2 9ndash12]

subgrade-tunnel transitions [13] subgrade-culvert transi-tions [14 15] and cut-fill transitions on buried culverts [16]

Currently the problems of track irregularity in sub-grade-bridge (or tunnel) transition zones are more prom-inent [17] To achieve a smooth transition of track stiffnessbetween subgrade and bridge or tunnel trapezoidal tran-sition section is recommended in the code China [8] and itis specified that the length of the transition section betweensubgrade and bridge shall not be less than 20m (seeFigure 1(a)) and the length of transition section betweenbridge and tunnel shall not be less than 40m (seeFigure 1(b)) However when it comes to a mountainousarea the actual distance between bridge and tunnel may beeven smaller than the length requirement specified in the

HindawiAdvances in Civil EngineeringVolume 2020 Article ID 8885535 16 pageshttpsdoiorg10115520208885535

code [8] and the trapezoidal transition section is notpracticable anymore As a typical transition section inShanghaindashKunming high-speed railway China the length ofthe transition section between bridge and tunnel is only260m In this case a deeply buried pile-plank structure(DBPPS) subgrade was applied to achieve a short-distancetransition (see Figure 2) [18]

For the pile-plank structure some studies have focusedon its dynamic responses and load transfer behaviors in thegeneral subgrade Su et al [19] carried out a field test on anonburied pile-plank structure (NBPPS) subgrade )eyindicated that the upper load can be transferred to a deeperbearing layer by the NBPPS Zhan et al [20] proposed adesign method of NBPPS subgrade based on the ultimatelimit state and serviceability limit state and studied thedynamic characteristics of the NBPPS subgrade )e resultsare in general agreement with those of Su et al [19] Ma [21]developed a three-dimensional finite element model thatconsiders NBPPS-foundation coupled vibration to analyzethe dynamic characteristics of the NBPPS subgrade but themodel could not reflect the effect of the train-track inter-action In addition Huang et al [22] carried out a centrifugalmodel test to investigate the settlement deformation ofDBPPS subgrade under soft ground conditions and foundthat the settlement deformation mainly occurs during theconstruction period with a settlement ratio that exceeds 80Huang et al [23] carried out excitation tests on a DBPPSsubgrade and found that the DBPPS subgrade exhibits gooddynamic performance

Nevertheless it should be noted that there is no dis-cussion in the literature on the dynamic performances of the

DBPPS subgrade used to transition sections (such as thebridge-tunnel transition section) As a new type of transitionsection its dynamic characteristics and transition perfor-mances are worthy of further study In this study a three-dimensional (3D) finite element (FE) model consideringvehicle-track-subgrade coupling vibration is proposed toinvestigate the dynamic performances of a bridge-tunneltransition zone with a DBPPS in the ShanghaindashKunminghigh-speed railway and the model is validated by measuredresponses from field tests With this model some topicsrelated to the vertical track stiffness distribution dynamicperformance and structural optimization of the DBPPStransition section are discussed )e conclusions of thisstudy may be helpful for the design and optimization of theDBPPS transition section

2 Description of the Case Study

)e present case study is the transition zone in theShanghaindashKunming high-speed railway in China as shownin Figure 2 )e line comprises a double-block ballastlesstrack (China Railway Track System II see Figure 3) usingcontinuously welded U71MnG type rails with a unit weightof 60 kgm concrete sleepers with a spacing of 065m )edesign speed of the line is 350 kmh and the operation speedis 300 kmh

)e length between the abutment and the filled concretelayer is only 260m According to the code [8] the limiteddistance leads to the common transition section mentionedabove that is not practicable To reduce the amount of soilexcavation and engineering cost a DBPPS subgrade is

Bridge

Abutment

L ge 20m

Subgrade surface layer

Subgrade base layer

Embankment

Drainage pipe

Graded gravel

Graded gravel + 5 cement

a

(a)

Step excavation line

Bridge

Abutment

L ge 40m

Subgrade surface layer

Subgrade base layer

Embankment

Drainage pipe

Graded gravel

Graded gravel + 5 cement

a

Tunnel bedrock

Ground surface line

Tunnel

(b)

Figure 1 Schematic diagram of specified length for transition section in the code [8] (a) )e transition section between subgrade andbridge (b) )e transition section between bridge and tunnel

2 Advances in Civil Engineering

adopted to achieve a short-distance transition )e DBPPSconsists of piles and bearing planks which are used tosupport the upper track structure It is set below the sub-grade base layer and divided into two parts by joints (seeFigure 2(b)) )e bearing planks are reinforced concretestructure which is rigidly coupled with the cast-in-situ

bored piles To facilitate description in this case study thesection including the tunnel entrance the DBPPS subgradeand the abutment is named transition zone and the DBPPSsubgrade is named transition section (Figure 2(a))

Two layers with different fillers are laid on the pile-plankstructure as shown in Figure 3)e subgrade base layer with

Ground levelBridge pier

Pile

Bridge deckCRTScentograveTunnel

Abutment

Pile

Layer line

Limestone(P1m)

392mB0

S1S2

S3

T0

Kunming

Subgrade

322m217m

167m

Filled concrete

Bearing plank

Transition section

Transition zone

Shanghai

Water table

Tunnel Bridge

T0 S3 S2 S1 B0

Silty clayQ4

(el+dl)

(a)

13m13m

10m13m

16m23m

5m 5m 5m 5m3m 5m

1m

1m

Bearing plank

Pile

14m

(b)

Figure 2 Schematic profile of the transition zone (a) Longitudinal profile of the transition zone (b) Detailed components of the pile-plankstructure

Advances in Civil Engineering 3

a thickness of 23m was filled with graded gravel +5 ce-ment and the subgrade surface layer with a thickness of04m was filled with graded gravel Hu et al [15] previouslycarried out a series of laboratory tests and field tests toevaluate the particle size strength indices and dynamicproperties of the fillers )e test results showed that thedynamic elastic modulus Poissonrsquos ratio cohesion andinternal friction angle of graded gravel +5 cement were178GPa 030 1326MPa and 458deg respectively Corre-spondingly the values of graded gravel were 158GPa 024016MPa and 395deg respectively)ese parameters would beapplied to the FE model in this study

)e natural foundation of the transition zone consistsmostly of a silty clay layer with a gradually changing depthand limestone layer (Figure 2(a)) To adapt the stiffnessvariations between the transition section and the abutmentan improvement strategy with varying-length piles in thepile-plank structure is adopted Actually the stiffness dif-ference between the transition section and the abutment (orthe tunnel) is inevitable but the keys aspect of this study arethat it contributes to understanding the adverse effectscaused by the stiffness difference on the track and to eval-uating whether the transition section can meet the re-quirements of line smoothness

3 NumericalModel considering Vehicle-Track-Subgrade Interaction

31 Model Establishment To adequately reproduce the be-havior and geometry of the problem in the DBPPS transitionzone a 3D FE model was developed with ABAQUSreg soft-ware [24] using an element mesh as close as was deemednecessary )e connections between the DBPPS subgradeand the abutment or tunnel are important positions forobservation of dynamic responses )erefore a tunnelsection and a bridge section in the FEmodel were establishedto connect the DBPPS subgrade (Figure 4(a)) All modelcomponents were discretized using a three-dimensionalreduced integrated solid element (C3D8R)

To obtain accurate simulation results the mechanicalcontacts between the pile-plank structure and the sur-rounding soil should be defined properly In this studycontact elements were attached at the interfaces between thepile-plank and the surrounding soil (see Figure 4(b)) Aldquohard contactrdquo that considers the pressure-overclosure re-lationship was adopted to simulate the normal behavior ofcontact elements )e contact pressure would occur onlywhen two surfaces were in contact Moreover a ldquopenaltyfunctionrdquo with a friction coefficient of 03 was adopted tosimulate the tangential behavior of contact elements

Linear spring-dashpot elements were attached between therail and the track slab to simulate the fasteners with a spacing of065m (Figure 4(a)) )e vertical stiffness of the fastener was60MNmmand the dampingwas 60 kNsm [25] To reflect thedynamic interaction of wheel-rail a nonlinear elastic contacttheory proposed by Hertz [26] was adopted to describe normalbehavior )e normal force of wheel-rail interaction could beobtained by the following formula [26]

P(t) 1GΔz(t)1113876 1113877

32 (1)

where P(t) is the normal force of wheel-rail interaction G isthe wheel-rail contact constant the value is related to theouter profile of the wheel tread and Δz(t) is the normalelastic compression deformation between wheel and rail Forthe wheel with a worn type tread the constant G could beaddressed by the following [27]

G 386Rminus 0115

times 10minus 8 (2)

where R(m) is the radius of the wheel the value is 046m in thisstudy Subsequently the relationship curve between P(t) andΔz(t) could be obtained as shown in (Figure 4(c)) In thisstudy contact elements were attached at the interfaces betweenthe wheel tread and the rail which took the tread surface as themaster surface and the rail surface as the slave surface(Figure 4(d)) Meanwhile a ldquosoft contactrdquo model that con-sidered the relationship between P(t) and Δz(t) using a

Ground level

Cast-in-situ bored pile

Bearing plank-reinforced concrete

Q4(el+dl)-silty clay

P1m-linestone

U71MnG railTrack slab

Base slabThickness 005mCA layer

Subgrade base layer graded gravel + 5 cement 23m

Wire notch03m

024m

10m

50 m1435m

04mSubgradesurface layer

Figure 3 Transverse profile of the transition section

4 Advances in Civil Engineering

300m

220m

260m

320m

400m

Pier foundation

Abutment Train (two carriages)

Subgrade

Spring-damping boundary elements

Tunnel sectionTransition section

Bridge section

Fastener(spring-dashpot element)

RailTrack slabBase slab

(a)

Silty clay

Plank

Pile

Limestone

Subgrade

(b)

Nor

mal

forc

e (times1

07 N)

00

05

10

15

20

25

30

05 10 15 20 25 30 35 4000Normal compression deformation (mm)

(c)

Carbody

Bogie

Wheelset

RailMasterSurface Slave

Surface

(d)

Primarysuspension

Secondarysuspension

(e)

Figure 4 Finite element model (a) Full model (b) Grid of pile-plank and surrounding soil (c) Relationship between normal force andcompression deformation (d) Contact elements between the wheel tread and the rail (e) Vehicle model

Advances in Civil Engineering 5

ldquoTabularrdquo type in ABAQUS was proposed to simulate thenormal behavior of the wheel-rail interactionWith this settingthe change rate of the wheel-rail contact force would be sloweddown which was beneficial to the convergence of the calcu-lation For the tangential behavior of the wheel-rail interactiona ldquopenalty functionrdquo model with a friction coefficient of 02 wasadopted Considering that the rail was newly laid it wasregarded as an idealized horizontal track in the model

To reflect the coupling vibration inside the vehicle thedoubled suspension system was considered Based on thetheoretical model proposed by Zhai [28 29] for investigatingvertical interactions between railway vehicle and track thevehicle in this model was simplified to be composed ofwheelsets bogies and carbodies Connector elements withelastic-damping properties were adopted to simulate thesuspension systems between the wheelsets and bogies andbetween the bogies and carbody (Figure 4(e)) Consideringthe influence of adjacent wheelsets on wheel-rail interactiontwo carriages of the vehicle were selected in the model )esimulation of train speed was realized by applying the ve-locity (including translation velocity and rotation velocity)to the carbodies bogies and wheelsets along the rails

In general to reduce the reflection of stress waves at themodel boundary the model size should be as large as possiblebut more time and computer resources would be costly Toaddress this problem many scholars introduced an artificialboundary for simulation analysis Currently there are twomainstream modeling methods to minimize the reflected dy-namic wave at the boundary (i) using infinite elements at theboundary and setting viscous property between finite andinfinite elements [30 31] and (ii) introducing an artificialspring-damping boundary to absorb the dynamic wave[12 15 32] In this study the viscoelastic artificial boundarieswere adopted to reproduce the dynamic response using spring-damping elements )ese spring-damping elements were ap-plied in the boundary components in three directions at eachnode )e normal damping coefficient and stiffness coefficientwere determined according to the test results carried out by Huet al [15] Besides the bottom boundary of the model was fixedby a three-degree-of-freedom displacement constraint and thelateral and longitudinal boundaries were constrained by normaldisplacements

In this model the fillers in subgrade layers were modeledas MohrndashCoulomb material to consider the possibility ofplastic yield in the subgrade under heavy axle load (such asmore than 30 t) and the other components were modeled aslinear-elastic material )e parameters of different materialsare shown in Table 1 )e Rayleigh damping was adopted todescribe the damping properties of the components in thetransition zone the mass matrix coefficient α and stiffnessmatrix coefficient β are referenced from [33] To obtainaccurate calculation results the dynamic implicit algorithmwas adopted with a maximum time step of 25ms

32 Model Validation with Field Tests

321 Field Tests To validate the FE model field tests werecarried out )e 891-II type vibration sensors (Figure 5(a))were applied to measure the horizontal and vertical dynamic

responses including acceleration and velocity )e acceler-ation measurement range is plusmn40ms2 with a sensitivity of01V s2m (V is a voltage unit) and the velocity measure-ment range is plusmn05ms with a sensitivity of 300 V sm )evibration signals were collected by an INV3060D type ac-quisition analyzer (Figure 5(b)) With the vibration sensorsdata acquisition analyzer and network module data ac-quisition and wireless transmission test system for automatictrain triggering was established Measuring sections of B0S1 S2 S3 and T0 were established for the attempt to reflectthe variations of dynamic responses along the transitionzone Section B0 was set at the abutment section T0 was setat the tunnel entrance and sections of S1 S2 and S3 were setat the DBPPS subgrade (see Figures 2(a) and 5(c)) )evibration sensors were placed on the center of the subgradeon both sides of the base slab and on the slope of thesubgrade to investigate the transverse distribution of thedynamic response (Figure 5(d))

)e CRH380AM type trains with an axle weight of 150 tand a speed range of 236ndash335 kmh were tested )eschematic profile of CRH380AM type train is depicted inFigure 6 As an example the test results of this type of trainwere selected to verify the reliability of the FEmodel and thevehicle parameters are shown in Table 2

It is worth explaining that the field tests were carried outduring the period of the joint commissioning test whichmeans that the railway line was not officially operated in thatperiod )erefore there is no significant uneven permanentsettlement deformation that occurred in the transition zoneduring the field tests In the FE model the influence ofstiffness variations along the transition zone on dynamicresponse is considered while the influence of permanentsettlement deformation is ignored

322 Comparison between Numerical Results and FieldMeasurement )e test results of the CRH380AM train witha running speed of 300 kmh from a bridge to a tunnel arecompared with the numerical results for validation Figure 7shows the comparison of vertical acceleration and velocitytime-history curves at measuring points B0-3 S2-3 and T0-3 between the numerical results and the field measurement)ese signal curves have been filtered with a cutoff frequencyof 120Hz It can be seen that the amplitude and the curvetrend of the numerical results are in good agreement withthe measured results on the whole

Figure 8 shows the comparison of vertical accelerationand velocity peaks between the numerical results and thefield measurement Considering the randomness of trackvibration caused by the wheelsets the measured peaks hereare the average values of vibration peaks caused by twoadjacent bogies (ie four wheelsets) It also indicates that thegood agreement that is obtained between the numerical andthe experimental vertical acceleration and velocity peaksand the differences of vertical acceleration and velocity peaksbetween the numerical results and the field measurement arewithin 30 in most measuring points However a con-siderable difference is still observed at measuring points ofsection T0 on the base slab such as T0-3 (Figures 7(a) and

6 Advances in Civil Engineering

Table 1 Material properties of the components in the transition zone [15 22 33]

Components or material Youngrsquos modulus E (MPa) Poissonrsquos ratio μ Density ρ (kgm3)Rayleigh dampingα (sminus1) β (s)

Rail 205900 030 7830 0022 0002Track slab 32500 016 2500 0098 0009Base slab 25500 016 2500 0098 0009Graded gravel + 5 cement 1780 030 2100 0229 0021Graded gravel 1580 024 2000 0252 0022Bearing plank 56000 020 2500 0085 0009Cast-in-situ bores pile 38000 020 2500 0098 0008Silty clay 15 030 1930 0262 0024Sand layer 75 030 1950 0270 0023Limestone 600 029 2090 0235 002Abutment 30000 020 2300 0098 0009Bridge deck 22000 018 2550 0098 0009Tunnel filled concrete 20000 020 2400 0098 0009Tunnel bedrock 12000 020 2300 015 0015

(a) (b)

Kunming Shanghai

T0-6

T0-5T0-3

T0-2

T0 S2 S1 B0S3

S2-7S2-6

S2-5S2-3

S2-4S3-4S3-3

S3-2S3-1

S1-4S1-3

B0-5B0-3 B0-4

B0-2S1-2S1-1

S2-2S2-1

Track slab

RailPile

Up-line

Down-line

Base slab

Horizontal acceleration sensorldquoT0-2rdquo ndash ldquoT0rdquo (monitoring section) ldquo2rdquo (monitoring point number)

Vertical acceleration sensorVertical velocity sensor

(c)

S2-5 S2-6

S2-7

S2-3

S2-4

S2-2

S2-1

Up-lineDown-line

Base slab

Track slab

Subgrade surface layer

Subgrade base layer

Bearing plank

Pile

(d)

Figure 5 Measuring equipment and layout (a) 891-II type vibration sensor (b) INV3060D type acquisition analyzer and network module(c) Layout of measuring points in the transition zone (d) Layout of measuring points in the section S2

Advances in Civil Engineering 7

8(a)) )e differences of vertical acceleration peak and ve-locity peak at T0-3 between the numerical results and thefield measurement are approximately 543 and 408respectively )e main reason may be that an aerodynamiceffect [35] is generated at the tunnel entrance when the trainpasses by which aggravates the vibration of track compo-nents at section T0 But the effect is not well simulated in thenumerical model which induces a significant differencebetween the numerical results and the field measurementespecially in section T0

4 Results and Discussion

41 Dynamic Response along the Transition ZoneFigure 9 shows the distribution of vertical acceleration on thebase slab and the vertical track stiffness obtained from theformula proposed by [36] along the transition zone when theCRH380AM trainmoves from the bridge to the tunnel It can beseen that the vertical acceleration of the DBPPS transitionsection is less than that of the abutment and the tunnel sectionCompared with the tunnel section and the abutment the fillersin the DBPPS subgrade have the properties of low stiffness andlarge damping resulting in lower vibration levels in the DBPPSsubgrade Moreover a considerable amplification effect for thevertical acceleration can be observed at the connections(x 102m and x 362m) between the transition section andthe tunnel (or abutment) )e authors consider that the am-plification effect is caused by the abrupt change of wheel-railinteraction caused by the stiffness difference at the connections)is phenomenon was also found by Sanudo [37] and Shahraki[38]

It should be noted that the vertical acceleration of sectionS1 is higher than that of the sections S2 and S3 )is can beexplained that when the train passes through the connectionbetween the abutment and the transition section with anabrupt change stiffness an additional load on the trackcomponents is generated by the train load which aggravates

the vibration at the connection and its adjacent arearesulting in the vertical acceleration of section S1 beinghigher than that of sections S2 and S3

Although the dynamic response at connections is in-tensified due to the amplification effect the maximumvertical vibration acceleration of the transition zone is only023ms2 which is less than 50ms2 specified in the code[8] indicating that the DBPPS transition section exhibitsgood dynamic performance

)e coupling vibration inside the vehicle is considered inthe FE model and the line smoothness of the transition zonecan be evaluated by the dynamic response of the vehicleFigure 10 shows the vertical acceleration distribution of thevehicle which is comprised of an axle bogie and carbody alongthe transition zone Due to the dynamic contact interactionbetween the wheel and the rail the acceleration amplitude ofthe axle changes more dramatically and the vibration fre-quency is higher than that of bogie and carbody Furthermorebecause of the damping effect of the suspension system(connector elements) the acceleration amplitude and vibrationfrequency of the bogie and carbody are greatly reduced

It can be seen from Figure 10(b) that the frequencycomponents of the axle mainly consist of a low frequency of27Hz and a high frequency of 128Hz )e high frequencycomponent is caused by the excitation of fasteners (spring-dashpot elements) which can be verified as follows )espacing (L) of the fasteners is 065m then the excitationperiod (T) is as follows

T Lv (3)

where v is the train speed taken as 300 kmh or 8333ms)e excitation frequency f is determined as follows

f 1T vL 8333065 1282Hz (4)

)e results coincide well with the high frequencycomponent of the axle obtained from the numerical resultsFor the low frequency component it is mainly caused by theinteraction between the axle and the bogie On the whole thevibration frequency of the vehicle obtained from this FEmodel is close to the test results measured by Alves Ribeiro[39] which further indicates that the model is reliable

In addition the vibration response of the vehicle at theconnections (x 102m or x 362m) between the transitionsection and the tunnel (or abutment) is slightly higher than thatat other positions due to the sudden change of wheel-railinteraction caused by the stiffness difference (Figure 10(a)) Toensure the stable operation of the train and the comfort ofpassengers the standard [40] stipulates that the vertical ac-celeration of the carbody with excellent passenger comfort levelshall be less than 245ms2 As can be seen from Figure 10(a)

250 1500 500450

370

250 250 250 250 2501500 1500500

2 carriages simulated in the FE modelLength unit m

Figure 6 Schematic profile of CRH380AM type train

Table 2 Parameters of the vehicle [25 34]

Parameters ValueMass of the carbody 44320 kgMass of the bogie 3136 kgMass of the wheelset 2352 kgPitch inertia of the carbody 520e5 kgm2

Pitch inertia of the bogie 6400 kgm2

Stiffness of primary suspension 1040 kNmStiffness of secondary suspension 400 kNmDamping of primary suspension 40 kNmiddotsmDamping of secondary suspension 60 kNmiddotsm

8 Advances in Civil Engineering

the maximum vertical acceleration of the carbody is 075ms2indicating the train reaches an excellent comfort level and theDBPPS transition section fulfills its purpose in that it provides asmooth stiffness transition

42 Distribution of Vertical Dynamic Stress in the SubgradeTo analyze the vertical dynamic stress distribution in thesubgrade when the train passes by some observation points

at sections of S1 S2 and S3 in the FE model were selected asshown in Figure 11 Observation points of P1 P3 and P5 arelocated on the subgrade surface below the line center andobservation points of P2 P4 and P6 are located on thesubgrade surface directly below the rail Figure 11 shows thetime-history curves of vertical dynamic stress at these ob-servation points It can be seen that the vertical dynamicstress on the subgrade surface at observation points of P2P4 and P6 is 17sim18 higher than that at observation

ndash02

ndash01

0

01

02

03

04

Ver

tical

acce

lera

tion

(ms

2 )

101 103 105 107 10999Time (s)

FieldNum

ndash12

ndash06

0

06

12

18

24

Ver

tical

vel

ocity

(ms

)

101 103 105 107 10999Time (s)

FieldNum

times10ndash3

(a)

ndash04

ndash02

0

02

04

06

08

Ver

tical

acce

lera

tion

(ms

2 )

99 101 103 105 10797Time (s)

FieldNum

ndash1

ndash05

0

05

1

15

2

Ver

tical

vel

ocity

(ms

)

97 99 107103 105101Time (s)

FieldNum

times10ndash3

(b)

ndash06

ndash03

0

03

06

09

12

Ver

tical

acce

lera

tion

(ms

2 )

102 104 106 10810 11Time (s)

FieldNum

ndash2

ndash1

0

1

2

3

4

Ver

tical

vel

ocity

(ms

)

102 104 106 10810 11Time (s)

FieldNum

times10ndash3

(c)

Figure 7 Comparison of time-history curves between the numerical results and the field measurement (a) B0-3 (b) S1-3 (c) T0-3

Advances in Civil Engineering 9

points of P1 P3 and P5 More importantly the verticaldynamic stress of section S1 is higher than that of sections S2and S3 Figure 12 visually shows the vertical dynamic stresscontour of the train passing through section S1 and sectionS3 successively )e maximum vertical dynamic stress ofsection S1 is higher than that of section S3 which verifies theexistence of the additional loadmentioned above It becomesevident that when the train moves from the bridge to the

tunnel the additional load caused by the train load increasesthe dynamic stress on the subgrade surface of section S1which is also the reason why the vibration responses ofsection S1 are higher than that of sections S2 and S3 in thefield measurement (see Figure 8)

43 Influences of Train Speed Axle Weight and Direction onDynamic Response To investigate the influences of differentfactors on the dynamic responses of the transition sectionthree factors including train speed axle weight and runningdirection are selected for sensitivity analysis Figure 13(a)shows the relationship between the vertical acceleration onthe base slab and the train speed With the train speedincreasing from 200 kmh to 400 kmh the vertical accel-eration also increases in which the vertical accelerationincreases from 020ms2 to 044ms2 at measuring point T0-3 and increases from 0007ms2 to 030ms2 at measuringpoint S3-3 If the aerodynamic effect mentioned above is notconsidered in practice even if the train speed reaches400 kmh the vertical acceleration on the base slab is lessthan 50ms2 specified in the code [8] indicating that thetrack structure is still in safe service

In addition with the train speed increasing from200 kmh to 400 kmh the dynamic stress at observation

Ver

tical

acce

lera

tion

(ms

2 )

S1-3 S2-3 S3-3 T0-3B0-3Measuring points

00

01

02

03

04

05

FieldNum

Ver

tical

vel

ocity

(10ndash3

middotms

2 )

S1-3 S2-3 S3-3 T0-3B0-3Measuring points

03

06

09

12

15

18

FieldNum

(a)

Ver

tical

acce

lera

tion

(ms

2 )

S1-4 S2-4 S3-4B0-4Measuring points

000

005

010

015

020

025

FieldNum

Ver

tical

vel

ocity

(10ndash3

middotms

2 )

S1-4 S2-4 S3-4B0-4Measuring points

00

02

04

06

08

10

FieldNum

(b)

Figure 8 Comparison of vertical acceleration and velocity peaks between the numerical results and the field measurement (a) Measuringpoints on the base slab (b) Measuring points on the subgrade center

Ver

tical

stiff

ness

(kN

mm

) BridgeTransition sectionTunnel

70

80

90

100

110

120

Ver

tical

acce

lera

tion

(ms

2 )

010

015

020

025

030

035

4 8 12 16 20 24 28 32 36 400Distance from section T0 x (m)

Vertical stiffnessVertical acceleration

Figure 9 Distribution of the vertical acceleration and trackstiffness along the transition zone

10 Advances in Civil Engineering

points P4 and P6 is almost unchanged as shown inFigure 13(b) Nevertheless the dynamic stress at observationpoint P2 (at section S1) increases slightly from 305 kPa to316 kPa )e authors consider that the increase of dynamicstress at observation point P2 is related to the additionalload and with the increase of train speed the additional loadcaused by train load also increases in the connections with alarge stiffness difference

Figure 14(a) shows the relationship between the verticalacceleration on the base slab and the axle weight With the axleweight increasing from 10 t to 30 t the vertical accelerationincreases approximately exponentially and the vertical dy-namic stress increases approximately linearly (Figure 14(b))Consequently the axle weight is quite sensitive to the dynamicresponses of the DBPPS transition section

To reflect the influence of train direction on the dynamicresponses except for the vertical acceleration at originalobservation points the authors also select the vertical ac-celeration from other observation points at both sides of theconnections (ie x 102m and x 362m) wherex 89m 115m 349m and 375m as shown in Figure 15When the train moves from the tunnel to the bridge the

amplification effect can be observed at x 115m andx 375m while when the train moves from the bridge tothe tunnel the amplification effect occurs near x 89m andx 349m It can be concluded that under different traindirections the position with an amplification effect for vi-bration is also different which is determined by the positionand stiffness difference of the connections

44 Optimization of Pile Length in the Pile-Plank StructureIn the case study described in Section 2 an improvementstrategy with varying-length piles is adopted to achieve abetter transition due to the thickness of soft soil is uneven(Figure 2) Figure 16 shows the vertical displacement onthe pile top for different pile lengths It can be seen that thevertical displacement on the pile top is negatively cor-related with the pile length )e main reason is that thepiles with longer pile length can transfer the upper load toa deeper bearing layer But for shorter piles they bear theupper load together with the shallow soil with a lowerstiffness resulting in higher vertical displacement on thepile top According to the distribution of vertical

Ver

tical

acce

lera

tion

(ms

2 )4 8 12 16 20 24 28 32 36 400

Distance from section T0 x (m)

ndash15

ndash10

ndash5

0

5

10

15

AxleBogieCarbody

(a)

Am

plitu

de (m

s2 )

50 100 150 2000Frequency (Hz)

0

1

2

3

4

5

Axle

Am

plitu

de (m

s2 )

50 100 150 2000Frequency (Hz)

000

008

016

024

032

040

Bogie

Am

plitu

de (m

s2 )

50 100 150 2000Frequency (Hz)

000

006

012

018

024

030

Carbody

(b)

Figure 10 Vertical acceleration distribution of the train along the transition zone (a) Acceleration (b) Frequency

Advances in Civil Engineering 11

displacement for different pile lengths the strategy ofvarying-length piles is conducive to the stiffnesssmoothness in the transition zone

For general soil layers with uniform thickness Li andBian [30] discussed the influences of varying-length pilesand constant-length piles on the vertical track stiffness ina subgrade-bridge transition section and found that thevarying-length piles strategy can effectively smooth thevertical track stiffness transition Nevertheless for theDBPPS transition section under the general conditionsthe necessity of variable pile-length design is still de-batable In this study four comparative cases including

two improvement strategies varying-length piles andconstant-length piles are established to investigate theinfluences of pile length and the properties of soil on theDBPPS transition section as shown in Figure 17 In thesecases it is assumed that the ground consists of twohorizontal soil layers the upper layer is the silty clay layerthe bearing layer is the sand layer or limestone layer with ahigher stiffness than the silty clay layer )e materialproperties are shown in Table 1 and other parameters andwork conditions remain unchanged

Figure 18 shows the vertical track stiffness distributionalong the transition zone under four cases It can be seen thatthe smoothness of vertical track stiffness along the transitionsection can be improved by adopting the strategy of varying-length piles especially when the bearing layer is the sandlayer )e authors consider that when the bearing layer islimestone the bearing mode is similar to end-bearing pilesand the upper load is mainly transferred by piles to thebearing layer Consequently the change in pile length has asmall effect on the upper load transfer But when the bearinglayer is the sand layer with a lower stiffness the bearingmode is similar to friction-bearing piles and the upper loadis mainly shared by piles and the shallow ground )e in-crease of pile length effectively improves the friction resis-tance which indirectly enhances the overall stiffness of theground )erefore the strategy of varying-length piles caneffectively smooth the vertical track stiffness in the DBPPStransition section with a bearing layer of low stiffness

P1P2S1 sectionD

ynam

ic st

ress

(kPa

)10

0

ndash10

ndash20

ndash30

ndash40

ndash5002 04 06 08 1 12 14

Time (s)

P1P2

(a)

P3P4S2 sectionD

ynam

ic st

ress

(kPa

)

10

0

ndash10

ndash20

ndash30

ndash40

ndash5002 04 06 08 1 12 14

Time (s)

P3P4

(b)

P5P6S3 sectionD

ynam

ic st

ress

(kPa

)

10

0

ndash10

ndash20

ndash30

ndash40

ndash5002 04 06 08 1 12 14

Time (s)

P5P6

(c)

Figure 11 Time-history curves of the vertical dynamic stress (a) Observation points of section S1 (b) Observation points of section S2 (c)Observation points of section S3

+261e + 03+000e + 03ndash261e + 03ndash523e + 03ndash784e + 03ndash105e + 04ndash131e + 04ndash156e + 04ndash183e + 04ndash209e + 04ndash235e + 04ndash261e + 04ndash288e + 04ndash312e + 04

Fieldndash1 S33Unit Pa (Avg 75)

Maximum 291 kPa

S3 S1

Maximum 312 kPa

Train direction

x

yz

Figure 12 Vertical stress contour of the train passing throughsection S1 and section S3 successively

12 Advances in Civil Engineering

Changes in longitudinal stresses are more prone toactivate track slab cracking Figure 19(a) shows thelongitudinal stress (S22) contour on the track slab sur-face at a certain time for Case 3 A positive value

represents tensile stress and a negative value representscompressive stress It can be seen that under the trainload significant concentrated tension stresses are

250 300 350 400200Train speed (kmh)

0

01

02

03

04

05V

ertic

al v

ibra

tion

acce

lera

tion

(ms

2 )

B0-3S1-3S2-3

S3-3T0-3

(a)

250 300 350 400200Train speed (kmh)

25

27

29

31

33

35

Ver

tical

dyn

amic

stre

ss (k

Pa)

P2P4P6

(b)

Figure 13 Influences of the train speed on dynamic responses (a) Vertical acceleration (b) Vertical dynamic stress

S3-3T0-3

15 20 25 3010Vehicle axle weight (t)

0

02

04

06

08

Ver

tical

vib

ratio

nac

cele

ratio

n (m

s2 )

B0-3S1-3S2-3

(a)

15 20 25 3010Vehicle axle weight (t)

0

30

60

90

120

Ver

tical

dyn

amic

stre

ss (k

Pa)

P2P4P6

(b)

Figure 14 Influences of the axle weight on dynamic responses (a) Vertical acceleration (b) Vertical dynamic stress

x = 375

x = 349

x = 115

x = 89

B0S1

S2S3

T0

Tunnel Transition section Bridge

3 6 9 12 15 18 21 24 27 30 33 36 39 420Distance from section T0 x (m)

Ver

tical

acce

lera

tion

(ms

2 )

012

015

018

021

024

027

030

From bridge to tunnelFrom tunnel to bridge

Figure 15 Influence of the train direction on dynamic responses

Pile length = 23mPile length = 16m

Pile length = 13mPile length = 10m

ndash003

ndash0025

ndash002

ndash0015

ndash001

ndash0005

0

Ver

tical

disp

lace

men

t (m

m)

090603 12 150Time (s)

Figure 16 Vertical displacement on the pile top for piles of dif-ferent lengths

Advances in Civil Engineering 13

generated on the track slab surface at the positions I andII (Figure 19(a)) with the maximum value of 5374 kPaNevertheless long-term cyclic dynamic load caused bytrain may activate cracks at these positions

Figure 19(b) shows the comparison of maximum tensilestress along the DBPPS transition section in four cases )emaximum tensile stresses at positions I and II are signifi-cantly higher than those at other positions due to the largerstiffness difference When the bearing layer is limestonelayer the maximum tensile stress on the track slab surface at

positions I and II can be reduced by 109 and 78 re-spectively using varying-length piles while when thebearing layer is the sand layer the values can be reduced by278 and 182 respectively indicating that the strategy ofvarying-length piles can significantly reduce the tensile stresson the track slab surface and the lower the stiffness of thebearing layer the more the tensile stress reduces

In general to prevent cracks at the connection betweenabutment and transition section expansion joints or otherimproved measures would be applied to address these

5m 5m 3m 5m 5m

13mSilty clay

Limestone

(a)

5m 5m 3m 5m 5m

16m

23m

13mSilty clay

Limestone

(b)

5m 5m 3m 5m 5m

13mSilty clay

Sand

(c)

5m 5m 3m 5m 5m

16m13m

23m

Silty clay

Sand

(d)

Figure 17 Optimization cases of the pile-plank structure (a) Case 1 (b) Case 2 (c) Case 3 (d) Case 4

60

70

80

90

100

110

Ver

tical

stiff

ness

(kN

mm

)

3510 15 20 25 30 400 5Distance from T0 section (m)

Case 1Case 2

Case 3Case 4

Figure 18 Vertical stiffness along the transition zone for different cases

14 Advances in Civil Engineering

problems in practical engineering From the above resultsthe authors suggest that in addition to the connection be-tween the bridge and the DBPPS transition section theconnection between the tunnel and the DBPPS transitionsection should also be reinforced or treated

5 Conclusions

In this study the authors present a numerical modelingapproach to investigate the dynamic performances of a newtype of bridge-tunnel transition section with a DBPPSwhich can be used as a tool to improve the design andapplication of DBPPS subgrade )e obtained research re-sults of this study lead to the following conclusions

(1) )e vibration level of the DBPPS transition section islower than that of the abutment and the tunnelsection when the train passes by Meanwhile theadditional load caused by vertical track stiffnessdifference can aggravate the vibration at the con-nections and its adjacent areas (such as section S1)between the DBPPS transition section and theabutment (or tunnel) In addition the vertical ac-celeration of the carbody also shows abrupt change atthese connections

(2) With train speed increases the vertical accelerationof the base slab increases and the vertical dynamicstress on the subgrade surface near the connections(such as section S1) also increases With axle weightincreases the vertical acceleration increases ap-proximately exponentially and the vertical dynamicstress increases approximately linearly )e traindirection has a significant influence on the con-nections and its adjacent areas with a large stiffnessdifference

(3) For general soil layers with uniform thickness theimprovement strategy with varying-length piles caneffectively smooth the track stiffness and reduce thetensile stress on the track slab surface at the

connections and the effect is more significant whenthe stiffness of the bearing layer is low

Data Availability

)e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

)e authors declare that they have no conflicts of interestregarding the publication of this paper

Acknowledgments

)is paper reports research developed under financialsupport provided by the Key Project of Science and Tech-nology Research and Development Program of ChinaRailway Corporation (Grant No 2014T003-D) and theNational Natural Science Foundation of China (Grant nos51878671 and 51678575)

References

[1] X Lei ldquoEffects of abrupt changes in track foundation stiffnesson track vibration under moving loadsrdquo Journal of VibrationEngineering vol 19 no 2 pp 195ndash199 2006

[2] A Paixatildeo E Fortunato and R Calccedilada ldquoTransition zones torailway bridges track measurements and numerical model-lingrdquo Engineering Structures vol 80 pp 435ndash443 2014

[3] K K Ang and J Dai ldquoResponse analysis of high-speed railsystem accounting for abrupt change of foundation stiffnessrdquoJournal of Sound and Vibration vol 332 no 12 pp 2954ndash2970 2013

[4] P Holscher and P Meijers Literature Study of Knowledge andExperience of Transition Zones Report of GeoDelft DelftNetherlands 2007

[5] European Committee for Standardisation(CEN) Basis ofstructural design European Committee for Stand-ardisation(CEN) Brussels Belgium 2005

Tunnel section Transition section Abutment

Track slab

Carbody

Rail

I II

Unit Pa+537e + 05+423e + 05+309e + 05+195e + 05+807e + 04ndash335e + 04ndash148e + 05ndash262e + 05ndash376e + 05ndash490e + 05ndash604e + 05ndash718e + 05ndash832e + 05

S S22(Average 75)

(a)

3510 15 20 25 30 400 5Distance from section T0 (m)

ndash200

0

200

400

600

800

Max

imum

tens

ile st

ress

(kPa

)

Case 1Case 2

Case 3Case 4

(b)

Figure 19 Tensile stress distribution for different cases (a) Tensile stress contour of Case 3 at a certain time (b) Maximum tensile stress fordifferent cases

Advances in Civil Engineering 15

[6] )e Swedish Rail Administration Design standard for railwaybridges Standard BVS 58310 )e Swedish Rail Adminis-tration Borlange Sweden 2006

[7] Canadian Standards AssociationndashInternational CanadianHighway Bridge Design Code Canadian Standards Associa-tionndashInternational Toronto Canada 2000

[8] National Railway Administration Code for Design of HighSpeed Railway (TB10621-2014) China Railway PublishingHouse Beijing China 2015

[9] D Li and D Davis ldquoTransition of railroad bridge ap-proachesrdquo Journal of Geotechnical and GeoenvironmentalEngineering vol 131 no 11 pp 1392ndash1398 2005

[10] P Hu C Zhang S J Chen Y Wang W Wang andW H Duan ldquoDynamic responses of bridge-embankmenttransitions in high speed railway field tests and data analysesrdquoEngineering Structures vol 175 pp 565ndash576 2018

[11] Y Shan B Albers and S A Savidis ldquoInfluence of differenttransition zones on the dynamic response of track-subgradesystemsrdquo Computers and Geotechnics vol 48 pp 21ndash28 2013

[12] Y Shan Y Shu and S Zhou ldquoFinite-infinite element coupledanalysis on the influence of material parameters on the dy-namic properties of transition zonesrdquo Construction andBuilding Materials vol 148 no 1 pp 548ndash558 2017

[13] J Ren H Zhao X Li et al ldquoDynamic performances of CRTSIII prefabricated slab track with anti-vibration structure insubgrade-tunnel transition sectionrdquo Journal of SouthwestJiaotong University vol 51 no 6 pp 1047ndash1054 2016

[14] J N Varandas P Holscher and M A G Silva ldquo)ree-di-mensional track-ballast interaction model for the study of aculvert transitionrdquo Soil Dynamics and Earthquake Engi-neering vol 89 pp 116ndash127 2016

[15] P Hu C Zhang S Wen and Y Wang ldquoDynamic responsesof high-speed railway transition zone with various subgradefillingsrdquoComputers and Geotechnics vol 108 pp 17ndash26 2019

[16] J N Varandas A Paixatildeo and E Fortunato ldquoA study on thedynamic train-track interaction over cut-fill transitions onburied culvertsrdquo Computers amp Structures vol 189 no 9pp 49ndash61 2017

[17] R Santildeudo L DellrsquoOlio J A Casado I A Carrascal andS Diego ldquoTrack transitions in railways a reviewrdquo Con-struction and Building Materials vol 112 pp 140ndash157 2016

[18] L Wei C He and Z Yang Comprehensive Test Study Reportof Nanchang West to Yichun East Section of Shanghai-Kunming Railway Passenger Dedicated Line Central SouthUniversity Changsha China 2014

[19] Q SuWWang H Bai et al ldquoBearing capacity mechanism ofnon-embedded pile-plank structure subgraderdquo Journal ofTraffic and Transportation Engineering vol 12 no 1pp 19ndash24 2012

[20] Y-X Zhan H-L Yao and G-L Jiang ldquoDesign method ofpile-slab structure roadbed of ballastless track on soil sub-graderdquo Journal of Central South University vol 20 no 7pp 2072ndash2082 2013

[21] KMa ldquoAnalysis on space vibration performance of pile-plankstructuremdashfoundation soil system under the condition ofhigh-speed trains runningrdquo Journal of the China RailwaySociety vol 35 no 1 pp 93ndash100 2013

[22] L Huang B Wang and S Zhou ldquoCentrifugal model test ofpile-plank subgrade in soft groundrdquo Rock and Soil Mechanicsvol 34 no S1 pp 192ndash196 2013

[23] J Huang Q Su T Liu and X Wang ldquoVibration and long-term performance analysis of pile-plank-supported lowsubgrade of ballastless track under excitation loadsrdquo Shockand Vibration vol 2015 pp 1ndash12 2015

[24] Dassault Systemes Simulia Corp Abaqus Analysis UserrsquosManual Version 612 Dassault Systemes Simulia CorpJohnston Rhode Island USA 2012

[25] C Cheng ldquoStudy on dynamic responses of irregularity bal-lastless track for high-speed railwayrdquo PhD )esis ZhejiangUniversity Zhejiang China 2015

[26] H Hertz ldquoOn the contact of elastic solidsrdquo Journal fur die rneund angewandte Mathematik (Crelles Journal) vol 92no 156 2008

[27] P Ni K Wang W Zhang et al ldquoCalculation method ofwheel-rail contact relationrdquo Journal of Traffic and Trans-portation Engineering vol 04 pp 14ndash17 2006

[28] W Zhai and X Sun ldquoA detailed model for investigatingvertical interaction between railway vehicle and trackrdquo Ve-hicle System Dynamics vol 23 pp 603ndash615 1994

[29] W Zhai Vehicle-track Coupled Dynamics Jeory and Ap-plication Science Press and Springer Nature Singapore PteLtd Berlin Germany 2020

[30] W Li and X Bian ldquoDynamic performance of pile-supportedbridge-embankment transition zones under high-speed trainmoving loadsrdquo Procedia Engineering vol 143 pp 1059ndash10672016

[31] P Ni S Mangalathu G Mei and Y Zhao ldquoPermeable pilesan alternative to improve the performance of driven pilesrdquoComputers and Geotechnics vol 84 pp 78ndash87 2017

[32] K Liu Q Su P Ni C Zhou W Zhao and F Yue ldquoEval-uation on the dynamic performance of bridge approachbackfilled with fibre reinforced lightweight concrete underhigh-speed train loadingrdquo Computers and Geotechnicsvol 104 pp 42ndash53 2018

[33] F Xue and J Zhang ldquoAttenuations of acceleration spectra ofhigh-speed railway embankment subjected to moving loadsrdquoRock and Soil Mechanics vol 36 pp 445ndash451 2015

[34] Y Xuan ldquoSimulation research on the dynamic characteristicsof vehicle-track coupling system on curved track and thevibration response of ballastless track strucure of passengertraffic railwayrdquo PhD )esis China Academy of RailwaySciences Beijing China 2008

[35] P Ricco A Baron and P Molteni ldquoNature of pressure wavesinduced by a high-speed train travelling through a tunnelrdquoJournal of Wind Engineering and Industrial Aerodynamicsvol 95 no 8 pp 781ndash808 2007

[36] C Esveld Modern Railway Track MRT-Productions Zalt-bommel Netherlands 2001

[37] R Santildeudo M Cerrada B Alonso and L dellrsquoOlio ldquoAnalysisof the influence of support positions in transition zones Anumerical analysisrdquo Construction and Building Materialsvol 145 no 1 pp 207ndash217 2017

[38] M Shahraki CWarnakulasooriya and K JWitt ldquoNumericalstudy of transition zone between ballasted and ballastlessrailway trackrdquo Transportation Geotechnics vol 3 pp 58ndash672015

[39] C Alves Ribeiro R Calccedilada and R Delgado ldquoExperimentalassessment of the dynamic behaviour of the train-track systemat a culvert transition zonerdquo Engineering Structures vol 138no 1 pp 215ndash228 2017

[40] Ministry of Railways Institute of StandardMetrology RailwayLocomotive Dynamic Performance Test Identification Methodand Evaluation Standard (TBT2360-1993) Ministry of Rail-ways Institute of Standard Metrology Beijing China 1994

16 Advances in Civil Engineering

adopted to achieve a short-distance transition )e DBPPSconsists of piles and bearing planks which are used tosupport the upper track structure It is set below the sub-grade base layer and divided into two parts by joints (seeFigure 2(b)) )e bearing planks are reinforced concretestructure which is rigidly coupled with the cast-in-situ

bored piles To facilitate description in this case study thesection including the tunnel entrance the DBPPS subgradeand the abutment is named transition zone and the DBPPSsubgrade is named transition section (Figure 2(a))

Two layers with different fillers are laid on the pile-plankstructure as shown in Figure 3)e subgrade base layer with

Ground levelBridge pier

Pile

Bridge deckCRTScentograveTunnel

Abutment

Pile

Layer line

Limestone(P1m)

392mB0

S1S2

S3

T0

Kunming

Subgrade

322m217m

167m

Filled concrete

Bearing plank

Transition section

Transition zone

Shanghai

Water table

Tunnel Bridge

T0 S3 S2 S1 B0

Silty clayQ4

(el+dl)

(a)

13m13m

10m13m

16m23m

5m 5m 5m 5m3m 5m

1m

1m

Bearing plank

Pile

14m

(b)

Figure 2 Schematic profile of the transition zone (a) Longitudinal profile of the transition zone (b) Detailed components of the pile-plankstructure

Advances in Civil Engineering 3

a thickness of 23m was filled with graded gravel +5 ce-ment and the subgrade surface layer with a thickness of04m was filled with graded gravel Hu et al [15] previouslycarried out a series of laboratory tests and field tests toevaluate the particle size strength indices and dynamicproperties of the fillers )e test results showed that thedynamic elastic modulus Poissonrsquos ratio cohesion andinternal friction angle of graded gravel +5 cement were178GPa 030 1326MPa and 458deg respectively Corre-spondingly the values of graded gravel were 158GPa 024016MPa and 395deg respectively)ese parameters would beapplied to the FE model in this study

)e natural foundation of the transition zone consistsmostly of a silty clay layer with a gradually changing depthand limestone layer (Figure 2(a)) To adapt the stiffnessvariations between the transition section and the abutmentan improvement strategy with varying-length piles in thepile-plank structure is adopted Actually the stiffness dif-ference between the transition section and the abutment (orthe tunnel) is inevitable but the keys aspect of this study arethat it contributes to understanding the adverse effectscaused by the stiffness difference on the track and to eval-uating whether the transition section can meet the re-quirements of line smoothness

3 NumericalModel considering Vehicle-Track-Subgrade Interaction

31 Model Establishment To adequately reproduce the be-havior and geometry of the problem in the DBPPS transitionzone a 3D FE model was developed with ABAQUSreg soft-ware [24] using an element mesh as close as was deemednecessary )e connections between the DBPPS subgradeand the abutment or tunnel are important positions forobservation of dynamic responses )erefore a tunnelsection and a bridge section in the FEmodel were establishedto connect the DBPPS subgrade (Figure 4(a)) All modelcomponents were discretized using a three-dimensionalreduced integrated solid element (C3D8R)

To obtain accurate simulation results the mechanicalcontacts between the pile-plank structure and the sur-rounding soil should be defined properly In this studycontact elements were attached at the interfaces between thepile-plank and the surrounding soil (see Figure 4(b)) Aldquohard contactrdquo that considers the pressure-overclosure re-lationship was adopted to simulate the normal behavior ofcontact elements )e contact pressure would occur onlywhen two surfaces were in contact Moreover a ldquopenaltyfunctionrdquo with a friction coefficient of 03 was adopted tosimulate the tangential behavior of contact elements

Linear spring-dashpot elements were attached between therail and the track slab to simulate the fasteners with a spacing of065m (Figure 4(a)) )e vertical stiffness of the fastener was60MNmmand the dampingwas 60 kNsm [25] To reflect thedynamic interaction of wheel-rail a nonlinear elastic contacttheory proposed by Hertz [26] was adopted to describe normalbehavior )e normal force of wheel-rail interaction could beobtained by the following formula [26]

P(t) 1GΔz(t)1113876 1113877

32 (1)

where P(t) is the normal force of wheel-rail interaction G isthe wheel-rail contact constant the value is related to theouter profile of the wheel tread and Δz(t) is the normalelastic compression deformation between wheel and rail Forthe wheel with a worn type tread the constant G could beaddressed by the following [27]

G 386Rminus 0115

times 10minus 8 (2)

where R(m) is the radius of the wheel the value is 046m in thisstudy Subsequently the relationship curve between P(t) andΔz(t) could be obtained as shown in (Figure 4(c)) In thisstudy contact elements were attached at the interfaces betweenthe wheel tread and the rail which took the tread surface as themaster surface and the rail surface as the slave surface(Figure 4(d)) Meanwhile a ldquosoft contactrdquo model that con-sidered the relationship between P(t) and Δz(t) using a

Ground level

Cast-in-situ bored pile

Bearing plank-reinforced concrete

Q4(el+dl)-silty clay

P1m-linestone

U71MnG railTrack slab

Base slabThickness 005mCA layer

Subgrade base layer graded gravel + 5 cement 23m

Wire notch03m

024m

10m

50 m1435m

04mSubgradesurface layer

Figure 3 Transverse profile of the transition section

4 Advances in Civil Engineering

300m

220m

260m

320m

400m

Pier foundation

Abutment Train (two carriages)

Subgrade

Spring-damping boundary elements

Tunnel sectionTransition section

Bridge section

Fastener(spring-dashpot element)

RailTrack slabBase slab

(a)

Silty clay

Plank

Pile

Limestone

Subgrade

(b)

Nor

mal

forc

e (times1

07 N)

00

05

10

15

20

25

30

05 10 15 20 25 30 35 4000Normal compression deformation (mm)

(c)

Carbody

Bogie

Wheelset

RailMasterSurface Slave

Surface

(d)

Primarysuspension

Secondarysuspension

(e)

Figure 4 Finite element model (a) Full model (b) Grid of pile-plank and surrounding soil (c) Relationship between normal force andcompression deformation (d) Contact elements between the wheel tread and the rail (e) Vehicle model

Advances in Civil Engineering 5

ldquoTabularrdquo type in ABAQUS was proposed to simulate thenormal behavior of the wheel-rail interactionWith this settingthe change rate of the wheel-rail contact force would be sloweddown which was beneficial to the convergence of the calcu-lation For the tangential behavior of the wheel-rail interactiona ldquopenalty functionrdquo model with a friction coefficient of 02 wasadopted Considering that the rail was newly laid it wasregarded as an idealized horizontal track in the model

To reflect the coupling vibration inside the vehicle thedoubled suspension system was considered Based on thetheoretical model proposed by Zhai [28 29] for investigatingvertical interactions between railway vehicle and track thevehicle in this model was simplified to be composed ofwheelsets bogies and carbodies Connector elements withelastic-damping properties were adopted to simulate thesuspension systems between the wheelsets and bogies andbetween the bogies and carbody (Figure 4(e)) Consideringthe influence of adjacent wheelsets on wheel-rail interactiontwo carriages of the vehicle were selected in the model )esimulation of train speed was realized by applying the ve-locity (including translation velocity and rotation velocity)to the carbodies bogies and wheelsets along the rails

In general to reduce the reflection of stress waves at themodel boundary the model size should be as large as possiblebut more time and computer resources would be costly Toaddress this problem many scholars introduced an artificialboundary for simulation analysis Currently there are twomainstream modeling methods to minimize the reflected dy-namic wave at the boundary (i) using infinite elements at theboundary and setting viscous property between finite andinfinite elements [30 31] and (ii) introducing an artificialspring-damping boundary to absorb the dynamic wave[12 15 32] In this study the viscoelastic artificial boundarieswere adopted to reproduce the dynamic response using spring-damping elements )ese spring-damping elements were ap-plied in the boundary components in three directions at eachnode )e normal damping coefficient and stiffness coefficientwere determined according to the test results carried out by Huet al [15] Besides the bottom boundary of the model was fixedby a three-degree-of-freedom displacement constraint and thelateral and longitudinal boundaries were constrained by normaldisplacements

In this model the fillers in subgrade layers were modeledas MohrndashCoulomb material to consider the possibility ofplastic yield in the subgrade under heavy axle load (such asmore than 30 t) and the other components were modeled aslinear-elastic material )e parameters of different materialsare shown in Table 1 )e Rayleigh damping was adopted todescribe the damping properties of the components in thetransition zone the mass matrix coefficient α and stiffnessmatrix coefficient β are referenced from [33] To obtainaccurate calculation results the dynamic implicit algorithmwas adopted with a maximum time step of 25ms

32 Model Validation with Field Tests

321 Field Tests To validate the FE model field tests werecarried out )e 891-II type vibration sensors (Figure 5(a))were applied to measure the horizontal and vertical dynamic

responses including acceleration and velocity )e acceler-ation measurement range is plusmn40ms2 with a sensitivity of01V s2m (V is a voltage unit) and the velocity measure-ment range is plusmn05ms with a sensitivity of 300 V sm )evibration signals were collected by an INV3060D type ac-quisition analyzer (Figure 5(b)) With the vibration sensorsdata acquisition analyzer and network module data ac-quisition and wireless transmission test system for automatictrain triggering was established Measuring sections of B0S1 S2 S3 and T0 were established for the attempt to reflectthe variations of dynamic responses along the transitionzone Section B0 was set at the abutment section T0 was setat the tunnel entrance and sections of S1 S2 and S3 were setat the DBPPS subgrade (see Figures 2(a) and 5(c)) )evibration sensors were placed on the center of the subgradeon both sides of the base slab and on the slope of thesubgrade to investigate the transverse distribution of thedynamic response (Figure 5(d))

)e CRH380AM type trains with an axle weight of 150 tand a speed range of 236ndash335 kmh were tested )eschematic profile of CRH380AM type train is depicted inFigure 6 As an example the test results of this type of trainwere selected to verify the reliability of the FEmodel and thevehicle parameters are shown in Table 2

It is worth explaining that the field tests were carried outduring the period of the joint commissioning test whichmeans that the railway line was not officially operated in thatperiod )erefore there is no significant uneven permanentsettlement deformation that occurred in the transition zoneduring the field tests In the FE model the influence ofstiffness variations along the transition zone on dynamicresponse is considered while the influence of permanentsettlement deformation is ignored

322 Comparison between Numerical Results and FieldMeasurement )e test results of the CRH380AM train witha running speed of 300 kmh from a bridge to a tunnel arecompared with the numerical results for validation Figure 7shows the comparison of vertical acceleration and velocitytime-history curves at measuring points B0-3 S2-3 and T0-3 between the numerical results and the field measurement)ese signal curves have been filtered with a cutoff frequencyof 120Hz It can be seen that the amplitude and the curvetrend of the numerical results are in good agreement withthe measured results on the whole

Figure 8 shows the comparison of vertical accelerationand velocity peaks between the numerical results and thefield measurement Considering the randomness of trackvibration caused by the wheelsets the measured peaks hereare the average values of vibration peaks caused by twoadjacent bogies (ie four wheelsets) It also indicates that thegood agreement that is obtained between the numerical andthe experimental vertical acceleration and velocity peaksand the differences of vertical acceleration and velocity peaksbetween the numerical results and the field measurement arewithin 30 in most measuring points However a con-siderable difference is still observed at measuring points ofsection T0 on the base slab such as T0-3 (Figures 7(a) and

6 Advances in Civil Engineering

Table 1 Material properties of the components in the transition zone [15 22 33]

Components or material Youngrsquos modulus E (MPa) Poissonrsquos ratio μ Density ρ (kgm3)Rayleigh dampingα (sminus1) β (s)

Rail 205900 030 7830 0022 0002Track slab 32500 016 2500 0098 0009Base slab 25500 016 2500 0098 0009Graded gravel + 5 cement 1780 030 2100 0229 0021Graded gravel 1580 024 2000 0252 0022Bearing plank 56000 020 2500 0085 0009Cast-in-situ bores pile 38000 020 2500 0098 0008Silty clay 15 030 1930 0262 0024Sand layer 75 030 1950 0270 0023Limestone 600 029 2090 0235 002Abutment 30000 020 2300 0098 0009Bridge deck 22000 018 2550 0098 0009Tunnel filled concrete 20000 020 2400 0098 0009Tunnel bedrock 12000 020 2300 015 0015

(a) (b)

Kunming Shanghai

T0-6

T0-5T0-3

T0-2

T0 S2 S1 B0S3

S2-7S2-6

S2-5S2-3

S2-4S3-4S3-3

S3-2S3-1

S1-4S1-3

B0-5B0-3 B0-4

B0-2S1-2S1-1

S2-2S2-1

Track slab

RailPile

Up-line

Down-line

Base slab

Horizontal acceleration sensorldquoT0-2rdquo ndash ldquoT0rdquo (monitoring section) ldquo2rdquo (monitoring point number)

Vertical acceleration sensorVertical velocity sensor

(c)

S2-5 S2-6

S2-7

S2-3

S2-4

S2-2

S2-1

Up-lineDown-line

Base slab

Track slab

Subgrade surface layer

Subgrade base layer

Bearing plank

Pile

(d)

Figure 5 Measuring equipment and layout (a) 891-II type vibration sensor (b) INV3060D type acquisition analyzer and network module(c) Layout of measuring points in the transition zone (d) Layout of measuring points in the section S2

Advances in Civil Engineering 7

8(a)) )e differences of vertical acceleration peak and ve-locity peak at T0-3 between the numerical results and thefield measurement are approximately 543 and 408respectively )e main reason may be that an aerodynamiceffect [35] is generated at the tunnel entrance when the trainpasses by which aggravates the vibration of track compo-nents at section T0 But the effect is not well simulated in thenumerical model which induces a significant differencebetween the numerical results and the field measurementespecially in section T0

4 Results and Discussion

41 Dynamic Response along the Transition ZoneFigure 9 shows the distribution of vertical acceleration on thebase slab and the vertical track stiffness obtained from theformula proposed by [36] along the transition zone when theCRH380AM trainmoves from the bridge to the tunnel It can beseen that the vertical acceleration of the DBPPS transitionsection is less than that of the abutment and the tunnel sectionCompared with the tunnel section and the abutment the fillersin the DBPPS subgrade have the properties of low stiffness andlarge damping resulting in lower vibration levels in the DBPPSsubgrade Moreover a considerable amplification effect for thevertical acceleration can be observed at the connections(x 102m and x 362m) between the transition section andthe tunnel (or abutment) )e authors consider that the am-plification effect is caused by the abrupt change of wheel-railinteraction caused by the stiffness difference at the connections)is phenomenon was also found by Sanudo [37] and Shahraki[38]

It should be noted that the vertical acceleration of sectionS1 is higher than that of the sections S2 and S3 )is can beexplained that when the train passes through the connectionbetween the abutment and the transition section with anabrupt change stiffness an additional load on the trackcomponents is generated by the train load which aggravates

the vibration at the connection and its adjacent arearesulting in the vertical acceleration of section S1 beinghigher than that of sections S2 and S3

Although the dynamic response at connections is in-tensified due to the amplification effect the maximumvertical vibration acceleration of the transition zone is only023ms2 which is less than 50ms2 specified in the code[8] indicating that the DBPPS transition section exhibitsgood dynamic performance

)e coupling vibration inside the vehicle is considered inthe FE model and the line smoothness of the transition zonecan be evaluated by the dynamic response of the vehicleFigure 10 shows the vertical acceleration distribution of thevehicle which is comprised of an axle bogie and carbody alongthe transition zone Due to the dynamic contact interactionbetween the wheel and the rail the acceleration amplitude ofthe axle changes more dramatically and the vibration fre-quency is higher than that of bogie and carbody Furthermorebecause of the damping effect of the suspension system(connector elements) the acceleration amplitude and vibrationfrequency of the bogie and carbody are greatly reduced

It can be seen from Figure 10(b) that the frequencycomponents of the axle mainly consist of a low frequency of27Hz and a high frequency of 128Hz )e high frequencycomponent is caused by the excitation of fasteners (spring-dashpot elements) which can be verified as follows )espacing (L) of the fasteners is 065m then the excitationperiod (T) is as follows

T Lv (3)

where v is the train speed taken as 300 kmh or 8333ms)e excitation frequency f is determined as follows

f 1T vL 8333065 1282Hz (4)

)e results coincide well with the high frequencycomponent of the axle obtained from the numerical resultsFor the low frequency component it is mainly caused by theinteraction between the axle and the bogie On the whole thevibration frequency of the vehicle obtained from this FEmodel is close to the test results measured by Alves Ribeiro[39] which further indicates that the model is reliable

In addition the vibration response of the vehicle at theconnections (x 102m or x 362m) between the transitionsection and the tunnel (or abutment) is slightly higher than thatat other positions due to the sudden change of wheel-railinteraction caused by the stiffness difference (Figure 10(a)) Toensure the stable operation of the train and the comfort ofpassengers the standard [40] stipulates that the vertical ac-celeration of the carbody with excellent passenger comfort levelshall be less than 245ms2 As can be seen from Figure 10(a)

250 1500 500450

370

250 250 250 250 2501500 1500500

2 carriages simulated in the FE modelLength unit m

Figure 6 Schematic profile of CRH380AM type train

Table 2 Parameters of the vehicle [25 34]

Parameters ValueMass of the carbody 44320 kgMass of the bogie 3136 kgMass of the wheelset 2352 kgPitch inertia of the carbody 520e5 kgm2

Pitch inertia of the bogie 6400 kgm2

Stiffness of primary suspension 1040 kNmStiffness of secondary suspension 400 kNmDamping of primary suspension 40 kNmiddotsmDamping of secondary suspension 60 kNmiddotsm

8 Advances in Civil Engineering

the maximum vertical acceleration of the carbody is 075ms2indicating the train reaches an excellent comfort level and theDBPPS transition section fulfills its purpose in that it provides asmooth stiffness transition

42 Distribution of Vertical Dynamic Stress in the SubgradeTo analyze the vertical dynamic stress distribution in thesubgrade when the train passes by some observation points

at sections of S1 S2 and S3 in the FE model were selected asshown in Figure 11 Observation points of P1 P3 and P5 arelocated on the subgrade surface below the line center andobservation points of P2 P4 and P6 are located on thesubgrade surface directly below the rail Figure 11 shows thetime-history curves of vertical dynamic stress at these ob-servation points It can be seen that the vertical dynamicstress on the subgrade surface at observation points of P2P4 and P6 is 17sim18 higher than that at observation

ndash02

ndash01

0

01

02

03

04

Ver

tical

acce

lera

tion

(ms

2 )

101 103 105 107 10999Time (s)

FieldNum

ndash12

ndash06

0

06

12

18

24

Ver

tical

vel

ocity

(ms

)

101 103 105 107 10999Time (s)

FieldNum

times10ndash3

(a)

ndash04

ndash02

0

02

04

06

08

Ver

tical

acce

lera

tion

(ms

2 )

99 101 103 105 10797Time (s)

FieldNum

ndash1

ndash05

0

05

1

15

2

Ver

tical

vel

ocity

(ms

)

97 99 107103 105101Time (s)

FieldNum

times10ndash3

(b)

ndash06

ndash03

0

03

06

09

12

Ver

tical

acce

lera

tion

(ms

2 )

102 104 106 10810 11Time (s)

FieldNum

ndash2

ndash1

0

1

2

3

4

Ver

tical

vel

ocity

(ms

)

102 104 106 10810 11Time (s)

FieldNum

times10ndash3

(c)

Figure 7 Comparison of time-history curves between the numerical results and the field measurement (a) B0-3 (b) S1-3 (c) T0-3

Advances in Civil Engineering 9

points of P1 P3 and P5 More importantly the verticaldynamic stress of section S1 is higher than that of sections S2and S3 Figure 12 visually shows the vertical dynamic stresscontour of the train passing through section S1 and sectionS3 successively )e maximum vertical dynamic stress ofsection S1 is higher than that of section S3 which verifies theexistence of the additional loadmentioned above It becomesevident that when the train moves from the bridge to the

tunnel the additional load caused by the train load increasesthe dynamic stress on the subgrade surface of section S1which is also the reason why the vibration responses ofsection S1 are higher than that of sections S2 and S3 in thefield measurement (see Figure 8)

43 Influences of Train Speed Axle Weight and Direction onDynamic Response To investigate the influences of differentfactors on the dynamic responses of the transition sectionthree factors including train speed axle weight and runningdirection are selected for sensitivity analysis Figure 13(a)shows the relationship between the vertical acceleration onthe base slab and the train speed With the train speedincreasing from 200 kmh to 400 kmh the vertical accel-eration also increases in which the vertical accelerationincreases from 020ms2 to 044ms2 at measuring point T0-3 and increases from 0007ms2 to 030ms2 at measuringpoint S3-3 If the aerodynamic effect mentioned above is notconsidered in practice even if the train speed reaches400 kmh the vertical acceleration on the base slab is lessthan 50ms2 specified in the code [8] indicating that thetrack structure is still in safe service

In addition with the train speed increasing from200 kmh to 400 kmh the dynamic stress at observation

Ver

tical

acce

lera

tion

(ms

2 )

S1-3 S2-3 S3-3 T0-3B0-3Measuring points

00

01

02

03

04

05

FieldNum

Ver

tical

vel

ocity

(10ndash3

middotms

2 )

S1-3 S2-3 S3-3 T0-3B0-3Measuring points

03

06

09

12

15

18

FieldNum

(a)

Ver

tical

acce

lera

tion

(ms

2 )

S1-4 S2-4 S3-4B0-4Measuring points

000

005

010

015

020

025

FieldNum

Ver

tical

vel

ocity

(10ndash3

middotms

2 )

S1-4 S2-4 S3-4B0-4Measuring points

00

02

04

06

08

10

FieldNum

(b)

Figure 8 Comparison of vertical acceleration and velocity peaks between the numerical results and the field measurement (a) Measuringpoints on the base slab (b) Measuring points on the subgrade center

Ver

tical

stiff

ness

(kN

mm

) BridgeTransition sectionTunnel

70

80

90

100

110

120

Ver

tical

acce

lera

tion

(ms

2 )

010

015

020

025

030

035

4 8 12 16 20 24 28 32 36 400Distance from section T0 x (m)

Vertical stiffnessVertical acceleration

Figure 9 Distribution of the vertical acceleration and trackstiffness along the transition zone

10 Advances in Civil Engineering

points P4 and P6 is almost unchanged as shown inFigure 13(b) Nevertheless the dynamic stress at observationpoint P2 (at section S1) increases slightly from 305 kPa to316 kPa )e authors consider that the increase of dynamicstress at observation point P2 is related to the additionalload and with the increase of train speed the additional loadcaused by train load also increases in the connections with alarge stiffness difference

Figure 14(a) shows the relationship between the verticalacceleration on the base slab and the axle weight With the axleweight increasing from 10 t to 30 t the vertical accelerationincreases approximately exponentially and the vertical dy-namic stress increases approximately linearly (Figure 14(b))Consequently the axle weight is quite sensitive to the dynamicresponses of the DBPPS transition section

To reflect the influence of train direction on the dynamicresponses except for the vertical acceleration at originalobservation points the authors also select the vertical ac-celeration from other observation points at both sides of theconnections (ie x 102m and x 362m) wherex 89m 115m 349m and 375m as shown in Figure 15When the train moves from the tunnel to the bridge the

amplification effect can be observed at x 115m andx 375m while when the train moves from the bridge tothe tunnel the amplification effect occurs near x 89m andx 349m It can be concluded that under different traindirections the position with an amplification effect for vi-bration is also different which is determined by the positionand stiffness difference of the connections

44 Optimization of Pile Length in the Pile-Plank StructureIn the case study described in Section 2 an improvementstrategy with varying-length piles is adopted to achieve abetter transition due to the thickness of soft soil is uneven(Figure 2) Figure 16 shows the vertical displacement onthe pile top for different pile lengths It can be seen that thevertical displacement on the pile top is negatively cor-related with the pile length )e main reason is that thepiles with longer pile length can transfer the upper load toa deeper bearing layer But for shorter piles they bear theupper load together with the shallow soil with a lowerstiffness resulting in higher vertical displacement on thepile top According to the distribution of vertical

Ver

tical

acce

lera

tion

(ms

2 )4 8 12 16 20 24 28 32 36 400

Distance from section T0 x (m)

ndash15

ndash10

ndash5

0

5

10

15

AxleBogieCarbody

(a)

Am

plitu

de (m

s2 )

50 100 150 2000Frequency (Hz)

0

1

2

3

4

5

Axle

Am

plitu

de (m

s2 )

50 100 150 2000Frequency (Hz)

000

008

016

024

032

040

Bogie

Am

plitu

de (m

s2 )

50 100 150 2000Frequency (Hz)

000

006

012

018

024

030

Carbody

(b)

Figure 10 Vertical acceleration distribution of the train along the transition zone (a) Acceleration (b) Frequency

Advances in Civil Engineering 11

displacement for different pile lengths the strategy ofvarying-length piles is conducive to the stiffnesssmoothness in the transition zone

For general soil layers with uniform thickness Li andBian [30] discussed the influences of varying-length pilesand constant-length piles on the vertical track stiffness ina subgrade-bridge transition section and found that thevarying-length piles strategy can effectively smooth thevertical track stiffness transition Nevertheless for theDBPPS transition section under the general conditionsthe necessity of variable pile-length design is still de-batable In this study four comparative cases including

two improvement strategies varying-length piles andconstant-length piles are established to investigate theinfluences of pile length and the properties of soil on theDBPPS transition section as shown in Figure 17 In thesecases it is assumed that the ground consists of twohorizontal soil layers the upper layer is the silty clay layerthe bearing layer is the sand layer or limestone layer with ahigher stiffness than the silty clay layer )e materialproperties are shown in Table 1 and other parameters andwork conditions remain unchanged

Figure 18 shows the vertical track stiffness distributionalong the transition zone under four cases It can be seen thatthe smoothness of vertical track stiffness along the transitionsection can be improved by adopting the strategy of varying-length piles especially when the bearing layer is the sandlayer )e authors consider that when the bearing layer islimestone the bearing mode is similar to end-bearing pilesand the upper load is mainly transferred by piles to thebearing layer Consequently the change in pile length has asmall effect on the upper load transfer But when the bearinglayer is the sand layer with a lower stiffness the bearingmode is similar to friction-bearing piles and the upper loadis mainly shared by piles and the shallow ground )e in-crease of pile length effectively improves the friction resis-tance which indirectly enhances the overall stiffness of theground )erefore the strategy of varying-length piles caneffectively smooth the vertical track stiffness in the DBPPStransition section with a bearing layer of low stiffness

P1P2S1 sectionD

ynam

ic st

ress

(kPa

)10

0

ndash10

ndash20

ndash30

ndash40

ndash5002 04 06 08 1 12 14

Time (s)

P1P2

(a)

P3P4S2 sectionD

ynam

ic st

ress

(kPa

)

10

0

ndash10

ndash20

ndash30

ndash40

ndash5002 04 06 08 1 12 14

Time (s)

P3P4

(b)

P5P6S3 sectionD

ynam

ic st

ress

(kPa

)

10

0

ndash10

ndash20

ndash30

ndash40

ndash5002 04 06 08 1 12 14

Time (s)

P5P6

(c)

Figure 11 Time-history curves of the vertical dynamic stress (a) Observation points of section S1 (b) Observation points of section S2 (c)Observation points of section S3

+261e + 03+000e + 03ndash261e + 03ndash523e + 03ndash784e + 03ndash105e + 04ndash131e + 04ndash156e + 04ndash183e + 04ndash209e + 04ndash235e + 04ndash261e + 04ndash288e + 04ndash312e + 04

Fieldndash1 S33Unit Pa (Avg 75)

Maximum 291 kPa

S3 S1

Maximum 312 kPa

Train direction

x

yz

Figure 12 Vertical stress contour of the train passing throughsection S1 and section S3 successively

12 Advances in Civil Engineering

Changes in longitudinal stresses are more prone toactivate track slab cracking Figure 19(a) shows thelongitudinal stress (S22) contour on the track slab sur-face at a certain time for Case 3 A positive value

represents tensile stress and a negative value representscompressive stress It can be seen that under the trainload significant concentrated tension stresses are

250 300 350 400200Train speed (kmh)

0

01

02

03

04

05V

ertic

al v

ibra

tion

acce

lera

tion

(ms

2 )

B0-3S1-3S2-3

S3-3T0-3

(a)

250 300 350 400200Train speed (kmh)

25

27

29

31

33

35

Ver

tical

dyn

amic

stre

ss (k

Pa)

P2P4P6

(b)

Figure 13 Influences of the train speed on dynamic responses (a) Vertical acceleration (b) Vertical dynamic stress

S3-3T0-3

15 20 25 3010Vehicle axle weight (t)

0

02

04

06

08

Ver

tical

vib

ratio

nac

cele

ratio

n (m

s2 )

B0-3S1-3S2-3

(a)

15 20 25 3010Vehicle axle weight (t)

0

30

60

90

120

Ver

tical

dyn

amic

stre

ss (k

Pa)

P2P4P6

(b)

Figure 14 Influences of the axle weight on dynamic responses (a) Vertical acceleration (b) Vertical dynamic stress

x = 375

x = 349

x = 115

x = 89

B0S1

S2S3

T0

Tunnel Transition section Bridge

3 6 9 12 15 18 21 24 27 30 33 36 39 420Distance from section T0 x (m)

Ver

tical

acce

lera

tion

(ms

2 )

012

015

018

021

024

027

030

From bridge to tunnelFrom tunnel to bridge

Figure 15 Influence of the train direction on dynamic responses

Pile length = 23mPile length = 16m

Pile length = 13mPile length = 10m

ndash003

ndash0025

ndash002

ndash0015

ndash001

ndash0005

0

Ver

tical

disp

lace

men

t (m

m)

090603 12 150Time (s)

Figure 16 Vertical displacement on the pile top for piles of dif-ferent lengths

Advances in Civil Engineering 13

generated on the track slab surface at the positions I andII (Figure 19(a)) with the maximum value of 5374 kPaNevertheless long-term cyclic dynamic load caused bytrain may activate cracks at these positions

Figure 19(b) shows the comparison of maximum tensilestress along the DBPPS transition section in four cases )emaximum tensile stresses at positions I and II are signifi-cantly higher than those at other positions due to the largerstiffness difference When the bearing layer is limestonelayer the maximum tensile stress on the track slab surface at

positions I and II can be reduced by 109 and 78 re-spectively using varying-length piles while when thebearing layer is the sand layer the values can be reduced by278 and 182 respectively indicating that the strategy ofvarying-length piles can significantly reduce the tensile stresson the track slab surface and the lower the stiffness of thebearing layer the more the tensile stress reduces

In general to prevent cracks at the connection betweenabutment and transition section expansion joints or otherimproved measures would be applied to address these

5m 5m 3m 5m 5m

13mSilty clay

Limestone

(a)

5m 5m 3m 5m 5m

16m

23m

13mSilty clay

Limestone

(b)

5m 5m 3m 5m 5m

13mSilty clay

Sand

(c)

5m 5m 3m 5m 5m

16m13m

23m

Silty clay

Sand

(d)

Figure 17 Optimization cases of the pile-plank structure (a) Case 1 (b) Case 2 (c) Case 3 (d) Case 4

60

70

80

90

100

110

Ver

tical

stiff

ness

(kN

mm

)

3510 15 20 25 30 400 5Distance from T0 section (m)

Case 1Case 2

Case 3Case 4

Figure 18 Vertical stiffness along the transition zone for different cases

14 Advances in Civil Engineering

problems in practical engineering From the above resultsthe authors suggest that in addition to the connection be-tween the bridge and the DBPPS transition section theconnection between the tunnel and the DBPPS transitionsection should also be reinforced or treated

5 Conclusions

In this study the authors present a numerical modelingapproach to investigate the dynamic performances of a newtype of bridge-tunnel transition section with a DBPPSwhich can be used as a tool to improve the design andapplication of DBPPS subgrade )e obtained research re-sults of this study lead to the following conclusions

(1) )e vibration level of the DBPPS transition section islower than that of the abutment and the tunnelsection when the train passes by Meanwhile theadditional load caused by vertical track stiffnessdifference can aggravate the vibration at the con-nections and its adjacent areas (such as section S1)between the DBPPS transition section and theabutment (or tunnel) In addition the vertical ac-celeration of the carbody also shows abrupt change atthese connections

(2) With train speed increases the vertical accelerationof the base slab increases and the vertical dynamicstress on the subgrade surface near the connections(such as section S1) also increases With axle weightincreases the vertical acceleration increases ap-proximately exponentially and the vertical dynamicstress increases approximately linearly )e traindirection has a significant influence on the con-nections and its adjacent areas with a large stiffnessdifference

(3) For general soil layers with uniform thickness theimprovement strategy with varying-length piles caneffectively smooth the track stiffness and reduce thetensile stress on the track slab surface at the

connections and the effect is more significant whenthe stiffness of the bearing layer is low

Data Availability

)e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

)e authors declare that they have no conflicts of interestregarding the publication of this paper

Acknowledgments

)is paper reports research developed under financialsupport provided by the Key Project of Science and Tech-nology Research and Development Program of ChinaRailway Corporation (Grant No 2014T003-D) and theNational Natural Science Foundation of China (Grant nos51878671 and 51678575)

References

[1] X Lei ldquoEffects of abrupt changes in track foundation stiffnesson track vibration under moving loadsrdquo Journal of VibrationEngineering vol 19 no 2 pp 195ndash199 2006

[2] A Paixatildeo E Fortunato and R Calccedilada ldquoTransition zones torailway bridges track measurements and numerical model-lingrdquo Engineering Structures vol 80 pp 435ndash443 2014

[3] K K Ang and J Dai ldquoResponse analysis of high-speed railsystem accounting for abrupt change of foundation stiffnessrdquoJournal of Sound and Vibration vol 332 no 12 pp 2954ndash2970 2013

[4] P Holscher and P Meijers Literature Study of Knowledge andExperience of Transition Zones Report of GeoDelft DelftNetherlands 2007

[5] European Committee for Standardisation(CEN) Basis ofstructural design European Committee for Stand-ardisation(CEN) Brussels Belgium 2005

Tunnel section Transition section Abutment

Track slab

Carbody

Rail

I II

Unit Pa+537e + 05+423e + 05+309e + 05+195e + 05+807e + 04ndash335e + 04ndash148e + 05ndash262e + 05ndash376e + 05ndash490e + 05ndash604e + 05ndash718e + 05ndash832e + 05

S S22(Average 75)

(a)

3510 15 20 25 30 400 5Distance from section T0 (m)

ndash200

0

200

400

600

800

Max

imum

tens

ile st

ress

(kPa

)

Case 1Case 2

Case 3Case 4

(b)

Figure 19 Tensile stress distribution for different cases (a) Tensile stress contour of Case 3 at a certain time (b) Maximum tensile stress fordifferent cases

Advances in Civil Engineering 15

[6] )e Swedish Rail Administration Design standard for railwaybridges Standard BVS 58310 )e Swedish Rail Adminis-tration Borlange Sweden 2006

[7] Canadian Standards AssociationndashInternational CanadianHighway Bridge Design Code Canadian Standards Associa-tionndashInternational Toronto Canada 2000

[8] National Railway Administration Code for Design of HighSpeed Railway (TB10621-2014) China Railway PublishingHouse Beijing China 2015

[9] D Li and D Davis ldquoTransition of railroad bridge ap-proachesrdquo Journal of Geotechnical and GeoenvironmentalEngineering vol 131 no 11 pp 1392ndash1398 2005

[10] P Hu C Zhang S J Chen Y Wang W Wang andW H Duan ldquoDynamic responses of bridge-embankmenttransitions in high speed railway field tests and data analysesrdquoEngineering Structures vol 175 pp 565ndash576 2018

[11] Y Shan B Albers and S A Savidis ldquoInfluence of differenttransition zones on the dynamic response of track-subgradesystemsrdquo Computers and Geotechnics vol 48 pp 21ndash28 2013

[12] Y Shan Y Shu and S Zhou ldquoFinite-infinite element coupledanalysis on the influence of material parameters on the dy-namic properties of transition zonesrdquo Construction andBuilding Materials vol 148 no 1 pp 548ndash558 2017

[13] J Ren H Zhao X Li et al ldquoDynamic performances of CRTSIII prefabricated slab track with anti-vibration structure insubgrade-tunnel transition sectionrdquo Journal of SouthwestJiaotong University vol 51 no 6 pp 1047ndash1054 2016

[14] J N Varandas P Holscher and M A G Silva ldquo)ree-di-mensional track-ballast interaction model for the study of aculvert transitionrdquo Soil Dynamics and Earthquake Engi-neering vol 89 pp 116ndash127 2016

[15] P Hu C Zhang S Wen and Y Wang ldquoDynamic responsesof high-speed railway transition zone with various subgradefillingsrdquoComputers and Geotechnics vol 108 pp 17ndash26 2019

[16] J N Varandas A Paixatildeo and E Fortunato ldquoA study on thedynamic train-track interaction over cut-fill transitions onburied culvertsrdquo Computers amp Structures vol 189 no 9pp 49ndash61 2017

[17] R Santildeudo L DellrsquoOlio J A Casado I A Carrascal andS Diego ldquoTrack transitions in railways a reviewrdquo Con-struction and Building Materials vol 112 pp 140ndash157 2016

[18] L Wei C He and Z Yang Comprehensive Test Study Reportof Nanchang West to Yichun East Section of Shanghai-Kunming Railway Passenger Dedicated Line Central SouthUniversity Changsha China 2014

[19] Q SuWWang H Bai et al ldquoBearing capacity mechanism ofnon-embedded pile-plank structure subgraderdquo Journal ofTraffic and Transportation Engineering vol 12 no 1pp 19ndash24 2012

[20] Y-X Zhan H-L Yao and G-L Jiang ldquoDesign method ofpile-slab structure roadbed of ballastless track on soil sub-graderdquo Journal of Central South University vol 20 no 7pp 2072ndash2082 2013

[21] KMa ldquoAnalysis on space vibration performance of pile-plankstructuremdashfoundation soil system under the condition ofhigh-speed trains runningrdquo Journal of the China RailwaySociety vol 35 no 1 pp 93ndash100 2013

[22] L Huang B Wang and S Zhou ldquoCentrifugal model test ofpile-plank subgrade in soft groundrdquo Rock and Soil Mechanicsvol 34 no S1 pp 192ndash196 2013

[23] J Huang Q Su T Liu and X Wang ldquoVibration and long-term performance analysis of pile-plank-supported lowsubgrade of ballastless track under excitation loadsrdquo Shockand Vibration vol 2015 pp 1ndash12 2015

[24] Dassault Systemes Simulia Corp Abaqus Analysis UserrsquosManual Version 612 Dassault Systemes Simulia CorpJohnston Rhode Island USA 2012

[25] C Cheng ldquoStudy on dynamic responses of irregularity bal-lastless track for high-speed railwayrdquo PhD )esis ZhejiangUniversity Zhejiang China 2015

[26] H Hertz ldquoOn the contact of elastic solidsrdquo Journal fur die rneund angewandte Mathematik (Crelles Journal) vol 92no 156 2008

[27] P Ni K Wang W Zhang et al ldquoCalculation method ofwheel-rail contact relationrdquo Journal of Traffic and Trans-portation Engineering vol 04 pp 14ndash17 2006

[28] W Zhai and X Sun ldquoA detailed model for investigatingvertical interaction between railway vehicle and trackrdquo Ve-hicle System Dynamics vol 23 pp 603ndash615 1994

[29] W Zhai Vehicle-track Coupled Dynamics Jeory and Ap-plication Science Press and Springer Nature Singapore PteLtd Berlin Germany 2020

[30] W Li and X Bian ldquoDynamic performance of pile-supportedbridge-embankment transition zones under high-speed trainmoving loadsrdquo Procedia Engineering vol 143 pp 1059ndash10672016

[31] P Ni S Mangalathu G Mei and Y Zhao ldquoPermeable pilesan alternative to improve the performance of driven pilesrdquoComputers and Geotechnics vol 84 pp 78ndash87 2017

[32] K Liu Q Su P Ni C Zhou W Zhao and F Yue ldquoEval-uation on the dynamic performance of bridge approachbackfilled with fibre reinforced lightweight concrete underhigh-speed train loadingrdquo Computers and Geotechnicsvol 104 pp 42ndash53 2018

[33] F Xue and J Zhang ldquoAttenuations of acceleration spectra ofhigh-speed railway embankment subjected to moving loadsrdquoRock and Soil Mechanics vol 36 pp 445ndash451 2015

[34] Y Xuan ldquoSimulation research on the dynamic characteristicsof vehicle-track coupling system on curved track and thevibration response of ballastless track strucure of passengertraffic railwayrdquo PhD )esis China Academy of RailwaySciences Beijing China 2008

[35] P Ricco A Baron and P Molteni ldquoNature of pressure wavesinduced by a high-speed train travelling through a tunnelrdquoJournal of Wind Engineering and Industrial Aerodynamicsvol 95 no 8 pp 781ndash808 2007

[36] C Esveld Modern Railway Track MRT-Productions Zalt-bommel Netherlands 2001

[37] R Santildeudo M Cerrada B Alonso and L dellrsquoOlio ldquoAnalysisof the influence of support positions in transition zones Anumerical analysisrdquo Construction and Building Materialsvol 145 no 1 pp 207ndash217 2017

[38] M Shahraki CWarnakulasooriya and K JWitt ldquoNumericalstudy of transition zone between ballasted and ballastlessrailway trackrdquo Transportation Geotechnics vol 3 pp 58ndash672015

[39] C Alves Ribeiro R Calccedilada and R Delgado ldquoExperimentalassessment of the dynamic behaviour of the train-track systemat a culvert transition zonerdquo Engineering Structures vol 138no 1 pp 215ndash228 2017

[40] Ministry of Railways Institute of StandardMetrology RailwayLocomotive Dynamic Performance Test Identification Methodand Evaluation Standard (TBT2360-1993) Ministry of Rail-ways Institute of Standard Metrology Beijing China 1994

16 Advances in Civil Engineering

a thickness of 23m was filled with graded gravel +5 ce-ment and the subgrade surface layer with a thickness of04m was filled with graded gravel Hu et al [15] previouslycarried out a series of laboratory tests and field tests toevaluate the particle size strength indices and dynamicproperties of the fillers )e test results showed that thedynamic elastic modulus Poissonrsquos ratio cohesion andinternal friction angle of graded gravel +5 cement were178GPa 030 1326MPa and 458deg respectively Corre-spondingly the values of graded gravel were 158GPa 024016MPa and 395deg respectively)ese parameters would beapplied to the FE model in this study

)e natural foundation of the transition zone consistsmostly of a silty clay layer with a gradually changing depthand limestone layer (Figure 2(a)) To adapt the stiffnessvariations between the transition section and the abutmentan improvement strategy with varying-length piles in thepile-plank structure is adopted Actually the stiffness dif-ference between the transition section and the abutment (orthe tunnel) is inevitable but the keys aspect of this study arethat it contributes to understanding the adverse effectscaused by the stiffness difference on the track and to eval-uating whether the transition section can meet the re-quirements of line smoothness

3 NumericalModel considering Vehicle-Track-Subgrade Interaction

31 Model Establishment To adequately reproduce the be-havior and geometry of the problem in the DBPPS transitionzone a 3D FE model was developed with ABAQUSreg soft-ware [24] using an element mesh as close as was deemednecessary )e connections between the DBPPS subgradeand the abutment or tunnel are important positions forobservation of dynamic responses )erefore a tunnelsection and a bridge section in the FEmodel were establishedto connect the DBPPS subgrade (Figure 4(a)) All modelcomponents were discretized using a three-dimensionalreduced integrated solid element (C3D8R)

To obtain accurate simulation results the mechanicalcontacts between the pile-plank structure and the sur-rounding soil should be defined properly In this studycontact elements were attached at the interfaces between thepile-plank and the surrounding soil (see Figure 4(b)) Aldquohard contactrdquo that considers the pressure-overclosure re-lationship was adopted to simulate the normal behavior ofcontact elements )e contact pressure would occur onlywhen two surfaces were in contact Moreover a ldquopenaltyfunctionrdquo with a friction coefficient of 03 was adopted tosimulate the tangential behavior of contact elements

Linear spring-dashpot elements were attached between therail and the track slab to simulate the fasteners with a spacing of065m (Figure 4(a)) )e vertical stiffness of the fastener was60MNmmand the dampingwas 60 kNsm [25] To reflect thedynamic interaction of wheel-rail a nonlinear elastic contacttheory proposed by Hertz [26] was adopted to describe normalbehavior )e normal force of wheel-rail interaction could beobtained by the following formula [26]

P(t) 1GΔz(t)1113876 1113877

32 (1)

where P(t) is the normal force of wheel-rail interaction G isthe wheel-rail contact constant the value is related to theouter profile of the wheel tread and Δz(t) is the normalelastic compression deformation between wheel and rail Forthe wheel with a worn type tread the constant G could beaddressed by the following [27]

G 386Rminus 0115

times 10minus 8 (2)

where R(m) is the radius of the wheel the value is 046m in thisstudy Subsequently the relationship curve between P(t) andΔz(t) could be obtained as shown in (Figure 4(c)) In thisstudy contact elements were attached at the interfaces betweenthe wheel tread and the rail which took the tread surface as themaster surface and the rail surface as the slave surface(Figure 4(d)) Meanwhile a ldquosoft contactrdquo model that con-sidered the relationship between P(t) and Δz(t) using a

Ground level

Cast-in-situ bored pile

Bearing plank-reinforced concrete

Q4(el+dl)-silty clay

P1m-linestone

U71MnG railTrack slab

Base slabThickness 005mCA layer

Subgrade base layer graded gravel + 5 cement 23m

Wire notch03m

024m

10m

50 m1435m

04mSubgradesurface layer

Figure 3 Transverse profile of the transition section

4 Advances in Civil Engineering

300m

220m

260m

320m

400m

Pier foundation

Abutment Train (two carriages)

Subgrade

Spring-damping boundary elements

Tunnel sectionTransition section

Bridge section

Fastener(spring-dashpot element)

RailTrack slabBase slab

(a)

Silty clay

Plank

Pile

Limestone

Subgrade

(b)

Nor

mal

forc

e (times1

07 N)

00

05

10

15

20

25

30

05 10 15 20 25 30 35 4000Normal compression deformation (mm)

(c)

Carbody

Bogie

Wheelset

RailMasterSurface Slave

Surface

(d)

Primarysuspension

Secondarysuspension

(e)

Figure 4 Finite element model (a) Full model (b) Grid of pile-plank and surrounding soil (c) Relationship between normal force andcompression deformation (d) Contact elements between the wheel tread and the rail (e) Vehicle model

Advances in Civil Engineering 5

ldquoTabularrdquo type in ABAQUS was proposed to simulate thenormal behavior of the wheel-rail interactionWith this settingthe change rate of the wheel-rail contact force would be sloweddown which was beneficial to the convergence of the calcu-lation For the tangential behavior of the wheel-rail interactiona ldquopenalty functionrdquo model with a friction coefficient of 02 wasadopted Considering that the rail was newly laid it wasregarded as an idealized horizontal track in the model

To reflect the coupling vibration inside the vehicle thedoubled suspension system was considered Based on thetheoretical model proposed by Zhai [28 29] for investigatingvertical interactions between railway vehicle and track thevehicle in this model was simplified to be composed ofwheelsets bogies and carbodies Connector elements withelastic-damping properties were adopted to simulate thesuspension systems between the wheelsets and bogies andbetween the bogies and carbody (Figure 4(e)) Consideringthe influence of adjacent wheelsets on wheel-rail interactiontwo carriages of the vehicle were selected in the model )esimulation of train speed was realized by applying the ve-locity (including translation velocity and rotation velocity)to the carbodies bogies and wheelsets along the rails

In general to reduce the reflection of stress waves at themodel boundary the model size should be as large as possiblebut more time and computer resources would be costly Toaddress this problem many scholars introduced an artificialboundary for simulation analysis Currently there are twomainstream modeling methods to minimize the reflected dy-namic wave at the boundary (i) using infinite elements at theboundary and setting viscous property between finite andinfinite elements [30 31] and (ii) introducing an artificialspring-damping boundary to absorb the dynamic wave[12 15 32] In this study the viscoelastic artificial boundarieswere adopted to reproduce the dynamic response using spring-damping elements )ese spring-damping elements were ap-plied in the boundary components in three directions at eachnode )e normal damping coefficient and stiffness coefficientwere determined according to the test results carried out by Huet al [15] Besides the bottom boundary of the model was fixedby a three-degree-of-freedom displacement constraint and thelateral and longitudinal boundaries were constrained by normaldisplacements

In this model the fillers in subgrade layers were modeledas MohrndashCoulomb material to consider the possibility ofplastic yield in the subgrade under heavy axle load (such asmore than 30 t) and the other components were modeled aslinear-elastic material )e parameters of different materialsare shown in Table 1 )e Rayleigh damping was adopted todescribe the damping properties of the components in thetransition zone the mass matrix coefficient α and stiffnessmatrix coefficient β are referenced from [33] To obtainaccurate calculation results the dynamic implicit algorithmwas adopted with a maximum time step of 25ms

32 Model Validation with Field Tests

321 Field Tests To validate the FE model field tests werecarried out )e 891-II type vibration sensors (Figure 5(a))were applied to measure the horizontal and vertical dynamic

responses including acceleration and velocity )e acceler-ation measurement range is plusmn40ms2 with a sensitivity of01V s2m (V is a voltage unit) and the velocity measure-ment range is plusmn05ms with a sensitivity of 300 V sm )evibration signals were collected by an INV3060D type ac-quisition analyzer (Figure 5(b)) With the vibration sensorsdata acquisition analyzer and network module data ac-quisition and wireless transmission test system for automatictrain triggering was established Measuring sections of B0S1 S2 S3 and T0 were established for the attempt to reflectthe variations of dynamic responses along the transitionzone Section B0 was set at the abutment section T0 was setat the tunnel entrance and sections of S1 S2 and S3 were setat the DBPPS subgrade (see Figures 2(a) and 5(c)) )evibration sensors were placed on the center of the subgradeon both sides of the base slab and on the slope of thesubgrade to investigate the transverse distribution of thedynamic response (Figure 5(d))

)e CRH380AM type trains with an axle weight of 150 tand a speed range of 236ndash335 kmh were tested )eschematic profile of CRH380AM type train is depicted inFigure 6 As an example the test results of this type of trainwere selected to verify the reliability of the FEmodel and thevehicle parameters are shown in Table 2

It is worth explaining that the field tests were carried outduring the period of the joint commissioning test whichmeans that the railway line was not officially operated in thatperiod )erefore there is no significant uneven permanentsettlement deformation that occurred in the transition zoneduring the field tests In the FE model the influence ofstiffness variations along the transition zone on dynamicresponse is considered while the influence of permanentsettlement deformation is ignored

322 Comparison between Numerical Results and FieldMeasurement )e test results of the CRH380AM train witha running speed of 300 kmh from a bridge to a tunnel arecompared with the numerical results for validation Figure 7shows the comparison of vertical acceleration and velocitytime-history curves at measuring points B0-3 S2-3 and T0-3 between the numerical results and the field measurement)ese signal curves have been filtered with a cutoff frequencyof 120Hz It can be seen that the amplitude and the curvetrend of the numerical results are in good agreement withthe measured results on the whole

Figure 8 shows the comparison of vertical accelerationand velocity peaks between the numerical results and thefield measurement Considering the randomness of trackvibration caused by the wheelsets the measured peaks hereare the average values of vibration peaks caused by twoadjacent bogies (ie four wheelsets) It also indicates that thegood agreement that is obtained between the numerical andthe experimental vertical acceleration and velocity peaksand the differences of vertical acceleration and velocity peaksbetween the numerical results and the field measurement arewithin 30 in most measuring points However a con-siderable difference is still observed at measuring points ofsection T0 on the base slab such as T0-3 (Figures 7(a) and

6 Advances in Civil Engineering

Table 1 Material properties of the components in the transition zone [15 22 33]

Components or material Youngrsquos modulus E (MPa) Poissonrsquos ratio μ Density ρ (kgm3)Rayleigh dampingα (sminus1) β (s)

Rail 205900 030 7830 0022 0002Track slab 32500 016 2500 0098 0009Base slab 25500 016 2500 0098 0009Graded gravel + 5 cement 1780 030 2100 0229 0021Graded gravel 1580 024 2000 0252 0022Bearing plank 56000 020 2500 0085 0009Cast-in-situ bores pile 38000 020 2500 0098 0008Silty clay 15 030 1930 0262 0024Sand layer 75 030 1950 0270 0023Limestone 600 029 2090 0235 002Abutment 30000 020 2300 0098 0009Bridge deck 22000 018 2550 0098 0009Tunnel filled concrete 20000 020 2400 0098 0009Tunnel bedrock 12000 020 2300 015 0015

(a) (b)

Kunming Shanghai

T0-6

T0-5T0-3

T0-2

T0 S2 S1 B0S3

S2-7S2-6

S2-5S2-3

S2-4S3-4S3-3

S3-2S3-1

S1-4S1-3

B0-5B0-3 B0-4

B0-2S1-2S1-1

S2-2S2-1

Track slab

RailPile

Up-line

Down-line

Base slab

Horizontal acceleration sensorldquoT0-2rdquo ndash ldquoT0rdquo (monitoring section) ldquo2rdquo (monitoring point number)

Vertical acceleration sensorVertical velocity sensor

(c)

S2-5 S2-6

S2-7

S2-3

S2-4

S2-2

S2-1

Up-lineDown-line

Base slab

Track slab

Subgrade surface layer

Subgrade base layer

Bearing plank

Pile

(d)

Figure 5 Measuring equipment and layout (a) 891-II type vibration sensor (b) INV3060D type acquisition analyzer and network module(c) Layout of measuring points in the transition zone (d) Layout of measuring points in the section S2

Advances in Civil Engineering 7

8(a)) )e differences of vertical acceleration peak and ve-locity peak at T0-3 between the numerical results and thefield measurement are approximately 543 and 408respectively )e main reason may be that an aerodynamiceffect [35] is generated at the tunnel entrance when the trainpasses by which aggravates the vibration of track compo-nents at section T0 But the effect is not well simulated in thenumerical model which induces a significant differencebetween the numerical results and the field measurementespecially in section T0

4 Results and Discussion

41 Dynamic Response along the Transition ZoneFigure 9 shows the distribution of vertical acceleration on thebase slab and the vertical track stiffness obtained from theformula proposed by [36] along the transition zone when theCRH380AM trainmoves from the bridge to the tunnel It can beseen that the vertical acceleration of the DBPPS transitionsection is less than that of the abutment and the tunnel sectionCompared with the tunnel section and the abutment the fillersin the DBPPS subgrade have the properties of low stiffness andlarge damping resulting in lower vibration levels in the DBPPSsubgrade Moreover a considerable amplification effect for thevertical acceleration can be observed at the connections(x 102m and x 362m) between the transition section andthe tunnel (or abutment) )e authors consider that the am-plification effect is caused by the abrupt change of wheel-railinteraction caused by the stiffness difference at the connections)is phenomenon was also found by Sanudo [37] and Shahraki[38]

It should be noted that the vertical acceleration of sectionS1 is higher than that of the sections S2 and S3 )is can beexplained that when the train passes through the connectionbetween the abutment and the transition section with anabrupt change stiffness an additional load on the trackcomponents is generated by the train load which aggravates

the vibration at the connection and its adjacent arearesulting in the vertical acceleration of section S1 beinghigher than that of sections S2 and S3

Although the dynamic response at connections is in-tensified due to the amplification effect the maximumvertical vibration acceleration of the transition zone is only023ms2 which is less than 50ms2 specified in the code[8] indicating that the DBPPS transition section exhibitsgood dynamic performance

)e coupling vibration inside the vehicle is considered inthe FE model and the line smoothness of the transition zonecan be evaluated by the dynamic response of the vehicleFigure 10 shows the vertical acceleration distribution of thevehicle which is comprised of an axle bogie and carbody alongthe transition zone Due to the dynamic contact interactionbetween the wheel and the rail the acceleration amplitude ofthe axle changes more dramatically and the vibration fre-quency is higher than that of bogie and carbody Furthermorebecause of the damping effect of the suspension system(connector elements) the acceleration amplitude and vibrationfrequency of the bogie and carbody are greatly reduced

It can be seen from Figure 10(b) that the frequencycomponents of the axle mainly consist of a low frequency of27Hz and a high frequency of 128Hz )e high frequencycomponent is caused by the excitation of fasteners (spring-dashpot elements) which can be verified as follows )espacing (L) of the fasteners is 065m then the excitationperiod (T) is as follows

T Lv (3)

where v is the train speed taken as 300 kmh or 8333ms)e excitation frequency f is determined as follows

f 1T vL 8333065 1282Hz (4)

)e results coincide well with the high frequencycomponent of the axle obtained from the numerical resultsFor the low frequency component it is mainly caused by theinteraction between the axle and the bogie On the whole thevibration frequency of the vehicle obtained from this FEmodel is close to the test results measured by Alves Ribeiro[39] which further indicates that the model is reliable

In addition the vibration response of the vehicle at theconnections (x 102m or x 362m) between the transitionsection and the tunnel (or abutment) is slightly higher than thatat other positions due to the sudden change of wheel-railinteraction caused by the stiffness difference (Figure 10(a)) Toensure the stable operation of the train and the comfort ofpassengers the standard [40] stipulates that the vertical ac-celeration of the carbody with excellent passenger comfort levelshall be less than 245ms2 As can be seen from Figure 10(a)

250 1500 500450

370

250 250 250 250 2501500 1500500

2 carriages simulated in the FE modelLength unit m

Figure 6 Schematic profile of CRH380AM type train

Table 2 Parameters of the vehicle [25 34]

Parameters ValueMass of the carbody 44320 kgMass of the bogie 3136 kgMass of the wheelset 2352 kgPitch inertia of the carbody 520e5 kgm2

Pitch inertia of the bogie 6400 kgm2

Stiffness of primary suspension 1040 kNmStiffness of secondary suspension 400 kNmDamping of primary suspension 40 kNmiddotsmDamping of secondary suspension 60 kNmiddotsm

8 Advances in Civil Engineering

the maximum vertical acceleration of the carbody is 075ms2indicating the train reaches an excellent comfort level and theDBPPS transition section fulfills its purpose in that it provides asmooth stiffness transition

42 Distribution of Vertical Dynamic Stress in the SubgradeTo analyze the vertical dynamic stress distribution in thesubgrade when the train passes by some observation points

at sections of S1 S2 and S3 in the FE model were selected asshown in Figure 11 Observation points of P1 P3 and P5 arelocated on the subgrade surface below the line center andobservation points of P2 P4 and P6 are located on thesubgrade surface directly below the rail Figure 11 shows thetime-history curves of vertical dynamic stress at these ob-servation points It can be seen that the vertical dynamicstress on the subgrade surface at observation points of P2P4 and P6 is 17sim18 higher than that at observation

ndash02

ndash01

0

01

02

03

04

Ver

tical

acce

lera

tion

(ms

2 )

101 103 105 107 10999Time (s)

FieldNum

ndash12

ndash06

0

06

12

18

24

Ver

tical

vel

ocity

(ms

)

101 103 105 107 10999Time (s)

FieldNum

times10ndash3

(a)

ndash04

ndash02

0

02

04

06

08

Ver

tical

acce

lera

tion

(ms

2 )

99 101 103 105 10797Time (s)

FieldNum

ndash1

ndash05

0

05

1

15

2

Ver

tical

vel

ocity

(ms

)

97 99 107103 105101Time (s)

FieldNum

times10ndash3

(b)

ndash06

ndash03

0

03

06

09

12

Ver

tical

acce

lera

tion

(ms

2 )

102 104 106 10810 11Time (s)

FieldNum

ndash2

ndash1

0

1

2

3

4

Ver

tical

vel

ocity

(ms

)

102 104 106 10810 11Time (s)

FieldNum

times10ndash3

(c)

Figure 7 Comparison of time-history curves between the numerical results and the field measurement (a) B0-3 (b) S1-3 (c) T0-3

Advances in Civil Engineering 9

points of P1 P3 and P5 More importantly the verticaldynamic stress of section S1 is higher than that of sections S2and S3 Figure 12 visually shows the vertical dynamic stresscontour of the train passing through section S1 and sectionS3 successively )e maximum vertical dynamic stress ofsection S1 is higher than that of section S3 which verifies theexistence of the additional loadmentioned above It becomesevident that when the train moves from the bridge to the

tunnel the additional load caused by the train load increasesthe dynamic stress on the subgrade surface of section S1which is also the reason why the vibration responses ofsection S1 are higher than that of sections S2 and S3 in thefield measurement (see Figure 8)

43 Influences of Train Speed Axle Weight and Direction onDynamic Response To investigate the influences of differentfactors on the dynamic responses of the transition sectionthree factors including train speed axle weight and runningdirection are selected for sensitivity analysis Figure 13(a)shows the relationship between the vertical acceleration onthe base slab and the train speed With the train speedincreasing from 200 kmh to 400 kmh the vertical accel-eration also increases in which the vertical accelerationincreases from 020ms2 to 044ms2 at measuring point T0-3 and increases from 0007ms2 to 030ms2 at measuringpoint S3-3 If the aerodynamic effect mentioned above is notconsidered in practice even if the train speed reaches400 kmh the vertical acceleration on the base slab is lessthan 50ms2 specified in the code [8] indicating that thetrack structure is still in safe service

In addition with the train speed increasing from200 kmh to 400 kmh the dynamic stress at observation

Ver

tical

acce

lera

tion

(ms

2 )

S1-3 S2-3 S3-3 T0-3B0-3Measuring points

00

01

02

03

04

05

FieldNum

Ver

tical

vel

ocity

(10ndash3

middotms

2 )

S1-3 S2-3 S3-3 T0-3B0-3Measuring points

03

06

09

12

15

18

FieldNum

(a)

Ver

tical

acce

lera

tion

(ms

2 )

S1-4 S2-4 S3-4B0-4Measuring points

000

005

010

015

020

025

FieldNum

Ver

tical

vel

ocity

(10ndash3

middotms

2 )

S1-4 S2-4 S3-4B0-4Measuring points

00

02

04

06

08

10

FieldNum

(b)

Figure 8 Comparison of vertical acceleration and velocity peaks between the numerical results and the field measurement (a) Measuringpoints on the base slab (b) Measuring points on the subgrade center

Ver

tical

stiff

ness

(kN

mm

) BridgeTransition sectionTunnel

70

80

90

100

110

120

Ver

tical

acce

lera

tion

(ms

2 )

010

015

020

025

030

035

4 8 12 16 20 24 28 32 36 400Distance from section T0 x (m)

Vertical stiffnessVertical acceleration

Figure 9 Distribution of the vertical acceleration and trackstiffness along the transition zone

10 Advances in Civil Engineering

points P4 and P6 is almost unchanged as shown inFigure 13(b) Nevertheless the dynamic stress at observationpoint P2 (at section S1) increases slightly from 305 kPa to316 kPa )e authors consider that the increase of dynamicstress at observation point P2 is related to the additionalload and with the increase of train speed the additional loadcaused by train load also increases in the connections with alarge stiffness difference

Figure 14(a) shows the relationship between the verticalacceleration on the base slab and the axle weight With the axleweight increasing from 10 t to 30 t the vertical accelerationincreases approximately exponentially and the vertical dy-namic stress increases approximately linearly (Figure 14(b))Consequently the axle weight is quite sensitive to the dynamicresponses of the DBPPS transition section

To reflect the influence of train direction on the dynamicresponses except for the vertical acceleration at originalobservation points the authors also select the vertical ac-celeration from other observation points at both sides of theconnections (ie x 102m and x 362m) wherex 89m 115m 349m and 375m as shown in Figure 15When the train moves from the tunnel to the bridge the

amplification effect can be observed at x 115m andx 375m while when the train moves from the bridge tothe tunnel the amplification effect occurs near x 89m andx 349m It can be concluded that under different traindirections the position with an amplification effect for vi-bration is also different which is determined by the positionand stiffness difference of the connections

44 Optimization of Pile Length in the Pile-Plank StructureIn the case study described in Section 2 an improvementstrategy with varying-length piles is adopted to achieve abetter transition due to the thickness of soft soil is uneven(Figure 2) Figure 16 shows the vertical displacement onthe pile top for different pile lengths It can be seen that thevertical displacement on the pile top is negatively cor-related with the pile length )e main reason is that thepiles with longer pile length can transfer the upper load toa deeper bearing layer But for shorter piles they bear theupper load together with the shallow soil with a lowerstiffness resulting in higher vertical displacement on thepile top According to the distribution of vertical

Ver

tical

acce

lera

tion

(ms

2 )4 8 12 16 20 24 28 32 36 400

Distance from section T0 x (m)

ndash15

ndash10

ndash5

0

5

10

15

AxleBogieCarbody

(a)

Am

plitu

de (m

s2 )

50 100 150 2000Frequency (Hz)

0

1

2

3

4

5

Axle

Am

plitu

de (m

s2 )

50 100 150 2000Frequency (Hz)

000

008

016

024

032

040

Bogie

Am

plitu

de (m

s2 )

50 100 150 2000Frequency (Hz)

000

006

012

018

024

030

Carbody

(b)

Figure 10 Vertical acceleration distribution of the train along the transition zone (a) Acceleration (b) Frequency

Advances in Civil Engineering 11

displacement for different pile lengths the strategy ofvarying-length piles is conducive to the stiffnesssmoothness in the transition zone

For general soil layers with uniform thickness Li andBian [30] discussed the influences of varying-length pilesand constant-length piles on the vertical track stiffness ina subgrade-bridge transition section and found that thevarying-length piles strategy can effectively smooth thevertical track stiffness transition Nevertheless for theDBPPS transition section under the general conditionsthe necessity of variable pile-length design is still de-batable In this study four comparative cases including

two improvement strategies varying-length piles andconstant-length piles are established to investigate theinfluences of pile length and the properties of soil on theDBPPS transition section as shown in Figure 17 In thesecases it is assumed that the ground consists of twohorizontal soil layers the upper layer is the silty clay layerthe bearing layer is the sand layer or limestone layer with ahigher stiffness than the silty clay layer )e materialproperties are shown in Table 1 and other parameters andwork conditions remain unchanged

Figure 18 shows the vertical track stiffness distributionalong the transition zone under four cases It can be seen thatthe smoothness of vertical track stiffness along the transitionsection can be improved by adopting the strategy of varying-length piles especially when the bearing layer is the sandlayer )e authors consider that when the bearing layer islimestone the bearing mode is similar to end-bearing pilesand the upper load is mainly transferred by piles to thebearing layer Consequently the change in pile length has asmall effect on the upper load transfer But when the bearinglayer is the sand layer with a lower stiffness the bearingmode is similar to friction-bearing piles and the upper loadis mainly shared by piles and the shallow ground )e in-crease of pile length effectively improves the friction resis-tance which indirectly enhances the overall stiffness of theground )erefore the strategy of varying-length piles caneffectively smooth the vertical track stiffness in the DBPPStransition section with a bearing layer of low stiffness

P1P2S1 sectionD

ynam

ic st

ress

(kPa

)10

0

ndash10

ndash20

ndash30

ndash40

ndash5002 04 06 08 1 12 14

Time (s)

P1P2

(a)

P3P4S2 sectionD

ynam

ic st

ress

(kPa

)

10

0

ndash10

ndash20

ndash30

ndash40

ndash5002 04 06 08 1 12 14

Time (s)

P3P4

(b)

P5P6S3 sectionD

ynam

ic st

ress

(kPa

)

10

0

ndash10

ndash20

ndash30

ndash40

ndash5002 04 06 08 1 12 14

Time (s)

P5P6

(c)

Figure 11 Time-history curves of the vertical dynamic stress (a) Observation points of section S1 (b) Observation points of section S2 (c)Observation points of section S3

+261e + 03+000e + 03ndash261e + 03ndash523e + 03ndash784e + 03ndash105e + 04ndash131e + 04ndash156e + 04ndash183e + 04ndash209e + 04ndash235e + 04ndash261e + 04ndash288e + 04ndash312e + 04

Fieldndash1 S33Unit Pa (Avg 75)

Maximum 291 kPa

S3 S1

Maximum 312 kPa

Train direction

x

yz

Figure 12 Vertical stress contour of the train passing throughsection S1 and section S3 successively

12 Advances in Civil Engineering

Changes in longitudinal stresses are more prone toactivate track slab cracking Figure 19(a) shows thelongitudinal stress (S22) contour on the track slab sur-face at a certain time for Case 3 A positive value

represents tensile stress and a negative value representscompressive stress It can be seen that under the trainload significant concentrated tension stresses are

250 300 350 400200Train speed (kmh)

0

01

02

03

04

05V

ertic

al v

ibra

tion

acce

lera

tion

(ms

2 )

B0-3S1-3S2-3

S3-3T0-3

(a)

250 300 350 400200Train speed (kmh)

25

27

29

31

33

35

Ver

tical

dyn

amic

stre

ss (k

Pa)

P2P4P6

(b)

Figure 13 Influences of the train speed on dynamic responses (a) Vertical acceleration (b) Vertical dynamic stress

S3-3T0-3

15 20 25 3010Vehicle axle weight (t)

0

02

04

06

08

Ver

tical

vib

ratio

nac

cele

ratio

n (m

s2 )

B0-3S1-3S2-3

(a)

15 20 25 3010Vehicle axle weight (t)

0

30

60

90

120

Ver

tical

dyn

amic

stre

ss (k

Pa)

P2P4P6

(b)

Figure 14 Influences of the axle weight on dynamic responses (a) Vertical acceleration (b) Vertical dynamic stress

x = 375

x = 349

x = 115

x = 89

B0S1

S2S3

T0

Tunnel Transition section Bridge

3 6 9 12 15 18 21 24 27 30 33 36 39 420Distance from section T0 x (m)

Ver

tical

acce

lera

tion

(ms

2 )

012

015

018

021

024

027

030

From bridge to tunnelFrom tunnel to bridge

Figure 15 Influence of the train direction on dynamic responses

Pile length = 23mPile length = 16m

Pile length = 13mPile length = 10m

ndash003

ndash0025

ndash002

ndash0015

ndash001

ndash0005

0

Ver

tical

disp

lace

men

t (m

m)

090603 12 150Time (s)

Figure 16 Vertical displacement on the pile top for piles of dif-ferent lengths

Advances in Civil Engineering 13

generated on the track slab surface at the positions I andII (Figure 19(a)) with the maximum value of 5374 kPaNevertheless long-term cyclic dynamic load caused bytrain may activate cracks at these positions

Figure 19(b) shows the comparison of maximum tensilestress along the DBPPS transition section in four cases )emaximum tensile stresses at positions I and II are signifi-cantly higher than those at other positions due to the largerstiffness difference When the bearing layer is limestonelayer the maximum tensile stress on the track slab surface at

positions I and II can be reduced by 109 and 78 re-spectively using varying-length piles while when thebearing layer is the sand layer the values can be reduced by278 and 182 respectively indicating that the strategy ofvarying-length piles can significantly reduce the tensile stresson the track slab surface and the lower the stiffness of thebearing layer the more the tensile stress reduces

In general to prevent cracks at the connection betweenabutment and transition section expansion joints or otherimproved measures would be applied to address these

5m 5m 3m 5m 5m

13mSilty clay

Limestone

(a)

5m 5m 3m 5m 5m

16m

23m

13mSilty clay

Limestone

(b)

5m 5m 3m 5m 5m

13mSilty clay

Sand

(c)

5m 5m 3m 5m 5m

16m13m

23m

Silty clay

Sand

(d)

Figure 17 Optimization cases of the pile-plank structure (a) Case 1 (b) Case 2 (c) Case 3 (d) Case 4

60

70

80

90

100

110

Ver

tical

stiff

ness

(kN

mm

)

3510 15 20 25 30 400 5Distance from T0 section (m)

Case 1Case 2

Case 3Case 4

Figure 18 Vertical stiffness along the transition zone for different cases

14 Advances in Civil Engineering

problems in practical engineering From the above resultsthe authors suggest that in addition to the connection be-tween the bridge and the DBPPS transition section theconnection between the tunnel and the DBPPS transitionsection should also be reinforced or treated

5 Conclusions

In this study the authors present a numerical modelingapproach to investigate the dynamic performances of a newtype of bridge-tunnel transition section with a DBPPSwhich can be used as a tool to improve the design andapplication of DBPPS subgrade )e obtained research re-sults of this study lead to the following conclusions

(1) )e vibration level of the DBPPS transition section islower than that of the abutment and the tunnelsection when the train passes by Meanwhile theadditional load caused by vertical track stiffnessdifference can aggravate the vibration at the con-nections and its adjacent areas (such as section S1)between the DBPPS transition section and theabutment (or tunnel) In addition the vertical ac-celeration of the carbody also shows abrupt change atthese connections

(2) With train speed increases the vertical accelerationof the base slab increases and the vertical dynamicstress on the subgrade surface near the connections(such as section S1) also increases With axle weightincreases the vertical acceleration increases ap-proximately exponentially and the vertical dynamicstress increases approximately linearly )e traindirection has a significant influence on the con-nections and its adjacent areas with a large stiffnessdifference

(3) For general soil layers with uniform thickness theimprovement strategy with varying-length piles caneffectively smooth the track stiffness and reduce thetensile stress on the track slab surface at the

connections and the effect is more significant whenthe stiffness of the bearing layer is low

Data Availability

)e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

)e authors declare that they have no conflicts of interestregarding the publication of this paper

Acknowledgments

)is paper reports research developed under financialsupport provided by the Key Project of Science and Tech-nology Research and Development Program of ChinaRailway Corporation (Grant No 2014T003-D) and theNational Natural Science Foundation of China (Grant nos51878671 and 51678575)

References

[1] X Lei ldquoEffects of abrupt changes in track foundation stiffnesson track vibration under moving loadsrdquo Journal of VibrationEngineering vol 19 no 2 pp 195ndash199 2006

[2] A Paixatildeo E Fortunato and R Calccedilada ldquoTransition zones torailway bridges track measurements and numerical model-lingrdquo Engineering Structures vol 80 pp 435ndash443 2014

[3] K K Ang and J Dai ldquoResponse analysis of high-speed railsystem accounting for abrupt change of foundation stiffnessrdquoJournal of Sound and Vibration vol 332 no 12 pp 2954ndash2970 2013

[4] P Holscher and P Meijers Literature Study of Knowledge andExperience of Transition Zones Report of GeoDelft DelftNetherlands 2007

[5] European Committee for Standardisation(CEN) Basis ofstructural design European Committee for Stand-ardisation(CEN) Brussels Belgium 2005

Tunnel section Transition section Abutment

Track slab

Carbody

Rail

I II

Unit Pa+537e + 05+423e + 05+309e + 05+195e + 05+807e + 04ndash335e + 04ndash148e + 05ndash262e + 05ndash376e + 05ndash490e + 05ndash604e + 05ndash718e + 05ndash832e + 05

S S22(Average 75)

(a)

3510 15 20 25 30 400 5Distance from section T0 (m)

ndash200

0

200

400

600

800

Max

imum

tens

ile st

ress

(kPa

)

Case 1Case 2

Case 3Case 4

(b)

Figure 19 Tensile stress distribution for different cases (a) Tensile stress contour of Case 3 at a certain time (b) Maximum tensile stress fordifferent cases

Advances in Civil Engineering 15

[6] )e Swedish Rail Administration Design standard for railwaybridges Standard BVS 58310 )e Swedish Rail Adminis-tration Borlange Sweden 2006

[7] Canadian Standards AssociationndashInternational CanadianHighway Bridge Design Code Canadian Standards Associa-tionndashInternational Toronto Canada 2000

[8] National Railway Administration Code for Design of HighSpeed Railway (TB10621-2014) China Railway PublishingHouse Beijing China 2015

[9] D Li and D Davis ldquoTransition of railroad bridge ap-proachesrdquo Journal of Geotechnical and GeoenvironmentalEngineering vol 131 no 11 pp 1392ndash1398 2005

[10] P Hu C Zhang S J Chen Y Wang W Wang andW H Duan ldquoDynamic responses of bridge-embankmenttransitions in high speed railway field tests and data analysesrdquoEngineering Structures vol 175 pp 565ndash576 2018

[11] Y Shan B Albers and S A Savidis ldquoInfluence of differenttransition zones on the dynamic response of track-subgradesystemsrdquo Computers and Geotechnics vol 48 pp 21ndash28 2013

[12] Y Shan Y Shu and S Zhou ldquoFinite-infinite element coupledanalysis on the influence of material parameters on the dy-namic properties of transition zonesrdquo Construction andBuilding Materials vol 148 no 1 pp 548ndash558 2017

[13] J Ren H Zhao X Li et al ldquoDynamic performances of CRTSIII prefabricated slab track with anti-vibration structure insubgrade-tunnel transition sectionrdquo Journal of SouthwestJiaotong University vol 51 no 6 pp 1047ndash1054 2016

[14] J N Varandas P Holscher and M A G Silva ldquo)ree-di-mensional track-ballast interaction model for the study of aculvert transitionrdquo Soil Dynamics and Earthquake Engi-neering vol 89 pp 116ndash127 2016

[15] P Hu C Zhang S Wen and Y Wang ldquoDynamic responsesof high-speed railway transition zone with various subgradefillingsrdquoComputers and Geotechnics vol 108 pp 17ndash26 2019

[16] J N Varandas A Paixatildeo and E Fortunato ldquoA study on thedynamic train-track interaction over cut-fill transitions onburied culvertsrdquo Computers amp Structures vol 189 no 9pp 49ndash61 2017

[17] R Santildeudo L DellrsquoOlio J A Casado I A Carrascal andS Diego ldquoTrack transitions in railways a reviewrdquo Con-struction and Building Materials vol 112 pp 140ndash157 2016

[18] L Wei C He and Z Yang Comprehensive Test Study Reportof Nanchang West to Yichun East Section of Shanghai-Kunming Railway Passenger Dedicated Line Central SouthUniversity Changsha China 2014

[19] Q SuWWang H Bai et al ldquoBearing capacity mechanism ofnon-embedded pile-plank structure subgraderdquo Journal ofTraffic and Transportation Engineering vol 12 no 1pp 19ndash24 2012

[20] Y-X Zhan H-L Yao and G-L Jiang ldquoDesign method ofpile-slab structure roadbed of ballastless track on soil sub-graderdquo Journal of Central South University vol 20 no 7pp 2072ndash2082 2013

[21] KMa ldquoAnalysis on space vibration performance of pile-plankstructuremdashfoundation soil system under the condition ofhigh-speed trains runningrdquo Journal of the China RailwaySociety vol 35 no 1 pp 93ndash100 2013

[22] L Huang B Wang and S Zhou ldquoCentrifugal model test ofpile-plank subgrade in soft groundrdquo Rock and Soil Mechanicsvol 34 no S1 pp 192ndash196 2013

[23] J Huang Q Su T Liu and X Wang ldquoVibration and long-term performance analysis of pile-plank-supported lowsubgrade of ballastless track under excitation loadsrdquo Shockand Vibration vol 2015 pp 1ndash12 2015

[24] Dassault Systemes Simulia Corp Abaqus Analysis UserrsquosManual Version 612 Dassault Systemes Simulia CorpJohnston Rhode Island USA 2012

[25] C Cheng ldquoStudy on dynamic responses of irregularity bal-lastless track for high-speed railwayrdquo PhD )esis ZhejiangUniversity Zhejiang China 2015

[26] H Hertz ldquoOn the contact of elastic solidsrdquo Journal fur die rneund angewandte Mathematik (Crelles Journal) vol 92no 156 2008

[27] P Ni K Wang W Zhang et al ldquoCalculation method ofwheel-rail contact relationrdquo Journal of Traffic and Trans-portation Engineering vol 04 pp 14ndash17 2006

[28] W Zhai and X Sun ldquoA detailed model for investigatingvertical interaction between railway vehicle and trackrdquo Ve-hicle System Dynamics vol 23 pp 603ndash615 1994

[29] W Zhai Vehicle-track Coupled Dynamics Jeory and Ap-plication Science Press and Springer Nature Singapore PteLtd Berlin Germany 2020

[30] W Li and X Bian ldquoDynamic performance of pile-supportedbridge-embankment transition zones under high-speed trainmoving loadsrdquo Procedia Engineering vol 143 pp 1059ndash10672016

[31] P Ni S Mangalathu G Mei and Y Zhao ldquoPermeable pilesan alternative to improve the performance of driven pilesrdquoComputers and Geotechnics vol 84 pp 78ndash87 2017

[32] K Liu Q Su P Ni C Zhou W Zhao and F Yue ldquoEval-uation on the dynamic performance of bridge approachbackfilled with fibre reinforced lightweight concrete underhigh-speed train loadingrdquo Computers and Geotechnicsvol 104 pp 42ndash53 2018

[33] F Xue and J Zhang ldquoAttenuations of acceleration spectra ofhigh-speed railway embankment subjected to moving loadsrdquoRock and Soil Mechanics vol 36 pp 445ndash451 2015

[34] Y Xuan ldquoSimulation research on the dynamic characteristicsof vehicle-track coupling system on curved track and thevibration response of ballastless track strucure of passengertraffic railwayrdquo PhD )esis China Academy of RailwaySciences Beijing China 2008

[35] P Ricco A Baron and P Molteni ldquoNature of pressure wavesinduced by a high-speed train travelling through a tunnelrdquoJournal of Wind Engineering and Industrial Aerodynamicsvol 95 no 8 pp 781ndash808 2007

[36] C Esveld Modern Railway Track MRT-Productions Zalt-bommel Netherlands 2001

[37] R Santildeudo M Cerrada B Alonso and L dellrsquoOlio ldquoAnalysisof the influence of support positions in transition zones Anumerical analysisrdquo Construction and Building Materialsvol 145 no 1 pp 207ndash217 2017

[38] M Shahraki CWarnakulasooriya and K JWitt ldquoNumericalstudy of transition zone between ballasted and ballastlessrailway trackrdquo Transportation Geotechnics vol 3 pp 58ndash672015

[39] C Alves Ribeiro R Calccedilada and R Delgado ldquoExperimentalassessment of the dynamic behaviour of the train-track systemat a culvert transition zonerdquo Engineering Structures vol 138no 1 pp 215ndash228 2017

[40] Ministry of Railways Institute of StandardMetrology RailwayLocomotive Dynamic Performance Test Identification Methodand Evaluation Standard (TBT2360-1993) Ministry of Rail-ways Institute of Standard Metrology Beijing China 1994

16 Advances in Civil Engineering

300m

220m

260m

320m

400m

Pier foundation

Abutment Train (two carriages)

Subgrade

Spring-damping boundary elements

Tunnel sectionTransition section

Bridge section

Fastener(spring-dashpot element)

RailTrack slabBase slab

(a)

Silty clay

Plank

Pile

Limestone

Subgrade

(b)

Nor

mal

forc

e (times1

07 N)

00

05

10

15

20

25

30

05 10 15 20 25 30 35 4000Normal compression deformation (mm)

(c)

Carbody

Bogie

Wheelset

RailMasterSurface Slave

Surface

(d)

Primarysuspension

Secondarysuspension

(e)

Figure 4 Finite element model (a) Full model (b) Grid of pile-plank and surrounding soil (c) Relationship between normal force andcompression deformation (d) Contact elements between the wheel tread and the rail (e) Vehicle model

Advances in Civil Engineering 5

ldquoTabularrdquo type in ABAQUS was proposed to simulate thenormal behavior of the wheel-rail interactionWith this settingthe change rate of the wheel-rail contact force would be sloweddown which was beneficial to the convergence of the calcu-lation For the tangential behavior of the wheel-rail interactiona ldquopenalty functionrdquo model with a friction coefficient of 02 wasadopted Considering that the rail was newly laid it wasregarded as an idealized horizontal track in the model

To reflect the coupling vibration inside the vehicle thedoubled suspension system was considered Based on thetheoretical model proposed by Zhai [28 29] for investigatingvertical interactions between railway vehicle and track thevehicle in this model was simplified to be composed ofwheelsets bogies and carbodies Connector elements withelastic-damping properties were adopted to simulate thesuspension systems between the wheelsets and bogies andbetween the bogies and carbody (Figure 4(e)) Consideringthe influence of adjacent wheelsets on wheel-rail interactiontwo carriages of the vehicle were selected in the model )esimulation of train speed was realized by applying the ve-locity (including translation velocity and rotation velocity)to the carbodies bogies and wheelsets along the rails

In general to reduce the reflection of stress waves at themodel boundary the model size should be as large as possiblebut more time and computer resources would be costly Toaddress this problem many scholars introduced an artificialboundary for simulation analysis Currently there are twomainstream modeling methods to minimize the reflected dy-namic wave at the boundary (i) using infinite elements at theboundary and setting viscous property between finite andinfinite elements [30 31] and (ii) introducing an artificialspring-damping boundary to absorb the dynamic wave[12 15 32] In this study the viscoelastic artificial boundarieswere adopted to reproduce the dynamic response using spring-damping elements )ese spring-damping elements were ap-plied in the boundary components in three directions at eachnode )e normal damping coefficient and stiffness coefficientwere determined according to the test results carried out by Huet al [15] Besides the bottom boundary of the model was fixedby a three-degree-of-freedom displacement constraint and thelateral and longitudinal boundaries were constrained by normaldisplacements

In this model the fillers in subgrade layers were modeledas MohrndashCoulomb material to consider the possibility ofplastic yield in the subgrade under heavy axle load (such asmore than 30 t) and the other components were modeled aslinear-elastic material )e parameters of different materialsare shown in Table 1 )e Rayleigh damping was adopted todescribe the damping properties of the components in thetransition zone the mass matrix coefficient α and stiffnessmatrix coefficient β are referenced from [33] To obtainaccurate calculation results the dynamic implicit algorithmwas adopted with a maximum time step of 25ms

32 Model Validation with Field Tests

321 Field Tests To validate the FE model field tests werecarried out )e 891-II type vibration sensors (Figure 5(a))were applied to measure the horizontal and vertical dynamic

responses including acceleration and velocity )e acceler-ation measurement range is plusmn40ms2 with a sensitivity of01V s2m (V is a voltage unit) and the velocity measure-ment range is plusmn05ms with a sensitivity of 300 V sm )evibration signals were collected by an INV3060D type ac-quisition analyzer (Figure 5(b)) With the vibration sensorsdata acquisition analyzer and network module data ac-quisition and wireless transmission test system for automatictrain triggering was established Measuring sections of B0S1 S2 S3 and T0 were established for the attempt to reflectthe variations of dynamic responses along the transitionzone Section B0 was set at the abutment section T0 was setat the tunnel entrance and sections of S1 S2 and S3 were setat the DBPPS subgrade (see Figures 2(a) and 5(c)) )evibration sensors were placed on the center of the subgradeon both sides of the base slab and on the slope of thesubgrade to investigate the transverse distribution of thedynamic response (Figure 5(d))

)e CRH380AM type trains with an axle weight of 150 tand a speed range of 236ndash335 kmh were tested )eschematic profile of CRH380AM type train is depicted inFigure 6 As an example the test results of this type of trainwere selected to verify the reliability of the FEmodel and thevehicle parameters are shown in Table 2

It is worth explaining that the field tests were carried outduring the period of the joint commissioning test whichmeans that the railway line was not officially operated in thatperiod )erefore there is no significant uneven permanentsettlement deformation that occurred in the transition zoneduring the field tests In the FE model the influence ofstiffness variations along the transition zone on dynamicresponse is considered while the influence of permanentsettlement deformation is ignored

322 Comparison between Numerical Results and FieldMeasurement )e test results of the CRH380AM train witha running speed of 300 kmh from a bridge to a tunnel arecompared with the numerical results for validation Figure 7shows the comparison of vertical acceleration and velocitytime-history curves at measuring points B0-3 S2-3 and T0-3 between the numerical results and the field measurement)ese signal curves have been filtered with a cutoff frequencyof 120Hz It can be seen that the amplitude and the curvetrend of the numerical results are in good agreement withthe measured results on the whole

Figure 8 shows the comparison of vertical accelerationand velocity peaks between the numerical results and thefield measurement Considering the randomness of trackvibration caused by the wheelsets the measured peaks hereare the average values of vibration peaks caused by twoadjacent bogies (ie four wheelsets) It also indicates that thegood agreement that is obtained between the numerical andthe experimental vertical acceleration and velocity peaksand the differences of vertical acceleration and velocity peaksbetween the numerical results and the field measurement arewithin 30 in most measuring points However a con-siderable difference is still observed at measuring points ofsection T0 on the base slab such as T0-3 (Figures 7(a) and

6 Advances in Civil Engineering

Table 1 Material properties of the components in the transition zone [15 22 33]

Components or material Youngrsquos modulus E (MPa) Poissonrsquos ratio μ Density ρ (kgm3)Rayleigh dampingα (sminus1) β (s)

Rail 205900 030 7830 0022 0002Track slab 32500 016 2500 0098 0009Base slab 25500 016 2500 0098 0009Graded gravel + 5 cement 1780 030 2100 0229 0021Graded gravel 1580 024 2000 0252 0022Bearing plank 56000 020 2500 0085 0009Cast-in-situ bores pile 38000 020 2500 0098 0008Silty clay 15 030 1930 0262 0024Sand layer 75 030 1950 0270 0023Limestone 600 029 2090 0235 002Abutment 30000 020 2300 0098 0009Bridge deck 22000 018 2550 0098 0009Tunnel filled concrete 20000 020 2400 0098 0009Tunnel bedrock 12000 020 2300 015 0015

(a) (b)

Kunming Shanghai

T0-6

T0-5T0-3

T0-2

T0 S2 S1 B0S3

S2-7S2-6

S2-5S2-3

S2-4S3-4S3-3

S3-2S3-1

S1-4S1-3

B0-5B0-3 B0-4

B0-2S1-2S1-1

S2-2S2-1

Track slab

RailPile

Up-line

Down-line

Base slab

Horizontal acceleration sensorldquoT0-2rdquo ndash ldquoT0rdquo (monitoring section) ldquo2rdquo (monitoring point number)

Vertical acceleration sensorVertical velocity sensor

(c)

S2-5 S2-6

S2-7

S2-3

S2-4

S2-2

S2-1

Up-lineDown-line

Base slab

Track slab

Subgrade surface layer

Subgrade base layer

Bearing plank

Pile

(d)

Figure 5 Measuring equipment and layout (a) 891-II type vibration sensor (b) INV3060D type acquisition analyzer and network module(c) Layout of measuring points in the transition zone (d) Layout of measuring points in the section S2

Advances in Civil Engineering 7

8(a)) )e differences of vertical acceleration peak and ve-locity peak at T0-3 between the numerical results and thefield measurement are approximately 543 and 408respectively )e main reason may be that an aerodynamiceffect [35] is generated at the tunnel entrance when the trainpasses by which aggravates the vibration of track compo-nents at section T0 But the effect is not well simulated in thenumerical model which induces a significant differencebetween the numerical results and the field measurementespecially in section T0

4 Results and Discussion

41 Dynamic Response along the Transition ZoneFigure 9 shows the distribution of vertical acceleration on thebase slab and the vertical track stiffness obtained from theformula proposed by [36] along the transition zone when theCRH380AM trainmoves from the bridge to the tunnel It can beseen that the vertical acceleration of the DBPPS transitionsection is less than that of the abutment and the tunnel sectionCompared with the tunnel section and the abutment the fillersin the DBPPS subgrade have the properties of low stiffness andlarge damping resulting in lower vibration levels in the DBPPSsubgrade Moreover a considerable amplification effect for thevertical acceleration can be observed at the connections(x 102m and x 362m) between the transition section andthe tunnel (or abutment) )e authors consider that the am-plification effect is caused by the abrupt change of wheel-railinteraction caused by the stiffness difference at the connections)is phenomenon was also found by Sanudo [37] and Shahraki[38]

It should be noted that the vertical acceleration of sectionS1 is higher than that of the sections S2 and S3 )is can beexplained that when the train passes through the connectionbetween the abutment and the transition section with anabrupt change stiffness an additional load on the trackcomponents is generated by the train load which aggravates

the vibration at the connection and its adjacent arearesulting in the vertical acceleration of section S1 beinghigher than that of sections S2 and S3

Although the dynamic response at connections is in-tensified due to the amplification effect the maximumvertical vibration acceleration of the transition zone is only023ms2 which is less than 50ms2 specified in the code[8] indicating that the DBPPS transition section exhibitsgood dynamic performance

)e coupling vibration inside the vehicle is considered inthe FE model and the line smoothness of the transition zonecan be evaluated by the dynamic response of the vehicleFigure 10 shows the vertical acceleration distribution of thevehicle which is comprised of an axle bogie and carbody alongthe transition zone Due to the dynamic contact interactionbetween the wheel and the rail the acceleration amplitude ofthe axle changes more dramatically and the vibration fre-quency is higher than that of bogie and carbody Furthermorebecause of the damping effect of the suspension system(connector elements) the acceleration amplitude and vibrationfrequency of the bogie and carbody are greatly reduced

It can be seen from Figure 10(b) that the frequencycomponents of the axle mainly consist of a low frequency of27Hz and a high frequency of 128Hz )e high frequencycomponent is caused by the excitation of fasteners (spring-dashpot elements) which can be verified as follows )espacing (L) of the fasteners is 065m then the excitationperiod (T) is as follows

T Lv (3)

where v is the train speed taken as 300 kmh or 8333ms)e excitation frequency f is determined as follows

f 1T vL 8333065 1282Hz (4)

)e results coincide well with the high frequencycomponent of the axle obtained from the numerical resultsFor the low frequency component it is mainly caused by theinteraction between the axle and the bogie On the whole thevibration frequency of the vehicle obtained from this FEmodel is close to the test results measured by Alves Ribeiro[39] which further indicates that the model is reliable

In addition the vibration response of the vehicle at theconnections (x 102m or x 362m) between the transitionsection and the tunnel (or abutment) is slightly higher than thatat other positions due to the sudden change of wheel-railinteraction caused by the stiffness difference (Figure 10(a)) Toensure the stable operation of the train and the comfort ofpassengers the standard [40] stipulates that the vertical ac-celeration of the carbody with excellent passenger comfort levelshall be less than 245ms2 As can be seen from Figure 10(a)

250 1500 500450

370

250 250 250 250 2501500 1500500

2 carriages simulated in the FE modelLength unit m

Figure 6 Schematic profile of CRH380AM type train

Table 2 Parameters of the vehicle [25 34]

Parameters ValueMass of the carbody 44320 kgMass of the bogie 3136 kgMass of the wheelset 2352 kgPitch inertia of the carbody 520e5 kgm2

Pitch inertia of the bogie 6400 kgm2

Stiffness of primary suspension 1040 kNmStiffness of secondary suspension 400 kNmDamping of primary suspension 40 kNmiddotsmDamping of secondary suspension 60 kNmiddotsm

8 Advances in Civil Engineering

the maximum vertical acceleration of the carbody is 075ms2indicating the train reaches an excellent comfort level and theDBPPS transition section fulfills its purpose in that it provides asmooth stiffness transition

42 Distribution of Vertical Dynamic Stress in the SubgradeTo analyze the vertical dynamic stress distribution in thesubgrade when the train passes by some observation points

at sections of S1 S2 and S3 in the FE model were selected asshown in Figure 11 Observation points of P1 P3 and P5 arelocated on the subgrade surface below the line center andobservation points of P2 P4 and P6 are located on thesubgrade surface directly below the rail Figure 11 shows thetime-history curves of vertical dynamic stress at these ob-servation points It can be seen that the vertical dynamicstress on the subgrade surface at observation points of P2P4 and P6 is 17sim18 higher than that at observation

ndash02

ndash01

0

01

02

03

04

Ver

tical

acce

lera

tion

(ms

2 )

101 103 105 107 10999Time (s)

FieldNum

ndash12

ndash06

0

06

12

18

24

Ver

tical

vel

ocity

(ms

)

101 103 105 107 10999Time (s)

FieldNum

times10ndash3

(a)

ndash04

ndash02

0

02

04

06

08

Ver

tical

acce

lera

tion

(ms

2 )

99 101 103 105 10797Time (s)

FieldNum

ndash1

ndash05

0

05

1

15

2

Ver

tical

vel

ocity

(ms

)

97 99 107103 105101Time (s)

FieldNum

times10ndash3

(b)

ndash06

ndash03

0

03

06

09

12

Ver

tical

acce

lera

tion

(ms

2 )

102 104 106 10810 11Time (s)

FieldNum

ndash2

ndash1

0

1

2

3

4

Ver

tical

vel

ocity

(ms

)

102 104 106 10810 11Time (s)

FieldNum

times10ndash3

(c)

Figure 7 Comparison of time-history curves between the numerical results and the field measurement (a) B0-3 (b) S1-3 (c) T0-3

Advances in Civil Engineering 9

points of P1 P3 and P5 More importantly the verticaldynamic stress of section S1 is higher than that of sections S2and S3 Figure 12 visually shows the vertical dynamic stresscontour of the train passing through section S1 and sectionS3 successively )e maximum vertical dynamic stress ofsection S1 is higher than that of section S3 which verifies theexistence of the additional loadmentioned above It becomesevident that when the train moves from the bridge to the

tunnel the additional load caused by the train load increasesthe dynamic stress on the subgrade surface of section S1which is also the reason why the vibration responses ofsection S1 are higher than that of sections S2 and S3 in thefield measurement (see Figure 8)

43 Influences of Train Speed Axle Weight and Direction onDynamic Response To investigate the influences of differentfactors on the dynamic responses of the transition sectionthree factors including train speed axle weight and runningdirection are selected for sensitivity analysis Figure 13(a)shows the relationship between the vertical acceleration onthe base slab and the train speed With the train speedincreasing from 200 kmh to 400 kmh the vertical accel-eration also increases in which the vertical accelerationincreases from 020ms2 to 044ms2 at measuring point T0-3 and increases from 0007ms2 to 030ms2 at measuringpoint S3-3 If the aerodynamic effect mentioned above is notconsidered in practice even if the train speed reaches400 kmh the vertical acceleration on the base slab is lessthan 50ms2 specified in the code [8] indicating that thetrack structure is still in safe service

In addition with the train speed increasing from200 kmh to 400 kmh the dynamic stress at observation

Ver

tical

acce

lera

tion

(ms

2 )

S1-3 S2-3 S3-3 T0-3B0-3Measuring points

00

01

02

03

04

05

FieldNum

Ver

tical

vel

ocity

(10ndash3

middotms

2 )

S1-3 S2-3 S3-3 T0-3B0-3Measuring points

03

06

09

12

15

18

FieldNum

(a)

Ver

tical

acce

lera

tion

(ms

2 )

S1-4 S2-4 S3-4B0-4Measuring points

000

005

010

015

020

025

FieldNum

Ver

tical

vel

ocity

(10ndash3

middotms

2 )

S1-4 S2-4 S3-4B0-4Measuring points

00

02

04

06

08

10

FieldNum

(b)

Figure 8 Comparison of vertical acceleration and velocity peaks between the numerical results and the field measurement (a) Measuringpoints on the base slab (b) Measuring points on the subgrade center

Ver

tical

stiff

ness

(kN

mm

) BridgeTransition sectionTunnel

70

80

90

100

110

120

Ver

tical

acce

lera

tion

(ms

2 )

010

015

020

025

030

035

4 8 12 16 20 24 28 32 36 400Distance from section T0 x (m)

Vertical stiffnessVertical acceleration

Figure 9 Distribution of the vertical acceleration and trackstiffness along the transition zone

10 Advances in Civil Engineering

points P4 and P6 is almost unchanged as shown inFigure 13(b) Nevertheless the dynamic stress at observationpoint P2 (at section S1) increases slightly from 305 kPa to316 kPa )e authors consider that the increase of dynamicstress at observation point P2 is related to the additionalload and with the increase of train speed the additional loadcaused by train load also increases in the connections with alarge stiffness difference

Figure 14(a) shows the relationship between the verticalacceleration on the base slab and the axle weight With the axleweight increasing from 10 t to 30 t the vertical accelerationincreases approximately exponentially and the vertical dy-namic stress increases approximately linearly (Figure 14(b))Consequently the axle weight is quite sensitive to the dynamicresponses of the DBPPS transition section

To reflect the influence of train direction on the dynamicresponses except for the vertical acceleration at originalobservation points the authors also select the vertical ac-celeration from other observation points at both sides of theconnections (ie x 102m and x 362m) wherex 89m 115m 349m and 375m as shown in Figure 15When the train moves from the tunnel to the bridge the

amplification effect can be observed at x 115m andx 375m while when the train moves from the bridge tothe tunnel the amplification effect occurs near x 89m andx 349m It can be concluded that under different traindirections the position with an amplification effect for vi-bration is also different which is determined by the positionand stiffness difference of the connections

44 Optimization of Pile Length in the Pile-Plank StructureIn the case study described in Section 2 an improvementstrategy with varying-length piles is adopted to achieve abetter transition due to the thickness of soft soil is uneven(Figure 2) Figure 16 shows the vertical displacement onthe pile top for different pile lengths It can be seen that thevertical displacement on the pile top is negatively cor-related with the pile length )e main reason is that thepiles with longer pile length can transfer the upper load toa deeper bearing layer But for shorter piles they bear theupper load together with the shallow soil with a lowerstiffness resulting in higher vertical displacement on thepile top According to the distribution of vertical

Ver

tical

acce

lera

tion

(ms

2 )4 8 12 16 20 24 28 32 36 400

Distance from section T0 x (m)

ndash15

ndash10

ndash5

0

5

10

15

AxleBogieCarbody

(a)

Am

plitu

de (m

s2 )

50 100 150 2000Frequency (Hz)

0

1

2

3

4

5

Axle

Am

plitu

de (m

s2 )

50 100 150 2000Frequency (Hz)

000

008

016

024

032

040

Bogie

Am

plitu

de (m

s2 )

50 100 150 2000Frequency (Hz)

000

006

012

018

024

030

Carbody

(b)

Figure 10 Vertical acceleration distribution of the train along the transition zone (a) Acceleration (b) Frequency

Advances in Civil Engineering 11

displacement for different pile lengths the strategy ofvarying-length piles is conducive to the stiffnesssmoothness in the transition zone

For general soil layers with uniform thickness Li andBian [30] discussed the influences of varying-length pilesand constant-length piles on the vertical track stiffness ina subgrade-bridge transition section and found that thevarying-length piles strategy can effectively smooth thevertical track stiffness transition Nevertheless for theDBPPS transition section under the general conditionsthe necessity of variable pile-length design is still de-batable In this study four comparative cases including

two improvement strategies varying-length piles andconstant-length piles are established to investigate theinfluences of pile length and the properties of soil on theDBPPS transition section as shown in Figure 17 In thesecases it is assumed that the ground consists of twohorizontal soil layers the upper layer is the silty clay layerthe bearing layer is the sand layer or limestone layer with ahigher stiffness than the silty clay layer )e materialproperties are shown in Table 1 and other parameters andwork conditions remain unchanged

Figure 18 shows the vertical track stiffness distributionalong the transition zone under four cases It can be seen thatthe smoothness of vertical track stiffness along the transitionsection can be improved by adopting the strategy of varying-length piles especially when the bearing layer is the sandlayer )e authors consider that when the bearing layer islimestone the bearing mode is similar to end-bearing pilesand the upper load is mainly transferred by piles to thebearing layer Consequently the change in pile length has asmall effect on the upper load transfer But when the bearinglayer is the sand layer with a lower stiffness the bearingmode is similar to friction-bearing piles and the upper loadis mainly shared by piles and the shallow ground )e in-crease of pile length effectively improves the friction resis-tance which indirectly enhances the overall stiffness of theground )erefore the strategy of varying-length piles caneffectively smooth the vertical track stiffness in the DBPPStransition section with a bearing layer of low stiffness

P1P2S1 sectionD

ynam

ic st

ress

(kPa

)10

0

ndash10

ndash20

ndash30

ndash40

ndash5002 04 06 08 1 12 14

Time (s)

P1P2

(a)

P3P4S2 sectionD

ynam

ic st

ress

(kPa

)

10

0

ndash10

ndash20

ndash30

ndash40

ndash5002 04 06 08 1 12 14

Time (s)

P3P4

(b)

P5P6S3 sectionD

ynam

ic st

ress

(kPa

)

10

0

ndash10

ndash20

ndash30

ndash40

ndash5002 04 06 08 1 12 14

Time (s)

P5P6

(c)

Figure 11 Time-history curves of the vertical dynamic stress (a) Observation points of section S1 (b) Observation points of section S2 (c)Observation points of section S3

+261e + 03+000e + 03ndash261e + 03ndash523e + 03ndash784e + 03ndash105e + 04ndash131e + 04ndash156e + 04ndash183e + 04ndash209e + 04ndash235e + 04ndash261e + 04ndash288e + 04ndash312e + 04

Fieldndash1 S33Unit Pa (Avg 75)

Maximum 291 kPa

S3 S1

Maximum 312 kPa

Train direction

x

yz

Figure 12 Vertical stress contour of the train passing throughsection S1 and section S3 successively

12 Advances in Civil Engineering

Changes in longitudinal stresses are more prone toactivate track slab cracking Figure 19(a) shows thelongitudinal stress (S22) contour on the track slab sur-face at a certain time for Case 3 A positive value

represents tensile stress and a negative value representscompressive stress It can be seen that under the trainload significant concentrated tension stresses are

250 300 350 400200Train speed (kmh)

0

01

02

03

04

05V

ertic

al v

ibra

tion

acce

lera

tion

(ms

2 )

B0-3S1-3S2-3

S3-3T0-3

(a)

250 300 350 400200Train speed (kmh)

25

27

29

31

33

35

Ver

tical

dyn

amic

stre

ss (k

Pa)

P2P4P6

(b)

Figure 13 Influences of the train speed on dynamic responses (a) Vertical acceleration (b) Vertical dynamic stress

S3-3T0-3

15 20 25 3010Vehicle axle weight (t)

0

02

04

06

08

Ver

tical

vib

ratio

nac

cele

ratio

n (m

s2 )

B0-3S1-3S2-3

(a)

15 20 25 3010Vehicle axle weight (t)

0

30

60

90

120

Ver

tical

dyn

amic

stre

ss (k

Pa)

P2P4P6

(b)

Figure 14 Influences of the axle weight on dynamic responses (a) Vertical acceleration (b) Vertical dynamic stress

x = 375

x = 349

x = 115

x = 89

B0S1

S2S3

T0

Tunnel Transition section Bridge

3 6 9 12 15 18 21 24 27 30 33 36 39 420Distance from section T0 x (m)

Ver

tical

acce

lera

tion

(ms

2 )

012

015

018

021

024

027

030

From bridge to tunnelFrom tunnel to bridge

Figure 15 Influence of the train direction on dynamic responses

Pile length = 23mPile length = 16m

Pile length = 13mPile length = 10m

ndash003

ndash0025

ndash002

ndash0015

ndash001

ndash0005

0

Ver

tical

disp

lace

men

t (m

m)

090603 12 150Time (s)

Figure 16 Vertical displacement on the pile top for piles of dif-ferent lengths

Advances in Civil Engineering 13

generated on the track slab surface at the positions I andII (Figure 19(a)) with the maximum value of 5374 kPaNevertheless long-term cyclic dynamic load caused bytrain may activate cracks at these positions

Figure 19(b) shows the comparison of maximum tensilestress along the DBPPS transition section in four cases )emaximum tensile stresses at positions I and II are signifi-cantly higher than those at other positions due to the largerstiffness difference When the bearing layer is limestonelayer the maximum tensile stress on the track slab surface at

positions I and II can be reduced by 109 and 78 re-spectively using varying-length piles while when thebearing layer is the sand layer the values can be reduced by278 and 182 respectively indicating that the strategy ofvarying-length piles can significantly reduce the tensile stresson the track slab surface and the lower the stiffness of thebearing layer the more the tensile stress reduces

In general to prevent cracks at the connection betweenabutment and transition section expansion joints or otherimproved measures would be applied to address these

5m 5m 3m 5m 5m

13mSilty clay

Limestone

(a)

5m 5m 3m 5m 5m

16m

23m

13mSilty clay

Limestone

(b)

5m 5m 3m 5m 5m

13mSilty clay

Sand

(c)

5m 5m 3m 5m 5m

16m13m

23m

Silty clay

Sand

(d)

Figure 17 Optimization cases of the pile-plank structure (a) Case 1 (b) Case 2 (c) Case 3 (d) Case 4

60

70

80

90

100

110

Ver

tical

stiff

ness

(kN

mm

)

3510 15 20 25 30 400 5Distance from T0 section (m)

Case 1Case 2

Case 3Case 4

Figure 18 Vertical stiffness along the transition zone for different cases

14 Advances in Civil Engineering

problems in practical engineering From the above resultsthe authors suggest that in addition to the connection be-tween the bridge and the DBPPS transition section theconnection between the tunnel and the DBPPS transitionsection should also be reinforced or treated

5 Conclusions

In this study the authors present a numerical modelingapproach to investigate the dynamic performances of a newtype of bridge-tunnel transition section with a DBPPSwhich can be used as a tool to improve the design andapplication of DBPPS subgrade )e obtained research re-sults of this study lead to the following conclusions

(1) )e vibration level of the DBPPS transition section islower than that of the abutment and the tunnelsection when the train passes by Meanwhile theadditional load caused by vertical track stiffnessdifference can aggravate the vibration at the con-nections and its adjacent areas (such as section S1)between the DBPPS transition section and theabutment (or tunnel) In addition the vertical ac-celeration of the carbody also shows abrupt change atthese connections

(2) With train speed increases the vertical accelerationof the base slab increases and the vertical dynamicstress on the subgrade surface near the connections(such as section S1) also increases With axle weightincreases the vertical acceleration increases ap-proximately exponentially and the vertical dynamicstress increases approximately linearly )e traindirection has a significant influence on the con-nections and its adjacent areas with a large stiffnessdifference

(3) For general soil layers with uniform thickness theimprovement strategy with varying-length piles caneffectively smooth the track stiffness and reduce thetensile stress on the track slab surface at the

connections and the effect is more significant whenthe stiffness of the bearing layer is low

Data Availability

)e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

)e authors declare that they have no conflicts of interestregarding the publication of this paper

Acknowledgments

)is paper reports research developed under financialsupport provided by the Key Project of Science and Tech-nology Research and Development Program of ChinaRailway Corporation (Grant No 2014T003-D) and theNational Natural Science Foundation of China (Grant nos51878671 and 51678575)

References

[1] X Lei ldquoEffects of abrupt changes in track foundation stiffnesson track vibration under moving loadsrdquo Journal of VibrationEngineering vol 19 no 2 pp 195ndash199 2006

[2] A Paixatildeo E Fortunato and R Calccedilada ldquoTransition zones torailway bridges track measurements and numerical model-lingrdquo Engineering Structures vol 80 pp 435ndash443 2014

[3] K K Ang and J Dai ldquoResponse analysis of high-speed railsystem accounting for abrupt change of foundation stiffnessrdquoJournal of Sound and Vibration vol 332 no 12 pp 2954ndash2970 2013

[4] P Holscher and P Meijers Literature Study of Knowledge andExperience of Transition Zones Report of GeoDelft DelftNetherlands 2007

[5] European Committee for Standardisation(CEN) Basis ofstructural design European Committee for Stand-ardisation(CEN) Brussels Belgium 2005

Tunnel section Transition section Abutment

Track slab

Carbody

Rail

I II

Unit Pa+537e + 05+423e + 05+309e + 05+195e + 05+807e + 04ndash335e + 04ndash148e + 05ndash262e + 05ndash376e + 05ndash490e + 05ndash604e + 05ndash718e + 05ndash832e + 05

S S22(Average 75)

(a)

3510 15 20 25 30 400 5Distance from section T0 (m)

ndash200

0

200

400

600

800

Max

imum

tens

ile st

ress

(kPa

)

Case 1Case 2

Case 3Case 4

(b)

Figure 19 Tensile stress distribution for different cases (a) Tensile stress contour of Case 3 at a certain time (b) Maximum tensile stress fordifferent cases

Advances in Civil Engineering 15

[6] )e Swedish Rail Administration Design standard for railwaybridges Standard BVS 58310 )e Swedish Rail Adminis-tration Borlange Sweden 2006

[7] Canadian Standards AssociationndashInternational CanadianHighway Bridge Design Code Canadian Standards Associa-tionndashInternational Toronto Canada 2000

[8] National Railway Administration Code for Design of HighSpeed Railway (TB10621-2014) China Railway PublishingHouse Beijing China 2015

[9] D Li and D Davis ldquoTransition of railroad bridge ap-proachesrdquo Journal of Geotechnical and GeoenvironmentalEngineering vol 131 no 11 pp 1392ndash1398 2005

[10] P Hu C Zhang S J Chen Y Wang W Wang andW H Duan ldquoDynamic responses of bridge-embankmenttransitions in high speed railway field tests and data analysesrdquoEngineering Structures vol 175 pp 565ndash576 2018

[11] Y Shan B Albers and S A Savidis ldquoInfluence of differenttransition zones on the dynamic response of track-subgradesystemsrdquo Computers and Geotechnics vol 48 pp 21ndash28 2013

[12] Y Shan Y Shu and S Zhou ldquoFinite-infinite element coupledanalysis on the influence of material parameters on the dy-namic properties of transition zonesrdquo Construction andBuilding Materials vol 148 no 1 pp 548ndash558 2017

[13] J Ren H Zhao X Li et al ldquoDynamic performances of CRTSIII prefabricated slab track with anti-vibration structure insubgrade-tunnel transition sectionrdquo Journal of SouthwestJiaotong University vol 51 no 6 pp 1047ndash1054 2016

[14] J N Varandas P Holscher and M A G Silva ldquo)ree-di-mensional track-ballast interaction model for the study of aculvert transitionrdquo Soil Dynamics and Earthquake Engi-neering vol 89 pp 116ndash127 2016

[15] P Hu C Zhang S Wen and Y Wang ldquoDynamic responsesof high-speed railway transition zone with various subgradefillingsrdquoComputers and Geotechnics vol 108 pp 17ndash26 2019

[16] J N Varandas A Paixatildeo and E Fortunato ldquoA study on thedynamic train-track interaction over cut-fill transitions onburied culvertsrdquo Computers amp Structures vol 189 no 9pp 49ndash61 2017

[17] R Santildeudo L DellrsquoOlio J A Casado I A Carrascal andS Diego ldquoTrack transitions in railways a reviewrdquo Con-struction and Building Materials vol 112 pp 140ndash157 2016

[18] L Wei C He and Z Yang Comprehensive Test Study Reportof Nanchang West to Yichun East Section of Shanghai-Kunming Railway Passenger Dedicated Line Central SouthUniversity Changsha China 2014

[19] Q SuWWang H Bai et al ldquoBearing capacity mechanism ofnon-embedded pile-plank structure subgraderdquo Journal ofTraffic and Transportation Engineering vol 12 no 1pp 19ndash24 2012

[20] Y-X Zhan H-L Yao and G-L Jiang ldquoDesign method ofpile-slab structure roadbed of ballastless track on soil sub-graderdquo Journal of Central South University vol 20 no 7pp 2072ndash2082 2013

[21] KMa ldquoAnalysis on space vibration performance of pile-plankstructuremdashfoundation soil system under the condition ofhigh-speed trains runningrdquo Journal of the China RailwaySociety vol 35 no 1 pp 93ndash100 2013

[22] L Huang B Wang and S Zhou ldquoCentrifugal model test ofpile-plank subgrade in soft groundrdquo Rock and Soil Mechanicsvol 34 no S1 pp 192ndash196 2013

[23] J Huang Q Su T Liu and X Wang ldquoVibration and long-term performance analysis of pile-plank-supported lowsubgrade of ballastless track under excitation loadsrdquo Shockand Vibration vol 2015 pp 1ndash12 2015

[24] Dassault Systemes Simulia Corp Abaqus Analysis UserrsquosManual Version 612 Dassault Systemes Simulia CorpJohnston Rhode Island USA 2012

[25] C Cheng ldquoStudy on dynamic responses of irregularity bal-lastless track for high-speed railwayrdquo PhD )esis ZhejiangUniversity Zhejiang China 2015

[26] H Hertz ldquoOn the contact of elastic solidsrdquo Journal fur die rneund angewandte Mathematik (Crelles Journal) vol 92no 156 2008

[27] P Ni K Wang W Zhang et al ldquoCalculation method ofwheel-rail contact relationrdquo Journal of Traffic and Trans-portation Engineering vol 04 pp 14ndash17 2006

[28] W Zhai and X Sun ldquoA detailed model for investigatingvertical interaction between railway vehicle and trackrdquo Ve-hicle System Dynamics vol 23 pp 603ndash615 1994

[29] W Zhai Vehicle-track Coupled Dynamics Jeory and Ap-plication Science Press and Springer Nature Singapore PteLtd Berlin Germany 2020

[30] W Li and X Bian ldquoDynamic performance of pile-supportedbridge-embankment transition zones under high-speed trainmoving loadsrdquo Procedia Engineering vol 143 pp 1059ndash10672016

[31] P Ni S Mangalathu G Mei and Y Zhao ldquoPermeable pilesan alternative to improve the performance of driven pilesrdquoComputers and Geotechnics vol 84 pp 78ndash87 2017

[32] K Liu Q Su P Ni C Zhou W Zhao and F Yue ldquoEval-uation on the dynamic performance of bridge approachbackfilled with fibre reinforced lightweight concrete underhigh-speed train loadingrdquo Computers and Geotechnicsvol 104 pp 42ndash53 2018

[33] F Xue and J Zhang ldquoAttenuations of acceleration spectra ofhigh-speed railway embankment subjected to moving loadsrdquoRock and Soil Mechanics vol 36 pp 445ndash451 2015

[34] Y Xuan ldquoSimulation research on the dynamic characteristicsof vehicle-track coupling system on curved track and thevibration response of ballastless track strucure of passengertraffic railwayrdquo PhD )esis China Academy of RailwaySciences Beijing China 2008

[35] P Ricco A Baron and P Molteni ldquoNature of pressure wavesinduced by a high-speed train travelling through a tunnelrdquoJournal of Wind Engineering and Industrial Aerodynamicsvol 95 no 8 pp 781ndash808 2007

[36] C Esveld Modern Railway Track MRT-Productions Zalt-bommel Netherlands 2001

[37] R Santildeudo M Cerrada B Alonso and L dellrsquoOlio ldquoAnalysisof the influence of support positions in transition zones Anumerical analysisrdquo Construction and Building Materialsvol 145 no 1 pp 207ndash217 2017

[38] M Shahraki CWarnakulasooriya and K JWitt ldquoNumericalstudy of transition zone between ballasted and ballastlessrailway trackrdquo Transportation Geotechnics vol 3 pp 58ndash672015

[39] C Alves Ribeiro R Calccedilada and R Delgado ldquoExperimentalassessment of the dynamic behaviour of the train-track systemat a culvert transition zonerdquo Engineering Structures vol 138no 1 pp 215ndash228 2017

[40] Ministry of Railways Institute of StandardMetrology RailwayLocomotive Dynamic Performance Test Identification Methodand Evaluation Standard (TBT2360-1993) Ministry of Rail-ways Institute of Standard Metrology Beijing China 1994

16 Advances in Civil Engineering

ldquoTabularrdquo type in ABAQUS was proposed to simulate thenormal behavior of the wheel-rail interactionWith this settingthe change rate of the wheel-rail contact force would be sloweddown which was beneficial to the convergence of the calcu-lation For the tangential behavior of the wheel-rail interactiona ldquopenalty functionrdquo model with a friction coefficient of 02 wasadopted Considering that the rail was newly laid it wasregarded as an idealized horizontal track in the model

To reflect the coupling vibration inside the vehicle thedoubled suspension system was considered Based on thetheoretical model proposed by Zhai [28 29] for investigatingvertical interactions between railway vehicle and track thevehicle in this model was simplified to be composed ofwheelsets bogies and carbodies Connector elements withelastic-damping properties were adopted to simulate thesuspension systems between the wheelsets and bogies andbetween the bogies and carbody (Figure 4(e)) Consideringthe influence of adjacent wheelsets on wheel-rail interactiontwo carriages of the vehicle were selected in the model )esimulation of train speed was realized by applying the ve-locity (including translation velocity and rotation velocity)to the carbodies bogies and wheelsets along the rails

In general to reduce the reflection of stress waves at themodel boundary the model size should be as large as possiblebut more time and computer resources would be costly Toaddress this problem many scholars introduced an artificialboundary for simulation analysis Currently there are twomainstream modeling methods to minimize the reflected dy-namic wave at the boundary (i) using infinite elements at theboundary and setting viscous property between finite andinfinite elements [30 31] and (ii) introducing an artificialspring-damping boundary to absorb the dynamic wave[12 15 32] In this study the viscoelastic artificial boundarieswere adopted to reproduce the dynamic response using spring-damping elements )ese spring-damping elements were ap-plied in the boundary components in three directions at eachnode )e normal damping coefficient and stiffness coefficientwere determined according to the test results carried out by Huet al [15] Besides the bottom boundary of the model was fixedby a three-degree-of-freedom displacement constraint and thelateral and longitudinal boundaries were constrained by normaldisplacements

In this model the fillers in subgrade layers were modeledas MohrndashCoulomb material to consider the possibility ofplastic yield in the subgrade under heavy axle load (such asmore than 30 t) and the other components were modeled aslinear-elastic material )e parameters of different materialsare shown in Table 1 )e Rayleigh damping was adopted todescribe the damping properties of the components in thetransition zone the mass matrix coefficient α and stiffnessmatrix coefficient β are referenced from [33] To obtainaccurate calculation results the dynamic implicit algorithmwas adopted with a maximum time step of 25ms

32 Model Validation with Field Tests

321 Field Tests To validate the FE model field tests werecarried out )e 891-II type vibration sensors (Figure 5(a))were applied to measure the horizontal and vertical dynamic

responses including acceleration and velocity )e acceler-ation measurement range is plusmn40ms2 with a sensitivity of01V s2m (V is a voltage unit) and the velocity measure-ment range is plusmn05ms with a sensitivity of 300 V sm )evibration signals were collected by an INV3060D type ac-quisition analyzer (Figure 5(b)) With the vibration sensorsdata acquisition analyzer and network module data ac-quisition and wireless transmission test system for automatictrain triggering was established Measuring sections of B0S1 S2 S3 and T0 were established for the attempt to reflectthe variations of dynamic responses along the transitionzone Section B0 was set at the abutment section T0 was setat the tunnel entrance and sections of S1 S2 and S3 were setat the DBPPS subgrade (see Figures 2(a) and 5(c)) )evibration sensors were placed on the center of the subgradeon both sides of the base slab and on the slope of thesubgrade to investigate the transverse distribution of thedynamic response (Figure 5(d))

)e CRH380AM type trains with an axle weight of 150 tand a speed range of 236ndash335 kmh were tested )eschematic profile of CRH380AM type train is depicted inFigure 6 As an example the test results of this type of trainwere selected to verify the reliability of the FEmodel and thevehicle parameters are shown in Table 2

It is worth explaining that the field tests were carried outduring the period of the joint commissioning test whichmeans that the railway line was not officially operated in thatperiod )erefore there is no significant uneven permanentsettlement deformation that occurred in the transition zoneduring the field tests In the FE model the influence ofstiffness variations along the transition zone on dynamicresponse is considered while the influence of permanentsettlement deformation is ignored

322 Comparison between Numerical Results and FieldMeasurement )e test results of the CRH380AM train witha running speed of 300 kmh from a bridge to a tunnel arecompared with the numerical results for validation Figure 7shows the comparison of vertical acceleration and velocitytime-history curves at measuring points B0-3 S2-3 and T0-3 between the numerical results and the field measurement)ese signal curves have been filtered with a cutoff frequencyof 120Hz It can be seen that the amplitude and the curvetrend of the numerical results are in good agreement withthe measured results on the whole

Figure 8 shows the comparison of vertical accelerationand velocity peaks between the numerical results and thefield measurement Considering the randomness of trackvibration caused by the wheelsets the measured peaks hereare the average values of vibration peaks caused by twoadjacent bogies (ie four wheelsets) It also indicates that thegood agreement that is obtained between the numerical andthe experimental vertical acceleration and velocity peaksand the differences of vertical acceleration and velocity peaksbetween the numerical results and the field measurement arewithin 30 in most measuring points However a con-siderable difference is still observed at measuring points ofsection T0 on the base slab such as T0-3 (Figures 7(a) and

6 Advances in Civil Engineering

Table 1 Material properties of the components in the transition zone [15 22 33]

Components or material Youngrsquos modulus E (MPa) Poissonrsquos ratio μ Density ρ (kgm3)Rayleigh dampingα (sminus1) β (s)

Rail 205900 030 7830 0022 0002Track slab 32500 016 2500 0098 0009Base slab 25500 016 2500 0098 0009Graded gravel + 5 cement 1780 030 2100 0229 0021Graded gravel 1580 024 2000 0252 0022Bearing plank 56000 020 2500 0085 0009Cast-in-situ bores pile 38000 020 2500 0098 0008Silty clay 15 030 1930 0262 0024Sand layer 75 030 1950 0270 0023Limestone 600 029 2090 0235 002Abutment 30000 020 2300 0098 0009Bridge deck 22000 018 2550 0098 0009Tunnel filled concrete 20000 020 2400 0098 0009Tunnel bedrock 12000 020 2300 015 0015

(a) (b)

Kunming Shanghai

T0-6

T0-5T0-3

T0-2

T0 S2 S1 B0S3

S2-7S2-6

S2-5S2-3

S2-4S3-4S3-3

S3-2S3-1

S1-4S1-3

B0-5B0-3 B0-4

B0-2S1-2S1-1

S2-2S2-1

Track slab

RailPile

Up-line

Down-line

Base slab

Horizontal acceleration sensorldquoT0-2rdquo ndash ldquoT0rdquo (monitoring section) ldquo2rdquo (monitoring point number)

Vertical acceleration sensorVertical velocity sensor

(c)

S2-5 S2-6

S2-7

S2-3

S2-4

S2-2

S2-1

Up-lineDown-line

Base slab

Track slab

Subgrade surface layer

Subgrade base layer

Bearing plank

Pile

(d)

Figure 5 Measuring equipment and layout (a) 891-II type vibration sensor (b) INV3060D type acquisition analyzer and network module(c) Layout of measuring points in the transition zone (d) Layout of measuring points in the section S2

Advances in Civil Engineering 7

8(a)) )e differences of vertical acceleration peak and ve-locity peak at T0-3 between the numerical results and thefield measurement are approximately 543 and 408respectively )e main reason may be that an aerodynamiceffect [35] is generated at the tunnel entrance when the trainpasses by which aggravates the vibration of track compo-nents at section T0 But the effect is not well simulated in thenumerical model which induces a significant differencebetween the numerical results and the field measurementespecially in section T0

4 Results and Discussion

41 Dynamic Response along the Transition ZoneFigure 9 shows the distribution of vertical acceleration on thebase slab and the vertical track stiffness obtained from theformula proposed by [36] along the transition zone when theCRH380AM trainmoves from the bridge to the tunnel It can beseen that the vertical acceleration of the DBPPS transitionsection is less than that of the abutment and the tunnel sectionCompared with the tunnel section and the abutment the fillersin the DBPPS subgrade have the properties of low stiffness andlarge damping resulting in lower vibration levels in the DBPPSsubgrade Moreover a considerable amplification effect for thevertical acceleration can be observed at the connections(x 102m and x 362m) between the transition section andthe tunnel (or abutment) )e authors consider that the am-plification effect is caused by the abrupt change of wheel-railinteraction caused by the stiffness difference at the connections)is phenomenon was also found by Sanudo [37] and Shahraki[38]

It should be noted that the vertical acceleration of sectionS1 is higher than that of the sections S2 and S3 )is can beexplained that when the train passes through the connectionbetween the abutment and the transition section with anabrupt change stiffness an additional load on the trackcomponents is generated by the train load which aggravates

the vibration at the connection and its adjacent arearesulting in the vertical acceleration of section S1 beinghigher than that of sections S2 and S3

Although the dynamic response at connections is in-tensified due to the amplification effect the maximumvertical vibration acceleration of the transition zone is only023ms2 which is less than 50ms2 specified in the code[8] indicating that the DBPPS transition section exhibitsgood dynamic performance

)e coupling vibration inside the vehicle is considered inthe FE model and the line smoothness of the transition zonecan be evaluated by the dynamic response of the vehicleFigure 10 shows the vertical acceleration distribution of thevehicle which is comprised of an axle bogie and carbody alongthe transition zone Due to the dynamic contact interactionbetween the wheel and the rail the acceleration amplitude ofthe axle changes more dramatically and the vibration fre-quency is higher than that of bogie and carbody Furthermorebecause of the damping effect of the suspension system(connector elements) the acceleration amplitude and vibrationfrequency of the bogie and carbody are greatly reduced

It can be seen from Figure 10(b) that the frequencycomponents of the axle mainly consist of a low frequency of27Hz and a high frequency of 128Hz )e high frequencycomponent is caused by the excitation of fasteners (spring-dashpot elements) which can be verified as follows )espacing (L) of the fasteners is 065m then the excitationperiod (T) is as follows

T Lv (3)

where v is the train speed taken as 300 kmh or 8333ms)e excitation frequency f is determined as follows

f 1T vL 8333065 1282Hz (4)

)e results coincide well with the high frequencycomponent of the axle obtained from the numerical resultsFor the low frequency component it is mainly caused by theinteraction between the axle and the bogie On the whole thevibration frequency of the vehicle obtained from this FEmodel is close to the test results measured by Alves Ribeiro[39] which further indicates that the model is reliable

In addition the vibration response of the vehicle at theconnections (x 102m or x 362m) between the transitionsection and the tunnel (or abutment) is slightly higher than thatat other positions due to the sudden change of wheel-railinteraction caused by the stiffness difference (Figure 10(a)) Toensure the stable operation of the train and the comfort ofpassengers the standard [40] stipulates that the vertical ac-celeration of the carbody with excellent passenger comfort levelshall be less than 245ms2 As can be seen from Figure 10(a)

250 1500 500450

370

250 250 250 250 2501500 1500500

2 carriages simulated in the FE modelLength unit m

Figure 6 Schematic profile of CRH380AM type train

Table 2 Parameters of the vehicle [25 34]

Parameters ValueMass of the carbody 44320 kgMass of the bogie 3136 kgMass of the wheelset 2352 kgPitch inertia of the carbody 520e5 kgm2

Pitch inertia of the bogie 6400 kgm2

Stiffness of primary suspension 1040 kNmStiffness of secondary suspension 400 kNmDamping of primary suspension 40 kNmiddotsmDamping of secondary suspension 60 kNmiddotsm

8 Advances in Civil Engineering

the maximum vertical acceleration of the carbody is 075ms2indicating the train reaches an excellent comfort level and theDBPPS transition section fulfills its purpose in that it provides asmooth stiffness transition

42 Distribution of Vertical Dynamic Stress in the SubgradeTo analyze the vertical dynamic stress distribution in thesubgrade when the train passes by some observation points

at sections of S1 S2 and S3 in the FE model were selected asshown in Figure 11 Observation points of P1 P3 and P5 arelocated on the subgrade surface below the line center andobservation points of P2 P4 and P6 are located on thesubgrade surface directly below the rail Figure 11 shows thetime-history curves of vertical dynamic stress at these ob-servation points It can be seen that the vertical dynamicstress on the subgrade surface at observation points of P2P4 and P6 is 17sim18 higher than that at observation

ndash02

ndash01

0

01

02

03

04

Ver

tical

acce

lera

tion

(ms

2 )

101 103 105 107 10999Time (s)

FieldNum

ndash12

ndash06

0

06

12

18

24

Ver

tical

vel

ocity

(ms

)

101 103 105 107 10999Time (s)

FieldNum

times10ndash3

(a)

ndash04

ndash02

0

02

04

06

08

Ver

tical

acce

lera

tion

(ms

2 )

99 101 103 105 10797Time (s)

FieldNum

ndash1

ndash05

0

05

1

15

2

Ver

tical

vel

ocity

(ms

)

97 99 107103 105101Time (s)

FieldNum

times10ndash3

(b)

ndash06

ndash03

0

03

06

09

12

Ver

tical

acce

lera

tion

(ms

2 )

102 104 106 10810 11Time (s)

FieldNum

ndash2

ndash1

0

1

2

3

4

Ver

tical

vel

ocity

(ms

)

102 104 106 10810 11Time (s)

FieldNum

times10ndash3

(c)

Figure 7 Comparison of time-history curves between the numerical results and the field measurement (a) B0-3 (b) S1-3 (c) T0-3

Advances in Civil Engineering 9

points of P1 P3 and P5 More importantly the verticaldynamic stress of section S1 is higher than that of sections S2and S3 Figure 12 visually shows the vertical dynamic stresscontour of the train passing through section S1 and sectionS3 successively )e maximum vertical dynamic stress ofsection S1 is higher than that of section S3 which verifies theexistence of the additional loadmentioned above It becomesevident that when the train moves from the bridge to the

tunnel the additional load caused by the train load increasesthe dynamic stress on the subgrade surface of section S1which is also the reason why the vibration responses ofsection S1 are higher than that of sections S2 and S3 in thefield measurement (see Figure 8)

43 Influences of Train Speed Axle Weight and Direction onDynamic Response To investigate the influences of differentfactors on the dynamic responses of the transition sectionthree factors including train speed axle weight and runningdirection are selected for sensitivity analysis Figure 13(a)shows the relationship between the vertical acceleration onthe base slab and the train speed With the train speedincreasing from 200 kmh to 400 kmh the vertical accel-eration also increases in which the vertical accelerationincreases from 020ms2 to 044ms2 at measuring point T0-3 and increases from 0007ms2 to 030ms2 at measuringpoint S3-3 If the aerodynamic effect mentioned above is notconsidered in practice even if the train speed reaches400 kmh the vertical acceleration on the base slab is lessthan 50ms2 specified in the code [8] indicating that thetrack structure is still in safe service

In addition with the train speed increasing from200 kmh to 400 kmh the dynamic stress at observation

Ver

tical

acce

lera

tion

(ms

2 )

S1-3 S2-3 S3-3 T0-3B0-3Measuring points

00

01

02

03

04

05

FieldNum

Ver

tical

vel

ocity

(10ndash3

middotms

2 )

S1-3 S2-3 S3-3 T0-3B0-3Measuring points

03

06

09

12

15

18

FieldNum

(a)

Ver

tical

acce

lera

tion

(ms

2 )

S1-4 S2-4 S3-4B0-4Measuring points

000

005

010

015

020

025

FieldNum

Ver

tical

vel

ocity

(10ndash3

middotms

2 )

S1-4 S2-4 S3-4B0-4Measuring points

00

02

04

06

08

10

FieldNum

(b)

Figure 8 Comparison of vertical acceleration and velocity peaks between the numerical results and the field measurement (a) Measuringpoints on the base slab (b) Measuring points on the subgrade center

Ver

tical

stiff

ness

(kN

mm

) BridgeTransition sectionTunnel

70

80

90

100

110

120

Ver

tical

acce

lera

tion

(ms

2 )

010

015

020

025

030

035

4 8 12 16 20 24 28 32 36 400Distance from section T0 x (m)

Vertical stiffnessVertical acceleration

Figure 9 Distribution of the vertical acceleration and trackstiffness along the transition zone

10 Advances in Civil Engineering

points P4 and P6 is almost unchanged as shown inFigure 13(b) Nevertheless the dynamic stress at observationpoint P2 (at section S1) increases slightly from 305 kPa to316 kPa )e authors consider that the increase of dynamicstress at observation point P2 is related to the additionalload and with the increase of train speed the additional loadcaused by train load also increases in the connections with alarge stiffness difference

Figure 14(a) shows the relationship between the verticalacceleration on the base slab and the axle weight With the axleweight increasing from 10 t to 30 t the vertical accelerationincreases approximately exponentially and the vertical dy-namic stress increases approximately linearly (Figure 14(b))Consequently the axle weight is quite sensitive to the dynamicresponses of the DBPPS transition section

To reflect the influence of train direction on the dynamicresponses except for the vertical acceleration at originalobservation points the authors also select the vertical ac-celeration from other observation points at both sides of theconnections (ie x 102m and x 362m) wherex 89m 115m 349m and 375m as shown in Figure 15When the train moves from the tunnel to the bridge the

amplification effect can be observed at x 115m andx 375m while when the train moves from the bridge tothe tunnel the amplification effect occurs near x 89m andx 349m It can be concluded that under different traindirections the position with an amplification effect for vi-bration is also different which is determined by the positionand stiffness difference of the connections

44 Optimization of Pile Length in the Pile-Plank StructureIn the case study described in Section 2 an improvementstrategy with varying-length piles is adopted to achieve abetter transition due to the thickness of soft soil is uneven(Figure 2) Figure 16 shows the vertical displacement onthe pile top for different pile lengths It can be seen that thevertical displacement on the pile top is negatively cor-related with the pile length )e main reason is that thepiles with longer pile length can transfer the upper load toa deeper bearing layer But for shorter piles they bear theupper load together with the shallow soil with a lowerstiffness resulting in higher vertical displacement on thepile top According to the distribution of vertical

Ver

tical

acce

lera

tion

(ms

2 )4 8 12 16 20 24 28 32 36 400

Distance from section T0 x (m)

ndash15

ndash10

ndash5

0

5

10

15

AxleBogieCarbody

(a)

Am

plitu

de (m

s2 )

50 100 150 2000Frequency (Hz)

0

1

2

3

4

5

Axle

Am

plitu

de (m

s2 )

50 100 150 2000Frequency (Hz)

000

008

016

024

032

040

Bogie

Am

plitu

de (m

s2 )

50 100 150 2000Frequency (Hz)

000

006

012

018

024

030

Carbody

(b)

Figure 10 Vertical acceleration distribution of the train along the transition zone (a) Acceleration (b) Frequency

Advances in Civil Engineering 11

displacement for different pile lengths the strategy ofvarying-length piles is conducive to the stiffnesssmoothness in the transition zone

For general soil layers with uniform thickness Li andBian [30] discussed the influences of varying-length pilesand constant-length piles on the vertical track stiffness ina subgrade-bridge transition section and found that thevarying-length piles strategy can effectively smooth thevertical track stiffness transition Nevertheless for theDBPPS transition section under the general conditionsthe necessity of variable pile-length design is still de-batable In this study four comparative cases including

two improvement strategies varying-length piles andconstant-length piles are established to investigate theinfluences of pile length and the properties of soil on theDBPPS transition section as shown in Figure 17 In thesecases it is assumed that the ground consists of twohorizontal soil layers the upper layer is the silty clay layerthe bearing layer is the sand layer or limestone layer with ahigher stiffness than the silty clay layer )e materialproperties are shown in Table 1 and other parameters andwork conditions remain unchanged

Figure 18 shows the vertical track stiffness distributionalong the transition zone under four cases It can be seen thatthe smoothness of vertical track stiffness along the transitionsection can be improved by adopting the strategy of varying-length piles especially when the bearing layer is the sandlayer )e authors consider that when the bearing layer islimestone the bearing mode is similar to end-bearing pilesand the upper load is mainly transferred by piles to thebearing layer Consequently the change in pile length has asmall effect on the upper load transfer But when the bearinglayer is the sand layer with a lower stiffness the bearingmode is similar to friction-bearing piles and the upper loadis mainly shared by piles and the shallow ground )e in-crease of pile length effectively improves the friction resis-tance which indirectly enhances the overall stiffness of theground )erefore the strategy of varying-length piles caneffectively smooth the vertical track stiffness in the DBPPStransition section with a bearing layer of low stiffness

P1P2S1 sectionD

ynam

ic st

ress

(kPa

)10

0

ndash10

ndash20

ndash30

ndash40

ndash5002 04 06 08 1 12 14

Time (s)

P1P2

(a)

P3P4S2 sectionD

ynam

ic st

ress

(kPa

)

10

0

ndash10

ndash20

ndash30

ndash40

ndash5002 04 06 08 1 12 14

Time (s)

P3P4

(b)

P5P6S3 sectionD

ynam

ic st

ress

(kPa

)

10

0

ndash10

ndash20

ndash30

ndash40

ndash5002 04 06 08 1 12 14

Time (s)

P5P6

(c)

Figure 11 Time-history curves of the vertical dynamic stress (a) Observation points of section S1 (b) Observation points of section S2 (c)Observation points of section S3

+261e + 03+000e + 03ndash261e + 03ndash523e + 03ndash784e + 03ndash105e + 04ndash131e + 04ndash156e + 04ndash183e + 04ndash209e + 04ndash235e + 04ndash261e + 04ndash288e + 04ndash312e + 04

Fieldndash1 S33Unit Pa (Avg 75)

Maximum 291 kPa

S3 S1

Maximum 312 kPa

Train direction

x

yz

Figure 12 Vertical stress contour of the train passing throughsection S1 and section S3 successively

12 Advances in Civil Engineering

Changes in longitudinal stresses are more prone toactivate track slab cracking Figure 19(a) shows thelongitudinal stress (S22) contour on the track slab sur-face at a certain time for Case 3 A positive value

represents tensile stress and a negative value representscompressive stress It can be seen that under the trainload significant concentrated tension stresses are

250 300 350 400200Train speed (kmh)

0

01

02

03

04

05V

ertic

al v

ibra

tion

acce

lera

tion

(ms

2 )

B0-3S1-3S2-3

S3-3T0-3

(a)

250 300 350 400200Train speed (kmh)

25

27

29

31

33

35

Ver

tical

dyn

amic

stre

ss (k

Pa)

P2P4P6

(b)

Figure 13 Influences of the train speed on dynamic responses (a) Vertical acceleration (b) Vertical dynamic stress

S3-3T0-3

15 20 25 3010Vehicle axle weight (t)

0

02

04

06

08

Ver

tical

vib

ratio

nac

cele

ratio

n (m

s2 )

B0-3S1-3S2-3

(a)

15 20 25 3010Vehicle axle weight (t)

0

30

60

90

120

Ver

tical

dyn

amic

stre

ss (k

Pa)

P2P4P6

(b)

Figure 14 Influences of the axle weight on dynamic responses (a) Vertical acceleration (b) Vertical dynamic stress

x = 375

x = 349

x = 115

x = 89

B0S1

S2S3

T0

Tunnel Transition section Bridge

3 6 9 12 15 18 21 24 27 30 33 36 39 420Distance from section T0 x (m)

Ver

tical

acce

lera

tion

(ms

2 )

012

015

018

021

024

027

030

From bridge to tunnelFrom tunnel to bridge

Figure 15 Influence of the train direction on dynamic responses

Pile length = 23mPile length = 16m

Pile length = 13mPile length = 10m

ndash003

ndash0025

ndash002

ndash0015

ndash001

ndash0005

0

Ver

tical

disp

lace

men

t (m

m)

090603 12 150Time (s)

Figure 16 Vertical displacement on the pile top for piles of dif-ferent lengths

Advances in Civil Engineering 13

generated on the track slab surface at the positions I andII (Figure 19(a)) with the maximum value of 5374 kPaNevertheless long-term cyclic dynamic load caused bytrain may activate cracks at these positions

Figure 19(b) shows the comparison of maximum tensilestress along the DBPPS transition section in four cases )emaximum tensile stresses at positions I and II are signifi-cantly higher than those at other positions due to the largerstiffness difference When the bearing layer is limestonelayer the maximum tensile stress on the track slab surface at

positions I and II can be reduced by 109 and 78 re-spectively using varying-length piles while when thebearing layer is the sand layer the values can be reduced by278 and 182 respectively indicating that the strategy ofvarying-length piles can significantly reduce the tensile stresson the track slab surface and the lower the stiffness of thebearing layer the more the tensile stress reduces

In general to prevent cracks at the connection betweenabutment and transition section expansion joints or otherimproved measures would be applied to address these

5m 5m 3m 5m 5m

13mSilty clay

Limestone

(a)

5m 5m 3m 5m 5m

16m

23m

13mSilty clay

Limestone

(b)

5m 5m 3m 5m 5m

13mSilty clay

Sand

(c)

5m 5m 3m 5m 5m

16m13m

23m

Silty clay

Sand

(d)

Figure 17 Optimization cases of the pile-plank structure (a) Case 1 (b) Case 2 (c) Case 3 (d) Case 4

60

70

80

90

100

110

Ver

tical

stiff

ness

(kN

mm

)

3510 15 20 25 30 400 5Distance from T0 section (m)

Case 1Case 2

Case 3Case 4

Figure 18 Vertical stiffness along the transition zone for different cases

14 Advances in Civil Engineering

problems in practical engineering From the above resultsthe authors suggest that in addition to the connection be-tween the bridge and the DBPPS transition section theconnection between the tunnel and the DBPPS transitionsection should also be reinforced or treated

5 Conclusions

In this study the authors present a numerical modelingapproach to investigate the dynamic performances of a newtype of bridge-tunnel transition section with a DBPPSwhich can be used as a tool to improve the design andapplication of DBPPS subgrade )e obtained research re-sults of this study lead to the following conclusions

(1) )e vibration level of the DBPPS transition section islower than that of the abutment and the tunnelsection when the train passes by Meanwhile theadditional load caused by vertical track stiffnessdifference can aggravate the vibration at the con-nections and its adjacent areas (such as section S1)between the DBPPS transition section and theabutment (or tunnel) In addition the vertical ac-celeration of the carbody also shows abrupt change atthese connections

(2) With train speed increases the vertical accelerationof the base slab increases and the vertical dynamicstress on the subgrade surface near the connections(such as section S1) also increases With axle weightincreases the vertical acceleration increases ap-proximately exponentially and the vertical dynamicstress increases approximately linearly )e traindirection has a significant influence on the con-nections and its adjacent areas with a large stiffnessdifference

(3) For general soil layers with uniform thickness theimprovement strategy with varying-length piles caneffectively smooth the track stiffness and reduce thetensile stress on the track slab surface at the

connections and the effect is more significant whenthe stiffness of the bearing layer is low

Data Availability

)e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

)e authors declare that they have no conflicts of interestregarding the publication of this paper

Acknowledgments

)is paper reports research developed under financialsupport provided by the Key Project of Science and Tech-nology Research and Development Program of ChinaRailway Corporation (Grant No 2014T003-D) and theNational Natural Science Foundation of China (Grant nos51878671 and 51678575)

References

[1] X Lei ldquoEffects of abrupt changes in track foundation stiffnesson track vibration under moving loadsrdquo Journal of VibrationEngineering vol 19 no 2 pp 195ndash199 2006

[2] A Paixatildeo E Fortunato and R Calccedilada ldquoTransition zones torailway bridges track measurements and numerical model-lingrdquo Engineering Structures vol 80 pp 435ndash443 2014

[3] K K Ang and J Dai ldquoResponse analysis of high-speed railsystem accounting for abrupt change of foundation stiffnessrdquoJournal of Sound and Vibration vol 332 no 12 pp 2954ndash2970 2013

[4] P Holscher and P Meijers Literature Study of Knowledge andExperience of Transition Zones Report of GeoDelft DelftNetherlands 2007

[5] European Committee for Standardisation(CEN) Basis ofstructural design European Committee for Stand-ardisation(CEN) Brussels Belgium 2005

Tunnel section Transition section Abutment

Track slab

Carbody

Rail

I II

Unit Pa+537e + 05+423e + 05+309e + 05+195e + 05+807e + 04ndash335e + 04ndash148e + 05ndash262e + 05ndash376e + 05ndash490e + 05ndash604e + 05ndash718e + 05ndash832e + 05

S S22(Average 75)

(a)

3510 15 20 25 30 400 5Distance from section T0 (m)

ndash200

0

200

400

600

800

Max

imum

tens

ile st

ress

(kPa

)

Case 1Case 2

Case 3Case 4

(b)

Figure 19 Tensile stress distribution for different cases (a) Tensile stress contour of Case 3 at a certain time (b) Maximum tensile stress fordifferent cases

Advances in Civil Engineering 15

[6] )e Swedish Rail Administration Design standard for railwaybridges Standard BVS 58310 )e Swedish Rail Adminis-tration Borlange Sweden 2006

[7] Canadian Standards AssociationndashInternational CanadianHighway Bridge Design Code Canadian Standards Associa-tionndashInternational Toronto Canada 2000

[8] National Railway Administration Code for Design of HighSpeed Railway (TB10621-2014) China Railway PublishingHouse Beijing China 2015

[9] D Li and D Davis ldquoTransition of railroad bridge ap-proachesrdquo Journal of Geotechnical and GeoenvironmentalEngineering vol 131 no 11 pp 1392ndash1398 2005

[10] P Hu C Zhang S J Chen Y Wang W Wang andW H Duan ldquoDynamic responses of bridge-embankmenttransitions in high speed railway field tests and data analysesrdquoEngineering Structures vol 175 pp 565ndash576 2018

[11] Y Shan B Albers and S A Savidis ldquoInfluence of differenttransition zones on the dynamic response of track-subgradesystemsrdquo Computers and Geotechnics vol 48 pp 21ndash28 2013

[12] Y Shan Y Shu and S Zhou ldquoFinite-infinite element coupledanalysis on the influence of material parameters on the dy-namic properties of transition zonesrdquo Construction andBuilding Materials vol 148 no 1 pp 548ndash558 2017

[13] J Ren H Zhao X Li et al ldquoDynamic performances of CRTSIII prefabricated slab track with anti-vibration structure insubgrade-tunnel transition sectionrdquo Journal of SouthwestJiaotong University vol 51 no 6 pp 1047ndash1054 2016

[14] J N Varandas P Holscher and M A G Silva ldquo)ree-di-mensional track-ballast interaction model for the study of aculvert transitionrdquo Soil Dynamics and Earthquake Engi-neering vol 89 pp 116ndash127 2016

[15] P Hu C Zhang S Wen and Y Wang ldquoDynamic responsesof high-speed railway transition zone with various subgradefillingsrdquoComputers and Geotechnics vol 108 pp 17ndash26 2019

[16] J N Varandas A Paixatildeo and E Fortunato ldquoA study on thedynamic train-track interaction over cut-fill transitions onburied culvertsrdquo Computers amp Structures vol 189 no 9pp 49ndash61 2017

[17] R Santildeudo L DellrsquoOlio J A Casado I A Carrascal andS Diego ldquoTrack transitions in railways a reviewrdquo Con-struction and Building Materials vol 112 pp 140ndash157 2016

[18] L Wei C He and Z Yang Comprehensive Test Study Reportof Nanchang West to Yichun East Section of Shanghai-Kunming Railway Passenger Dedicated Line Central SouthUniversity Changsha China 2014

[19] Q SuWWang H Bai et al ldquoBearing capacity mechanism ofnon-embedded pile-plank structure subgraderdquo Journal ofTraffic and Transportation Engineering vol 12 no 1pp 19ndash24 2012

[20] Y-X Zhan H-L Yao and G-L Jiang ldquoDesign method ofpile-slab structure roadbed of ballastless track on soil sub-graderdquo Journal of Central South University vol 20 no 7pp 2072ndash2082 2013

[21] KMa ldquoAnalysis on space vibration performance of pile-plankstructuremdashfoundation soil system under the condition ofhigh-speed trains runningrdquo Journal of the China RailwaySociety vol 35 no 1 pp 93ndash100 2013

[22] L Huang B Wang and S Zhou ldquoCentrifugal model test ofpile-plank subgrade in soft groundrdquo Rock and Soil Mechanicsvol 34 no S1 pp 192ndash196 2013

[23] J Huang Q Su T Liu and X Wang ldquoVibration and long-term performance analysis of pile-plank-supported lowsubgrade of ballastless track under excitation loadsrdquo Shockand Vibration vol 2015 pp 1ndash12 2015

[24] Dassault Systemes Simulia Corp Abaqus Analysis UserrsquosManual Version 612 Dassault Systemes Simulia CorpJohnston Rhode Island USA 2012

[25] C Cheng ldquoStudy on dynamic responses of irregularity bal-lastless track for high-speed railwayrdquo PhD )esis ZhejiangUniversity Zhejiang China 2015

[26] H Hertz ldquoOn the contact of elastic solidsrdquo Journal fur die rneund angewandte Mathematik (Crelles Journal) vol 92no 156 2008

[27] P Ni K Wang W Zhang et al ldquoCalculation method ofwheel-rail contact relationrdquo Journal of Traffic and Trans-portation Engineering vol 04 pp 14ndash17 2006

[28] W Zhai and X Sun ldquoA detailed model for investigatingvertical interaction between railway vehicle and trackrdquo Ve-hicle System Dynamics vol 23 pp 603ndash615 1994

[29] W Zhai Vehicle-track Coupled Dynamics Jeory and Ap-plication Science Press and Springer Nature Singapore PteLtd Berlin Germany 2020

[30] W Li and X Bian ldquoDynamic performance of pile-supportedbridge-embankment transition zones under high-speed trainmoving loadsrdquo Procedia Engineering vol 143 pp 1059ndash10672016

[31] P Ni S Mangalathu G Mei and Y Zhao ldquoPermeable pilesan alternative to improve the performance of driven pilesrdquoComputers and Geotechnics vol 84 pp 78ndash87 2017

[32] K Liu Q Su P Ni C Zhou W Zhao and F Yue ldquoEval-uation on the dynamic performance of bridge approachbackfilled with fibre reinforced lightweight concrete underhigh-speed train loadingrdquo Computers and Geotechnicsvol 104 pp 42ndash53 2018

[33] F Xue and J Zhang ldquoAttenuations of acceleration spectra ofhigh-speed railway embankment subjected to moving loadsrdquoRock and Soil Mechanics vol 36 pp 445ndash451 2015

[34] Y Xuan ldquoSimulation research on the dynamic characteristicsof vehicle-track coupling system on curved track and thevibration response of ballastless track strucure of passengertraffic railwayrdquo PhD )esis China Academy of RailwaySciences Beijing China 2008

[35] P Ricco A Baron and P Molteni ldquoNature of pressure wavesinduced by a high-speed train travelling through a tunnelrdquoJournal of Wind Engineering and Industrial Aerodynamicsvol 95 no 8 pp 781ndash808 2007

[36] C Esveld Modern Railway Track MRT-Productions Zalt-bommel Netherlands 2001

[37] R Santildeudo M Cerrada B Alonso and L dellrsquoOlio ldquoAnalysisof the influence of support positions in transition zones Anumerical analysisrdquo Construction and Building Materialsvol 145 no 1 pp 207ndash217 2017

[38] M Shahraki CWarnakulasooriya and K JWitt ldquoNumericalstudy of transition zone between ballasted and ballastlessrailway trackrdquo Transportation Geotechnics vol 3 pp 58ndash672015

[39] C Alves Ribeiro R Calccedilada and R Delgado ldquoExperimentalassessment of the dynamic behaviour of the train-track systemat a culvert transition zonerdquo Engineering Structures vol 138no 1 pp 215ndash228 2017

[40] Ministry of Railways Institute of StandardMetrology RailwayLocomotive Dynamic Performance Test Identification Methodand Evaluation Standard (TBT2360-1993) Ministry of Rail-ways Institute of Standard Metrology Beijing China 1994

16 Advances in Civil Engineering

Table 1 Material properties of the components in the transition zone [15 22 33]

Components or material Youngrsquos modulus E (MPa) Poissonrsquos ratio μ Density ρ (kgm3)Rayleigh dampingα (sminus1) β (s)

Rail 205900 030 7830 0022 0002Track slab 32500 016 2500 0098 0009Base slab 25500 016 2500 0098 0009Graded gravel + 5 cement 1780 030 2100 0229 0021Graded gravel 1580 024 2000 0252 0022Bearing plank 56000 020 2500 0085 0009Cast-in-situ bores pile 38000 020 2500 0098 0008Silty clay 15 030 1930 0262 0024Sand layer 75 030 1950 0270 0023Limestone 600 029 2090 0235 002Abutment 30000 020 2300 0098 0009Bridge deck 22000 018 2550 0098 0009Tunnel filled concrete 20000 020 2400 0098 0009Tunnel bedrock 12000 020 2300 015 0015

(a) (b)

Kunming Shanghai

T0-6

T0-5T0-3

T0-2

T0 S2 S1 B0S3

S2-7S2-6

S2-5S2-3

S2-4S3-4S3-3

S3-2S3-1

S1-4S1-3

B0-5B0-3 B0-4

B0-2S1-2S1-1

S2-2S2-1

Track slab

RailPile

Up-line

Down-line

Base slab

Horizontal acceleration sensorldquoT0-2rdquo ndash ldquoT0rdquo (monitoring section) ldquo2rdquo (monitoring point number)

Vertical acceleration sensorVertical velocity sensor

(c)

S2-5 S2-6

S2-7

S2-3

S2-4

S2-2

S2-1

Up-lineDown-line

Base slab

Track slab

Subgrade surface layer

Subgrade base layer

Bearing plank

Pile

(d)

Figure 5 Measuring equipment and layout (a) 891-II type vibration sensor (b) INV3060D type acquisition analyzer and network module(c) Layout of measuring points in the transition zone (d) Layout of measuring points in the section S2

Advances in Civil Engineering 7

8(a)) )e differences of vertical acceleration peak and ve-locity peak at T0-3 between the numerical results and thefield measurement are approximately 543 and 408respectively )e main reason may be that an aerodynamiceffect [35] is generated at the tunnel entrance when the trainpasses by which aggravates the vibration of track compo-nents at section T0 But the effect is not well simulated in thenumerical model which induces a significant differencebetween the numerical results and the field measurementespecially in section T0

4 Results and Discussion

41 Dynamic Response along the Transition ZoneFigure 9 shows the distribution of vertical acceleration on thebase slab and the vertical track stiffness obtained from theformula proposed by [36] along the transition zone when theCRH380AM trainmoves from the bridge to the tunnel It can beseen that the vertical acceleration of the DBPPS transitionsection is less than that of the abutment and the tunnel sectionCompared with the tunnel section and the abutment the fillersin the DBPPS subgrade have the properties of low stiffness andlarge damping resulting in lower vibration levels in the DBPPSsubgrade Moreover a considerable amplification effect for thevertical acceleration can be observed at the connections(x 102m and x 362m) between the transition section andthe tunnel (or abutment) )e authors consider that the am-plification effect is caused by the abrupt change of wheel-railinteraction caused by the stiffness difference at the connections)is phenomenon was also found by Sanudo [37] and Shahraki[38]

It should be noted that the vertical acceleration of sectionS1 is higher than that of the sections S2 and S3 )is can beexplained that when the train passes through the connectionbetween the abutment and the transition section with anabrupt change stiffness an additional load on the trackcomponents is generated by the train load which aggravates

the vibration at the connection and its adjacent arearesulting in the vertical acceleration of section S1 beinghigher than that of sections S2 and S3

Although the dynamic response at connections is in-tensified due to the amplification effect the maximumvertical vibration acceleration of the transition zone is only023ms2 which is less than 50ms2 specified in the code[8] indicating that the DBPPS transition section exhibitsgood dynamic performance

)e coupling vibration inside the vehicle is considered inthe FE model and the line smoothness of the transition zonecan be evaluated by the dynamic response of the vehicleFigure 10 shows the vertical acceleration distribution of thevehicle which is comprised of an axle bogie and carbody alongthe transition zone Due to the dynamic contact interactionbetween the wheel and the rail the acceleration amplitude ofthe axle changes more dramatically and the vibration fre-quency is higher than that of bogie and carbody Furthermorebecause of the damping effect of the suspension system(connector elements) the acceleration amplitude and vibrationfrequency of the bogie and carbody are greatly reduced

It can be seen from Figure 10(b) that the frequencycomponents of the axle mainly consist of a low frequency of27Hz and a high frequency of 128Hz )e high frequencycomponent is caused by the excitation of fasteners (spring-dashpot elements) which can be verified as follows )espacing (L) of the fasteners is 065m then the excitationperiod (T) is as follows

T Lv (3)

where v is the train speed taken as 300 kmh or 8333ms)e excitation frequency f is determined as follows

f 1T vL 8333065 1282Hz (4)

)e results coincide well with the high frequencycomponent of the axle obtained from the numerical resultsFor the low frequency component it is mainly caused by theinteraction between the axle and the bogie On the whole thevibration frequency of the vehicle obtained from this FEmodel is close to the test results measured by Alves Ribeiro[39] which further indicates that the model is reliable

In addition the vibration response of the vehicle at theconnections (x 102m or x 362m) between the transitionsection and the tunnel (or abutment) is slightly higher than thatat other positions due to the sudden change of wheel-railinteraction caused by the stiffness difference (Figure 10(a)) Toensure the stable operation of the train and the comfort ofpassengers the standard [40] stipulates that the vertical ac-celeration of the carbody with excellent passenger comfort levelshall be less than 245ms2 As can be seen from Figure 10(a)

250 1500 500450

370

250 250 250 250 2501500 1500500

2 carriages simulated in the FE modelLength unit m

Figure 6 Schematic profile of CRH380AM type train

Table 2 Parameters of the vehicle [25 34]

Parameters ValueMass of the carbody 44320 kgMass of the bogie 3136 kgMass of the wheelset 2352 kgPitch inertia of the carbody 520e5 kgm2

Pitch inertia of the bogie 6400 kgm2

Stiffness of primary suspension 1040 kNmStiffness of secondary suspension 400 kNmDamping of primary suspension 40 kNmiddotsmDamping of secondary suspension 60 kNmiddotsm

8 Advances in Civil Engineering

the maximum vertical acceleration of the carbody is 075ms2indicating the train reaches an excellent comfort level and theDBPPS transition section fulfills its purpose in that it provides asmooth stiffness transition

42 Distribution of Vertical Dynamic Stress in the SubgradeTo analyze the vertical dynamic stress distribution in thesubgrade when the train passes by some observation points

at sections of S1 S2 and S3 in the FE model were selected asshown in Figure 11 Observation points of P1 P3 and P5 arelocated on the subgrade surface below the line center andobservation points of P2 P4 and P6 are located on thesubgrade surface directly below the rail Figure 11 shows thetime-history curves of vertical dynamic stress at these ob-servation points It can be seen that the vertical dynamicstress on the subgrade surface at observation points of P2P4 and P6 is 17sim18 higher than that at observation

ndash02

ndash01

0

01

02

03

04

Ver

tical

acce

lera

tion

(ms

2 )

101 103 105 107 10999Time (s)

FieldNum

ndash12

ndash06

0

06

12

18

24

Ver

tical

vel

ocity

(ms

)

101 103 105 107 10999Time (s)

FieldNum

times10ndash3

(a)

ndash04

ndash02

0

02

04

06

08

Ver

tical

acce

lera

tion

(ms

2 )

99 101 103 105 10797Time (s)

FieldNum

ndash1

ndash05

0

05

1

15

2

Ver

tical

vel

ocity

(ms

)

97 99 107103 105101Time (s)

FieldNum

times10ndash3

(b)

ndash06

ndash03

0

03

06

09

12

Ver

tical

acce

lera

tion

(ms

2 )

102 104 106 10810 11Time (s)

FieldNum

ndash2

ndash1

0

1

2

3

4

Ver

tical

vel

ocity

(ms

)

102 104 106 10810 11Time (s)

FieldNum

times10ndash3

(c)

Figure 7 Comparison of time-history curves between the numerical results and the field measurement (a) B0-3 (b) S1-3 (c) T0-3

Advances in Civil Engineering 9

points of P1 P3 and P5 More importantly the verticaldynamic stress of section S1 is higher than that of sections S2and S3 Figure 12 visually shows the vertical dynamic stresscontour of the train passing through section S1 and sectionS3 successively )e maximum vertical dynamic stress ofsection S1 is higher than that of section S3 which verifies theexistence of the additional loadmentioned above It becomesevident that when the train moves from the bridge to the

tunnel the additional load caused by the train load increasesthe dynamic stress on the subgrade surface of section S1which is also the reason why the vibration responses ofsection S1 are higher than that of sections S2 and S3 in thefield measurement (see Figure 8)

43 Influences of Train Speed Axle Weight and Direction onDynamic Response To investigate the influences of differentfactors on the dynamic responses of the transition sectionthree factors including train speed axle weight and runningdirection are selected for sensitivity analysis Figure 13(a)shows the relationship between the vertical acceleration onthe base slab and the train speed With the train speedincreasing from 200 kmh to 400 kmh the vertical accel-eration also increases in which the vertical accelerationincreases from 020ms2 to 044ms2 at measuring point T0-3 and increases from 0007ms2 to 030ms2 at measuringpoint S3-3 If the aerodynamic effect mentioned above is notconsidered in practice even if the train speed reaches400 kmh the vertical acceleration on the base slab is lessthan 50ms2 specified in the code [8] indicating that thetrack structure is still in safe service

In addition with the train speed increasing from200 kmh to 400 kmh the dynamic stress at observation

Ver

tical

acce

lera

tion

(ms

2 )

S1-3 S2-3 S3-3 T0-3B0-3Measuring points

00

01

02

03

04

05

FieldNum

Ver

tical

vel

ocity

(10ndash3

middotms

2 )

S1-3 S2-3 S3-3 T0-3B0-3Measuring points

03

06

09

12

15

18

FieldNum

(a)

Ver

tical

acce

lera

tion

(ms

2 )

S1-4 S2-4 S3-4B0-4Measuring points

000

005

010

015

020

025

FieldNum

Ver

tical

vel

ocity

(10ndash3

middotms

2 )

S1-4 S2-4 S3-4B0-4Measuring points

00

02

04

06

08

10

FieldNum

(b)

Figure 8 Comparison of vertical acceleration and velocity peaks between the numerical results and the field measurement (a) Measuringpoints on the base slab (b) Measuring points on the subgrade center

Ver

tical

stiff

ness

(kN

mm

) BridgeTransition sectionTunnel

70

80

90

100

110

120

Ver

tical

acce

lera

tion

(ms

2 )

010

015

020

025

030

035

4 8 12 16 20 24 28 32 36 400Distance from section T0 x (m)

Vertical stiffnessVertical acceleration

Figure 9 Distribution of the vertical acceleration and trackstiffness along the transition zone

10 Advances in Civil Engineering

points P4 and P6 is almost unchanged as shown inFigure 13(b) Nevertheless the dynamic stress at observationpoint P2 (at section S1) increases slightly from 305 kPa to316 kPa )e authors consider that the increase of dynamicstress at observation point P2 is related to the additionalload and with the increase of train speed the additional loadcaused by train load also increases in the connections with alarge stiffness difference

Figure 14(a) shows the relationship between the verticalacceleration on the base slab and the axle weight With the axleweight increasing from 10 t to 30 t the vertical accelerationincreases approximately exponentially and the vertical dy-namic stress increases approximately linearly (Figure 14(b))Consequently the axle weight is quite sensitive to the dynamicresponses of the DBPPS transition section

To reflect the influence of train direction on the dynamicresponses except for the vertical acceleration at originalobservation points the authors also select the vertical ac-celeration from other observation points at both sides of theconnections (ie x 102m and x 362m) wherex 89m 115m 349m and 375m as shown in Figure 15When the train moves from the tunnel to the bridge the

amplification effect can be observed at x 115m andx 375m while when the train moves from the bridge tothe tunnel the amplification effect occurs near x 89m andx 349m It can be concluded that under different traindirections the position with an amplification effect for vi-bration is also different which is determined by the positionand stiffness difference of the connections

44 Optimization of Pile Length in the Pile-Plank StructureIn the case study described in Section 2 an improvementstrategy with varying-length piles is adopted to achieve abetter transition due to the thickness of soft soil is uneven(Figure 2) Figure 16 shows the vertical displacement onthe pile top for different pile lengths It can be seen that thevertical displacement on the pile top is negatively cor-related with the pile length )e main reason is that thepiles with longer pile length can transfer the upper load toa deeper bearing layer But for shorter piles they bear theupper load together with the shallow soil with a lowerstiffness resulting in higher vertical displacement on thepile top According to the distribution of vertical

Ver

tical

acce

lera

tion

(ms

2 )4 8 12 16 20 24 28 32 36 400

Distance from section T0 x (m)

ndash15

ndash10

ndash5

0

5

10

15

AxleBogieCarbody

(a)

Am

plitu

de (m

s2 )

50 100 150 2000Frequency (Hz)

0

1

2

3

4

5

Axle

Am

plitu

de (m

s2 )

50 100 150 2000Frequency (Hz)

000

008

016

024

032

040

Bogie

Am

plitu

de (m

s2 )

50 100 150 2000Frequency (Hz)

000

006

012

018

024

030

Carbody

(b)

Figure 10 Vertical acceleration distribution of the train along the transition zone (a) Acceleration (b) Frequency

Advances in Civil Engineering 11

displacement for different pile lengths the strategy ofvarying-length piles is conducive to the stiffnesssmoothness in the transition zone

For general soil layers with uniform thickness Li andBian [30] discussed the influences of varying-length pilesand constant-length piles on the vertical track stiffness ina subgrade-bridge transition section and found that thevarying-length piles strategy can effectively smooth thevertical track stiffness transition Nevertheless for theDBPPS transition section under the general conditionsthe necessity of variable pile-length design is still de-batable In this study four comparative cases including

two improvement strategies varying-length piles andconstant-length piles are established to investigate theinfluences of pile length and the properties of soil on theDBPPS transition section as shown in Figure 17 In thesecases it is assumed that the ground consists of twohorizontal soil layers the upper layer is the silty clay layerthe bearing layer is the sand layer or limestone layer with ahigher stiffness than the silty clay layer )e materialproperties are shown in Table 1 and other parameters andwork conditions remain unchanged

Figure 18 shows the vertical track stiffness distributionalong the transition zone under four cases It can be seen thatthe smoothness of vertical track stiffness along the transitionsection can be improved by adopting the strategy of varying-length piles especially when the bearing layer is the sandlayer )e authors consider that when the bearing layer islimestone the bearing mode is similar to end-bearing pilesand the upper load is mainly transferred by piles to thebearing layer Consequently the change in pile length has asmall effect on the upper load transfer But when the bearinglayer is the sand layer with a lower stiffness the bearingmode is similar to friction-bearing piles and the upper loadis mainly shared by piles and the shallow ground )e in-crease of pile length effectively improves the friction resis-tance which indirectly enhances the overall stiffness of theground )erefore the strategy of varying-length piles caneffectively smooth the vertical track stiffness in the DBPPStransition section with a bearing layer of low stiffness

P1P2S1 sectionD

ynam

ic st

ress

(kPa

)10

0

ndash10

ndash20

ndash30

ndash40

ndash5002 04 06 08 1 12 14

Time (s)

P1P2

(a)

P3P4S2 sectionD

ynam

ic st

ress

(kPa

)

10

0

ndash10

ndash20

ndash30

ndash40

ndash5002 04 06 08 1 12 14

Time (s)

P3P4

(b)

P5P6S3 sectionD

ynam

ic st

ress

(kPa

)

10

0

ndash10

ndash20

ndash30

ndash40

ndash5002 04 06 08 1 12 14

Time (s)

P5P6

(c)

Figure 11 Time-history curves of the vertical dynamic stress (a) Observation points of section S1 (b) Observation points of section S2 (c)Observation points of section S3

+261e + 03+000e + 03ndash261e + 03ndash523e + 03ndash784e + 03ndash105e + 04ndash131e + 04ndash156e + 04ndash183e + 04ndash209e + 04ndash235e + 04ndash261e + 04ndash288e + 04ndash312e + 04

Fieldndash1 S33Unit Pa (Avg 75)

Maximum 291 kPa

S3 S1

Maximum 312 kPa

Train direction

x

yz

Figure 12 Vertical stress contour of the train passing throughsection S1 and section S3 successively

12 Advances in Civil Engineering

Changes in longitudinal stresses are more prone toactivate track slab cracking Figure 19(a) shows thelongitudinal stress (S22) contour on the track slab sur-face at a certain time for Case 3 A positive value

represents tensile stress and a negative value representscompressive stress It can be seen that under the trainload significant concentrated tension stresses are

250 300 350 400200Train speed (kmh)

0

01

02

03

04

05V

ertic

al v

ibra

tion

acce

lera

tion

(ms

2 )

B0-3S1-3S2-3

S3-3T0-3

(a)

250 300 350 400200Train speed (kmh)

25

27

29

31

33

35

Ver

tical

dyn

amic

stre

ss (k

Pa)

P2P4P6

(b)

Figure 13 Influences of the train speed on dynamic responses (a) Vertical acceleration (b) Vertical dynamic stress

S3-3T0-3

15 20 25 3010Vehicle axle weight (t)

0

02

04

06

08

Ver

tical

vib

ratio

nac

cele

ratio

n (m

s2 )

B0-3S1-3S2-3

(a)

15 20 25 3010Vehicle axle weight (t)

0

30

60

90

120

Ver

tical

dyn

amic

stre

ss (k

Pa)

P2P4P6

(b)

Figure 14 Influences of the axle weight on dynamic responses (a) Vertical acceleration (b) Vertical dynamic stress

x = 375

x = 349

x = 115

x = 89

B0S1

S2S3

T0

Tunnel Transition section Bridge

3 6 9 12 15 18 21 24 27 30 33 36 39 420Distance from section T0 x (m)

Ver

tical

acce

lera

tion

(ms

2 )

012

015

018

021

024

027

030

From bridge to tunnelFrom tunnel to bridge

Figure 15 Influence of the train direction on dynamic responses

Pile length = 23mPile length = 16m

Pile length = 13mPile length = 10m

ndash003

ndash0025

ndash002

ndash0015

ndash001

ndash0005

0

Ver

tical

disp

lace

men

t (m

m)

090603 12 150Time (s)

Figure 16 Vertical displacement on the pile top for piles of dif-ferent lengths

Advances in Civil Engineering 13

generated on the track slab surface at the positions I andII (Figure 19(a)) with the maximum value of 5374 kPaNevertheless long-term cyclic dynamic load caused bytrain may activate cracks at these positions

Figure 19(b) shows the comparison of maximum tensilestress along the DBPPS transition section in four cases )emaximum tensile stresses at positions I and II are signifi-cantly higher than those at other positions due to the largerstiffness difference When the bearing layer is limestonelayer the maximum tensile stress on the track slab surface at

positions I and II can be reduced by 109 and 78 re-spectively using varying-length piles while when thebearing layer is the sand layer the values can be reduced by278 and 182 respectively indicating that the strategy ofvarying-length piles can significantly reduce the tensile stresson the track slab surface and the lower the stiffness of thebearing layer the more the tensile stress reduces

In general to prevent cracks at the connection betweenabutment and transition section expansion joints or otherimproved measures would be applied to address these

5m 5m 3m 5m 5m

13mSilty clay

Limestone

(a)

5m 5m 3m 5m 5m

16m

23m

13mSilty clay

Limestone

(b)

5m 5m 3m 5m 5m

13mSilty clay

Sand

(c)

5m 5m 3m 5m 5m

16m13m

23m

Silty clay

Sand

(d)

Figure 17 Optimization cases of the pile-plank structure (a) Case 1 (b) Case 2 (c) Case 3 (d) Case 4

60

70

80

90

100

110

Ver

tical

stiff

ness

(kN

mm

)

3510 15 20 25 30 400 5Distance from T0 section (m)

Case 1Case 2

Case 3Case 4

Figure 18 Vertical stiffness along the transition zone for different cases

14 Advances in Civil Engineering

problems in practical engineering From the above resultsthe authors suggest that in addition to the connection be-tween the bridge and the DBPPS transition section theconnection between the tunnel and the DBPPS transitionsection should also be reinforced or treated

5 Conclusions

In this study the authors present a numerical modelingapproach to investigate the dynamic performances of a newtype of bridge-tunnel transition section with a DBPPSwhich can be used as a tool to improve the design andapplication of DBPPS subgrade )e obtained research re-sults of this study lead to the following conclusions

(1) )e vibration level of the DBPPS transition section islower than that of the abutment and the tunnelsection when the train passes by Meanwhile theadditional load caused by vertical track stiffnessdifference can aggravate the vibration at the con-nections and its adjacent areas (such as section S1)between the DBPPS transition section and theabutment (or tunnel) In addition the vertical ac-celeration of the carbody also shows abrupt change atthese connections

(2) With train speed increases the vertical accelerationof the base slab increases and the vertical dynamicstress on the subgrade surface near the connections(such as section S1) also increases With axle weightincreases the vertical acceleration increases ap-proximately exponentially and the vertical dynamicstress increases approximately linearly )e traindirection has a significant influence on the con-nections and its adjacent areas with a large stiffnessdifference

(3) For general soil layers with uniform thickness theimprovement strategy with varying-length piles caneffectively smooth the track stiffness and reduce thetensile stress on the track slab surface at the

connections and the effect is more significant whenthe stiffness of the bearing layer is low

Data Availability

)e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

)e authors declare that they have no conflicts of interestregarding the publication of this paper

Acknowledgments

)is paper reports research developed under financialsupport provided by the Key Project of Science and Tech-nology Research and Development Program of ChinaRailway Corporation (Grant No 2014T003-D) and theNational Natural Science Foundation of China (Grant nos51878671 and 51678575)

References

[1] X Lei ldquoEffects of abrupt changes in track foundation stiffnesson track vibration under moving loadsrdquo Journal of VibrationEngineering vol 19 no 2 pp 195ndash199 2006

[2] A Paixatildeo E Fortunato and R Calccedilada ldquoTransition zones torailway bridges track measurements and numerical model-lingrdquo Engineering Structures vol 80 pp 435ndash443 2014

[3] K K Ang and J Dai ldquoResponse analysis of high-speed railsystem accounting for abrupt change of foundation stiffnessrdquoJournal of Sound and Vibration vol 332 no 12 pp 2954ndash2970 2013

[4] P Holscher and P Meijers Literature Study of Knowledge andExperience of Transition Zones Report of GeoDelft DelftNetherlands 2007

[5] European Committee for Standardisation(CEN) Basis ofstructural design European Committee for Stand-ardisation(CEN) Brussels Belgium 2005

Tunnel section Transition section Abutment

Track slab

Carbody

Rail

I II

Unit Pa+537e + 05+423e + 05+309e + 05+195e + 05+807e + 04ndash335e + 04ndash148e + 05ndash262e + 05ndash376e + 05ndash490e + 05ndash604e + 05ndash718e + 05ndash832e + 05

S S22(Average 75)

(a)

3510 15 20 25 30 400 5Distance from section T0 (m)

ndash200

0

200

400

600

800

Max

imum

tens

ile st

ress

(kPa

)

Case 1Case 2

Case 3Case 4

(b)

Figure 19 Tensile stress distribution for different cases (a) Tensile stress contour of Case 3 at a certain time (b) Maximum tensile stress fordifferent cases

Advances in Civil Engineering 15

[6] )e Swedish Rail Administration Design standard for railwaybridges Standard BVS 58310 )e Swedish Rail Adminis-tration Borlange Sweden 2006

[7] Canadian Standards AssociationndashInternational CanadianHighway Bridge Design Code Canadian Standards Associa-tionndashInternational Toronto Canada 2000

[8] National Railway Administration Code for Design of HighSpeed Railway (TB10621-2014) China Railway PublishingHouse Beijing China 2015

[9] D Li and D Davis ldquoTransition of railroad bridge ap-proachesrdquo Journal of Geotechnical and GeoenvironmentalEngineering vol 131 no 11 pp 1392ndash1398 2005

[10] P Hu C Zhang S J Chen Y Wang W Wang andW H Duan ldquoDynamic responses of bridge-embankmenttransitions in high speed railway field tests and data analysesrdquoEngineering Structures vol 175 pp 565ndash576 2018

[11] Y Shan B Albers and S A Savidis ldquoInfluence of differenttransition zones on the dynamic response of track-subgradesystemsrdquo Computers and Geotechnics vol 48 pp 21ndash28 2013

[12] Y Shan Y Shu and S Zhou ldquoFinite-infinite element coupledanalysis on the influence of material parameters on the dy-namic properties of transition zonesrdquo Construction andBuilding Materials vol 148 no 1 pp 548ndash558 2017

[13] J Ren H Zhao X Li et al ldquoDynamic performances of CRTSIII prefabricated slab track with anti-vibration structure insubgrade-tunnel transition sectionrdquo Journal of SouthwestJiaotong University vol 51 no 6 pp 1047ndash1054 2016

[14] J N Varandas P Holscher and M A G Silva ldquo)ree-di-mensional track-ballast interaction model for the study of aculvert transitionrdquo Soil Dynamics and Earthquake Engi-neering vol 89 pp 116ndash127 2016

[15] P Hu C Zhang S Wen and Y Wang ldquoDynamic responsesof high-speed railway transition zone with various subgradefillingsrdquoComputers and Geotechnics vol 108 pp 17ndash26 2019

[16] J N Varandas A Paixatildeo and E Fortunato ldquoA study on thedynamic train-track interaction over cut-fill transitions onburied culvertsrdquo Computers amp Structures vol 189 no 9pp 49ndash61 2017

[17] R Santildeudo L DellrsquoOlio J A Casado I A Carrascal andS Diego ldquoTrack transitions in railways a reviewrdquo Con-struction and Building Materials vol 112 pp 140ndash157 2016

[18] L Wei C He and Z Yang Comprehensive Test Study Reportof Nanchang West to Yichun East Section of Shanghai-Kunming Railway Passenger Dedicated Line Central SouthUniversity Changsha China 2014

[19] Q SuWWang H Bai et al ldquoBearing capacity mechanism ofnon-embedded pile-plank structure subgraderdquo Journal ofTraffic and Transportation Engineering vol 12 no 1pp 19ndash24 2012

[20] Y-X Zhan H-L Yao and G-L Jiang ldquoDesign method ofpile-slab structure roadbed of ballastless track on soil sub-graderdquo Journal of Central South University vol 20 no 7pp 2072ndash2082 2013

[21] KMa ldquoAnalysis on space vibration performance of pile-plankstructuremdashfoundation soil system under the condition ofhigh-speed trains runningrdquo Journal of the China RailwaySociety vol 35 no 1 pp 93ndash100 2013

[22] L Huang B Wang and S Zhou ldquoCentrifugal model test ofpile-plank subgrade in soft groundrdquo Rock and Soil Mechanicsvol 34 no S1 pp 192ndash196 2013

[23] J Huang Q Su T Liu and X Wang ldquoVibration and long-term performance analysis of pile-plank-supported lowsubgrade of ballastless track under excitation loadsrdquo Shockand Vibration vol 2015 pp 1ndash12 2015

[24] Dassault Systemes Simulia Corp Abaqus Analysis UserrsquosManual Version 612 Dassault Systemes Simulia CorpJohnston Rhode Island USA 2012

[25] C Cheng ldquoStudy on dynamic responses of irregularity bal-lastless track for high-speed railwayrdquo PhD )esis ZhejiangUniversity Zhejiang China 2015

[26] H Hertz ldquoOn the contact of elastic solidsrdquo Journal fur die rneund angewandte Mathematik (Crelles Journal) vol 92no 156 2008

[27] P Ni K Wang W Zhang et al ldquoCalculation method ofwheel-rail contact relationrdquo Journal of Traffic and Trans-portation Engineering vol 04 pp 14ndash17 2006

[28] W Zhai and X Sun ldquoA detailed model for investigatingvertical interaction between railway vehicle and trackrdquo Ve-hicle System Dynamics vol 23 pp 603ndash615 1994

[29] W Zhai Vehicle-track Coupled Dynamics Jeory and Ap-plication Science Press and Springer Nature Singapore PteLtd Berlin Germany 2020

[30] W Li and X Bian ldquoDynamic performance of pile-supportedbridge-embankment transition zones under high-speed trainmoving loadsrdquo Procedia Engineering vol 143 pp 1059ndash10672016

[31] P Ni S Mangalathu G Mei and Y Zhao ldquoPermeable pilesan alternative to improve the performance of driven pilesrdquoComputers and Geotechnics vol 84 pp 78ndash87 2017

[32] K Liu Q Su P Ni C Zhou W Zhao and F Yue ldquoEval-uation on the dynamic performance of bridge approachbackfilled with fibre reinforced lightweight concrete underhigh-speed train loadingrdquo Computers and Geotechnicsvol 104 pp 42ndash53 2018

[33] F Xue and J Zhang ldquoAttenuations of acceleration spectra ofhigh-speed railway embankment subjected to moving loadsrdquoRock and Soil Mechanics vol 36 pp 445ndash451 2015

[34] Y Xuan ldquoSimulation research on the dynamic characteristicsof vehicle-track coupling system on curved track and thevibration response of ballastless track strucure of passengertraffic railwayrdquo PhD )esis China Academy of RailwaySciences Beijing China 2008

[35] P Ricco A Baron and P Molteni ldquoNature of pressure wavesinduced by a high-speed train travelling through a tunnelrdquoJournal of Wind Engineering and Industrial Aerodynamicsvol 95 no 8 pp 781ndash808 2007

[36] C Esveld Modern Railway Track MRT-Productions Zalt-bommel Netherlands 2001

[37] R Santildeudo M Cerrada B Alonso and L dellrsquoOlio ldquoAnalysisof the influence of support positions in transition zones Anumerical analysisrdquo Construction and Building Materialsvol 145 no 1 pp 207ndash217 2017

[38] M Shahraki CWarnakulasooriya and K JWitt ldquoNumericalstudy of transition zone between ballasted and ballastlessrailway trackrdquo Transportation Geotechnics vol 3 pp 58ndash672015

[39] C Alves Ribeiro R Calccedilada and R Delgado ldquoExperimentalassessment of the dynamic behaviour of the train-track systemat a culvert transition zonerdquo Engineering Structures vol 138no 1 pp 215ndash228 2017

[40] Ministry of Railways Institute of StandardMetrology RailwayLocomotive Dynamic Performance Test Identification Methodand Evaluation Standard (TBT2360-1993) Ministry of Rail-ways Institute of Standard Metrology Beijing China 1994

16 Advances in Civil Engineering

8(a)) )e differences of vertical acceleration peak and ve-locity peak at T0-3 between the numerical results and thefield measurement are approximately 543 and 408respectively )e main reason may be that an aerodynamiceffect [35] is generated at the tunnel entrance when the trainpasses by which aggravates the vibration of track compo-nents at section T0 But the effect is not well simulated in thenumerical model which induces a significant differencebetween the numerical results and the field measurementespecially in section T0

4 Results and Discussion

41 Dynamic Response along the Transition ZoneFigure 9 shows the distribution of vertical acceleration on thebase slab and the vertical track stiffness obtained from theformula proposed by [36] along the transition zone when theCRH380AM trainmoves from the bridge to the tunnel It can beseen that the vertical acceleration of the DBPPS transitionsection is less than that of the abutment and the tunnel sectionCompared with the tunnel section and the abutment the fillersin the DBPPS subgrade have the properties of low stiffness andlarge damping resulting in lower vibration levels in the DBPPSsubgrade Moreover a considerable amplification effect for thevertical acceleration can be observed at the connections(x 102m and x 362m) between the transition section andthe tunnel (or abutment) )e authors consider that the am-plification effect is caused by the abrupt change of wheel-railinteraction caused by the stiffness difference at the connections)is phenomenon was also found by Sanudo [37] and Shahraki[38]

It should be noted that the vertical acceleration of sectionS1 is higher than that of the sections S2 and S3 )is can beexplained that when the train passes through the connectionbetween the abutment and the transition section with anabrupt change stiffness an additional load on the trackcomponents is generated by the train load which aggravates

the vibration at the connection and its adjacent arearesulting in the vertical acceleration of section S1 beinghigher than that of sections S2 and S3

Although the dynamic response at connections is in-tensified due to the amplification effect the maximumvertical vibration acceleration of the transition zone is only023ms2 which is less than 50ms2 specified in the code[8] indicating that the DBPPS transition section exhibitsgood dynamic performance

)e coupling vibration inside the vehicle is considered inthe FE model and the line smoothness of the transition zonecan be evaluated by the dynamic response of the vehicleFigure 10 shows the vertical acceleration distribution of thevehicle which is comprised of an axle bogie and carbody alongthe transition zone Due to the dynamic contact interactionbetween the wheel and the rail the acceleration amplitude ofthe axle changes more dramatically and the vibration fre-quency is higher than that of bogie and carbody Furthermorebecause of the damping effect of the suspension system(connector elements) the acceleration amplitude and vibrationfrequency of the bogie and carbody are greatly reduced

It can be seen from Figure 10(b) that the frequencycomponents of the axle mainly consist of a low frequency of27Hz and a high frequency of 128Hz )e high frequencycomponent is caused by the excitation of fasteners (spring-dashpot elements) which can be verified as follows )espacing (L) of the fasteners is 065m then the excitationperiod (T) is as follows

T Lv (3)

where v is the train speed taken as 300 kmh or 8333ms)e excitation frequency f is determined as follows

f 1T vL 8333065 1282Hz (4)

)e results coincide well with the high frequencycomponent of the axle obtained from the numerical resultsFor the low frequency component it is mainly caused by theinteraction between the axle and the bogie On the whole thevibration frequency of the vehicle obtained from this FEmodel is close to the test results measured by Alves Ribeiro[39] which further indicates that the model is reliable

In addition the vibration response of the vehicle at theconnections (x 102m or x 362m) between the transitionsection and the tunnel (or abutment) is slightly higher than thatat other positions due to the sudden change of wheel-railinteraction caused by the stiffness difference (Figure 10(a)) Toensure the stable operation of the train and the comfort ofpassengers the standard [40] stipulates that the vertical ac-celeration of the carbody with excellent passenger comfort levelshall be less than 245ms2 As can be seen from Figure 10(a)

250 1500 500450

370

250 250 250 250 2501500 1500500

2 carriages simulated in the FE modelLength unit m

Figure 6 Schematic profile of CRH380AM type train

Table 2 Parameters of the vehicle [25 34]

Parameters ValueMass of the carbody 44320 kgMass of the bogie 3136 kgMass of the wheelset 2352 kgPitch inertia of the carbody 520e5 kgm2

Pitch inertia of the bogie 6400 kgm2

Stiffness of primary suspension 1040 kNmStiffness of secondary suspension 400 kNmDamping of primary suspension 40 kNmiddotsmDamping of secondary suspension 60 kNmiddotsm

8 Advances in Civil Engineering

the maximum vertical acceleration of the carbody is 075ms2indicating the train reaches an excellent comfort level and theDBPPS transition section fulfills its purpose in that it provides asmooth stiffness transition

42 Distribution of Vertical Dynamic Stress in the SubgradeTo analyze the vertical dynamic stress distribution in thesubgrade when the train passes by some observation points

at sections of S1 S2 and S3 in the FE model were selected asshown in Figure 11 Observation points of P1 P3 and P5 arelocated on the subgrade surface below the line center andobservation points of P2 P4 and P6 are located on thesubgrade surface directly below the rail Figure 11 shows thetime-history curves of vertical dynamic stress at these ob-servation points It can be seen that the vertical dynamicstress on the subgrade surface at observation points of P2P4 and P6 is 17sim18 higher than that at observation

ndash02

ndash01

0

01

02

03

04

Ver

tical

acce

lera

tion

(ms

2 )

101 103 105 107 10999Time (s)

FieldNum

ndash12

ndash06

0

06

12

18

24

Ver

tical

vel

ocity

(ms

)

101 103 105 107 10999Time (s)

FieldNum

times10ndash3

(a)

ndash04

ndash02

0

02

04

06

08

Ver

tical

acce

lera

tion

(ms

2 )

99 101 103 105 10797Time (s)

FieldNum

ndash1

ndash05

0

05

1

15

2

Ver

tical

vel

ocity

(ms

)

97 99 107103 105101Time (s)

FieldNum

times10ndash3

(b)

ndash06

ndash03

0

03

06

09

12

Ver

tical

acce

lera

tion

(ms

2 )

102 104 106 10810 11Time (s)

FieldNum

ndash2

ndash1

0

1

2

3

4

Ver

tical

vel

ocity

(ms

)

102 104 106 10810 11Time (s)

FieldNum

times10ndash3

(c)

Figure 7 Comparison of time-history curves between the numerical results and the field measurement (a) B0-3 (b) S1-3 (c) T0-3

Advances in Civil Engineering 9

points of P1 P3 and P5 More importantly the verticaldynamic stress of section S1 is higher than that of sections S2and S3 Figure 12 visually shows the vertical dynamic stresscontour of the train passing through section S1 and sectionS3 successively )e maximum vertical dynamic stress ofsection S1 is higher than that of section S3 which verifies theexistence of the additional loadmentioned above It becomesevident that when the train moves from the bridge to the

tunnel the additional load caused by the train load increasesthe dynamic stress on the subgrade surface of section S1which is also the reason why the vibration responses ofsection S1 are higher than that of sections S2 and S3 in thefield measurement (see Figure 8)

43 Influences of Train Speed Axle Weight and Direction onDynamic Response To investigate the influences of differentfactors on the dynamic responses of the transition sectionthree factors including train speed axle weight and runningdirection are selected for sensitivity analysis Figure 13(a)shows the relationship between the vertical acceleration onthe base slab and the train speed With the train speedincreasing from 200 kmh to 400 kmh the vertical accel-eration also increases in which the vertical accelerationincreases from 020ms2 to 044ms2 at measuring point T0-3 and increases from 0007ms2 to 030ms2 at measuringpoint S3-3 If the aerodynamic effect mentioned above is notconsidered in practice even if the train speed reaches400 kmh the vertical acceleration on the base slab is lessthan 50ms2 specified in the code [8] indicating that thetrack structure is still in safe service

In addition with the train speed increasing from200 kmh to 400 kmh the dynamic stress at observation

Ver

tical

acce

lera

tion

(ms

2 )

S1-3 S2-3 S3-3 T0-3B0-3Measuring points

00

01

02

03

04

05

FieldNum

Ver

tical

vel

ocity

(10ndash3

middotms

2 )

S1-3 S2-3 S3-3 T0-3B0-3Measuring points

03

06

09

12

15

18

FieldNum

(a)

Ver

tical

acce

lera

tion

(ms

2 )

S1-4 S2-4 S3-4B0-4Measuring points

000

005

010

015

020

025

FieldNum

Ver

tical

vel

ocity

(10ndash3

middotms

2 )

S1-4 S2-4 S3-4B0-4Measuring points

00

02

04

06

08

10

FieldNum

(b)

Figure 8 Comparison of vertical acceleration and velocity peaks between the numerical results and the field measurement (a) Measuringpoints on the base slab (b) Measuring points on the subgrade center

Ver

tical

stiff

ness

(kN

mm

) BridgeTransition sectionTunnel

70

80

90

100

110

120

Ver

tical

acce

lera

tion

(ms

2 )

010

015

020

025

030

035

4 8 12 16 20 24 28 32 36 400Distance from section T0 x (m)

Vertical stiffnessVertical acceleration

Figure 9 Distribution of the vertical acceleration and trackstiffness along the transition zone

10 Advances in Civil Engineering

points P4 and P6 is almost unchanged as shown inFigure 13(b) Nevertheless the dynamic stress at observationpoint P2 (at section S1) increases slightly from 305 kPa to316 kPa )e authors consider that the increase of dynamicstress at observation point P2 is related to the additionalload and with the increase of train speed the additional loadcaused by train load also increases in the connections with alarge stiffness difference

Figure 14(a) shows the relationship between the verticalacceleration on the base slab and the axle weight With the axleweight increasing from 10 t to 30 t the vertical accelerationincreases approximately exponentially and the vertical dy-namic stress increases approximately linearly (Figure 14(b))Consequently the axle weight is quite sensitive to the dynamicresponses of the DBPPS transition section

To reflect the influence of train direction on the dynamicresponses except for the vertical acceleration at originalobservation points the authors also select the vertical ac-celeration from other observation points at both sides of theconnections (ie x 102m and x 362m) wherex 89m 115m 349m and 375m as shown in Figure 15When the train moves from the tunnel to the bridge the

amplification effect can be observed at x 115m andx 375m while when the train moves from the bridge tothe tunnel the amplification effect occurs near x 89m andx 349m It can be concluded that under different traindirections the position with an amplification effect for vi-bration is also different which is determined by the positionand stiffness difference of the connections

44 Optimization of Pile Length in the Pile-Plank StructureIn the case study described in Section 2 an improvementstrategy with varying-length piles is adopted to achieve abetter transition due to the thickness of soft soil is uneven(Figure 2) Figure 16 shows the vertical displacement onthe pile top for different pile lengths It can be seen that thevertical displacement on the pile top is negatively cor-related with the pile length )e main reason is that thepiles with longer pile length can transfer the upper load toa deeper bearing layer But for shorter piles they bear theupper load together with the shallow soil with a lowerstiffness resulting in higher vertical displacement on thepile top According to the distribution of vertical

Ver

tical

acce

lera

tion

(ms

2 )4 8 12 16 20 24 28 32 36 400

Distance from section T0 x (m)

ndash15

ndash10

ndash5

0

5

10

15

AxleBogieCarbody

(a)

Am

plitu

de (m

s2 )

50 100 150 2000Frequency (Hz)

0

1

2

3

4

5

Axle

Am

plitu

de (m

s2 )

50 100 150 2000Frequency (Hz)

000

008

016

024

032

040

Bogie

Am

plitu

de (m

s2 )

50 100 150 2000Frequency (Hz)

000

006

012

018

024

030

Carbody

(b)

Figure 10 Vertical acceleration distribution of the train along the transition zone (a) Acceleration (b) Frequency

Advances in Civil Engineering 11

displacement for different pile lengths the strategy ofvarying-length piles is conducive to the stiffnesssmoothness in the transition zone

For general soil layers with uniform thickness Li andBian [30] discussed the influences of varying-length pilesand constant-length piles on the vertical track stiffness ina subgrade-bridge transition section and found that thevarying-length piles strategy can effectively smooth thevertical track stiffness transition Nevertheless for theDBPPS transition section under the general conditionsthe necessity of variable pile-length design is still de-batable In this study four comparative cases including

two improvement strategies varying-length piles andconstant-length piles are established to investigate theinfluences of pile length and the properties of soil on theDBPPS transition section as shown in Figure 17 In thesecases it is assumed that the ground consists of twohorizontal soil layers the upper layer is the silty clay layerthe bearing layer is the sand layer or limestone layer with ahigher stiffness than the silty clay layer )e materialproperties are shown in Table 1 and other parameters andwork conditions remain unchanged

Figure 18 shows the vertical track stiffness distributionalong the transition zone under four cases It can be seen thatthe smoothness of vertical track stiffness along the transitionsection can be improved by adopting the strategy of varying-length piles especially when the bearing layer is the sandlayer )e authors consider that when the bearing layer islimestone the bearing mode is similar to end-bearing pilesand the upper load is mainly transferred by piles to thebearing layer Consequently the change in pile length has asmall effect on the upper load transfer But when the bearinglayer is the sand layer with a lower stiffness the bearingmode is similar to friction-bearing piles and the upper loadis mainly shared by piles and the shallow ground )e in-crease of pile length effectively improves the friction resis-tance which indirectly enhances the overall stiffness of theground )erefore the strategy of varying-length piles caneffectively smooth the vertical track stiffness in the DBPPStransition section with a bearing layer of low stiffness

P1P2S1 sectionD

ynam

ic st

ress

(kPa

)10

0

ndash10

ndash20

ndash30

ndash40

ndash5002 04 06 08 1 12 14

Time (s)

P1P2

(a)

P3P4S2 sectionD

ynam

ic st

ress

(kPa

)

10

0

ndash10

ndash20

ndash30

ndash40

ndash5002 04 06 08 1 12 14

Time (s)

P3P4

(b)

P5P6S3 sectionD

ynam

ic st

ress

(kPa

)

10

0

ndash10

ndash20

ndash30

ndash40

ndash5002 04 06 08 1 12 14

Time (s)

P5P6

(c)

Figure 11 Time-history curves of the vertical dynamic stress (a) Observation points of section S1 (b) Observation points of section S2 (c)Observation points of section S3

+261e + 03+000e + 03ndash261e + 03ndash523e + 03ndash784e + 03ndash105e + 04ndash131e + 04ndash156e + 04ndash183e + 04ndash209e + 04ndash235e + 04ndash261e + 04ndash288e + 04ndash312e + 04

Fieldndash1 S33Unit Pa (Avg 75)

Maximum 291 kPa

S3 S1

Maximum 312 kPa

Train direction

x

yz

Figure 12 Vertical stress contour of the train passing throughsection S1 and section S3 successively

12 Advances in Civil Engineering

Changes in longitudinal stresses are more prone toactivate track slab cracking Figure 19(a) shows thelongitudinal stress (S22) contour on the track slab sur-face at a certain time for Case 3 A positive value

represents tensile stress and a negative value representscompressive stress It can be seen that under the trainload significant concentrated tension stresses are

250 300 350 400200Train speed (kmh)

0

01

02

03

04

05V

ertic

al v

ibra

tion

acce

lera

tion

(ms

2 )

B0-3S1-3S2-3

S3-3T0-3

(a)

250 300 350 400200Train speed (kmh)

25

27

29

31

33

35

Ver

tical

dyn

amic

stre

ss (k

Pa)

P2P4P6

(b)

Figure 13 Influences of the train speed on dynamic responses (a) Vertical acceleration (b) Vertical dynamic stress

S3-3T0-3

15 20 25 3010Vehicle axle weight (t)

0

02

04

06

08

Ver

tical

vib

ratio

nac

cele

ratio

n (m

s2 )

B0-3S1-3S2-3

(a)

15 20 25 3010Vehicle axle weight (t)

0

30

60

90

120

Ver

tical

dyn

amic

stre

ss (k

Pa)

P2P4P6

(b)

Figure 14 Influences of the axle weight on dynamic responses (a) Vertical acceleration (b) Vertical dynamic stress

x = 375

x = 349

x = 115

x = 89

B0S1

S2S3

T0

Tunnel Transition section Bridge

3 6 9 12 15 18 21 24 27 30 33 36 39 420Distance from section T0 x (m)

Ver

tical

acce

lera

tion

(ms

2 )

012

015

018

021

024

027

030

From bridge to tunnelFrom tunnel to bridge

Figure 15 Influence of the train direction on dynamic responses

Pile length = 23mPile length = 16m

Pile length = 13mPile length = 10m

ndash003

ndash0025

ndash002

ndash0015

ndash001

ndash0005

0

Ver

tical

disp

lace

men

t (m

m)

090603 12 150Time (s)

Figure 16 Vertical displacement on the pile top for piles of dif-ferent lengths

Advances in Civil Engineering 13

generated on the track slab surface at the positions I andII (Figure 19(a)) with the maximum value of 5374 kPaNevertheless long-term cyclic dynamic load caused bytrain may activate cracks at these positions

Figure 19(b) shows the comparison of maximum tensilestress along the DBPPS transition section in four cases )emaximum tensile stresses at positions I and II are signifi-cantly higher than those at other positions due to the largerstiffness difference When the bearing layer is limestonelayer the maximum tensile stress on the track slab surface at

positions I and II can be reduced by 109 and 78 re-spectively using varying-length piles while when thebearing layer is the sand layer the values can be reduced by278 and 182 respectively indicating that the strategy ofvarying-length piles can significantly reduce the tensile stresson the track slab surface and the lower the stiffness of thebearing layer the more the tensile stress reduces

In general to prevent cracks at the connection betweenabutment and transition section expansion joints or otherimproved measures would be applied to address these

5m 5m 3m 5m 5m

13mSilty clay

Limestone

(a)

5m 5m 3m 5m 5m

16m

23m

13mSilty clay

Limestone

(b)

5m 5m 3m 5m 5m

13mSilty clay

Sand

(c)

5m 5m 3m 5m 5m

16m13m

23m

Silty clay

Sand

(d)

Figure 17 Optimization cases of the pile-plank structure (a) Case 1 (b) Case 2 (c) Case 3 (d) Case 4

60

70

80

90

100

110

Ver

tical

stiff

ness

(kN

mm

)

3510 15 20 25 30 400 5Distance from T0 section (m)

Case 1Case 2

Case 3Case 4

Figure 18 Vertical stiffness along the transition zone for different cases

14 Advances in Civil Engineering

problems in practical engineering From the above resultsthe authors suggest that in addition to the connection be-tween the bridge and the DBPPS transition section theconnection between the tunnel and the DBPPS transitionsection should also be reinforced or treated

5 Conclusions

In this study the authors present a numerical modelingapproach to investigate the dynamic performances of a newtype of bridge-tunnel transition section with a DBPPSwhich can be used as a tool to improve the design andapplication of DBPPS subgrade )e obtained research re-sults of this study lead to the following conclusions

(1) )e vibration level of the DBPPS transition section islower than that of the abutment and the tunnelsection when the train passes by Meanwhile theadditional load caused by vertical track stiffnessdifference can aggravate the vibration at the con-nections and its adjacent areas (such as section S1)between the DBPPS transition section and theabutment (or tunnel) In addition the vertical ac-celeration of the carbody also shows abrupt change atthese connections

(2) With train speed increases the vertical accelerationof the base slab increases and the vertical dynamicstress on the subgrade surface near the connections(such as section S1) also increases With axle weightincreases the vertical acceleration increases ap-proximately exponentially and the vertical dynamicstress increases approximately linearly )e traindirection has a significant influence on the con-nections and its adjacent areas with a large stiffnessdifference

(3) For general soil layers with uniform thickness theimprovement strategy with varying-length piles caneffectively smooth the track stiffness and reduce thetensile stress on the track slab surface at the

connections and the effect is more significant whenthe stiffness of the bearing layer is low

Data Availability

)e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

)e authors declare that they have no conflicts of interestregarding the publication of this paper

Acknowledgments

)is paper reports research developed under financialsupport provided by the Key Project of Science and Tech-nology Research and Development Program of ChinaRailway Corporation (Grant No 2014T003-D) and theNational Natural Science Foundation of China (Grant nos51878671 and 51678575)

References

[1] X Lei ldquoEffects of abrupt changes in track foundation stiffnesson track vibration under moving loadsrdquo Journal of VibrationEngineering vol 19 no 2 pp 195ndash199 2006

[2] A Paixatildeo E Fortunato and R Calccedilada ldquoTransition zones torailway bridges track measurements and numerical model-lingrdquo Engineering Structures vol 80 pp 435ndash443 2014

[3] K K Ang and J Dai ldquoResponse analysis of high-speed railsystem accounting for abrupt change of foundation stiffnessrdquoJournal of Sound and Vibration vol 332 no 12 pp 2954ndash2970 2013

[4] P Holscher and P Meijers Literature Study of Knowledge andExperience of Transition Zones Report of GeoDelft DelftNetherlands 2007

[5] European Committee for Standardisation(CEN) Basis ofstructural design European Committee for Stand-ardisation(CEN) Brussels Belgium 2005

Tunnel section Transition section Abutment

Track slab

Carbody

Rail

I II

Unit Pa+537e + 05+423e + 05+309e + 05+195e + 05+807e + 04ndash335e + 04ndash148e + 05ndash262e + 05ndash376e + 05ndash490e + 05ndash604e + 05ndash718e + 05ndash832e + 05

S S22(Average 75)

(a)

3510 15 20 25 30 400 5Distance from section T0 (m)

ndash200

0

200

400

600

800

Max

imum

tens

ile st

ress

(kPa

)

Case 1Case 2

Case 3Case 4

(b)

Figure 19 Tensile stress distribution for different cases (a) Tensile stress contour of Case 3 at a certain time (b) Maximum tensile stress fordifferent cases

Advances in Civil Engineering 15

[6] )e Swedish Rail Administration Design standard for railwaybridges Standard BVS 58310 )e Swedish Rail Adminis-tration Borlange Sweden 2006

[7] Canadian Standards AssociationndashInternational CanadianHighway Bridge Design Code Canadian Standards Associa-tionndashInternational Toronto Canada 2000

[8] National Railway Administration Code for Design of HighSpeed Railway (TB10621-2014) China Railway PublishingHouse Beijing China 2015

[9] D Li and D Davis ldquoTransition of railroad bridge ap-proachesrdquo Journal of Geotechnical and GeoenvironmentalEngineering vol 131 no 11 pp 1392ndash1398 2005

[10] P Hu C Zhang S J Chen Y Wang W Wang andW H Duan ldquoDynamic responses of bridge-embankmenttransitions in high speed railway field tests and data analysesrdquoEngineering Structures vol 175 pp 565ndash576 2018

[11] Y Shan B Albers and S A Savidis ldquoInfluence of differenttransition zones on the dynamic response of track-subgradesystemsrdquo Computers and Geotechnics vol 48 pp 21ndash28 2013

[12] Y Shan Y Shu and S Zhou ldquoFinite-infinite element coupledanalysis on the influence of material parameters on the dy-namic properties of transition zonesrdquo Construction andBuilding Materials vol 148 no 1 pp 548ndash558 2017

[13] J Ren H Zhao X Li et al ldquoDynamic performances of CRTSIII prefabricated slab track with anti-vibration structure insubgrade-tunnel transition sectionrdquo Journal of SouthwestJiaotong University vol 51 no 6 pp 1047ndash1054 2016

[14] J N Varandas P Holscher and M A G Silva ldquo)ree-di-mensional track-ballast interaction model for the study of aculvert transitionrdquo Soil Dynamics and Earthquake Engi-neering vol 89 pp 116ndash127 2016

[15] P Hu C Zhang S Wen and Y Wang ldquoDynamic responsesof high-speed railway transition zone with various subgradefillingsrdquoComputers and Geotechnics vol 108 pp 17ndash26 2019

[16] J N Varandas A Paixatildeo and E Fortunato ldquoA study on thedynamic train-track interaction over cut-fill transitions onburied culvertsrdquo Computers amp Structures vol 189 no 9pp 49ndash61 2017

[17] R Santildeudo L DellrsquoOlio J A Casado I A Carrascal andS Diego ldquoTrack transitions in railways a reviewrdquo Con-struction and Building Materials vol 112 pp 140ndash157 2016

[18] L Wei C He and Z Yang Comprehensive Test Study Reportof Nanchang West to Yichun East Section of Shanghai-Kunming Railway Passenger Dedicated Line Central SouthUniversity Changsha China 2014

[19] Q SuWWang H Bai et al ldquoBearing capacity mechanism ofnon-embedded pile-plank structure subgraderdquo Journal ofTraffic and Transportation Engineering vol 12 no 1pp 19ndash24 2012

[20] Y-X Zhan H-L Yao and G-L Jiang ldquoDesign method ofpile-slab structure roadbed of ballastless track on soil sub-graderdquo Journal of Central South University vol 20 no 7pp 2072ndash2082 2013

[21] KMa ldquoAnalysis on space vibration performance of pile-plankstructuremdashfoundation soil system under the condition ofhigh-speed trains runningrdquo Journal of the China RailwaySociety vol 35 no 1 pp 93ndash100 2013

[22] L Huang B Wang and S Zhou ldquoCentrifugal model test ofpile-plank subgrade in soft groundrdquo Rock and Soil Mechanicsvol 34 no S1 pp 192ndash196 2013

[23] J Huang Q Su T Liu and X Wang ldquoVibration and long-term performance analysis of pile-plank-supported lowsubgrade of ballastless track under excitation loadsrdquo Shockand Vibration vol 2015 pp 1ndash12 2015

[24] Dassault Systemes Simulia Corp Abaqus Analysis UserrsquosManual Version 612 Dassault Systemes Simulia CorpJohnston Rhode Island USA 2012

[25] C Cheng ldquoStudy on dynamic responses of irregularity bal-lastless track for high-speed railwayrdquo PhD )esis ZhejiangUniversity Zhejiang China 2015

[26] H Hertz ldquoOn the contact of elastic solidsrdquo Journal fur die rneund angewandte Mathematik (Crelles Journal) vol 92no 156 2008

[27] P Ni K Wang W Zhang et al ldquoCalculation method ofwheel-rail contact relationrdquo Journal of Traffic and Trans-portation Engineering vol 04 pp 14ndash17 2006

[28] W Zhai and X Sun ldquoA detailed model for investigatingvertical interaction between railway vehicle and trackrdquo Ve-hicle System Dynamics vol 23 pp 603ndash615 1994

[29] W Zhai Vehicle-track Coupled Dynamics Jeory and Ap-plication Science Press and Springer Nature Singapore PteLtd Berlin Germany 2020

[30] W Li and X Bian ldquoDynamic performance of pile-supportedbridge-embankment transition zones under high-speed trainmoving loadsrdquo Procedia Engineering vol 143 pp 1059ndash10672016

[31] P Ni S Mangalathu G Mei and Y Zhao ldquoPermeable pilesan alternative to improve the performance of driven pilesrdquoComputers and Geotechnics vol 84 pp 78ndash87 2017

[32] K Liu Q Su P Ni C Zhou W Zhao and F Yue ldquoEval-uation on the dynamic performance of bridge approachbackfilled with fibre reinforced lightweight concrete underhigh-speed train loadingrdquo Computers and Geotechnicsvol 104 pp 42ndash53 2018

[33] F Xue and J Zhang ldquoAttenuations of acceleration spectra ofhigh-speed railway embankment subjected to moving loadsrdquoRock and Soil Mechanics vol 36 pp 445ndash451 2015

[34] Y Xuan ldquoSimulation research on the dynamic characteristicsof vehicle-track coupling system on curved track and thevibration response of ballastless track strucure of passengertraffic railwayrdquo PhD )esis China Academy of RailwaySciences Beijing China 2008

[35] P Ricco A Baron and P Molteni ldquoNature of pressure wavesinduced by a high-speed train travelling through a tunnelrdquoJournal of Wind Engineering and Industrial Aerodynamicsvol 95 no 8 pp 781ndash808 2007

[36] C Esveld Modern Railway Track MRT-Productions Zalt-bommel Netherlands 2001

[37] R Santildeudo M Cerrada B Alonso and L dellrsquoOlio ldquoAnalysisof the influence of support positions in transition zones Anumerical analysisrdquo Construction and Building Materialsvol 145 no 1 pp 207ndash217 2017

[38] M Shahraki CWarnakulasooriya and K JWitt ldquoNumericalstudy of transition zone between ballasted and ballastlessrailway trackrdquo Transportation Geotechnics vol 3 pp 58ndash672015

[39] C Alves Ribeiro R Calccedilada and R Delgado ldquoExperimentalassessment of the dynamic behaviour of the train-track systemat a culvert transition zonerdquo Engineering Structures vol 138no 1 pp 215ndash228 2017

[40] Ministry of Railways Institute of StandardMetrology RailwayLocomotive Dynamic Performance Test Identification Methodand Evaluation Standard (TBT2360-1993) Ministry of Rail-ways Institute of Standard Metrology Beijing China 1994

16 Advances in Civil Engineering

the maximum vertical acceleration of the carbody is 075ms2indicating the train reaches an excellent comfort level and theDBPPS transition section fulfills its purpose in that it provides asmooth stiffness transition

42 Distribution of Vertical Dynamic Stress in the SubgradeTo analyze the vertical dynamic stress distribution in thesubgrade when the train passes by some observation points

at sections of S1 S2 and S3 in the FE model were selected asshown in Figure 11 Observation points of P1 P3 and P5 arelocated on the subgrade surface below the line center andobservation points of P2 P4 and P6 are located on thesubgrade surface directly below the rail Figure 11 shows thetime-history curves of vertical dynamic stress at these ob-servation points It can be seen that the vertical dynamicstress on the subgrade surface at observation points of P2P4 and P6 is 17sim18 higher than that at observation

ndash02

ndash01

0

01

02

03

04

Ver

tical

acce

lera

tion

(ms

2 )

101 103 105 107 10999Time (s)

FieldNum

ndash12

ndash06

0

06

12

18

24

Ver

tical

vel

ocity

(ms

)

101 103 105 107 10999Time (s)

FieldNum

times10ndash3

(a)

ndash04

ndash02

0

02

04

06

08

Ver

tical

acce

lera

tion

(ms

2 )

99 101 103 105 10797Time (s)

FieldNum

ndash1

ndash05

0

05

1

15

2

Ver

tical

vel

ocity

(ms

)

97 99 107103 105101Time (s)

FieldNum

times10ndash3

(b)

ndash06

ndash03

0

03

06

09

12

Ver

tical

acce

lera

tion

(ms

2 )

102 104 106 10810 11Time (s)

FieldNum

ndash2

ndash1

0

1

2

3

4

Ver

tical

vel

ocity

(ms

)

102 104 106 10810 11Time (s)

FieldNum

times10ndash3

(c)

Figure 7 Comparison of time-history curves between the numerical results and the field measurement (a) B0-3 (b) S1-3 (c) T0-3

Advances in Civil Engineering 9

points of P1 P3 and P5 More importantly the verticaldynamic stress of section S1 is higher than that of sections S2and S3 Figure 12 visually shows the vertical dynamic stresscontour of the train passing through section S1 and sectionS3 successively )e maximum vertical dynamic stress ofsection S1 is higher than that of section S3 which verifies theexistence of the additional loadmentioned above It becomesevident that when the train moves from the bridge to the

tunnel the additional load caused by the train load increasesthe dynamic stress on the subgrade surface of section S1which is also the reason why the vibration responses ofsection S1 are higher than that of sections S2 and S3 in thefield measurement (see Figure 8)

43 Influences of Train Speed Axle Weight and Direction onDynamic Response To investigate the influences of differentfactors on the dynamic responses of the transition sectionthree factors including train speed axle weight and runningdirection are selected for sensitivity analysis Figure 13(a)shows the relationship between the vertical acceleration onthe base slab and the train speed With the train speedincreasing from 200 kmh to 400 kmh the vertical accel-eration also increases in which the vertical accelerationincreases from 020ms2 to 044ms2 at measuring point T0-3 and increases from 0007ms2 to 030ms2 at measuringpoint S3-3 If the aerodynamic effect mentioned above is notconsidered in practice even if the train speed reaches400 kmh the vertical acceleration on the base slab is lessthan 50ms2 specified in the code [8] indicating that thetrack structure is still in safe service

In addition with the train speed increasing from200 kmh to 400 kmh the dynamic stress at observation

Ver

tical

acce

lera

tion

(ms

2 )

S1-3 S2-3 S3-3 T0-3B0-3Measuring points

00

01

02

03

04

05

FieldNum

Ver

tical

vel

ocity

(10ndash3

middotms

2 )

S1-3 S2-3 S3-3 T0-3B0-3Measuring points

03

06

09

12

15

18

FieldNum

(a)

Ver

tical

acce

lera

tion

(ms

2 )

S1-4 S2-4 S3-4B0-4Measuring points

000

005

010

015

020

025

FieldNum

Ver

tical

vel

ocity

(10ndash3

middotms

2 )

S1-4 S2-4 S3-4B0-4Measuring points

00

02

04

06

08

10

FieldNum

(b)

Figure 8 Comparison of vertical acceleration and velocity peaks between the numerical results and the field measurement (a) Measuringpoints on the base slab (b) Measuring points on the subgrade center

Ver

tical

stiff

ness

(kN

mm

) BridgeTransition sectionTunnel

70

80

90

100

110

120

Ver

tical

acce

lera

tion

(ms

2 )

010

015

020

025

030

035

4 8 12 16 20 24 28 32 36 400Distance from section T0 x (m)

Vertical stiffnessVertical acceleration

Figure 9 Distribution of the vertical acceleration and trackstiffness along the transition zone

10 Advances in Civil Engineering

points P4 and P6 is almost unchanged as shown inFigure 13(b) Nevertheless the dynamic stress at observationpoint P2 (at section S1) increases slightly from 305 kPa to316 kPa )e authors consider that the increase of dynamicstress at observation point P2 is related to the additionalload and with the increase of train speed the additional loadcaused by train load also increases in the connections with alarge stiffness difference

Figure 14(a) shows the relationship between the verticalacceleration on the base slab and the axle weight With the axleweight increasing from 10 t to 30 t the vertical accelerationincreases approximately exponentially and the vertical dy-namic stress increases approximately linearly (Figure 14(b))Consequently the axle weight is quite sensitive to the dynamicresponses of the DBPPS transition section

To reflect the influence of train direction on the dynamicresponses except for the vertical acceleration at originalobservation points the authors also select the vertical ac-celeration from other observation points at both sides of theconnections (ie x 102m and x 362m) wherex 89m 115m 349m and 375m as shown in Figure 15When the train moves from the tunnel to the bridge the

amplification effect can be observed at x 115m andx 375m while when the train moves from the bridge tothe tunnel the amplification effect occurs near x 89m andx 349m It can be concluded that under different traindirections the position with an amplification effect for vi-bration is also different which is determined by the positionand stiffness difference of the connections

44 Optimization of Pile Length in the Pile-Plank StructureIn the case study described in Section 2 an improvementstrategy with varying-length piles is adopted to achieve abetter transition due to the thickness of soft soil is uneven(Figure 2) Figure 16 shows the vertical displacement onthe pile top for different pile lengths It can be seen that thevertical displacement on the pile top is negatively cor-related with the pile length )e main reason is that thepiles with longer pile length can transfer the upper load toa deeper bearing layer But for shorter piles they bear theupper load together with the shallow soil with a lowerstiffness resulting in higher vertical displacement on thepile top According to the distribution of vertical

Ver

tical

acce

lera

tion

(ms

2 )4 8 12 16 20 24 28 32 36 400

Distance from section T0 x (m)

ndash15

ndash10

ndash5

0

5

10

15

AxleBogieCarbody

(a)

Am

plitu

de (m

s2 )

50 100 150 2000Frequency (Hz)

0

1

2

3

4

5

Axle

Am

plitu

de (m

s2 )

50 100 150 2000Frequency (Hz)

000

008

016

024

032

040

Bogie

Am

plitu

de (m

s2 )

50 100 150 2000Frequency (Hz)

000

006

012

018

024

030

Carbody

(b)

Figure 10 Vertical acceleration distribution of the train along the transition zone (a) Acceleration (b) Frequency

Advances in Civil Engineering 11

displacement for different pile lengths the strategy ofvarying-length piles is conducive to the stiffnesssmoothness in the transition zone

For general soil layers with uniform thickness Li andBian [30] discussed the influences of varying-length pilesand constant-length piles on the vertical track stiffness ina subgrade-bridge transition section and found that thevarying-length piles strategy can effectively smooth thevertical track stiffness transition Nevertheless for theDBPPS transition section under the general conditionsthe necessity of variable pile-length design is still de-batable In this study four comparative cases including

two improvement strategies varying-length piles andconstant-length piles are established to investigate theinfluences of pile length and the properties of soil on theDBPPS transition section as shown in Figure 17 In thesecases it is assumed that the ground consists of twohorizontal soil layers the upper layer is the silty clay layerthe bearing layer is the sand layer or limestone layer with ahigher stiffness than the silty clay layer )e materialproperties are shown in Table 1 and other parameters andwork conditions remain unchanged

Figure 18 shows the vertical track stiffness distributionalong the transition zone under four cases It can be seen thatthe smoothness of vertical track stiffness along the transitionsection can be improved by adopting the strategy of varying-length piles especially when the bearing layer is the sandlayer )e authors consider that when the bearing layer islimestone the bearing mode is similar to end-bearing pilesand the upper load is mainly transferred by piles to thebearing layer Consequently the change in pile length has asmall effect on the upper load transfer But when the bearinglayer is the sand layer with a lower stiffness the bearingmode is similar to friction-bearing piles and the upper loadis mainly shared by piles and the shallow ground )e in-crease of pile length effectively improves the friction resis-tance which indirectly enhances the overall stiffness of theground )erefore the strategy of varying-length piles caneffectively smooth the vertical track stiffness in the DBPPStransition section with a bearing layer of low stiffness

P1P2S1 sectionD

ynam

ic st

ress

(kPa

)10

0

ndash10

ndash20

ndash30

ndash40

ndash5002 04 06 08 1 12 14

Time (s)

P1P2

(a)

P3P4S2 sectionD

ynam

ic st

ress

(kPa

)

10

0

ndash10

ndash20

ndash30

ndash40

ndash5002 04 06 08 1 12 14

Time (s)

P3P4

(b)

P5P6S3 sectionD

ynam

ic st

ress

(kPa

)

10

0

ndash10

ndash20

ndash30

ndash40

ndash5002 04 06 08 1 12 14

Time (s)

P5P6

(c)

Figure 11 Time-history curves of the vertical dynamic stress (a) Observation points of section S1 (b) Observation points of section S2 (c)Observation points of section S3

+261e + 03+000e + 03ndash261e + 03ndash523e + 03ndash784e + 03ndash105e + 04ndash131e + 04ndash156e + 04ndash183e + 04ndash209e + 04ndash235e + 04ndash261e + 04ndash288e + 04ndash312e + 04

Fieldndash1 S33Unit Pa (Avg 75)

Maximum 291 kPa

S3 S1

Maximum 312 kPa

Train direction

x

yz

Figure 12 Vertical stress contour of the train passing throughsection S1 and section S3 successively

12 Advances in Civil Engineering

Changes in longitudinal stresses are more prone toactivate track slab cracking Figure 19(a) shows thelongitudinal stress (S22) contour on the track slab sur-face at a certain time for Case 3 A positive value

represents tensile stress and a negative value representscompressive stress It can be seen that under the trainload significant concentrated tension stresses are

250 300 350 400200Train speed (kmh)

0

01

02

03

04

05V

ertic

al v

ibra

tion

acce

lera

tion

(ms

2 )

B0-3S1-3S2-3

S3-3T0-3

(a)

250 300 350 400200Train speed (kmh)

25

27

29

31

33

35

Ver

tical

dyn

amic

stre

ss (k

Pa)

P2P4P6

(b)

Figure 13 Influences of the train speed on dynamic responses (a) Vertical acceleration (b) Vertical dynamic stress

S3-3T0-3

15 20 25 3010Vehicle axle weight (t)

0

02

04

06

08

Ver

tical

vib

ratio

nac

cele

ratio

n (m

s2 )

B0-3S1-3S2-3

(a)

15 20 25 3010Vehicle axle weight (t)

0

30

60

90

120

Ver

tical

dyn

amic

stre

ss (k

Pa)

P2P4P6

(b)

Figure 14 Influences of the axle weight on dynamic responses (a) Vertical acceleration (b) Vertical dynamic stress

x = 375

x = 349

x = 115

x = 89

B0S1

S2S3

T0

Tunnel Transition section Bridge

3 6 9 12 15 18 21 24 27 30 33 36 39 420Distance from section T0 x (m)

Ver

tical

acce

lera

tion

(ms

2 )

012

015

018

021

024

027

030

From bridge to tunnelFrom tunnel to bridge

Figure 15 Influence of the train direction on dynamic responses

Pile length = 23mPile length = 16m

Pile length = 13mPile length = 10m

ndash003

ndash0025

ndash002

ndash0015

ndash001

ndash0005

0

Ver

tical

disp

lace

men

t (m

m)

090603 12 150Time (s)

Figure 16 Vertical displacement on the pile top for piles of dif-ferent lengths

Advances in Civil Engineering 13

generated on the track slab surface at the positions I andII (Figure 19(a)) with the maximum value of 5374 kPaNevertheless long-term cyclic dynamic load caused bytrain may activate cracks at these positions

Figure 19(b) shows the comparison of maximum tensilestress along the DBPPS transition section in four cases )emaximum tensile stresses at positions I and II are signifi-cantly higher than those at other positions due to the largerstiffness difference When the bearing layer is limestonelayer the maximum tensile stress on the track slab surface at

positions I and II can be reduced by 109 and 78 re-spectively using varying-length piles while when thebearing layer is the sand layer the values can be reduced by278 and 182 respectively indicating that the strategy ofvarying-length piles can significantly reduce the tensile stresson the track slab surface and the lower the stiffness of thebearing layer the more the tensile stress reduces

In general to prevent cracks at the connection betweenabutment and transition section expansion joints or otherimproved measures would be applied to address these

5m 5m 3m 5m 5m

13mSilty clay

Limestone

(a)

5m 5m 3m 5m 5m

16m

23m

13mSilty clay

Limestone

(b)

5m 5m 3m 5m 5m

13mSilty clay

Sand

(c)

5m 5m 3m 5m 5m

16m13m

23m

Silty clay

Sand

(d)

Figure 17 Optimization cases of the pile-plank structure (a) Case 1 (b) Case 2 (c) Case 3 (d) Case 4

60

70

80

90

100

110

Ver

tical

stiff

ness

(kN

mm

)

3510 15 20 25 30 400 5Distance from T0 section (m)

Case 1Case 2

Case 3Case 4

Figure 18 Vertical stiffness along the transition zone for different cases

14 Advances in Civil Engineering

problems in practical engineering From the above resultsthe authors suggest that in addition to the connection be-tween the bridge and the DBPPS transition section theconnection between the tunnel and the DBPPS transitionsection should also be reinforced or treated

5 Conclusions

In this study the authors present a numerical modelingapproach to investigate the dynamic performances of a newtype of bridge-tunnel transition section with a DBPPSwhich can be used as a tool to improve the design andapplication of DBPPS subgrade )e obtained research re-sults of this study lead to the following conclusions

(1) )e vibration level of the DBPPS transition section islower than that of the abutment and the tunnelsection when the train passes by Meanwhile theadditional load caused by vertical track stiffnessdifference can aggravate the vibration at the con-nections and its adjacent areas (such as section S1)between the DBPPS transition section and theabutment (or tunnel) In addition the vertical ac-celeration of the carbody also shows abrupt change atthese connections

(2) With train speed increases the vertical accelerationof the base slab increases and the vertical dynamicstress on the subgrade surface near the connections(such as section S1) also increases With axle weightincreases the vertical acceleration increases ap-proximately exponentially and the vertical dynamicstress increases approximately linearly )e traindirection has a significant influence on the con-nections and its adjacent areas with a large stiffnessdifference

(3) For general soil layers with uniform thickness theimprovement strategy with varying-length piles caneffectively smooth the track stiffness and reduce thetensile stress on the track slab surface at the

connections and the effect is more significant whenthe stiffness of the bearing layer is low

Data Availability

)e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

)e authors declare that they have no conflicts of interestregarding the publication of this paper

Acknowledgments

)is paper reports research developed under financialsupport provided by the Key Project of Science and Tech-nology Research and Development Program of ChinaRailway Corporation (Grant No 2014T003-D) and theNational Natural Science Foundation of China (Grant nos51878671 and 51678575)

References

[1] X Lei ldquoEffects of abrupt changes in track foundation stiffnesson track vibration under moving loadsrdquo Journal of VibrationEngineering vol 19 no 2 pp 195ndash199 2006

[2] A Paixatildeo E Fortunato and R Calccedilada ldquoTransition zones torailway bridges track measurements and numerical model-lingrdquo Engineering Structures vol 80 pp 435ndash443 2014

[3] K K Ang and J Dai ldquoResponse analysis of high-speed railsystem accounting for abrupt change of foundation stiffnessrdquoJournal of Sound and Vibration vol 332 no 12 pp 2954ndash2970 2013

[4] P Holscher and P Meijers Literature Study of Knowledge andExperience of Transition Zones Report of GeoDelft DelftNetherlands 2007

[5] European Committee for Standardisation(CEN) Basis ofstructural design European Committee for Stand-ardisation(CEN) Brussels Belgium 2005

Tunnel section Transition section Abutment

Track slab

Carbody

Rail

I II

Unit Pa+537e + 05+423e + 05+309e + 05+195e + 05+807e + 04ndash335e + 04ndash148e + 05ndash262e + 05ndash376e + 05ndash490e + 05ndash604e + 05ndash718e + 05ndash832e + 05

S S22(Average 75)

(a)

3510 15 20 25 30 400 5Distance from section T0 (m)

ndash200

0

200

400

600

800

Max

imum

tens

ile st

ress

(kPa

)

Case 1Case 2

Case 3Case 4

(b)

Figure 19 Tensile stress distribution for different cases (a) Tensile stress contour of Case 3 at a certain time (b) Maximum tensile stress fordifferent cases

Advances in Civil Engineering 15

[6] )e Swedish Rail Administration Design standard for railwaybridges Standard BVS 58310 )e Swedish Rail Adminis-tration Borlange Sweden 2006

[7] Canadian Standards AssociationndashInternational CanadianHighway Bridge Design Code Canadian Standards Associa-tionndashInternational Toronto Canada 2000

[8] National Railway Administration Code for Design of HighSpeed Railway (TB10621-2014) China Railway PublishingHouse Beijing China 2015

[9] D Li and D Davis ldquoTransition of railroad bridge ap-proachesrdquo Journal of Geotechnical and GeoenvironmentalEngineering vol 131 no 11 pp 1392ndash1398 2005

[10] P Hu C Zhang S J Chen Y Wang W Wang andW H Duan ldquoDynamic responses of bridge-embankmenttransitions in high speed railway field tests and data analysesrdquoEngineering Structures vol 175 pp 565ndash576 2018

[11] Y Shan B Albers and S A Savidis ldquoInfluence of differenttransition zones on the dynamic response of track-subgradesystemsrdquo Computers and Geotechnics vol 48 pp 21ndash28 2013

[12] Y Shan Y Shu and S Zhou ldquoFinite-infinite element coupledanalysis on the influence of material parameters on the dy-namic properties of transition zonesrdquo Construction andBuilding Materials vol 148 no 1 pp 548ndash558 2017

[13] J Ren H Zhao X Li et al ldquoDynamic performances of CRTSIII prefabricated slab track with anti-vibration structure insubgrade-tunnel transition sectionrdquo Journal of SouthwestJiaotong University vol 51 no 6 pp 1047ndash1054 2016

[14] J N Varandas P Holscher and M A G Silva ldquo)ree-di-mensional track-ballast interaction model for the study of aculvert transitionrdquo Soil Dynamics and Earthquake Engi-neering vol 89 pp 116ndash127 2016

[15] P Hu C Zhang S Wen and Y Wang ldquoDynamic responsesof high-speed railway transition zone with various subgradefillingsrdquoComputers and Geotechnics vol 108 pp 17ndash26 2019

[16] J N Varandas A Paixatildeo and E Fortunato ldquoA study on thedynamic train-track interaction over cut-fill transitions onburied culvertsrdquo Computers amp Structures vol 189 no 9pp 49ndash61 2017

[17] R Santildeudo L DellrsquoOlio J A Casado I A Carrascal andS Diego ldquoTrack transitions in railways a reviewrdquo Con-struction and Building Materials vol 112 pp 140ndash157 2016

[18] L Wei C He and Z Yang Comprehensive Test Study Reportof Nanchang West to Yichun East Section of Shanghai-Kunming Railway Passenger Dedicated Line Central SouthUniversity Changsha China 2014

[19] Q SuWWang H Bai et al ldquoBearing capacity mechanism ofnon-embedded pile-plank structure subgraderdquo Journal ofTraffic and Transportation Engineering vol 12 no 1pp 19ndash24 2012

[20] Y-X Zhan H-L Yao and G-L Jiang ldquoDesign method ofpile-slab structure roadbed of ballastless track on soil sub-graderdquo Journal of Central South University vol 20 no 7pp 2072ndash2082 2013

[21] KMa ldquoAnalysis on space vibration performance of pile-plankstructuremdashfoundation soil system under the condition ofhigh-speed trains runningrdquo Journal of the China RailwaySociety vol 35 no 1 pp 93ndash100 2013

[22] L Huang B Wang and S Zhou ldquoCentrifugal model test ofpile-plank subgrade in soft groundrdquo Rock and Soil Mechanicsvol 34 no S1 pp 192ndash196 2013

[23] J Huang Q Su T Liu and X Wang ldquoVibration and long-term performance analysis of pile-plank-supported lowsubgrade of ballastless track under excitation loadsrdquo Shockand Vibration vol 2015 pp 1ndash12 2015

[24] Dassault Systemes Simulia Corp Abaqus Analysis UserrsquosManual Version 612 Dassault Systemes Simulia CorpJohnston Rhode Island USA 2012

[25] C Cheng ldquoStudy on dynamic responses of irregularity bal-lastless track for high-speed railwayrdquo PhD )esis ZhejiangUniversity Zhejiang China 2015

[26] H Hertz ldquoOn the contact of elastic solidsrdquo Journal fur die rneund angewandte Mathematik (Crelles Journal) vol 92no 156 2008

[27] P Ni K Wang W Zhang et al ldquoCalculation method ofwheel-rail contact relationrdquo Journal of Traffic and Trans-portation Engineering vol 04 pp 14ndash17 2006

[28] W Zhai and X Sun ldquoA detailed model for investigatingvertical interaction between railway vehicle and trackrdquo Ve-hicle System Dynamics vol 23 pp 603ndash615 1994

[29] W Zhai Vehicle-track Coupled Dynamics Jeory and Ap-plication Science Press and Springer Nature Singapore PteLtd Berlin Germany 2020

[30] W Li and X Bian ldquoDynamic performance of pile-supportedbridge-embankment transition zones under high-speed trainmoving loadsrdquo Procedia Engineering vol 143 pp 1059ndash10672016

[31] P Ni S Mangalathu G Mei and Y Zhao ldquoPermeable pilesan alternative to improve the performance of driven pilesrdquoComputers and Geotechnics vol 84 pp 78ndash87 2017

[32] K Liu Q Su P Ni C Zhou W Zhao and F Yue ldquoEval-uation on the dynamic performance of bridge approachbackfilled with fibre reinforced lightweight concrete underhigh-speed train loadingrdquo Computers and Geotechnicsvol 104 pp 42ndash53 2018

[33] F Xue and J Zhang ldquoAttenuations of acceleration spectra ofhigh-speed railway embankment subjected to moving loadsrdquoRock and Soil Mechanics vol 36 pp 445ndash451 2015

[34] Y Xuan ldquoSimulation research on the dynamic characteristicsof vehicle-track coupling system on curved track and thevibration response of ballastless track strucure of passengertraffic railwayrdquo PhD )esis China Academy of RailwaySciences Beijing China 2008

[35] P Ricco A Baron and P Molteni ldquoNature of pressure wavesinduced by a high-speed train travelling through a tunnelrdquoJournal of Wind Engineering and Industrial Aerodynamicsvol 95 no 8 pp 781ndash808 2007

[36] C Esveld Modern Railway Track MRT-Productions Zalt-bommel Netherlands 2001

[37] R Santildeudo M Cerrada B Alonso and L dellrsquoOlio ldquoAnalysisof the influence of support positions in transition zones Anumerical analysisrdquo Construction and Building Materialsvol 145 no 1 pp 207ndash217 2017

[38] M Shahraki CWarnakulasooriya and K JWitt ldquoNumericalstudy of transition zone between ballasted and ballastlessrailway trackrdquo Transportation Geotechnics vol 3 pp 58ndash672015

[39] C Alves Ribeiro R Calccedilada and R Delgado ldquoExperimentalassessment of the dynamic behaviour of the train-track systemat a culvert transition zonerdquo Engineering Structures vol 138no 1 pp 215ndash228 2017

[40] Ministry of Railways Institute of StandardMetrology RailwayLocomotive Dynamic Performance Test Identification Methodand Evaluation Standard (TBT2360-1993) Ministry of Rail-ways Institute of Standard Metrology Beijing China 1994

16 Advances in Civil Engineering

points of P1 P3 and P5 More importantly the verticaldynamic stress of section S1 is higher than that of sections S2and S3 Figure 12 visually shows the vertical dynamic stresscontour of the train passing through section S1 and sectionS3 successively )e maximum vertical dynamic stress ofsection S1 is higher than that of section S3 which verifies theexistence of the additional loadmentioned above It becomesevident that when the train moves from the bridge to the

tunnel the additional load caused by the train load increasesthe dynamic stress on the subgrade surface of section S1which is also the reason why the vibration responses ofsection S1 are higher than that of sections S2 and S3 in thefield measurement (see Figure 8)

43 Influences of Train Speed Axle Weight and Direction onDynamic Response To investigate the influences of differentfactors on the dynamic responses of the transition sectionthree factors including train speed axle weight and runningdirection are selected for sensitivity analysis Figure 13(a)shows the relationship between the vertical acceleration onthe base slab and the train speed With the train speedincreasing from 200 kmh to 400 kmh the vertical accel-eration also increases in which the vertical accelerationincreases from 020ms2 to 044ms2 at measuring point T0-3 and increases from 0007ms2 to 030ms2 at measuringpoint S3-3 If the aerodynamic effect mentioned above is notconsidered in practice even if the train speed reaches400 kmh the vertical acceleration on the base slab is lessthan 50ms2 specified in the code [8] indicating that thetrack structure is still in safe service

In addition with the train speed increasing from200 kmh to 400 kmh the dynamic stress at observation

Ver

tical

acce

lera

tion

(ms

2 )

S1-3 S2-3 S3-3 T0-3B0-3Measuring points

00

01

02

03

04

05

FieldNum

Ver

tical

vel

ocity

(10ndash3

middotms

2 )

S1-3 S2-3 S3-3 T0-3B0-3Measuring points

03

06

09

12

15

18

FieldNum

(a)

Ver

tical

acce

lera

tion

(ms

2 )

S1-4 S2-4 S3-4B0-4Measuring points

000

005

010

015

020

025

FieldNum

Ver

tical

vel

ocity

(10ndash3

middotms

2 )

S1-4 S2-4 S3-4B0-4Measuring points

00

02

04

06

08

10

FieldNum

(b)

Figure 8 Comparison of vertical acceleration and velocity peaks between the numerical results and the field measurement (a) Measuringpoints on the base slab (b) Measuring points on the subgrade center

Ver

tical

stiff

ness

(kN

mm

) BridgeTransition sectionTunnel

70

80

90

100

110

120

Ver

tical

acce

lera

tion

(ms

2 )

010

015

020

025

030

035

4 8 12 16 20 24 28 32 36 400Distance from section T0 x (m)

Vertical stiffnessVertical acceleration

Figure 9 Distribution of the vertical acceleration and trackstiffness along the transition zone

10 Advances in Civil Engineering

points P4 and P6 is almost unchanged as shown inFigure 13(b) Nevertheless the dynamic stress at observationpoint P2 (at section S1) increases slightly from 305 kPa to316 kPa )e authors consider that the increase of dynamicstress at observation point P2 is related to the additionalload and with the increase of train speed the additional loadcaused by train load also increases in the connections with alarge stiffness difference

Figure 14(a) shows the relationship between the verticalacceleration on the base slab and the axle weight With the axleweight increasing from 10 t to 30 t the vertical accelerationincreases approximately exponentially and the vertical dy-namic stress increases approximately linearly (Figure 14(b))Consequently the axle weight is quite sensitive to the dynamicresponses of the DBPPS transition section

To reflect the influence of train direction on the dynamicresponses except for the vertical acceleration at originalobservation points the authors also select the vertical ac-celeration from other observation points at both sides of theconnections (ie x 102m and x 362m) wherex 89m 115m 349m and 375m as shown in Figure 15When the train moves from the tunnel to the bridge the

amplification effect can be observed at x 115m andx 375m while when the train moves from the bridge tothe tunnel the amplification effect occurs near x 89m andx 349m It can be concluded that under different traindirections the position with an amplification effect for vi-bration is also different which is determined by the positionand stiffness difference of the connections

44 Optimization of Pile Length in the Pile-Plank StructureIn the case study described in Section 2 an improvementstrategy with varying-length piles is adopted to achieve abetter transition due to the thickness of soft soil is uneven(Figure 2) Figure 16 shows the vertical displacement onthe pile top for different pile lengths It can be seen that thevertical displacement on the pile top is negatively cor-related with the pile length )e main reason is that thepiles with longer pile length can transfer the upper load toa deeper bearing layer But for shorter piles they bear theupper load together with the shallow soil with a lowerstiffness resulting in higher vertical displacement on thepile top According to the distribution of vertical

Ver

tical

acce

lera

tion

(ms

2 )4 8 12 16 20 24 28 32 36 400

Distance from section T0 x (m)

ndash15

ndash10

ndash5

0

5

10

15

AxleBogieCarbody

(a)

Am

plitu

de (m

s2 )

50 100 150 2000Frequency (Hz)

0

1

2

3

4

5

Axle

Am

plitu

de (m

s2 )

50 100 150 2000Frequency (Hz)

000

008

016

024

032

040

Bogie

Am

plitu

de (m

s2 )

50 100 150 2000Frequency (Hz)

000

006

012

018

024

030

Carbody

(b)

Figure 10 Vertical acceleration distribution of the train along the transition zone (a) Acceleration (b) Frequency

Advances in Civil Engineering 11

displacement for different pile lengths the strategy ofvarying-length piles is conducive to the stiffnesssmoothness in the transition zone

For general soil layers with uniform thickness Li andBian [30] discussed the influences of varying-length pilesand constant-length piles on the vertical track stiffness ina subgrade-bridge transition section and found that thevarying-length piles strategy can effectively smooth thevertical track stiffness transition Nevertheless for theDBPPS transition section under the general conditionsthe necessity of variable pile-length design is still de-batable In this study four comparative cases including

two improvement strategies varying-length piles andconstant-length piles are established to investigate theinfluences of pile length and the properties of soil on theDBPPS transition section as shown in Figure 17 In thesecases it is assumed that the ground consists of twohorizontal soil layers the upper layer is the silty clay layerthe bearing layer is the sand layer or limestone layer with ahigher stiffness than the silty clay layer )e materialproperties are shown in Table 1 and other parameters andwork conditions remain unchanged

Figure 18 shows the vertical track stiffness distributionalong the transition zone under four cases It can be seen thatthe smoothness of vertical track stiffness along the transitionsection can be improved by adopting the strategy of varying-length piles especially when the bearing layer is the sandlayer )e authors consider that when the bearing layer islimestone the bearing mode is similar to end-bearing pilesand the upper load is mainly transferred by piles to thebearing layer Consequently the change in pile length has asmall effect on the upper load transfer But when the bearinglayer is the sand layer with a lower stiffness the bearingmode is similar to friction-bearing piles and the upper loadis mainly shared by piles and the shallow ground )e in-crease of pile length effectively improves the friction resis-tance which indirectly enhances the overall stiffness of theground )erefore the strategy of varying-length piles caneffectively smooth the vertical track stiffness in the DBPPStransition section with a bearing layer of low stiffness

P1P2S1 sectionD

ynam

ic st

ress

(kPa

)10

0

ndash10

ndash20

ndash30

ndash40

ndash5002 04 06 08 1 12 14

Time (s)

P1P2

(a)

P3P4S2 sectionD

ynam

ic st

ress

(kPa

)

10

0

ndash10

ndash20

ndash30

ndash40

ndash5002 04 06 08 1 12 14

Time (s)

P3P4

(b)

P5P6S3 sectionD

ynam

ic st

ress

(kPa

)

10

0

ndash10

ndash20

ndash30

ndash40

ndash5002 04 06 08 1 12 14

Time (s)

P5P6

(c)

Figure 11 Time-history curves of the vertical dynamic stress (a) Observation points of section S1 (b) Observation points of section S2 (c)Observation points of section S3

+261e + 03+000e + 03ndash261e + 03ndash523e + 03ndash784e + 03ndash105e + 04ndash131e + 04ndash156e + 04ndash183e + 04ndash209e + 04ndash235e + 04ndash261e + 04ndash288e + 04ndash312e + 04

Fieldndash1 S33Unit Pa (Avg 75)

Maximum 291 kPa

S3 S1

Maximum 312 kPa

Train direction

x

yz

Figure 12 Vertical stress contour of the train passing throughsection S1 and section S3 successively

12 Advances in Civil Engineering

Changes in longitudinal stresses are more prone toactivate track slab cracking Figure 19(a) shows thelongitudinal stress (S22) contour on the track slab sur-face at a certain time for Case 3 A positive value

represents tensile stress and a negative value representscompressive stress It can be seen that under the trainload significant concentrated tension stresses are

250 300 350 400200Train speed (kmh)

0

01

02

03

04

05V

ertic

al v

ibra

tion

acce

lera

tion

(ms

2 )

B0-3S1-3S2-3

S3-3T0-3

(a)

250 300 350 400200Train speed (kmh)

25

27

29

31

33

35

Ver

tical

dyn

amic

stre

ss (k

Pa)

P2P4P6

(b)

Figure 13 Influences of the train speed on dynamic responses (a) Vertical acceleration (b) Vertical dynamic stress

S3-3T0-3

15 20 25 3010Vehicle axle weight (t)

0

02

04

06

08

Ver

tical

vib

ratio

nac

cele

ratio

n (m

s2 )

B0-3S1-3S2-3

(a)

15 20 25 3010Vehicle axle weight (t)

0

30

60

90

120

Ver

tical

dyn

amic

stre

ss (k

Pa)

P2P4P6

(b)

Figure 14 Influences of the axle weight on dynamic responses (a) Vertical acceleration (b) Vertical dynamic stress

x = 375

x = 349

x = 115

x = 89

B0S1

S2S3

T0

Tunnel Transition section Bridge

3 6 9 12 15 18 21 24 27 30 33 36 39 420Distance from section T0 x (m)

Ver

tical

acce

lera

tion

(ms

2 )

012

015

018

021

024

027

030

From bridge to tunnelFrom tunnel to bridge

Figure 15 Influence of the train direction on dynamic responses

Pile length = 23mPile length = 16m

Pile length = 13mPile length = 10m

ndash003

ndash0025

ndash002

ndash0015

ndash001

ndash0005

0

Ver

tical

disp

lace

men

t (m

m)

090603 12 150Time (s)

Figure 16 Vertical displacement on the pile top for piles of dif-ferent lengths

Advances in Civil Engineering 13

generated on the track slab surface at the positions I andII (Figure 19(a)) with the maximum value of 5374 kPaNevertheless long-term cyclic dynamic load caused bytrain may activate cracks at these positions

Figure 19(b) shows the comparison of maximum tensilestress along the DBPPS transition section in four cases )emaximum tensile stresses at positions I and II are signifi-cantly higher than those at other positions due to the largerstiffness difference When the bearing layer is limestonelayer the maximum tensile stress on the track slab surface at

positions I and II can be reduced by 109 and 78 re-spectively using varying-length piles while when thebearing layer is the sand layer the values can be reduced by278 and 182 respectively indicating that the strategy ofvarying-length piles can significantly reduce the tensile stresson the track slab surface and the lower the stiffness of thebearing layer the more the tensile stress reduces

In general to prevent cracks at the connection betweenabutment and transition section expansion joints or otherimproved measures would be applied to address these

5m 5m 3m 5m 5m

13mSilty clay

Limestone

(a)

5m 5m 3m 5m 5m

16m

23m

13mSilty clay

Limestone

(b)

5m 5m 3m 5m 5m

13mSilty clay

Sand

(c)

5m 5m 3m 5m 5m

16m13m

23m

Silty clay

Sand

(d)

Figure 17 Optimization cases of the pile-plank structure (a) Case 1 (b) Case 2 (c) Case 3 (d) Case 4

60

70

80

90

100

110

Ver

tical

stiff

ness

(kN

mm

)

3510 15 20 25 30 400 5Distance from T0 section (m)

Case 1Case 2

Case 3Case 4

Figure 18 Vertical stiffness along the transition zone for different cases

14 Advances in Civil Engineering

problems in practical engineering From the above resultsthe authors suggest that in addition to the connection be-tween the bridge and the DBPPS transition section theconnection between the tunnel and the DBPPS transitionsection should also be reinforced or treated

5 Conclusions

In this study the authors present a numerical modelingapproach to investigate the dynamic performances of a newtype of bridge-tunnel transition section with a DBPPSwhich can be used as a tool to improve the design andapplication of DBPPS subgrade )e obtained research re-sults of this study lead to the following conclusions

(1) )e vibration level of the DBPPS transition section islower than that of the abutment and the tunnelsection when the train passes by Meanwhile theadditional load caused by vertical track stiffnessdifference can aggravate the vibration at the con-nections and its adjacent areas (such as section S1)between the DBPPS transition section and theabutment (or tunnel) In addition the vertical ac-celeration of the carbody also shows abrupt change atthese connections

(2) With train speed increases the vertical accelerationof the base slab increases and the vertical dynamicstress on the subgrade surface near the connections(such as section S1) also increases With axle weightincreases the vertical acceleration increases ap-proximately exponentially and the vertical dynamicstress increases approximately linearly )e traindirection has a significant influence on the con-nections and its adjacent areas with a large stiffnessdifference

(3) For general soil layers with uniform thickness theimprovement strategy with varying-length piles caneffectively smooth the track stiffness and reduce thetensile stress on the track slab surface at the

connections and the effect is more significant whenthe stiffness of the bearing layer is low

Data Availability

)e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

)e authors declare that they have no conflicts of interestregarding the publication of this paper

Acknowledgments

)is paper reports research developed under financialsupport provided by the Key Project of Science and Tech-nology Research and Development Program of ChinaRailway Corporation (Grant No 2014T003-D) and theNational Natural Science Foundation of China (Grant nos51878671 and 51678575)

References

[1] X Lei ldquoEffects of abrupt changes in track foundation stiffnesson track vibration under moving loadsrdquo Journal of VibrationEngineering vol 19 no 2 pp 195ndash199 2006

[2] A Paixatildeo E Fortunato and R Calccedilada ldquoTransition zones torailway bridges track measurements and numerical model-lingrdquo Engineering Structures vol 80 pp 435ndash443 2014

[3] K K Ang and J Dai ldquoResponse analysis of high-speed railsystem accounting for abrupt change of foundation stiffnessrdquoJournal of Sound and Vibration vol 332 no 12 pp 2954ndash2970 2013

[4] P Holscher and P Meijers Literature Study of Knowledge andExperience of Transition Zones Report of GeoDelft DelftNetherlands 2007

[5] European Committee for Standardisation(CEN) Basis ofstructural design European Committee for Stand-ardisation(CEN) Brussels Belgium 2005

Tunnel section Transition section Abutment

Track slab

Carbody

Rail

I II

Unit Pa+537e + 05+423e + 05+309e + 05+195e + 05+807e + 04ndash335e + 04ndash148e + 05ndash262e + 05ndash376e + 05ndash490e + 05ndash604e + 05ndash718e + 05ndash832e + 05

S S22(Average 75)

(a)

3510 15 20 25 30 400 5Distance from section T0 (m)

ndash200

0

200

400

600

800

Max

imum

tens

ile st

ress

(kPa

)

Case 1Case 2

Case 3Case 4

(b)

Figure 19 Tensile stress distribution for different cases (a) Tensile stress contour of Case 3 at a certain time (b) Maximum tensile stress fordifferent cases

Advances in Civil Engineering 15

[6] )e Swedish Rail Administration Design standard for railwaybridges Standard BVS 58310 )e Swedish Rail Adminis-tration Borlange Sweden 2006

[7] Canadian Standards AssociationndashInternational CanadianHighway Bridge Design Code Canadian Standards Associa-tionndashInternational Toronto Canada 2000

[8] National Railway Administration Code for Design of HighSpeed Railway (TB10621-2014) China Railway PublishingHouse Beijing China 2015

[9] D Li and D Davis ldquoTransition of railroad bridge ap-proachesrdquo Journal of Geotechnical and GeoenvironmentalEngineering vol 131 no 11 pp 1392ndash1398 2005

[10] P Hu C Zhang S J Chen Y Wang W Wang andW H Duan ldquoDynamic responses of bridge-embankmenttransitions in high speed railway field tests and data analysesrdquoEngineering Structures vol 175 pp 565ndash576 2018

[11] Y Shan B Albers and S A Savidis ldquoInfluence of differenttransition zones on the dynamic response of track-subgradesystemsrdquo Computers and Geotechnics vol 48 pp 21ndash28 2013

[12] Y Shan Y Shu and S Zhou ldquoFinite-infinite element coupledanalysis on the influence of material parameters on the dy-namic properties of transition zonesrdquo Construction andBuilding Materials vol 148 no 1 pp 548ndash558 2017

[13] J Ren H Zhao X Li et al ldquoDynamic performances of CRTSIII prefabricated slab track with anti-vibration structure insubgrade-tunnel transition sectionrdquo Journal of SouthwestJiaotong University vol 51 no 6 pp 1047ndash1054 2016

[14] J N Varandas P Holscher and M A G Silva ldquo)ree-di-mensional track-ballast interaction model for the study of aculvert transitionrdquo Soil Dynamics and Earthquake Engi-neering vol 89 pp 116ndash127 2016

[15] P Hu C Zhang S Wen and Y Wang ldquoDynamic responsesof high-speed railway transition zone with various subgradefillingsrdquoComputers and Geotechnics vol 108 pp 17ndash26 2019

[16] J N Varandas A Paixatildeo and E Fortunato ldquoA study on thedynamic train-track interaction over cut-fill transitions onburied culvertsrdquo Computers amp Structures vol 189 no 9pp 49ndash61 2017

[17] R Santildeudo L DellrsquoOlio J A Casado I A Carrascal andS Diego ldquoTrack transitions in railways a reviewrdquo Con-struction and Building Materials vol 112 pp 140ndash157 2016

[18] L Wei C He and Z Yang Comprehensive Test Study Reportof Nanchang West to Yichun East Section of Shanghai-Kunming Railway Passenger Dedicated Line Central SouthUniversity Changsha China 2014

[19] Q SuWWang H Bai et al ldquoBearing capacity mechanism ofnon-embedded pile-plank structure subgraderdquo Journal ofTraffic and Transportation Engineering vol 12 no 1pp 19ndash24 2012

[20] Y-X Zhan H-L Yao and G-L Jiang ldquoDesign method ofpile-slab structure roadbed of ballastless track on soil sub-graderdquo Journal of Central South University vol 20 no 7pp 2072ndash2082 2013

[21] KMa ldquoAnalysis on space vibration performance of pile-plankstructuremdashfoundation soil system under the condition ofhigh-speed trains runningrdquo Journal of the China RailwaySociety vol 35 no 1 pp 93ndash100 2013

[22] L Huang B Wang and S Zhou ldquoCentrifugal model test ofpile-plank subgrade in soft groundrdquo Rock and Soil Mechanicsvol 34 no S1 pp 192ndash196 2013

[23] J Huang Q Su T Liu and X Wang ldquoVibration and long-term performance analysis of pile-plank-supported lowsubgrade of ballastless track under excitation loadsrdquo Shockand Vibration vol 2015 pp 1ndash12 2015

[24] Dassault Systemes Simulia Corp Abaqus Analysis UserrsquosManual Version 612 Dassault Systemes Simulia CorpJohnston Rhode Island USA 2012

[25] C Cheng ldquoStudy on dynamic responses of irregularity bal-lastless track for high-speed railwayrdquo PhD )esis ZhejiangUniversity Zhejiang China 2015

[26] H Hertz ldquoOn the contact of elastic solidsrdquo Journal fur die rneund angewandte Mathematik (Crelles Journal) vol 92no 156 2008

[27] P Ni K Wang W Zhang et al ldquoCalculation method ofwheel-rail contact relationrdquo Journal of Traffic and Trans-portation Engineering vol 04 pp 14ndash17 2006

[28] W Zhai and X Sun ldquoA detailed model for investigatingvertical interaction between railway vehicle and trackrdquo Ve-hicle System Dynamics vol 23 pp 603ndash615 1994

[29] W Zhai Vehicle-track Coupled Dynamics Jeory and Ap-plication Science Press and Springer Nature Singapore PteLtd Berlin Germany 2020

[30] W Li and X Bian ldquoDynamic performance of pile-supportedbridge-embankment transition zones under high-speed trainmoving loadsrdquo Procedia Engineering vol 143 pp 1059ndash10672016

[31] P Ni S Mangalathu G Mei and Y Zhao ldquoPermeable pilesan alternative to improve the performance of driven pilesrdquoComputers and Geotechnics vol 84 pp 78ndash87 2017

[32] K Liu Q Su P Ni C Zhou W Zhao and F Yue ldquoEval-uation on the dynamic performance of bridge approachbackfilled with fibre reinforced lightweight concrete underhigh-speed train loadingrdquo Computers and Geotechnicsvol 104 pp 42ndash53 2018

[33] F Xue and J Zhang ldquoAttenuations of acceleration spectra ofhigh-speed railway embankment subjected to moving loadsrdquoRock and Soil Mechanics vol 36 pp 445ndash451 2015

[34] Y Xuan ldquoSimulation research on the dynamic characteristicsof vehicle-track coupling system on curved track and thevibration response of ballastless track strucure of passengertraffic railwayrdquo PhD )esis China Academy of RailwaySciences Beijing China 2008

[35] P Ricco A Baron and P Molteni ldquoNature of pressure wavesinduced by a high-speed train travelling through a tunnelrdquoJournal of Wind Engineering and Industrial Aerodynamicsvol 95 no 8 pp 781ndash808 2007

[36] C Esveld Modern Railway Track MRT-Productions Zalt-bommel Netherlands 2001

[37] R Santildeudo M Cerrada B Alonso and L dellrsquoOlio ldquoAnalysisof the influence of support positions in transition zones Anumerical analysisrdquo Construction and Building Materialsvol 145 no 1 pp 207ndash217 2017

[38] M Shahraki CWarnakulasooriya and K JWitt ldquoNumericalstudy of transition zone between ballasted and ballastlessrailway trackrdquo Transportation Geotechnics vol 3 pp 58ndash672015

[39] C Alves Ribeiro R Calccedilada and R Delgado ldquoExperimentalassessment of the dynamic behaviour of the train-track systemat a culvert transition zonerdquo Engineering Structures vol 138no 1 pp 215ndash228 2017

[40] Ministry of Railways Institute of StandardMetrology RailwayLocomotive Dynamic Performance Test Identification Methodand Evaluation Standard (TBT2360-1993) Ministry of Rail-ways Institute of Standard Metrology Beijing China 1994

16 Advances in Civil Engineering

points P4 and P6 is almost unchanged as shown inFigure 13(b) Nevertheless the dynamic stress at observationpoint P2 (at section S1) increases slightly from 305 kPa to316 kPa )e authors consider that the increase of dynamicstress at observation point P2 is related to the additionalload and with the increase of train speed the additional loadcaused by train load also increases in the connections with alarge stiffness difference

Figure 14(a) shows the relationship between the verticalacceleration on the base slab and the axle weight With the axleweight increasing from 10 t to 30 t the vertical accelerationincreases approximately exponentially and the vertical dy-namic stress increases approximately linearly (Figure 14(b))Consequently the axle weight is quite sensitive to the dynamicresponses of the DBPPS transition section

To reflect the influence of train direction on the dynamicresponses except for the vertical acceleration at originalobservation points the authors also select the vertical ac-celeration from other observation points at both sides of theconnections (ie x 102m and x 362m) wherex 89m 115m 349m and 375m as shown in Figure 15When the train moves from the tunnel to the bridge the

amplification effect can be observed at x 115m andx 375m while when the train moves from the bridge tothe tunnel the amplification effect occurs near x 89m andx 349m It can be concluded that under different traindirections the position with an amplification effect for vi-bration is also different which is determined by the positionand stiffness difference of the connections

44 Optimization of Pile Length in the Pile-Plank StructureIn the case study described in Section 2 an improvementstrategy with varying-length piles is adopted to achieve abetter transition due to the thickness of soft soil is uneven(Figure 2) Figure 16 shows the vertical displacement onthe pile top for different pile lengths It can be seen that thevertical displacement on the pile top is negatively cor-related with the pile length )e main reason is that thepiles with longer pile length can transfer the upper load toa deeper bearing layer But for shorter piles they bear theupper load together with the shallow soil with a lowerstiffness resulting in higher vertical displacement on thepile top According to the distribution of vertical

Ver

tical

acce

lera

tion

(ms

2 )4 8 12 16 20 24 28 32 36 400

Distance from section T0 x (m)

ndash15

ndash10

ndash5

0

5

10

15

AxleBogieCarbody

(a)

Am

plitu

de (m

s2 )

50 100 150 2000Frequency (Hz)

0

1

2

3

4

5

Axle

Am

plitu

de (m

s2 )

50 100 150 2000Frequency (Hz)

000

008

016

024

032

040

Bogie

Am

plitu

de (m

s2 )

50 100 150 2000Frequency (Hz)

000

006

012

018

024

030

Carbody

(b)

Figure 10 Vertical acceleration distribution of the train along the transition zone (a) Acceleration (b) Frequency

Advances in Civil Engineering 11

displacement for different pile lengths the strategy ofvarying-length piles is conducive to the stiffnesssmoothness in the transition zone

For general soil layers with uniform thickness Li andBian [30] discussed the influences of varying-length pilesand constant-length piles on the vertical track stiffness ina subgrade-bridge transition section and found that thevarying-length piles strategy can effectively smooth thevertical track stiffness transition Nevertheless for theDBPPS transition section under the general conditionsthe necessity of variable pile-length design is still de-batable In this study four comparative cases including

two improvement strategies varying-length piles andconstant-length piles are established to investigate theinfluences of pile length and the properties of soil on theDBPPS transition section as shown in Figure 17 In thesecases it is assumed that the ground consists of twohorizontal soil layers the upper layer is the silty clay layerthe bearing layer is the sand layer or limestone layer with ahigher stiffness than the silty clay layer )e materialproperties are shown in Table 1 and other parameters andwork conditions remain unchanged

Figure 18 shows the vertical track stiffness distributionalong the transition zone under four cases It can be seen thatthe smoothness of vertical track stiffness along the transitionsection can be improved by adopting the strategy of varying-length piles especially when the bearing layer is the sandlayer )e authors consider that when the bearing layer islimestone the bearing mode is similar to end-bearing pilesand the upper load is mainly transferred by piles to thebearing layer Consequently the change in pile length has asmall effect on the upper load transfer But when the bearinglayer is the sand layer with a lower stiffness the bearingmode is similar to friction-bearing piles and the upper loadis mainly shared by piles and the shallow ground )e in-crease of pile length effectively improves the friction resis-tance which indirectly enhances the overall stiffness of theground )erefore the strategy of varying-length piles caneffectively smooth the vertical track stiffness in the DBPPStransition section with a bearing layer of low stiffness

P1P2S1 sectionD

ynam

ic st

ress

(kPa

)10

0

ndash10

ndash20

ndash30

ndash40

ndash5002 04 06 08 1 12 14

Time (s)

P1P2

(a)

P3P4S2 sectionD

ynam

ic st

ress

(kPa

)

10

0

ndash10

ndash20

ndash30

ndash40

ndash5002 04 06 08 1 12 14

Time (s)

P3P4

(b)

P5P6S3 sectionD

ynam

ic st

ress

(kPa

)

10

0

ndash10

ndash20

ndash30

ndash40

ndash5002 04 06 08 1 12 14

Time (s)

P5P6

(c)

Figure 11 Time-history curves of the vertical dynamic stress (a) Observation points of section S1 (b) Observation points of section S2 (c)Observation points of section S3

+261e + 03+000e + 03ndash261e + 03ndash523e + 03ndash784e + 03ndash105e + 04ndash131e + 04ndash156e + 04ndash183e + 04ndash209e + 04ndash235e + 04ndash261e + 04ndash288e + 04ndash312e + 04

Fieldndash1 S33Unit Pa (Avg 75)

Maximum 291 kPa

S3 S1

Maximum 312 kPa

Train direction

x

yz

Figure 12 Vertical stress contour of the train passing throughsection S1 and section S3 successively

12 Advances in Civil Engineering

Changes in longitudinal stresses are more prone toactivate track slab cracking Figure 19(a) shows thelongitudinal stress (S22) contour on the track slab sur-face at a certain time for Case 3 A positive value

represents tensile stress and a negative value representscompressive stress It can be seen that under the trainload significant concentrated tension stresses are

250 300 350 400200Train speed (kmh)

0

01

02

03

04

05V

ertic

al v

ibra

tion

acce

lera

tion

(ms

2 )

B0-3S1-3S2-3

S3-3T0-3

(a)

250 300 350 400200Train speed (kmh)

25

27

29

31

33

35

Ver

tical

dyn

amic

stre

ss (k

Pa)

P2P4P6

(b)

Figure 13 Influences of the train speed on dynamic responses (a) Vertical acceleration (b) Vertical dynamic stress

S3-3T0-3

15 20 25 3010Vehicle axle weight (t)

0

02

04

06

08

Ver

tical

vib

ratio

nac

cele

ratio

n (m

s2 )

B0-3S1-3S2-3

(a)

15 20 25 3010Vehicle axle weight (t)

0

30

60

90

120

Ver

tical

dyn

amic

stre

ss (k

Pa)

P2P4P6

(b)

Figure 14 Influences of the axle weight on dynamic responses (a) Vertical acceleration (b) Vertical dynamic stress

x = 375

x = 349

x = 115

x = 89

B0S1

S2S3

T0

Tunnel Transition section Bridge

3 6 9 12 15 18 21 24 27 30 33 36 39 420Distance from section T0 x (m)

Ver

tical

acce

lera

tion

(ms

2 )

012

015

018

021

024

027

030

From bridge to tunnelFrom tunnel to bridge

Figure 15 Influence of the train direction on dynamic responses

Pile length = 23mPile length = 16m

Pile length = 13mPile length = 10m

ndash003

ndash0025

ndash002

ndash0015

ndash001

ndash0005

0

Ver

tical

disp

lace

men

t (m

m)

090603 12 150Time (s)

Figure 16 Vertical displacement on the pile top for piles of dif-ferent lengths

Advances in Civil Engineering 13

generated on the track slab surface at the positions I andII (Figure 19(a)) with the maximum value of 5374 kPaNevertheless long-term cyclic dynamic load caused bytrain may activate cracks at these positions

Figure 19(b) shows the comparison of maximum tensilestress along the DBPPS transition section in four cases )emaximum tensile stresses at positions I and II are signifi-cantly higher than those at other positions due to the largerstiffness difference When the bearing layer is limestonelayer the maximum tensile stress on the track slab surface at

positions I and II can be reduced by 109 and 78 re-spectively using varying-length piles while when thebearing layer is the sand layer the values can be reduced by278 and 182 respectively indicating that the strategy ofvarying-length piles can significantly reduce the tensile stresson the track slab surface and the lower the stiffness of thebearing layer the more the tensile stress reduces

In general to prevent cracks at the connection betweenabutment and transition section expansion joints or otherimproved measures would be applied to address these

5m 5m 3m 5m 5m

13mSilty clay

Limestone

(a)

5m 5m 3m 5m 5m

16m

23m

13mSilty clay

Limestone

(b)

5m 5m 3m 5m 5m

13mSilty clay

Sand

(c)

5m 5m 3m 5m 5m

16m13m

23m

Silty clay

Sand

(d)

Figure 17 Optimization cases of the pile-plank structure (a) Case 1 (b) Case 2 (c) Case 3 (d) Case 4

60

70

80

90

100

110

Ver

tical

stiff

ness

(kN

mm

)

3510 15 20 25 30 400 5Distance from T0 section (m)

Case 1Case 2

Case 3Case 4

Figure 18 Vertical stiffness along the transition zone for different cases

14 Advances in Civil Engineering

problems in practical engineering From the above resultsthe authors suggest that in addition to the connection be-tween the bridge and the DBPPS transition section theconnection between the tunnel and the DBPPS transitionsection should also be reinforced or treated

5 Conclusions

In this study the authors present a numerical modelingapproach to investigate the dynamic performances of a newtype of bridge-tunnel transition section with a DBPPSwhich can be used as a tool to improve the design andapplication of DBPPS subgrade )e obtained research re-sults of this study lead to the following conclusions

(1) )e vibration level of the DBPPS transition section islower than that of the abutment and the tunnelsection when the train passes by Meanwhile theadditional load caused by vertical track stiffnessdifference can aggravate the vibration at the con-nections and its adjacent areas (such as section S1)between the DBPPS transition section and theabutment (or tunnel) In addition the vertical ac-celeration of the carbody also shows abrupt change atthese connections

(2) With train speed increases the vertical accelerationof the base slab increases and the vertical dynamicstress on the subgrade surface near the connections(such as section S1) also increases With axle weightincreases the vertical acceleration increases ap-proximately exponentially and the vertical dynamicstress increases approximately linearly )e traindirection has a significant influence on the con-nections and its adjacent areas with a large stiffnessdifference

(3) For general soil layers with uniform thickness theimprovement strategy with varying-length piles caneffectively smooth the track stiffness and reduce thetensile stress on the track slab surface at the

connections and the effect is more significant whenthe stiffness of the bearing layer is low

Data Availability

)e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

)e authors declare that they have no conflicts of interestregarding the publication of this paper

Acknowledgments

)is paper reports research developed under financialsupport provided by the Key Project of Science and Tech-nology Research and Development Program of ChinaRailway Corporation (Grant No 2014T003-D) and theNational Natural Science Foundation of China (Grant nos51878671 and 51678575)

References

[1] X Lei ldquoEffects of abrupt changes in track foundation stiffnesson track vibration under moving loadsrdquo Journal of VibrationEngineering vol 19 no 2 pp 195ndash199 2006

[2] A Paixatildeo E Fortunato and R Calccedilada ldquoTransition zones torailway bridges track measurements and numerical model-lingrdquo Engineering Structures vol 80 pp 435ndash443 2014

[3] K K Ang and J Dai ldquoResponse analysis of high-speed railsystem accounting for abrupt change of foundation stiffnessrdquoJournal of Sound and Vibration vol 332 no 12 pp 2954ndash2970 2013

[4] P Holscher and P Meijers Literature Study of Knowledge andExperience of Transition Zones Report of GeoDelft DelftNetherlands 2007

[5] European Committee for Standardisation(CEN) Basis ofstructural design European Committee for Stand-ardisation(CEN) Brussels Belgium 2005

Tunnel section Transition section Abutment

Track slab

Carbody

Rail

I II

Unit Pa+537e + 05+423e + 05+309e + 05+195e + 05+807e + 04ndash335e + 04ndash148e + 05ndash262e + 05ndash376e + 05ndash490e + 05ndash604e + 05ndash718e + 05ndash832e + 05

S S22(Average 75)

(a)

3510 15 20 25 30 400 5Distance from section T0 (m)

ndash200

0

200

400

600

800

Max

imum

tens

ile st

ress

(kPa

)

Case 1Case 2

Case 3Case 4

(b)

Figure 19 Tensile stress distribution for different cases (a) Tensile stress contour of Case 3 at a certain time (b) Maximum tensile stress fordifferent cases

Advances in Civil Engineering 15

[6] )e Swedish Rail Administration Design standard for railwaybridges Standard BVS 58310 )e Swedish Rail Adminis-tration Borlange Sweden 2006

[7] Canadian Standards AssociationndashInternational CanadianHighway Bridge Design Code Canadian Standards Associa-tionndashInternational Toronto Canada 2000

[8] National Railway Administration Code for Design of HighSpeed Railway (TB10621-2014) China Railway PublishingHouse Beijing China 2015

[9] D Li and D Davis ldquoTransition of railroad bridge ap-proachesrdquo Journal of Geotechnical and GeoenvironmentalEngineering vol 131 no 11 pp 1392ndash1398 2005

[10] P Hu C Zhang S J Chen Y Wang W Wang andW H Duan ldquoDynamic responses of bridge-embankmenttransitions in high speed railway field tests and data analysesrdquoEngineering Structures vol 175 pp 565ndash576 2018

[11] Y Shan B Albers and S A Savidis ldquoInfluence of differenttransition zones on the dynamic response of track-subgradesystemsrdquo Computers and Geotechnics vol 48 pp 21ndash28 2013

[12] Y Shan Y Shu and S Zhou ldquoFinite-infinite element coupledanalysis on the influence of material parameters on the dy-namic properties of transition zonesrdquo Construction andBuilding Materials vol 148 no 1 pp 548ndash558 2017

[13] J Ren H Zhao X Li et al ldquoDynamic performances of CRTSIII prefabricated slab track with anti-vibration structure insubgrade-tunnel transition sectionrdquo Journal of SouthwestJiaotong University vol 51 no 6 pp 1047ndash1054 2016

[14] J N Varandas P Holscher and M A G Silva ldquo)ree-di-mensional track-ballast interaction model for the study of aculvert transitionrdquo Soil Dynamics and Earthquake Engi-neering vol 89 pp 116ndash127 2016

[15] P Hu C Zhang S Wen and Y Wang ldquoDynamic responsesof high-speed railway transition zone with various subgradefillingsrdquoComputers and Geotechnics vol 108 pp 17ndash26 2019

[16] J N Varandas A Paixatildeo and E Fortunato ldquoA study on thedynamic train-track interaction over cut-fill transitions onburied culvertsrdquo Computers amp Structures vol 189 no 9pp 49ndash61 2017

[17] R Santildeudo L DellrsquoOlio J A Casado I A Carrascal andS Diego ldquoTrack transitions in railways a reviewrdquo Con-struction and Building Materials vol 112 pp 140ndash157 2016

[18] L Wei C He and Z Yang Comprehensive Test Study Reportof Nanchang West to Yichun East Section of Shanghai-Kunming Railway Passenger Dedicated Line Central SouthUniversity Changsha China 2014

[19] Q SuWWang H Bai et al ldquoBearing capacity mechanism ofnon-embedded pile-plank structure subgraderdquo Journal ofTraffic and Transportation Engineering vol 12 no 1pp 19ndash24 2012

[20] Y-X Zhan H-L Yao and G-L Jiang ldquoDesign method ofpile-slab structure roadbed of ballastless track on soil sub-graderdquo Journal of Central South University vol 20 no 7pp 2072ndash2082 2013

[21] KMa ldquoAnalysis on space vibration performance of pile-plankstructuremdashfoundation soil system under the condition ofhigh-speed trains runningrdquo Journal of the China RailwaySociety vol 35 no 1 pp 93ndash100 2013

[22] L Huang B Wang and S Zhou ldquoCentrifugal model test ofpile-plank subgrade in soft groundrdquo Rock and Soil Mechanicsvol 34 no S1 pp 192ndash196 2013

[23] J Huang Q Su T Liu and X Wang ldquoVibration and long-term performance analysis of pile-plank-supported lowsubgrade of ballastless track under excitation loadsrdquo Shockand Vibration vol 2015 pp 1ndash12 2015

[24] Dassault Systemes Simulia Corp Abaqus Analysis UserrsquosManual Version 612 Dassault Systemes Simulia CorpJohnston Rhode Island USA 2012

[25] C Cheng ldquoStudy on dynamic responses of irregularity bal-lastless track for high-speed railwayrdquo PhD )esis ZhejiangUniversity Zhejiang China 2015

[26] H Hertz ldquoOn the contact of elastic solidsrdquo Journal fur die rneund angewandte Mathematik (Crelles Journal) vol 92no 156 2008

[27] P Ni K Wang W Zhang et al ldquoCalculation method ofwheel-rail contact relationrdquo Journal of Traffic and Trans-portation Engineering vol 04 pp 14ndash17 2006

[28] W Zhai and X Sun ldquoA detailed model for investigatingvertical interaction between railway vehicle and trackrdquo Ve-hicle System Dynamics vol 23 pp 603ndash615 1994

[29] W Zhai Vehicle-track Coupled Dynamics Jeory and Ap-plication Science Press and Springer Nature Singapore PteLtd Berlin Germany 2020

[30] W Li and X Bian ldquoDynamic performance of pile-supportedbridge-embankment transition zones under high-speed trainmoving loadsrdquo Procedia Engineering vol 143 pp 1059ndash10672016

[31] P Ni S Mangalathu G Mei and Y Zhao ldquoPermeable pilesan alternative to improve the performance of driven pilesrdquoComputers and Geotechnics vol 84 pp 78ndash87 2017

[32] K Liu Q Su P Ni C Zhou W Zhao and F Yue ldquoEval-uation on the dynamic performance of bridge approachbackfilled with fibre reinforced lightweight concrete underhigh-speed train loadingrdquo Computers and Geotechnicsvol 104 pp 42ndash53 2018

[33] F Xue and J Zhang ldquoAttenuations of acceleration spectra ofhigh-speed railway embankment subjected to moving loadsrdquoRock and Soil Mechanics vol 36 pp 445ndash451 2015

[34] Y Xuan ldquoSimulation research on the dynamic characteristicsof vehicle-track coupling system on curved track and thevibration response of ballastless track strucure of passengertraffic railwayrdquo PhD )esis China Academy of RailwaySciences Beijing China 2008

[35] P Ricco A Baron and P Molteni ldquoNature of pressure wavesinduced by a high-speed train travelling through a tunnelrdquoJournal of Wind Engineering and Industrial Aerodynamicsvol 95 no 8 pp 781ndash808 2007

[36] C Esveld Modern Railway Track MRT-Productions Zalt-bommel Netherlands 2001

[37] R Santildeudo M Cerrada B Alonso and L dellrsquoOlio ldquoAnalysisof the influence of support positions in transition zones Anumerical analysisrdquo Construction and Building Materialsvol 145 no 1 pp 207ndash217 2017

[38] M Shahraki CWarnakulasooriya and K JWitt ldquoNumericalstudy of transition zone between ballasted and ballastlessrailway trackrdquo Transportation Geotechnics vol 3 pp 58ndash672015

[39] C Alves Ribeiro R Calccedilada and R Delgado ldquoExperimentalassessment of the dynamic behaviour of the train-track systemat a culvert transition zonerdquo Engineering Structures vol 138no 1 pp 215ndash228 2017

[40] Ministry of Railways Institute of StandardMetrology RailwayLocomotive Dynamic Performance Test Identification Methodand Evaluation Standard (TBT2360-1993) Ministry of Rail-ways Institute of Standard Metrology Beijing China 1994

16 Advances in Civil Engineering

displacement for different pile lengths the strategy ofvarying-length piles is conducive to the stiffnesssmoothness in the transition zone

For general soil layers with uniform thickness Li andBian [30] discussed the influences of varying-length pilesand constant-length piles on the vertical track stiffness ina subgrade-bridge transition section and found that thevarying-length piles strategy can effectively smooth thevertical track stiffness transition Nevertheless for theDBPPS transition section under the general conditionsthe necessity of variable pile-length design is still de-batable In this study four comparative cases including

two improvement strategies varying-length piles andconstant-length piles are established to investigate theinfluences of pile length and the properties of soil on theDBPPS transition section as shown in Figure 17 In thesecases it is assumed that the ground consists of twohorizontal soil layers the upper layer is the silty clay layerthe bearing layer is the sand layer or limestone layer with ahigher stiffness than the silty clay layer )e materialproperties are shown in Table 1 and other parameters andwork conditions remain unchanged

Figure 18 shows the vertical track stiffness distributionalong the transition zone under four cases It can be seen thatthe smoothness of vertical track stiffness along the transitionsection can be improved by adopting the strategy of varying-length piles especially when the bearing layer is the sandlayer )e authors consider that when the bearing layer islimestone the bearing mode is similar to end-bearing pilesand the upper load is mainly transferred by piles to thebearing layer Consequently the change in pile length has asmall effect on the upper load transfer But when the bearinglayer is the sand layer with a lower stiffness the bearingmode is similar to friction-bearing piles and the upper loadis mainly shared by piles and the shallow ground )e in-crease of pile length effectively improves the friction resis-tance which indirectly enhances the overall stiffness of theground )erefore the strategy of varying-length piles caneffectively smooth the vertical track stiffness in the DBPPStransition section with a bearing layer of low stiffness

P1P2S1 sectionD

ynam

ic st

ress

(kPa

)10

0

ndash10

ndash20

ndash30

ndash40

ndash5002 04 06 08 1 12 14

Time (s)

P1P2

(a)

P3P4S2 sectionD

ynam

ic st

ress

(kPa

)

10

0

ndash10

ndash20

ndash30

ndash40

ndash5002 04 06 08 1 12 14

Time (s)

P3P4

(b)

P5P6S3 sectionD

ynam

ic st

ress

(kPa

)

10

0

ndash10

ndash20

ndash30

ndash40

ndash5002 04 06 08 1 12 14

Time (s)

P5P6

(c)

Figure 11 Time-history curves of the vertical dynamic stress (a) Observation points of section S1 (b) Observation points of section S2 (c)Observation points of section S3

+261e + 03+000e + 03ndash261e + 03ndash523e + 03ndash784e + 03ndash105e + 04ndash131e + 04ndash156e + 04ndash183e + 04ndash209e + 04ndash235e + 04ndash261e + 04ndash288e + 04ndash312e + 04

Fieldndash1 S33Unit Pa (Avg 75)

Maximum 291 kPa

S3 S1

Maximum 312 kPa

Train direction

x

yz

Figure 12 Vertical stress contour of the train passing throughsection S1 and section S3 successively

12 Advances in Civil Engineering

Changes in longitudinal stresses are more prone toactivate track slab cracking Figure 19(a) shows thelongitudinal stress (S22) contour on the track slab sur-face at a certain time for Case 3 A positive value

represents tensile stress and a negative value representscompressive stress It can be seen that under the trainload significant concentrated tension stresses are

250 300 350 400200Train speed (kmh)

0

01

02

03

04

05V

ertic

al v

ibra

tion

acce

lera

tion

(ms

2 )

B0-3S1-3S2-3

S3-3T0-3

(a)

250 300 350 400200Train speed (kmh)

25

27

29

31

33

35

Ver

tical

dyn

amic

stre

ss (k

Pa)

P2P4P6

(b)

Figure 13 Influences of the train speed on dynamic responses (a) Vertical acceleration (b) Vertical dynamic stress

S3-3T0-3

15 20 25 3010Vehicle axle weight (t)

0

02

04

06

08

Ver

tical

vib

ratio

nac

cele

ratio

n (m

s2 )

B0-3S1-3S2-3

(a)

15 20 25 3010Vehicle axle weight (t)

0

30

60

90

120

Ver

tical

dyn

amic

stre

ss (k

Pa)

P2P4P6

(b)

Figure 14 Influences of the axle weight on dynamic responses (a) Vertical acceleration (b) Vertical dynamic stress

x = 375

x = 349

x = 115

x = 89

B0S1

S2S3

T0

Tunnel Transition section Bridge

3 6 9 12 15 18 21 24 27 30 33 36 39 420Distance from section T0 x (m)

Ver

tical

acce

lera

tion

(ms

2 )

012

015

018

021

024

027

030

From bridge to tunnelFrom tunnel to bridge

Figure 15 Influence of the train direction on dynamic responses

Pile length = 23mPile length = 16m

Pile length = 13mPile length = 10m

ndash003

ndash0025

ndash002

ndash0015

ndash001

ndash0005

0

Ver

tical

disp

lace

men

t (m

m)

090603 12 150Time (s)

Figure 16 Vertical displacement on the pile top for piles of dif-ferent lengths

Advances in Civil Engineering 13

generated on the track slab surface at the positions I andII (Figure 19(a)) with the maximum value of 5374 kPaNevertheless long-term cyclic dynamic load caused bytrain may activate cracks at these positions

Figure 19(b) shows the comparison of maximum tensilestress along the DBPPS transition section in four cases )emaximum tensile stresses at positions I and II are signifi-cantly higher than those at other positions due to the largerstiffness difference When the bearing layer is limestonelayer the maximum tensile stress on the track slab surface at

positions I and II can be reduced by 109 and 78 re-spectively using varying-length piles while when thebearing layer is the sand layer the values can be reduced by278 and 182 respectively indicating that the strategy ofvarying-length piles can significantly reduce the tensile stresson the track slab surface and the lower the stiffness of thebearing layer the more the tensile stress reduces

In general to prevent cracks at the connection betweenabutment and transition section expansion joints or otherimproved measures would be applied to address these

5m 5m 3m 5m 5m

13mSilty clay

Limestone

(a)

5m 5m 3m 5m 5m

16m

23m

13mSilty clay

Limestone

(b)

5m 5m 3m 5m 5m

13mSilty clay

Sand

(c)

5m 5m 3m 5m 5m

16m13m

23m

Silty clay

Sand

(d)

Figure 17 Optimization cases of the pile-plank structure (a) Case 1 (b) Case 2 (c) Case 3 (d) Case 4

60

70

80

90

100

110

Ver

tical

stiff

ness

(kN

mm

)

3510 15 20 25 30 400 5Distance from T0 section (m)

Case 1Case 2

Case 3Case 4

Figure 18 Vertical stiffness along the transition zone for different cases

14 Advances in Civil Engineering

problems in practical engineering From the above resultsthe authors suggest that in addition to the connection be-tween the bridge and the DBPPS transition section theconnection between the tunnel and the DBPPS transitionsection should also be reinforced or treated

5 Conclusions

In this study the authors present a numerical modelingapproach to investigate the dynamic performances of a newtype of bridge-tunnel transition section with a DBPPSwhich can be used as a tool to improve the design andapplication of DBPPS subgrade )e obtained research re-sults of this study lead to the following conclusions

(1) )e vibration level of the DBPPS transition section islower than that of the abutment and the tunnelsection when the train passes by Meanwhile theadditional load caused by vertical track stiffnessdifference can aggravate the vibration at the con-nections and its adjacent areas (such as section S1)between the DBPPS transition section and theabutment (or tunnel) In addition the vertical ac-celeration of the carbody also shows abrupt change atthese connections

(2) With train speed increases the vertical accelerationof the base slab increases and the vertical dynamicstress on the subgrade surface near the connections(such as section S1) also increases With axle weightincreases the vertical acceleration increases ap-proximately exponentially and the vertical dynamicstress increases approximately linearly )e traindirection has a significant influence on the con-nections and its adjacent areas with a large stiffnessdifference

(3) For general soil layers with uniform thickness theimprovement strategy with varying-length piles caneffectively smooth the track stiffness and reduce thetensile stress on the track slab surface at the

connections and the effect is more significant whenthe stiffness of the bearing layer is low

Data Availability

)e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

)e authors declare that they have no conflicts of interestregarding the publication of this paper

Acknowledgments

)is paper reports research developed under financialsupport provided by the Key Project of Science and Tech-nology Research and Development Program of ChinaRailway Corporation (Grant No 2014T003-D) and theNational Natural Science Foundation of China (Grant nos51878671 and 51678575)

References

[1] X Lei ldquoEffects of abrupt changes in track foundation stiffnesson track vibration under moving loadsrdquo Journal of VibrationEngineering vol 19 no 2 pp 195ndash199 2006

[2] A Paixatildeo E Fortunato and R Calccedilada ldquoTransition zones torailway bridges track measurements and numerical model-lingrdquo Engineering Structures vol 80 pp 435ndash443 2014

[3] K K Ang and J Dai ldquoResponse analysis of high-speed railsystem accounting for abrupt change of foundation stiffnessrdquoJournal of Sound and Vibration vol 332 no 12 pp 2954ndash2970 2013

[4] P Holscher and P Meijers Literature Study of Knowledge andExperience of Transition Zones Report of GeoDelft DelftNetherlands 2007

[5] European Committee for Standardisation(CEN) Basis ofstructural design European Committee for Stand-ardisation(CEN) Brussels Belgium 2005

Tunnel section Transition section Abutment

Track slab

Carbody

Rail

I II

Unit Pa+537e + 05+423e + 05+309e + 05+195e + 05+807e + 04ndash335e + 04ndash148e + 05ndash262e + 05ndash376e + 05ndash490e + 05ndash604e + 05ndash718e + 05ndash832e + 05

S S22(Average 75)

(a)

3510 15 20 25 30 400 5Distance from section T0 (m)

ndash200

0

200

400

600

800

Max

imum

tens

ile st

ress

(kPa

)

Case 1Case 2

Case 3Case 4

(b)

Figure 19 Tensile stress distribution for different cases (a) Tensile stress contour of Case 3 at a certain time (b) Maximum tensile stress fordifferent cases

Advances in Civil Engineering 15

[6] )e Swedish Rail Administration Design standard for railwaybridges Standard BVS 58310 )e Swedish Rail Adminis-tration Borlange Sweden 2006

[7] Canadian Standards AssociationndashInternational CanadianHighway Bridge Design Code Canadian Standards Associa-tionndashInternational Toronto Canada 2000

[8] National Railway Administration Code for Design of HighSpeed Railway (TB10621-2014) China Railway PublishingHouse Beijing China 2015

[9] D Li and D Davis ldquoTransition of railroad bridge ap-proachesrdquo Journal of Geotechnical and GeoenvironmentalEngineering vol 131 no 11 pp 1392ndash1398 2005

[10] P Hu C Zhang S J Chen Y Wang W Wang andW H Duan ldquoDynamic responses of bridge-embankmenttransitions in high speed railway field tests and data analysesrdquoEngineering Structures vol 175 pp 565ndash576 2018

[11] Y Shan B Albers and S A Savidis ldquoInfluence of differenttransition zones on the dynamic response of track-subgradesystemsrdquo Computers and Geotechnics vol 48 pp 21ndash28 2013

[12] Y Shan Y Shu and S Zhou ldquoFinite-infinite element coupledanalysis on the influence of material parameters on the dy-namic properties of transition zonesrdquo Construction andBuilding Materials vol 148 no 1 pp 548ndash558 2017

[13] J Ren H Zhao X Li et al ldquoDynamic performances of CRTSIII prefabricated slab track with anti-vibration structure insubgrade-tunnel transition sectionrdquo Journal of SouthwestJiaotong University vol 51 no 6 pp 1047ndash1054 2016

[14] J N Varandas P Holscher and M A G Silva ldquo)ree-di-mensional track-ballast interaction model for the study of aculvert transitionrdquo Soil Dynamics and Earthquake Engi-neering vol 89 pp 116ndash127 2016

[15] P Hu C Zhang S Wen and Y Wang ldquoDynamic responsesof high-speed railway transition zone with various subgradefillingsrdquoComputers and Geotechnics vol 108 pp 17ndash26 2019

[16] J N Varandas A Paixatildeo and E Fortunato ldquoA study on thedynamic train-track interaction over cut-fill transitions onburied culvertsrdquo Computers amp Structures vol 189 no 9pp 49ndash61 2017

[17] R Santildeudo L DellrsquoOlio J A Casado I A Carrascal andS Diego ldquoTrack transitions in railways a reviewrdquo Con-struction and Building Materials vol 112 pp 140ndash157 2016

[18] L Wei C He and Z Yang Comprehensive Test Study Reportof Nanchang West to Yichun East Section of Shanghai-Kunming Railway Passenger Dedicated Line Central SouthUniversity Changsha China 2014

[19] Q SuWWang H Bai et al ldquoBearing capacity mechanism ofnon-embedded pile-plank structure subgraderdquo Journal ofTraffic and Transportation Engineering vol 12 no 1pp 19ndash24 2012

[20] Y-X Zhan H-L Yao and G-L Jiang ldquoDesign method ofpile-slab structure roadbed of ballastless track on soil sub-graderdquo Journal of Central South University vol 20 no 7pp 2072ndash2082 2013

[21] KMa ldquoAnalysis on space vibration performance of pile-plankstructuremdashfoundation soil system under the condition ofhigh-speed trains runningrdquo Journal of the China RailwaySociety vol 35 no 1 pp 93ndash100 2013

[22] L Huang B Wang and S Zhou ldquoCentrifugal model test ofpile-plank subgrade in soft groundrdquo Rock and Soil Mechanicsvol 34 no S1 pp 192ndash196 2013

[23] J Huang Q Su T Liu and X Wang ldquoVibration and long-term performance analysis of pile-plank-supported lowsubgrade of ballastless track under excitation loadsrdquo Shockand Vibration vol 2015 pp 1ndash12 2015

[24] Dassault Systemes Simulia Corp Abaqus Analysis UserrsquosManual Version 612 Dassault Systemes Simulia CorpJohnston Rhode Island USA 2012

[25] C Cheng ldquoStudy on dynamic responses of irregularity bal-lastless track for high-speed railwayrdquo PhD )esis ZhejiangUniversity Zhejiang China 2015

[26] H Hertz ldquoOn the contact of elastic solidsrdquo Journal fur die rneund angewandte Mathematik (Crelles Journal) vol 92no 156 2008

[27] P Ni K Wang W Zhang et al ldquoCalculation method ofwheel-rail contact relationrdquo Journal of Traffic and Trans-portation Engineering vol 04 pp 14ndash17 2006

[28] W Zhai and X Sun ldquoA detailed model for investigatingvertical interaction between railway vehicle and trackrdquo Ve-hicle System Dynamics vol 23 pp 603ndash615 1994

[29] W Zhai Vehicle-track Coupled Dynamics Jeory and Ap-plication Science Press and Springer Nature Singapore PteLtd Berlin Germany 2020

[30] W Li and X Bian ldquoDynamic performance of pile-supportedbridge-embankment transition zones under high-speed trainmoving loadsrdquo Procedia Engineering vol 143 pp 1059ndash10672016

[31] P Ni S Mangalathu G Mei and Y Zhao ldquoPermeable pilesan alternative to improve the performance of driven pilesrdquoComputers and Geotechnics vol 84 pp 78ndash87 2017

[32] K Liu Q Su P Ni C Zhou W Zhao and F Yue ldquoEval-uation on the dynamic performance of bridge approachbackfilled with fibre reinforced lightweight concrete underhigh-speed train loadingrdquo Computers and Geotechnicsvol 104 pp 42ndash53 2018

[33] F Xue and J Zhang ldquoAttenuations of acceleration spectra ofhigh-speed railway embankment subjected to moving loadsrdquoRock and Soil Mechanics vol 36 pp 445ndash451 2015

[34] Y Xuan ldquoSimulation research on the dynamic characteristicsof vehicle-track coupling system on curved track and thevibration response of ballastless track strucure of passengertraffic railwayrdquo PhD )esis China Academy of RailwaySciences Beijing China 2008

[35] P Ricco A Baron and P Molteni ldquoNature of pressure wavesinduced by a high-speed train travelling through a tunnelrdquoJournal of Wind Engineering and Industrial Aerodynamicsvol 95 no 8 pp 781ndash808 2007

[36] C Esveld Modern Railway Track MRT-Productions Zalt-bommel Netherlands 2001

[37] R Santildeudo M Cerrada B Alonso and L dellrsquoOlio ldquoAnalysisof the influence of support positions in transition zones Anumerical analysisrdquo Construction and Building Materialsvol 145 no 1 pp 207ndash217 2017

[38] M Shahraki CWarnakulasooriya and K JWitt ldquoNumericalstudy of transition zone between ballasted and ballastlessrailway trackrdquo Transportation Geotechnics vol 3 pp 58ndash672015

[39] C Alves Ribeiro R Calccedilada and R Delgado ldquoExperimentalassessment of the dynamic behaviour of the train-track systemat a culvert transition zonerdquo Engineering Structures vol 138no 1 pp 215ndash228 2017

[40] Ministry of Railways Institute of StandardMetrology RailwayLocomotive Dynamic Performance Test Identification Methodand Evaluation Standard (TBT2360-1993) Ministry of Rail-ways Institute of Standard Metrology Beijing China 1994

16 Advances in Civil Engineering

Changes in longitudinal stresses are more prone toactivate track slab cracking Figure 19(a) shows thelongitudinal stress (S22) contour on the track slab sur-face at a certain time for Case 3 A positive value

represents tensile stress and a negative value representscompressive stress It can be seen that under the trainload significant concentrated tension stresses are

250 300 350 400200Train speed (kmh)

0

01

02

03

04

05V

ertic

al v

ibra

tion

acce

lera

tion

(ms

2 )

B0-3S1-3S2-3

S3-3T0-3

(a)

250 300 350 400200Train speed (kmh)

25

27

29

31

33

35

Ver

tical

dyn

amic

stre

ss (k

Pa)

P2P4P6

(b)

Figure 13 Influences of the train speed on dynamic responses (a) Vertical acceleration (b) Vertical dynamic stress

S3-3T0-3

15 20 25 3010Vehicle axle weight (t)

0

02

04

06

08

Ver

tical

vib

ratio

nac

cele

ratio

n (m

s2 )

B0-3S1-3S2-3

(a)

15 20 25 3010Vehicle axle weight (t)

0

30

60

90

120

Ver

tical

dyn

amic

stre

ss (k

Pa)

P2P4P6

(b)

Figure 14 Influences of the axle weight on dynamic responses (a) Vertical acceleration (b) Vertical dynamic stress

x = 375

x = 349

x = 115

x = 89

B0S1

S2S3

T0

Tunnel Transition section Bridge

3 6 9 12 15 18 21 24 27 30 33 36 39 420Distance from section T0 x (m)

Ver

tical

acce

lera

tion

(ms

2 )

012

015

018

021

024

027

030

From bridge to tunnelFrom tunnel to bridge

Figure 15 Influence of the train direction on dynamic responses

Pile length = 23mPile length = 16m

Pile length = 13mPile length = 10m

ndash003

ndash0025

ndash002

ndash0015

ndash001

ndash0005

0

Ver

tical

disp

lace

men

t (m

m)

090603 12 150Time (s)

Figure 16 Vertical displacement on the pile top for piles of dif-ferent lengths

Advances in Civil Engineering 13

generated on the track slab surface at the positions I andII (Figure 19(a)) with the maximum value of 5374 kPaNevertheless long-term cyclic dynamic load caused bytrain may activate cracks at these positions

Figure 19(b) shows the comparison of maximum tensilestress along the DBPPS transition section in four cases )emaximum tensile stresses at positions I and II are signifi-cantly higher than those at other positions due to the largerstiffness difference When the bearing layer is limestonelayer the maximum tensile stress on the track slab surface at

positions I and II can be reduced by 109 and 78 re-spectively using varying-length piles while when thebearing layer is the sand layer the values can be reduced by278 and 182 respectively indicating that the strategy ofvarying-length piles can significantly reduce the tensile stresson the track slab surface and the lower the stiffness of thebearing layer the more the tensile stress reduces

In general to prevent cracks at the connection betweenabutment and transition section expansion joints or otherimproved measures would be applied to address these

5m 5m 3m 5m 5m

13mSilty clay

Limestone

(a)

5m 5m 3m 5m 5m

16m

23m

13mSilty clay

Limestone

(b)

5m 5m 3m 5m 5m

13mSilty clay

Sand

(c)

5m 5m 3m 5m 5m

16m13m

23m

Silty clay

Sand

(d)

Figure 17 Optimization cases of the pile-plank structure (a) Case 1 (b) Case 2 (c) Case 3 (d) Case 4

60

70

80

90

100

110

Ver

tical

stiff

ness

(kN

mm

)

3510 15 20 25 30 400 5Distance from T0 section (m)

Case 1Case 2

Case 3Case 4

Figure 18 Vertical stiffness along the transition zone for different cases

14 Advances in Civil Engineering

problems in practical engineering From the above resultsthe authors suggest that in addition to the connection be-tween the bridge and the DBPPS transition section theconnection between the tunnel and the DBPPS transitionsection should also be reinforced or treated

5 Conclusions

In this study the authors present a numerical modelingapproach to investigate the dynamic performances of a newtype of bridge-tunnel transition section with a DBPPSwhich can be used as a tool to improve the design andapplication of DBPPS subgrade )e obtained research re-sults of this study lead to the following conclusions

(1) )e vibration level of the DBPPS transition section islower than that of the abutment and the tunnelsection when the train passes by Meanwhile theadditional load caused by vertical track stiffnessdifference can aggravate the vibration at the con-nections and its adjacent areas (such as section S1)between the DBPPS transition section and theabutment (or tunnel) In addition the vertical ac-celeration of the carbody also shows abrupt change atthese connections

(2) With train speed increases the vertical accelerationof the base slab increases and the vertical dynamicstress on the subgrade surface near the connections(such as section S1) also increases With axle weightincreases the vertical acceleration increases ap-proximately exponentially and the vertical dynamicstress increases approximately linearly )e traindirection has a significant influence on the con-nections and its adjacent areas with a large stiffnessdifference

(3) For general soil layers with uniform thickness theimprovement strategy with varying-length piles caneffectively smooth the track stiffness and reduce thetensile stress on the track slab surface at the

connections and the effect is more significant whenthe stiffness of the bearing layer is low

Data Availability

)e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

)e authors declare that they have no conflicts of interestregarding the publication of this paper

Acknowledgments

)is paper reports research developed under financialsupport provided by the Key Project of Science and Tech-nology Research and Development Program of ChinaRailway Corporation (Grant No 2014T003-D) and theNational Natural Science Foundation of China (Grant nos51878671 and 51678575)

References

[1] X Lei ldquoEffects of abrupt changes in track foundation stiffnesson track vibration under moving loadsrdquo Journal of VibrationEngineering vol 19 no 2 pp 195ndash199 2006

[2] A Paixatildeo E Fortunato and R Calccedilada ldquoTransition zones torailway bridges track measurements and numerical model-lingrdquo Engineering Structures vol 80 pp 435ndash443 2014

[3] K K Ang and J Dai ldquoResponse analysis of high-speed railsystem accounting for abrupt change of foundation stiffnessrdquoJournal of Sound and Vibration vol 332 no 12 pp 2954ndash2970 2013

[4] P Holscher and P Meijers Literature Study of Knowledge andExperience of Transition Zones Report of GeoDelft DelftNetherlands 2007

[5] European Committee for Standardisation(CEN) Basis ofstructural design European Committee for Stand-ardisation(CEN) Brussels Belgium 2005

Tunnel section Transition section Abutment

Track slab

Carbody

Rail

I II

Unit Pa+537e + 05+423e + 05+309e + 05+195e + 05+807e + 04ndash335e + 04ndash148e + 05ndash262e + 05ndash376e + 05ndash490e + 05ndash604e + 05ndash718e + 05ndash832e + 05

S S22(Average 75)

(a)

3510 15 20 25 30 400 5Distance from section T0 (m)

ndash200

0

200

400

600

800

Max

imum

tens

ile st

ress

(kPa

)

Case 1Case 2

Case 3Case 4

(b)

Figure 19 Tensile stress distribution for different cases (a) Tensile stress contour of Case 3 at a certain time (b) Maximum tensile stress fordifferent cases

Advances in Civil Engineering 15

[6] )e Swedish Rail Administration Design standard for railwaybridges Standard BVS 58310 )e Swedish Rail Adminis-tration Borlange Sweden 2006

[7] Canadian Standards AssociationndashInternational CanadianHighway Bridge Design Code Canadian Standards Associa-tionndashInternational Toronto Canada 2000

[8] National Railway Administration Code for Design of HighSpeed Railway (TB10621-2014) China Railway PublishingHouse Beijing China 2015

[9] D Li and D Davis ldquoTransition of railroad bridge ap-proachesrdquo Journal of Geotechnical and GeoenvironmentalEngineering vol 131 no 11 pp 1392ndash1398 2005

[10] P Hu C Zhang S J Chen Y Wang W Wang andW H Duan ldquoDynamic responses of bridge-embankmenttransitions in high speed railway field tests and data analysesrdquoEngineering Structures vol 175 pp 565ndash576 2018

[11] Y Shan B Albers and S A Savidis ldquoInfluence of differenttransition zones on the dynamic response of track-subgradesystemsrdquo Computers and Geotechnics vol 48 pp 21ndash28 2013

[12] Y Shan Y Shu and S Zhou ldquoFinite-infinite element coupledanalysis on the influence of material parameters on the dy-namic properties of transition zonesrdquo Construction andBuilding Materials vol 148 no 1 pp 548ndash558 2017

[13] J Ren H Zhao X Li et al ldquoDynamic performances of CRTSIII prefabricated slab track with anti-vibration structure insubgrade-tunnel transition sectionrdquo Journal of SouthwestJiaotong University vol 51 no 6 pp 1047ndash1054 2016

[14] J N Varandas P Holscher and M A G Silva ldquo)ree-di-mensional track-ballast interaction model for the study of aculvert transitionrdquo Soil Dynamics and Earthquake Engi-neering vol 89 pp 116ndash127 2016

[15] P Hu C Zhang S Wen and Y Wang ldquoDynamic responsesof high-speed railway transition zone with various subgradefillingsrdquoComputers and Geotechnics vol 108 pp 17ndash26 2019

[16] J N Varandas A Paixatildeo and E Fortunato ldquoA study on thedynamic train-track interaction over cut-fill transitions onburied culvertsrdquo Computers amp Structures vol 189 no 9pp 49ndash61 2017

[17] R Santildeudo L DellrsquoOlio J A Casado I A Carrascal andS Diego ldquoTrack transitions in railways a reviewrdquo Con-struction and Building Materials vol 112 pp 140ndash157 2016

[18] L Wei C He and Z Yang Comprehensive Test Study Reportof Nanchang West to Yichun East Section of Shanghai-Kunming Railway Passenger Dedicated Line Central SouthUniversity Changsha China 2014

[19] Q SuWWang H Bai et al ldquoBearing capacity mechanism ofnon-embedded pile-plank structure subgraderdquo Journal ofTraffic and Transportation Engineering vol 12 no 1pp 19ndash24 2012

[20] Y-X Zhan H-L Yao and G-L Jiang ldquoDesign method ofpile-slab structure roadbed of ballastless track on soil sub-graderdquo Journal of Central South University vol 20 no 7pp 2072ndash2082 2013

[21] KMa ldquoAnalysis on space vibration performance of pile-plankstructuremdashfoundation soil system under the condition ofhigh-speed trains runningrdquo Journal of the China RailwaySociety vol 35 no 1 pp 93ndash100 2013

[22] L Huang B Wang and S Zhou ldquoCentrifugal model test ofpile-plank subgrade in soft groundrdquo Rock and Soil Mechanicsvol 34 no S1 pp 192ndash196 2013

[23] J Huang Q Su T Liu and X Wang ldquoVibration and long-term performance analysis of pile-plank-supported lowsubgrade of ballastless track under excitation loadsrdquo Shockand Vibration vol 2015 pp 1ndash12 2015

[24] Dassault Systemes Simulia Corp Abaqus Analysis UserrsquosManual Version 612 Dassault Systemes Simulia CorpJohnston Rhode Island USA 2012

[25] C Cheng ldquoStudy on dynamic responses of irregularity bal-lastless track for high-speed railwayrdquo PhD )esis ZhejiangUniversity Zhejiang China 2015

[26] H Hertz ldquoOn the contact of elastic solidsrdquo Journal fur die rneund angewandte Mathematik (Crelles Journal) vol 92no 156 2008

[27] P Ni K Wang W Zhang et al ldquoCalculation method ofwheel-rail contact relationrdquo Journal of Traffic and Trans-portation Engineering vol 04 pp 14ndash17 2006

[28] W Zhai and X Sun ldquoA detailed model for investigatingvertical interaction between railway vehicle and trackrdquo Ve-hicle System Dynamics vol 23 pp 603ndash615 1994

[29] W Zhai Vehicle-track Coupled Dynamics Jeory and Ap-plication Science Press and Springer Nature Singapore PteLtd Berlin Germany 2020

[30] W Li and X Bian ldquoDynamic performance of pile-supportedbridge-embankment transition zones under high-speed trainmoving loadsrdquo Procedia Engineering vol 143 pp 1059ndash10672016

[31] P Ni S Mangalathu G Mei and Y Zhao ldquoPermeable pilesan alternative to improve the performance of driven pilesrdquoComputers and Geotechnics vol 84 pp 78ndash87 2017

[32] K Liu Q Su P Ni C Zhou W Zhao and F Yue ldquoEval-uation on the dynamic performance of bridge approachbackfilled with fibre reinforced lightweight concrete underhigh-speed train loadingrdquo Computers and Geotechnicsvol 104 pp 42ndash53 2018

[33] F Xue and J Zhang ldquoAttenuations of acceleration spectra ofhigh-speed railway embankment subjected to moving loadsrdquoRock and Soil Mechanics vol 36 pp 445ndash451 2015

[34] Y Xuan ldquoSimulation research on the dynamic characteristicsof vehicle-track coupling system on curved track and thevibration response of ballastless track strucure of passengertraffic railwayrdquo PhD )esis China Academy of RailwaySciences Beijing China 2008

[35] P Ricco A Baron and P Molteni ldquoNature of pressure wavesinduced by a high-speed train travelling through a tunnelrdquoJournal of Wind Engineering and Industrial Aerodynamicsvol 95 no 8 pp 781ndash808 2007

[36] C Esveld Modern Railway Track MRT-Productions Zalt-bommel Netherlands 2001

[37] R Santildeudo M Cerrada B Alonso and L dellrsquoOlio ldquoAnalysisof the influence of support positions in transition zones Anumerical analysisrdquo Construction and Building Materialsvol 145 no 1 pp 207ndash217 2017

[38] M Shahraki CWarnakulasooriya and K JWitt ldquoNumericalstudy of transition zone between ballasted and ballastlessrailway trackrdquo Transportation Geotechnics vol 3 pp 58ndash672015

[39] C Alves Ribeiro R Calccedilada and R Delgado ldquoExperimentalassessment of the dynamic behaviour of the train-track systemat a culvert transition zonerdquo Engineering Structures vol 138no 1 pp 215ndash228 2017

[40] Ministry of Railways Institute of StandardMetrology RailwayLocomotive Dynamic Performance Test Identification Methodand Evaluation Standard (TBT2360-1993) Ministry of Rail-ways Institute of Standard Metrology Beijing China 1994

16 Advances in Civil Engineering

generated on the track slab surface at the positions I andII (Figure 19(a)) with the maximum value of 5374 kPaNevertheless long-term cyclic dynamic load caused bytrain may activate cracks at these positions

Figure 19(b) shows the comparison of maximum tensilestress along the DBPPS transition section in four cases )emaximum tensile stresses at positions I and II are signifi-cantly higher than those at other positions due to the largerstiffness difference When the bearing layer is limestonelayer the maximum tensile stress on the track slab surface at

positions I and II can be reduced by 109 and 78 re-spectively using varying-length piles while when thebearing layer is the sand layer the values can be reduced by278 and 182 respectively indicating that the strategy ofvarying-length piles can significantly reduce the tensile stresson the track slab surface and the lower the stiffness of thebearing layer the more the tensile stress reduces

In general to prevent cracks at the connection betweenabutment and transition section expansion joints or otherimproved measures would be applied to address these

5m 5m 3m 5m 5m

13mSilty clay

Limestone

(a)

5m 5m 3m 5m 5m

16m

23m

13mSilty clay

Limestone

(b)

5m 5m 3m 5m 5m

13mSilty clay

Sand

(c)

5m 5m 3m 5m 5m

16m13m

23m

Silty clay

Sand

(d)

Figure 17 Optimization cases of the pile-plank structure (a) Case 1 (b) Case 2 (c) Case 3 (d) Case 4

60

70

80

90

100

110

Ver

tical

stiff

ness

(kN

mm

)

3510 15 20 25 30 400 5Distance from T0 section (m)

Case 1Case 2

Case 3Case 4

Figure 18 Vertical stiffness along the transition zone for different cases

14 Advances in Civil Engineering

problems in practical engineering From the above resultsthe authors suggest that in addition to the connection be-tween the bridge and the DBPPS transition section theconnection between the tunnel and the DBPPS transitionsection should also be reinforced or treated

5 Conclusions

In this study the authors present a numerical modelingapproach to investigate the dynamic performances of a newtype of bridge-tunnel transition section with a DBPPSwhich can be used as a tool to improve the design andapplication of DBPPS subgrade )e obtained research re-sults of this study lead to the following conclusions

(1) )e vibration level of the DBPPS transition section islower than that of the abutment and the tunnelsection when the train passes by Meanwhile theadditional load caused by vertical track stiffnessdifference can aggravate the vibration at the con-nections and its adjacent areas (such as section S1)between the DBPPS transition section and theabutment (or tunnel) In addition the vertical ac-celeration of the carbody also shows abrupt change atthese connections

(2) With train speed increases the vertical accelerationof the base slab increases and the vertical dynamicstress on the subgrade surface near the connections(such as section S1) also increases With axle weightincreases the vertical acceleration increases ap-proximately exponentially and the vertical dynamicstress increases approximately linearly )e traindirection has a significant influence on the con-nections and its adjacent areas with a large stiffnessdifference

(3) For general soil layers with uniform thickness theimprovement strategy with varying-length piles caneffectively smooth the track stiffness and reduce thetensile stress on the track slab surface at the

connections and the effect is more significant whenthe stiffness of the bearing layer is low

Data Availability

)e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

)e authors declare that they have no conflicts of interestregarding the publication of this paper

Acknowledgments

)is paper reports research developed under financialsupport provided by the Key Project of Science and Tech-nology Research and Development Program of ChinaRailway Corporation (Grant No 2014T003-D) and theNational Natural Science Foundation of China (Grant nos51878671 and 51678575)

References

[1] X Lei ldquoEffects of abrupt changes in track foundation stiffnesson track vibration under moving loadsrdquo Journal of VibrationEngineering vol 19 no 2 pp 195ndash199 2006

[2] A Paixatildeo E Fortunato and R Calccedilada ldquoTransition zones torailway bridges track measurements and numerical model-lingrdquo Engineering Structures vol 80 pp 435ndash443 2014

[3] K K Ang and J Dai ldquoResponse analysis of high-speed railsystem accounting for abrupt change of foundation stiffnessrdquoJournal of Sound and Vibration vol 332 no 12 pp 2954ndash2970 2013

[4] P Holscher and P Meijers Literature Study of Knowledge andExperience of Transition Zones Report of GeoDelft DelftNetherlands 2007

[5] European Committee for Standardisation(CEN) Basis ofstructural design European Committee for Stand-ardisation(CEN) Brussels Belgium 2005

Tunnel section Transition section Abutment

Track slab

Carbody

Rail

I II

Unit Pa+537e + 05+423e + 05+309e + 05+195e + 05+807e + 04ndash335e + 04ndash148e + 05ndash262e + 05ndash376e + 05ndash490e + 05ndash604e + 05ndash718e + 05ndash832e + 05

S S22(Average 75)

(a)

3510 15 20 25 30 400 5Distance from section T0 (m)

ndash200

0

200

400

600

800

Max

imum

tens

ile st

ress

(kPa

)

Case 1Case 2

Case 3Case 4

(b)

Figure 19 Tensile stress distribution for different cases (a) Tensile stress contour of Case 3 at a certain time (b) Maximum tensile stress fordifferent cases

Advances in Civil Engineering 15

[6] )e Swedish Rail Administration Design standard for railwaybridges Standard BVS 58310 )e Swedish Rail Adminis-tration Borlange Sweden 2006

[7] Canadian Standards AssociationndashInternational CanadianHighway Bridge Design Code Canadian Standards Associa-tionndashInternational Toronto Canada 2000

[8] National Railway Administration Code for Design of HighSpeed Railway (TB10621-2014) China Railway PublishingHouse Beijing China 2015

[9] D Li and D Davis ldquoTransition of railroad bridge ap-proachesrdquo Journal of Geotechnical and GeoenvironmentalEngineering vol 131 no 11 pp 1392ndash1398 2005

[10] P Hu C Zhang S J Chen Y Wang W Wang andW H Duan ldquoDynamic responses of bridge-embankmenttransitions in high speed railway field tests and data analysesrdquoEngineering Structures vol 175 pp 565ndash576 2018

[11] Y Shan B Albers and S A Savidis ldquoInfluence of differenttransition zones on the dynamic response of track-subgradesystemsrdquo Computers and Geotechnics vol 48 pp 21ndash28 2013

[12] Y Shan Y Shu and S Zhou ldquoFinite-infinite element coupledanalysis on the influence of material parameters on the dy-namic properties of transition zonesrdquo Construction andBuilding Materials vol 148 no 1 pp 548ndash558 2017

[13] J Ren H Zhao X Li et al ldquoDynamic performances of CRTSIII prefabricated slab track with anti-vibration structure insubgrade-tunnel transition sectionrdquo Journal of SouthwestJiaotong University vol 51 no 6 pp 1047ndash1054 2016

[14] J N Varandas P Holscher and M A G Silva ldquo)ree-di-mensional track-ballast interaction model for the study of aculvert transitionrdquo Soil Dynamics and Earthquake Engi-neering vol 89 pp 116ndash127 2016

[15] P Hu C Zhang S Wen and Y Wang ldquoDynamic responsesof high-speed railway transition zone with various subgradefillingsrdquoComputers and Geotechnics vol 108 pp 17ndash26 2019

[16] J N Varandas A Paixatildeo and E Fortunato ldquoA study on thedynamic train-track interaction over cut-fill transitions onburied culvertsrdquo Computers amp Structures vol 189 no 9pp 49ndash61 2017

[17] R Santildeudo L DellrsquoOlio J A Casado I A Carrascal andS Diego ldquoTrack transitions in railways a reviewrdquo Con-struction and Building Materials vol 112 pp 140ndash157 2016

[18] L Wei C He and Z Yang Comprehensive Test Study Reportof Nanchang West to Yichun East Section of Shanghai-Kunming Railway Passenger Dedicated Line Central SouthUniversity Changsha China 2014

[19] Q SuWWang H Bai et al ldquoBearing capacity mechanism ofnon-embedded pile-plank structure subgraderdquo Journal ofTraffic and Transportation Engineering vol 12 no 1pp 19ndash24 2012

[20] Y-X Zhan H-L Yao and G-L Jiang ldquoDesign method ofpile-slab structure roadbed of ballastless track on soil sub-graderdquo Journal of Central South University vol 20 no 7pp 2072ndash2082 2013

[21] KMa ldquoAnalysis on space vibration performance of pile-plankstructuremdashfoundation soil system under the condition ofhigh-speed trains runningrdquo Journal of the China RailwaySociety vol 35 no 1 pp 93ndash100 2013

[22] L Huang B Wang and S Zhou ldquoCentrifugal model test ofpile-plank subgrade in soft groundrdquo Rock and Soil Mechanicsvol 34 no S1 pp 192ndash196 2013

[23] J Huang Q Su T Liu and X Wang ldquoVibration and long-term performance analysis of pile-plank-supported lowsubgrade of ballastless track under excitation loadsrdquo Shockand Vibration vol 2015 pp 1ndash12 2015

[24] Dassault Systemes Simulia Corp Abaqus Analysis UserrsquosManual Version 612 Dassault Systemes Simulia CorpJohnston Rhode Island USA 2012

[25] C Cheng ldquoStudy on dynamic responses of irregularity bal-lastless track for high-speed railwayrdquo PhD )esis ZhejiangUniversity Zhejiang China 2015

[26] H Hertz ldquoOn the contact of elastic solidsrdquo Journal fur die rneund angewandte Mathematik (Crelles Journal) vol 92no 156 2008

[27] P Ni K Wang W Zhang et al ldquoCalculation method ofwheel-rail contact relationrdquo Journal of Traffic and Trans-portation Engineering vol 04 pp 14ndash17 2006

[28] W Zhai and X Sun ldquoA detailed model for investigatingvertical interaction between railway vehicle and trackrdquo Ve-hicle System Dynamics vol 23 pp 603ndash615 1994

[29] W Zhai Vehicle-track Coupled Dynamics Jeory and Ap-plication Science Press and Springer Nature Singapore PteLtd Berlin Germany 2020

[30] W Li and X Bian ldquoDynamic performance of pile-supportedbridge-embankment transition zones under high-speed trainmoving loadsrdquo Procedia Engineering vol 143 pp 1059ndash10672016

[31] P Ni S Mangalathu G Mei and Y Zhao ldquoPermeable pilesan alternative to improve the performance of driven pilesrdquoComputers and Geotechnics vol 84 pp 78ndash87 2017

[32] K Liu Q Su P Ni C Zhou W Zhao and F Yue ldquoEval-uation on the dynamic performance of bridge approachbackfilled with fibre reinforced lightweight concrete underhigh-speed train loadingrdquo Computers and Geotechnicsvol 104 pp 42ndash53 2018

[33] F Xue and J Zhang ldquoAttenuations of acceleration spectra ofhigh-speed railway embankment subjected to moving loadsrdquoRock and Soil Mechanics vol 36 pp 445ndash451 2015

[34] Y Xuan ldquoSimulation research on the dynamic characteristicsof vehicle-track coupling system on curved track and thevibration response of ballastless track strucure of passengertraffic railwayrdquo PhD )esis China Academy of RailwaySciences Beijing China 2008

[35] P Ricco A Baron and P Molteni ldquoNature of pressure wavesinduced by a high-speed train travelling through a tunnelrdquoJournal of Wind Engineering and Industrial Aerodynamicsvol 95 no 8 pp 781ndash808 2007

[36] C Esveld Modern Railway Track MRT-Productions Zalt-bommel Netherlands 2001

[37] R Santildeudo M Cerrada B Alonso and L dellrsquoOlio ldquoAnalysisof the influence of support positions in transition zones Anumerical analysisrdquo Construction and Building Materialsvol 145 no 1 pp 207ndash217 2017

[38] M Shahraki CWarnakulasooriya and K JWitt ldquoNumericalstudy of transition zone between ballasted and ballastlessrailway trackrdquo Transportation Geotechnics vol 3 pp 58ndash672015

[39] C Alves Ribeiro R Calccedilada and R Delgado ldquoExperimentalassessment of the dynamic behaviour of the train-track systemat a culvert transition zonerdquo Engineering Structures vol 138no 1 pp 215ndash228 2017

[40] Ministry of Railways Institute of StandardMetrology RailwayLocomotive Dynamic Performance Test Identification Methodand Evaluation Standard (TBT2360-1993) Ministry of Rail-ways Institute of Standard Metrology Beijing China 1994

16 Advances in Civil Engineering

problems in practical engineering From the above resultsthe authors suggest that in addition to the connection be-tween the bridge and the DBPPS transition section theconnection between the tunnel and the DBPPS transitionsection should also be reinforced or treated

5 Conclusions

In this study the authors present a numerical modelingapproach to investigate the dynamic performances of a newtype of bridge-tunnel transition section with a DBPPSwhich can be used as a tool to improve the design andapplication of DBPPS subgrade )e obtained research re-sults of this study lead to the following conclusions

(1) )e vibration level of the DBPPS transition section islower than that of the abutment and the tunnelsection when the train passes by Meanwhile theadditional load caused by vertical track stiffnessdifference can aggravate the vibration at the con-nections and its adjacent areas (such as section S1)between the DBPPS transition section and theabutment (or tunnel) In addition the vertical ac-celeration of the carbody also shows abrupt change atthese connections

(2) With train speed increases the vertical accelerationof the base slab increases and the vertical dynamicstress on the subgrade surface near the connections(such as section S1) also increases With axle weightincreases the vertical acceleration increases ap-proximately exponentially and the vertical dynamicstress increases approximately linearly )e traindirection has a significant influence on the con-nections and its adjacent areas with a large stiffnessdifference

(3) For general soil layers with uniform thickness theimprovement strategy with varying-length piles caneffectively smooth the track stiffness and reduce thetensile stress on the track slab surface at the

connections and the effect is more significant whenthe stiffness of the bearing layer is low

Data Availability

)e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

)e authors declare that they have no conflicts of interestregarding the publication of this paper

Acknowledgments

)is paper reports research developed under financialsupport provided by the Key Project of Science and Tech-nology Research and Development Program of ChinaRailway Corporation (Grant No 2014T003-D) and theNational Natural Science Foundation of China (Grant nos51878671 and 51678575)

References

[1] X Lei ldquoEffects of abrupt changes in track foundation stiffnesson track vibration under moving loadsrdquo Journal of VibrationEngineering vol 19 no 2 pp 195ndash199 2006

[2] A Paixatildeo E Fortunato and R Calccedilada ldquoTransition zones torailway bridges track measurements and numerical model-lingrdquo Engineering Structures vol 80 pp 435ndash443 2014

[3] K K Ang and J Dai ldquoResponse analysis of high-speed railsystem accounting for abrupt change of foundation stiffnessrdquoJournal of Sound and Vibration vol 332 no 12 pp 2954ndash2970 2013

[4] P Holscher and P Meijers Literature Study of Knowledge andExperience of Transition Zones Report of GeoDelft DelftNetherlands 2007

[5] European Committee for Standardisation(CEN) Basis ofstructural design European Committee for Stand-ardisation(CEN) Brussels Belgium 2005

Tunnel section Transition section Abutment

Track slab

Carbody

Rail

I II

Unit Pa+537e + 05+423e + 05+309e + 05+195e + 05+807e + 04ndash335e + 04ndash148e + 05ndash262e + 05ndash376e + 05ndash490e + 05ndash604e + 05ndash718e + 05ndash832e + 05

S S22(Average 75)

(a)

3510 15 20 25 30 400 5Distance from section T0 (m)

ndash200

0

200

400

600

800

Max

imum

tens

ile st

ress

(kPa

)

Case 1Case 2

Case 3Case 4

(b)

Figure 19 Tensile stress distribution for different cases (a) Tensile stress contour of Case 3 at a certain time (b) Maximum tensile stress fordifferent cases

Advances in Civil Engineering 15

[6] )e Swedish Rail Administration Design standard for railwaybridges Standard BVS 58310 )e Swedish Rail Adminis-tration Borlange Sweden 2006

[7] Canadian Standards AssociationndashInternational CanadianHighway Bridge Design Code Canadian Standards Associa-tionndashInternational Toronto Canada 2000

[8] National Railway Administration Code for Design of HighSpeed Railway (TB10621-2014) China Railway PublishingHouse Beijing China 2015

[9] D Li and D Davis ldquoTransition of railroad bridge ap-proachesrdquo Journal of Geotechnical and GeoenvironmentalEngineering vol 131 no 11 pp 1392ndash1398 2005

[10] P Hu C Zhang S J Chen Y Wang W Wang andW H Duan ldquoDynamic responses of bridge-embankmenttransitions in high speed railway field tests and data analysesrdquoEngineering Structures vol 175 pp 565ndash576 2018

[11] Y Shan B Albers and S A Savidis ldquoInfluence of differenttransition zones on the dynamic response of track-subgradesystemsrdquo Computers and Geotechnics vol 48 pp 21ndash28 2013

[12] Y Shan Y Shu and S Zhou ldquoFinite-infinite element coupledanalysis on the influence of material parameters on the dy-namic properties of transition zonesrdquo Construction andBuilding Materials vol 148 no 1 pp 548ndash558 2017

[13] J Ren H Zhao X Li et al ldquoDynamic performances of CRTSIII prefabricated slab track with anti-vibration structure insubgrade-tunnel transition sectionrdquo Journal of SouthwestJiaotong University vol 51 no 6 pp 1047ndash1054 2016

[14] J N Varandas P Holscher and M A G Silva ldquo)ree-di-mensional track-ballast interaction model for the study of aculvert transitionrdquo Soil Dynamics and Earthquake Engi-neering vol 89 pp 116ndash127 2016

[15] P Hu C Zhang S Wen and Y Wang ldquoDynamic responsesof high-speed railway transition zone with various subgradefillingsrdquoComputers and Geotechnics vol 108 pp 17ndash26 2019

[16] J N Varandas A Paixatildeo and E Fortunato ldquoA study on thedynamic train-track interaction over cut-fill transitions onburied culvertsrdquo Computers amp Structures vol 189 no 9pp 49ndash61 2017

[17] R Santildeudo L DellrsquoOlio J A Casado I A Carrascal andS Diego ldquoTrack transitions in railways a reviewrdquo Con-struction and Building Materials vol 112 pp 140ndash157 2016

[18] L Wei C He and Z Yang Comprehensive Test Study Reportof Nanchang West to Yichun East Section of Shanghai-Kunming Railway Passenger Dedicated Line Central SouthUniversity Changsha China 2014

[19] Q SuWWang H Bai et al ldquoBearing capacity mechanism ofnon-embedded pile-plank structure subgraderdquo Journal ofTraffic and Transportation Engineering vol 12 no 1pp 19ndash24 2012

[20] Y-X Zhan H-L Yao and G-L Jiang ldquoDesign method ofpile-slab structure roadbed of ballastless track on soil sub-graderdquo Journal of Central South University vol 20 no 7pp 2072ndash2082 2013

[21] KMa ldquoAnalysis on space vibration performance of pile-plankstructuremdashfoundation soil system under the condition ofhigh-speed trains runningrdquo Journal of the China RailwaySociety vol 35 no 1 pp 93ndash100 2013

[22] L Huang B Wang and S Zhou ldquoCentrifugal model test ofpile-plank subgrade in soft groundrdquo Rock and Soil Mechanicsvol 34 no S1 pp 192ndash196 2013

[23] J Huang Q Su T Liu and X Wang ldquoVibration and long-term performance analysis of pile-plank-supported lowsubgrade of ballastless track under excitation loadsrdquo Shockand Vibration vol 2015 pp 1ndash12 2015

[24] Dassault Systemes Simulia Corp Abaqus Analysis UserrsquosManual Version 612 Dassault Systemes Simulia CorpJohnston Rhode Island USA 2012

[25] C Cheng ldquoStudy on dynamic responses of irregularity bal-lastless track for high-speed railwayrdquo PhD )esis ZhejiangUniversity Zhejiang China 2015

[26] H Hertz ldquoOn the contact of elastic solidsrdquo Journal fur die rneund angewandte Mathematik (Crelles Journal) vol 92no 156 2008

[27] P Ni K Wang W Zhang et al ldquoCalculation method ofwheel-rail contact relationrdquo Journal of Traffic and Trans-portation Engineering vol 04 pp 14ndash17 2006

[28] W Zhai and X Sun ldquoA detailed model for investigatingvertical interaction between railway vehicle and trackrdquo Ve-hicle System Dynamics vol 23 pp 603ndash615 1994

[29] W Zhai Vehicle-track Coupled Dynamics Jeory and Ap-plication Science Press and Springer Nature Singapore PteLtd Berlin Germany 2020

[30] W Li and X Bian ldquoDynamic performance of pile-supportedbridge-embankment transition zones under high-speed trainmoving loadsrdquo Procedia Engineering vol 143 pp 1059ndash10672016

[31] P Ni S Mangalathu G Mei and Y Zhao ldquoPermeable pilesan alternative to improve the performance of driven pilesrdquoComputers and Geotechnics vol 84 pp 78ndash87 2017

[32] K Liu Q Su P Ni C Zhou W Zhao and F Yue ldquoEval-uation on the dynamic performance of bridge approachbackfilled with fibre reinforced lightweight concrete underhigh-speed train loadingrdquo Computers and Geotechnicsvol 104 pp 42ndash53 2018

[33] F Xue and J Zhang ldquoAttenuations of acceleration spectra ofhigh-speed railway embankment subjected to moving loadsrdquoRock and Soil Mechanics vol 36 pp 445ndash451 2015

[34] Y Xuan ldquoSimulation research on the dynamic characteristicsof vehicle-track coupling system on curved track and thevibration response of ballastless track strucure of passengertraffic railwayrdquo PhD )esis China Academy of RailwaySciences Beijing China 2008

[35] P Ricco A Baron and P Molteni ldquoNature of pressure wavesinduced by a high-speed train travelling through a tunnelrdquoJournal of Wind Engineering and Industrial Aerodynamicsvol 95 no 8 pp 781ndash808 2007

[36] C Esveld Modern Railway Track MRT-Productions Zalt-bommel Netherlands 2001

[37] R Santildeudo M Cerrada B Alonso and L dellrsquoOlio ldquoAnalysisof the influence of support positions in transition zones Anumerical analysisrdquo Construction and Building Materialsvol 145 no 1 pp 207ndash217 2017

[38] M Shahraki CWarnakulasooriya and K JWitt ldquoNumericalstudy of transition zone between ballasted and ballastlessrailway trackrdquo Transportation Geotechnics vol 3 pp 58ndash672015

[39] C Alves Ribeiro R Calccedilada and R Delgado ldquoExperimentalassessment of the dynamic behaviour of the train-track systemat a culvert transition zonerdquo Engineering Structures vol 138no 1 pp 215ndash228 2017

[40] Ministry of Railways Institute of StandardMetrology RailwayLocomotive Dynamic Performance Test Identification Methodand Evaluation Standard (TBT2360-1993) Ministry of Rail-ways Institute of Standard Metrology Beijing China 1994

16 Advances in Civil Engineering

[6] )e Swedish Rail Administration Design standard for railwaybridges Standard BVS 58310 )e Swedish Rail Adminis-tration Borlange Sweden 2006

[7] Canadian Standards AssociationndashInternational CanadianHighway Bridge Design Code Canadian Standards Associa-tionndashInternational Toronto Canada 2000

[8] National Railway Administration Code for Design of HighSpeed Railway (TB10621-2014) China Railway PublishingHouse Beijing China 2015

[9] D Li and D Davis ldquoTransition of railroad bridge ap-proachesrdquo Journal of Geotechnical and GeoenvironmentalEngineering vol 131 no 11 pp 1392ndash1398 2005

[10] P Hu C Zhang S J Chen Y Wang W Wang andW H Duan ldquoDynamic responses of bridge-embankmenttransitions in high speed railway field tests and data analysesrdquoEngineering Structures vol 175 pp 565ndash576 2018

[11] Y Shan B Albers and S A Savidis ldquoInfluence of differenttransition zones on the dynamic response of track-subgradesystemsrdquo Computers and Geotechnics vol 48 pp 21ndash28 2013

[12] Y Shan Y Shu and S Zhou ldquoFinite-infinite element coupledanalysis on the influence of material parameters on the dy-namic properties of transition zonesrdquo Construction andBuilding Materials vol 148 no 1 pp 548ndash558 2017

[13] J Ren H Zhao X Li et al ldquoDynamic performances of CRTSIII prefabricated slab track with anti-vibration structure insubgrade-tunnel transition sectionrdquo Journal of SouthwestJiaotong University vol 51 no 6 pp 1047ndash1054 2016

[14] J N Varandas P Holscher and M A G Silva ldquo)ree-di-mensional track-ballast interaction model for the study of aculvert transitionrdquo Soil Dynamics and Earthquake Engi-neering vol 89 pp 116ndash127 2016

[15] P Hu C Zhang S Wen and Y Wang ldquoDynamic responsesof high-speed railway transition zone with various subgradefillingsrdquoComputers and Geotechnics vol 108 pp 17ndash26 2019

[16] J N Varandas A Paixatildeo and E Fortunato ldquoA study on thedynamic train-track interaction over cut-fill transitions onburied culvertsrdquo Computers amp Structures vol 189 no 9pp 49ndash61 2017

[17] R Santildeudo L DellrsquoOlio J A Casado I A Carrascal andS Diego ldquoTrack transitions in railways a reviewrdquo Con-struction and Building Materials vol 112 pp 140ndash157 2016

[18] L Wei C He and Z Yang Comprehensive Test Study Reportof Nanchang West to Yichun East Section of Shanghai-Kunming Railway Passenger Dedicated Line Central SouthUniversity Changsha China 2014

[19] Q SuWWang H Bai et al ldquoBearing capacity mechanism ofnon-embedded pile-plank structure subgraderdquo Journal ofTraffic and Transportation Engineering vol 12 no 1pp 19ndash24 2012

[20] Y-X Zhan H-L Yao and G-L Jiang ldquoDesign method ofpile-slab structure roadbed of ballastless track on soil sub-graderdquo Journal of Central South University vol 20 no 7pp 2072ndash2082 2013

[21] KMa ldquoAnalysis on space vibration performance of pile-plankstructuremdashfoundation soil system under the condition ofhigh-speed trains runningrdquo Journal of the China RailwaySociety vol 35 no 1 pp 93ndash100 2013

[22] L Huang B Wang and S Zhou ldquoCentrifugal model test ofpile-plank subgrade in soft groundrdquo Rock and Soil Mechanicsvol 34 no S1 pp 192ndash196 2013

[23] J Huang Q Su T Liu and X Wang ldquoVibration and long-term performance analysis of pile-plank-supported lowsubgrade of ballastless track under excitation loadsrdquo Shockand Vibration vol 2015 pp 1ndash12 2015

[24] Dassault Systemes Simulia Corp Abaqus Analysis UserrsquosManual Version 612 Dassault Systemes Simulia CorpJohnston Rhode Island USA 2012

[25] C Cheng ldquoStudy on dynamic responses of irregularity bal-lastless track for high-speed railwayrdquo PhD )esis ZhejiangUniversity Zhejiang China 2015

[26] H Hertz ldquoOn the contact of elastic solidsrdquo Journal fur die rneund angewandte Mathematik (Crelles Journal) vol 92no 156 2008

[27] P Ni K Wang W Zhang et al ldquoCalculation method ofwheel-rail contact relationrdquo Journal of Traffic and Trans-portation Engineering vol 04 pp 14ndash17 2006

[28] W Zhai and X Sun ldquoA detailed model for investigatingvertical interaction between railway vehicle and trackrdquo Ve-hicle System Dynamics vol 23 pp 603ndash615 1994

[29] W Zhai Vehicle-track Coupled Dynamics Jeory and Ap-plication Science Press and Springer Nature Singapore PteLtd Berlin Germany 2020

[30] W Li and X Bian ldquoDynamic performance of pile-supportedbridge-embankment transition zones under high-speed trainmoving loadsrdquo Procedia Engineering vol 143 pp 1059ndash10672016

[31] P Ni S Mangalathu G Mei and Y Zhao ldquoPermeable pilesan alternative to improve the performance of driven pilesrdquoComputers and Geotechnics vol 84 pp 78ndash87 2017

[32] K Liu Q Su P Ni C Zhou W Zhao and F Yue ldquoEval-uation on the dynamic performance of bridge approachbackfilled with fibre reinforced lightweight concrete underhigh-speed train loadingrdquo Computers and Geotechnicsvol 104 pp 42ndash53 2018

[33] F Xue and J Zhang ldquoAttenuations of acceleration spectra ofhigh-speed railway embankment subjected to moving loadsrdquoRock and Soil Mechanics vol 36 pp 445ndash451 2015

[34] Y Xuan ldquoSimulation research on the dynamic characteristicsof vehicle-track coupling system on curved track and thevibration response of ballastless track strucure of passengertraffic railwayrdquo PhD )esis China Academy of RailwaySciences Beijing China 2008

[35] P Ricco A Baron and P Molteni ldquoNature of pressure wavesinduced by a high-speed train travelling through a tunnelrdquoJournal of Wind Engineering and Industrial Aerodynamicsvol 95 no 8 pp 781ndash808 2007

[36] C Esveld Modern Railway Track MRT-Productions Zalt-bommel Netherlands 2001

[37] R Santildeudo M Cerrada B Alonso and L dellrsquoOlio ldquoAnalysisof the influence of support positions in transition zones Anumerical analysisrdquo Construction and Building Materialsvol 145 no 1 pp 207ndash217 2017

[38] M Shahraki CWarnakulasooriya and K JWitt ldquoNumericalstudy of transition zone between ballasted and ballastlessrailway trackrdquo Transportation Geotechnics vol 3 pp 58ndash672015

[39] C Alves Ribeiro R Calccedilada and R Delgado ldquoExperimentalassessment of the dynamic behaviour of the train-track systemat a culvert transition zonerdquo Engineering Structures vol 138no 1 pp 215ndash228 2017

[40] Ministry of Railways Institute of StandardMetrology RailwayLocomotive Dynamic Performance Test Identification Methodand Evaluation Standard (TBT2360-1993) Ministry of Rail-ways Institute of Standard Metrology Beijing China 1994

16 Advances in Civil Engineering