Research ArticleModel Test Study on the Influence of Train Speed on the DynamicResponse of an X-Section Pile-Net Composite Foundation

Shanshan Xue 12 Yumin Chen 12 and Hanlong Liu 123

1Key Laboratory of Ministry of Education for Geomechanics and Embankment Engineering Hohai UniversityNanjing 210024 China2College of Civil and Transportation Engineering Hohai University Nanjing 210024 China3Key Laboratory of New Technology for Construction of Cities in Mountain Area Chongqing UniversityChongqing 400044 China

Correspondence should be addressed to Yumin Chen ymchhhueducn

Received 17 April 2019 Accepted 16 July 2019 Published 6 August 2019

Academic Editor Nuno M Maia

Copyright copy 2019 Shanshan Xue 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

Based on a large-scale X-section pile-net composite foundation model we experimentally studied the dynamic characteristics ofthe pile-net composite foundation under a high-speed railway train load analyzed the distribution characteristics of the dynamicstress dynamic displacement speed and acceleration of the foundation soil under different train speeds and investigated thevibration response of the track subgrade foundation system as well as the distribution characteristics and attenuation pattern ofthe dynamic stress inside the subgrade foundation under cyclic train loading)e following results are obtained)e peak verticalvibration speed and the peak acceleration attenuate by 90 and 625 respectively after passing through the embankment )evibration velocity increases linearly with the train speed the ratio of the peak dynamic soil stresses at the top of the piles andbetween the piles is approximately 34 )e change in train speed does not have a large influence on the peak dynamic dis-placement or peak dynamic soil stress )e peak spectral vibration acceleration caused by the train loading is located within therange of medium-to-low-frequency vibrations and the characteristic frequency corresponds to the passing frequency of the bogiesand carriages as the train speed increases the peak spectral vibration acceleration increases and the high-frequency componentsincrease significantly

1 Introduction

Along with the rapid development of the national economyin China the high-speed railway has been developed rapidlyBecause of its characteristics of a long operational cycle andfast train speed the high-speed railway has much stricterrequirements on the settlement control than those of anordinary railway )e pile-net composite foundation has theadvantages of fast construction low cost small settlementand high stability and has thus been widely applied as aground treatment for high-speed railways in China such asthe WuhanndashGuangzhou BeijingndashShanghai and SuiningndashChongqing high-speed railway lines

)e strengthening performance of the pile-net com-posite foundation has resulted in its widespread practicalapplication However because of its complicated working

mechanism under train loading the studies on this foun-dation are not adequate at present and have mainly beencarried out by means of field testing and laboratoryexperimentation

Heck [1] analyzed the mechanism of the train vibrationand found that besides the sleeper-passing frequency thepassing frequency of the wheelsets is also a main frequencythat is produced by the train vibration Takemiya and Bian[2] analyzed the test data of the Shinkansen line with a trainspeed of 240 kmh and concluded that the pulse impact onthe subgrade is related to the distance between wheelsetsBahrekazemi and Bodare [3] analyzed the fundamentaldynamic patterns of vibration induced by a train usingmeasurement data In China Bo and Ying [4] recordedrelevant data for the dynamic response of a subgradeby field measurements of the DatongndashQinhuangdao

HindawiShock and VibrationVolume 2019 Article ID 2614709 13 pageshttpsdoiorg10115520192614709

ChengdundashKunming and BaojindashChengdu railway linesChen and Lu Wentian [5] carried out field tests on a road-bridge transition section of the QinhuangdaondashShenyangpassenger railway line and studied the dynamic responseunder the operation of a high-speed train

Compared to field testing with its limitations large-scalemodel experimentation is an effective approach to study theinteraction between the track and subgrade and can satis-factorily reveal the mechanism for the response of the tracksubgrade foundation of a high-speed railway to trainloading Anderson and Key [6] established a physical modelfor a 1m long 08m wide and 06m high two-layer railwaytrack ballast bed and studied the dynamic performance ofthe structure layer material of the ballast bed under long-term repeated loading Cox et al [7] conducted a com-parative study via laboratory experiments on the differenttypes of floating slab and fastener system and simulated thevibration characteristics of the floating slab under fixed-point loading by a single-wheel axle load Using a laboratory1 2 slab track model Zhan and Jiang [8] studied the dy-namic response (eg dynamic stress dynamic displacementand propagation of acceleration along the cross section anddepth of subgrade) of different structural layers in a bal-lastless track subgrade system under fixed-point loadingUnder a moving train load the principal stress axis of thesoil inside the subgrade rotates significantly affecting theworking performance of the subgrade )erefore it isnecessary to introduce a moving load into experimentsMomoya et al [9] conducted a laboratory experiment usinga 1 5 ballasted track model and studied the distributioncharacteristics and settlement development of stress insidethe subgrade under a moving load but the simulated trainspeed was only 42 kmh Al Shaer et al [10] constructed a1 3 ballasted track model containing three sleepers adoptedan M-shaped wave to represent a bogie load and studied therelationship between the subgrade settlement and sleepervibration acceleration )rough experiments using a labo-ratory 1 5 ballasted track model Ishikawa et al [11]compared the difference in the stress paths inside thesubgrade under two loading scenarios (ie fixed-pointloading and moving loading) and revealed the rotationalcharacteristics of the principal stress axis under a movingload and its influence on the permanent deformation of thesubgrade )eir results showed that a moving load generatesa larger permanent deformation of the subgrade Howeverthe transient dynamic response of a pile-net compositefoundation under different actual train speeds has rarelybeen studied by experiments

)e X-section pile is an irregular pile with an X-shapedcross section Because of its large perimeter-to-area ratio theX-section pile can significantly improve the bearing capacityof a single pile without increasing the amount of concrete init thus increasing the cost performance [12ndash14] )e Liugroup conducted numerous studies on the load-bearingmechanism of an X-section pipe under static loading [15ndash17]and its engineering application [18] Using a large pilefoundation model test system Guang-Chao et al [19]conducted a dynamic model test of an X-section pile-raftcomposite foundation in sandy soil with a focus on the

patterns of change in the cumulative settlement displace-ment amplitude dynamic stiffness and vibration velocity ofthe X-section pile-raft composite foundation under cyclicloading in the forms of the M-shaped wave and sinusoidalwave that are often used to simulate high-speed train loads

In this study according to the typical design workingconditions for the pile-net subgrade foundation as well asthe construction standards for a high-speed railway andusing a 1 5 large-scale pile-net composite foundation in alarge test tank we conducted an experimental study on thedynamic response of a track-subgrade-pile-net compositefoundation system under train load with a focus on theanalysis of the vibration response of the system as well as thedistribution characteristics and attenuation pattern of thedynamic stress inside the subgrade foundation undervarying train speeds

2 Large-Scale Pile-Net CompositeFoundation Model

21 Overview of Model To ensure the safe and effectiveoperation of high-speed trains there are strict requirementsfor the size and filling quality of the various structural layers ofhigh-speed railways In an earlier stage we constructed a 1 5scale high-speed railway subgrade foundation model withdimensions of 5m 4m and 7m in length width and heightrespectively )e model included from top to bottom a trackslab CA mortar geogrid surface and bottom layers of thesubgrade bed and foundation A schematic diagram of thetank section of the model is shown in Figure 1

)e static and dynamic loading control system used inthe test is composed of JAW-200K static and dynamic ac-tuators a load input and control machine a vibrator con-troller and a hydraulic oil source)emaximum test force ofthe vibrator equipment in this system is 200 kN with ameasurement accuracy of plusmn05 )e actuator has a traveldistance of plusmn150mm with a displacement readout accuracyof plusmn1 and an actuator frequency of 01 to 30Hz Manu-factured byMoog Inc Germany the vibrator controller canset up different vibration waveforms and simulate the cyclicloading of the high-speed railway according to the magni-tude of the train load and running speed

22 Foundation Soil and Gravel Cushion Layer )e basicphysical parameters of the foundation filling silt adopted inthe test were measured by a laboratory consolidation testwith the test results shown in Table 1

)e test model used 28 X-section piles of the samematerial and size )e test pile has a design length of3950mm an open arc spacing of 395mm a circumscribedcircle radius of 76mm and an open arc angle of 90deg Whenthe foundation soil was filled and compacted to a height of0887m from the bottom of the tank the X-section pileswere buried and laid out in a quincunx shape with a pilespacing of 600mm To ensure perpendicularity during thelaying out the piles were secured with scaffolding and thenfilled and compacted layer by layer according to the fillingrequirements

2 Shock and Vibration

Graded gravels were used for the surface layer of thesubgrade bed group A and B fillers were used for the bottomlayer of the subgrade bed and well-graded unweatheredgravels or gravel fillers with a maximum particle size ofsmaller than 25mm were used for the cushion layer Ap-proximately 10ndash12 stone powder or fine particles wereblended in the gravels for filling after mixing well)e tensileyield strength of the geogrid used in the pile-net compositefoundation is 300 kNm as shown in Figure 2

Considering the dynamic response characteristics of theX-section pile-net composite foundation we installed in themodel test a complete set of dynamic and static test in-struments including displacement gauge dynamic pressurebox speedometer accelerometer and pore pressure gaugeto measure the vibration displacement dynamic earthpressure velocity and acceleration at different locations)especific layout is shown in Figure 3 Figure 3(a) is the frontview and Figure 3(b) is the top view

23 LoadingMethod andDesign Different train speeds weresimulated by controlling the loading frequency of the ac-tuators )e actuators were equipped with load transducersthat monitored the loads of the actuators in real time )ewheel-track load generated by the interaction of the wheel

shaft of the train and the track was transferred to the trackstructure and subgrade through the fastener systemAccording to field measurement data the wheel-track load ofan operating train is transferred in the form of a dynamic loadsimilar to an M-shaped wave to the foundation of the em-bankment)erefore anM-shaped wave was also adopted forloading in the test with the load waveform shown in Figure 4)e M-shaped wave shown in the figure is the dynamic loadof a train with a speed of 300 kmh and an axle load of 10 kN)is waveform was fitted using a 3rd-order Fourier seriesaccording to the variation pattern and periodic characteristicsof the time-history curve Let t be the running time of the trainand F(t) be the equation of the force applied by the actuator)e expression is shown in equation (1)

F(t) a0 + a1 cos2πnt

T1113874 1113875 + b1 sin

2πnt

T1113874 1113875 + a2 cos

4πnt

T1113874 1113875

+ b2 sin4πnt

T1113874 1113875 + a3 cos

6πnt

T1113874 1113875 + b3 sin

6πnt

T1113874 1113875

(1)

where T is the vibration period of the actuator load and anand bn are constants obtained based on the actual parametersof a train

Reaction beam

Actuator

Slit

XCC pile

1330

4300

1000

6800

Sand cushion

5000

Flexiblematerial

Figure 1 Schematic diagram of tank section of the model (unit mm)

Table 1 Basic physical indexes of silt

Water content () Unit weight (kNm3) Void ratio Liquid limit () Plastic limit () Plasticity index Liquid limit index278 186 0817 310 241 69 056

Shock and Vibration 3

K1

K2

K3

K4

K5

K6

D1 D2 D5

1670

860

780

2000

2000

1500

D6

V8

V9 V11

V10V7

V3V4

V2V1

S2

S3

S4

S5 S8

S9S6

S7

A8

A7

A6

A5

V13S1V12

(a)

Figure 3 Continued

Rail

Surface layer of subgradeBottom layer of subgrade

Broken stone hardcoreGeogrid

3340

1720

600 60 108

8046

072

012

0

Track slab

Figure 2 Schematic diagram of the embankment section (unit mm)

4 Shock and Vibration

)e train simulated in this test refers to the main type ofCRH3CRH380 D-series high-speed train operated on thehigh-speed railway in China )e applied force is the loadfrom the four pairs of wheels of the adjacent bogies of ad-jacent carriages)e time for passing through the distance of a25m bogie is two load cycles)emagnitude of the train loadand the running speed is reflected through the load output

and frequency of a servo vibrator )e relationship betweenthe train speed and loading frequency is shown in Table 2

3 TestWorking Conditions and Result Analysis

31 Analysis of Vertical Velocity Taking a train speed of300kmh as an example the time-history response curves of thevertical vibration velocities at different locations of the X-sectionpile-net composite foundation system are shown in Figure 5

Under the cyclic load of an M-shaped wave the time-history response curve of the velocity of the entire compositefoundation exhibits significant periodicity with the cyclicloading process and the frequency of its velocity response isconsistent with the frequency of the cyclic loading

At the surface and bottom layers of the subgrade bed thetime-history response curves of the velocity induced by thecyclic loading exhibits a significant M shape and as thedepth increases the amplitude of the M-shaped velocitygradually decreases )erefore the dynamic cyclic load in-duced by the operating train has an important influence onthe embankment and the vibration response of this region ismainly caused by the dynamic load of the train wheel shaftAs they propagate to the foundation the various reflectedwaves gradually account for a certain percentage of the totalcausing the response waveform to be insignificant

Figure 5 shows that the response of the velocity at thesurface layer of the subgrade bed in the embankment is

0

10

20

30

40

50

60

70

8025m25m25m

25m175m

Dyn

amic

load

ing

Q(t)

(kN

)

Time (s)

25mLoad cycle T

Figure 4 ldquoMrdquo-shaped wave

D1

600

520

D2

D3

D4

D5 D6V1A1

V2 V3A3A2

V4A4

V5 V6

S1

S4 S7

Pore pressure gauge (K)

Dynamic pressure box (S)

Speedometer (V)

Accelerometer (A)

Displacement gauge (D)

(b)

Figure 3 Layout of test instrument (unit mm) (a) front view (b) top view

Shock and Vibration 5

mainly caused by the cyclic dynamic load of the train and itis relatively consistent with the waveform of the loadingwave but without the influence of a large number of reflectedwaves in the foundation soil Hence it can better assist in thestudy of the relationship between the velocity response andthe train speed )erefore the peak responses of the verticalvelocity at the surface layer of the subgrade bed underdifferent train speeds are averaged for analysis Under dif-ferent train speeds the velocity responses of the X-sectionpile-net composite foundation at different depths are shownin Figure 6 We can see that with the track slab plane as the0m depth 1m is the surface layer of the subgrade Underdifferent train speeds the vibration velocity of the foun-dation soil rapidly attenuates as the depth increases and themaximum vibration response occurs at the surface layer ofthe subgrade bed It can be seen that within the depth of 1mie within the embankment the dynamic velocity attenuatesby approximately 90 indicating that the embankment hasa very good reduction effect on the propagation of the vi-bration load while the attenuation rate of the speed after itreaches the foundation decreases

Figure 7 shows the relationship curve between the re-sponse of the vertical velocity at the track slab and the trainspeed )e peak response of the velocity at the track slabunder three different train speeds is shown )e distributionof the scattered points reveals that the peak response of thevibration velocity at the track slab and the train speed arelinearly related As the train speed increases from 160 kmh to350 kmh the peak response of the vibration velocity in-creases from 2299mms to 4600mms an increase of 100

)e distribution of the vertical vibration velocity re-sponse of the track under train operation along the trans-verse direction of the track is shown in Figure 8 We can seethat in the whole system the track structure that is closest tothe actuator exhibits the most intense vibration responseWith a train speed of 350 kmh the peak vibration velocityreaches 4378mms while the maximum vibration velocityof the subgrade structure is only 102mms )e vibration ofthe subgrade system gradually attenuates going farther awayfrom the vibration source and the vibration velocity at thebottom layer of the subgrade bed as well as within the rangeof the lower foundation is at a relatively low level and with a

00 01 02 03 04 05 06Time (s)

ndash45ndash30ndash15

0153045

Vel

ocity

resp

onse

(mm

s)

(a)

ndash3ndash2ndash1

0123

00 01 02 03 04 05 06Time (s)

Vel

ocity

resp

onse

(mm

s)

(b)

00 01 02 03 04 05 06Time (s)

ndash3ndash2ndash1

0123

Vel

ocity

resp

onse

(mm

s)

(c)

00 01 02 03 04 05 06Time (s)

ndash3ndash2ndash1

0123

Vel

ocity

resp

onse

(mm

s)

(d)

00 01 02 03 04 05 06Time (s)

ndash3ndash2ndash1

0123

Vel

ocity

resp

onse

(mm

s)

(e)

Figure 5 Vertical velocity with respect to time (a) track slab (b) surface layer of subgrade (c) bottom layer of subgrade (d) surface layer offoundation (e) bottom layer of foundation

Table 2 Train speed and frequency

Actuator frequency Two peak period (s) Corresponding train speed (kmh) Two trough periods (s) Carriage cycle (s)18 0056 160 0173 055622 0045 200 0142 045528 0036 250 0111 035733 0030 300 0095 030339 0026 350 0080 0256

6 Shock and Vibration

significantly slow attenuation rate indicating that the sub-grade bed has a significant reduction effect on the verticalvibration

32 Analysis of Dynamic Earth Pressure Figure 9 showstime-history curves of the dynamic soil stress at the pile topand between piles when the train speed is 300 kmh)e waveis affected by the embankment and hence attenuates during

the propagation process causing the waveform characteristicsof the M-shaped wave to have already been significantlyweakened when it reaches the surface of the foundation Wecan see that the stress at the pile top is greater than thedynamic stress of the soil between piles and the soil arch has a

V4V3

160kmh200kmh250kmh

300kmh350kmh

V0 V1 V2

05 10 15 20 2500Distance to the center (m)

0

5

10

15

20

25

30

35

40

45

Vel

ocity

resp

onse

(mm

s)

Figure 8 Vertical velocity with respect to horizontal dimension

00 01 02 03 04 05 0602468

1012

Load

(kN

)

Waveform

Time (s)

(a)

ndash202468

1012

Dyn

amic

stre

ss (k

Pa)

Pile topSoil

00 01 02Time (s)

03 04 05 06

(b)

Figure 9 Dynamic stresses of pile and soil with respect to time

6

5

4

3

2

1

0ndash5 0 5 10 15 20 25 30 35 40 45 50

6

5

4

3

2

1

0 1 2 3

Velocity response (mms)

Dep

th (m

)

160kmh200kmh250kmh

300kmh350kmh

Figure 6 Vertical velocity with respect to depth

0

10

20

30

40

50

60

Vel

ocity

resp

onse

pea

k of

the t

rack

slab

(mm

s)

A groupB groupC group

50 100 150 200 250 300 350 4000Train speed (kmh)

Figure 7 Vertical velocity with respect to train speed

Shock and Vibration 7

significant influence on the distribution of the dynamic stressIn the soil arch region a greater dynamic load is transferredabove the top of the pile )e average of the peak dynamicstresses at the pile top is approximately 62 kPa which is 34times the average of the peak dynamic earth pressure (ap-proximately 18 kPa) on the soil between the piles

Figure 10 shows relationship curves of the changes in thepeak dynamic stresses at the pile top and in the soil betweenthe piles of the foundation and the train speed We can seethat under the vibration load of the high-speed train theload carried at the pile top in the foundation is much largerthan that by the soil between the piles

Although the vibration frequency of the dynamic loadincreases as the train speed increases the influence of thetrain speed on the response of the dynamic stress is weak)is is likely because the wave gradually attenuates in theprocess of reaching the foundation through the subgradebed and its effect gradually decreases

33 Analysis of Dynamic Displacement Figure 11 shows thetime-history response curve of the dynamic displacementon the track surface under different train speeds We cansee that the change in the train speed does not have a largeinfluence on the peak transient dynamic displacementresponse on the track surface A comparison of dynamicdisplacement responses under different train speeds re-veals that the faster the train speed the more intense andshorter the induced vibration)is is because the faster thetrain speed the higher the dynamic loading frequencyWhen the train speed is not high (160 kmh) the time-history curve between the peak displacements attenuatesWhen the train speed reaches 250 kmh the displacementtime history does not significantly attenuate but insteadgradually fluctuates with time In fact the attenuationprocess is not completed

34 Analysis of Acceleration Figure 12 shows the time-history curve of the acceleration at different locations in thepile-net composite foundation when the train speed is300 kmh We can see that the vibration close to the actuatorhas a relatively large amplitude As the distance from thevibration source increases the amplitude of the accelerationgradually decreases and the high-frequency componentsattenuate especially rapidly Because the track slab is rela-tively close to the subgrade bed its peak acceleration is ap-proximately 80mms2 After passing through the track slabthe waveform at the surface layer of the subgrade bed is not assignificant as that at the track slab

It can be clearly seen from Figure 12 that after passingthrough the subgrade bed the peak acceleration decreasesfrom 80mms2 to 30mms2 that is it attenuates by 625)is is mainly because the high-frequency components areabsorbed due to the damping effect of the soil in the em-bankment while the attenuation of the low-frequencycomponents is relatively slow When reaching the bottomlayer of the foundation due to the influence of the reflectedwaves the M-shaped waveform has essentially disappearedAs a result only a simple harmonic oscillation curve is

presented and the amplitude of the acceleration vibration isonly 2 of that at the surface layer of the foundation As thedepth increases the peak acceleration responses of theM-shaped waveform at different locations do not appear atthe same time )is is because it takes time for the wave topropagate causing some lag in the acceleration response

Figure 13 shows a spectral curve of the vertical accel-eration at different locations from the vibration source whenthe train speed is 300 kmh We can see that the frequency isdistributed in the range of 0ndash100Hz and is mainly con-centrated between 10 and 50Hz making it low-frequencyvibrations As the distance from the vibration source in-creases the maximum vibration accelerations at differentlocations are 4352mms2 4082mms2 3152mms2352mms2 and 014mms2 It can be seen that as thedistance from the vibration source increases the amplitudeof the acceleration generally attenuates )e high-frequencycomponent is relatively rich at locations close to the vi-bration source and the width of the spectrum graduallydecreases when moving away from the vibration source )emost significant frequency band becomes that of the lowfrequency because the high-frequency components attenu-ate faster than the low-frequency components

We can see from the peaks in Figure 13 that the fourcharacteristic frequencies with the largest contributions to thevibration are 199Hz 233Hz 299Hz and 332Hz Amongthem 332Hz corresponds to the actuator frequency At themeasurement site of the track slab the frequency of theground vibration caused by the train is distributed within50ndash85Hz and relatively rich in the main frequency

Figure 14 shows the time-history curve of the accelerationat the surface layer of the foundation under different trainspeeds We can clearly see that as the train speed increases thehigh-frequency components significantly increase Whenthe train speed is 160 kmh the peak acceleration at the sur-face layer of the foundation is 359mms2 and when thetrain velocity increases to 200 kmh the peak acceleration atthe surface layer of the foundation reaches 724mms2

Pile topSoil

0

2

4

6

8

10

Dyn

amic

stre

ss (k

Pa)

200 300 400100Train speed (kmh)

Figure 10 Relationship curves between dynamic stress responsesof soil at pipe top and between piles and the train speed

8 Shock and Vibration

00

02

04

06

08

Dyn

amic

disp

lace

men

tof

the t

rack

slab

(mm

)

02 04 06 08 10 1200Time (s)

160kmh

(a)

00

02

04

06

08

Dyn

amic

disp

lace

men

tof

the t

rack

slab

(mm

)

02 04 06 08 10 1200Time (s)

200kmh

(b)

00

02

04

06

08

Dyn

amic

disp

lace

men

tof

the t

rack

slab

(mm

)

02 04 06 08 10 1200Time (s)

250kmh(c)

00

02

04

06

08

Dyn

amic

disp

lace

men

tof

the t

rack

slab

(mm

)

02 04 06 08 10 1200Time (s)

300kmh

(d)

00

02

04

06

08

Dyn

amic

disp

lace

men

tof

the t

rack

slab

(mm

)

02 04 06 08 10 1200Time (s)

350kmh

(e)

Figure 11 Dynamic displacement of track with respect to time

120

ndash120

80

ndash80

40

ndash400

Acc

eler

atio

nre

spon

se (m

ms

2 )

01 02 03 04 05 0600Time (s)

(a)

120

ndash120

80

ndash80

40

ndash400

Acc

eler

atio

nre

spon

se (m

ms

2 )

01 02 03 04 05 0600Time (s)

(b)120

ndash120

80

ndash80

40

ndash400

Acc

eler

atio

nre

spon

se (m

ms

2 )

01 02 03 04 05 0600Time (s)

(c)

120

ndash120

80

ndash80

40

ndash400

Acc

eler

atio

nre

spon

se (m

ms

2 )

01 02 03 04 05 0600Time (s)

(d)

Figure 12 Acceleration at different layers with respect to time (a) track slab (b) surface layer of subgrade (c) bottom layer of subgrade (d)surface layer of foundation

Shock and Vibration 9

332Hz299Hz199Hz

233Hz

0 20 30 40 50 60 70 80 90 10010Frequency (Hz)

01020304050

Acc

eler

atio

nam

plitu

de (m

ms

2 )

(a)

233Hz

332Hz299Hz199Hz

0 20 30 40 50 60 70 80 90 10010Frequency (Hz)

01020304050

Acc

eler

atio

nam

plitu

de (m

ms

2 )

(b)

332Hz299Hz

233Hz

199Hz

0 20 30 40 50 60 70 80 90 10010Frequency (Hz)

01020304050

Acc

eler

atio

nam

plitu

de (m

ms

2 )

(c)

299Hz332Hz

233Hz199Hz

0 20 30 40 50 60 70 80 90 1001Frequency (Hz)

01020304050

Acc

eler

atio

nam

plitu

de (m

ms

2 )

(d)

Figure 13 Spectral curve of acceleration at different locations (a) track slab (b) surface layer of subgrade (c) bottom layer of subgrade (d)surface layer of foundation

00 02 04Time (s)

06 08 10 12ndash10

ndash5

0

5

10

Acc

eler

atio

n re

spon

se(s

urfa

ce la

yer o

f fou

ndat

ion)

(mm

s2 )

160kmh

(a)

00 02 04 06 08 10 12ndash10

ndash5

0

5

10

Acc

eler

atio

n re

spon

se(s

urfa

ce la

yer o

f fou

ndat

ion)

(mm

s2 )

Time (s)

200kmh

(b)

00 02 04 06 08 10 12ndash10

ndash5

0

5

10

Acc

eler

atio

n re

spon

se(s

urfa

ce la

yer o

f fou

ndat

ion)

(mm

s2 )

Time (s)

250kmh

(c)

Figure 14 Continued

10 Shock and Vibration

00 02 04 06 08 10 12ndash10

ndash5

0

5

10

Acc

eler

atio

n re

spon

se(s

urfa

ce la

yer o

f fou

ndat

ion)

(mm

s2 )

Time (s)

300kmh

(d)

00 02 04 06 08 10 12ndash10

ndash5

0

5

10

Acc

eler

atio

n re

spon

se(s

urfa

ce la

yer o

f fou

ndat

ion)

(mm

s2 )

Time (s)

350kmh

(e)

Figure 14 Acceleration under different speeds with respect to time

177Hz

160kmh

0

1

2

3

Acc

eler

atio

nam

plitu

de (m

ms

2 )

20 40 60 80 1000Time (s)

(a)

200kmh

200Hz 222Hz

0

1

2

3

Acc

eler

atio

nam

plitu

de (m

ms

2 )

20 40 60 80 1000Time (s)

(b)

Figure 15 Continued

Shock and Vibration 11

(approximately double) However when the train speed rea-ches 250 kmh the increase on the peak is negligible Becausethe increase in the train speed is achieved by increasing thevibration frequency the superposition of the surroundingreflected waves in this process likely produces a counteractionto the vibration of the subgrade foundation explaining thisresult

Figure 15 shows the spectral curve of the acceleration atthe surface layer of the foundation under different trainspeeds We can see that the ground vibration caused by thetrain is mainly contributed by relatively low-frequencycomponents (mainly below 100Hz) As the train speedincreases the amplitude of the acceleration increases andthe base frequencies of the vibration also gradually increase177Hz in the base frequencies when the train velocity is160 kmh 222Hz when the train speed is 200 kmh 277Hzwhen the train speed is 250 kmh 332Hz when the trainspeed is 300 kmh and 388Hz when the train speed is350 kmh are all the vibration frequency of the actuatorunder the current working condition

As the train speed increases the peak spectral vibrationacceleration response also increases and the frequencycorresponding to the peak spectral vibration accelerationalso gradually moves to a medium frequency as the trainspeed increases )e higher the train speed the richer thefrequency components of the ground vibration

4 Conclusions

In this study by conducting a large-scale dynamic model teston an X-section pile-net composite foundation under dif-ferent train speeds we can draw the following conclusions

(1) )e response of the vertical dynamic velocity is thelargest at the surface layer of the embankment andattenuates by approximately 90 in the embank-ment )e speed rapidly attenuates as the depthincreases the vibration gradually attenuates as thedistance from the vibration source increases At thebottom layer of the subgrade bed and in the range of

250kmh

277Hz

250Hz194Hz

0

1

2

3

Acc

eler

atio

nam

plitu

de (m

ms

2 )20 40 60 80 1000

Time (s)

(c)

300kmh

199Hz

233Hz

299Hz

332Hz

0

1

2

3

4

Acc

eler

atio

nam

plitu

de (m

ms

2 )

20 40 60 80 1000Time (s)

(d)

350kmh

233Hz272Hz

349Hz

0

1

2

3

4

Acc

eler

atio

nam

plitu

de (m

ms

2 )

20 40 60 80 1000Time (s)

(e)

Figure 15 Spectrum curve of acceleration under different speeds

12 Shock and Vibration

the lower foundation the attenuation rate signifi-cantly decreases and the vibration velocity is linearlyrelated to the train speed

(2) Inside the pile-net foundation the peak dynamicstress at the top of the pile is 34 times than that in thesoil between piles and the dynamic stress attenuateswith the depth

(3) )e change in train speed does not have a largeinfluence on the peak transient dynamic displace-ment response at the surface of the track afterpassing through the subgrade bed the peak verticalacceleration decreases from approximately 80mms2to 30mms2 attenuating by 625 )is is mainlybecause the high-frequency components are absor-bed due to soil damping effects and the low-frequency components attenuate relatively slowly)e foundation vibration caused by the train is a low-frequency vibration and the subgrade foundationhas an attenuation impact on the high-frequencyvibration the vibration gradually decreases as thedistance from the vibration source increases andincreases as the train speed increases

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 there are no conflicts of interestregarding the publication of this paper

Acknowledgments

)is project was supported by the Funds for InternationalCooperation and Exchange of the National Natural ScienceFoundation of China (Grant no 51420105013)

References

[1] M A Heckl ldquoRailway noise-can random sleeper spacingshelprdquo Acta Acustica United with Acustica vol 81 no 6pp 559ndash564 1995

[2] H Takemiya and X Bian ldquoSubstructure simulation of in-homogeneous track and layered ground dynamic interactionunder train passagerdquo Journal of Engineering Mechanicsvol 131 no 7 pp 699ndash711 2005

[3] M Bahrekazemi and A Bodare ldquoEffects of lime-cement soilstabilization against train induced ground vibrationsrdquo inProceedings of the 3rd International Specialty Conference onGrouting and Ground Treatment New Orleans LA USAFebruary 2003

[4] L Bo and C Ying ldquoDynamic analysis on subgrade of highspeed railways in geometric irregular conditionrdquo Journal ofthe China Railway Society vol 21 pp 84ndash88 1999

[5] X Chen and W Y Lu Wentian ldquoStudy on the dynamic re-sponse of high speed railway bridge-subgrade transition sec-tionrdquo Journal of Vibration and Shock vol 25 pp 95ndash98 2006

[6] W F Anderson and A J Key ldquoModel testing of two-layerrailway track ballastrdquo Journal of Geotechnical and Geo-environmental Engineering vol 126 no 4 pp 317ndash323 2000

[7] S J Cox A Wang C Morison P Carels R Kelly andO G Bewes ldquoA test rig to investigate slab track structures forcontrolling ground vibrationrdquo Journal of Sound and Vibra-tion vol 293 no 3ndash5 pp 901ndash909 2006

[8] Y Zhan and G Jiang ldquoStudy of dynamic characteristics of soilsubgrade bed for ballastless trackrdquo Rock and Soil Mechanicsvol 31 pp 392ndash396 2010

[9] Y Momoya E Sekine and F Tatsuoka ldquoDeformationcharacteristics of railway roadbed and subgrade undermoving-wheel loadrdquo Soils and Foundations vol 45 no 4pp 99ndash118 2005

[10] A Al Shaer D Duhamel K Sab G Foret and L SchmittldquoExperimental settlement and dynamic behavior of a portionof ballasted railway track under high speed trainsrdquo Journal ofSound and Vibration vol 316 no 1ndash5 pp 211ndash233 2008

[11] T Ishikawa E Sekine and S Miura ldquoCyclic deformation ofgranular material subjected to moving-wheel loadsrdquo Cana-dian Geotechnical Journal vol 48 no 5 pp 691ndash703 2011

[12] G Q Kong X M Ding Y M Chen and G Yang ldquoVerticaluplift capacity characteristics and influence factor analysis ofcast-in-situ X-section reinforced concrete pile grouprdquo Journalof Civil Engineering and Architecture vol 29 pp 49ndash54 2012

[13] M X Zhang H L Liu X M Ding and Z Q WangldquoComparative tests on bearing capacity of cast-in-situX-shaped concrete piles and circular pilerdquo Chinese Journal ofGeotechnical Engineering vol 33 pp 1469ndash1476 2011

[14] Z QWang H L Liu M X Zhang J Yuan and J Yong ldquoFullscale model tests on vertical bearing characteristics of cast-in-place X-section pilesrdquo Chinese Journal of Geotechnical Engi-neering vol 32 pp 903ndash907 2010

[15] Y Jun L Xiao-Min and L Han-Long ldquoModel test study ofanti-pulling property of X-shaped concrete pilerdquo Rock andSoil Mechanics vol 31 pp 3430ndash3434 2010

[16] L Han-Long L Zhi-Ping and W Xin-Quan ldquoStudy on thegeometric characteristics of the cast-in-place X-type vibro-pilesectionrdquo China Railway Science vol 30 pp 17ndash23 2009

[17] M X Zhang S M Ding and Y M Chen ldquoTest on verticalbehavior of cast-in-situ X-shaped concrete pile and its ulti-mate bearing capacity predictionrdquo Journal of China CoalSociety vol 36 pp 267ndash271 2011

[18] L Han-Long J Hui and D Xuan-Ming ldquoField test researchon squeezing effects of X-section cast-in-place concrete pilerdquoRock and Soil Mechanics vol 33 pp 219ndash224 2012

[19] S Guang-Chao L Han-Long K Gang-Qiang and D Xuan-Ming ldquoModel tests on effect of vibration waves on dynamicresponse of XCC pile-raft composite foundationrdquo ChineseJournal of Geotechnical Engineering vol 38 pp 1021ndash10292015

Shock and Vibration 13

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Graded gravels were used for the surface layer of thesubgrade bed group A and B fillers were used for the bottomlayer of the subgrade bed and well-graded unweatheredgravels or gravel fillers with a maximum particle size ofsmaller than 25mm were used for the cushion layer Ap-proximately 10ndash12 stone powder or fine particles wereblended in the gravels for filling after mixing well)e tensileyield strength of the geogrid used in the pile-net compositefoundation is 300 kNm as shown in Figure 2

Considering the dynamic response characteristics of theX-section pile-net composite foundation we installed in themodel test a complete set of dynamic and static test in-struments including displacement gauge dynamic pressurebox speedometer accelerometer and pore pressure gaugeto measure the vibration displacement dynamic earthpressure velocity and acceleration at different locations)especific layout is shown in Figure 3 Figure 3(a) is the frontview and Figure 3(b) is the top view

23 LoadingMethod andDesign Different train speeds weresimulated by controlling the loading frequency of the ac-tuators )e actuators were equipped with load transducersthat monitored the loads of the actuators in real time )ewheel-track load generated by the interaction of the wheel

shaft of the train and the track was transferred to the trackstructure and subgrade through the fastener systemAccording to field measurement data the wheel-track load ofan operating train is transferred in the form of a dynamic loadsimilar to an M-shaped wave to the foundation of the em-bankment)erefore anM-shaped wave was also adopted forloading in the test with the load waveform shown in Figure 4)e M-shaped wave shown in the figure is the dynamic loadof a train with a speed of 300 kmh and an axle load of 10 kN)is waveform was fitted using a 3rd-order Fourier seriesaccording to the variation pattern and periodic characteristicsof the time-history curve Let t be the running time of the trainand F(t) be the equation of the force applied by the actuator)e expression is shown in equation (1)

F(t) a0 + a1 cos2πnt

T1113874 1113875 + b1 sin

2πnt

T1113874 1113875 + a2 cos

4πnt

T1113874 1113875

+ b2 sin4πnt

T1113874 1113875 + a3 cos

6πnt

T1113874 1113875 + b3 sin

6πnt

T1113874 1113875

(1)

where T is the vibration period of the actuator load and anand bn are constants obtained based on the actual parametersof a train

Reaction beam

Actuator

Slit

XCC pile

1330

4300

1000

6800

Sand cushion

5000

Flexiblematerial

Figure 1 Schematic diagram of tank section of the model (unit mm)

Table 1 Basic physical indexes of silt

Water content () Unit weight (kNm3) Void ratio Liquid limit () Plastic limit () Plasticity index Liquid limit index278 186 0817 310 241 69 056

Shock and Vibration 3

K1

K2

K3

K4

K5

K6

D1 D2 D5

1670

860

780

2000

2000

1500

D6

V8

V9 V11

V10V7

V3V4

V2V1

S2

S3

S4

S5 S8

S9S6

S7

A8

A7

A6

A5

V13S1V12

(a)

Figure 3 Continued

Rail

Surface layer of subgradeBottom layer of subgrade

Broken stone hardcoreGeogrid

3340

1720

600 60 108

8046

072

012

0

Track slab

Figure 2 Schematic diagram of the embankment section (unit mm)

4 Shock and Vibration

)e train simulated in this test refers to the main type ofCRH3CRH380 D-series high-speed train operated on thehigh-speed railway in China )e applied force is the loadfrom the four pairs of wheels of the adjacent bogies of ad-jacent carriages)e time for passing through the distance of a25m bogie is two load cycles)emagnitude of the train loadand the running speed is reflected through the load output

and frequency of a servo vibrator )e relationship betweenthe train speed and loading frequency is shown in Table 2

3 TestWorking Conditions and Result Analysis

31 Analysis of Vertical Velocity Taking a train speed of300kmh as an example the time-history response curves of thevertical vibration velocities at different locations of the X-sectionpile-net composite foundation system are shown in Figure 5

Under the cyclic load of an M-shaped wave the time-history response curve of the velocity of the entire compositefoundation exhibits significant periodicity with the cyclicloading process and the frequency of its velocity response isconsistent with the frequency of the cyclic loading

At the surface and bottom layers of the subgrade bed thetime-history response curves of the velocity induced by thecyclic loading exhibits a significant M shape and as thedepth increases the amplitude of the M-shaped velocitygradually decreases )erefore the dynamic cyclic load in-duced by the operating train has an important influence onthe embankment and the vibration response of this region ismainly caused by the dynamic load of the train wheel shaftAs they propagate to the foundation the various reflectedwaves gradually account for a certain percentage of the totalcausing the response waveform to be insignificant

Figure 5 shows that the response of the velocity at thesurface layer of the subgrade bed in the embankment is

0

10

20

30

40

50

60

70

8025m25m25m

25m175m

Dyn

amic

load

ing

Q(t)

(kN

)

Time (s)

25mLoad cycle T

Figure 4 ldquoMrdquo-shaped wave

D1

600

520

D2

D3

D4

D5 D6V1A1

V2 V3A3A2

V4A4

V5 V6

S1

S4 S7

Pore pressure gauge (K)

Dynamic pressure box (S)

Speedometer (V)

Accelerometer (A)

Displacement gauge (D)

(b)

Figure 3 Layout of test instrument (unit mm) (a) front view (b) top view

Shock and Vibration 5

mainly caused by the cyclic dynamic load of the train and itis relatively consistent with the waveform of the loadingwave but without the influence of a large number of reflectedwaves in the foundation soil Hence it can better assist in thestudy of the relationship between the velocity response andthe train speed )erefore the peak responses of the verticalvelocity at the surface layer of the subgrade bed underdifferent train speeds are averaged for analysis Under dif-ferent train speeds the velocity responses of the X-sectionpile-net composite foundation at different depths are shownin Figure 6 We can see that with the track slab plane as the0m depth 1m is the surface layer of the subgrade Underdifferent train speeds the vibration velocity of the foun-dation soil rapidly attenuates as the depth increases and themaximum vibration response occurs at the surface layer ofthe subgrade bed It can be seen that within the depth of 1mie within the embankment the dynamic velocity attenuatesby approximately 90 indicating that the embankment hasa very good reduction effect on the propagation of the vi-bration load while the attenuation rate of the speed after itreaches the foundation decreases

Figure 7 shows the relationship curve between the re-sponse of the vertical velocity at the track slab and the trainspeed )e peak response of the velocity at the track slabunder three different train speeds is shown )e distributionof the scattered points reveals that the peak response of thevibration velocity at the track slab and the train speed arelinearly related As the train speed increases from 160 kmh to350 kmh the peak response of the vibration velocity in-creases from 2299mms to 4600mms an increase of 100

)e distribution of the vertical vibration velocity re-sponse of the track under train operation along the trans-verse direction of the track is shown in Figure 8 We can seethat in the whole system the track structure that is closest tothe actuator exhibits the most intense vibration responseWith a train speed of 350 kmh the peak vibration velocityreaches 4378mms while the maximum vibration velocityof the subgrade structure is only 102mms )e vibration ofthe subgrade system gradually attenuates going farther awayfrom the vibration source and the vibration velocity at thebottom layer of the subgrade bed as well as within the rangeof the lower foundation is at a relatively low level and with a

00 01 02 03 04 05 06Time (s)

ndash45ndash30ndash15

0153045

Vel

ocity

resp

onse

(mm

s)

(a)

ndash3ndash2ndash1

0123

00 01 02 03 04 05 06Time (s)

Vel

ocity

resp

onse

(mm

s)

(b)

00 01 02 03 04 05 06Time (s)

ndash3ndash2ndash1

0123

Vel

ocity

resp

onse

(mm

s)

(c)

00 01 02 03 04 05 06Time (s)

ndash3ndash2ndash1

0123

Vel

ocity

resp

onse

(mm

s)

(d)

00 01 02 03 04 05 06Time (s)

ndash3ndash2ndash1

0123

Vel

ocity

resp

onse

(mm

s)

(e)

Figure 5 Vertical velocity with respect to time (a) track slab (b) surface layer of subgrade (c) bottom layer of subgrade (d) surface layer offoundation (e) bottom layer of foundation

Table 2 Train speed and frequency

Actuator frequency Two peak period (s) Corresponding train speed (kmh) Two trough periods (s) Carriage cycle (s)18 0056 160 0173 055622 0045 200 0142 045528 0036 250 0111 035733 0030 300 0095 030339 0026 350 0080 0256

6 Shock and Vibration

significantly slow attenuation rate indicating that the sub-grade bed has a significant reduction effect on the verticalvibration

32 Analysis of Dynamic Earth Pressure Figure 9 showstime-history curves of the dynamic soil stress at the pile topand between piles when the train speed is 300 kmh)e waveis affected by the embankment and hence attenuates during

the propagation process causing the waveform characteristicsof the M-shaped wave to have already been significantlyweakened when it reaches the surface of the foundation Wecan see that the stress at the pile top is greater than thedynamic stress of the soil between piles and the soil arch has a

V4V3

160kmh200kmh250kmh

300kmh350kmh

V0 V1 V2

05 10 15 20 2500Distance to the center (m)

0

5

10

15

20

25

30

35

40

45

Vel

ocity

resp

onse

(mm

s)

Figure 8 Vertical velocity with respect to horizontal dimension

00 01 02 03 04 05 0602468

1012

Load

(kN

)

Waveform

Time (s)

(a)

ndash202468

1012

Dyn

amic

stre

ss (k

Pa)

Pile topSoil

00 01 02Time (s)

03 04 05 06

(b)

Figure 9 Dynamic stresses of pile and soil with respect to time

6

5

4

3

2

1

0ndash5 0 5 10 15 20 25 30 35 40 45 50

6

5

4

3

2

1

0 1 2 3

Velocity response (mms)

Dep

th (m

)

160kmh200kmh250kmh

300kmh350kmh

Figure 6 Vertical velocity with respect to depth

0

10

20

30

40

50

60

Vel

ocity

resp

onse

pea

k of

the t

rack

slab

(mm

s)

A groupB groupC group

50 100 150 200 250 300 350 4000Train speed (kmh)

Figure 7 Vertical velocity with respect to train speed

Shock and Vibration 7

significant influence on the distribution of the dynamic stressIn the soil arch region a greater dynamic load is transferredabove the top of the pile )e average of the peak dynamicstresses at the pile top is approximately 62 kPa which is 34times the average of the peak dynamic earth pressure (ap-proximately 18 kPa) on the soil between the piles

Figure 10 shows relationship curves of the changes in thepeak dynamic stresses at the pile top and in the soil betweenthe piles of the foundation and the train speed We can seethat under the vibration load of the high-speed train theload carried at the pile top in the foundation is much largerthan that by the soil between the piles

Although the vibration frequency of the dynamic loadincreases as the train speed increases the influence of thetrain speed on the response of the dynamic stress is weak)is is likely because the wave gradually attenuates in theprocess of reaching the foundation through the subgradebed and its effect gradually decreases

33 Analysis of Dynamic Displacement Figure 11 shows thetime-history response curve of the dynamic displacementon the track surface under different train speeds We cansee that the change in the train speed does not have a largeinfluence on the peak transient dynamic displacementresponse on the track surface A comparison of dynamicdisplacement responses under different train speeds re-veals that the faster the train speed the more intense andshorter the induced vibration)is is because the faster thetrain speed the higher the dynamic loading frequencyWhen the train speed is not high (160 kmh) the time-history curve between the peak displacements attenuatesWhen the train speed reaches 250 kmh the displacementtime history does not significantly attenuate but insteadgradually fluctuates with time In fact the attenuationprocess is not completed

34 Analysis of Acceleration Figure 12 shows the time-history curve of the acceleration at different locations in thepile-net composite foundation when the train speed is300 kmh We can see that the vibration close to the actuatorhas a relatively large amplitude As the distance from thevibration source increases the amplitude of the accelerationgradually decreases and the high-frequency componentsattenuate especially rapidly Because the track slab is rela-tively close to the subgrade bed its peak acceleration is ap-proximately 80mms2 After passing through the track slabthe waveform at the surface layer of the subgrade bed is not assignificant as that at the track slab

It can be clearly seen from Figure 12 that after passingthrough the subgrade bed the peak acceleration decreasesfrom 80mms2 to 30mms2 that is it attenuates by 625)is is mainly because the high-frequency components areabsorbed due to the damping effect of the soil in the em-bankment while the attenuation of the low-frequencycomponents is relatively slow When reaching the bottomlayer of the foundation due to the influence of the reflectedwaves the M-shaped waveform has essentially disappearedAs a result only a simple harmonic oscillation curve is

presented and the amplitude of the acceleration vibration isonly 2 of that at the surface layer of the foundation As thedepth increases the peak acceleration responses of theM-shaped waveform at different locations do not appear atthe same time )is is because it takes time for the wave topropagate causing some lag in the acceleration response

Figure 13 shows a spectral curve of the vertical accel-eration at different locations from the vibration source whenthe train speed is 300 kmh We can see that the frequency isdistributed in the range of 0ndash100Hz and is mainly con-centrated between 10 and 50Hz making it low-frequencyvibrations As the distance from the vibration source in-creases the maximum vibration accelerations at differentlocations are 4352mms2 4082mms2 3152mms2352mms2 and 014mms2 It can be seen that as thedistance from the vibration source increases the amplitudeof the acceleration generally attenuates )e high-frequencycomponent is relatively rich at locations close to the vi-bration source and the width of the spectrum graduallydecreases when moving away from the vibration source )emost significant frequency band becomes that of the lowfrequency because the high-frequency components attenu-ate faster than the low-frequency components

We can see from the peaks in Figure 13 that the fourcharacteristic frequencies with the largest contributions to thevibration are 199Hz 233Hz 299Hz and 332Hz Amongthem 332Hz corresponds to the actuator frequency At themeasurement site of the track slab the frequency of theground vibration caused by the train is distributed within50ndash85Hz and relatively rich in the main frequency

Figure 14 shows the time-history curve of the accelerationat the surface layer of the foundation under different trainspeeds We can clearly see that as the train speed increases thehigh-frequency components significantly increase Whenthe train speed is 160 kmh the peak acceleration at the sur-face layer of the foundation is 359mms2 and when thetrain velocity increases to 200 kmh the peak acceleration atthe surface layer of the foundation reaches 724mms2

Pile topSoil

0

2

4

6

8

10

Dyn

amic

stre

ss (k

Pa)

200 300 400100Train speed (kmh)

Figure 10 Relationship curves between dynamic stress responsesof soil at pipe top and between piles and the train speed

8 Shock and Vibration

00

02

04

06

08

Dyn

amic

disp

lace

men

tof

the t

rack

slab

(mm

)

02 04 06 08 10 1200Time (s)

160kmh

(a)

00

02

04

06

08

Dyn

amic

disp

lace

men

tof

the t

rack

slab

(mm

)

02 04 06 08 10 1200Time (s)

200kmh

(b)

00

02

04

06

08

Dyn

amic

disp

lace

men

tof

the t

rack

slab

(mm

)

02 04 06 08 10 1200Time (s)

250kmh(c)

00

02

04

06

08

Dyn

amic

disp

lace

men

tof

the t

rack

slab

(mm

)

02 04 06 08 10 1200Time (s)

300kmh

(d)

00

02

04

06

08

Dyn

amic

disp

lace

men

tof

the t

rack

slab

(mm

)

02 04 06 08 10 1200Time (s)

350kmh

(e)

Figure 11 Dynamic displacement of track with respect to time

120

ndash120

80

ndash80

40

ndash400

Acc

eler

atio

nre

spon

se (m

ms

2 )

01 02 03 04 05 0600Time (s)

(a)

120

ndash120

80

ndash80

40

ndash400

Acc

eler

atio

nre

spon

se (m

ms

2 )

01 02 03 04 05 0600Time (s)

(b)120

ndash120

80

ndash80

40

ndash400

Acc

eler

atio

nre

spon

se (m

ms

2 )

01 02 03 04 05 0600Time (s)

(c)

120

ndash120

80

ndash80

40

ndash400

Acc

eler

atio

nre

spon

se (m

ms

2 )

01 02 03 04 05 0600Time (s)

(d)

Figure 12 Acceleration at different layers with respect to time (a) track slab (b) surface layer of subgrade (c) bottom layer of subgrade (d)surface layer of foundation

Shock and Vibration 9

332Hz299Hz199Hz

233Hz

0 20 30 40 50 60 70 80 90 10010Frequency (Hz)

01020304050

Acc

eler

atio

nam

plitu

de (m

ms

2 )

(a)

233Hz

332Hz299Hz199Hz

0 20 30 40 50 60 70 80 90 10010Frequency (Hz)

01020304050

Acc

eler

atio

nam

plitu

de (m

ms

2 )

(b)

332Hz299Hz

233Hz

199Hz

0 20 30 40 50 60 70 80 90 10010Frequency (Hz)

01020304050

Acc

eler

atio

nam

plitu

de (m

ms

2 )

(c)

299Hz332Hz

233Hz199Hz

0 20 30 40 50 60 70 80 90 1001Frequency (Hz)

01020304050

Acc

eler

atio

nam

plitu

de (m

ms

2 )

(d)

Figure 13 Spectral curve of acceleration at different locations (a) track slab (b) surface layer of subgrade (c) bottom layer of subgrade (d)surface layer of foundation

00 02 04Time (s)

06 08 10 12ndash10

ndash5

0

5

10

Acc

eler

atio

n re

spon

se(s

urfa

ce la

yer o

f fou

ndat

ion)

(mm

s2 )

160kmh

(a)

00 02 04 06 08 10 12ndash10

ndash5

0

5

10

Acc

eler

atio

n re

spon

se(s

urfa

ce la

yer o

f fou

ndat

ion)

(mm

s2 )

Time (s)

200kmh

(b)

00 02 04 06 08 10 12ndash10

ndash5

0

5

10

Acc

eler

atio

n re

spon

se(s

urfa

ce la

yer o

f fou

ndat

ion)

(mm

s2 )

Time (s)

250kmh

(c)

Figure 14 Continued

10 Shock and Vibration

00 02 04 06 08 10 12ndash10

ndash5

0

5

10

Acc

eler

atio

n re

spon

se(s

urfa

ce la

yer o

f fou

ndat

ion)

(mm

s2 )

Time (s)

300kmh

(d)

00 02 04 06 08 10 12ndash10

ndash5

0

5

10

Acc

eler

atio

n re

spon

se(s

urfa

ce la

yer o

f fou

ndat

ion)

(mm

s2 )

Time (s)

350kmh

(e)

Figure 14 Acceleration under different speeds with respect to time

177Hz

160kmh

0

1

2

3

Acc

eler

atio

nam

plitu

de (m

ms

2 )

20 40 60 80 1000Time (s)

(a)

200kmh

200Hz 222Hz

0

1

2

3

Acc

eler

atio

nam

plitu

de (m

ms

2 )

20 40 60 80 1000Time (s)

(b)

Figure 15 Continued

Shock and Vibration 11

(approximately double) However when the train speed rea-ches 250 kmh the increase on the peak is negligible Becausethe increase in the train speed is achieved by increasing thevibration frequency the superposition of the surroundingreflected waves in this process likely produces a counteractionto the vibration of the subgrade foundation explaining thisresult

Figure 15 shows the spectral curve of the acceleration atthe surface layer of the foundation under different trainspeeds We can see that the ground vibration caused by thetrain is mainly contributed by relatively low-frequencycomponents (mainly below 100Hz) As the train speedincreases the amplitude of the acceleration increases andthe base frequencies of the vibration also gradually increase177Hz in the base frequencies when the train velocity is160 kmh 222Hz when the train speed is 200 kmh 277Hzwhen the train speed is 250 kmh 332Hz when the trainspeed is 300 kmh and 388Hz when the train speed is350 kmh are all the vibration frequency of the actuatorunder the current working condition

As the train speed increases the peak spectral vibrationacceleration response also increases and the frequencycorresponding to the peak spectral vibration accelerationalso gradually moves to a medium frequency as the trainspeed increases )e higher the train speed the richer thefrequency components of the ground vibration

4 Conclusions

In this study by conducting a large-scale dynamic model teston an X-section pile-net composite foundation under dif-ferent train speeds we can draw the following conclusions

(1) )e response of the vertical dynamic velocity is thelargest at the surface layer of the embankment andattenuates by approximately 90 in the embank-ment )e speed rapidly attenuates as the depthincreases the vibration gradually attenuates as thedistance from the vibration source increases At thebottom layer of the subgrade bed and in the range of

250kmh

277Hz

250Hz194Hz

0

1

2

3

Acc

eler

atio

nam

plitu

de (m

ms

2 )20 40 60 80 1000

Time (s)

(c)

300kmh

199Hz

233Hz

299Hz

332Hz

0

1

2

3

4

Acc

eler

atio

nam

plitu

de (m

ms

2 )

20 40 60 80 1000Time (s)

(d)

350kmh

233Hz272Hz

349Hz

0

1

2

3

4

Acc

eler

atio

nam

plitu

de (m

ms

2 )

20 40 60 80 1000Time (s)

(e)

Figure 15 Spectrum curve of acceleration under different speeds

12 Shock and Vibration

the lower foundation the attenuation rate signifi-cantly decreases and the vibration velocity is linearlyrelated to the train speed

(2) Inside the pile-net foundation the peak dynamicstress at the top of the pile is 34 times than that in thesoil between piles and the dynamic stress attenuateswith the depth

(3) )e change in train speed does not have a largeinfluence on the peak transient dynamic displace-ment response at the surface of the track afterpassing through the subgrade bed the peak verticalacceleration decreases from approximately 80mms2to 30mms2 attenuating by 625 )is is mainlybecause the high-frequency components are absor-bed due to soil damping effects and the low-frequency components attenuate relatively slowly)e foundation vibration caused by the train is a low-frequency vibration and the subgrade foundationhas an attenuation impact on the high-frequencyvibration the vibration gradually decreases as thedistance from the vibration source increases andincreases as the train speed increases

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 there are no conflicts of interestregarding the publication of this paper

Acknowledgments

)is project was supported by the Funds for InternationalCooperation and Exchange of the National Natural ScienceFoundation of China (Grant no 51420105013)

References

[1] M A Heckl ldquoRailway noise-can random sleeper spacingshelprdquo Acta Acustica United with Acustica vol 81 no 6pp 559ndash564 1995

[2] H Takemiya and X Bian ldquoSubstructure simulation of in-homogeneous track and layered ground dynamic interactionunder train passagerdquo Journal of Engineering Mechanicsvol 131 no 7 pp 699ndash711 2005

[3] M Bahrekazemi and A Bodare ldquoEffects of lime-cement soilstabilization against train induced ground vibrationsrdquo inProceedings of the 3rd International Specialty Conference onGrouting and Ground Treatment New Orleans LA USAFebruary 2003

[4] L Bo and C Ying ldquoDynamic analysis on subgrade of highspeed railways in geometric irregular conditionrdquo Journal ofthe China Railway Society vol 21 pp 84ndash88 1999

[5] X Chen and W Y Lu Wentian ldquoStudy on the dynamic re-sponse of high speed railway bridge-subgrade transition sec-tionrdquo Journal of Vibration and Shock vol 25 pp 95ndash98 2006

[6] W F Anderson and A J Key ldquoModel testing of two-layerrailway track ballastrdquo Journal of Geotechnical and Geo-environmental Engineering vol 126 no 4 pp 317ndash323 2000

[7] S J Cox A Wang C Morison P Carels R Kelly andO G Bewes ldquoA test rig to investigate slab track structures forcontrolling ground vibrationrdquo Journal of Sound and Vibra-tion vol 293 no 3ndash5 pp 901ndash909 2006

[8] Y Zhan and G Jiang ldquoStudy of dynamic characteristics of soilsubgrade bed for ballastless trackrdquo Rock and Soil Mechanicsvol 31 pp 392ndash396 2010

[9] Y Momoya E Sekine and F Tatsuoka ldquoDeformationcharacteristics of railway roadbed and subgrade undermoving-wheel loadrdquo Soils and Foundations vol 45 no 4pp 99ndash118 2005

[10] A Al Shaer D Duhamel K Sab G Foret and L SchmittldquoExperimental settlement and dynamic behavior of a portionof ballasted railway track under high speed trainsrdquo Journal ofSound and Vibration vol 316 no 1ndash5 pp 211ndash233 2008

[11] T Ishikawa E Sekine and S Miura ldquoCyclic deformation ofgranular material subjected to moving-wheel loadsrdquo Cana-dian Geotechnical Journal vol 48 no 5 pp 691ndash703 2011

[12] G Q Kong X M Ding Y M Chen and G Yang ldquoVerticaluplift capacity characteristics and influence factor analysis ofcast-in-situ X-section reinforced concrete pile grouprdquo Journalof Civil Engineering and Architecture vol 29 pp 49ndash54 2012

[13] M X Zhang H L Liu X M Ding and Z Q WangldquoComparative tests on bearing capacity of cast-in-situX-shaped concrete piles and circular pilerdquo Chinese Journal ofGeotechnical Engineering vol 33 pp 1469ndash1476 2011

[14] Z QWang H L Liu M X Zhang J Yuan and J Yong ldquoFullscale model tests on vertical bearing characteristics of cast-in-place X-section pilesrdquo Chinese Journal of Geotechnical Engi-neering vol 32 pp 903ndash907 2010

[15] Y Jun L Xiao-Min and L Han-Long ldquoModel test study ofanti-pulling property of X-shaped concrete pilerdquo Rock andSoil Mechanics vol 31 pp 3430ndash3434 2010

[16] L Han-Long L Zhi-Ping and W Xin-Quan ldquoStudy on thegeometric characteristics of the cast-in-place X-type vibro-pilesectionrdquo China Railway Science vol 30 pp 17ndash23 2009

[17] M X Zhang S M Ding and Y M Chen ldquoTest on verticalbehavior of cast-in-situ X-shaped concrete pile and its ulti-mate bearing capacity predictionrdquo Journal of China CoalSociety vol 36 pp 267ndash271 2011

[18] L Han-Long J Hui and D Xuan-Ming ldquoField test researchon squeezing effects of X-section cast-in-place concrete pilerdquoRock and Soil Mechanics vol 33 pp 219ndash224 2012

[19] S Guang-Chao L Han-Long K Gang-Qiang and D Xuan-Ming ldquoModel tests on effect of vibration waves on dynamicresponse of XCC pile-raft composite foundationrdquo ChineseJournal of Geotechnical Engineering vol 38 pp 1021ndash10292015

Shock and Vibration 13

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Submit your manuscripts atwwwhindawicom

K1

K2

K3

K4

K5

K6

D1 D2 D5

1670

860

780

2000

2000

1500

D6

V8

V9 V11

V10V7

V3V4

V2V1

S2

S3

S4

S5 S8

S9S6

S7

A8

A7

A6

A5

V13S1V12

(a)

Figure 3 Continued

Rail

Surface layer of subgradeBottom layer of subgrade

Broken stone hardcoreGeogrid

3340

1720

600 60 108

8046

072

012

0

Track slab

Figure 2 Schematic diagram of the embankment section (unit mm)

4 Shock and Vibration

)e train simulated in this test refers to the main type ofCRH3CRH380 D-series high-speed train operated on thehigh-speed railway in China )e applied force is the loadfrom the four pairs of wheels of the adjacent bogies of ad-jacent carriages)e time for passing through the distance of a25m bogie is two load cycles)emagnitude of the train loadand the running speed is reflected through the load output

and frequency of a servo vibrator )e relationship betweenthe train speed and loading frequency is shown in Table 2

3 TestWorking Conditions and Result Analysis

31 Analysis of Vertical Velocity Taking a train speed of300kmh as an example the time-history response curves of thevertical vibration velocities at different locations of the X-sectionpile-net composite foundation system are shown in Figure 5

Under the cyclic load of an M-shaped wave the time-history response curve of the velocity of the entire compositefoundation exhibits significant periodicity with the cyclicloading process and the frequency of its velocity response isconsistent with the frequency of the cyclic loading

At the surface and bottom layers of the subgrade bed thetime-history response curves of the velocity induced by thecyclic loading exhibits a significant M shape and as thedepth increases the amplitude of the M-shaped velocitygradually decreases )erefore the dynamic cyclic load in-duced by the operating train has an important influence onthe embankment and the vibration response of this region ismainly caused by the dynamic load of the train wheel shaftAs they propagate to the foundation the various reflectedwaves gradually account for a certain percentage of the totalcausing the response waveform to be insignificant

Figure 5 shows that the response of the velocity at thesurface layer of the subgrade bed in the embankment is

0

10

20

30

40

50

60

70

8025m25m25m

25m175m

Dyn

amic

load

ing

Q(t)

(kN

)

Time (s)

25mLoad cycle T

Figure 4 ldquoMrdquo-shaped wave

D1

600

520

D2

D3

D4

D5 D6V1A1

V2 V3A3A2

V4A4

V5 V6

S1

S4 S7

Pore pressure gauge (K)

Dynamic pressure box (S)

Speedometer (V)

Accelerometer (A)

Displacement gauge (D)

(b)

Figure 3 Layout of test instrument (unit mm) (a) front view (b) top view

Shock and Vibration 5

mainly caused by the cyclic dynamic load of the train and itis relatively consistent with the waveform of the loadingwave but without the influence of a large number of reflectedwaves in the foundation soil Hence it can better assist in thestudy of the relationship between the velocity response andthe train speed )erefore the peak responses of the verticalvelocity at the surface layer of the subgrade bed underdifferent train speeds are averaged for analysis Under dif-ferent train speeds the velocity responses of the X-sectionpile-net composite foundation at different depths are shownin Figure 6 We can see that with the track slab plane as the0m depth 1m is the surface layer of the subgrade Underdifferent train speeds the vibration velocity of the foun-dation soil rapidly attenuates as the depth increases and themaximum vibration response occurs at the surface layer ofthe subgrade bed It can be seen that within the depth of 1mie within the embankment the dynamic velocity attenuatesby approximately 90 indicating that the embankment hasa very good reduction effect on the propagation of the vi-bration load while the attenuation rate of the speed after itreaches the foundation decreases

Figure 7 shows the relationship curve between the re-sponse of the vertical velocity at the track slab and the trainspeed )e peak response of the velocity at the track slabunder three different train speeds is shown )e distributionof the scattered points reveals that the peak response of thevibration velocity at the track slab and the train speed arelinearly related As the train speed increases from 160 kmh to350 kmh the peak response of the vibration velocity in-creases from 2299mms to 4600mms an increase of 100

)e distribution of the vertical vibration velocity re-sponse of the track under train operation along the trans-verse direction of the track is shown in Figure 8 We can seethat in the whole system the track structure that is closest tothe actuator exhibits the most intense vibration responseWith a train speed of 350 kmh the peak vibration velocityreaches 4378mms while the maximum vibration velocityof the subgrade structure is only 102mms )e vibration ofthe subgrade system gradually attenuates going farther awayfrom the vibration source and the vibration velocity at thebottom layer of the subgrade bed as well as within the rangeof the lower foundation is at a relatively low level and with a

00 01 02 03 04 05 06Time (s)

ndash45ndash30ndash15

0153045

Vel

ocity

resp

onse

(mm

s)

(a)

ndash3ndash2ndash1

0123

00 01 02 03 04 05 06Time (s)

Vel

ocity

resp

onse

(mm

s)

(b)

00 01 02 03 04 05 06Time (s)

ndash3ndash2ndash1

0123

Vel

ocity

resp

onse

(mm

s)

(c)

00 01 02 03 04 05 06Time (s)

ndash3ndash2ndash1

0123

Vel

ocity

resp

onse

(mm

s)

(d)

00 01 02 03 04 05 06Time (s)

ndash3ndash2ndash1

0123

Vel

ocity

resp

onse

(mm

s)

(e)

Figure 5 Vertical velocity with respect to time (a) track slab (b) surface layer of subgrade (c) bottom layer of subgrade (d) surface layer offoundation (e) bottom layer of foundation

Table 2 Train speed and frequency

Actuator frequency Two peak period (s) Corresponding train speed (kmh) Two trough periods (s) Carriage cycle (s)18 0056 160 0173 055622 0045 200 0142 045528 0036 250 0111 035733 0030 300 0095 030339 0026 350 0080 0256

6 Shock and Vibration

significantly slow attenuation rate indicating that the sub-grade bed has a significant reduction effect on the verticalvibration

32 Analysis of Dynamic Earth Pressure Figure 9 showstime-history curves of the dynamic soil stress at the pile topand between piles when the train speed is 300 kmh)e waveis affected by the embankment and hence attenuates during

the propagation process causing the waveform characteristicsof the M-shaped wave to have already been significantlyweakened when it reaches the surface of the foundation Wecan see that the stress at the pile top is greater than thedynamic stress of the soil between piles and the soil arch has a

V4V3

160kmh200kmh250kmh

300kmh350kmh

V0 V1 V2

05 10 15 20 2500Distance to the center (m)

0

5

10

15

20

25

30

35

40

45

Vel

ocity

resp

onse

(mm

s)

Figure 8 Vertical velocity with respect to horizontal dimension

00 01 02 03 04 05 0602468

1012

Load

(kN

)

Waveform

Time (s)

(a)

ndash202468

1012

Dyn

amic

stre

ss (k

Pa)

Pile topSoil

00 01 02Time (s)

03 04 05 06

(b)

Figure 9 Dynamic stresses of pile and soil with respect to time

6

5

4

3

2

1

0ndash5 0 5 10 15 20 25 30 35 40 45 50

6

5

4

3

2

1

0 1 2 3

Velocity response (mms)

Dep

th (m

)

160kmh200kmh250kmh

300kmh350kmh

Figure 6 Vertical velocity with respect to depth

0

10

20

30

40

50

60

Vel

ocity

resp

onse

pea

k of

the t

rack

slab

(mm

s)

A groupB groupC group

50 100 150 200 250 300 350 4000Train speed (kmh)

Figure 7 Vertical velocity with respect to train speed

Shock and Vibration 7

significant influence on the distribution of the dynamic stressIn the soil arch region a greater dynamic load is transferredabove the top of the pile )e average of the peak dynamicstresses at the pile top is approximately 62 kPa which is 34times the average of the peak dynamic earth pressure (ap-proximately 18 kPa) on the soil between the piles

Figure 10 shows relationship curves of the changes in thepeak dynamic stresses at the pile top and in the soil betweenthe piles of the foundation and the train speed We can seethat under the vibration load of the high-speed train theload carried at the pile top in the foundation is much largerthan that by the soil between the piles

Although the vibration frequency of the dynamic loadincreases as the train speed increases the influence of thetrain speed on the response of the dynamic stress is weak)is is likely because the wave gradually attenuates in theprocess of reaching the foundation through the subgradebed and its effect gradually decreases

33 Analysis of Dynamic Displacement Figure 11 shows thetime-history response curve of the dynamic displacementon the track surface under different train speeds We cansee that the change in the train speed does not have a largeinfluence on the peak transient dynamic displacementresponse on the track surface A comparison of dynamicdisplacement responses under different train speeds re-veals that the faster the train speed the more intense andshorter the induced vibration)is is because the faster thetrain speed the higher the dynamic loading frequencyWhen the train speed is not high (160 kmh) the time-history curve between the peak displacements attenuatesWhen the train speed reaches 250 kmh the displacementtime history does not significantly attenuate but insteadgradually fluctuates with time In fact the attenuationprocess is not completed

34 Analysis of Acceleration Figure 12 shows the time-history curve of the acceleration at different locations in thepile-net composite foundation when the train speed is300 kmh We can see that the vibration close to the actuatorhas a relatively large amplitude As the distance from thevibration source increases the amplitude of the accelerationgradually decreases and the high-frequency componentsattenuate especially rapidly Because the track slab is rela-tively close to the subgrade bed its peak acceleration is ap-proximately 80mms2 After passing through the track slabthe waveform at the surface layer of the subgrade bed is not assignificant as that at the track slab

It can be clearly seen from Figure 12 that after passingthrough the subgrade bed the peak acceleration decreasesfrom 80mms2 to 30mms2 that is it attenuates by 625)is is mainly because the high-frequency components areabsorbed due to the damping effect of the soil in the em-bankment while the attenuation of the low-frequencycomponents is relatively slow When reaching the bottomlayer of the foundation due to the influence of the reflectedwaves the M-shaped waveform has essentially disappearedAs a result only a simple harmonic oscillation curve is

presented and the amplitude of the acceleration vibration isonly 2 of that at the surface layer of the foundation As thedepth increases the peak acceleration responses of theM-shaped waveform at different locations do not appear atthe same time )is is because it takes time for the wave topropagate causing some lag in the acceleration response

Figure 13 shows a spectral curve of the vertical accel-eration at different locations from the vibration source whenthe train speed is 300 kmh We can see that the frequency isdistributed in the range of 0ndash100Hz and is mainly con-centrated between 10 and 50Hz making it low-frequencyvibrations As the distance from the vibration source in-creases the maximum vibration accelerations at differentlocations are 4352mms2 4082mms2 3152mms2352mms2 and 014mms2 It can be seen that as thedistance from the vibration source increases the amplitudeof the acceleration generally attenuates )e high-frequencycomponent is relatively rich at locations close to the vi-bration source and the width of the spectrum graduallydecreases when moving away from the vibration source )emost significant frequency band becomes that of the lowfrequency because the high-frequency components attenu-ate faster than the low-frequency components

We can see from the peaks in Figure 13 that the fourcharacteristic frequencies with the largest contributions to thevibration are 199Hz 233Hz 299Hz and 332Hz Amongthem 332Hz corresponds to the actuator frequency At themeasurement site of the track slab the frequency of theground vibration caused by the train is distributed within50ndash85Hz and relatively rich in the main frequency

Figure 14 shows the time-history curve of the accelerationat the surface layer of the foundation under different trainspeeds We can clearly see that as the train speed increases thehigh-frequency components significantly increase Whenthe train speed is 160 kmh the peak acceleration at the sur-face layer of the foundation is 359mms2 and when thetrain velocity increases to 200 kmh the peak acceleration atthe surface layer of the foundation reaches 724mms2

Pile topSoil

0

2

4

6

8

10

Dyn

amic

stre

ss (k

Pa)

200 300 400100Train speed (kmh)

Figure 10 Relationship curves between dynamic stress responsesof soil at pipe top and between piles and the train speed

8 Shock and Vibration

00

02

04

06

08

Dyn

amic

disp

lace

men

tof

the t

rack

slab

(mm

)

02 04 06 08 10 1200Time (s)

160kmh

(a)

00

02

04

06

08

Dyn

amic

disp

lace

men

tof

the t

rack

slab

(mm

)

02 04 06 08 10 1200Time (s)

200kmh

(b)

00

02

04

06

08

Dyn

amic

disp

lace

men

tof

the t

rack

slab

(mm

)

02 04 06 08 10 1200Time (s)

250kmh(c)

00

02

04

06

08

Dyn

amic

disp

lace

men

tof

the t

rack

slab

(mm

)

02 04 06 08 10 1200Time (s)

300kmh

(d)

00

02

04

06

08

Dyn

amic

disp

lace

men

tof

the t

rack

slab

(mm

)

02 04 06 08 10 1200Time (s)

350kmh

(e)

Figure 11 Dynamic displacement of track with respect to time

120

ndash120

80

ndash80

40

ndash400

Acc

eler

atio

nre

spon

se (m

ms

2 )

01 02 03 04 05 0600Time (s)

(a)

120

ndash120

80

ndash80

40

ndash400

Acc

eler

atio

nre

spon

se (m

ms

2 )

01 02 03 04 05 0600Time (s)

(b)120

ndash120

80

ndash80

40

ndash400

Acc

eler

atio

nre

spon

se (m

ms

2 )

01 02 03 04 05 0600Time (s)

(c)

120

ndash120

80

ndash80

40

ndash400

Acc

eler

atio

nre

spon

se (m

ms

2 )

01 02 03 04 05 0600Time (s)

(d)

Figure 12 Acceleration at different layers with respect to time (a) track slab (b) surface layer of subgrade (c) bottom layer of subgrade (d)surface layer of foundation

Shock and Vibration 9

332Hz299Hz199Hz

233Hz

0 20 30 40 50 60 70 80 90 10010Frequency (Hz)

01020304050

Acc

eler

atio

nam

plitu

de (m

ms

2 )

(a)

233Hz

332Hz299Hz199Hz

0 20 30 40 50 60 70 80 90 10010Frequency (Hz)

01020304050

Acc

eler

atio

nam

plitu

de (m

ms

2 )

(b)

332Hz299Hz

233Hz

199Hz

0 20 30 40 50 60 70 80 90 10010Frequency (Hz)

01020304050

Acc

eler

atio

nam

plitu

de (m

ms

2 )

(c)

299Hz332Hz

233Hz199Hz

0 20 30 40 50 60 70 80 90 1001Frequency (Hz)

01020304050

Acc

eler

atio

nam

plitu

de (m

ms

2 )

(d)

Figure 13 Spectral curve of acceleration at different locations (a) track slab (b) surface layer of subgrade (c) bottom layer of subgrade (d)surface layer of foundation

00 02 04Time (s)

06 08 10 12ndash10

ndash5

0

5

10

Acc

eler

atio

n re

spon

se(s

urfa

ce la

yer o

f fou

ndat

ion)

(mm

s2 )

160kmh

(a)

00 02 04 06 08 10 12ndash10

ndash5

0

5

10

Acc

eler

atio

n re

spon

se(s

urfa

ce la

yer o

f fou

ndat

ion)

(mm

s2 )

Time (s)

200kmh

(b)

00 02 04 06 08 10 12ndash10

ndash5

0

5

10

Acc

eler

atio

n re

spon

se(s

urfa

ce la

yer o

f fou

ndat

ion)

(mm

s2 )

Time (s)

250kmh

(c)

Figure 14 Continued

10 Shock and Vibration

00 02 04 06 08 10 12ndash10

ndash5

0

5

10

Acc

eler

atio

n re

spon

se(s

urfa

ce la

yer o

f fou

ndat

ion)

(mm

s2 )

Time (s)

300kmh

(d)

00 02 04 06 08 10 12ndash10

ndash5

0

5

10

Acc

eler

atio

n re

spon

se(s

urfa

ce la

yer o

f fou

ndat

ion)

(mm

s2 )

Time (s)

350kmh

(e)

Figure 14 Acceleration under different speeds with respect to time

177Hz

160kmh

0

1

2

3

Acc

eler

atio

nam

plitu

de (m

ms

2 )

20 40 60 80 1000Time (s)

(a)

200kmh

200Hz 222Hz

0

1

2

3

Acc

eler

atio

nam

plitu

de (m

ms

2 )

20 40 60 80 1000Time (s)

(b)

Figure 15 Continued

Shock and Vibration 11

(approximately double) However when the train speed rea-ches 250 kmh the increase on the peak is negligible Becausethe increase in the train speed is achieved by increasing thevibration frequency the superposition of the surroundingreflected waves in this process likely produces a counteractionto the vibration of the subgrade foundation explaining thisresult

Figure 15 shows the spectral curve of the acceleration atthe surface layer of the foundation under different trainspeeds We can see that the ground vibration caused by thetrain is mainly contributed by relatively low-frequencycomponents (mainly below 100Hz) As the train speedincreases the amplitude of the acceleration increases andthe base frequencies of the vibration also gradually increase177Hz in the base frequencies when the train velocity is160 kmh 222Hz when the train speed is 200 kmh 277Hzwhen the train speed is 250 kmh 332Hz when the trainspeed is 300 kmh and 388Hz when the train speed is350 kmh are all the vibration frequency of the actuatorunder the current working condition

As the train speed increases the peak spectral vibrationacceleration response also increases and the frequencycorresponding to the peak spectral vibration accelerationalso gradually moves to a medium frequency as the trainspeed increases )e higher the train speed the richer thefrequency components of the ground vibration

4 Conclusions

In this study by conducting a large-scale dynamic model teston an X-section pile-net composite foundation under dif-ferent train speeds we can draw the following conclusions

(1) )e response of the vertical dynamic velocity is thelargest at the surface layer of the embankment andattenuates by approximately 90 in the embank-ment )e speed rapidly attenuates as the depthincreases the vibration gradually attenuates as thedistance from the vibration source increases At thebottom layer of the subgrade bed and in the range of

250kmh

277Hz

250Hz194Hz

0

1

2

3

Acc

eler

atio

nam

plitu

de (m

ms

2 )20 40 60 80 1000

Time (s)

(c)

300kmh

199Hz

233Hz

299Hz

332Hz

0

1

2

3

4

Acc

eler

atio

nam

plitu

de (m

ms

2 )

20 40 60 80 1000Time (s)

(d)

350kmh

233Hz272Hz

349Hz

0

1

2

3

4

Acc

eler

atio

nam

plitu

de (m

ms

2 )

20 40 60 80 1000Time (s)

(e)

Figure 15 Spectrum curve of acceleration under different speeds

12 Shock and Vibration

the lower foundation the attenuation rate signifi-cantly decreases and the vibration velocity is linearlyrelated to the train speed

(2) Inside the pile-net foundation the peak dynamicstress at the top of the pile is 34 times than that in thesoil between piles and the dynamic stress attenuateswith the depth

(3) )e change in train speed does not have a largeinfluence on the peak transient dynamic displace-ment response at the surface of the track afterpassing through the subgrade bed the peak verticalacceleration decreases from approximately 80mms2to 30mms2 attenuating by 625 )is is mainlybecause the high-frequency components are absor-bed due to soil damping effects and the low-frequency components attenuate relatively slowly)e foundation vibration caused by the train is a low-frequency vibration and the subgrade foundationhas an attenuation impact on the high-frequencyvibration the vibration gradually decreases as thedistance from the vibration source increases andincreases as the train speed increases

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 there are no conflicts of interestregarding the publication of this paper

Acknowledgments

)is project was supported by the Funds for InternationalCooperation and Exchange of the National Natural ScienceFoundation of China (Grant no 51420105013)

References

[1] M A Heckl ldquoRailway noise-can random sleeper spacingshelprdquo Acta Acustica United with Acustica vol 81 no 6pp 559ndash564 1995

[2] H Takemiya and X Bian ldquoSubstructure simulation of in-homogeneous track and layered ground dynamic interactionunder train passagerdquo Journal of Engineering Mechanicsvol 131 no 7 pp 699ndash711 2005

[3] M Bahrekazemi and A Bodare ldquoEffects of lime-cement soilstabilization against train induced ground vibrationsrdquo inProceedings of the 3rd International Specialty Conference onGrouting and Ground Treatment New Orleans LA USAFebruary 2003

[4] L Bo and C Ying ldquoDynamic analysis on subgrade of highspeed railways in geometric irregular conditionrdquo Journal ofthe China Railway Society vol 21 pp 84ndash88 1999

[5] X Chen and W Y Lu Wentian ldquoStudy on the dynamic re-sponse of high speed railway bridge-subgrade transition sec-tionrdquo Journal of Vibration and Shock vol 25 pp 95ndash98 2006

[6] W F Anderson and A J Key ldquoModel testing of two-layerrailway track ballastrdquo Journal of Geotechnical and Geo-environmental Engineering vol 126 no 4 pp 317ndash323 2000

[7] S J Cox A Wang C Morison P Carels R Kelly andO G Bewes ldquoA test rig to investigate slab track structures forcontrolling ground vibrationrdquo Journal of Sound and Vibra-tion vol 293 no 3ndash5 pp 901ndash909 2006

[8] Y Zhan and G Jiang ldquoStudy of dynamic characteristics of soilsubgrade bed for ballastless trackrdquo Rock and Soil Mechanicsvol 31 pp 392ndash396 2010

[9] Y Momoya E Sekine and F Tatsuoka ldquoDeformationcharacteristics of railway roadbed and subgrade undermoving-wheel loadrdquo Soils and Foundations vol 45 no 4pp 99ndash118 2005

[10] A Al Shaer D Duhamel K Sab G Foret and L SchmittldquoExperimental settlement and dynamic behavior of a portionof ballasted railway track under high speed trainsrdquo Journal ofSound and Vibration vol 316 no 1ndash5 pp 211ndash233 2008

[11] T Ishikawa E Sekine and S Miura ldquoCyclic deformation ofgranular material subjected to moving-wheel loadsrdquo Cana-dian Geotechnical Journal vol 48 no 5 pp 691ndash703 2011

[12] G Q Kong X M Ding Y M Chen and G Yang ldquoVerticaluplift capacity characteristics and influence factor analysis ofcast-in-situ X-section reinforced concrete pile grouprdquo Journalof Civil Engineering and Architecture vol 29 pp 49ndash54 2012

[13] M X Zhang H L Liu X M Ding and Z Q WangldquoComparative tests on bearing capacity of cast-in-situX-shaped concrete piles and circular pilerdquo Chinese Journal ofGeotechnical Engineering vol 33 pp 1469ndash1476 2011

[14] Z QWang H L Liu M X Zhang J Yuan and J Yong ldquoFullscale model tests on vertical bearing characteristics of cast-in-place X-section pilesrdquo Chinese Journal of Geotechnical Engi-neering vol 32 pp 903ndash907 2010

[15] Y Jun L Xiao-Min and L Han-Long ldquoModel test study ofanti-pulling property of X-shaped concrete pilerdquo Rock andSoil Mechanics vol 31 pp 3430ndash3434 2010

[16] L Han-Long L Zhi-Ping and W Xin-Quan ldquoStudy on thegeometric characteristics of the cast-in-place X-type vibro-pilesectionrdquo China Railway Science vol 30 pp 17ndash23 2009

[17] M X Zhang S M Ding and Y M Chen ldquoTest on verticalbehavior of cast-in-situ X-shaped concrete pile and its ulti-mate bearing capacity predictionrdquo Journal of China CoalSociety vol 36 pp 267ndash271 2011

[18] L Han-Long J Hui and D Xuan-Ming ldquoField test researchon squeezing effects of X-section cast-in-place concrete pilerdquoRock and Soil Mechanics vol 33 pp 219ndash224 2012

[19] S Guang-Chao L Han-Long K Gang-Qiang and D Xuan-Ming ldquoModel tests on effect of vibration waves on dynamicresponse of XCC pile-raft composite foundationrdquo ChineseJournal of Geotechnical Engineering vol 38 pp 1021ndash10292015

Shock and Vibration 13

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)e train simulated in this test refers to the main type ofCRH3CRH380 D-series high-speed train operated on thehigh-speed railway in China )e applied force is the loadfrom the four pairs of wheels of the adjacent bogies of ad-jacent carriages)e time for passing through the distance of a25m bogie is two load cycles)emagnitude of the train loadand the running speed is reflected through the load output

and frequency of a servo vibrator )e relationship betweenthe train speed and loading frequency is shown in Table 2

3 TestWorking Conditions and Result Analysis

31 Analysis of Vertical Velocity Taking a train speed of300kmh as an example the time-history response curves of thevertical vibration velocities at different locations of the X-sectionpile-net composite foundation system are shown in Figure 5

Under the cyclic load of an M-shaped wave the time-history response curve of the velocity of the entire compositefoundation exhibits significant periodicity with the cyclicloading process and the frequency of its velocity response isconsistent with the frequency of the cyclic loading

At the surface and bottom layers of the subgrade bed thetime-history response curves of the velocity induced by thecyclic loading exhibits a significant M shape and as thedepth increases the amplitude of the M-shaped velocitygradually decreases )erefore the dynamic cyclic load in-duced by the operating train has an important influence onthe embankment and the vibration response of this region ismainly caused by the dynamic load of the train wheel shaftAs they propagate to the foundation the various reflectedwaves gradually account for a certain percentage of the totalcausing the response waveform to be insignificant

Figure 5 shows that the response of the velocity at thesurface layer of the subgrade bed in the embankment is

0

10

20

30

40

50

60

70

8025m25m25m

25m175m

Dyn

amic

load

ing

Q(t)

(kN

)

Time (s)

25mLoad cycle T

Figure 4 ldquoMrdquo-shaped wave

D1

600

520

D2

D3

D4

D5 D6V1A1

V2 V3A3A2

V4A4

V5 V6

S1

S4 S7

Pore pressure gauge (K)

Dynamic pressure box (S)

Speedometer (V)

Accelerometer (A)

Displacement gauge (D)

(b)

Figure 3 Layout of test instrument (unit mm) (a) front view (b) top view

Shock and Vibration 5

mainly caused by the cyclic dynamic load of the train and itis relatively consistent with the waveform of the loadingwave but without the influence of a large number of reflectedwaves in the foundation soil Hence it can better assist in thestudy of the relationship between the velocity response andthe train speed )erefore the peak responses of the verticalvelocity at the surface layer of the subgrade bed underdifferent train speeds are averaged for analysis Under dif-ferent train speeds the velocity responses of the X-sectionpile-net composite foundation at different depths are shownin Figure 6 We can see that with the track slab plane as the0m depth 1m is the surface layer of the subgrade Underdifferent train speeds the vibration velocity of the foun-dation soil rapidly attenuates as the depth increases and themaximum vibration response occurs at the surface layer ofthe subgrade bed It can be seen that within the depth of 1mie within the embankment the dynamic velocity attenuatesby approximately 90 indicating that the embankment hasa very good reduction effect on the propagation of the vi-bration load while the attenuation rate of the speed after itreaches the foundation decreases

Figure 7 shows the relationship curve between the re-sponse of the vertical velocity at the track slab and the trainspeed )e peak response of the velocity at the track slabunder three different train speeds is shown )e distributionof the scattered points reveals that the peak response of thevibration velocity at the track slab and the train speed arelinearly related As the train speed increases from 160 kmh to350 kmh the peak response of the vibration velocity in-creases from 2299mms to 4600mms an increase of 100

)e distribution of the vertical vibration velocity re-sponse of the track under train operation along the trans-verse direction of the track is shown in Figure 8 We can seethat in the whole system the track structure that is closest tothe actuator exhibits the most intense vibration responseWith a train speed of 350 kmh the peak vibration velocityreaches 4378mms while the maximum vibration velocityof the subgrade structure is only 102mms )e vibration ofthe subgrade system gradually attenuates going farther awayfrom the vibration source and the vibration velocity at thebottom layer of the subgrade bed as well as within the rangeof the lower foundation is at a relatively low level and with a

00 01 02 03 04 05 06Time (s)

ndash45ndash30ndash15

0153045

Vel

ocity

resp

onse

(mm

s)

(a)

ndash3ndash2ndash1

0123

00 01 02 03 04 05 06Time (s)

Vel

ocity

resp

onse

(mm

s)

(b)

00 01 02 03 04 05 06Time (s)

ndash3ndash2ndash1

0123

Vel

ocity

resp

onse

(mm

s)

(c)

00 01 02 03 04 05 06Time (s)

ndash3ndash2ndash1

0123

Vel

ocity

resp

onse

(mm

s)

(d)

00 01 02 03 04 05 06Time (s)

ndash3ndash2ndash1

0123

Vel

ocity

resp

onse

(mm

s)

(e)

Figure 5 Vertical velocity with respect to time (a) track slab (b) surface layer of subgrade (c) bottom layer of subgrade (d) surface layer offoundation (e) bottom layer of foundation

Table 2 Train speed and frequency

Actuator frequency Two peak period (s) Corresponding train speed (kmh) Two trough periods (s) Carriage cycle (s)18 0056 160 0173 055622 0045 200 0142 045528 0036 250 0111 035733 0030 300 0095 030339 0026 350 0080 0256

6 Shock and Vibration

significantly slow attenuation rate indicating that the sub-grade bed has a significant reduction effect on the verticalvibration

32 Analysis of Dynamic Earth Pressure Figure 9 showstime-history curves of the dynamic soil stress at the pile topand between piles when the train speed is 300 kmh)e waveis affected by the embankment and hence attenuates during

the propagation process causing the waveform characteristicsof the M-shaped wave to have already been significantlyweakened when it reaches the surface of the foundation Wecan see that the stress at the pile top is greater than thedynamic stress of the soil between piles and the soil arch has a

V4V3

160kmh200kmh250kmh

300kmh350kmh

V0 V1 V2

05 10 15 20 2500Distance to the center (m)

0

5

10

15

20

25

30

35

40

45

Vel

ocity

resp

onse

(mm

s)

Figure 8 Vertical velocity with respect to horizontal dimension

00 01 02 03 04 05 0602468

1012

Load

(kN

)

Waveform

Time (s)

(a)

ndash202468

1012

Dyn

amic

stre

ss (k

Pa)

Pile topSoil

00 01 02Time (s)

03 04 05 06

(b)

Figure 9 Dynamic stresses of pile and soil with respect to time

6

5

4

3

2

1

0ndash5 0 5 10 15 20 25 30 35 40 45 50

6

5

4

3

2

1

0 1 2 3

Velocity response (mms)

Dep

th (m

)

160kmh200kmh250kmh

300kmh350kmh

Figure 6 Vertical velocity with respect to depth

0

10

20

30

40

50

60

Vel

ocity

resp

onse

pea

k of

the t

rack

slab

(mm

s)

A groupB groupC group

50 100 150 200 250 300 350 4000Train speed (kmh)

Figure 7 Vertical velocity with respect to train speed

Shock and Vibration 7

significant influence on the distribution of the dynamic stressIn the soil arch region a greater dynamic load is transferredabove the top of the pile )e average of the peak dynamicstresses at the pile top is approximately 62 kPa which is 34times the average of the peak dynamic earth pressure (ap-proximately 18 kPa) on the soil between the piles

Figure 10 shows relationship curves of the changes in thepeak dynamic stresses at the pile top and in the soil betweenthe piles of the foundation and the train speed We can seethat under the vibration load of the high-speed train theload carried at the pile top in the foundation is much largerthan that by the soil between the piles

Although the vibration frequency of the dynamic loadincreases as the train speed increases the influence of thetrain speed on the response of the dynamic stress is weak)is is likely because the wave gradually attenuates in theprocess of reaching the foundation through the subgradebed and its effect gradually decreases

33 Analysis of Dynamic Displacement Figure 11 shows thetime-history response curve of the dynamic displacementon the track surface under different train speeds We cansee that the change in the train speed does not have a largeinfluence on the peak transient dynamic displacementresponse on the track surface A comparison of dynamicdisplacement responses under different train speeds re-veals that the faster the train speed the more intense andshorter the induced vibration)is is because the faster thetrain speed the higher the dynamic loading frequencyWhen the train speed is not high (160 kmh) the time-history curve between the peak displacements attenuatesWhen the train speed reaches 250 kmh the displacementtime history does not significantly attenuate but insteadgradually fluctuates with time In fact the attenuationprocess is not completed

34 Analysis of Acceleration Figure 12 shows the time-history curve of the acceleration at different locations in thepile-net composite foundation when the train speed is300 kmh We can see that the vibration close to the actuatorhas a relatively large amplitude As the distance from thevibration source increases the amplitude of the accelerationgradually decreases and the high-frequency componentsattenuate especially rapidly Because the track slab is rela-tively close to the subgrade bed its peak acceleration is ap-proximately 80mms2 After passing through the track slabthe waveform at the surface layer of the subgrade bed is not assignificant as that at the track slab

It can be clearly seen from Figure 12 that after passingthrough the subgrade bed the peak acceleration decreasesfrom 80mms2 to 30mms2 that is it attenuates by 625)is is mainly because the high-frequency components areabsorbed due to the damping effect of the soil in the em-bankment while the attenuation of the low-frequencycomponents is relatively slow When reaching the bottomlayer of the foundation due to the influence of the reflectedwaves the M-shaped waveform has essentially disappearedAs a result only a simple harmonic oscillation curve is

presented and the amplitude of the acceleration vibration isonly 2 of that at the surface layer of the foundation As thedepth increases the peak acceleration responses of theM-shaped waveform at different locations do not appear atthe same time )is is because it takes time for the wave topropagate causing some lag in the acceleration response

Figure 13 shows a spectral curve of the vertical accel-eration at different locations from the vibration source whenthe train speed is 300 kmh We can see that the frequency isdistributed in the range of 0ndash100Hz and is mainly con-centrated between 10 and 50Hz making it low-frequencyvibrations As the distance from the vibration source in-creases the maximum vibration accelerations at differentlocations are 4352mms2 4082mms2 3152mms2352mms2 and 014mms2 It can be seen that as thedistance from the vibration source increases the amplitudeof the acceleration generally attenuates )e high-frequencycomponent is relatively rich at locations close to the vi-bration source and the width of the spectrum graduallydecreases when moving away from the vibration source )emost significant frequency band becomes that of the lowfrequency because the high-frequency components attenu-ate faster than the low-frequency components

We can see from the peaks in Figure 13 that the fourcharacteristic frequencies with the largest contributions to thevibration are 199Hz 233Hz 299Hz and 332Hz Amongthem 332Hz corresponds to the actuator frequency At themeasurement site of the track slab the frequency of theground vibration caused by the train is distributed within50ndash85Hz and relatively rich in the main frequency

Figure 14 shows the time-history curve of the accelerationat the surface layer of the foundation under different trainspeeds We can clearly see that as the train speed increases thehigh-frequency components significantly increase Whenthe train speed is 160 kmh the peak acceleration at the sur-face layer of the foundation is 359mms2 and when thetrain velocity increases to 200 kmh the peak acceleration atthe surface layer of the foundation reaches 724mms2

Pile topSoil

0

2

4

6

8

10

Dyn

amic

stre

ss (k

Pa)

200 300 400100Train speed (kmh)

Figure 10 Relationship curves between dynamic stress responsesof soil at pipe top and between piles and the train speed

8 Shock and Vibration

00

02

04

06

08

Dyn

amic

disp

lace

men

tof

the t

rack

slab

(mm

)

02 04 06 08 10 1200Time (s)

160kmh

(a)

00

02

04

06

08

Dyn

amic

disp

lace

men

tof

the t

rack

slab

(mm

)

02 04 06 08 10 1200Time (s)

200kmh

(b)

00

02

04

06

08

Dyn

amic

disp

lace

men

tof

the t

rack

slab

(mm

)

02 04 06 08 10 1200Time (s)

250kmh(c)

00

02

04

06

08

Dyn

amic

disp

lace

men

tof

the t

rack

slab

(mm

)

02 04 06 08 10 1200Time (s)

300kmh

(d)

00

02

04

06

08

Dyn

amic

disp

lace

men

tof

the t

rack

slab

(mm

)

02 04 06 08 10 1200Time (s)

350kmh

(e)

Figure 11 Dynamic displacement of track with respect to time

120

ndash120

80

ndash80

40

ndash400

Acc

eler

atio

nre

spon

se (m

ms

2 )

01 02 03 04 05 0600Time (s)

(a)

120

ndash120

80

ndash80

40

ndash400

Acc

eler

atio

nre

spon

se (m

ms

2 )

01 02 03 04 05 0600Time (s)

(b)120

ndash120

80

ndash80

40

ndash400

Acc

eler

atio

nre

spon

se (m

ms

2 )

01 02 03 04 05 0600Time (s)

(c)

120

ndash120

80

ndash80

40

ndash400

Acc

eler

atio

nre

spon

se (m

ms

2 )

01 02 03 04 05 0600Time (s)

(d)

Figure 12 Acceleration at different layers with respect to time (a) track slab (b) surface layer of subgrade (c) bottom layer of subgrade (d)surface layer of foundation

Shock and Vibration 9

332Hz299Hz199Hz

233Hz

0 20 30 40 50 60 70 80 90 10010Frequency (Hz)

01020304050

Acc

eler

atio

nam

plitu

de (m

ms

2 )

(a)

233Hz

332Hz299Hz199Hz

0 20 30 40 50 60 70 80 90 10010Frequency (Hz)

01020304050

Acc

eler

atio

nam

plitu

de (m

ms

2 )

(b)

332Hz299Hz

233Hz

199Hz

0 20 30 40 50 60 70 80 90 10010Frequency (Hz)

01020304050

Acc

eler

atio

nam

plitu

de (m

ms

2 )

(c)

299Hz332Hz

233Hz199Hz

0 20 30 40 50 60 70 80 90 1001Frequency (Hz)

01020304050

Acc

eler

atio

nam

plitu

de (m

ms

2 )

(d)

Figure 13 Spectral curve of acceleration at different locations (a) track slab (b) surface layer of subgrade (c) bottom layer of subgrade (d)surface layer of foundation

00 02 04Time (s)

06 08 10 12ndash10

ndash5

0

5

10

Acc

eler

atio

n re

spon

se(s

urfa

ce la

yer o

f fou

ndat

ion)

(mm

s2 )

160kmh

(a)

00 02 04 06 08 10 12ndash10

ndash5

0

5

10

Acc

eler

atio

n re

spon

se(s

urfa

ce la

yer o

f fou

ndat

ion)

(mm

s2 )

Time (s)

200kmh

(b)

00 02 04 06 08 10 12ndash10

ndash5

0

5

10

Acc

eler

atio

n re

spon

se(s

urfa

ce la

yer o

f fou

ndat

ion)

(mm

s2 )

Time (s)

250kmh

(c)

Figure 14 Continued

10 Shock and Vibration

00 02 04 06 08 10 12ndash10

ndash5

0

5

10

Acc

eler

atio

n re

spon

se(s

urfa

ce la

yer o

f fou

ndat

ion)

(mm

s2 )

Time (s)

300kmh

(d)

00 02 04 06 08 10 12ndash10

ndash5

0

5

10

Acc

eler

atio

n re

spon

se(s

urfa

ce la

yer o

f fou

ndat

ion)

(mm

s2 )

Time (s)

350kmh

(e)

Figure 14 Acceleration under different speeds with respect to time

177Hz

160kmh

0

1

2

3

Acc

eler

atio

nam

plitu

de (m

ms

2 )

20 40 60 80 1000Time (s)

(a)

200kmh

200Hz 222Hz

0

1

2

3

Acc

eler

atio

nam

plitu

de (m

ms

2 )

20 40 60 80 1000Time (s)

(b)

Figure 15 Continued

Shock and Vibration 11

(approximately double) However when the train speed rea-ches 250 kmh the increase on the peak is negligible Becausethe increase in the train speed is achieved by increasing thevibration frequency the superposition of the surroundingreflected waves in this process likely produces a counteractionto the vibration of the subgrade foundation explaining thisresult

Figure 15 shows the spectral curve of the acceleration atthe surface layer of the foundation under different trainspeeds We can see that the ground vibration caused by thetrain is mainly contributed by relatively low-frequencycomponents (mainly below 100Hz) As the train speedincreases the amplitude of the acceleration increases andthe base frequencies of the vibration also gradually increase177Hz in the base frequencies when the train velocity is160 kmh 222Hz when the train speed is 200 kmh 277Hzwhen the train speed is 250 kmh 332Hz when the trainspeed is 300 kmh and 388Hz when the train speed is350 kmh are all the vibration frequency of the actuatorunder the current working condition

As the train speed increases the peak spectral vibrationacceleration response also increases and the frequencycorresponding to the peak spectral vibration accelerationalso gradually moves to a medium frequency as the trainspeed increases )e higher the train speed the richer thefrequency components of the ground vibration

4 Conclusions

In this study by conducting a large-scale dynamic model teston an X-section pile-net composite foundation under dif-ferent train speeds we can draw the following conclusions

(1) )e response of the vertical dynamic velocity is thelargest at the surface layer of the embankment andattenuates by approximately 90 in the embank-ment )e speed rapidly attenuates as the depthincreases the vibration gradually attenuates as thedistance from the vibration source increases At thebottom layer of the subgrade bed and in the range of

250kmh

277Hz

250Hz194Hz

0

1

2

3

Acc

eler

atio

nam

plitu

de (m

ms

2 )20 40 60 80 1000

Time (s)

(c)

300kmh

199Hz

233Hz

299Hz

332Hz

0

1

2

3

4

Acc

eler

atio

nam

plitu

de (m

ms

2 )

20 40 60 80 1000Time (s)

(d)

350kmh

233Hz272Hz

349Hz

0

1

2

3

4

Acc

eler

atio

nam

plitu

de (m

ms

2 )

20 40 60 80 1000Time (s)

(e)

Figure 15 Spectrum curve of acceleration under different speeds

12 Shock and Vibration

the lower foundation the attenuation rate signifi-cantly decreases and the vibration velocity is linearlyrelated to the train speed

(2) Inside the pile-net foundation the peak dynamicstress at the top of the pile is 34 times than that in thesoil between piles and the dynamic stress attenuateswith the depth

(3) )e change in train speed does not have a largeinfluence on the peak transient dynamic displace-ment response at the surface of the track afterpassing through the subgrade bed the peak verticalacceleration decreases from approximately 80mms2to 30mms2 attenuating by 625 )is is mainlybecause the high-frequency components are absor-bed due to soil damping effects and the low-frequency components attenuate relatively slowly)e foundation vibration caused by the train is a low-frequency vibration and the subgrade foundationhas an attenuation impact on the high-frequencyvibration the vibration gradually decreases as thedistance from the vibration source increases andincreases as the train speed increases

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 there are no conflicts of interestregarding the publication of this paper

Acknowledgments

)is project was supported by the Funds for InternationalCooperation and Exchange of the National Natural ScienceFoundation of China (Grant no 51420105013)

References

[1] M A Heckl ldquoRailway noise-can random sleeper spacingshelprdquo Acta Acustica United with Acustica vol 81 no 6pp 559ndash564 1995

[2] H Takemiya and X Bian ldquoSubstructure simulation of in-homogeneous track and layered ground dynamic interactionunder train passagerdquo Journal of Engineering Mechanicsvol 131 no 7 pp 699ndash711 2005

[3] M Bahrekazemi and A Bodare ldquoEffects of lime-cement soilstabilization against train induced ground vibrationsrdquo inProceedings of the 3rd International Specialty Conference onGrouting and Ground Treatment New Orleans LA USAFebruary 2003

[4] L Bo and C Ying ldquoDynamic analysis on subgrade of highspeed railways in geometric irregular conditionrdquo Journal ofthe China Railway Society vol 21 pp 84ndash88 1999

[5] X Chen and W Y Lu Wentian ldquoStudy on the dynamic re-sponse of high speed railway bridge-subgrade transition sec-tionrdquo Journal of Vibration and Shock vol 25 pp 95ndash98 2006

[6] W F Anderson and A J Key ldquoModel testing of two-layerrailway track ballastrdquo Journal of Geotechnical and Geo-environmental Engineering vol 126 no 4 pp 317ndash323 2000

[7] S J Cox A Wang C Morison P Carels R Kelly andO G Bewes ldquoA test rig to investigate slab track structures forcontrolling ground vibrationrdquo Journal of Sound and Vibra-tion vol 293 no 3ndash5 pp 901ndash909 2006

[8] Y Zhan and G Jiang ldquoStudy of dynamic characteristics of soilsubgrade bed for ballastless trackrdquo Rock and Soil Mechanicsvol 31 pp 392ndash396 2010

[9] Y Momoya E Sekine and F Tatsuoka ldquoDeformationcharacteristics of railway roadbed and subgrade undermoving-wheel loadrdquo Soils and Foundations vol 45 no 4pp 99ndash118 2005

[10] A Al Shaer D Duhamel K Sab G Foret and L SchmittldquoExperimental settlement and dynamic behavior of a portionof ballasted railway track under high speed trainsrdquo Journal ofSound and Vibration vol 316 no 1ndash5 pp 211ndash233 2008

[11] T Ishikawa E Sekine and S Miura ldquoCyclic deformation ofgranular material subjected to moving-wheel loadsrdquo Cana-dian Geotechnical Journal vol 48 no 5 pp 691ndash703 2011

[12] G Q Kong X M Ding Y M Chen and G Yang ldquoVerticaluplift capacity characteristics and influence factor analysis ofcast-in-situ X-section reinforced concrete pile grouprdquo Journalof Civil Engineering and Architecture vol 29 pp 49ndash54 2012

[13] M X Zhang H L Liu X M Ding and Z Q WangldquoComparative tests on bearing capacity of cast-in-situX-shaped concrete piles and circular pilerdquo Chinese Journal ofGeotechnical Engineering vol 33 pp 1469ndash1476 2011

[14] Z QWang H L Liu M X Zhang J Yuan and J Yong ldquoFullscale model tests on vertical bearing characteristics of cast-in-place X-section pilesrdquo Chinese Journal of Geotechnical Engi-neering vol 32 pp 903ndash907 2010

[15] Y Jun L Xiao-Min and L Han-Long ldquoModel test study ofanti-pulling property of X-shaped concrete pilerdquo Rock andSoil Mechanics vol 31 pp 3430ndash3434 2010

[16] L Han-Long L Zhi-Ping and W Xin-Quan ldquoStudy on thegeometric characteristics of the cast-in-place X-type vibro-pilesectionrdquo China Railway Science vol 30 pp 17ndash23 2009

[17] M X Zhang S M Ding and Y M Chen ldquoTest on verticalbehavior of cast-in-situ X-shaped concrete pile and its ulti-mate bearing capacity predictionrdquo Journal of China CoalSociety vol 36 pp 267ndash271 2011

[18] L Han-Long J Hui and D Xuan-Ming ldquoField test researchon squeezing effects of X-section cast-in-place concrete pilerdquoRock and Soil Mechanics vol 33 pp 219ndash224 2012

[19] S Guang-Chao L Han-Long K Gang-Qiang and D Xuan-Ming ldquoModel tests on effect of vibration waves on dynamicresponse of XCC pile-raft composite foundationrdquo ChineseJournal of Geotechnical Engineering vol 38 pp 1021ndash10292015

Shock and Vibration 13

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

mainly caused by the cyclic dynamic load of the train and itis relatively consistent with the waveform of the loadingwave but without the influence of a large number of reflectedwaves in the foundation soil Hence it can better assist in thestudy of the relationship between the velocity response andthe train speed )erefore the peak responses of the verticalvelocity at the surface layer of the subgrade bed underdifferent train speeds are averaged for analysis Under dif-ferent train speeds the velocity responses of the X-sectionpile-net composite foundation at different depths are shownin Figure 6 We can see that with the track slab plane as the0m depth 1m is the surface layer of the subgrade Underdifferent train speeds the vibration velocity of the foun-dation soil rapidly attenuates as the depth increases and themaximum vibration response occurs at the surface layer ofthe subgrade bed It can be seen that within the depth of 1mie within the embankment the dynamic velocity attenuatesby approximately 90 indicating that the embankment hasa very good reduction effect on the propagation of the vi-bration load while the attenuation rate of the speed after itreaches the foundation decreases

Figure 7 shows the relationship curve between the re-sponse of the vertical velocity at the track slab and the trainspeed )e peak response of the velocity at the track slabunder three different train speeds is shown )e distributionof the scattered points reveals that the peak response of thevibration velocity at the track slab and the train speed arelinearly related As the train speed increases from 160 kmh to350 kmh the peak response of the vibration velocity in-creases from 2299mms to 4600mms an increase of 100

)e distribution of the vertical vibration velocity re-sponse of the track under train operation along the trans-verse direction of the track is shown in Figure 8 We can seethat in the whole system the track structure that is closest tothe actuator exhibits the most intense vibration responseWith a train speed of 350 kmh the peak vibration velocityreaches 4378mms while the maximum vibration velocityof the subgrade structure is only 102mms )e vibration ofthe subgrade system gradually attenuates going farther awayfrom the vibration source and the vibration velocity at thebottom layer of the subgrade bed as well as within the rangeof the lower foundation is at a relatively low level and with a

00 01 02 03 04 05 06Time (s)

ndash45ndash30ndash15

0153045

Vel

ocity

resp

onse

(mm

s)

(a)

ndash3ndash2ndash1

0123

00 01 02 03 04 05 06Time (s)

Vel

ocity

resp

onse

(mm

s)

(b)

00 01 02 03 04 05 06Time (s)

ndash3ndash2ndash1

0123

Vel

ocity

resp

onse

(mm

s)

(c)

00 01 02 03 04 05 06Time (s)

ndash3ndash2ndash1

0123

Vel

ocity

resp

onse

(mm

s)

(d)

00 01 02 03 04 05 06Time (s)

ndash3ndash2ndash1

0123

Vel

ocity

resp

onse

(mm

s)

(e)

Figure 5 Vertical velocity with respect to time (a) track slab (b) surface layer of subgrade (c) bottom layer of subgrade (d) surface layer offoundation (e) bottom layer of foundation

Table 2 Train speed and frequency

Actuator frequency Two peak period (s) Corresponding train speed (kmh) Two trough periods (s) Carriage cycle (s)18 0056 160 0173 055622 0045 200 0142 045528 0036 250 0111 035733 0030 300 0095 030339 0026 350 0080 0256

6 Shock and Vibration

significantly slow attenuation rate indicating that the sub-grade bed has a significant reduction effect on the verticalvibration

32 Analysis of Dynamic Earth Pressure Figure 9 showstime-history curves of the dynamic soil stress at the pile topand between piles when the train speed is 300 kmh)e waveis affected by the embankment and hence attenuates during

the propagation process causing the waveform characteristicsof the M-shaped wave to have already been significantlyweakened when it reaches the surface of the foundation Wecan see that the stress at the pile top is greater than thedynamic stress of the soil between piles and the soil arch has a

V4V3

160kmh200kmh250kmh

300kmh350kmh

V0 V1 V2

05 10 15 20 2500Distance to the center (m)

0

5

10

15

20

25

30

35

40

45

Vel

ocity

resp

onse

(mm

s)

Figure 8 Vertical velocity with respect to horizontal dimension

00 01 02 03 04 05 0602468

1012

Load

(kN

)

Waveform

Time (s)

(a)

ndash202468

1012

Dyn

amic

stre

ss (k

Pa)

Pile topSoil

00 01 02Time (s)

03 04 05 06

(b)

Figure 9 Dynamic stresses of pile and soil with respect to time

6

5

4

3

2

1

0ndash5 0 5 10 15 20 25 30 35 40 45 50

6

5

4

3

2

1

0 1 2 3

Velocity response (mms)

Dep

th (m

)

160kmh200kmh250kmh

300kmh350kmh

Figure 6 Vertical velocity with respect to depth

0

10

20

30

40

50

60

Vel

ocity

resp

onse

pea

k of

the t

rack

slab

(mm

s)

A groupB groupC group

50 100 150 200 250 300 350 4000Train speed (kmh)

Figure 7 Vertical velocity with respect to train speed

Shock and Vibration 7

significant influence on the distribution of the dynamic stressIn the soil arch region a greater dynamic load is transferredabove the top of the pile )e average of the peak dynamicstresses at the pile top is approximately 62 kPa which is 34times the average of the peak dynamic earth pressure (ap-proximately 18 kPa) on the soil between the piles

Figure 10 shows relationship curves of the changes in thepeak dynamic stresses at the pile top and in the soil betweenthe piles of the foundation and the train speed We can seethat under the vibration load of the high-speed train theload carried at the pile top in the foundation is much largerthan that by the soil between the piles

Although the vibration frequency of the dynamic loadincreases as the train speed increases the influence of thetrain speed on the response of the dynamic stress is weak)is is likely because the wave gradually attenuates in theprocess of reaching the foundation through the subgradebed and its effect gradually decreases

33 Analysis of Dynamic Displacement Figure 11 shows thetime-history response curve of the dynamic displacementon the track surface under different train speeds We cansee that the change in the train speed does not have a largeinfluence on the peak transient dynamic displacementresponse on the track surface A comparison of dynamicdisplacement responses under different train speeds re-veals that the faster the train speed the more intense andshorter the induced vibration)is is because the faster thetrain speed the higher the dynamic loading frequencyWhen the train speed is not high (160 kmh) the time-history curve between the peak displacements attenuatesWhen the train speed reaches 250 kmh the displacementtime history does not significantly attenuate but insteadgradually fluctuates with time In fact the attenuationprocess is not completed

34 Analysis of Acceleration Figure 12 shows the time-history curve of the acceleration at different locations in thepile-net composite foundation when the train speed is300 kmh We can see that the vibration close to the actuatorhas a relatively large amplitude As the distance from thevibration source increases the amplitude of the accelerationgradually decreases and the high-frequency componentsattenuate especially rapidly Because the track slab is rela-tively close to the subgrade bed its peak acceleration is ap-proximately 80mms2 After passing through the track slabthe waveform at the surface layer of the subgrade bed is not assignificant as that at the track slab

It can be clearly seen from Figure 12 that after passingthrough the subgrade bed the peak acceleration decreasesfrom 80mms2 to 30mms2 that is it attenuates by 625)is is mainly because the high-frequency components areabsorbed due to the damping effect of the soil in the em-bankment while the attenuation of the low-frequencycomponents is relatively slow When reaching the bottomlayer of the foundation due to the influence of the reflectedwaves the M-shaped waveform has essentially disappearedAs a result only a simple harmonic oscillation curve is

presented and the amplitude of the acceleration vibration isonly 2 of that at the surface layer of the foundation As thedepth increases the peak acceleration responses of theM-shaped waveform at different locations do not appear atthe same time )is is because it takes time for the wave topropagate causing some lag in the acceleration response

Figure 13 shows a spectral curve of the vertical accel-eration at different locations from the vibration source whenthe train speed is 300 kmh We can see that the frequency isdistributed in the range of 0ndash100Hz and is mainly con-centrated between 10 and 50Hz making it low-frequencyvibrations As the distance from the vibration source in-creases the maximum vibration accelerations at differentlocations are 4352mms2 4082mms2 3152mms2352mms2 and 014mms2 It can be seen that as thedistance from the vibration source increases the amplitudeof the acceleration generally attenuates )e high-frequencycomponent is relatively rich at locations close to the vi-bration source and the width of the spectrum graduallydecreases when moving away from the vibration source )emost significant frequency band becomes that of the lowfrequency because the high-frequency components attenu-ate faster than the low-frequency components

We can see from the peaks in Figure 13 that the fourcharacteristic frequencies with the largest contributions to thevibration are 199Hz 233Hz 299Hz and 332Hz Amongthem 332Hz corresponds to the actuator frequency At themeasurement site of the track slab the frequency of theground vibration caused by the train is distributed within50ndash85Hz and relatively rich in the main frequency

Figure 14 shows the time-history curve of the accelerationat the surface layer of the foundation under different trainspeeds We can clearly see that as the train speed increases thehigh-frequency components significantly increase Whenthe train speed is 160 kmh the peak acceleration at the sur-face layer of the foundation is 359mms2 and when thetrain velocity increases to 200 kmh the peak acceleration atthe surface layer of the foundation reaches 724mms2

Pile topSoil

0

2

4

6

8

10

Dyn

amic

stre

ss (k

Pa)

200 300 400100Train speed (kmh)

Figure 10 Relationship curves between dynamic stress responsesof soil at pipe top and between piles and the train speed

8 Shock and Vibration

00

02

04

06

08

Dyn

amic

disp

lace

men

tof

the t

rack

slab

(mm

)

02 04 06 08 10 1200Time (s)

160kmh

(a)

00

02

04

06

08

Dyn

amic

disp

lace

men

tof

the t

rack

slab

(mm

)

02 04 06 08 10 1200Time (s)

200kmh

(b)

00

02

04

06

08

Dyn

amic

disp

lace

men

tof

the t

rack

slab

(mm

)

02 04 06 08 10 1200Time (s)

250kmh(c)

00

02

04

06

08

Dyn

amic

disp

lace

men

tof

the t

rack

slab

(mm

)

02 04 06 08 10 1200Time (s)

300kmh

(d)

00

02

04

06

08

Dyn

amic

disp

lace

men

tof

the t

rack

slab

(mm

)

02 04 06 08 10 1200Time (s)

350kmh

(e)

Figure 11 Dynamic displacement of track with respect to time

120

ndash120

80

ndash80

40

ndash400

Acc

eler

atio

nre

spon

se (m

ms

2 )

01 02 03 04 05 0600Time (s)

(a)

120

ndash120

80

ndash80

40

ndash400

Acc

eler

atio

nre

spon

se (m

ms

2 )

01 02 03 04 05 0600Time (s)

(b)120

ndash120

80

ndash80

40

ndash400

Acc

eler

atio

nre

spon

se (m

ms

2 )

01 02 03 04 05 0600Time (s)

(c)

120

ndash120

80

ndash80

40

ndash400

Acc

eler

atio

nre

spon

se (m

ms

2 )

01 02 03 04 05 0600Time (s)

(d)

Figure 12 Acceleration at different layers with respect to time (a) track slab (b) surface layer of subgrade (c) bottom layer of subgrade (d)surface layer of foundation

Shock and Vibration 9

332Hz299Hz199Hz

233Hz

0 20 30 40 50 60 70 80 90 10010Frequency (Hz)

01020304050

Acc

eler

atio

nam

plitu

de (m

ms

2 )

(a)

233Hz

332Hz299Hz199Hz

0 20 30 40 50 60 70 80 90 10010Frequency (Hz)

01020304050

Acc

eler

atio

nam

plitu

de (m

ms

2 )

(b)

332Hz299Hz

233Hz

199Hz

0 20 30 40 50 60 70 80 90 10010Frequency (Hz)

01020304050

Acc

eler

atio

nam

plitu

de (m

ms

2 )

(c)

299Hz332Hz

233Hz199Hz

0 20 30 40 50 60 70 80 90 1001Frequency (Hz)

01020304050

Acc

eler

atio

nam

plitu

de (m

ms

2 )

(d)

Figure 13 Spectral curve of acceleration at different locations (a) track slab (b) surface layer of subgrade (c) bottom layer of subgrade (d)surface layer of foundation

00 02 04Time (s)

06 08 10 12ndash10

ndash5

0

5

10

Acc

eler

atio

n re

spon

se(s

urfa

ce la

yer o

f fou

ndat

ion)

(mm

s2 )

160kmh

(a)

00 02 04 06 08 10 12ndash10

ndash5

0

5

10

Acc

eler

atio

n re

spon

se(s

urfa

ce la

yer o

f fou

ndat

ion)

(mm

s2 )

Time (s)

200kmh

(b)

00 02 04 06 08 10 12ndash10

ndash5

0

5

10

Acc

eler

atio

n re

spon

se(s

urfa

ce la

yer o

f fou

ndat

ion)

(mm

s2 )

Time (s)

250kmh

(c)

Figure 14 Continued

10 Shock and Vibration

00 02 04 06 08 10 12ndash10

ndash5

0

5

10

Acc

eler

atio

n re

spon

se(s

urfa

ce la

yer o

f fou

ndat

ion)

(mm

s2 )

Time (s)

300kmh

(d)

00 02 04 06 08 10 12ndash10

ndash5

0

5

10

Acc

eler

atio

n re

spon

se(s

urfa

ce la

yer o

f fou

ndat

ion)

(mm

s2 )

Time (s)

350kmh

(e)

Figure 14 Acceleration under different speeds with respect to time

177Hz

160kmh

0

1

2

3

Acc

eler

atio

nam

plitu

de (m

ms

2 )

20 40 60 80 1000Time (s)

(a)

200kmh

200Hz 222Hz

0

1

2

3

Acc

eler

atio

nam

plitu

de (m

ms

2 )

20 40 60 80 1000Time (s)

(b)

Figure 15 Continued

Shock and Vibration 11

(approximately double) However when the train speed rea-ches 250 kmh the increase on the peak is negligible Becausethe increase in the train speed is achieved by increasing thevibration frequency the superposition of the surroundingreflected waves in this process likely produces a counteractionto the vibration of the subgrade foundation explaining thisresult

Figure 15 shows the spectral curve of the acceleration atthe surface layer of the foundation under different trainspeeds We can see that the ground vibration caused by thetrain is mainly contributed by relatively low-frequencycomponents (mainly below 100Hz) As the train speedincreases the amplitude of the acceleration increases andthe base frequencies of the vibration also gradually increase177Hz in the base frequencies when the train velocity is160 kmh 222Hz when the train speed is 200 kmh 277Hzwhen the train speed is 250 kmh 332Hz when the trainspeed is 300 kmh and 388Hz when the train speed is350 kmh are all the vibration frequency of the actuatorunder the current working condition

As the train speed increases the peak spectral vibrationacceleration response also increases and the frequencycorresponding to the peak spectral vibration accelerationalso gradually moves to a medium frequency as the trainspeed increases )e higher the train speed the richer thefrequency components of the ground vibration

4 Conclusions

In this study by conducting a large-scale dynamic model teston an X-section pile-net composite foundation under dif-ferent train speeds we can draw the following conclusions

(1) )e response of the vertical dynamic velocity is thelargest at the surface layer of the embankment andattenuates by approximately 90 in the embank-ment )e speed rapidly attenuates as the depthincreases the vibration gradually attenuates as thedistance from the vibration source increases At thebottom layer of the subgrade bed and in the range of

250kmh

277Hz

250Hz194Hz

0

1

2

3

Acc

eler

atio

nam

plitu

de (m

ms

2 )20 40 60 80 1000

Time (s)

(c)

300kmh

199Hz

233Hz

299Hz

332Hz

0

1

2

3

4

Acc

eler

atio

nam

plitu

de (m

ms

2 )

20 40 60 80 1000Time (s)

(d)

350kmh

233Hz272Hz

349Hz

0

1

2

3

4

Acc

eler

atio

nam

plitu

de (m

ms

2 )

20 40 60 80 1000Time (s)

(e)

Figure 15 Spectrum curve of acceleration under different speeds

12 Shock and Vibration

the lower foundation the attenuation rate signifi-cantly decreases and the vibration velocity is linearlyrelated to the train speed

(2) Inside the pile-net foundation the peak dynamicstress at the top of the pile is 34 times than that in thesoil between piles and the dynamic stress attenuateswith the depth

(3) )e change in train speed does not have a largeinfluence on the peak transient dynamic displace-ment response at the surface of the track afterpassing through the subgrade bed the peak verticalacceleration decreases from approximately 80mms2to 30mms2 attenuating by 625 )is is mainlybecause the high-frequency components are absor-bed due to soil damping effects and the low-frequency components attenuate relatively slowly)e foundation vibration caused by the train is a low-frequency vibration and the subgrade foundationhas an attenuation impact on the high-frequencyvibration the vibration gradually decreases as thedistance from the vibration source increases andincreases as the train speed increases

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 there are no conflicts of interestregarding the publication of this paper

Acknowledgments

)is project was supported by the Funds for InternationalCooperation and Exchange of the National Natural ScienceFoundation of China (Grant no 51420105013)

References

[1] M A Heckl ldquoRailway noise-can random sleeper spacingshelprdquo Acta Acustica United with Acustica vol 81 no 6pp 559ndash564 1995

[2] H Takemiya and X Bian ldquoSubstructure simulation of in-homogeneous track and layered ground dynamic interactionunder train passagerdquo Journal of Engineering Mechanicsvol 131 no 7 pp 699ndash711 2005

[3] M Bahrekazemi and A Bodare ldquoEffects of lime-cement soilstabilization against train induced ground vibrationsrdquo inProceedings of the 3rd International Specialty Conference onGrouting and Ground Treatment New Orleans LA USAFebruary 2003

[4] L Bo and C Ying ldquoDynamic analysis on subgrade of highspeed railways in geometric irregular conditionrdquo Journal ofthe China Railway Society vol 21 pp 84ndash88 1999

[5] X Chen and W Y Lu Wentian ldquoStudy on the dynamic re-sponse of high speed railway bridge-subgrade transition sec-tionrdquo Journal of Vibration and Shock vol 25 pp 95ndash98 2006

[6] W F Anderson and A J Key ldquoModel testing of two-layerrailway track ballastrdquo Journal of Geotechnical and Geo-environmental Engineering vol 126 no 4 pp 317ndash323 2000

[7] S J Cox A Wang C Morison P Carels R Kelly andO G Bewes ldquoA test rig to investigate slab track structures forcontrolling ground vibrationrdquo Journal of Sound and Vibra-tion vol 293 no 3ndash5 pp 901ndash909 2006

[8] Y Zhan and G Jiang ldquoStudy of dynamic characteristics of soilsubgrade bed for ballastless trackrdquo Rock and Soil Mechanicsvol 31 pp 392ndash396 2010

[9] Y Momoya E Sekine and F Tatsuoka ldquoDeformationcharacteristics of railway roadbed and subgrade undermoving-wheel loadrdquo Soils and Foundations vol 45 no 4pp 99ndash118 2005

[10] A Al Shaer D Duhamel K Sab G Foret and L SchmittldquoExperimental settlement and dynamic behavior of a portionof ballasted railway track under high speed trainsrdquo Journal ofSound and Vibration vol 316 no 1ndash5 pp 211ndash233 2008

[11] T Ishikawa E Sekine and S Miura ldquoCyclic deformation ofgranular material subjected to moving-wheel loadsrdquo Cana-dian Geotechnical Journal vol 48 no 5 pp 691ndash703 2011

[12] G Q Kong X M Ding Y M Chen and G Yang ldquoVerticaluplift capacity characteristics and influence factor analysis ofcast-in-situ X-section reinforced concrete pile grouprdquo Journalof Civil Engineering and Architecture vol 29 pp 49ndash54 2012

[13] M X Zhang H L Liu X M Ding and Z Q WangldquoComparative tests on bearing capacity of cast-in-situX-shaped concrete piles and circular pilerdquo Chinese Journal ofGeotechnical Engineering vol 33 pp 1469ndash1476 2011

[14] Z QWang H L Liu M X Zhang J Yuan and J Yong ldquoFullscale model tests on vertical bearing characteristics of cast-in-place X-section pilesrdquo Chinese Journal of Geotechnical Engi-neering vol 32 pp 903ndash907 2010

[15] Y Jun L Xiao-Min and L Han-Long ldquoModel test study ofanti-pulling property of X-shaped concrete pilerdquo Rock andSoil Mechanics vol 31 pp 3430ndash3434 2010

[16] L Han-Long L Zhi-Ping and W Xin-Quan ldquoStudy on thegeometric characteristics of the cast-in-place X-type vibro-pilesectionrdquo China Railway Science vol 30 pp 17ndash23 2009

[17] M X Zhang S M Ding and Y M Chen ldquoTest on verticalbehavior of cast-in-situ X-shaped concrete pile and its ulti-mate bearing capacity predictionrdquo Journal of China CoalSociety vol 36 pp 267ndash271 2011

[18] L Han-Long J Hui and D Xuan-Ming ldquoField test researchon squeezing effects of X-section cast-in-place concrete pilerdquoRock and Soil Mechanics vol 33 pp 219ndash224 2012

[19] S Guang-Chao L Han-Long K Gang-Qiang and D Xuan-Ming ldquoModel tests on effect of vibration waves on dynamicresponse of XCC pile-raft composite foundationrdquo ChineseJournal of Geotechnical Engineering vol 38 pp 1021ndash10292015

Shock and Vibration 13

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

significantly slow attenuation rate indicating that the sub-grade bed has a significant reduction effect on the verticalvibration

32 Analysis of Dynamic Earth Pressure Figure 9 showstime-history curves of the dynamic soil stress at the pile topand between piles when the train speed is 300 kmh)e waveis affected by the embankment and hence attenuates during

the propagation process causing the waveform characteristicsof the M-shaped wave to have already been significantlyweakened when it reaches the surface of the foundation Wecan see that the stress at the pile top is greater than thedynamic stress of the soil between piles and the soil arch has a

V4V3

160kmh200kmh250kmh

300kmh350kmh

V0 V1 V2

05 10 15 20 2500Distance to the center (m)

0

5

10

15

20

25

30

35

40

45

Vel

ocity

resp

onse

(mm

s)

Figure 8 Vertical velocity with respect to horizontal dimension

00 01 02 03 04 05 0602468

1012

Load

(kN

)

Waveform

Time (s)

(a)

ndash202468

1012

Dyn

amic

stre

ss (k

Pa)

Pile topSoil

00 01 02Time (s)

03 04 05 06

(b)

Figure 9 Dynamic stresses of pile and soil with respect to time

6

5

4

3

2

1

0ndash5 0 5 10 15 20 25 30 35 40 45 50

6

5

4

3

2

1

0 1 2 3

Velocity response (mms)

Dep

th (m

)

160kmh200kmh250kmh

300kmh350kmh

Figure 6 Vertical velocity with respect to depth

0

10

20

30

40

50

60

Vel

ocity

resp

onse

pea

k of

the t

rack

slab

(mm

s)

A groupB groupC group

50 100 150 200 250 300 350 4000Train speed (kmh)

Figure 7 Vertical velocity with respect to train speed

Shock and Vibration 7

significant influence on the distribution of the dynamic stressIn the soil arch region a greater dynamic load is transferredabove the top of the pile )e average of the peak dynamicstresses at the pile top is approximately 62 kPa which is 34times the average of the peak dynamic earth pressure (ap-proximately 18 kPa) on the soil between the piles

Figure 10 shows relationship curves of the changes in thepeak dynamic stresses at the pile top and in the soil betweenthe piles of the foundation and the train speed We can seethat under the vibration load of the high-speed train theload carried at the pile top in the foundation is much largerthan that by the soil between the piles

Although the vibration frequency of the dynamic loadincreases as the train speed increases the influence of thetrain speed on the response of the dynamic stress is weak)is is likely because the wave gradually attenuates in theprocess of reaching the foundation through the subgradebed and its effect gradually decreases

33 Analysis of Dynamic Displacement Figure 11 shows thetime-history response curve of the dynamic displacementon the track surface under different train speeds We cansee that the change in the train speed does not have a largeinfluence on the peak transient dynamic displacementresponse on the track surface A comparison of dynamicdisplacement responses under different train speeds re-veals that the faster the train speed the more intense andshorter the induced vibration)is is because the faster thetrain speed the higher the dynamic loading frequencyWhen the train speed is not high (160 kmh) the time-history curve between the peak displacements attenuatesWhen the train speed reaches 250 kmh the displacementtime history does not significantly attenuate but insteadgradually fluctuates with time In fact the attenuationprocess is not completed

34 Analysis of Acceleration Figure 12 shows the time-history curve of the acceleration at different locations in thepile-net composite foundation when the train speed is300 kmh We can see that the vibration close to the actuatorhas a relatively large amplitude As the distance from thevibration source increases the amplitude of the accelerationgradually decreases and the high-frequency componentsattenuate especially rapidly Because the track slab is rela-tively close to the subgrade bed its peak acceleration is ap-proximately 80mms2 After passing through the track slabthe waveform at the surface layer of the subgrade bed is not assignificant as that at the track slab

It can be clearly seen from Figure 12 that after passingthrough the subgrade bed the peak acceleration decreasesfrom 80mms2 to 30mms2 that is it attenuates by 625)is is mainly because the high-frequency components areabsorbed due to the damping effect of the soil in the em-bankment while the attenuation of the low-frequencycomponents is relatively slow When reaching the bottomlayer of the foundation due to the influence of the reflectedwaves the M-shaped waveform has essentially disappearedAs a result only a simple harmonic oscillation curve is

presented and the amplitude of the acceleration vibration isonly 2 of that at the surface layer of the foundation As thedepth increases the peak acceleration responses of theM-shaped waveform at different locations do not appear atthe same time )is is because it takes time for the wave topropagate causing some lag in the acceleration response

Figure 13 shows a spectral curve of the vertical accel-eration at different locations from the vibration source whenthe train speed is 300 kmh We can see that the frequency isdistributed in the range of 0ndash100Hz and is mainly con-centrated between 10 and 50Hz making it low-frequencyvibrations As the distance from the vibration source in-creases the maximum vibration accelerations at differentlocations are 4352mms2 4082mms2 3152mms2352mms2 and 014mms2 It can be seen that as thedistance from the vibration source increases the amplitudeof the acceleration generally attenuates )e high-frequencycomponent is relatively rich at locations close to the vi-bration source and the width of the spectrum graduallydecreases when moving away from the vibration source )emost significant frequency band becomes that of the lowfrequency because the high-frequency components attenu-ate faster than the low-frequency components

We can see from the peaks in Figure 13 that the fourcharacteristic frequencies with the largest contributions to thevibration are 199Hz 233Hz 299Hz and 332Hz Amongthem 332Hz corresponds to the actuator frequency At themeasurement site of the track slab the frequency of theground vibration caused by the train is distributed within50ndash85Hz and relatively rich in the main frequency

Figure 14 shows the time-history curve of the accelerationat the surface layer of the foundation under different trainspeeds We can clearly see that as the train speed increases thehigh-frequency components significantly increase Whenthe train speed is 160 kmh the peak acceleration at the sur-face layer of the foundation is 359mms2 and when thetrain velocity increases to 200 kmh the peak acceleration atthe surface layer of the foundation reaches 724mms2

Pile topSoil

0

2

4

6

8

10

Dyn

amic

stre

ss (k

Pa)

200 300 400100Train speed (kmh)

Figure 10 Relationship curves between dynamic stress responsesof soil at pipe top and between piles and the train speed

8 Shock and Vibration

00

02

04

06

08

Dyn

amic

disp

lace

men

tof

the t

rack

slab

(mm

)

02 04 06 08 10 1200Time (s)

160kmh

(a)

00

02

04

06

08

Dyn

amic

disp

lace

men

tof

the t

rack

slab

(mm

)

02 04 06 08 10 1200Time (s)

200kmh

(b)

00

02

04

06

08

Dyn

amic

disp

lace

men

tof

the t

rack

slab

(mm

)

02 04 06 08 10 1200Time (s)

250kmh(c)

00

02

04

06

08

Dyn

amic

disp

lace

men

tof

the t

rack

slab

(mm

)

02 04 06 08 10 1200Time (s)

300kmh

(d)

00

02

04

06

08

Dyn

amic

disp

lace

men

tof

the t

rack

slab

(mm

)

02 04 06 08 10 1200Time (s)

350kmh

(e)

Figure 11 Dynamic displacement of track with respect to time

120

ndash120

80

ndash80

40

ndash400

Acc

eler

atio

nre

spon

se (m

ms

2 )

01 02 03 04 05 0600Time (s)

(a)

120

ndash120

80

ndash80

40

ndash400

Acc

eler

atio

nre

spon

se (m

ms

2 )

01 02 03 04 05 0600Time (s)

(b)120

ndash120

80

ndash80

40

ndash400

Acc

eler

atio

nre

spon

se (m

ms

2 )

01 02 03 04 05 0600Time (s)

(c)

120

ndash120

80

ndash80

40

ndash400

Acc

eler

atio

nre

spon

se (m

ms

2 )

01 02 03 04 05 0600Time (s)

(d)

Figure 12 Acceleration at different layers with respect to time (a) track slab (b) surface layer of subgrade (c) bottom layer of subgrade (d)surface layer of foundation

Shock and Vibration 9

332Hz299Hz199Hz

233Hz

0 20 30 40 50 60 70 80 90 10010Frequency (Hz)

01020304050

Acc

eler

atio

nam

plitu

de (m

ms

2 )

(a)

233Hz

332Hz299Hz199Hz

0 20 30 40 50 60 70 80 90 10010Frequency (Hz)

01020304050

Acc

eler

atio

nam

plitu

de (m

ms

2 )

(b)

332Hz299Hz

233Hz

199Hz

0 20 30 40 50 60 70 80 90 10010Frequency (Hz)

01020304050

Acc

eler

atio

nam

plitu

de (m

ms

2 )

(c)

299Hz332Hz

233Hz199Hz

0 20 30 40 50 60 70 80 90 1001Frequency (Hz)

01020304050

Acc

eler

atio

nam

plitu

de (m

ms

2 )

(d)

Figure 13 Spectral curve of acceleration at different locations (a) track slab (b) surface layer of subgrade (c) bottom layer of subgrade (d)surface layer of foundation

00 02 04Time (s)

06 08 10 12ndash10

ndash5

0

5

10

Acc

eler

atio

n re

spon

se(s

urfa

ce la

yer o

f fou

ndat

ion)

(mm

s2 )

160kmh

(a)

00 02 04 06 08 10 12ndash10

ndash5

0

5

10

Acc

eler

atio

n re

spon

se(s

urfa

ce la

yer o

f fou

ndat

ion)

(mm

s2 )

Time (s)

200kmh

(b)

00 02 04 06 08 10 12ndash10

ndash5

0

5

10

Acc

eler

atio

n re

spon

se(s

urfa

ce la

yer o

f fou

ndat

ion)

(mm

s2 )

Time (s)

250kmh

(c)

Figure 14 Continued

10 Shock and Vibration

00 02 04 06 08 10 12ndash10

ndash5

0

5

10

Acc

eler

atio

n re

spon

se(s

urfa

ce la

yer o

f fou

ndat

ion)

(mm

s2 )

Time (s)

300kmh

(d)

00 02 04 06 08 10 12ndash10

ndash5

0

5

10

Acc

eler

atio

n re

spon

se(s

urfa

ce la

yer o

f fou

ndat

ion)

(mm

s2 )

Time (s)

350kmh

(e)

Figure 14 Acceleration under different speeds with respect to time

177Hz

160kmh

0

1

2

3

Acc

eler

atio

nam

plitu

de (m

ms

2 )

20 40 60 80 1000Time (s)

(a)

200kmh

200Hz 222Hz

0

1

2

3

Acc

eler

atio

nam

plitu

de (m

ms

2 )

20 40 60 80 1000Time (s)

(b)

Figure 15 Continued

Shock and Vibration 11

(approximately double) However when the train speed rea-ches 250 kmh the increase on the peak is negligible Becausethe increase in the train speed is achieved by increasing thevibration frequency the superposition of the surroundingreflected waves in this process likely produces a counteractionto the vibration of the subgrade foundation explaining thisresult

Figure 15 shows the spectral curve of the acceleration atthe surface layer of the foundation under different trainspeeds We can see that the ground vibration caused by thetrain is mainly contributed by relatively low-frequencycomponents (mainly below 100Hz) As the train speedincreases the amplitude of the acceleration increases andthe base frequencies of the vibration also gradually increase177Hz in the base frequencies when the train velocity is160 kmh 222Hz when the train speed is 200 kmh 277Hzwhen the train speed is 250 kmh 332Hz when the trainspeed is 300 kmh and 388Hz when the train speed is350 kmh are all the vibration frequency of the actuatorunder the current working condition

As the train speed increases the peak spectral vibrationacceleration response also increases and the frequencycorresponding to the peak spectral vibration accelerationalso gradually moves to a medium frequency as the trainspeed increases )e higher the train speed the richer thefrequency components of the ground vibration

4 Conclusions

In this study by conducting a large-scale dynamic model teston an X-section pile-net composite foundation under dif-ferent train speeds we can draw the following conclusions

(1) )e response of the vertical dynamic velocity is thelargest at the surface layer of the embankment andattenuates by approximately 90 in the embank-ment )e speed rapidly attenuates as the depthincreases the vibration gradually attenuates as thedistance from the vibration source increases At thebottom layer of the subgrade bed and in the range of

250kmh

277Hz

250Hz194Hz

0

1

2

3

Acc

eler

atio

nam

plitu

de (m

ms

2 )20 40 60 80 1000

Time (s)

(c)

300kmh

199Hz

233Hz

299Hz

332Hz

0

1

2

3

4

Acc

eler

atio

nam

plitu

de (m

ms

2 )

20 40 60 80 1000Time (s)

(d)

350kmh

233Hz272Hz

349Hz

0

1

2

3

4

Acc

eler

atio

nam

plitu

de (m

ms

2 )

20 40 60 80 1000Time (s)

(e)

Figure 15 Spectrum curve of acceleration under different speeds

12 Shock and Vibration

the lower foundation the attenuation rate signifi-cantly decreases and the vibration velocity is linearlyrelated to the train speed

(2) Inside the pile-net foundation the peak dynamicstress at the top of the pile is 34 times than that in thesoil between piles and the dynamic stress attenuateswith the depth

(3) )e change in train speed does not have a largeinfluence on the peak transient dynamic displace-ment response at the surface of the track afterpassing through the subgrade bed the peak verticalacceleration decreases from approximately 80mms2to 30mms2 attenuating by 625 )is is mainlybecause the high-frequency components are absor-bed due to soil damping effects and the low-frequency components attenuate relatively slowly)e foundation vibration caused by the train is a low-frequency vibration and the subgrade foundationhas an attenuation impact on the high-frequencyvibration the vibration gradually decreases as thedistance from the vibration source increases andincreases as the train speed increases

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 there are no conflicts of interestregarding the publication of this paper

Acknowledgments

)is project was supported by the Funds for InternationalCooperation and Exchange of the National Natural ScienceFoundation of China (Grant no 51420105013)

References

[1] M A Heckl ldquoRailway noise-can random sleeper spacingshelprdquo Acta Acustica United with Acustica vol 81 no 6pp 559ndash564 1995

[2] H Takemiya and X Bian ldquoSubstructure simulation of in-homogeneous track and layered ground dynamic interactionunder train passagerdquo Journal of Engineering Mechanicsvol 131 no 7 pp 699ndash711 2005

[3] M Bahrekazemi and A Bodare ldquoEffects of lime-cement soilstabilization against train induced ground vibrationsrdquo inProceedings of the 3rd International Specialty Conference onGrouting and Ground Treatment New Orleans LA USAFebruary 2003

[4] L Bo and C Ying ldquoDynamic analysis on subgrade of highspeed railways in geometric irregular conditionrdquo Journal ofthe China Railway Society vol 21 pp 84ndash88 1999

[5] X Chen and W Y Lu Wentian ldquoStudy on the dynamic re-sponse of high speed railway bridge-subgrade transition sec-tionrdquo Journal of Vibration and Shock vol 25 pp 95ndash98 2006

[6] W F Anderson and A J Key ldquoModel testing of two-layerrailway track ballastrdquo Journal of Geotechnical and Geo-environmental Engineering vol 126 no 4 pp 317ndash323 2000

[7] S J Cox A Wang C Morison P Carels R Kelly andO G Bewes ldquoA test rig to investigate slab track structures forcontrolling ground vibrationrdquo Journal of Sound and Vibra-tion vol 293 no 3ndash5 pp 901ndash909 2006

[8] Y Zhan and G Jiang ldquoStudy of dynamic characteristics of soilsubgrade bed for ballastless trackrdquo Rock and Soil Mechanicsvol 31 pp 392ndash396 2010

[9] Y Momoya E Sekine and F Tatsuoka ldquoDeformationcharacteristics of railway roadbed and subgrade undermoving-wheel loadrdquo Soils and Foundations vol 45 no 4pp 99ndash118 2005

[10] A Al Shaer D Duhamel K Sab G Foret and L SchmittldquoExperimental settlement and dynamic behavior of a portionof ballasted railway track under high speed trainsrdquo Journal ofSound and Vibration vol 316 no 1ndash5 pp 211ndash233 2008

[11] T Ishikawa E Sekine and S Miura ldquoCyclic deformation ofgranular material subjected to moving-wheel loadsrdquo Cana-dian Geotechnical Journal vol 48 no 5 pp 691ndash703 2011

[12] G Q Kong X M Ding Y M Chen and G Yang ldquoVerticaluplift capacity characteristics and influence factor analysis ofcast-in-situ X-section reinforced concrete pile grouprdquo Journalof Civil Engineering and Architecture vol 29 pp 49ndash54 2012

[13] M X Zhang H L Liu X M Ding and Z Q WangldquoComparative tests on bearing capacity of cast-in-situX-shaped concrete piles and circular pilerdquo Chinese Journal ofGeotechnical Engineering vol 33 pp 1469ndash1476 2011

[14] Z QWang H L Liu M X Zhang J Yuan and J Yong ldquoFullscale model tests on vertical bearing characteristics of cast-in-place X-section pilesrdquo Chinese Journal of Geotechnical Engi-neering vol 32 pp 903ndash907 2010

[15] Y Jun L Xiao-Min and L Han-Long ldquoModel test study ofanti-pulling property of X-shaped concrete pilerdquo Rock andSoil Mechanics vol 31 pp 3430ndash3434 2010

[16] L Han-Long L Zhi-Ping and W Xin-Quan ldquoStudy on thegeometric characteristics of the cast-in-place X-type vibro-pilesectionrdquo China Railway Science vol 30 pp 17ndash23 2009

[17] M X Zhang S M Ding and Y M Chen ldquoTest on verticalbehavior of cast-in-situ X-shaped concrete pile and its ulti-mate bearing capacity predictionrdquo Journal of China CoalSociety vol 36 pp 267ndash271 2011

[18] L Han-Long J Hui and D Xuan-Ming ldquoField test researchon squeezing effects of X-section cast-in-place concrete pilerdquoRock and Soil Mechanics vol 33 pp 219ndash224 2012

[19] S Guang-Chao L Han-Long K Gang-Qiang and D Xuan-Ming ldquoModel tests on effect of vibration waves on dynamicresponse of XCC pile-raft composite foundationrdquo ChineseJournal of Geotechnical Engineering vol 38 pp 1021ndash10292015

Shock and Vibration 13

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significant influence on the distribution of the dynamic stressIn the soil arch region a greater dynamic load is transferredabove the top of the pile )e average of the peak dynamicstresses at the pile top is approximately 62 kPa which is 34times the average of the peak dynamic earth pressure (ap-proximately 18 kPa) on the soil between the piles

Figure 10 shows relationship curves of the changes in thepeak dynamic stresses at the pile top and in the soil betweenthe piles of the foundation and the train speed We can seethat under the vibration load of the high-speed train theload carried at the pile top in the foundation is much largerthan that by the soil between the piles

Although the vibration frequency of the dynamic loadincreases as the train speed increases the influence of thetrain speed on the response of the dynamic stress is weak)is is likely because the wave gradually attenuates in theprocess of reaching the foundation through the subgradebed and its effect gradually decreases

33 Analysis of Dynamic Displacement Figure 11 shows thetime-history response curve of the dynamic displacementon the track surface under different train speeds We cansee that the change in the train speed does not have a largeinfluence on the peak transient dynamic displacementresponse on the track surface A comparison of dynamicdisplacement responses under different train speeds re-veals that the faster the train speed the more intense andshorter the induced vibration)is is because the faster thetrain speed the higher the dynamic loading frequencyWhen the train speed is not high (160 kmh) the time-history curve between the peak displacements attenuatesWhen the train speed reaches 250 kmh the displacementtime history does not significantly attenuate but insteadgradually fluctuates with time In fact the attenuationprocess is not completed

34 Analysis of Acceleration Figure 12 shows the time-history curve of the acceleration at different locations in thepile-net composite foundation when the train speed is300 kmh We can see that the vibration close to the actuatorhas a relatively large amplitude As the distance from thevibration source increases the amplitude of the accelerationgradually decreases and the high-frequency componentsattenuate especially rapidly Because the track slab is rela-tively close to the subgrade bed its peak acceleration is ap-proximately 80mms2 After passing through the track slabthe waveform at the surface layer of the subgrade bed is not assignificant as that at the track slab

It can be clearly seen from Figure 12 that after passingthrough the subgrade bed the peak acceleration decreasesfrom 80mms2 to 30mms2 that is it attenuates by 625)is is mainly because the high-frequency components areabsorbed due to the damping effect of the soil in the em-bankment while the attenuation of the low-frequencycomponents is relatively slow When reaching the bottomlayer of the foundation due to the influence of the reflectedwaves the M-shaped waveform has essentially disappearedAs a result only a simple harmonic oscillation curve is

presented and the amplitude of the acceleration vibration isonly 2 of that at the surface layer of the foundation As thedepth increases the peak acceleration responses of theM-shaped waveform at different locations do not appear atthe same time )is is because it takes time for the wave topropagate causing some lag in the acceleration response

Figure 13 shows a spectral curve of the vertical accel-eration at different locations from the vibration source whenthe train speed is 300 kmh We can see that the frequency isdistributed in the range of 0ndash100Hz and is mainly con-centrated between 10 and 50Hz making it low-frequencyvibrations As the distance from the vibration source in-creases the maximum vibration accelerations at differentlocations are 4352mms2 4082mms2 3152mms2352mms2 and 014mms2 It can be seen that as thedistance from the vibration source increases the amplitudeof the acceleration generally attenuates )e high-frequencycomponent is relatively rich at locations close to the vi-bration source and the width of the spectrum graduallydecreases when moving away from the vibration source )emost significant frequency band becomes that of the lowfrequency because the high-frequency components attenu-ate faster than the low-frequency components

We can see from the peaks in Figure 13 that the fourcharacteristic frequencies with the largest contributions to thevibration are 199Hz 233Hz 299Hz and 332Hz Amongthem 332Hz corresponds to the actuator frequency At themeasurement site of the track slab the frequency of theground vibration caused by the train is distributed within50ndash85Hz and relatively rich in the main frequency

Figure 14 shows the time-history curve of the accelerationat the surface layer of the foundation under different trainspeeds We can clearly see that as the train speed increases thehigh-frequency components significantly increase Whenthe train speed is 160 kmh the peak acceleration at the sur-face layer of the foundation is 359mms2 and when thetrain velocity increases to 200 kmh the peak acceleration atthe surface layer of the foundation reaches 724mms2

Pile topSoil

0

2

4

6

8

10

Dyn

amic

stre

ss (k

Pa)

200 300 400100Train speed (kmh)

Figure 10 Relationship curves between dynamic stress responsesof soil at pipe top and between piles and the train speed

8 Shock and Vibration

00

02

04

06

08

Dyn

amic

disp

lace

men

tof

the t

rack

slab

(mm

)

02 04 06 08 10 1200Time (s)

160kmh

(a)

00

02

04

06

08

Dyn

amic

disp

lace

men

tof

the t

rack

slab

(mm

)

02 04 06 08 10 1200Time (s)

200kmh

(b)

00

02

04

06

08

Dyn

amic

disp

lace

men

tof

the t

rack

slab

(mm

)

02 04 06 08 10 1200Time (s)

250kmh(c)

00

02

04

06

08

Dyn

amic

disp

lace

men

tof

the t

rack

slab

(mm

)

02 04 06 08 10 1200Time (s)

300kmh

(d)

00

02

04

06

08

Dyn

amic

disp

lace

men

tof

the t

rack

slab

(mm

)

02 04 06 08 10 1200Time (s)

350kmh

(e)

Figure 11 Dynamic displacement of track with respect to time

120

ndash120

80

ndash80

40

ndash400

Acc

eler

atio

nre

spon

se (m

ms

2 )

01 02 03 04 05 0600Time (s)

(a)

120

ndash120

80

ndash80

40

ndash400

Acc

eler

atio

nre

spon

se (m

ms

2 )

01 02 03 04 05 0600Time (s)

(b)120

ndash120

80

ndash80

40

ndash400

Acc

eler

atio

nre

spon

se (m

ms

2 )

01 02 03 04 05 0600Time (s)

(c)

120

ndash120

80

ndash80

40

ndash400

Acc

eler

atio

nre

spon

se (m

ms

2 )

01 02 03 04 05 0600Time (s)

(d)

Figure 12 Acceleration at different layers with respect to time (a) track slab (b) surface layer of subgrade (c) bottom layer of subgrade (d)surface layer of foundation

Shock and Vibration 9

332Hz299Hz199Hz

233Hz

0 20 30 40 50 60 70 80 90 10010Frequency (Hz)

01020304050

Acc

eler

atio

nam

plitu

de (m

ms

2 )

(a)

233Hz

332Hz299Hz199Hz

0 20 30 40 50 60 70 80 90 10010Frequency (Hz)

01020304050

Acc

eler

atio

nam

plitu

de (m

ms

2 )

(b)

332Hz299Hz

233Hz

199Hz

0 20 30 40 50 60 70 80 90 10010Frequency (Hz)

01020304050

Acc

eler

atio

nam

plitu

de (m

ms

2 )

(c)

299Hz332Hz

233Hz199Hz

0 20 30 40 50 60 70 80 90 1001Frequency (Hz)

01020304050

Acc

eler

atio

nam

plitu

de (m

ms

2 )

(d)

Figure 13 Spectral curve of acceleration at different locations (a) track slab (b) surface layer of subgrade (c) bottom layer of subgrade (d)surface layer of foundation

00 02 04Time (s)

06 08 10 12ndash10

ndash5

0

5

10

Acc

eler

atio

n re

spon

se(s

urfa

ce la

yer o

f fou

ndat

ion)

(mm

s2 )

160kmh

(a)

00 02 04 06 08 10 12ndash10

ndash5

0

5

10

Acc

eler

atio

n re

spon

se(s

urfa

ce la

yer o

f fou

ndat

ion)

(mm

s2 )

Time (s)

200kmh

(b)

00 02 04 06 08 10 12ndash10

ndash5

0

5

10

Acc

eler

atio

n re

spon

se(s

urfa

ce la

yer o

f fou

ndat

ion)

(mm

s2 )

Time (s)

250kmh

(c)

Figure 14 Continued

10 Shock and Vibration

00 02 04 06 08 10 12ndash10

ndash5

0

5

10

Acc

eler

atio

n re

spon

se(s

urfa

ce la

yer o

f fou

ndat

ion)

(mm

s2 )

Time (s)

300kmh

(d)

00 02 04 06 08 10 12ndash10

ndash5

0

5

10

Acc

eler

atio

n re

spon

se(s

urfa

ce la

yer o

f fou

ndat

ion)

(mm

s2 )

Time (s)

350kmh

(e)

Figure 14 Acceleration under different speeds with respect to time

177Hz

160kmh

0

1

2

3

Acc

eler

atio

nam

plitu

de (m

ms

2 )

20 40 60 80 1000Time (s)

(a)

200kmh

200Hz 222Hz

0

1

2

3

Acc

eler

atio

nam

plitu

de (m

ms

2 )

20 40 60 80 1000Time (s)

(b)

Figure 15 Continued

Shock and Vibration 11

(approximately double) However when the train speed rea-ches 250 kmh the increase on the peak is negligible Becausethe increase in the train speed is achieved by increasing thevibration frequency the superposition of the surroundingreflected waves in this process likely produces a counteractionto the vibration of the subgrade foundation explaining thisresult

Figure 15 shows the spectral curve of the acceleration atthe surface layer of the foundation under different trainspeeds We can see that the ground vibration caused by thetrain is mainly contributed by relatively low-frequencycomponents (mainly below 100Hz) As the train speedincreases the amplitude of the acceleration increases andthe base frequencies of the vibration also gradually increase177Hz in the base frequencies when the train velocity is160 kmh 222Hz when the train speed is 200 kmh 277Hzwhen the train speed is 250 kmh 332Hz when the trainspeed is 300 kmh and 388Hz when the train speed is350 kmh are all the vibration frequency of the actuatorunder the current working condition

As the train speed increases the peak spectral vibrationacceleration response also increases and the frequencycorresponding to the peak spectral vibration accelerationalso gradually moves to a medium frequency as the trainspeed increases )e higher the train speed the richer thefrequency components of the ground vibration

4 Conclusions

In this study by conducting a large-scale dynamic model teston an X-section pile-net composite foundation under dif-ferent train speeds we can draw the following conclusions

(1) )e response of the vertical dynamic velocity is thelargest at the surface layer of the embankment andattenuates by approximately 90 in the embank-ment )e speed rapidly attenuates as the depthincreases the vibration gradually attenuates as thedistance from the vibration source increases At thebottom layer of the subgrade bed and in the range of

250kmh

277Hz

250Hz194Hz

0

1

2

3

Acc

eler

atio

nam

plitu

de (m

ms

2 )20 40 60 80 1000

Time (s)

(c)

300kmh

199Hz

233Hz

299Hz

332Hz

0

1

2

3

4

Acc

eler

atio

nam

plitu

de (m

ms

2 )

20 40 60 80 1000Time (s)

(d)

350kmh

233Hz272Hz

349Hz

0

1

2

3

4

Acc

eler

atio

nam

plitu

de (m

ms

2 )

20 40 60 80 1000Time (s)

(e)

Figure 15 Spectrum curve of acceleration under different speeds

12 Shock and Vibration

the lower foundation the attenuation rate signifi-cantly decreases and the vibration velocity is linearlyrelated to the train speed

(2) Inside the pile-net foundation the peak dynamicstress at the top of the pile is 34 times than that in thesoil between piles and the dynamic stress attenuateswith the depth

(3) )e change in train speed does not have a largeinfluence on the peak transient dynamic displace-ment response at the surface of the track afterpassing through the subgrade bed the peak verticalacceleration decreases from approximately 80mms2to 30mms2 attenuating by 625 )is is mainlybecause the high-frequency components are absor-bed due to soil damping effects and the low-frequency components attenuate relatively slowly)e foundation vibration caused by the train is a low-frequency vibration and the subgrade foundationhas an attenuation impact on the high-frequencyvibration the vibration gradually decreases as thedistance from the vibration source increases andincreases as the train speed increases

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 there are no conflicts of interestregarding the publication of this paper

Acknowledgments

)is project was supported by the Funds for InternationalCooperation and Exchange of the National Natural ScienceFoundation of China (Grant no 51420105013)

References

[1] M A Heckl ldquoRailway noise-can random sleeper spacingshelprdquo Acta Acustica United with Acustica vol 81 no 6pp 559ndash564 1995

[2] H Takemiya and X Bian ldquoSubstructure simulation of in-homogeneous track and layered ground dynamic interactionunder train passagerdquo Journal of Engineering Mechanicsvol 131 no 7 pp 699ndash711 2005

[3] M Bahrekazemi and A Bodare ldquoEffects of lime-cement soilstabilization against train induced ground vibrationsrdquo inProceedings of the 3rd International Specialty Conference onGrouting and Ground Treatment New Orleans LA USAFebruary 2003

[4] L Bo and C Ying ldquoDynamic analysis on subgrade of highspeed railways in geometric irregular conditionrdquo Journal ofthe China Railway Society vol 21 pp 84ndash88 1999

[5] X Chen and W Y Lu Wentian ldquoStudy on the dynamic re-sponse of high speed railway bridge-subgrade transition sec-tionrdquo Journal of Vibration and Shock vol 25 pp 95ndash98 2006

[6] W F Anderson and A J Key ldquoModel testing of two-layerrailway track ballastrdquo Journal of Geotechnical and Geo-environmental Engineering vol 126 no 4 pp 317ndash323 2000

[7] S J Cox A Wang C Morison P Carels R Kelly andO G Bewes ldquoA test rig to investigate slab track structures forcontrolling ground vibrationrdquo Journal of Sound and Vibra-tion vol 293 no 3ndash5 pp 901ndash909 2006

[8] Y Zhan and G Jiang ldquoStudy of dynamic characteristics of soilsubgrade bed for ballastless trackrdquo Rock and Soil Mechanicsvol 31 pp 392ndash396 2010

[9] Y Momoya E Sekine and F Tatsuoka ldquoDeformationcharacteristics of railway roadbed and subgrade undermoving-wheel loadrdquo Soils and Foundations vol 45 no 4pp 99ndash118 2005

[10] A Al Shaer D Duhamel K Sab G Foret and L SchmittldquoExperimental settlement and dynamic behavior of a portionof ballasted railway track under high speed trainsrdquo Journal ofSound and Vibration vol 316 no 1ndash5 pp 211ndash233 2008

[11] T Ishikawa E Sekine and S Miura ldquoCyclic deformation ofgranular material subjected to moving-wheel loadsrdquo Cana-dian Geotechnical Journal vol 48 no 5 pp 691ndash703 2011

[12] G Q Kong X M Ding Y M Chen and G Yang ldquoVerticaluplift capacity characteristics and influence factor analysis ofcast-in-situ X-section reinforced concrete pile grouprdquo Journalof Civil Engineering and Architecture vol 29 pp 49ndash54 2012

[13] M X Zhang H L Liu X M Ding and Z Q WangldquoComparative tests on bearing capacity of cast-in-situX-shaped concrete piles and circular pilerdquo Chinese Journal ofGeotechnical Engineering vol 33 pp 1469ndash1476 2011

[14] Z QWang H L Liu M X Zhang J Yuan and J Yong ldquoFullscale model tests on vertical bearing characteristics of cast-in-place X-section pilesrdquo Chinese Journal of Geotechnical Engi-neering vol 32 pp 903ndash907 2010

[15] Y Jun L Xiao-Min and L Han-Long ldquoModel test study ofanti-pulling property of X-shaped concrete pilerdquo Rock andSoil Mechanics vol 31 pp 3430ndash3434 2010

[16] L Han-Long L Zhi-Ping and W Xin-Quan ldquoStudy on thegeometric characteristics of the cast-in-place X-type vibro-pilesectionrdquo China Railway Science vol 30 pp 17ndash23 2009

[17] M X Zhang S M Ding and Y M Chen ldquoTest on verticalbehavior of cast-in-situ X-shaped concrete pile and its ulti-mate bearing capacity predictionrdquo Journal of China CoalSociety vol 36 pp 267ndash271 2011

[18] L Han-Long J Hui and D Xuan-Ming ldquoField test researchon squeezing effects of X-section cast-in-place concrete pilerdquoRock and Soil Mechanics vol 33 pp 219ndash224 2012

[19] S Guang-Chao L Han-Long K Gang-Qiang and D Xuan-Ming ldquoModel tests on effect of vibration waves on dynamicresponse of XCC pile-raft composite foundationrdquo ChineseJournal of Geotechnical Engineering vol 38 pp 1021ndash10292015

Shock and Vibration 13

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

00

02

04

06

08

Dyn

amic

disp

lace

men

tof

the t

rack

slab

(mm

)

02 04 06 08 10 1200Time (s)

160kmh

(a)

00

02

04

06

08

Dyn

amic

disp

lace

men

tof

the t

rack

slab

(mm

)

02 04 06 08 10 1200Time (s)

200kmh

(b)

00

02

04

06

08

Dyn

amic

disp

lace

men

tof

the t

rack

slab

(mm

)

02 04 06 08 10 1200Time (s)

250kmh(c)

00

02

04

06

08

Dyn

amic

disp

lace

men

tof

the t

rack

slab

(mm

)

02 04 06 08 10 1200Time (s)

300kmh

(d)

00

02

04

06

08

Dyn

amic

disp

lace

men

tof

the t

rack

slab

(mm

)

02 04 06 08 10 1200Time (s)

350kmh

(e)

Figure 11 Dynamic displacement of track with respect to time

120

ndash120

80

ndash80

40

ndash400

Acc

eler

atio

nre

spon

se (m

ms

2 )

01 02 03 04 05 0600Time (s)

(a)

120

ndash120

80

ndash80

40

ndash400

Acc

eler

atio

nre

spon

se (m

ms

2 )

01 02 03 04 05 0600Time (s)

(b)120

ndash120

80

ndash80

40

ndash400

Acc

eler

atio

nre

spon

se (m

ms

2 )

01 02 03 04 05 0600Time (s)

(c)

120

ndash120

80

ndash80

40

ndash400

Acc

eler

atio

nre

spon

se (m

ms

2 )

01 02 03 04 05 0600Time (s)

(d)

Figure 12 Acceleration at different layers with respect to time (a) track slab (b) surface layer of subgrade (c) bottom layer of subgrade (d)surface layer of foundation

Shock and Vibration 9

332Hz299Hz199Hz

233Hz

0 20 30 40 50 60 70 80 90 10010Frequency (Hz)

01020304050

Acc

eler

atio

nam

plitu

de (m

ms

2 )

(a)

233Hz

332Hz299Hz199Hz

0 20 30 40 50 60 70 80 90 10010Frequency (Hz)

01020304050

Acc

eler

atio

nam

plitu

de (m

ms

2 )

(b)

332Hz299Hz

233Hz

199Hz

0 20 30 40 50 60 70 80 90 10010Frequency (Hz)

01020304050

Acc

eler

atio

nam

plitu

de (m

ms

2 )

(c)

299Hz332Hz

233Hz199Hz

0 20 30 40 50 60 70 80 90 1001Frequency (Hz)

01020304050

Acc

eler

atio

nam

plitu

de (m

ms

2 )

(d)

Figure 13 Spectral curve of acceleration at different locations (a) track slab (b) surface layer of subgrade (c) bottom layer of subgrade (d)surface layer of foundation

00 02 04Time (s)

06 08 10 12ndash10

ndash5

0

5

10

Acc

eler

atio

n re

spon

se(s

urfa

ce la

yer o

f fou

ndat

ion)

(mm

s2 )

160kmh

(a)

00 02 04 06 08 10 12ndash10

ndash5

0

5

10

Acc

eler

atio

n re

spon

se(s

urfa

ce la

yer o

f fou

ndat

ion)

(mm

s2 )

Time (s)

200kmh

(b)

00 02 04 06 08 10 12ndash10

ndash5

0

5

10

Acc

eler

atio

n re

spon

se(s

urfa

ce la

yer o

f fou

ndat

ion)

(mm

s2 )

Time (s)

250kmh

(c)

Figure 14 Continued

10 Shock and Vibration

00 02 04 06 08 10 12ndash10

ndash5

0

5

10

Acc

eler

atio

n re

spon

se(s

urfa

ce la

yer o

f fou

ndat

ion)

(mm

s2 )

Time (s)

300kmh

(d)

00 02 04 06 08 10 12ndash10

ndash5

0

5

10

Acc

eler

atio

n re

spon

se(s

urfa

ce la

yer o

f fou

ndat

ion)

(mm

s2 )

Time (s)

350kmh

(e)

Figure 14 Acceleration under different speeds with respect to time

177Hz

160kmh

0

1

2

3

Acc

eler

atio

nam

plitu

de (m

ms

2 )

20 40 60 80 1000Time (s)

(a)

200kmh

200Hz 222Hz

0

1

2

3

Acc

eler

atio

nam

plitu

de (m

ms

2 )

20 40 60 80 1000Time (s)

(b)

Figure 15 Continued

Shock and Vibration 11

(approximately double) However when the train speed rea-ches 250 kmh the increase on the peak is negligible Becausethe increase in the train speed is achieved by increasing thevibration frequency the superposition of the surroundingreflected waves in this process likely produces a counteractionto the vibration of the subgrade foundation explaining thisresult

Figure 15 shows the spectral curve of the acceleration atthe surface layer of the foundation under different trainspeeds We can see that the ground vibration caused by thetrain is mainly contributed by relatively low-frequencycomponents (mainly below 100Hz) As the train speedincreases the amplitude of the acceleration increases andthe base frequencies of the vibration also gradually increase177Hz in the base frequencies when the train velocity is160 kmh 222Hz when the train speed is 200 kmh 277Hzwhen the train speed is 250 kmh 332Hz when the trainspeed is 300 kmh and 388Hz when the train speed is350 kmh are all the vibration frequency of the actuatorunder the current working condition

As the train speed increases the peak spectral vibrationacceleration response also increases and the frequencycorresponding to the peak spectral vibration accelerationalso gradually moves to a medium frequency as the trainspeed increases )e higher the train speed the richer thefrequency components of the ground vibration

4 Conclusions

In this study by conducting a large-scale dynamic model teston an X-section pile-net composite foundation under dif-ferent train speeds we can draw the following conclusions

(1) )e response of the vertical dynamic velocity is thelargest at the surface layer of the embankment andattenuates by approximately 90 in the embank-ment )e speed rapidly attenuates as the depthincreases the vibration gradually attenuates as thedistance from the vibration source increases At thebottom layer of the subgrade bed and in the range of

250kmh

277Hz

250Hz194Hz

0

1

2

3

Acc

eler

atio

nam

plitu

de (m

ms

2 )20 40 60 80 1000

Time (s)

(c)

300kmh

199Hz

233Hz

299Hz

332Hz

0

1

2

3

4

Acc

eler

atio

nam

plitu

de (m

ms

2 )

20 40 60 80 1000Time (s)

(d)

350kmh

233Hz272Hz

349Hz

0

1

2

3

4

Acc

eler

atio

nam

plitu

de (m

ms

2 )

20 40 60 80 1000Time (s)

(e)

Figure 15 Spectrum curve of acceleration under different speeds

12 Shock and Vibration

the lower foundation the attenuation rate signifi-cantly decreases and the vibration velocity is linearlyrelated to the train speed

(2) Inside the pile-net foundation the peak dynamicstress at the top of the pile is 34 times than that in thesoil between piles and the dynamic stress attenuateswith the depth

(3) )e change in train speed does not have a largeinfluence on the peak transient dynamic displace-ment response at the surface of the track afterpassing through the subgrade bed the peak verticalacceleration decreases from approximately 80mms2to 30mms2 attenuating by 625 )is is mainlybecause the high-frequency components are absor-bed due to soil damping effects and the low-frequency components attenuate relatively slowly)e foundation vibration caused by the train is a low-frequency vibration and the subgrade foundationhas an attenuation impact on the high-frequencyvibration the vibration gradually decreases as thedistance from the vibration source increases andincreases as the train speed increases

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 there are no conflicts of interestregarding the publication of this paper

Acknowledgments

)is project was supported by the Funds for InternationalCooperation and Exchange of the National Natural ScienceFoundation of China (Grant no 51420105013)

References

[1] M A Heckl ldquoRailway noise-can random sleeper spacingshelprdquo Acta Acustica United with Acustica vol 81 no 6pp 559ndash564 1995

[2] H Takemiya and X Bian ldquoSubstructure simulation of in-homogeneous track and layered ground dynamic interactionunder train passagerdquo Journal of Engineering Mechanicsvol 131 no 7 pp 699ndash711 2005

[3] M Bahrekazemi and A Bodare ldquoEffects of lime-cement soilstabilization against train induced ground vibrationsrdquo inProceedings of the 3rd International Specialty Conference onGrouting and Ground Treatment New Orleans LA USAFebruary 2003

[4] L Bo and C Ying ldquoDynamic analysis on subgrade of highspeed railways in geometric irregular conditionrdquo Journal ofthe China Railway Society vol 21 pp 84ndash88 1999

[5] X Chen and W Y Lu Wentian ldquoStudy on the dynamic re-sponse of high speed railway bridge-subgrade transition sec-tionrdquo Journal of Vibration and Shock vol 25 pp 95ndash98 2006

[6] W F Anderson and A J Key ldquoModel testing of two-layerrailway track ballastrdquo Journal of Geotechnical and Geo-environmental Engineering vol 126 no 4 pp 317ndash323 2000

[7] S J Cox A Wang C Morison P Carels R Kelly andO G Bewes ldquoA test rig to investigate slab track structures forcontrolling ground vibrationrdquo Journal of Sound and Vibra-tion vol 293 no 3ndash5 pp 901ndash909 2006

[8] Y Zhan and G Jiang ldquoStudy of dynamic characteristics of soilsubgrade bed for ballastless trackrdquo Rock and Soil Mechanicsvol 31 pp 392ndash396 2010

[9] Y Momoya E Sekine and F Tatsuoka ldquoDeformationcharacteristics of railway roadbed and subgrade undermoving-wheel loadrdquo Soils and Foundations vol 45 no 4pp 99ndash118 2005

[10] A Al Shaer D Duhamel K Sab G Foret and L SchmittldquoExperimental settlement and dynamic behavior of a portionof ballasted railway track under high speed trainsrdquo Journal ofSound and Vibration vol 316 no 1ndash5 pp 211ndash233 2008

[11] T Ishikawa E Sekine and S Miura ldquoCyclic deformation ofgranular material subjected to moving-wheel loadsrdquo Cana-dian Geotechnical Journal vol 48 no 5 pp 691ndash703 2011

[12] G Q Kong X M Ding Y M Chen and G Yang ldquoVerticaluplift capacity characteristics and influence factor analysis ofcast-in-situ X-section reinforced concrete pile grouprdquo Journalof Civil Engineering and Architecture vol 29 pp 49ndash54 2012

[13] M X Zhang H L Liu X M Ding and Z Q WangldquoComparative tests on bearing capacity of cast-in-situX-shaped concrete piles and circular pilerdquo Chinese Journal ofGeotechnical Engineering vol 33 pp 1469ndash1476 2011

[14] Z QWang H L Liu M X Zhang J Yuan and J Yong ldquoFullscale model tests on vertical bearing characteristics of cast-in-place X-section pilesrdquo Chinese Journal of Geotechnical Engi-neering vol 32 pp 903ndash907 2010

[15] Y Jun L Xiao-Min and L Han-Long ldquoModel test study ofanti-pulling property of X-shaped concrete pilerdquo Rock andSoil Mechanics vol 31 pp 3430ndash3434 2010

[16] L Han-Long L Zhi-Ping and W Xin-Quan ldquoStudy on thegeometric characteristics of the cast-in-place X-type vibro-pilesectionrdquo China Railway Science vol 30 pp 17ndash23 2009

[17] M X Zhang S M Ding and Y M Chen ldquoTest on verticalbehavior of cast-in-situ X-shaped concrete pile and its ulti-mate bearing capacity predictionrdquo Journal of China CoalSociety vol 36 pp 267ndash271 2011

[18] L Han-Long J Hui and D Xuan-Ming ldquoField test researchon squeezing effects of X-section cast-in-place concrete pilerdquoRock and Soil Mechanics vol 33 pp 219ndash224 2012

[19] S Guang-Chao L Han-Long K Gang-Qiang and D Xuan-Ming ldquoModel tests on effect of vibration waves on dynamicresponse of XCC pile-raft composite foundationrdquo ChineseJournal of Geotechnical Engineering vol 38 pp 1021ndash10292015

Shock and Vibration 13

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

332Hz299Hz199Hz

233Hz

0 20 30 40 50 60 70 80 90 10010Frequency (Hz)

01020304050

Acc

eler

atio

nam

plitu

de (m

ms

2 )

(a)

233Hz

332Hz299Hz199Hz

0 20 30 40 50 60 70 80 90 10010Frequency (Hz)

01020304050

Acc

eler

atio

nam

plitu

de (m

ms

2 )

(b)

332Hz299Hz

233Hz

199Hz

0 20 30 40 50 60 70 80 90 10010Frequency (Hz)

01020304050

Acc

eler

atio

nam

plitu

de (m

ms

2 )

(c)

299Hz332Hz

233Hz199Hz

0 20 30 40 50 60 70 80 90 1001Frequency (Hz)

01020304050

Acc

eler

atio

nam

plitu

de (m

ms

2 )

(d)

Figure 13 Spectral curve of acceleration at different locations (a) track slab (b) surface layer of subgrade (c) bottom layer of subgrade (d)surface layer of foundation

00 02 04Time (s)

06 08 10 12ndash10

ndash5

0

5

10

Acc

eler

atio

n re

spon

se(s

urfa

ce la

yer o

f fou

ndat

ion)

(mm

s2 )

160kmh

(a)

00 02 04 06 08 10 12ndash10

ndash5

0

5

10

Acc

eler

atio

n re

spon

se(s

urfa

ce la

yer o

f fou

ndat

ion)

(mm

s2 )

Time (s)

200kmh

(b)

00 02 04 06 08 10 12ndash10

ndash5

0

5

10

Acc

eler

atio

n re

spon

se(s

urfa

ce la

yer o

f fou

ndat

ion)

(mm

s2 )

Time (s)

250kmh

(c)

Figure 14 Continued

10 Shock and Vibration

00 02 04 06 08 10 12ndash10

ndash5

0

5

10

Acc

eler

atio

n re

spon

se(s

urfa

ce la

yer o

f fou

ndat

ion)

(mm

s2 )

Time (s)

300kmh

(d)

00 02 04 06 08 10 12ndash10

ndash5

0

5

10

Acc

eler

atio

n re

spon

se(s

urfa

ce la

yer o

f fou

ndat

ion)

(mm

s2 )

Time (s)

350kmh

(e)

Figure 14 Acceleration under different speeds with respect to time

177Hz

160kmh

0

1

2

3

Acc

eler

atio

nam

plitu

de (m

ms

2 )

20 40 60 80 1000Time (s)

(a)

200kmh

200Hz 222Hz

0

1

2

3

Acc

eler

atio

nam

plitu

de (m

ms

2 )

20 40 60 80 1000Time (s)

(b)

Figure 15 Continued

Shock and Vibration 11

(approximately double) However when the train speed rea-ches 250 kmh the increase on the peak is negligible Becausethe increase in the train speed is achieved by increasing thevibration frequency the superposition of the surroundingreflected waves in this process likely produces a counteractionto the vibration of the subgrade foundation explaining thisresult

Figure 15 shows the spectral curve of the acceleration atthe surface layer of the foundation under different trainspeeds We can see that the ground vibration caused by thetrain is mainly contributed by relatively low-frequencycomponents (mainly below 100Hz) As the train speedincreases the amplitude of the acceleration increases andthe base frequencies of the vibration also gradually increase177Hz in the base frequencies when the train velocity is160 kmh 222Hz when the train speed is 200 kmh 277Hzwhen the train speed is 250 kmh 332Hz when the trainspeed is 300 kmh and 388Hz when the train speed is350 kmh are all the vibration frequency of the actuatorunder the current working condition

As the train speed increases the peak spectral vibrationacceleration response also increases and the frequencycorresponding to the peak spectral vibration accelerationalso gradually moves to a medium frequency as the trainspeed increases )e higher the train speed the richer thefrequency components of the ground vibration

4 Conclusions

In this study by conducting a large-scale dynamic model teston an X-section pile-net composite foundation under dif-ferent train speeds we can draw the following conclusions

(1) )e response of the vertical dynamic velocity is thelargest at the surface layer of the embankment andattenuates by approximately 90 in the embank-ment )e speed rapidly attenuates as the depthincreases the vibration gradually attenuates as thedistance from the vibration source increases At thebottom layer of the subgrade bed and in the range of

250kmh

277Hz

250Hz194Hz

0

1

2

3

Acc

eler

atio

nam

plitu

de (m

ms

2 )20 40 60 80 1000

Time (s)

(c)

300kmh

199Hz

233Hz

299Hz

332Hz

0

1

2

3

4

Acc

eler

atio

nam

plitu

de (m

ms

2 )

20 40 60 80 1000Time (s)

(d)

350kmh

233Hz272Hz

349Hz

0

1

2

3

4

Acc

eler

atio

nam

plitu

de (m

ms

2 )

20 40 60 80 1000Time (s)

(e)

Figure 15 Spectrum curve of acceleration under different speeds

12 Shock and Vibration

the lower foundation the attenuation rate signifi-cantly decreases and the vibration velocity is linearlyrelated to the train speed

(2) Inside the pile-net foundation the peak dynamicstress at the top of the pile is 34 times than that in thesoil between piles and the dynamic stress attenuateswith the depth

(3) )e change in train speed does not have a largeinfluence on the peak transient dynamic displace-ment response at the surface of the track afterpassing through the subgrade bed the peak verticalacceleration decreases from approximately 80mms2to 30mms2 attenuating by 625 )is is mainlybecause the high-frequency components are absor-bed due to soil damping effects and the low-frequency components attenuate relatively slowly)e foundation vibration caused by the train is a low-frequency vibration and the subgrade foundationhas an attenuation impact on the high-frequencyvibration the vibration gradually decreases as thedistance from the vibration source increases andincreases as the train speed increases

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 there are no conflicts of interestregarding the publication of this paper

Acknowledgments

)is project was supported by the Funds for InternationalCooperation and Exchange of the National Natural ScienceFoundation of China (Grant no 51420105013)

References

[1] M A Heckl ldquoRailway noise-can random sleeper spacingshelprdquo Acta Acustica United with Acustica vol 81 no 6pp 559ndash564 1995

[2] H Takemiya and X Bian ldquoSubstructure simulation of in-homogeneous track and layered ground dynamic interactionunder train passagerdquo Journal of Engineering Mechanicsvol 131 no 7 pp 699ndash711 2005

[3] M Bahrekazemi and A Bodare ldquoEffects of lime-cement soilstabilization against train induced ground vibrationsrdquo inProceedings of the 3rd International Specialty Conference onGrouting and Ground Treatment New Orleans LA USAFebruary 2003

[4] L Bo and C Ying ldquoDynamic analysis on subgrade of highspeed railways in geometric irregular conditionrdquo Journal ofthe China Railway Society vol 21 pp 84ndash88 1999

[5] X Chen and W Y Lu Wentian ldquoStudy on the dynamic re-sponse of high speed railway bridge-subgrade transition sec-tionrdquo Journal of Vibration and Shock vol 25 pp 95ndash98 2006

[6] W F Anderson and A J Key ldquoModel testing of two-layerrailway track ballastrdquo Journal of Geotechnical and Geo-environmental Engineering vol 126 no 4 pp 317ndash323 2000

[7] S J Cox A Wang C Morison P Carels R Kelly andO G Bewes ldquoA test rig to investigate slab track structures forcontrolling ground vibrationrdquo Journal of Sound and Vibra-tion vol 293 no 3ndash5 pp 901ndash909 2006

[8] Y Zhan and G Jiang ldquoStudy of dynamic characteristics of soilsubgrade bed for ballastless trackrdquo Rock and Soil Mechanicsvol 31 pp 392ndash396 2010

[9] Y Momoya E Sekine and F Tatsuoka ldquoDeformationcharacteristics of railway roadbed and subgrade undermoving-wheel loadrdquo Soils and Foundations vol 45 no 4pp 99ndash118 2005

[10] A Al Shaer D Duhamel K Sab G Foret and L SchmittldquoExperimental settlement and dynamic behavior of a portionof ballasted railway track under high speed trainsrdquo Journal ofSound and Vibration vol 316 no 1ndash5 pp 211ndash233 2008

[11] T Ishikawa E Sekine and S Miura ldquoCyclic deformation ofgranular material subjected to moving-wheel loadsrdquo Cana-dian Geotechnical Journal vol 48 no 5 pp 691ndash703 2011

[12] G Q Kong X M Ding Y M Chen and G Yang ldquoVerticaluplift capacity characteristics and influence factor analysis ofcast-in-situ X-section reinforced concrete pile grouprdquo Journalof Civil Engineering and Architecture vol 29 pp 49ndash54 2012

[13] M X Zhang H L Liu X M Ding and Z Q WangldquoComparative tests on bearing capacity of cast-in-situX-shaped concrete piles and circular pilerdquo Chinese Journal ofGeotechnical Engineering vol 33 pp 1469ndash1476 2011

[14] Z QWang H L Liu M X Zhang J Yuan and J Yong ldquoFullscale model tests on vertical bearing characteristics of cast-in-place X-section pilesrdquo Chinese Journal of Geotechnical Engi-neering vol 32 pp 903ndash907 2010

[15] Y Jun L Xiao-Min and L Han-Long ldquoModel test study ofanti-pulling property of X-shaped concrete pilerdquo Rock andSoil Mechanics vol 31 pp 3430ndash3434 2010

[16] L Han-Long L Zhi-Ping and W Xin-Quan ldquoStudy on thegeometric characteristics of the cast-in-place X-type vibro-pilesectionrdquo China Railway Science vol 30 pp 17ndash23 2009

[17] M X Zhang S M Ding and Y M Chen ldquoTest on verticalbehavior of cast-in-situ X-shaped concrete pile and its ulti-mate bearing capacity predictionrdquo Journal of China CoalSociety vol 36 pp 267ndash271 2011

[18] L Han-Long J Hui and D Xuan-Ming ldquoField test researchon squeezing effects of X-section cast-in-place concrete pilerdquoRock and Soil Mechanics vol 33 pp 219ndash224 2012

[19] S Guang-Chao L Han-Long K Gang-Qiang and D Xuan-Ming ldquoModel tests on effect of vibration waves on dynamicresponse of XCC pile-raft composite foundationrdquo ChineseJournal of Geotechnical Engineering vol 38 pp 1021ndash10292015

Shock and Vibration 13

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

00 02 04 06 08 10 12ndash10

ndash5

0

5

10

Acc

eler

atio

n re

spon

se(s

urfa

ce la

yer o

f fou

ndat

ion)

(mm

s2 )

Time (s)

300kmh

(d)

00 02 04 06 08 10 12ndash10

ndash5

0

5

10

Acc

eler

atio

n re

spon

se(s

urfa

ce la

yer o

f fou

ndat

ion)

(mm

s2 )

Time (s)

350kmh

(e)

Figure 14 Acceleration under different speeds with respect to time

177Hz

160kmh

0

1

2

3

Acc

eler

atio

nam

plitu

de (m

ms

2 )

20 40 60 80 1000Time (s)

(a)

200kmh

200Hz 222Hz

0

1

2

3

Acc

eler

atio

nam

plitu

de (m

ms

2 )

20 40 60 80 1000Time (s)

(b)

Figure 15 Continued

Shock and Vibration 11

(approximately double) However when the train speed rea-ches 250 kmh the increase on the peak is negligible Becausethe increase in the train speed is achieved by increasing thevibration frequency the superposition of the surroundingreflected waves in this process likely produces a counteractionto the vibration of the subgrade foundation explaining thisresult

Figure 15 shows the spectral curve of the acceleration atthe surface layer of the foundation under different trainspeeds We can see that the ground vibration caused by thetrain is mainly contributed by relatively low-frequencycomponents (mainly below 100Hz) As the train speedincreases the amplitude of the acceleration increases andthe base frequencies of the vibration also gradually increase177Hz in the base frequencies when the train velocity is160 kmh 222Hz when the train speed is 200 kmh 277Hzwhen the train speed is 250 kmh 332Hz when the trainspeed is 300 kmh and 388Hz when the train speed is350 kmh are all the vibration frequency of the actuatorunder the current working condition

As the train speed increases the peak spectral vibrationacceleration response also increases and the frequencycorresponding to the peak spectral vibration accelerationalso gradually moves to a medium frequency as the trainspeed increases )e higher the train speed the richer thefrequency components of the ground vibration

4 Conclusions

In this study by conducting a large-scale dynamic model teston an X-section pile-net composite foundation under dif-ferent train speeds we can draw the following conclusions

(1) )e response of the vertical dynamic velocity is thelargest at the surface layer of the embankment andattenuates by approximately 90 in the embank-ment )e speed rapidly attenuates as the depthincreases the vibration gradually attenuates as thedistance from the vibration source increases At thebottom layer of the subgrade bed and in the range of

250kmh

277Hz

250Hz194Hz

0

1

2

3

Acc

eler

atio

nam

plitu

de (m

ms

2 )20 40 60 80 1000

Time (s)

(c)

300kmh

199Hz

233Hz

299Hz

332Hz

0

1

2

3

4

Acc

eler

atio

nam

plitu

de (m

ms

2 )

20 40 60 80 1000Time (s)

(d)

350kmh

233Hz272Hz

349Hz

0

1

2

3

4

Acc

eler

atio

nam

plitu

de (m

ms

2 )

20 40 60 80 1000Time (s)

(e)

Figure 15 Spectrum curve of acceleration under different speeds

12 Shock and Vibration

the lower foundation the attenuation rate signifi-cantly decreases and the vibration velocity is linearlyrelated to the train speed

(2) Inside the pile-net foundation the peak dynamicstress at the top of the pile is 34 times than that in thesoil between piles and the dynamic stress attenuateswith the depth

(3) )e change in train speed does not have a largeinfluence on the peak transient dynamic displace-ment response at the surface of the track afterpassing through the subgrade bed the peak verticalacceleration decreases from approximately 80mms2to 30mms2 attenuating by 625 )is is mainlybecause the high-frequency components are absor-bed due to soil damping effects and the low-frequency components attenuate relatively slowly)e foundation vibration caused by the train is a low-frequency vibration and the subgrade foundationhas an attenuation impact on the high-frequencyvibration the vibration gradually decreases as thedistance from the vibration source increases andincreases as the train speed increases

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 there are no conflicts of interestregarding the publication of this paper

Acknowledgments

)is project was supported by the Funds for InternationalCooperation and Exchange of the National Natural ScienceFoundation of China (Grant no 51420105013)

References

[1] M A Heckl ldquoRailway noise-can random sleeper spacingshelprdquo Acta Acustica United with Acustica vol 81 no 6pp 559ndash564 1995

[2] H Takemiya and X Bian ldquoSubstructure simulation of in-homogeneous track and layered ground dynamic interactionunder train passagerdquo Journal of Engineering Mechanicsvol 131 no 7 pp 699ndash711 2005

[3] M Bahrekazemi and A Bodare ldquoEffects of lime-cement soilstabilization against train induced ground vibrationsrdquo inProceedings of the 3rd International Specialty Conference onGrouting and Ground Treatment New Orleans LA USAFebruary 2003

[4] L Bo and C Ying ldquoDynamic analysis on subgrade of highspeed railways in geometric irregular conditionrdquo Journal ofthe China Railway Society vol 21 pp 84ndash88 1999

[5] X Chen and W Y Lu Wentian ldquoStudy on the dynamic re-sponse of high speed railway bridge-subgrade transition sec-tionrdquo Journal of Vibration and Shock vol 25 pp 95ndash98 2006

[6] W F Anderson and A J Key ldquoModel testing of two-layerrailway track ballastrdquo Journal of Geotechnical and Geo-environmental Engineering vol 126 no 4 pp 317ndash323 2000

[7] S J Cox A Wang C Morison P Carels R Kelly andO G Bewes ldquoA test rig to investigate slab track structures forcontrolling ground vibrationrdquo Journal of Sound and Vibra-tion vol 293 no 3ndash5 pp 901ndash909 2006

[8] Y Zhan and G Jiang ldquoStudy of dynamic characteristics of soilsubgrade bed for ballastless trackrdquo Rock and Soil Mechanicsvol 31 pp 392ndash396 2010

[9] Y Momoya E Sekine and F Tatsuoka ldquoDeformationcharacteristics of railway roadbed and subgrade undermoving-wheel loadrdquo Soils and Foundations vol 45 no 4pp 99ndash118 2005

[10] A Al Shaer D Duhamel K Sab G Foret and L SchmittldquoExperimental settlement and dynamic behavior of a portionof ballasted railway track under high speed trainsrdquo Journal ofSound and Vibration vol 316 no 1ndash5 pp 211ndash233 2008

[11] T Ishikawa E Sekine and S Miura ldquoCyclic deformation ofgranular material subjected to moving-wheel loadsrdquo Cana-dian Geotechnical Journal vol 48 no 5 pp 691ndash703 2011

[12] G Q Kong X M Ding Y M Chen and G Yang ldquoVerticaluplift capacity characteristics and influence factor analysis ofcast-in-situ X-section reinforced concrete pile grouprdquo Journalof Civil Engineering and Architecture vol 29 pp 49ndash54 2012

[13] M X Zhang H L Liu X M Ding and Z Q WangldquoComparative tests on bearing capacity of cast-in-situX-shaped concrete piles and circular pilerdquo Chinese Journal ofGeotechnical Engineering vol 33 pp 1469ndash1476 2011

[14] Z QWang H L Liu M X Zhang J Yuan and J Yong ldquoFullscale model tests on vertical bearing characteristics of cast-in-place X-section pilesrdquo Chinese Journal of Geotechnical Engi-neering vol 32 pp 903ndash907 2010

[15] Y Jun L Xiao-Min and L Han-Long ldquoModel test study ofanti-pulling property of X-shaped concrete pilerdquo Rock andSoil Mechanics vol 31 pp 3430ndash3434 2010

[16] L Han-Long L Zhi-Ping and W Xin-Quan ldquoStudy on thegeometric characteristics of the cast-in-place X-type vibro-pilesectionrdquo China Railway Science vol 30 pp 17ndash23 2009

[17] M X Zhang S M Ding and Y M Chen ldquoTest on verticalbehavior of cast-in-situ X-shaped concrete pile and its ulti-mate bearing capacity predictionrdquo Journal of China CoalSociety vol 36 pp 267ndash271 2011

[18] L Han-Long J Hui and D Xuan-Ming ldquoField test researchon squeezing effects of X-section cast-in-place concrete pilerdquoRock and Soil Mechanics vol 33 pp 219ndash224 2012

[19] S Guang-Chao L Han-Long K Gang-Qiang and D Xuan-Ming ldquoModel tests on effect of vibration waves on dynamicresponse of XCC pile-raft composite foundationrdquo ChineseJournal of Geotechnical Engineering vol 38 pp 1021ndash10292015

Shock and Vibration 13

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

(approximately double) However when the train speed rea-ches 250 kmh the increase on the peak is negligible Becausethe increase in the train speed is achieved by increasing thevibration frequency the superposition of the surroundingreflected waves in this process likely produces a counteractionto the vibration of the subgrade foundation explaining thisresult

Figure 15 shows the spectral curve of the acceleration atthe surface layer of the foundation under different trainspeeds We can see that the ground vibration caused by thetrain is mainly contributed by relatively low-frequencycomponents (mainly below 100Hz) As the train speedincreases the amplitude of the acceleration increases andthe base frequencies of the vibration also gradually increase177Hz in the base frequencies when the train velocity is160 kmh 222Hz when the train speed is 200 kmh 277Hzwhen the train speed is 250 kmh 332Hz when the trainspeed is 300 kmh and 388Hz when the train speed is350 kmh are all the vibration frequency of the actuatorunder the current working condition

As the train speed increases the peak spectral vibrationacceleration response also increases and the frequencycorresponding to the peak spectral vibration accelerationalso gradually moves to a medium frequency as the trainspeed increases )e higher the train speed the richer thefrequency components of the ground vibration

4 Conclusions

In this study by conducting a large-scale dynamic model teston an X-section pile-net composite foundation under dif-ferent train speeds we can draw the following conclusions

(1) )e response of the vertical dynamic velocity is thelargest at the surface layer of the embankment andattenuates by approximately 90 in the embank-ment )e speed rapidly attenuates as the depthincreases the vibration gradually attenuates as thedistance from the vibration source increases At thebottom layer of the subgrade bed and in the range of

250kmh

277Hz

250Hz194Hz

0

1

2

3

Acc

eler

atio

nam

plitu

de (m

ms

2 )20 40 60 80 1000

Time (s)

(c)

300kmh

199Hz

233Hz

299Hz

332Hz

0

1

2

3

4

Acc

eler

atio

nam

plitu

de (m

ms

2 )

20 40 60 80 1000Time (s)

(d)

350kmh

233Hz272Hz

349Hz

0

1

2

3

4

Acc

eler

atio

nam

plitu

de (m

ms

2 )

20 40 60 80 1000Time (s)

(e)

Figure 15 Spectrum curve of acceleration under different speeds

12 Shock and Vibration

the lower foundation the attenuation rate signifi-cantly decreases and the vibration velocity is linearlyrelated to the train speed

(2) Inside the pile-net foundation the peak dynamicstress at the top of the pile is 34 times than that in thesoil between piles and the dynamic stress attenuateswith the depth

(3) )e change in train speed does not have a largeinfluence on the peak transient dynamic displace-ment response at the surface of the track afterpassing through the subgrade bed the peak verticalacceleration decreases from approximately 80mms2to 30mms2 attenuating by 625 )is is mainlybecause the high-frequency components are absor-bed due to soil damping effects and the low-frequency components attenuate relatively slowly)e foundation vibration caused by the train is a low-frequency vibration and the subgrade foundationhas an attenuation impact on the high-frequencyvibration the vibration gradually decreases as thedistance from the vibration source increases andincreases as the train speed increases

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 there are no conflicts of interestregarding the publication of this paper

Acknowledgments

)is project was supported by the Funds for InternationalCooperation and Exchange of the National Natural ScienceFoundation of China (Grant no 51420105013)

References

[1] M A Heckl ldquoRailway noise-can random sleeper spacingshelprdquo Acta Acustica United with Acustica vol 81 no 6pp 559ndash564 1995

[2] H Takemiya and X Bian ldquoSubstructure simulation of in-homogeneous track and layered ground dynamic interactionunder train passagerdquo Journal of Engineering Mechanicsvol 131 no 7 pp 699ndash711 2005

[3] M Bahrekazemi and A Bodare ldquoEffects of lime-cement soilstabilization against train induced ground vibrationsrdquo inProceedings of the 3rd International Specialty Conference onGrouting and Ground Treatment New Orleans LA USAFebruary 2003

[4] L Bo and C Ying ldquoDynamic analysis on subgrade of highspeed railways in geometric irregular conditionrdquo Journal ofthe China Railway Society vol 21 pp 84ndash88 1999

[5] X Chen and W Y Lu Wentian ldquoStudy on the dynamic re-sponse of high speed railway bridge-subgrade transition sec-tionrdquo Journal of Vibration and Shock vol 25 pp 95ndash98 2006

[6] W F Anderson and A J Key ldquoModel testing of two-layerrailway track ballastrdquo Journal of Geotechnical and Geo-environmental Engineering vol 126 no 4 pp 317ndash323 2000

[7] S J Cox A Wang C Morison P Carels R Kelly andO G Bewes ldquoA test rig to investigate slab track structures forcontrolling ground vibrationrdquo Journal of Sound and Vibra-tion vol 293 no 3ndash5 pp 901ndash909 2006

[8] Y Zhan and G Jiang ldquoStudy of dynamic characteristics of soilsubgrade bed for ballastless trackrdquo Rock and Soil Mechanicsvol 31 pp 392ndash396 2010

[9] Y Momoya E Sekine and F Tatsuoka ldquoDeformationcharacteristics of railway roadbed and subgrade undermoving-wheel loadrdquo Soils and Foundations vol 45 no 4pp 99ndash118 2005

[10] A Al Shaer D Duhamel K Sab G Foret and L SchmittldquoExperimental settlement and dynamic behavior of a portionof ballasted railway track under high speed trainsrdquo Journal ofSound and Vibration vol 316 no 1ndash5 pp 211ndash233 2008

[11] T Ishikawa E Sekine and S Miura ldquoCyclic deformation ofgranular material subjected to moving-wheel loadsrdquo Cana-dian Geotechnical Journal vol 48 no 5 pp 691ndash703 2011

[12] G Q Kong X M Ding Y M Chen and G Yang ldquoVerticaluplift capacity characteristics and influence factor analysis ofcast-in-situ X-section reinforced concrete pile grouprdquo Journalof Civil Engineering and Architecture vol 29 pp 49ndash54 2012

[13] M X Zhang H L Liu X M Ding and Z Q WangldquoComparative tests on bearing capacity of cast-in-situX-shaped concrete piles and circular pilerdquo Chinese Journal ofGeotechnical Engineering vol 33 pp 1469ndash1476 2011

[14] Z QWang H L Liu M X Zhang J Yuan and J Yong ldquoFullscale model tests on vertical bearing characteristics of cast-in-place X-section pilesrdquo Chinese Journal of Geotechnical Engi-neering vol 32 pp 903ndash907 2010

[15] Y Jun L Xiao-Min and L Han-Long ldquoModel test study ofanti-pulling property of X-shaped concrete pilerdquo Rock andSoil Mechanics vol 31 pp 3430ndash3434 2010

[16] L Han-Long L Zhi-Ping and W Xin-Quan ldquoStudy on thegeometric characteristics of the cast-in-place X-type vibro-pilesectionrdquo China Railway Science vol 30 pp 17ndash23 2009

[17] M X Zhang S M Ding and Y M Chen ldquoTest on verticalbehavior of cast-in-situ X-shaped concrete pile and its ulti-mate bearing capacity predictionrdquo Journal of China CoalSociety vol 36 pp 267ndash271 2011

[18] L Han-Long J Hui and D Xuan-Ming ldquoField test researchon squeezing effects of X-section cast-in-place concrete pilerdquoRock and Soil Mechanics vol 33 pp 219ndash224 2012

[19] S Guang-Chao L Han-Long K Gang-Qiang and D Xuan-Ming ldquoModel tests on effect of vibration waves on dynamicresponse of XCC pile-raft composite foundationrdquo ChineseJournal of Geotechnical Engineering vol 38 pp 1021ndash10292015

Shock and Vibration 13

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

the lower foundation the attenuation rate signifi-cantly decreases and the vibration velocity is linearlyrelated to the train speed

(2) Inside the pile-net foundation the peak dynamicstress at the top of the pile is 34 times than that in thesoil between piles and the dynamic stress attenuateswith the depth

(3) )e change in train speed does not have a largeinfluence on the peak transient dynamic displace-ment response at the surface of the track afterpassing through the subgrade bed the peak verticalacceleration decreases from approximately 80mms2to 30mms2 attenuating by 625 )is is mainlybecause the high-frequency components are absor-bed due to soil damping effects and the low-frequency components attenuate relatively slowly)e foundation vibration caused by the train is a low-frequency vibration and the subgrade foundationhas an attenuation impact on the high-frequencyvibration the vibration gradually decreases as thedistance from the vibration source increases andincreases as the train speed increases

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 there are no conflicts of interestregarding the publication of this paper

Acknowledgments

)is project was supported by the Funds for InternationalCooperation and Exchange of the National Natural ScienceFoundation of China (Grant no 51420105013)

References

[1] M A Heckl ldquoRailway noise-can random sleeper spacingshelprdquo Acta Acustica United with Acustica vol 81 no 6pp 559ndash564 1995

[2] H Takemiya and X Bian ldquoSubstructure simulation of in-homogeneous track and layered ground dynamic interactionunder train passagerdquo Journal of Engineering Mechanicsvol 131 no 7 pp 699ndash711 2005

[3] M Bahrekazemi and A Bodare ldquoEffects of lime-cement soilstabilization against train induced ground vibrationsrdquo inProceedings of the 3rd International Specialty Conference onGrouting and Ground Treatment New Orleans LA USAFebruary 2003

[4] L Bo and C Ying ldquoDynamic analysis on subgrade of highspeed railways in geometric irregular conditionrdquo Journal ofthe China Railway Society vol 21 pp 84ndash88 1999

[5] X Chen and W Y Lu Wentian ldquoStudy on the dynamic re-sponse of high speed railway bridge-subgrade transition sec-tionrdquo Journal of Vibration and Shock vol 25 pp 95ndash98 2006

[6] W F Anderson and A J Key ldquoModel testing of two-layerrailway track ballastrdquo Journal of Geotechnical and Geo-environmental Engineering vol 126 no 4 pp 317ndash323 2000

[7] S J Cox A Wang C Morison P Carels R Kelly andO G Bewes ldquoA test rig to investigate slab track structures forcontrolling ground vibrationrdquo Journal of Sound and Vibra-tion vol 293 no 3ndash5 pp 901ndash909 2006

[8] Y Zhan and G Jiang ldquoStudy of dynamic characteristics of soilsubgrade bed for ballastless trackrdquo Rock and Soil Mechanicsvol 31 pp 392ndash396 2010

[9] Y Momoya E Sekine and F Tatsuoka ldquoDeformationcharacteristics of railway roadbed and subgrade undermoving-wheel loadrdquo Soils and Foundations vol 45 no 4pp 99ndash118 2005

[10] A Al Shaer D Duhamel K Sab G Foret and L SchmittldquoExperimental settlement and dynamic behavior of a portionof ballasted railway track under high speed trainsrdquo Journal ofSound and Vibration vol 316 no 1ndash5 pp 211ndash233 2008

[11] T Ishikawa E Sekine and S Miura ldquoCyclic deformation ofgranular material subjected to moving-wheel loadsrdquo Cana-dian Geotechnical Journal vol 48 no 5 pp 691ndash703 2011

[12] G Q Kong X M Ding Y M Chen and G Yang ldquoVerticaluplift capacity characteristics and influence factor analysis ofcast-in-situ X-section reinforced concrete pile grouprdquo Journalof Civil Engineering and Architecture vol 29 pp 49ndash54 2012

[13] M X Zhang H L Liu X M Ding and Z Q WangldquoComparative tests on bearing capacity of cast-in-situX-shaped concrete piles and circular pilerdquo Chinese Journal ofGeotechnical Engineering vol 33 pp 1469ndash1476 2011

[14] Z QWang H L Liu M X Zhang J Yuan and J Yong ldquoFullscale model tests on vertical bearing characteristics of cast-in-place X-section pilesrdquo Chinese Journal of Geotechnical Engi-neering vol 32 pp 903ndash907 2010

[15] Y Jun L Xiao-Min and L Han-Long ldquoModel test study ofanti-pulling property of X-shaped concrete pilerdquo Rock andSoil Mechanics vol 31 pp 3430ndash3434 2010

[16] L Han-Long L Zhi-Ping and W Xin-Quan ldquoStudy on thegeometric characteristics of the cast-in-place X-type vibro-pilesectionrdquo China Railway Science vol 30 pp 17ndash23 2009

[17] M X Zhang S M Ding and Y M Chen ldquoTest on verticalbehavior of cast-in-situ X-shaped concrete pile and its ulti-mate bearing capacity predictionrdquo Journal of China CoalSociety vol 36 pp 267ndash271 2011

[18] L Han-Long J Hui and D Xuan-Ming ldquoField test researchon squeezing effects of X-section cast-in-place concrete pilerdquoRock and Soil Mechanics vol 33 pp 219ndash224 2012

[19] S Guang-Chao L Han-Long K Gang-Qiang and D Xuan-Ming ldquoModel tests on effect of vibration waves on dynamicresponse of XCC pile-raft composite foundationrdquo ChineseJournal of Geotechnical Engineering vol 38 pp 1021ndash10292015

Shock and Vibration 13

International Journal of

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RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom