radialjointsbehaviorofaprecastasymmetricunderpass … · 2020. 3. 23. · segment itself due to the...

Research ArticleRadial Joints Behavior of a Precast Asymmetric UnderpassInduced by Long-Term Loads of Ground Vehicles

Zhiyi Jin Taiyue Qi Xiao Liang Bo Lei Yangyang Yu Yuchen Gong and Weidu Ji

Key Laboratory of Transportation Tunnel Engineering Ministry of Education Southwest Jiaotong UniversityChengdu 610031 China

Correspondence should be addressed to Taiyue Qi qitaiyue58126com

Received 10 July 2019 Revised 13 January 2020 Accepted 10 February 2020 Published 23 March 2020

Academic Editor Marco Lepidi

Copyright copy 2020 Zhiyi Jin et al-is is an open access article distributed under the Creative CommonsAttribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

With the rapid development of the urbanization many underpasses are designed and constructed in big cities to alleviate the hugetraffic pressure-e construction method has been changed from traditional on-site concrete pouring technology to prefabricatedassembly technology However this change will inevitably bring out some new problems to be studied such as the behaviour of theradial joints In this study the numerical simulation model of Moziqiao precast and assemble underpass with large asymmetriccross section was constructed by using the ABAQUS software to study the transient response of the underpass induced by groundsurface dynamic load Based on the similarity theory a 110 scaled model test was carried out to study the long-term radial jointbehaviour of the underpass considering the prestress loss during the 2000 000 loading cycles -e results transient dynamicresponse from computed and tested was compared in terms of acceleration -e comparison showed that the transient responseaccelerations have good consistency -e results of the physical model test were analysed in terms of joint opening closure andslipping -e accumulative joint opening was closely correlated to the prestress level and the joint opening at different prestresslevels increased with the loss of the prestress -e joints closure decreased with the increase of the previous accumulative colorvalue -e joint slipping mainly attributed to the slipping of the top segment Both the opening and slipping of the joints at RJ 1were larger than that of RJ3 due to the wider span of RJ1 which reflected an asymmetric effect -is study revealed the long-termaccumulative behaviour of the radial joints which convinced us that the long-term accumulative deformation of the joints shouldbe taken into consideration during the design stage for similar projects

1 Introduction

-e rapid growth of population in big cities has led to theurban ground traffic more and more crowded [1ndash3] Hencedifferent kinds of underground structures and spaces such asmetro tunnels metro stations utility tunnels undergroundshelters and underpasses may appear in any large cityUnderpasses constructed crossing underneath highways indowntown areas will become common -e underpassstructure will lose its function partly or completely due tolong-term repeated vibration from the ground surface ve-hicles -e vehicle dynamic loads can affect the underpasseswithin the depth of 14m and the effect decreases with theincrease of distance from the excitation source [4] -ere-fore the long-term dynamic effect on underpasses induced

by ground surface vehicles cannot be neglected during thedesign stage

Typically cut-and-cover underpasses are often boxshaped and constructed by using cast-in-place reinforcedconcrete liners Compared with cast-in-place concreteprecast structure has higher prefabrication precision andfaster construction speed [5ndash9] -e prefabrication tech-nology was used in Sendai subway in Japan and Tashkentsubway in Uzbekistan decades ago [10ndash12] For thoseadvantages of precast concrete the next decade is likely towitness a considerable rise of precast underpass in urbanareas Although the prefabrication concrete is a promisingalternative to the traditional cast-in-place concrete themain problem in its use in underpass is the size and weightcannot exceed the transport and crane ability under

HindawiShock and VibrationVolume 2020 Article ID 5952796 11 pageshttpsdoiorg10115520205952796

current conditions -erefore the large cross-sectionunderpass must be divided into segments [13] Radialjoints (RJs) are used to connect adjacent segments in theunderpass lining [14] Radial joints have two main func-tions for precast tunnel linings one is transferring loadsand the other is a sealant of the structure -e radial joint isthe potential weakest link of the tunnel compared to thesegment itself due to the lower stiffness [15ndash17] Radialjoints are not only the weak position of structural de-formation but also the high incidence of tunnel distress[18 19]

It has been presented in different papers that the radialjoints have a prominent influence on the tunnel deforma-tion Wang et al [20] found that the variation of tunneldiameter is closely related to the opening of radial joints byusing a simplified method to evaluate the deformation of ashield tunnel in soft soil in Shanghai From a field case studyof an operated metro tunnel under surface surcharge loadHuang et al [21] found that the convergence of the tunnel isclosely correlate to the radial joint width and less correlate tothe deformation of the circumferential joint Yi et al [22]carried out a model experiment to study the accumulativedeformation of a metro tunnel lining induced by dynamicload from the abovementioned high-speed train and indi-cated that the main contribution of the accumulative de-formation of the tunnel lining came from the opening anddislocation of the joints All these studies above showed thatthe behavior of radial joints play an important role in tunneldeformation

For this reason numerous studies focused on radialjoints behavior Jin et al [23] conducted a series of full-scaleexperiments to investigate the joint behavior of a water-conveyance tunnel Caratelli et al [14] performed a test ontwo steel fiber reinforced concrete elements to study thebehavior of longitudinal joints of a shield tunnel lining andinterpreted the behavior in an analytical manner Liu et al[24] through a full-scale test (with a whole ring) to inves-tigate the ultimate bearing capacity of a shield tunnel inShanghai the test result showed that the lining failure wascaused by joints failure However these studies mainly fo-cused on the behavior of shield tunnel and the loadingconditions on static loads

Although many research achievements were realizedon the joint behavior of shield tunnel linings under dif-ferent kinds of load conditions in the abovementionedreferences the long-term joint behavior of shallow buriedunderpass linings induced by ground surface vehicle dy-namic load is still not clear Motivated by this researchstatus this paper tries to make a thorough understandingof the effect of long-term ground surface vehicle loads onthe radial joint behavior of prefabricated and assembleunderpass Taking the Moziqiao underpass in Chengdu asan engineering background a numerical model wasconstructed to study the transient dynamic response of thestructure and 110 scaled model experiment were carriedout to study the long-term accumulative deformation ofthe joints According to the measured joint deformationdata of the model experiment characters of joint dis-placement were analyzed

2 Engineering Background

In the case of Moziqiao underpass crossing beneath thesouth section of the first ring road in Chengdu the locationof the project can be seen in Figure 1-e project is designedto relieve the heavy traffic in downtown Chengdu -eunderpass consists of two tubes one is 3-passing lane with awidth of 1185m and the other is 2-passing lane with a widthof 835m-e length of the project is 200m and the height ofthe underpass is 82m -e thickness of the plain fill is 3m-e cross section of the underpass is 1783m2 and the crosssection must be partitioned into segments -e partitionscheme was chosen by considering the internal force dis-tribution amounts of joints and construction time-e finalpartition scheme of the underpass was that the structure wascut at the middle in the height direction as shown inFigure 2(a) -e sketch of the project can be seen inFigure 2(b)

-e strength of the prefabricated concrete lining is C50-e mechanical and physical parameters of the plain fill andconcrete lining are shown in Tables 1 and 2 respectively

-e dynamic load induced by the vehicle moving on theground surface is not obvious due to the speed of the vehiclesis far slower than the wave velocity of the highway surface-erefore the influence of moving vehicle on the dynamicresponse of the ground surface can be neglected if thepavement is even enough However the pavement of anyhighway cannot be fully level and the pavement evennessbecomes worse with the service time It can be consideredthat the vertical vibration of vehicles is completely caused bythe unevenness of the ground surface [25ndash27] A harmonicloadmodel which can reflect the vehicle moving velocity andpavement unevenness was used to describe the vibrationinduced by highway vehicle by Chen [28] according to thesimplified form of dynamic load the cyclic load can beexpressed in the form of

F(t) P minus cos 2 times π timesv

ltimes t1113874 1113875 (1)

where P is the amplitude of the dynamic load assumed equalto 150 kN (vl) is the frequency of dynamic load v is themaximum vehicle velocity of the ground surface assumed as12ms and l is the wavelength of the pavement assumed as20m Hence equation (1) can be further simplified as

F(t) P minus cos(2 times π times 06 times t) (2)

3 Numerical and Physical Experiment Setups

31 Numerical Model Setup In order to study the behaviorof the underpass radial joints under dynamic load a 3Dnumerical model with the real project was constructed usingfinite element software ABAQUS 2016

-e flat radial joints were adopted in numerical mod-elling and connecters between the underpass segments werenot considered -ere are two shear keys which are installedat each radial joint

-e dimension of the model is 10m in length (in theaxial direction of the tunnel) 438m in width and 217m in

2 Shock and Vibration

height -e geometry of the model is shown in Figure 3(a)-e whole model contains soils plain concrete and tunnelFigure 3(b) plotted the segments and shear keys of thetunnel

-e type ldquohard contactrdquo [29] model was used to simulatethe interaction between contact surfaces of segments -iskind of contact does not allow segment penetrate to eachother at the compression state -e friction coefficient was

set at 04 according to laboratory test Contact surfacesbetween shear keys and tunnel segments were set as surface-to-surface contact type and the friction coefficient was set at02 -e ldquotierdquo mode was used to define the interaction be-tween soil and the underpass lining Parameters in thenumerical model were the same as the real project as listed inTables 1 and 3 In the finite element model prestressmentioned in Section 2 was applied by 5 pairs of

ChinaChengdu

Qingyang districtJinjiang district

The precast underpass

Jinjiang river

N

1km

Figure 1 Project location (map data from Google earth)

835 1185 7575

100

310

310

100

60

2230

(a) (b)

Figure 2 Partition scheme and sketch of the structure (a) Partition scheme of the structure (b) Sketch of the project

Table 1 -e mechanical parameters of segments in the prototype and model

Parameters Density Elastic modulus Poisonrsquos ratio Tensile strength Compressive strengthUnite (kgm3) (MPa) mdash (MPa) (MPa)Prototype 2600 34500 021 264 324Model 2600 3450 021 0264 324

Table 2 -e mechanical parameters of backfill soil in the prototype and model

Parameters -ickness Density Elastic modulus Poisonrsquos ratio Friction angle CohesionUnite (m) (kgm3) (MPa) mdash (deg) (KPa)Prototype 3 1910 1015 032 181 175Model 03 1900 101 032 18 17

Shock and Vibration 3

concentrated force at the top and bottom of the model foreach radial joint In the dynamic computation Rayleighdamping was applied -e damping coefficient of surroundsoil was determined by Liu [30] -e dynamic load wasapplied as shown in equation (2)

To study the behavior of radial joints under long-termsurface dynamic load amodel experiment was conducted-edetail of the model experiment was introduced as follows

32 Physical Model Experiment Setup

321 Similitude Relation Model experiment is an ordinarymethod to study the mechanical behavior and can obtaindecent results -e similitude relations between the scaledmodel and prototype can be derived by the law of similarity formodel experiment If the dominating features of the realproblem can be scaled by the model appropriately the value ofsimilar ratio will not significantly affect the experiment resultsIn the scaledmodel this paper prepared geometric dimensionL elastic modulus E and density ρ are the 3 basic physicalquantities According to Buckingham Pi theory other pa-rameters such as stress strain force acceleration and time canbe derived by the 3 basic physical quantities -e similituderelations can be seen in Table 3 In Table 3 C means thesimilitude ratio between the porotype and the model Sub-scripts p and m denote the porotype and model respectively

322 Materials and Ratio of the Model Plaster based ma-terial is a widely used material to simulate tunnel linings indifferent kinds of indoor experiments for its mechanical

similarity with concrete Fang et al [31] conducted a physicalmodel test the tunnel under the goaf of a thick coal seam andused a mixture of plaster and water to simulate C 25 con-crete Yang et al [32] used a mixture of plaster water andkieselguhr to simulate a metro tunnel lining in a test forstudying the effect of train-induced vibration for shieldtunnel Xu et al [33] carried out a shaking table test to studythe seismic response of a mountain tunnel by using plaster-based mixture to simulate the tunnel with a strength grade ofC 25 -us the plaster-based material can be used to sim-ulate both the cast in place and precast concrete tunnel liningunder both static and dynamic loads

According to Table 3 the scale of the porotype with respectto the physical model is 10 1 as a result the length width andheight of the model are 223m 14m and 1m respectively

-e mechanical properties of the model materials aresignificant for themodel test-e testmodel is composed by thetunnel segment and soil -e tunnel segment with the strengthgrade C50 in the real project segments in the model werefabricated by mixing water and plaster and kieselguhr are at aratio of 1 12 01 (by mass) materials according to the simu-lation rules in Table 3 by our previous study [34] -e me-chanical parameters of the protype and model of the segmentwere shown in Table 1-e soil of the model test was fabricatedby a mixture of coarse sand quarts sand pulverized fuel ashand waste oil with a ratio at 10 08 08 03 (by mass) througha series of orthogonal tests according to the simulation rules inTable 3 -e mechanical parameters of the porotype and modelof the backfill soil were shown in Table 2

-e pressure applied in height direction by the bolts in themodel is 005MPa according to the designed value at 05MPain the prototype and the similitude relation in Table 2-e areaof each steel plate is 0075m2 and the total force applied by the5 bolts is 3750N at each radial joint Every prestress boltrequires to afford the force at 750N In themodel the prestressis applied by bolts with a diameter of 10mm

323 Model Fabrication and Installation -e model boxwas welded by steel plate with 2mm thickness and rein-forced with channel-section steel -e dimension of themodel box is 3mtimes 1mtimes 14m as shown in Figure 4

-e underpass segments were casted in the woodenmode with plaster slurry and kieselguhr After 24 hdemould the segment mould -en the segments were driedfor 72 h at 30degC

(a)

Shear keyTop segmentBottom segment

(b)

Figure 3 Numerical modelling (a) -e whole model (b) -e segments and shear keys

Table 3 Similitude ratio of the physical quantities

Quantities Similarity relation RatioLength Cl lplm 10Density Cρ ρpρm 1Elastic modulus CE EpEm 10Stress Cσ σpσm 10Cohesion Cc CpCm 10Frequency Cf fPfm 0316Friction angle Cφ φpφm 1Strain Cε εpεm 1Poissonrsquos ratio cμ μpμm 1Acceleration Ca apam 1Force CF FPFm 1000


At the same time the surrounding soil was configuredwith coarse sand quarts sand pulverized fuel ash and wasteoil by a blender After the parts of the physical model wereprefabricated the installation of the parts followed thefollowing steps Firstly the bottom trough of the model boxwas filled with plain fill and then tampered with a temper-e plain fill should be leveled to make sure the surface isflat Secondly the bottom segment was hoisted to specifiedlocation -en the top segment was assembled on thebottom segment -e prestress was applied as a designatedvalue Measurement sensors were installed at designatedpositions of the model -e side plate front plate and back

plate were weld together Finally the load distributor wasconnected to the electronic actuator

For a long-term study connectors between segments willbe corroded thus in the physical model connectors werenot considered Connectors serve as a sealant componentnot structural function

324 Dynamic Load Selection and Input -e dynamic loadwas realized by a vertical actuator by a load distributor with 5plates at the bottom which were set to simulate the fivevehicles on the ground pavement

3m

14m

1m

Figure 4 -e dimensions of the model box

AB

CAcceleration transducer

Acceleration transducerAcceleration transducer

Figure 5 -e layout of acceleration transducers

Table 4 Prestress levels during the loading processCycle numbers (million) 0sim05 05sim1 1sim15 15sim2Prestress level (N) 375 250 125 0

Point APoint BPoint C

ndash40

ndash30

ndash20

ndash10

0

10

20

30

40

Acc

eler

atio

n (m

ms

2 )

0402 0600 1008Time (s)

(a)


ndash60ndash50ndash40ndash30ndash20ndash10

0102030405060

Acc

eler

atio

n (m

ms

2 )

02 04 06 08 10 12 14 16 18 20 22 24 2600Time (s)

(b)

Figure 6 -e response accelerations (a) Measured results (b) Computed results


Determination of the dynamic load according to theChina Code for Urban Road Design CJJ37-90 I grade themaximum of traffic load and vehicle driving speed are700 kN and 40 kmh thus the loading amplitude and fre-quency of the model test can be calculated by the real roadsurcharge load and cyclic frequency and the similitude re-lation which were shown in Table 3

According to equation (2) and the similitude ratio inTable 2 the amplitude and frequency of the applied load canbe calculated as 700N and 2Hz separately -us the load inphysical experiment follows 700 minus 700 times cos(2 times π times 2 times t)

-e cyclic number is set at 2 million times which is anequivalent of 500000 four-axle trucks passing through As apermanent structure the prestress applied the bolts between thetwo segments of the underpass is bound to be lost due to long-

term surface traffic cyclic loads and the creep of bolts-ereforewe considered the loss of prestress during the process of loading-e prestress was controlled as shown in Table 4

-emodel box and test field can be seen in Figures 4 and 5respectively

325 Monitoring System -e main purpose of this paper isto study the behavior of radial joints -ese behaviors in-cluded structure dynamic response to the surface traffic loadjoint opening and closing and slipping between segments

In order to study the dynamic response of the underpassto the ground surface vehicle loads 3 acceleration sensorswere installed at the top slab of the center of the two tubesand the center of 3 passing lane at the bottom slab

(I) (II) (III) (IV)

(a)

VerticalLVDT

HorizontalLVDT

(I) (II)

(III) (IV)

(b)

Figure 7 -e layout of LVDTs around the radial joints (a) Global view (b) Detailed view


respectively -e layout of acceleration transducers can beseen in Figure 5

Dynamic response of the structure was measured bythree acceleration sensors located at the center of-e layoutof acceleration sensors can be seen in Figure 5 -e openingand closing characters of RJrsquos were monitored by 4 verticalLinear Variable Differential Transducers (LVDTs) For eachvertical LVDT the base was fixed on one side of the RJ andthe top was contact with a steel plate flexibly -e length ofthe steel plate is 3 cm thus the lateral displacement of the RJ

will not affect the measurement precise of the RJ openingand closing -e opening and closing of RJ significantlyaffect the sealant of the structure Opening and closing of RJ2was not monitored for this joint did not attach to thesurrounding soil -us the opening and closing characterswere monitored in RJ 1 and RJ3 Each vertical LVDT wasinstalled at both inside and outside of RJ1 and RJ3 -elayout of vertical LVDTs was shown as Figure 6(b) -edislocation of RJ was monitored by horizontal LVDTsHorizontal LVDTs was fixed on two steel frames -e steel

RJ1

RJ1 Ope

ning

Ope

ning

Slipping

SlippingSlipping

Slipping

RJ2

RJ2

RJ3

RJ3

(a)

COPEN (mm)+2331e ndash 03+2136e ndash 03+1941e ndash 03+1746e ndash 03+1551e ndash 03+1356e ndash 03+1161e ndash 03

+7716e ndash 04+9664e ndash 04

+5767e ndash 04+3818e ndash 04+1869e ndash 04ndash7974e ndash 06

RJ1 RJ2 RJ3

(b)

CSLIP2 (mm)+1275e ndash 01+1036e ndash 01+7976e ndash 02+5588e ndash 02+3201e ndash 02+8128e ndash 03ndash1575e ndash 02

ndash6351e ndash 02ndash3963e ndash 02

ndash8739e ndash 02ndash1113e ndash 01ndash1351e ndash 01ndash1590e ndash 01

RJ1 RJ2 RJ3

(c)

Figure 8 Radial joints displacements by numerical computation (a) Global view (b) Detailed joints opening (c) Detailed joints slipping


frames were set on the floor of the laboratory to isolate fromthe model box -e layout of LVDTs can be seen in Figure 7

4 Dynamic Response of the Plain Fill andUnderpass Lining

-e load on the tunnel segment may include two parts one isthe static load caused by dead load of the underpass and thesurrounding soil and the other is the dynamic load causedby ground surface vehicles When the dynamic load reachesthe pipe segment it has not attenuated to 0 and the tunnellining will experience a dynamic load

In this section the response of surface dynamic loadsstudied by the response acceleration and radial joints be-havior -e response of acceleration and RJs behavior weremonitored and measured in both the numerical model andphysical model In the following sections the computationand measured results of dynamic response and radial jointsdisplacement were compared

41ResponseAccelerationof theUnderpassLining As plottedin Figure 6 both the results of numerical simulation andmodel experiment (see Figure 6(b)) showed that the biggestamplitude of response acceleration was observed at point A(the center of top slab of the 3-passing lane) and the smallestone was observed at point C (the center of the bottom slab of2-passing lane) -e computed acceleration amplitudes werenearly 10 times of the measured results -e computedresponse periods were nearly 3 times of the measured in themodel experiment -is exhibited that the simulation resultswere valid according to the similitude ratio between theprototype and the model

42Radial JointsBehavior InducedbySurfaceDynamicLoadsAs mentioned above the dynamic response of tunnel liningto the surface traffic is obvious -e traffic load may causedisplacement in the tunnel joints -e displacement caused

by dynamic loads in numerical simulation is shown inFigure 8

In Figure 8 there are both opening and slipping oc-curred at RJ1 and RJ3 but there is only slipping at RJ2 AtRJ 1 the top segment moves outward relative to the bottomsegment and the joint opens at the external edge At RJ3the joint behavior is the same as RJ1 At RJ2 the topsegment moves toward to the right direction relative to thebottom segment

-e detailed joint opening can be seen in Figure 8(b)-ejoint opening occurred at both radial joint 1 (RJ1) and radialjoint 3 (RJ3) but the opening amount of RJ1 was larger thanRJ3 at the same area of the joint However there was noopening at RJ2

Figure 8(c) showed the joint slipping at RJs slippingoccurred at each joint -e largest amount of slipping was atRJ1 and the smallest slipping occurred at RJ2 -e negativevalue means the top segment moves to the right relative tothe bottom segment at the joint -e positive value meansthe top segment moves to the left relative to the bottomsegment at the joint

-e response acceleration and joint behavior inducedby the dynamic load suggested that the surface traffic loadscan cause dynamic effect on the underpass lining Inaddition the response acceleration of numerical simula-tion was consistent with the results of the model test -isconvinced us that the model test can get reliable results oftunnel lining transient response induced by dynamicloads

In Section 5 the long-term behavior of RJs under dy-namic load was investigated via a model test

5 Long-Term Behavior of Radial JointsDynamic Loads

From Section 4 we found that the physical model experimentcan reflect the real behavior of underpass RJs induced bysurface vehicle loads Hence the model experiment was used

024

020

016

012

008

004

000

Ope

ning

(mm

)

RJ3 RJ2 RJ1

000

ndash004

ndash008

ndash012

ndash016

ndash020

ndash024

Clos

ure (

mm

)

ClosureOpening

10 times 10650 times 105 15 times 106 20 times 10600Number of cycle (ndash)

(a)

020

018

016

014

012

010

008

006

004

002

000

Ope

ning

(mm

)

RJ3 RJ2 RJ1

ClosureOpening


ndash020

ndash018

ndash016

ndash014

ndash012

ndash010

ndash008

ndash006

ndash004

ndash002

000

Clos

ure (

mm

)

(b)

Figure 9 Joint opening at (a) RJ1 and (b) RJ3


to study the long-term behavior of the RJs under dynamicloads -e behavior of RLJs in our study includes the jointopening and slipping In the following sections characters ofjoint opening and slipping at RJs under long-term dynamicloads were summarized

51 JointOpeningCharacters at Radial Joint1 andRadial Joint3 Figure 9(a) illustrates that the opening and closure of theradial joint at sidewall of the 3-passing lane (RJ1) of theunderpass -e opening at RJ1 increases at a higher speedthis mainly attributed to the readjustment of contact rela-tionship of the joint surfaces -e opening at RJ1 increasedslowly from 012times106 to 1times 106 while the opening has asharp rise shortly after 10times106 and 15times106 this may becaused by the release of prestress at the joint -e prestress is

released firstly at 05times106 but the prestress is still at a highlevel after 05times106 -e most drastic rise occurs at 15times106after which the prestress is released to 0 -is means that forRJ1 the prestress should not be less than that at10times106ndash15times106 interval -e slop of the opening curvebecomes the steepest at the end of the test -e closure curveof the RJ3 shows a decline tendency during the whole testprocess the accumulative closure of first 1times 106 accounts formore than 34 of the total closure -is means the closurerate decreased with the increase of accumulative closure ofthe joint -ere are two possible reasons for this tendencyone is the unevenness of the joint contact surface decreaseswith the increase in the amount of closure and the number ofcycles another maybe the whole structure becomes morestable with the increase of loading cycles Comparison ofFigures 9(a) and 9(b) suggests that the characters of

TopedgeBottomedge

Top edge of RJ1Bottom edge of RJ1

RJ3 RJ2 RJ1

00

05

10

15

20

25

30

Disp

lace

men

t (m

m)

50 times 105 10 times 106 15 times 106 20 times 10600Number of cycle (ndash)

(a)

TopedgeBottomedge

Top edge of J3Bottom edge of J3

RJ3RJ2 RJ1

000

005

010

015

020

025

030

035

040

Disp

lace

men

t (m

m)


(b)

TopedgeBottomedge

Top edge of J2 (right side)Bottom edge of J2 (right side)

RJ3 RJ2 RJ1

000

010

020

030

040

050

060

070

080

090

100

Disp

lace

men

t (m

m)


(c)

TopedgeBottomedge

Top edge of J2 (left side)Bottom edge of J2 (left side)

RJ3 RJ2 RJ1

ndash100

ndash090

ndash080

ndash070

ndash060

ndash050

ndash040

ndash030

ndash020

ndash010

000D

ispla

cem

ent (

mm

)


(d)

Figure 10 Joints slipping at (a) RJ1 (b) RJ3 (c) the right side of RJ2 and (d) the left side of RJ2


accumulative opening and closure at RJ3 are nearly the sameas RJ1 whereas the total amount of opening and closure atRJ1 is larger than that at RJ3 which caused by the shorterspan length at RJ3 than that at RJ1 -erefore the accu-mulative opening and closure show an asymmetric effect

52 Joint Slipping Characters Figure 10 plots that the hori-zontal deformation of the segments at RJ1 RJ3 and 2 sides ofRJ2 -e results show that at each joint the horizontal defor-mation at the top segment is larger than that of bottom segment-is means that the horizontal deformation at the top segmentis the source of the horizontal deformation at the joint -edeformation increases at a high level and then is decreased withthe increase of accumulative deformation thismay be caused bythe gap between of the outsider of the shear keys and the insiderof the holes to install the shears keys When the amount ofdeformation of the upper segment reaches a certain value thecontact surfaces of shear keys and the hole fit together and thenthe shear keys start to work the deformation decreases Anotherpossible reason is that the stiffness of soil increases with theincrease of the deformation at the joints which in turn providesstronger restrain for the joints

6 Conclusions

In order to study the radial joints behavior of a shallow buriedlarge cross-section underpass under long-term dynamic loadsfrom the ground surface Based on a real underpass crossingbeneath the south section of the first ring road in Chengdu anumerical model was constructed and a 110 scaled modelexperiment was conducted From the analysis of the resultsboth from numerical computation and experiment followingconclusions can be drawn

(1) According to the response accelerations of both thenumerical and model experiment the results fromnumerical simulation are in good accordance withthat of model experiment which convinces us thatthe numerical simulation is valid

(2) -e characters of radial joint displacement wereinvestigated by numerical and model experimentBoth the results exhibited the same characters thedisplacement consisted of joint opening and sippingopening and slipping occurred at RJ1 (sidewall of the3 passing lane) and RJ3 (sidewall of the 2 passinglane) but there was only slipping at RJ2 (middle wallof the structure)

(3) Although the characters of the behavior of RJ1 andRJ3 are similar the values of opening and slippingare different and both the values of long-termopening and slipping at RJ1 are greater than that atRJ3 which mainly due to the wider span of RJ1

(4) -e model experiment demonstrated that the jointopening is closely correlated with the prestress leveland the larger the prestress the smaller the opening-e relationship between the joint slipping and pre-stress level is not that significant as the relationshipbetween the joint opening and prestress level

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

We would like to thank National Natural Science Foun-dation of China (Grant nos 51478395 51678490 and5197080874) for the financial support -e anonymousreferees would likely to be acknowledged by the authors fortheir evaluation of the paper

References

[1] M H Baziar M R Moghadam D-S Kim and Y W ChooldquoEffect of underground tunnel on the ground surface accel-erationrdquo Tunnelling and Underground Space Technologyvol 44 pp 10ndash22 2014

[2] U Cilingir and S P G Madabhushi ldquoA model study on theeffects of input motion on the seismic behaviour of tunnelsrdquoSoil Dynamics and Earthquake Engineering vol 31 no 3pp 452ndash462 2011

[3] W Yang L Li Y Shang et al ldquoAn experimental study of thedynamic response of shield tunnels under long-term trainloadsrdquo Tunnelling and Underground Space Technology vol 79pp 67ndash75 2018

[4] J Lai K Wang J Qiu F Niu J Wang and J Chen ldquoVi-bration response characteristics of the cross tunnel structurerdquoShock and Vibration vol 2016 pp 1ndash16 2016

[5] L J Tao P Ding C Shi X W Wu S Wu and S C LildquoShaking table test on seismic response characteristics ofprefabricated subway station structurerdquo Tunnelling and Un-derground Space Technology vol 91 Article ID 102994pp 1ndash25 2019

[6] P Ding L Tao X Yang J Zhao and C Shi ldquo-ree-di-mensional dynamic response analysis of a single-ring struc-ture in a prefabricated subway stationrdquo Sustainable Cities andSociety vol 45 pp 271ndash286 2019

[7] Y B Lai M S Wang X H You and Z Y He ldquoOverview andoutlook for protection and prefabrication techniques oftunnel and underground projectsrdquo Building Technique De-velopment vol 42 no 1 pp 24ndash28 2015

[8] N S Rasmussen ldquoConcrete immersed tunnels - forty years ofexperiencerdquo Tunnelling and Underground Space Technologyvol 12 no 1 pp 33ndash46 1997

[9] D C Wang G F Wang N Qiao and C S Dai ldquo-e ap-plication and prospect analysis of prefabricated constructionin underground engineeringrdquo China Sciencepaper vol 13no 1 pp 115ndash119 2018

[10] H M Liu Study onMechanical Properties of Assembled Liningin Open-Cut Section of Underground Railway Masterrsquos thesisSouthwest Jiaotong University Chengdu China 2003

[11] M N Wang Z Y Li and B S Guan ldquoStudy on prefabricatedconcrete lining technology for open trench subway tunnelsrdquoJournal of China Railway Society vol 26 no 3 pp 88ndash922004


[12] P Yurkevich ldquoDevelopments in segmental concrete liningsfor subway tunnels in belarusrdquo Tunnelling and UndergroundSpace Technology vol 10 no 3 pp 353ndash365 1995

[13] B G Casteren Feasibility of Prefabricated Concrete Elements forUnderpasses MSCE thesis Delft University of TechnologyRotterdam Netherlands 2015

[14] A Caratelli A Meda Z Rinaldi S Giuliani-Leonardi andF Renault ldquoOn the behavior of radial joints in segmentaltunnel liningsrdquo Tunnelling and Underground Space Technol-ogy vol 71 pp 180ndash192 2018

[15] R L Wang and D M Zhang ldquoMechanism of transversedeformation and assessment index for shield tunnels in softclay under surface surchargerdquo Chinese Journal of GeotechnicalEngineering vol 36 pp 1092ndash1101 2013

[16] R L Wang ldquoLongitudinal deformation analysis for Shanghaisubway tunnel constructed by shield methodrdquo UndergroundEngineering and Tunnels vol 4 pp 1ndash7 2009

[17] F I Shalabi E J Cording and S L Paul ldquoConcrete segmenttunnel lining sealant performance under earthquake loadingrdquoTunnelling and Underground Space Technology vol 31pp 51ndash60 2012

[18] X Li Z Yan Z Wang and H Zhu ldquoA progressive model tosimulate the full mechanical behavior of concrete segmentallining longitudinal jointsrdquo Engineering Structures vol 93pp 97ndash113 2015

[19] X Li Z Yan Z Wang and H Zhu ldquoExperimental andanalytical study on longitudinal joint opening of concretesegmental liningrdquo Tunnelling and Underground Space Tech-nology vol 46 pp 52ndash63 2015

[20] J Sun and X Y Hou ldquoDesign theory and practice of circulartunnels in Shanghai areardquo China Civil Engineering Journalvol 17 no 8 pp 35ndash47 1984

[21] H Huang H Shao D Zhang and F Wang ldquoDeformationalresponses of operated shield tunnel to extreme surcharge acase studyrdquo Structure and Infrastructure Engineering vol 13no 3 pp 345ndash360 2017

[22] H Yi T Qi W Qian et al ldquoInfluence of long-term dynamicload induced by high-speed trains on the accumulative de-formation of shallow buried tunnel liningsrdquo Tunnelling andUnderground Space Technology vol 84 pp 166ndash176 2019

[23] Y Jin W Ding Z Yan K Soga and Z Li ldquoExperimentalinvestigation of the nonlinear behavior of segmental joints ina water-conveyance tunnelrdquo Tunnelling and UndergroundSpace Technology vol 68 pp 153ndash166 2017

[24] X Liu Y Bai Y Yuan and H A Mang ldquoExperimentalinvestigation of the ultimate bearing capacity of continuouslyjointed segmental tunnel liningsrdquo Structure and InfrastructureEngineering vol 12 no 10 pp 1364ndash1379 2016

[25] X J Deng ldquoStudy on dynamics of vehicle-ground pavementstructure systemrdquo Journal of Southeast University (NaturalScience Edition) vol 32 pp 474ndash479 2002

[26] Y Cai Y Chen Z Cao H Sun and L Guo ldquoDynamicresponses of a saturated poroelastic half-space generated by amoving truck on the uneven pavementrdquo Soil Dynamics andEarthquake Engineering vol 69 pp 172ndash181 2015

[27] L Sun and X Deng ldquoPredicting vertical dynamic loads causedby vehicle-pavement interactionrdquo Journal of TransportationEngineering vol 124 no 5 pp 470ndash478 1998

[28] H Chen ldquoDynamic finite element analysis of highway sub-grade under traffic loadrdquo Masterrsquos thesis Southwest JiaotongUniversity Chengdu China 2003

[29] ABAQUS Inc ldquoABAQUS userrsquos manual-version 2016rdquo 2010[30] Y X Liu ldquoStudy on fatigue failure form and life prediction of

shield segment under high-speed train dynamic loadrdquo

Masterrsquos thesis Southwest Jiaotong University ChengduChina 2017

[31] Y Fang Z Yao G Walton and Y Fu ldquoLiner behavior of atunnel constructed below a caved zonerdquo KSCE Journal of CivilEngineering vol 22 no 10 pp 4163ndash4172 2018

[32] W B Yang Z Q Chen Z Xu Q X Yan C He and W KaildquoDynamic response of shield tunnels and surrounding soilinduced by train vibrationrdquo Rock and Soil Mechanics vol 39no 2 pp 537ndash545 2018

[33] H Xu T Li L Xia J X Zhao and D Wang ldquoShaking tabletests on seismic measures of a model mountain tunnelrdquoTunnelling and Underground Space Technology vol 60pp 197ndash209 2016

[34] W P Qian T Y Qi H Y Yi et al ldquoEvaluation of structuralfatigue properties of metro tunnel by model test under dy-namic load of high-speed railwayrdquo Tunnelling and Under-ground Space Technology vol 93 Article ID 103099 pp 1ndash162019


current conditions -erefore the large cross-sectionunderpass must be divided into segments [13] Radialjoints (RJs) are used to connect adjacent segments in theunderpass lining [14] Radial joints have two main func-tions for precast tunnel linings one is transferring loadsand the other is a sealant of the structure -e radial joint isthe potential weakest link of the tunnel compared to thesegment itself due to the lower stiffness [15ndash17] Radialjoints are not only the weak position of structural de-formation but also the high incidence of tunnel distress[18 19]

It has been presented in different papers that the radialjoints have a prominent influence on the tunnel deforma-tion Wang et al [20] found that the variation of tunneldiameter is closely related to the opening of radial joints byusing a simplified method to evaluate the deformation of ashield tunnel in soft soil in Shanghai From a field case studyof an operated metro tunnel under surface surcharge loadHuang et al [21] found that the convergence of the tunnel isclosely correlate to the radial joint width and less correlate tothe deformation of the circumferential joint Yi et al [22]carried out a model experiment to study the accumulativedeformation of a metro tunnel lining induced by dynamicload from the abovementioned high-speed train and indi-cated that the main contribution of the accumulative de-formation of the tunnel lining came from the opening anddislocation of the joints All these studies above showed thatthe behavior of radial joints play an important role in tunneldeformation

For this reason numerous studies focused on radialjoints behavior Jin et al [23] conducted a series of full-scaleexperiments to investigate the joint behavior of a water-conveyance tunnel Caratelli et al [14] performed a test ontwo steel fiber reinforced concrete elements to study thebehavior of longitudinal joints of a shield tunnel lining andinterpreted the behavior in an analytical manner Liu et al[24] through a full-scale test (with a whole ring) to inves-tigate the ultimate bearing capacity of a shield tunnel inShanghai the test result showed that the lining failure wascaused by joints failure However these studies mainly fo-cused on the behavior of shield tunnel and the loadingconditions on static loads

Although many research achievements were realizedon the joint behavior of shield tunnel linings under dif-ferent kinds of load conditions in the abovementionedreferences the long-term joint behavior of shallow buriedunderpass linings induced by ground surface vehicle dy-namic load is still not clear Motivated by this researchstatus this paper tries to make a thorough understandingof the effect of long-term ground surface vehicle loads onthe radial joint behavior of prefabricated and assembleunderpass Taking the Moziqiao underpass in Chengdu asan engineering background a numerical model wasconstructed to study the transient dynamic response of thestructure and 110 scaled model experiment were carriedout to study the long-term accumulative deformation ofthe joints According to the measured joint deformationdata of the model experiment characters of joint dis-placement were analyzed

2 Engineering Background

In the case of Moziqiao underpass crossing beneath thesouth section of the first ring road in Chengdu the locationof the project can be seen in Figure 1-e project is designedto relieve the heavy traffic in downtown Chengdu -eunderpass consists of two tubes one is 3-passing lane with awidth of 1185m and the other is 2-passing lane with a widthof 835m-e length of the project is 200m and the height ofthe underpass is 82m -e thickness of the plain fill is 3m-e cross section of the underpass is 1783m2 and the crosssection must be partitioned into segments -e partitionscheme was chosen by considering the internal force dis-tribution amounts of joints and construction time-e finalpartition scheme of the underpass was that the structure wascut at the middle in the height direction as shown inFigure 2(a) -e sketch of the project can be seen inFigure 2(b)

-e strength of the prefabricated concrete lining is C50-e mechanical and physical parameters of the plain fill andconcrete lining are shown in Tables 1 and 2 respectively

-e dynamic load induced by the vehicle moving on theground surface is not obvious due to the speed of the vehiclesis far slower than the wave velocity of the highway surface-erefore the influence of moving vehicle on the dynamicresponse of the ground surface can be neglected if thepavement is even enough However the pavement of anyhighway cannot be fully level and the pavement evennessbecomes worse with the service time It can be consideredthat the vertical vibration of vehicles is completely caused bythe unevenness of the ground surface [25ndash27] A harmonicloadmodel which can reflect the vehicle moving velocity andpavement unevenness was used to describe the vibrationinduced by highway vehicle by Chen [28] according to thesimplified form of dynamic load the cyclic load can beexpressed in the form of

F(t) P minus cos 2 times π timesv

ltimes t1113874 1113875 (1)

where P is the amplitude of the dynamic load assumed equalto 150 kN (vl) is the frequency of dynamic load v is themaximum vehicle velocity of the ground surface assumed as12ms and l is the wavelength of the pavement assumed as20m Hence equation (1) can be further simplified as

F(t) P minus cos(2 times π times 06 times t) (2)

3 Numerical and Physical Experiment Setups

31 Numerical Model Setup In order to study the behaviorof the underpass radial joints under dynamic load a 3Dnumerical model with the real project was constructed usingfinite element software ABAQUS 2016

-e flat radial joints were adopted in numerical mod-elling and connecters between the underpass segments werenot considered -ere are two shear keys which are installedat each radial joint

-e dimension of the model is 10m in length (in theaxial direction of the tunnel) 438m in width and 217m in





ChinaChengdu



Jinjiang river

N

1km


835 1185 7575

100

310

310

100

60

2230

(a) (b)


















(a)


(b)









3m

14m

1m


AB






ndash40

ndash30

ndash20

ndash10

0

10

20

30

40

Acc

eler

atio

n (m

ms

2 )

0402 0600 1008Time (s)

(a)



0102030405060

Acc

eler

atio

n (m

ms

2 )

02 04 06 08 10 12 14 16 18 20 22 24 2600Time (s)

(b)










(I) (II) (III) (IV)

(a)

VerticalLVDT

HorizontalLVDT

(I) (II)

(III) (IV)

(b)






RJ1

RJ1 Ope

ning

Ope

ning

Slipping

SlippingSlipping

Slipping

RJ2

RJ2

RJ3

RJ3

(a)




RJ1 RJ2 RJ3

(b)




RJ1 RJ2 RJ3

(c)

















024

020

016

012

008

004

000

Ope

ning

(mm

)

RJ3 RJ2 RJ1

000

ndash004

ndash008

ndash012

ndash016

ndash020

ndash024

Clos

ure (

mm

)

ClosureOpening


(a)

020

018

016

014

012

010

008

006

004

002

000

Ope

ning

(mm

)

RJ3 RJ2 RJ1

ClosureOpening


ndash020

ndash018

ndash016

ndash014

ndash012

ndash010

ndash008

ndash006

ndash004

ndash002

000

Clos

ure (

mm

)

(b)






TopedgeBottomedge


RJ3 RJ2 RJ1

00

05

10

15

20

25

30

Disp

lace

men

t (m

m)


(a)

TopedgeBottomedge


RJ3RJ2 RJ1

000

005

010

015

020

025

030

035

040

Disp

lace

men

t (m

m)


(b)

TopedgeBottomedge


RJ3 RJ2 RJ1

000

010

020

030

040

050

060

070

080

090

100

Disp

lace

men

t (m

m)


(c)

TopedgeBottomedge


RJ3 RJ2 RJ1

ndash100

ndash090

ndash080

ndash070

ndash060

ndash050

ndash040

ndash030

ndash020

ndash010

000D

ispla

cem

ent (

mm

)


(d)





6 Conclusions






Data Availability




Acknowledgments


References









































ChinaChengdu



Jinjiang river

N

1km


835 1185 7575

100

310

310

100

60

2230

(a) (b)


















(a)


(b)









3m

14m

1m


AB






ndash40

ndash30

ndash20

ndash10

0

10

20

30

40

Acc

eler

atio

n (m

ms

2 )

0402 0600 1008Time (s)

(a)



0102030405060

Acc

eler

atio

n (m

ms

2 )

02 04 06 08 10 12 14 16 18 20 22 24 2600Time (s)

(b)










(I) (II) (III) (IV)

(a)

VerticalLVDT

HorizontalLVDT

(I) (II)

(III) (IV)

(b)






RJ1

RJ1 Ope

ning

Ope

ning

Slipping

SlippingSlipping

Slipping

RJ2

RJ2

RJ3

RJ3

(a)




RJ1 RJ2 RJ3

(b)




RJ1 RJ2 RJ3

(c)

















024

020

016

012

008

004

000

Ope

ning

(mm

)

RJ3 RJ2 RJ1

000

ndash004

ndash008

ndash012

ndash016

ndash020

ndash024

Clos

ure (

mm

)

ClosureOpening


(a)

020

018

016

014

012

010

008

006

004

002

000

Ope

ning

(mm

)

RJ3 RJ2 RJ1

ClosureOpening


ndash020

ndash018

ndash016

ndash014

ndash012

ndash010

ndash008

ndash006

ndash004

ndash002

000

Clos

ure (

mm

)

(b)






TopedgeBottomedge


RJ3 RJ2 RJ1

00

05

10

15

20

25

30

Disp

lace

men

t (m

m)


(a)

TopedgeBottomedge


RJ3RJ2 RJ1

000

005

010

015

020

025

030

035

040

Disp

lace

men

t (m

m)


(b)

TopedgeBottomedge


RJ3 RJ2 RJ1

000

010

020

030

040

050

060

070

080

090

100

Disp

lace

men

t (m

m)


(c)

TopedgeBottomedge


RJ3 RJ2 RJ1

ndash100

ndash090

ndash080

ndash070

ndash060

ndash050

ndash040

ndash030

ndash020

ndash010

000D

ispla

cem

ent (

mm

)


(d)





6 Conclusions






Data Availability




Acknowledgments


References

















































(a)


(b)









3m

14m

1m


AB






ndash40

ndash30

ndash20

ndash10

0

10

20

30

40

Acc

eler

atio

n (m

ms

2 )

0402 0600 1008Time (s)

(a)



0102030405060

Acc

eler

atio

n (m

ms

2 )

02 04 06 08 10 12 14 16 18 20 22 24 2600Time (s)

(b)










(I) (II) (III) (IV)

(a)

VerticalLVDT

HorizontalLVDT

(I) (II)

(III) (IV)

(b)






RJ1

RJ1 Ope

ning

Ope

ning

Slipping

SlippingSlipping

Slipping

RJ2

RJ2

RJ3

RJ3

(a)




RJ1 RJ2 RJ3

(b)




RJ1 RJ2 RJ3

(c)

















024

020

016

012

008

004

000

Ope

ning

(mm

)

RJ3 RJ2 RJ1

000

ndash004

ndash008

ndash012

ndash016

ndash020

ndash024

Clos

ure (

mm

)

ClosureOpening


(a)

020

018

016

014

012

010

008

006

004

002

000

Ope

ning

(mm

)

RJ3 RJ2 RJ1

ClosureOpening


ndash020

ndash018

ndash016

ndash014

ndash012

ndash010

ndash008

ndash006

ndash004

ndash002

000

Clos

ure (

mm

)

(b)






TopedgeBottomedge


RJ3 RJ2 RJ1

00

05

10

15

20

25

30

Disp

lace

men

t (m

m)


(a)

TopedgeBottomedge


RJ3RJ2 RJ1

000

005

010

015

020

025

030

035

040

Disp

lace

men

t (m

m)


(b)

TopedgeBottomedge


RJ3 RJ2 RJ1

000

010

020

030

040

050

060

070

080

090

100

Disp

lace

men

t (m

m)


(c)

TopedgeBottomedge


RJ3 RJ2 RJ1

ndash100

ndash090

ndash080

ndash070

ndash060

ndash050

ndash040

ndash030

ndash020

ndash010

000D

ispla

cem

ent (

mm

)


(d)





6 Conclusions






Data Availability




Acknowledgments


References










































3m

14m

1m


AB






ndash40

ndash30

ndash20

ndash10

0

10

20

30

40

Acc

eler

atio

n (m

ms

2 )

0402 0600 1008Time (s)

(a)



0102030405060

Acc

eler

atio

n (m

ms

2 )

02 04 06 08 10 12 14 16 18 20 22 24 2600Time (s)

(b)










(I) (II) (III) (IV)

(a)

VerticalLVDT

HorizontalLVDT

(I) (II)

(III) (IV)

(b)






RJ1

RJ1 Ope

ning

Ope

ning

Slipping

SlippingSlipping

Slipping

RJ2

RJ2

RJ3

RJ3

(a)




RJ1 RJ2 RJ3

(b)




RJ1 RJ2 RJ3

(c)

















024

020

016

012

008

004

000

Ope

ning

(mm

)

RJ3 RJ2 RJ1

000

ndash004

ndash008

ndash012

ndash016

ndash020

ndash024

Clos

ure (

mm

)

ClosureOpening


(a)

020

018

016

014

012

010

008

006

004

002

000

Ope

ning

(mm

)

RJ3 RJ2 RJ1

ClosureOpening


ndash020

ndash018

ndash016

ndash014

ndash012

ndash010

ndash008

ndash006

ndash004

ndash002

000

Clos

ure (

mm

)

(b)






TopedgeBottomedge


RJ3 RJ2 RJ1

00

05

10

15

20

25

30

Disp

lace

men

t (m

m)


(a)

TopedgeBottomedge


RJ3RJ2 RJ1

000

005

010

015

020

025

030

035

040

Disp

lace

men

t (m

m)


(b)

TopedgeBottomedge


RJ3 RJ2 RJ1

000

010

020

030

040

050

060

070

080

090

100

Disp

lace

men

t (m

m)


(c)

TopedgeBottomedge


RJ3 RJ2 RJ1

ndash100

ndash090

ndash080

ndash070

ndash060

ndash050

ndash040

ndash030

ndash020

ndash010

000D

ispla

cem

ent (

mm

)


(d)





6 Conclusions






Data Availability




Acknowledgments


References













































(I) (II) (III) (IV)

(a)

VerticalLVDT

HorizontalLVDT

(I) (II)

(III) (IV)

(b)






RJ1

RJ1 Ope

ning

Ope

ning

Slipping

SlippingSlipping

Slipping

RJ2

RJ2

RJ3

RJ3

(a)




RJ1 RJ2 RJ3

(b)




RJ1 RJ2 RJ3

(c)

















024

020

016

012

008

004

000

Ope

ning

(mm

)

RJ3 RJ2 RJ1

000

ndash004

ndash008

ndash012

ndash016

ndash020

ndash024

Clos

ure (

mm

)

ClosureOpening


(a)

020

018

016

014

012

010

008

006

004

002

000

Ope

ning

(mm

)

RJ3 RJ2 RJ1

ClosureOpening


ndash020

ndash018

ndash016

ndash014

ndash012

ndash010

ndash008

ndash006

ndash004

ndash002

000

Clos

ure (

mm

)

(b)






TopedgeBottomedge


RJ3 RJ2 RJ1

00

05

10

15

20

25

30

Disp

lace

men

t (m

m)


(a)

TopedgeBottomedge


RJ3RJ2 RJ1

000

005

010

015

020

025

030

035

040

Disp

lace

men

t (m

m)


(b)

TopedgeBottomedge


RJ3 RJ2 RJ1

000

010

020

030

040

050

060

070

080

090

100

Disp

lace

men

t (m

m)


(c)

TopedgeBottomedge


RJ3 RJ2 RJ1

ndash100

ndash090

ndash080

ndash070

ndash060

ndash050

ndash040

ndash030

ndash020

ndash010

000D

ispla

cem

ent (

mm

)


(d)





6 Conclusions






Data Availability




Acknowledgments


References









































RJ1

RJ1 Ope

ning

Ope

ning

Slipping

SlippingSlipping

Slipping

RJ2

RJ2

RJ3

RJ3

(a)




RJ1 RJ2 RJ3

(b)




RJ1 RJ2 RJ3

(c)

















024

020

016

012

008

004

000

Ope

ning

(mm

)

RJ3 RJ2 RJ1

000

ndash004

ndash008

ndash012

ndash016

ndash020

ndash024

Clos

ure (

mm

)

ClosureOpening


(a)

020

018

016

014

012

010

008

006

004

002

000

Ope

ning

(mm

)

RJ3 RJ2 RJ1

ClosureOpening


ndash020

ndash018

ndash016

ndash014

ndash012

ndash010

ndash008

ndash006

ndash004

ndash002

000

Clos

ure (

mm

)

(b)






TopedgeBottomedge


RJ3 RJ2 RJ1

00

05

10

15

20

25

30

Disp

lace

men

t (m

m)


(a)

TopedgeBottomedge


RJ3RJ2 RJ1

000

005

010

015

020

025

030

035

040

Disp

lace

men

t (m

m)


(b)

TopedgeBottomedge


RJ3 RJ2 RJ1

000

010

020

030

040

050

060

070

080

090

100

Disp

lace

men

t (m

m)


(c)

TopedgeBottomedge


RJ3 RJ2 RJ1

ndash100

ndash090

ndash080

ndash070

ndash060

ndash050

ndash040

ndash030

ndash020

ndash010

000D

ispla

cem

ent (

mm

)


(d)





6 Conclusions






Data Availability




Acknowledgments


References




















































024

020

016

012

008

004

000

Ope

ning

(mm

)

RJ3 RJ2 RJ1

000

ndash004

ndash008

ndash012

ndash016

ndash020

ndash024

Clos

ure (

mm

)

ClosureOpening


(a)

020

018

016

014

012

010

008

006

004

002

000

Ope

ning

(mm

)

RJ3 RJ2 RJ1

ClosureOpening


ndash020

ndash018

ndash016

ndash014

ndash012

ndash010

ndash008

ndash006

ndash004

ndash002

000

Clos

ure (

mm

)

(b)






TopedgeBottomedge


RJ3 RJ2 RJ1

00

05

10

15

20

25

30

Disp

lace

men

t (m

m)


(a)

TopedgeBottomedge


RJ3RJ2 RJ1

000

005

010

015

020

025

030

035

040

Disp

lace

men

t (m

m)


(b)

TopedgeBottomedge


RJ3 RJ2 RJ1

000

010

020

030

040

050

060

070

080

090

100

Disp

lace

men

t (m

m)


(c)

TopedgeBottomedge


RJ3 RJ2 RJ1

ndash100

ndash090

ndash080

ndash070

ndash060

ndash050

ndash040

ndash030

ndash020

ndash010

000D

ispla

cem

ent (

mm

)


(d)





6 Conclusions






Data Availability




Acknowledgments


References









































TopedgeBottomedge


RJ3 RJ2 RJ1

00

05

10

15

20

25

30

Disp

lace

men

t (m

m)


(a)

TopedgeBottomedge


RJ3RJ2 RJ1

000

005

010

015

020

025

030

035

040

Disp

lace

men

t (m

m)


(b)

TopedgeBottomedge


RJ3 RJ2 RJ1

000

010

020

030

040

050

060

070

080

090

100

Disp

lace

men

t (m

m)


(c)

TopedgeBottomedge


RJ3 RJ2 RJ1

ndash100

ndash090

ndash080

ndash070

ndash060

ndash050

ndash040

ndash030

ndash020

ndash010

000D

ispla

cem

ent (

mm

)


(d)





6 Conclusions






Data Availability




Acknowledgments


References








































6 Conclusions






Data Availability




Acknowledgments


References






































radialjointsbehaviorofaprecastasymmetricunderpass … · 2020. 3. 23. · segment itself due to the...

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