INTERNATIONAL SOCIETY FOR

SOIL MECHANICS AND

GEOTECHNICAL ENGINEERING

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Geotechnical Aspects of Underground Construction in Soft Ground – Yoo, Park, Kim & Ban (Eds)© 2014 Korean Geotechnical Society, Seoul, Korea, ISBN 978-1-138-02700-8

Evaluation of movements and structural forces resulting

from bored tunnelling in sand

B.C.B. HsiungCECI Engineering Consulting Inc. TaiwanNational Kaohsiung University of Applied Sciences, Kaohsiung City,Taiwan

C.C. TsaiNational Taipei University of Technology, Taipei City, Taiwan

H.N. Huang & W.Y. SongNational Kaohsiung University of Applied Sciences, Kaohsiung City, Taiwan

ABSTRACT: Case histories of bored tunnels in sand in southern Taiwan are selected as a research backgroundin this paper. Details of these tunnels and observations of ground movement induced by tunnel constructionare briefly described here. By using numerical analyses, this paper aims to interpret possible ground loss rateinduced by tunnel construction. Further, structural forces on tunnel segments are further evaluated associatedwith different approaches and output are compared and discussed. It is concluded that less than 0.5% of groundloss rate is reached during tunnel construction. Larger displacement was predicted from numerical analyses andthe possible reason shall be mainly related to larger contraction ratio used. In addition, from exercises of the useof two different constitutive models, the analyses using Hardening Soil model could give a better description ofsettlement trough since said model has an additional consideration regarding soil stiffness under unload-reloadconditions. Second, various approaches are adopted to explore structural forces, such as shear force, axial forceand bending moment during tunnel construction. Under the same load condition and soil profile, it is initiallyfound that the analyses using the beam-spring method to predict the smallest bending moment, shear force andaxial forces rather than others. It is aware that ground loss rate and twin tunnel interaction would not affect anyresult from analyses using elastic equation method and beam-spring method since only loads and details of ringare considered in these two approaches. Considering analytical results, it is understood that the middle of ring(90 degree from top of tunnel) have to take the maximum bending moment.

1 INTRODUCTION

Due to the increasing need for underground space inurban areas, bored tunnelling methods are commonlyadopted. However, construction of such tunnels in softground may induce significant displacement on thesurface so attention must be paid to tunnels located incrowded urban areas. By using an example of a tun-nel project in Kaohsiung, Taiwan, as the background,displacements simulated from various approaches arecompared with field observations. Further discussionsare delivered also.

In addition, structural forces on tunnel lining areconsidered in engineering practice for bored tun-nel design as such issues could determine the rein-forcement used for lining. Based on tunnels on theHanoi Metro, Do et al. (2013) delivered analyses byusing several methods, such as Einstein and Schwartz(1979), elastic solution method (JSCE, 1996) andtwo-dimensional analysis by using FLAC commercialsoftware. Such works indicated some differences in

terms of the bending moment and normal forces ontunnel lining structures.

In fact, structural forces stated above may possi-bly be affected by several factors, such as deformationand loading on the structures, ground conditions aswell as details of tunnel lining adopted and influ-ences on forces from these factors are essential to beexplored. This has resulted in the motivation to deliverthis study associated with different analytical schemeswith a bored tunnel case in Kaohsiung to examine suchimpact.

2 THE SITE AND THE OBSERVATIONS

A twin-parallel-bored tunnel located in Package CO2

on Orange Line of Kaohsiung MRT has been taken asbackground for the study. The tunnel was connectedbetween O6 and O7 Station and its internal diameter is5.6 m. The track length of said tunnel is 851.8 m. Thetunnel was constructed using a 6.23 m diameter earth

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pressure balance (EPB) machine and the main groundconsisted of a very deep and thick sandy material withoccasional clay content. As indicated in Figure 1, thesurface level above tunnel is quite uniform, in the rangeof elevation of 104 to 105 m. It also shows the tunnelwas mainly bored in sand.The twin tunnel remains par-allel at the same depth and the centre to centre distanceof the two tunnels is approximately 12.0 m at one endbut becomes slightly wider (14.0 m) at the other. Over-burden depth varies from 15 to 17 m. Table 1 presentssome basic information on the soil at the project site,such as description, depth, total unit weight (γt) andSPT-N value. Please refer to Hsiung (2011) for furtherdetails.

An intensive instrumentation system was installedwhich mainly aims to explore surface settlementsinduced by tunnel construction in both longitudinaland transverse directions. Figure 2 shows the loca-tion of settlement points above the tunnel and it isseen that the monitoring array starts at a central pointbetween two tunnels and further expands to two sidesfor measurement of surface settlement in transversedirections. The further most point is located at 19 mfrom the central point between two tunnels. Similarly,settlement measurement points are installed every 5 to40 m on surface level along the tunnel axis so settle-ment induced by tunnel construction in longitudinaltunnel could thus be monitored.

Hsiung (2011) shows settlement measured on sur-face level from the project. As indicated in Figure 1,the ground starts to settle once the shield machineapproaches and this is mainly related to loss of groundcaused by shield advance and tail void. After 20–40days of passing of the machine, the ground becomesstable since no consolidation settlement is expected.The ground may settle dramatically again due to the

Figure 1. Longitudinal and ground profile of the project.

Table 1. Basic soil information at the project site.

Layer Description of ground Depth γt (kN/m3) SPT-N value

I Grey silty sand Surface to 6.5 m below; groundwater 19.6 5 to 6level observed at 2.9 m below ground level

II Grey silt with sandy clay 6.5 m to 8.5 m below ground level 18.9 6III Grey silty sand occasionally 8.5 m to 23.0 m below ground level 20.0 6 to 15

with sandy siltIV Grey silty clay with sandy silt 23.0 m to 25.0 below ground level 19.3 12V Grey silty sand with sandy silt Beneath 25.9 m below the surface level 19.8 12 to 19

approaching of the 2nd shield machine for the otherparallel tunnel nearby. It is aware that surface settle-ments varying from 6 to 10 mm during the 1st drivebut can reach up to 8 to 12 mm at the end after thepassing of the 2nd machine.

3 MOVEMENT ANALYSES

Lake et al. (1996) commented that the displacementoccurred at a place ahead of the tunnel face but isdifficult to be verified by observations shown on thisproject (Hsiung, 2011) as the settlements here onlypresents data immediately after passing the shieldhead, though it is very unlikely since only very lim-ited settlement seen during the passing of shield head.

Figure 2. Location of layout of monitoring of settlement.

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The difference may be connected with ground condi-tions, workmanship and innovation of the machine butfurther exploration will be necessary.

Considering observations measured in the trans-verse direction at three sections on the ground surfaceabove tunnel named LUO08-1, LUO08-2 and LUO08-3 and details of the project, Hsiung (2011) carried outanalyses associated with empirical approaches sug-gested by Peck (1969) and O’Reilly and New (1982) toverify possible ground loss rate caused by tunnel con-struction. It is interpreted that ground loss rate inducedby tunnel construction is in a wide range of 0.12%to 0.75% but it is 0.27% to 0.57% for up-line tunneland 0.30% to 0.76% for down-line tunnel at SectionLUO08-1. In such method, surface settlement mea-sured has to be applied as a base of interpretation andthe settlement trough from empirical approaches hasto fit such measurement data. The ground loss rate canthus be determined.

Alternatively, similar works have been done byusing numerical tools. Similar to works accompa-nied with empirical approaches, measured settlementtrough in transverse direction shall be fit with settle-ment trough from numerical simulation by varyingground loss rate (contraction ratio) as well as fixedground and structural details. The commercial soft-ware PLAXIS was adopted for such works. SectionLUO08-1 was selected as the background of thisstudy and Table 2 presents soil parameters used for allnumerical analyses. In Table 2, φ′ is effective frictionangle of soil and γt is total unit weight of soil.

It is noted that elastic modulus of soil (E) isdetermined by:

E = 2000N (unit: kPa) for sand; andE = 500Su for clay

in which Su is undrained shear strength of clay and Nis SPT-N value.

Except soil parameters, structural parameters haveto be given based on actual tunnel lining properties.An elastic plate element is selected for simulation ofbehavior of tunnel lining. Pre-cast reinforcement con-crete was adopted for tunnel lining here and width andthickness of lining is 120 cm and 25 cm, respectively.Elastic modulus of reinforcement concrete lining isassumed to be 31,400,000 kPa associated with itsstrength. All parameters used for tunnel lining arelisted in Table 3.

Table 2. Soil parameters used for analyses.

Depth atSoil bottom of γt , Poisson

classification layer (m) kN/m3 φ′◦ E(kPa) ratio

SM 6.5 19.6 31 12000 0.30CL 8.5 18.9 30 21000 0.45SM 23.0 20.0 32 22000 0.30CL 25.0 19.3 32 45500 0.45SM 45.0 19.8 33 54000 0.30

In PLAXIS, the software provides a built-in ele-ment named “tunnel element”. In such element, it givesa function called “contraction ratio”. By assumingcontraction ratio, it indicates convergence of circulartunnel so the ground consequently settles accompaniedwith said convergence.

The constitutive model named Mohr-Coulomb(MC) is adopted for analyses. MC model is an elas-tic perfect plastic model and parameters of cohesionforce and effective friction angle of soils are adoptedfor determining yield surface of the soil. A single con-stant elastic modulus has to be provided to definestress-strain behavior of soil.

Similar to Chen (1997) previously the verticalboundary of the analysis is set at 50 m away from cen-terline between two tunnels, approximately 8 times oftunnel diameter. Similarly, the horizontal boundary hasto be ensured to be set at the depth which not affectedby any activity of construction so it was set at 45 mbelow surface level.

For comparison purposes, the other constitutivemodel called the Hardening Soil (HS) model isselected for analyses too. Main differences betweenthese two models (MC & HS) are elastic modulus ofsoil has to remain the same all the time in the analysisof MC model but different elastic modulus of soil canbe assigned for soil under unloaded condition in HSmodel.

As soil stiffness at small strain level is consideredfor ground behavior induced by deep excavations andas Hsiung (2002) commented that soil stiffness inter-preted from shear wave velocity measured on site ismore suitable to be adopted for simulation of deepexcavations in sand, said value thus was used for def-inition of reference soil modulus (E50) in HS modelin order to explore impact of selections of constitu-tive model and also soil stiffness. Again, referencesoil modulus under unload-reload condition (Eur) isassumed to be three times of E50.

Figure 3 presents numerical analyses by the use ofPLAXIS and the ground loss rate interpreted (0.7%)from analyses using empirical method were taken tobe contraction ratio in numerical analyses. It is seenfrom Figures 3 that no matter analyses using MC orHS model, the settlement from numerical simulationseems to be greater than observed settlements and rea-sons are further explored. First, a higher value forcontraction ratio is selected and this could possibly

Table 3. Structural parameters used for tunnellining.

Parameter

Internal radius (m) 2.8Thickness (m) 0.25

Axial stiffness (kN/m) 7.85 × 106

Bending stiffness (kN/m) 4.09 × 104

Equivalent thickness (m) 0.25Equivalent unit weight (kN/m/m) 6.0Poisson Ratio 0.2

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Figure 3. Comparison of predicted and observed surfacesettlement trough for down-line tunnel of LUO08.

give a larger displacement from numerical analyses.Second, as ground loss rate interpreted from empiricalapproach is directly based on settlement trough on sur-face but contraction ratio is taken from convergence oftunnel in deeper ground for numerical analyses, thesetwo numbers could be different.

Settlement troughs from predictions using MC andHS model were compared and it was found that settle-ment trough from HS model has a larger settlement atthe same location of tunnel centre and then becomesmuch smaller in the place away from the tunnel. In con-trast, the settlement trough from MC model becomesmuch flat and extends further in the place away fromthe tunnel. As tunnel construction is a stress-reliefactivity and HS model does have an additional descrip-tion in soil stiffness during unloaded condition, this isexpected to be the reason leading for such difference.In addition, a greater surface settlement at centre oftunnel predicted from analyses of HS model might beconnected with lower estimated value of Eur . However,neither of them could have good performance at far endof the excavation and this is expected to be related tolimit of both models in definition of soil stiffness ofsmall strain behavior.

As indicated above, the contraction ratio may not bethe same with ground loss rate interpreted from sur-face settlement trough.Therefore, a different approachis delivered by using TUNNEL 3D. Such software issimilar to PLAXIS, a finite element package but allowsthe user to generate 3-dimension mesh of tunnel toevaluate deformation and stability of tunnel instead of2-dimensional one. For each new 3-dimension project,a 2-dimensional cross section has to be first developedand then further define 3-dimension mesh by givendetails in longitudinal direction. Necessary nodes andelements for analyses are thus defined herein.

By using different contraction ratio directly, thesettlement troughs are compared with the one fromfield measurement so possible ground loss rate can bedefined. Therefore, ground loss rate from interpretedfrom empirical approach aren’t relied upon anymoreand the settlement trough in both longitudinal andtransverse directions can be explored.

First of all, boundaries and mesh of analytical mod-els of TUNNEL 3D have to be defined. The sameset-up of vertical and horizontal boundaries used foranalysis of PLAXIS is adopted but the boundary inlongitudinal direction has to be additional determinedhere. Sensitive analyses by the use of 1 m, 10 m and

100 m were carried out and results indicate no signifi-cant difference is seen from analyses having differencelength of model in longitudinal direction. Consideringresults of sensitivity analysis of boundaries conditions,100 m long boundary in longitudinal direction wasadopted. Again, elastic-perfect plastic Mohr-Coulombmodel is selected for analyses usingTUNNEL 3D. Soilparameters listed in Table 2 are used for analyses.

By varying contraction ratio in the range of 0.5to 2.0%, surface settlement troughs from numericalanalysis are presented and compared with field obser-vations. It is found that measured data in general fit thesettlement trough predicted using 0.5% or even less.Although additional conditions in longitudinal direc-tion can be defined in TUNNEL 3D but it is verylikely such function does not provide any advantagein comparison with analyses of PLAXIS as predictedsettlement troughs from analyses by use of both soft-ware are almost the same once the same contractionratio is used, though TUNNEL 3D is claimed as a3-dimensional analytical software.

4 STRUCTURAL FORCES ANALYSIS

As indicated above, except displacement induced bytunnel construction, stresses on tunnel lining, such asshear forces, bending moment and axial forces areimportant features and have to be explored so detailsof reinforcement can thus be designed. Previous stud-ies related evaluation of structural forces on tunnelsegments and related analytical approaches includeMuir-Wood (1975), Curtis (1976), and ITA (2000) etc.

In order to examine structural forces on tunnellining, several approaches, such as updated elasticequation method proposed by JSCE in Japan Stan-dard for Shield Tunneling (JSCE, 2006), beam-springmethod (Mitsuho Information & Research Institute,2006) and Finite Element Method (FEM) by usingTUNNEL 3D. Details of each approach are brieflydescribed, as follows.

First of all, similarly to Do et al. (2013) described,the elastic equation method is a simple method allowedto calculate forces, such as bending moment, shearforce and axial force of a circular tunnel associatedwith vertical load, horizontal load, horizontal triangu-lar load, soil reaction and dead load. Structural forcesare interpreted first individually and sum up togetherafterwards.

Secondly, structural forces are defined by a built-inbeam-spring model in a commercial software named“MOLEMAN-I” which is widely used and acceptedin Japan and other countries in Asia. The tunnels arebuilt with staggering joints in the model and up to 3rings are allowed to be assumed in the model. Sincethe dimension of the tunnel in longitudinal direction iscomparatively larger than the dimension in the othertwo directions, it can be expected that the tunnel willact as plane-strain behavior. Therefore, the analysiscan be delivered by assuming a model having twohalf-ring and one full ring to represent the tunnel

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structure. Each ring is assumed as a beam and soilsare assumed to act as springs to connect with the beamwith various stiffness which defined by the user.

By giving necessary input parameters, such asloads, details of number of segments, joint conditionsand imposed displacements on tunnel, displacementand structural forces, such as bending moment, shareforce and axial forces of tunnel segment.

5 DISCUSSIONS

In order to properly express structural forces on seg-ments, an index system was designed and adopted. Insaid system, the direction of 12 o’clock is designatedas “0 degree” and the direction of 6 o’clock is desig-nated as “180 degree”. As the structure of tunnel is asymmetric structure, only structural forces on half ofthe structure from different approaches are presented.

Predicted shear force is an important index ofdesign of shear reinforcement and Figures 4 presentsshear force on segment from up-line tunnel tunnel ofLUO08. As shown in Figure 6, it is indicated thatthe predicted shear force which segment has to takeis in the range of zero to 60 kN/m from analyses bythe use of TUNNEL 3D for the case having 0.5% ofground loss rate. Further, it seems that there is no defi-nitely relationship between axial force and ground lossrate. Since axial force of tunnel segment from analy-ses ofTUNNEL 3D is defined by relative displacementbetween two points on the segment, ground loss ratethus does not have direct impact on axial force of seg-ments. Similar results of axial force are reached fromanalyses using elastic equation method but such resultsare larger than results from beam-spring method (in therange of zero to 30 kN/m). However, the locations withthe maximum shear force is different from these threeapproaches.

Moreover, prediction of shear force of down-linetunnel presents that maximum value reaches up to40 kN/m from analyses by the use of TUNNEL 3D forthe case having 0.5% of ground loss rate. However, itis not consistent with results from analyses for up-linetunnel since shear force increases once the ground lossrate increases and the reason for such inconsistence hasto be further explored. The predicted shear forces fromboth elastic equation method and beam-spring methodare exactly the same for down-line tunnel with up-linetunnel.As only loads on tunnel are considered for anal-yses and factors of ground movements and interactionbetween twin tunnels are ignored in both methods, it isanticipated to be the reasons that predicted shear forcesfor up-line and down-line tunnel remain the same.

Secondly, predicted axial force on tunnel segment isfurther demonstrated and it is indicated that the max-imum axial force can reach up more than 800 kN/mfrom analyses using TUNNEL 3D for the case having0.5% of ground loss rate for up-line tunnel and axialforce can be further reduced once the ground loss ratedecreases. The maximum axial force is only 700 kN/m

Figure 4. Shear forces on tunnel segment for up-line tunnel.

Figure 5. Bending moment on tunnel segment for up-linetunnel.

for the case having 2.0% of ground loss rate. The max-imum axial force predicted from analyses using elasticequation method and beam-spring method is approxi-mately 730 kN/m and 600 kN/m, respectively. Similarto results of shear force, analyses using beam-springmethod give the smallest value rather than others.Attentions are paid to the location having the maxi-mum axial force and it looks like analyses associatedwith elastic equation method and beam-spring methodindicate the place having 90 degree from top of tun-nel shall take the maximum axial force during tunnelconstruction, though theory of interpretation is differ-ent. It is found that very similar results are reached fordown-line tunnel, even if a different approach is used.

At last, Figure 5 expresses the bending momentfrom predictions using different approaches for up-line tunnel. It is seen that predicted maximum bendingmoment by the use of TUNNEL 3D is in the clusterof 50 to 75 kN-m, no matter what ground loss rateis. The place having the maximum bending momentis seen in the place having 90 degree from top oftunnel. Moreover, the trend of prediction of bendingmoment from analyses using elastic equation methodand beam-spring method are similar to results fromanalyses using TUNNEL 3D but the magnitude seemsto be smaller, up to 50 kN-m only. Simulations alsoshow similar results for bending moment of down-line tunnel. It is herein concluded that impacts fromground loss rate (soil displacement) and twin-tunnelinteraction on magnitude of bending moments are lim-ited since both factors don’t cause differences in bothtunnels.

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6 CONCLUSIONS

The following conclusions are made associated withthe output of this study. Firstly, a wide range (0.12%to 0.76%) of ground loss rate was interpreted fromempirical approach for a bored tunnel constructed insand based on observed surface trough. In contrast,predictions from numerical analyses indicate less than0.5% of ground loss rate can be reached for said tun-nel construction. Secondly, a larger displacement waspredicted from the analyses using PLAXIS and thepossible reason shall be mainly related to larger con-traction ratio in analyses used. In addition, from theexercise of the use of two different constitutive models,the analyses using HS model can give a better descrip-tion of predicted settlement trough since said modelhas an additional consideration regarding soil stiffnessunder unload-reload conditions. However, surface set-tlements at locations far away from the tunnel can’t beproperly predicted by any model used in this study dueto limits in description of soil stiffness at small strainlevel.

Apart from displacement, structural forces on tun-nel segments are important features in tunnel design.Therefore, various approaches were adopted to explorestructural forces, such as shear force, axial force andbending moment during tunnel construction. Underthe same load condition and soil profile, it is first foundthat the analyses using beam-spring method predictthe smallest bending moment, shear force and axialforces rather than others. It is noticeable that groundloss rate and twin tunnel interaction would not affectany result from analyses using elastic equation methodand beam-spring method since only loads and detailsof ring are considered in these two approaches. Anal-yses using TUNNEL 3D for prediction of shear forceand axial forces are not recommended since there arestill some unknown to be solved. Considering analyti-cal results, it is understood that the middle of ring (90degree from top of tunnel) have to take the maximumaxial force and bending moment. At the end, it is alsoconcluded that limited impacts can be generated fromground loss rate and twin-tunnel interaction on mag-nitude of predicted bending moment, no matter whichmethod is adopted.

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