thesis stijn van hoye 0601 - lib.ugent.be · stijn van hoye multiple independent shield-driven...

Stijn Van Hoye

multiple independent shield-driven tunnels

Combining bored tunnels - Optimal construction order of

Academic year 2016-2017Faculty of Engineering and ArchitectureChair: Prof. dr. ir. Peter TrochDepartment of Civil Engineering

Master of Science in Civil EngineeringMaster's dissertation submitted in order to obtain the academic degree of

Counsellor: Dr. ir. Ken SchotteSupervisors: Prof. dr. ir. Hans De Backer, Prof. ir. Bart De Pauw

The author gives permission to make this master dissertation available for consultation

and to copy parts of this master dissertation for personal use. In the case of any other

use, the copyright terms have to be respected, in particular with regard to the obligation

to state expressly the source when quoting results from this master dissertation.

Ghent, June 2017

Acknowledgements

First of all, I would like to thank everyone who helped and supported me during the

writing of this master dissertation. It is impossible to mention everyone, but know that I

am very grateful to every single one of you.

In particular, I would like to thank my supervisors prof. dr. ir. Hans De Backer and

prof. ir. Bart De Pauw for their critical and constructive support throughout the entire

year. I also want to extent my gratitude to my counsellor Dr. ir. Ken Schotte for his

permanently available assistance throughout the year. In addition, I want to thank the

laboratory of Geotechnics at Ghent University for sharing their knowledge in the field of

tunnelling. Furthermore, special thanks to the ICT department in building 904 of the

Tech lane Ghent Science Park for solving all my software related issues within the day

every single time.

Finally, I would like to express my gratitude to the people that made this final year a

year full of great experiences. You, my parents, high school friends, sailing friends, the

C&C family and all the amazing people I met along the way.

Ghent, June 2017

Stijn Van Hoye

Combining bored Tunnels: Optimal construction order of multiple independent shield-driven tunnels

by

Stijn Van Hoye

Masters dissertation submitted to obtain the academic degree of Master of Science in Civil Engineering

Academic year 2015-2016

Ghent University

Faculty of Engineering and Architecture

Department of Civil Engineering

Chair: Prof. dr. ir. Peter Troch

Supervisors

Prof. dr. ir. Hans De Backer

Prof. ir. Bart De Pauw

Abstract Tucrail proposed a three tunnel configuration in which the area, enclosed by the three

tunnels, can be utilized as functional space. This master dissertation investigates the

optimal construction order of the bored tunnels, mainly focusing on the settlements and

deformations of the surrounding soil mass. All two tunnel and three tunnel construction

orders are investigated by mainly focusing on the surface settlements calculated with

Plaxis 2D. An extended variant of the grout pressure method is developed to also

incorporate the relative magnitude of the different settlement components due to shield

tunneling. The accuracy of a simplified version is simultaneously tested by comparison

of the obtained final settlement troughs. The influence of the constitutive model on the

settlement values is also verified. More specifically, the difference in results between the

Mohr-Coulomb model and the Hardened Strain model with small strain stiffness is

investigated. Finally, a simple empirical superposition principle is established based on

the method of Peck to approximate the Plaxis results. The research is based on the

geometry of and other assumptions made for a new tunnel connection in Brussels. The

findings can however be generalized to other multiple tunnel configurations.

Keywords: Multiple tunnels, Settlements, Construction order, Grout pressure method,

Plaxis 2D

Counsellor

Dr. ir. Ken Schotte

Combining bored Tunnels: Optimal construction order of multiple independent shield-driven tunnels

Stijn Van Hoye

Supervisor(s): Prof. dr. ir. Hans De Backer, Prof. ir. Bart De Pauw, Dr. ir. Ken Schotte

Abstract- A three tunnel configuration was proposed by

Tucrail to strengthen the North-South connection in Brussels. The optimal construction order of the bored tunnels, mainly focusing on the settlements and deformations of the surrounding soil mass is investigated here. All two tunnel and three tunnel construction orders are investigated by mainly focusing on the surface settlements calculated with Plaxis 2D. An extended variant of the grout pressure method is developed to also incorporate the relative magnitude of the different settlement components due to shield tunneling. The accuracy of a simplified version is simultaneously tested by comparison of the obtained final settlement troughs. The influence of the constitutive model on the settlement values is also verified. More specifically, the difference in results between the Mohr-Coulomb model and the Hardened Strain model with small strain stiffness is investigated. Finally, a simple empirical superposition principle is established based on the method of Peck to approximate the Plaxis results. The research is based on the geometry of and other assumptions made for a new tunnel connection in Brussels. The findings can however be generalized to other multiple tunnel configurations. Keywords- Multiple tunnels, Settlements, Construction order,

Grout pressure method, Plaxis 2D

I. INTRODUCTION Brussels has the largest mobility issues in Belgium. To

tackle these issues, kilometers of new metro lines including new substations are going to be build. Part of the plan is to strengthen the North-South connection starting from Schaarbeek. To minimize the amount of disruption to the daily city life, that part of the metro expansion is completely tunneled.

For the tunneled part between the main North and Central stations, Tucrail proposed a new type of tunnel design. In general, a tunnel diameter is chosen in function of the required space that is requested. The tunnel diameter is limited, therefore when more space is desired the roads or rails are fitted into two tunnels. Tucrails idea was to construct three smaller tunnels with TBMs and to also utilize the area, enclosed by the three tunnels, as functional space. Combining multiple tunnel tubes into a larger whole of independently drilled tunnels is a delicate operation. The University of Ghent has been asked to further investigate the feasibility of the idea for the North-Central connection. focusing on the settlements and deformations of the surrounding soil mass is investigated here.

S. Van Hoye is a graduate student civil engineering, Ghent University

(UGent), Gent, Belgium. E-mail: [email protected] .

II. CALCULATION METHODS

A. Empirical formulations The most globally used empirical method is to approximate

the surface settlement by a Gaussian curve according to Peck [1]:

!" # = !",&'( *+, - .

/

01/ (1) With !",$%& the maximal transversal settlement, y is the

horizontal distance from the tunnel axis and i is the horizontal distance from the tunnel axis to the point of inflection. OReilly and New proposed a straightforward linear relationship to the tunnel depth z0: ! = # %& [3]. The settlement trough is represented by a Gaussian curve in Figure II.1.

Figure II.1: Gaussian curve for transverse settlement through and

ground loss

The volume loss Vs is equal to the volume of the settlement through and can be achieved by integrating Equation II.1. The ground loss Vt is defined as the volume of ground that is over excavated compared to the installed tunnel volume as visualized in the bottom part of Figure II.1. The following can be assumed without introducing large errors: Vs = Vt [2]. The ground loss ratio (GLR) can thus be defined as follows with At the excavated tunnel volume:

!"# = %&'& %)'& (2)

The principle of superposition is often applied to determine the final settlement trough due to multiple tunnels. The transverse settlement troughs are then determined separately for each tunnel according to Peck and afterwards superimposed to estimate the final settlement trough. Many however confirmed its inaccuracy and recommended more complicated superposition relationships to among others obtain the correct trough skewness [4].

B. Finite element method Plaxis 2D The numerical calculations were performed in Plaxis 2D.

An extended version of the grout pressure method was developed. Numerical methods in general overestimate the trough width. The grout pressure method however is known to best estimate the trough width [6].

Moreover, the influence of the constitutive model on the results was verified for the MC model and the HSsmall model. In particular the Oedometer modulus Eoed,MC of the MC model was related to the unloading reloading modulus of the HSsmall Eur to improve the accuracy of the MC model.

Current research postulates the following conclusions concerning the influence of the constitutive model. Firstly, the settlement through becomes deeper when taking into account plastic deformations. Secondly, considering hardening mechanisms results in a wider settlement through. Lastly, taking into account the small strain stiffness leads to a reduction in maximal settlements without affecting the through width [5]. The HSsmall model is known to be superior in predicting the settlements.

The interaction between sequentially constructed tunnels is known to be overestimated by FEMs. The simulation of a series of tunnel excavations appeared to lead to an accumulation of undesirable shear strains around the existing tunnels due to the latest excavated tunnels. The undesirable shear strains reduce the soil stiffness and lead to higher peak values and a wider settlement through [7]. Chen et al. discovered that modelling the construction of all tunnels simultaneously could lead to better approximations of the field results [8].

III. MODEL VALIDATION

A. Extended grout pressure method The idea was to simulate all construction stages that belong

to a slurry TBM excavation process. Table III.1 provides an overview of the utilized construction phases and its characteristics. The face pressures [9][10] and tail void pressures [11][12][13][14] were carefully determined based on existing research.

Table III.1 Overview of the the grout pressure method

Phase Action Characteristics Phase 0 Initial Phase / Generation of initial state

Phase 1 Face pressure

- Deactivate soil cluster - Apply face pressure

P",$%" = P' + P)'*%$ + 20kPa P/01 = 12345/7

Phase 2 TBM

- Remove face pressure - Activate TBM

Undeformable TBM

Phase 3 Tail pressure 0

- Remove TBM - Apply tail void pressure 0

P*,$%"8 = P$%","'1% + 100kPa P/01 = 16kPa/m


- Apply tail void pressure 1

P*,$%"; = P*,$%"8 30kPa P/01 = 11kPa/m


- Apply tail void pressure 2

P*,$%"> = P)'*%$ + 30kPa P/01 = 11kPa/m

Phase 6 Final state

- Remove tail void pressure 2 - Activate tunnel lining

Deformation of tunnel lining

The simplified version of the proposed grout pressure method consists of the final two phases 5 and 6 listed in Table III.1.

B. Case study The proposed grout pressure method was validated by

estimating the settlements of the second Heienoord tunnel. The results were compared with the field measurements and the calculations of Mller [15]. The full model slightly underestimated the amount of settlements, while the simplified model approximated the field measurements to the mm.

IV. TUCRAIL PROPOSITION

A. General information The final three tunnel configuration holds space for four rail

tracks. The configuration is made up of the reinforced whole of three individually excavated tunnels and the enclosed area in between. The tunnel center of the bottom tunnels is situated at a depth of 20m. The water table is assumed to be located five meters below the ground level. The diameter of the two bottom tunnels and the top tunnel equal 10m and 8m respectively. After excavation of the three tunnels the soil surrounding the area enclosed by the three tunnels is grouted. The three tunnels are then reinforced and interconnected with concrete elements. Finally, the enclosed soil area can be excavated. The geometry of the Tucrail configuration is visualized in Figure IV.1.

Figure IV.1: Geometry of the Tucrail tunnel configuration

The soil layer profile is simplified to one thick clayey sand layer. All calculations were performed using the HSsmall constitutive model. The MC model came into play whenever the influence of the constitutive model on the results was investigated. The soil parameters corresponding to each model can be found in Table IV.1.

The material characteristics of the tunnel linings are listed in Table IV.2. The thicknesses of the tunnel lining are 0.5m and 0.4m for the 10m diameter tunnel and the 8m diameter tunnel respectively. The stiffness and other parameters are calculated based on these thicknesses. The weight of the lining is calculated per meter tunnel lining in plane of the tunnels cross section and per meter in the longitudinal direction of the tunnel axis. A density of 260 kg/m3 [12] is

assumed for the density of the gantry in order to be able to calculate the weight of the TBM. The TBM is assumed to be undeformable and is ascribed the following stiffnesses:

!" = 10' ()+,+' and !" = 10'

()*' (2)

Table IV.1: Overview of the soil parameters

Parameter Unit HSsmall MC ?@ABCD [kN/mF] 17 16 ?BCD [kN/mF] 19.8 20

GHIJ,KIL [MPa] 30 30 MN [kPa] 2 2 ON [ ] 34.3 32 P [ ] 4.3 5 Q [-] 0.3 0.3 RS [-] 0.47 0.47 TS,KIL [MPa] 94 8.57 UV [%] 50 - G@K,KIL [MPa] 90 - W [-] 0.544 - ?S.Y [-] 1.5 10&' - UL [-] 0.938 -

The chosen model characteristics consist of a full model

width of 100m, a model height of 40m, a fine mesh size with enhanced mesh refinements and 15 node triangular mesh elements.

Table IV.2: Overview of the tunnel lining parameters

Parameter Unit Bottom tunnel Top tunnel D [m] 10 8 GM [kPa] 37000 37000 ZM [kg/mF] 2450 2450 t [m] 0.5 0.4 A [m>] 14.92 9.55 I [m\] 168.8 69.1

EA [kN] 1.85 10` 1.48 10` EI [kN m>] 3.85 10b 1.97 10b

efgAgAh [kN/m] 12.02 9.61 eijk [kN/m] 18.1 14.5

B. Single tunnel configuration The main parameters of the final settlement trough of one of

the bottom tunnels are listed in Table IV.3. The obtained maximal settlement value and the GLR value are realistic. Peck classifies the soil as a sand below groundwater level based on the inflection width and the depth of the tunnel center [1], which is the case.

The final settlement trough and its empirical approximation according to Peck, for a mean sand and a GLR of 1%, are displayed in Figure IV.2. The final settlement value is very accurately estimated and the trough width is slightly underestimated by Peck. It can be concluded that both literature and the empirical results confirm the correctness of the Plaxis model. The Peck-modified trough is based on the Plaxis results and was created to be used as the base settlement trough to establish the superimposed settlement troughs for the two and three tunnel configurations.

Table IV.3: Main parameters final settlement trough

Tunnel Model Size lmno [mm] i

[mm] GLR [%]

Bottom HSsmall Simplified 44.9 9.38 1.13 Top HSsmall Simplified 22.7 6.5 1.28

Figure IV.2: Empirical approximation of the final settlement trough

bottom tunnel

A phase wise settlement trough is visualized in Figure IV.3. It is clear that mainly the face pressure face and the tail void 2 pressure phase contribute to the final settlement trough. The proposed grout pressure method can thus not be used to calculate the relative magnitude of all settlement components.

Figure IV.3: Phase wise settlement trough - bottom tunnel

C. Twin tunnel configuration The twin tunnel configurations were investigated in an

intermediate step. More literature is available concerning twin tunnels making it easier to validate the results and the main conclusions of the Tucrail configuration. Figure IV.4 gives an overview of the final settlement troughs of the investigated twin tunnel configurations. It can be noted that constructing the top tunnel first, leads to the least amount of settlements. Do keep in mind that the tunnel diameters equal 8m and 10m for the top tunnel and the bottom tunnels respectively.

Figure IV.4: Final settlement troughs of the investigated twin tunnel

configurations

D. Triangular tunnel configuration The three possible construction orders by which the Tucrail

configuration can be achieved were investigated. The final settlement troughs are displayed in Figure IV.5. The results indicate that constructing the top tunnel before the bottom tunnels leads to the least amount of settlements. It can even be stated that the sooner the top tunnel is constructed, the less settlements are generated. The maximum settlement value due to each tunnel is provided in Table IV.4, in order to give a better insight into the relative contributions. As such it can be noted that the later constructed tunnels lead to less settlements compared to its single tunnel variants constructed in greenfield conditions.

Table IV.4: Overview of the investigated tunnel configurations

Configuration lmno,pqp [mm]

lmno,r [mm]

lmno,s [mm]

lmno,t [mm]

GLR[%]

Top -Left - Right -58.9 -22.7 -31.5 -32.9 1.45 Left - Top -Right -68.2 -44.7 -17.6 -31.3 1.62 Left - Right - Top -76.9 -44.8 -44.2 -12.4 1.92 Bottom -Top -69.1 -42.6 -26.5 - 2.47 Top -Bottom -67.0 -44.9 -18.2 - 2.15 Horizontal*3D -59.4 -59.0 -56.4 - 2.51

*Alternative horizontal twin tunnel configuration with D = 11m

Figure IV.5: Final settlement troughs of the investigated three tunnel

configurations

Figure IV.6 displays the final settlement trough after each phase for the optimal Top Left Right construction order. The contribution due to each tunnel is clearly visualized, as is the contribution due to each phase.

Figure IV.6: Final settlement trough after each phase for the

Top Left Right configuration

The difference in absolute settlement values between using the HSsmall model or the MC model was approximately a factor 2. After extensive modelling research the value of the Oedometer modulus Eoed appeared to be the most important cause. The Oedometer moduli of both the MC and HSsmall model were chosen equal to 30MPa. The HSsmall model utilizes an additional unloading reloading modulus Eur, which was taken equal to 90MPa as listed in Table IV.1. The influence of the Oedometer modulus was investigated for the three tunnel configuration for which the top tunnel was excavated first. It can be concluded that the appropriate value of the MCs Oedometer modulus is situated in the range of Eoed to Eur of the HSsmall model. An Oedometer modulus of 60MPa (=66% of Eur) approximates the HSsmall model within 10% in this sandy soil situation. Another possibility to better model the soil conditions in the field is to linearly increase the Oedometer value with increasing depth [16].

Figure IV.7: Influence of the Oedometer modulus Eoed on the

settlement trough

Figure IV.8 indicates that simply superimposing the modified-Peck curves at the correct locations does not lead to a good empirical approximation of the Plaxis results. A modified superposition principle was established in order to better approximate the Plaxis results. The idea was to first approximate the shape of the settlement trough and to afterwards scale the settlement trough to the correct size. The correct shape was approximated by summing up the trough T1 due to the first tunnel and the scaled troughs Ti,scaled due to the later constructed tunnels. The summed trough is then sized by trial and error to best match the Plaxis trough by playing with value of the size factor S. Equations (3) and (4) illustrate the utilized expressions.

!"#$,'()(*' = , !. + !0,1234*' + !5,1234*' (3) with T",$%&'() = T" s-&.,/'&."$," s-&.,/(%0," (4)

The simple modified superposition principle accurately

estimates the trough shapes obtained by Plaxis for all investigated Tucrail configurations, both for the two tunnel as for the three tunnel variants. Table IV.5 gives an overview of the sizing factor for the investigated construction orders. It can be concluded that simply scaling the settlement troughs of the later constructed tunnels already provides a good approximation of the Plaxis results. The Plaxis results are almost perfectly approximated when the sizing factor is taken into acount. The trough width of the Plaxis results however always remain larger than obtained by the empirical calculations.

Table IV.5: Overview of the sizing factor for the investigated construction orders.

Configuration S [-]

Top -Left - Right 0.9 Left - Top -Right 0.87 Left - Right - Top 1.00

Figure IV.8: Empirical approximation of the final settlement trough

Top Left Right configuration

V. ALTERNATIVE CONFIGURATIONS

A. Vertically spaced twin tunnels The influence of the construction order for vertically spaced

twin tunnels is visualized in Table IV.4. It can be concluded that constructing the top tunnel first leads to smaller overall settlements. It was moreover noted that the horizontally spaced twin tunnel configuration led to less settlements that the vertically spaced twin tunnel configuration.

B. Horizontally spaced twin tunnels The idea behind the alternative horizontally spaced twin

tunnel configuration is to form an alternative to the three tunnel configuration proposed by Tucrail. The tunnel diameters were chosen equal to 11m, so that the space for the same four rails is provided within the two tunnels. At the same time, the influence of the intermediary distance between the tunnels is investigated. The reference situation is chosen to have the same intermediary distance as the Tucrail proposition of 5.5m, being half of the diameter of the tunnels. Figure V.1 displays the settlement troughs of the investigated intermediary distances. It can be concluded that the maximal

settlement value decreases when the intermediary distance between the tunnel is increased. Moreover, the interaction between both tunnels becomes negligible when the intermediary distance is larger than 2D.

Figure V.1: Influence of the intermediary distance on the settlement

trough

The results of the alternative tunnel configuration is compared with the Tucrail proposition in Table IV.4. The GLR and the total amount of settlement are higher for the alternative configuration. Both values are even underestimated in the respective calculations due to the considerable settlements at the vertical mesh boundaries. The Tucrail situation thus seems to be a good proposition settlement wise.

VI. CONCLUSIONS The main goal of the master dissertation was to investigate

the optimal construction sequence for the Tucrail situation. The results are clear and indicate that the construction of the top tunnel before the bottom tunnels leads to the least amount of settlements.

The following conclusions could be made concerning construction orders and relative tunnel positions. A horizontal twin tunnel configuration leads to less settlements than a vertical twin tunnel configuration. When the intermediary distance between horizontally spaced tunnels is increased, the maximal settlement value decreases and the overall settlement volume increases. Overall it could be concluded that the intermediary distance between the tunnels and the depth relative to the surface have a large influence on the settlement values. Moreover, it was the case that the sooner the top tunnel was constructed, the smaller the final settlements were. A final observation was that later constructed tunnels led to smaller individual settlements compared to its single tunnel variants in green field conditions.

The proposed grout pressure method turned out to provide accurate results. The simplified model approximated the full model very well. The determination of accurate tail void grout pressures is therefore crucial in obtaining accurate settlement troughs. Definitely with the encountered sensitivity of the settlement values to variations in the bentonite and grout pressures.

The choice of the constitutive model and its parameters has a large influence on the results obtained with Plaxis. The HSsmall model results in the best approximation of the settlement trough. The stiffness modulus of the soil should be carefully determined when utilizing the MC model.

The proposed superposition principle proved to be a simple empirical way to estimate the Plaxis results. A negative characteristic of the principle however is that the scaling and sizing factors need to be calibrated with Plaxis.

ACKNOWLEDGEMENTS The authors would like to acknowledge the suggestions of

Prof. dr. ir. Hans De Backer, Prof. ir. Bart De Pauw and Dr. ir. Ken Schotte.

REFERENCES [1] Peck, R. B. (1969). Deep excavations and tunnelling in soft ground.

In Proc. 7th int. conf. on SMFE (pp. 225-290). [2] Craig, R. N., & Muirwood, A. M. (1978). A review of tunnel lining

practice in the United Kingdom (No. TRRL Suppl Rpt 335 Monograph).

[3] O'reilly, M. P., & New, B. M. (1982). Settlements above tunnels in the United Kingdom-their magnitude and prediction (No. Monograph).

[4] Ma, L., Ding, L., & Luo, H. (2014). Non-linear description of ground settlement over twin tunnels in soil. Tunnelling and Underground Space Technology, 42, 144-151.

[5] Dias, T. G. S., and A. Bezuijen. "Tunnel modelling: Stress release and constitutive aspects." Geotechnical Aspects of Underground Construction in Soft Ground (2014): 197.

[6] Mller, S. C., and P. A. Vermeer. On numerical simulation of tunnel installation. Tunnelling and Underground Space Technology 23.4 (2008): 461-475.

[7] Addenbrooke, T. I., and D. M. Potts. "Twin tunnel interaction: surface and subsurface effects." International Journal of Geomechanics 1.2 (2001): 249-271.

[8] Chen, Shong-Loong, Meen-Wah Gui, and Mu-Chuan Yang. "Applicability of the principle of superposition in estimating ground surface settlement of twin-and quadruple-tube tunnels." Tunnelling and Underground Space Technology 28 (2012): 135-149.

[9] Broere, W. (2001). Tunnel face stability & new CPT applications (Doctoral dissertation, TU Delft, Delft University of Technology).

[10] Guglielmetti, V., Grasso, P., Mahtab, A., & Xu, S. (Eds.). (2008). Mechanized tunnelling in urban areas: design methodology and construction control. CRC Press.

[11] Talmon A.M., Aanen L., Bezuijen A. and W.H. van der Zon, 2001, Grout pressures around a tunnel lining, proc. IS- Kyoto 2001 conference on Modern Tunneling Science and Technology, A.A. Balkema, Rotterdam.

[12] Bezuijen, A., and A. M. Talmon. Grout pressures around a tunnel lining, influence of grout consolidation and loading on lining. Proceedings of world tunnel congress and 13th ITA assembly, Singapore. 2004.

[13] Talmon, A. M., and A. Bezuijen. Grouting the tail void of bored tunnels: the role of hardening and consolidation of grouts. (2006).

[14] Shirlaw, J. N. (2012). Setting operating pressures for TBM tunnelling. In Proceedings of the 32nd Geotechnical Divisions Annual Seminar, Hong Kong Institution of Engineers (HKIE), Hong Kong (pp. 7-28).

[15] Mller, S. C. (2006). Tunnel induced settlements and structural forces in linings. Univ. Stuttgart, Inst. f. Geotechnik.

[16] Vakili, K., Lavasan, A. A., Schanz, T., & Datcheva, M. (2014). The influence of the soil constitutive model on the numerical assessment of mechanized tunneling. In Proceedings of the 8th European conference on numerical methods in geotechnical engineering. Delft, The Netherlands (pp. 889-894).

Contents

Chapter1 Introduction.....................................................................................................11.1 Problemstatement..............................................................................................................1

Chapter2 Tunnellingmethods.........................................................................................22.1 Introduction.........................................................................................................................22.2 TunnelBoringMachines(TBMs)...........................................................................................22.3 Slurrytunnelboringmachine(STBM)...................................................................................32.4 HydroshieldTBM.................................................................................................................42.5 MixshieldTBM.....................................................................................................................5

Chapter3 Thesettlementprocess....................................................................................63.1 Introduction.........................................................................................................................63.2 Settlementcomponents.......................................................................................................73.3 Factorsinfluencingtheamountofsettlement......................................................................8

Chapter4 Empiricalcalculationmethods........................................................................104.1 Empiricalmethod...............................................................................................................10

4.1.1 Pecksingletunnel.................................................................................................................104.1.2 Multipletunnels...................................................................................................................13

4.2 Othercalculationmethods.................................................................................................16

Chapter5 FiniteelementmethodPlaxis.......................................................................175.1 Workingprinciples.............................................................................................................175.2 Constitutivemodels...........................................................................................................17

5.2.1 Mohr-Coulombmodel(MC).................................................................................................185.2.2 Thehardeningsoilmodel(HS)..............................................................................................185.2.3 Thehardeningsoilmodelwithsmall-strainstiffness(HSsmall).........................................195.2.4 Influenceoftheconstitutivemodelonthesettlementvalues............................................19

5.3 Modellingmethods............................................................................................................215.3.1 Groutpressuremethod........................................................................................................225.3.2 Contractionmethod.............................................................................................................225.3.3 Stressreductionmethod......................................................................................................235.3.4 Comparisonofthemodellingmethods................................................................................24

5.4 Comparisonbetween2D&3D...........................................................................................255.5 Multipletunnels................................................................................................................26

Chapter6 Modelvalidation.............................................................................................286.1 Extendedgroutpressuremethod.......................................................................................28

6.1.1 Overviewoftheconstructionstages....................................................................................286.1.2 Facepressuredistribution....................................................................................................316.1.3 Tailvoidpressuredistribution..............................................................................................326.1.4 Tailvoidgroutlayermodel...................................................................................................34

6.2 Casestudy..........................................................................................................................356.2.1 Generalinformation.............................................................................................................366.2.2 INPUTPlaxis..........................................................................................................................366.2.3 Results..................................................................................................................................38

6.3 Tucrail................................................................................................................................426.3.1 Sensibilityanalysis................................................................................................................426.3.2 Accuracyofthesettlementvalues.......................................................................................44

6.4 Conclusion.........................................................................................................................44

Chapter7 Tucrailpropositionoverview...........................................................................457.1 Generalinformation..........................................................................................................467.2 INPUTPlaxis.......................................................................................................................47

7.2.1 Constitutivemodels..............................................................................................................477.2.2 Materialcharacteristics........................................................................................................487.2.3 Othermodelcharacteristics.................................................................................................48

Chapter8 Singletunnelconfigurations............................................................................508.1 FEMPlaxis.......................................................................................................................50

8.1.1 Finalsettlementtrough........................................................................................................508.1.2 Phasewisesettlementprofilebottomtunnel...................................................................54

8.2 Empiricalapproximation....................................................................................................588.3 Conclusion.........................................................................................................................59

Chapter9 Twintunnelconfigurations.............................................................................619.1 Horizontallyspacedtwintunnels(Tucrail)..........................................................................62

9.1.1 FEMPlaxis..........................................................................................................................629.1.2 Empiricalapproximation.......................................................................................................64

9.2 Skewedspacedtwintunnels(Tucrail)................................................................................659.2.1 BottomTunnelfirstPlaxis..................................................................................................669.2.2 BottomTunnelfirstEmpirical............................................................................................679.2.3 TopTunnelfirst-Plaxis.........................................................................................................679.2.4 TopTunnelfirstEmpirical..................................................................................................68

9.3 Verticallyspacedtwintunnels(Reference).........................................................................699.3.1 BottomtunnelfirstPlaxis..................................................................................................709.3.2 ToptunnelfirstPlaxis........................................................................................................70

9.4 Horizontallyspacedtwintunnels(Alternative)...................................................................719.4.1 FEMPlaxis..........................................................................................................................72

9.5 Optimalconstructionsequence..........................................................................................74

9.5.1 Comparisonoftheinvestigatedtwintunnelconfigurations................................................74

Chapter10 Threetunnelconfigurations............................................................................7710.1 TopTunnelfirst(Tucrail)....................................................................................................77

10.1.1 FEMPlaxis......................................................................................................................7710.1.2 Empiricalapproximation..................................................................................................8010.1.3 InfluenceoftheOedometermodulusE...........................................................................81

10.2 TopTunnelSecond(Tucrail)...............................................................................................8210.2.1 FEMPlaxis......................................................................................................................8210.2.2 Empiricalapproximation..................................................................................................83

10.3 BottomTunnelsfirst(Tucrail).............................................................................................8410.3.1 FEMPlaxis......................................................................................................................8410.3.2 Empiricalapproximation..................................................................................................85

10.4 Optimalconstructionsequence..........................................................................................86

Chapter11Conclusion........................................................................................................89

Chapter12Furtherresearch...............................................................................................90

Bibliography..........................................................................................................................91

List of figures

Figure 2.1: Stages overview in TBM tunnelling (Mller, 2006) ................................... 3Figure 2.2: Slurry tunnel boring machine overview (Chapman et al., 2010) ................ 4Figure 2.3: Working principle hydroshield TBM (Mller, 2006) .................................. 4Figure 3.1: Evolution of settlements along a shield (Leca and New, 2007) .................. 7Figure 3.2: Detail of the back of the TBM shield (Mller,2006) .................................. 8Figure 4.1: Gaussian curve for transverse settlement trough and ground loss (Mller,

2006) ........................................................................................................ 11Figure 4.2: Variation of settlement trough width with depth of subsurface settlement

profiles above tunnels in clays (Mair et al., 1993) ................................... 12Figure 4.3: A typical ground settlement trough over twin tunnels (Ma et al., 2014) . 15Figure 5.1: Surface settlements for different constitutive models (Bezuijen and Dias,

2014) ........................................................................................................ 20Figure 5.2: Transverse settlement trough of Heienoord tunnel at four times the tunnel

diameter behind the TBM front: Grout pressure method with different

constitutive models (Mller and Vermeer, 2008) ..................................... 21Figure 5.3: Display of the grout pressure method (Mller,2007) ................................ 22Figure 5.4: Contraction method (Vermeer and Brinkgreve, 1993) .............................. 23Figure 5.5: Schematic representation of the -method for the analysis of NATM

tunnels (Schikora and Fink, 1982) ........................................................... 24Figure 5.6: Comparison of 2D and 3D transverse surface settlement troughs (Mller,

2006) ........................................................................................................ 25Figure 5.7: Cumulative ground settlement troughs obtained from various modelling

configurations of the study double-tube tunnel (Chen et al., 2012) ......... 27Figure 5.8: Cumulative ground settlement troughs obtained from various modelling

configurations of the study quadruple-tube tunnel (Chen et al., 2012) ) . 27Figure 6.1: Variation of the grout pressure distribution in time of the Sophia Rail

Tunnel (Bezuijen and Talmon, 2004) ...................................................... 33Figure 6.2: Variation of the grout pressure distribution behind the TBM of the

Sophia Rail Tunnel (Bezuijen and Talmon, 2006) ................................... 33Figure 6.3: Modelling of the tail void grout layer ....................................................... 35Figure 6.4: 2D Plaxis mesh of the second Heienoord tunnel (Mller,2006) ................ 36Figure 6.5: Comparison of the obtained settlement troughs with Mllers results

(2006) ....................................................................................................... 40Figure 7.1: Overview of the tunnel configuration proposed by Tucrail ....................... 45Figure 7.2: Geometry of the Tucrail tunnel configuration .......................................... 46

Figure 8.1: Final settlement trough Bottom tunnel ................................................. 51Figure 8.2: Relation between settlement trough width and tunnel depth for different

grounds (Peck, 1969) ................................................................................ 53Figure 8.3: Observed width of surface settlement trough as a function of tunnel

depth: a) In clays, b) in sands and gravels (Mair and Taylor, 1997) ....... 54Figure 8.4: Phase wise settlement trough (Full HSsmall) Bottom tunnel ................ 55Figure 8.5: Phase wise settlement trough (Simplified HSsmall) Bottom tunnel ...... 57Figure 8.6: Phase wise settlement trough (Full MC) Bottom tunnel ....................... 57Figure 8.7: Final settlement trough according to Peck Bottom tunnel .................... 59Figure 8.8: Final settlement trough according to Peck) Top tunnel ........................ 60Figure 9.1: Final settlement trough of the horizontal twin tunnel configuration (Full

HSsmall) ................................................................................................... 63Figure 9.2: Plastic point history .................................................................................. 63Figure 9.3: Phase wise settlement trough of the horizontal twin tunnel configuration

(Full HSsmall) .......................................................................................... 64Figure 9.4: Final settlement trough according to Peck Horizontally spaced twin

tunnels ...................................................................................................... 65Figure 9.5: Final settlement trough skewed spaced twin tunnel configuration Bottom

tunnel first ............................................................................................... 66Figure 9.6: Final settlement trough according to Peck Skewed twin tunnels (Bottom

tunnel first) .............................................................................................. 67Figure 9.7: Final settlement trough skewed spaced twin tunnel configuration Top

tunnel first ............................................................................................... 68Figure 9.8: Final settlement trough according to Peck Skewed twin tunnels (Top

tunnel first) .............................................................................................. 69Figure 9.9: Final settlement trough vertical twin tunnel configurationBottom tunnel

first ........................................................................................................... 70Figure 9.10: Final settlement trough vertical twin tunnel configuration Top tunnel

first ........................................................................................................... 71Figure 9.11: Dimensions of the Tucrail proposition [m] .............................................. 72Figure 9.12: Influence of the intermediary distance on the settlement trough ............ 73Figure 9.13: Final settlement troughs of the investigated two tunnel configurations . 76Figure 10.1: : Final settlement trough of the three tunnel configuration (Simplified

HSsmall) Top Left Right ................................................................... 78Figure 10.2: : Final settlement trough of the three tunnel configuration (FullHSsmall)

Top Left Right ................................................................................... 78Figure 10.3: Comparison of the phase wise settlement troughs due to the face

pressure and tail void pressure 2 phase (Full HSsmall) ........................... 79Figure 10.4: Final settlement trough according to Peck (Top Left Right) ........... 80Figure 10.5: Influence of the Young modulus E on the settlement trough ................. 82

Figure 10.6: Final settlement trough of the three tunnel configuration (SimplifiedHSsmall) Left Top Right ................................................................... 83

Figure 10.7: Final settlement trough according to Peck (Left Top Right) ........... 84Figure 10.8: Final settlement trough of the three tunnel configuration (Simplified

HSsmall) Left Right Top ................................................................... 85Figure 10.9: Final settlement trough according to Peck (Left Right Top) ........... 86Figure 10.10: Final settlement troughs of the investigated three tunnel configurations

(Simplified HSsmall) ................................................................................ 87

List of Tables

Table 6.1: Overview of the the grout pressure method ............................................... 30Table 6.2: Examples of face pressures used in Japan for EPB and Slurry Shield

according to Kanayasu et al. (1995) and Broere (2001). .......................... 31Table 6.3: Heienoord ground parameters of the MC model ........................................ 37Table 6.4: Additional ground parameters as used for the HS and HSsmall model

(Mller,2006) ............................................................................................ 37Table 6.5: Overview of the maximal settlement values smax [mm] concerning the

second Heienoord tunnel obtained with the grout pressure method. ....... 39Table 6.6: Overview of the influence of each phase by looking at the maximal

settlement value smax [mm]. .................................................................... 40Table 6.7: Comparison of the obtained maximal settlement values [mm] with Mllers

results (2006) for the contraction method. ............................................. 41Table 6.8: Comparison of the obtained maximal settlement values [mm] with Mllers

results (2006) for the stress reduction method. ........................................ 41Table 6.9: Influence of the model width on the maximal settlement value ................. 42Table 6.10: Influence of the model height on the maximal settlement value .............. 42Table 6.11: Influence of the mesh size on the maximal settlement value .................... 43Table 6.12: Influence of the mesh element on the maximal settlement value ............. 43Table 6.13: Validation of the chosen model characteristics for the top left right

tunnel configuration ................................................................................. 44Table 7.1: Overview of the soil parameters ................................................................. 47Table 7.2: Overview of the tunnel lining parameters .................................................. 49Table 8.1: Main parameters final settlement trough ................................................... 52Table 8.2: Overview phase wise settlement values Bottom tunnel .......................... 56Table 8.3: Determination of Sv,max - Empirical approximation ................................. 58Table 9.1: Overview of the investigated twin tunnel configurations ........................... 61Table 9.2: Influence of the constitutive model and the model size on smax ............... 62Table 9.3: Influence of the constitutive model and the model size on the relative

magnitude of smax corresponding to each tunnel .................................... 64Table 9.4: Influence of the intermediary distance on the settlement trough (HSsmall)

................................................................................................................. 73Table 9.5: Overview of the maximal settlement value corresponding to the discussed

twin tunnel configurations (Simplified HSsmall) ...................................... 74Table 10.1: Influence of the model size on the relative magnitude of smax

corresponding to each tunnel ................................................................... 80

Table 10.2: Influence of the Young modulus E on the settlement trough ................... 81Table 10.3: Overview of the relative magnitude of smax corresponding to each tunnel

................................................................................................................. 83Table 10.4: Overview of the relative magnitude of smax corresponding to each tunnel

................................................................................................................. 85Table 10.5: Overview of the maximal settlement value corresponding to the discussed

three tunnel configurations (Simplified HSsmall) .................................... 86Table 10.6: Comparison of the Tucrail configuration with a horizontal twin tunnel

alternative ................................................................................................ 88

Nomenclature

An alphabetic overview of all utilized symbols and abbreviations is given below with

their description.

Latin symbols Description

a Incorporates the effect of the inflection width i

A Tunnel surface area

)* Tunnel volume per unit meter in the longitudinal direction of the tunnel axis

c cohesion

C Soil cover

+,-. Volume loss as a percentage of the tunnels volume

D Tunnel diameter

D012 Required tunnel diameter

E Young modulus

EA Normal stiffness

EI Flexural rigidity

E415 Oedometer modulus

678,-.

Secant stiffness modulus

69-:,-.

Tangent stiffness modulus

E;0,01< Unloading reloading stiffness modulus

G Shear modulus

=8 Initial shear modulus

=> Shear strain modulus

H Height

i Inflection width

I Moment of inertia

K Trough width parameter

K8 Normal earth pressure coefficient

m Power indicating the stress-level dependency of the

stiffness

@A Initial soil stresses

PC Active soil pressure

P is reduced to 72.2%

hi Effective friction angle

j Dilatancy angle

kAQ Active soil pressure

kA8 At rest soil pressure

kl Face pressure

m Poisson ratio

n>*Qo- Ultimate stage level

Abbreviations Description

AFTES Association Franaise des Tunnels et de lEspace Souterrain

EPB Earth pressure balance

FEM Finite element method

GLR Ground loss ratio

HS Hardened strain

HSsmall Hardened strain with small strain stiffness

ITA International Tunnelling and underground space

Association

MC Mohr Coulomb

RD Relative density

STBM Slurry tunnel boring machine

TBM Tunnel boring machine

1

Chapter 1

Introduction

Belgium is said to have one of the largest mobility problems in Europe. Many people

take their car to work and most have to drive quite a while to get there. The road

congestion is increasing and commutes are becoming longer. Still the public transport

only seems to be a last resort, except in the large cities where the metro lines work

overtimes during the morning and evening peaks. Brussels has the largest mobility issue

in Belgium. To tackle these issues, kilometres of new metro lines including new

substations are going to be build. Part of the plan is to strengthen the North-South

connection starting from Schaarbeek. To minimise the amount of disruption to the daily

city life, that part of the metro expansion is completely tunnelled. TUC RAIL has

designed most of the present railway network in Belgium, including tunnelled parts.

1.1 Problem statement For the tunnelled part between the main North and Central stations, Tucrail proposed a

new type of tunnel design. In general, a tunnel diameter is chosen in function of the

required space that is requested. The tunnel diameter is limited, therefore when more

space is desired the roads or rails are fitted into two tunnels. Tucrails idea was to construct three smaller tunnels with TBMs and to also utilize the area, enclosed by the

three tunnels, as functional space. Combining multiple tunnel tubes into a larger whole

of independently drilled tunnels is a delicate operation. The University of Ghent has

been asked to further investigate the feasibility of the idea for the North-Central

connection. Four students have been chosen to take part in this research. The stability

of an individual tunnel when the openings are created is investigated. The strength and

stability of the final concept design is tested for three independently drilled tunnels and

for two parallel drilled tunnels. This master dissertation investigates the optimal

construction order of the bored tunnels, mainly focusing on the settlements and

deformations of the surrounding soil mass.

2

Chapter 2

Tunnelling methods

2.1 Introduction A large variety of tunnel methods are currently being utilized. Each with their own

advantages and disadvantages. The most optimal method differs for each project,

depending on the local soil conditions and the project specific challenges. Most

tunnelling methods were invented for certain soil conditions. Nowadays the complexity

of the project, the need for accuracy and the size of the tunnelling projects require more

robust methods. The modern tunnelling methods are developed to yield higher

efficiencies in a wide range of soil conditions (Chapman et al., 2010).

The soil layer profile in this master dissertation consists of one single sandy soil layer.

The pressurized slurry tunnel boring machine is most commonly used in this situation.

Definitely when the tunnelling project consists of several kilometres. Only the slurry

tunnel boring machine (STBM) will further be discussed in this master dissertation.

STBMs are closed face shielded tunnel boring machines. The term TBM will refer to all machines that have a full-face cutter head as defined by the AFTES (Xu et al., 2008)

and ITA classifications (Leca and New, 2007).

2.2 Tunnel Boring Machines (TBMs) The stand-up time, being the time the void remains stable without any support, is very

limited or even non-existing for soft soils. Most soft grounds require immediate support

and the construction is driven by the need to radially support the ground as fast as

possible after creation of the void. A shield has proven to be very efficient to

temporarily support the soil and ensure the stability of the created void until the

permanent support, the lining, is in position. The shield is mostly a cylindrical

construction out of steel surrounding the first part of the TBM. The design

considerations are focused on the realization of small deformations under all ground and

working loads (Chapman et al., 2010).

Chapter 2. Tunnelling methods

3

Figure 2.1: Stages overview in TBM tunnelling (Mller, 2006)

Figure 2.1 provides an overview of the different stages in the advancement of the TBM.

Jacks are incorporated in the shield to propel the shield forward by applying pressure

against the latest installed lining segments. After each sequential tunnel advance of one

segment length, the jacks are retracted to create space for a new lining segment ring to

be installed. As visualized in Figure 2.1 the linings are installed from the inside out

(Mller, 2006).

Contrary to open face tunnelling, closed face tunnelling applies a continuous face

support to the tunnel face. Here the face shield is combined with the cutting wheel. An

important motive is to reduce the ground deformations. The face support can be

achieved in several ways: shield tunnelling with mechanical support, with compressed

air, with earth pressure balance or with a slurry pressure (Mller, 2006).

2.3 Slurry tunnel boring machine (STBM) Slurry shields stabilize the tunnel face by applying a pressurized bentonite slurry. The

slurry is injected along the face shield. During the operation the slurry gets mixed with

the to be excavated soil. Bigger stones can still be present. Therefore, the mixed

suspension first passes trough a special stone crusher before being pumped out of the

excavation chamber. Afterwards the mixed suspension is directed towards a separation

plant in order to be able to reuse most of the bentonite slurry. The bulkhead separates

the working chamber from the tunnel. An overview of a slurry tunnel boring machine is

displayed in Figure 2.2.


4

Figure 2.2: Slurry tunnel boring machine overview (Chapman et al., 2010)

In order to maintain the desired face pressure not only the injection pressure needs to be

well calibrated. The slurry also needs to be capable to form a filter cake with a limited

permeability. The filter cake ensures that the slurry does not immediately dissipates in

the soil. So that the desired face pressure can be maintained (Mller, 2006; Chapman et al., 2010).

Figure 2.3: Working principle hydroshield TBM (Mller, 2006)

2.4 Hydroshield TBM A hydroshield TBM is practically identical to a STBM, but uses a more advanced way

of transferring the support pressure to the face. An additional bulkhead divides the

working chamber in two areas. The pressure exchange is controlled trough an opening in


5

the bottom of the bulkhead, similar as in a mixshield TBM (see next paragraph). The

upper part is filled with compressed air. The air pressure can be adjusted through a

valve system, making the support pressure at the face independent from the hydraulic

circuit. The hydraulic circuit consists of the supply of bentonite slurry and the

extraction of the mixed suspension. As a result, settlements can be minimized compared

to the original STBM design (Xu et al., 2008). The working principle of the hydroshield

TBM is demonstrated in Figure 2.3.

2.5 Mixshield TBM An example of another type of a slurry TBM is a mixshield TBM, which generates an

air bubble to control the face pressure. In a mixshield TBM a submerged wall divides

the pressurized section into two areas, the excavation chamber and the pressure

chamber. The pressure exchange is controlled trough an opening in the bottom of the

submerged wall (Chapman et al., 2010).

6

Chapter 3

The settlement process

3.1 Introduction In densely populated cities settlements have a direct impact on the surrounding existing

structures. A good understanding of which settlement components exist and what

factors have an impact on these components is thus imperative. To start, two

propagation modes of movement towards the surface corresponding to tunnel

construction are described to give an idea of how settlements are generated. The most

comprehensible propagation mode occurs when a shallow tunnel is constructed. A tunnel

is considered to be shallow when the ratio of the soil cover above the tunnel crown to

the tunnel diameter is smaller than 2.5 (C/D < 2.5) (Cording and Hansmire, l975; Leblais and Bochon, 1991; Pantet, 1991). When the soil excavation starts the soil cover

above the tunnel crown looses its bottom support. The weight of the soil cover block is

too large to be supported by the surrounding soil through arching of the soil. The soil

cover block will act as a rigid block and the weight will have to carried trough multiple

shear planes with the surrounding soil. When the shear plane capacity is insufficient, the

soil block slides downwards resulting in settlements. The displacements at the ground

surface are of the same order of magnitude as the the displacements generated at the

location of the soil excavation.

The settlement propagation mode is different for deeper tunnels (C/D < 2.5). When the soil excavation starts, a zone of loosened soil is formed. The small soil blocks just above

the created hole moves down when the shear capacity is reached. This process continues

until an equilibrium is formed. The equilibrium is reached when the load due to the

remaining soil weight can be transferred to the surrounding soil through a combination

of shear and arching. The soil above the created opening needs to settle in order to

reach this form of equilibrium. Note that from the moment the soil cover is sufficient to

generate the arching mechanism, the total soil settlement should remain the same. But

the deeper the tunnel is situated, the more the settlement is spread and the smaller the

maximum surface settlement directly above the tunnel centre is.

Chapter 3. The settlement process

7

3.2 Settlement components The amount of surface settlement consists of several main components. The components

will be described in a chronological order related to the advancement of the TBM, seen

from a fixed point located at the ground surface. A first settlement component is due to

the deformation of the soil towards the face due to stress relief. The stress relief in front

of the tunnel face is a result of reduced soil support due to the excavation of soil

material. A second settlement component is due to radial ground movements during the

passage of the TBM shield. The volume of the TBM shield is smaller than the volume of

excavated soil material at those locations. A third settlement component is due to the

diameter difference of the TBM shield and of a tunnel lining ring. The soil is prone to

fill the created void, which induces tail void settlements. A fourth settlement component

takes place when the tunnel linings start taking the ground loads. The linings deform

under these loads causing ground settlements. A fifth and final settlement component is

due to the time dependent consolidation of the affected soil volume (Xu et al., 2008;

Chapman et al., 2010). All five components are visualized in Figure 3.1, in which a

corresponds to the face settlements, b to the shield settlements, c to the tail void

settlements and d to the lining and time dependent settlements.

Figure 3.1: Evolution of settlements along a shield (Leca and New, 2007)


8

3.3 Factors influencing the amount of settlement The different settlement components are affected by several factors. These factors and

their relative magnitude will shortly be discussed. Note that the following is specifically

applied to STBMs, although many factors are also applicable for other excavation methods. The settlement components depend on a number of general aspects, the first

aspect being the geological, hydrogeological and geotechnical conditions. A second

aspect is the tunnel geometry and its position compared to the surface and other

boundary conditions. A third aspect is the excavation method. A fourth and final aspect

is the quality of workmanship and management during the projects duration (Leca and

New, 2007). Off course all four aspects are interrelated. In order to maintain a clear

overview all aspects and factors will be discussed from the perspective of the STBM.

Figure 3.2: Detail of the back of the TBM shield (Mller,2006)

The short-term settlements consist of the stress relief component, the shield component

and the tail void component (Chapman et al., 2010). These factors are mainly caused by

the excavation of the tunnel. The tunnel excavation and amount of settlement are

function of the stability of the tunnel face, the advancement rate of the TBM and the

required time to fill the tail void as visualized in Figure 3.2. Moreover, the inner shield

diameter is larger than the outer diameter of the lining as visualized in Figure 3.2. The

dimensions of the so called overcutting edge play an additional role for the shield

settlement component. This overcutting edge is required to provide sufficient

manoeuvrability of the TBM to provide the required steering capacity and curvature

whilst maintaining the desired alignment of the shield (Xu et al., 2008). The short-term

settlements are initiated a certain distance in front of the tunnel face. They become zero

the moment the tail grout has reached sufficient strength to withstand any further

ground displacements. The grout pressure, the grout penetration rate and the hardening

time of the grout thus also play an important role in the settlement process. The lining


9

component can be relevant for large diameter tunnels. Especially when the tunnel is

located at a shallow depth. But currently the loads can accurately be estimated. Hence

excessive lining deformations can easily be avoided by proper lining design. In general,

the observed tunnelling impact at the ground surface is limited for deeper tunnels. The

magnitude of the long-term time dependent settlements due to primary and secondary

consolidation depend on the type of soil. The finer the soil, the larger the component.

The primary consolidation is mainly due to dissipation of excess pore pressure. The

secondary consolidation is a form of soil creep, which is related to the rate at which the

soil skeleton yields and or compresses.

10

Chapter 4

Empirical calculation methods

4.1 Empirical method The settlement profiles are often described by empirical formulations to quickly obtain

an idea about the order of magnitude of the settlements. The empirical formulations are

based on several main parameters. Some empirical equations nowadays have even

become quite extensive. These equations are mostly only applicable in very specific soil

conditions in combination with a certain tunnelling technique. The most globally used

method is to approximate the surface settlement by a Gaussian curve according to Peck

(1969).

4.1.1 Peck single tunnel

The transverse settlement trough was first shown to be well described by a Gaussian

curve by Peck (1969) according to the following expression:

MN O = MN,PQR stuvwJv

(0.1)

Where MN,PQR is the surface settlement directly above the tunnel axis. Since the Gaussian curve is a symmetrical curve, the settlement reaches its maximum value there.

Furthermore, y is the horizontal distance from the tunnel axis and i is the horizontal

distance from the tunnel axis to the point of inflection of the transverse settlement

trough. See Figure 0.1 for a clear representation of a transverse settlement trough.

On top of the formerly mentioned interesting characteristics of the Gaussian

representation, it can also be used to estimate the volume loss per unit meter in the

longitudinal direction of the tunnel. The volume loss T> is equal to the volume of the settlement trough and can be achieved by integrating Equation 4.1:

T> = MN,PQR stuvwJv

yz

tz{O = 2} ~ MN,PQR (0.2)

Chapter 4. Empirical calculation methods

11

T> = MN,PQR s

tuv

wJvyz

tz{O = 2} ~ MN,PQR (4.3)

Figure 4.1: Gaussian curve for transverse settlement trough and ground loss

(Mller, 2006)

The ground loss T* is defined as the volume of ground that is over excavated compared to the installed tunnel volume per unit meter in the longitudinal direction of the tunnel,

as visualized in the bottom part of Figure 4.1. There is a strong correlation between the

volume loss and the ground loss. But the ground loss is highly influenced by the soil

conditions, water conditions and the tunnelling method. Specific expressions with

complex empirical factors have been formulated based on past experience by amongst

others Attewell et al. (1986) and Macklin (1999). It was noticed that the settlement

volume (volume loss T>) is practically equal to the ground loss for undrained conditions. For drained conditions, unloading can lead to soil expansion leading to higher ground

losses than volume losses (Cording and Hansmire, 1975). However the differences appear

to remain small so that the following can be assumed for all situations without

introducing large errors: T* = T> (Craig and Muirwood, 1978).

Equation 4.2 indicates that the maximal settlement value MN,PQR largely depends on the value of the ground loss. To talk about ground losses in a more representative way

related to the constructed tunnel itself, the ground loss ratio (GLR) was introduced.

The GLR is obtained by dividing the excavated ground volume by the tunnel volume as

shown in Equation 4.5. Similar to the the ground loss, the GLR is mainly influenced by


12

the soil conditions and the construction method of the tunnel. The size of the tunnel

and thus the excavations, the soil stiffness and the initial soil stresses also appear to

have a considerable impact according to Mair (1996). GLRs of 0.5-1% in homogenous

sandy soils and GLRs of 1-2% in clayey soils are currently achievable. When the soil

layer profile consists of a complex alternation of different geological soil layers, the GLR

is more likely to be between 2-4% (Mair and Taylor, 1997).

The width of the settlement trough is related to the distance from the tunnel axis to the

inflection point i. Many expressions have been developed for i and for the width of the

settlement trough. One of the most common expressions was suggested by OReilly and New (1982). OReilly and New proposed a straightforward linear relationship to the tunnel depth a8.

~ = a8

(4.4)

In Equation 4.3, K depends on the soil conditions and is called the trough width

parameter. Mean K values are K 0.35 for sandy soils and K 0.5 for clayey soils. The validity of Equation 4.3 and the resulting inflection width values have been confirmed

by many authors, such as Rankin (1988) and Mair et al. (1993). Mairs relationship is visualized in Figure 4.2 to give an impression of the importance of the different

parameters.

Figure 4.2: Variation of settlement trough width with depth of subsurface settlement

profiles above tunnels in clays (Mair et al., 1993)


13

The maximal settlement MN,PQR can be redefined using the former expressions and considering that:

=I =T*)*T>)* (4.5)

In Equation 4.4, )* represents the tunnel volume per unit meter in the longitudinal direction of the tunnel axis. The following expressions can be used to rapidly estimate

the maximal settlement value and the transverse settlement profile.

MN,PQR )*

~ 2} =I (4.6)

And

MN O

)*~ 2}

=I stuv

wJv (4.7)

All expressions can be generalized to become applicable for layered soils. Obviously the

obtained expressions will be more complex and time consuming. Similar expressions

exist for horizontal deformations, longitudinal settlement profiles and subsurface

settlement profiles. Each of them can contribute to get a better understanding of the

soil deformations close to and in proximity of the tunnel operations. In combination

with specialized monitoring techniques the effect on nearby structures both during and

after construction can be controlled as optimally as possible.

4.1.2 Multiple tunnels

A method to estimate the settlement profiles for multiple tunnel configurations is by

using the principle of superposition. The transverse settlement trough is determined

separately for each tunnel according to Peck. Afterwards the settlements troughs are

superimposed to obtain a final settlement trough of the multiple tunnel configuration.

Chen et al. (2012) have investigated the validity of the superposition principle. The

ground loss ratio was back calculated for each tunnel individually based on monitored

settlement data from the site. The back calculated GLR was used to determine the

transverse settlement curve per tunnel. Finally, the total transverse settlement trough

was obtained trough superposition for twin tunnel and quadruple tunnel configurations.

The results of Chen et al. showed that the transverse settlement profile could be reliably

estimated by using the empirical equation together with the principle of superposition,

both for horizontally spaced twin tunnels and for a quadruple parallelogram like

configuration. The validity and accuracy of the results can however not be generalized

because of a combination of two factors. Firstly, the individual settlement profiles are


14

almost perfectly estimated due to the back calculation process, which can never occur as

accurately for to be constructed tunnels. Secondly the distance between nearby tunnels

was 1.9 times the diameter or more. The overlap of the plastic zones is limited when the

ratio is larger than 1.36 times the diameter (Hoyaux and Ladanyi, 1970). The

interaction between both tunnels was hence limited for the investigated configurations.

It is noteworthy that the superposition principle also seems to be applicable for

configurations containing vertically spaced tunnels. The construction of the first tunnel

automatically affects the loading conditions of the second tunnel. For vertical twin

tunnels the way the soil conditions are altered always result in total settlement troughs

that are smaller than the superimposed ones, independently of which tunnel is

constructed first. When the top tunnel is constructed first, the second bottom tunnel is

subjected to lower loads. Because the tunnel weighs less than the soil it replaces,

resulting in less settlement. When the bottom tunnel is constructed first, the

construction of the top tunnel will reduce the loads on the lower tunnel. As a result, the

bottom tunnel will rise relative to its original position. Again resulting in less settlement

compared to the superposition of the individual settlement troughs (Liang et al. 2016).

Hence the superposition principle is expected to overestimated the settlements due to

vertical twin tunnels, contrary to what the results of Chen et al. imply. This situation is

investigated in section 9.3.

Several other authors mention the superposition principle in combination with Pecks method and or use it as the reference case. But practically all of them comment its

inaccuracy and try to find other ways to better predict the final settlement trough for

multiple tunnel configurations. A symmetric settlement trough only occurs in an ideal

situation. In reality a skewed settlement trough is observed in multiple tunnel

configurations as confirmed by among others Ercelebi et al. (2011) and Mahmutoglu

(2011). The tunnels are not constructed at the same time. The first tunnel disturbs the

soil in a certain area, affecting and altering the soil conditions compared to the initial

state conditions. The later tunnels are mostly constructed inside the disturbed zones for

multiple tunnel configurations. The shape of the settlement trough and the relative

magnitudes of the settlements troughs is highly dependent on the local soil conditions,

the excavation sequence, the intermediary distances and the tunnel depth relative to the

ground surface. Ma et al. (2014) encountered symmetrical, one peak skewed and two

peak skewed curves to both sides for similar horizontal twin tunnel configurations. The

effects are thus very local. The second tunnel in the twin tunnel configuration of the

Xindian line of Taipei Rapid Transit System for example generated more settlement

than the first one (Chen et al., 2012). The maximal surface settlement value was there

thus positioned closer to the centreline of the second tunnel. Addenbrooke and Potts

(2001) state that the total settlement volume of the second tunnel is larger when all


15

conditions are equal for both tunnels. But the volume difference compared to the first

tunnel decreases when the intermediary distance increases, since the interaction effects

decrease. The asymmetric settlement trough is thus a result of a certain degree of

interaction between chronologically constructed tunnels depending on the intermediary

distance (Mirhabibi and Soroush, 2012). A possible method to better take into account

these effects is to use a superposition expression as follows (Ma et al., 2014):

MN = MN,PQRsQuv+ MNPQR,wsQv(ut)

v (4.8)

In Equation 4.7 the meaning of most parameters is the same as in Equation 4.1 with the

subscript one referring to the first constructed tunnel and subscript two to the second

constructed tunnel. The parameter a here incorporates the effect of the inflection width

i, y denotes the horizontal distance compared to the firstly constructed reference tunnel

and u equals the intermediary distance to the reference tunnel. Similar expressions can

be proposed for multiple tunnel configurations. The parameters can be estimated based

on past experience or trough back calculations of field measurements. An example is

visualized below for a twin tunnel configuration (Ma et al., 2014). The figure is purely

indicative and thus does not correspond to a real life situation.

Figure 4.3: A typical ground settlement trough over twin tunnels (Ma et al., 2014)


16

Many recent developments include curve fitting methods, both linear and non-linear.

Similar to other methods the curve fitting method is based on measured settlement data

from on the site. Many current empirical and semi-empirical methods seem to have

reached a barrier for estimating settlements of future projects. Because their results are

a very good approximation of the settlements in case field measurements can be used to

better calibrate the relevant parameters. But for new future projects the parameters are

chosen based on past experience, resulting in an inevitable deviation of the actual

settlements. So most recent developments will only reach their full potential from the

moment a certain part of the tunnel is constructed. These methods will then be able to

accurately predict the settlements for the remainder of the tunnel in similar soil

conditions. The moment the soil conditions greatly vary, the parameters will have to be

recalibrated. The optimized methods will thus be particularly useful during construction

and their additional accuracy will be less prominent in tender phases. At those moments

numerical methods are and will remain the go to tool.

4.2 Other calculation methods Several other methods exist to estimate settlement profiles. On top of empirical and

semi-empirical methods some methods lead to closed form solutions. The most

commonly used closed form solution methods are the analytical ones, the bedded beam

models and continuum models. The latter methods are becoming less used and are

replaced by finite element approaches. These have become common practice since the

computer capacities resulted in a satisfying quality. The finite element method will be

discussed in more detail in the following section.

17

Chapter 5

Finite element method Plaxis

Engineering firms nowadays still use simplified empirical, semi-empirical or analytical

methods to quickly get an idea of the amount of settlements corresponding to a specific

situation. The actual full scale calculations however of all intermediary construction

stages at different time intervals are always determined by finite element methods

(FEM). Many FEMs exist for a variety of applications in the engineering world, all

based on the same working principle. The working principle will first be discussed in

general. Afterwards specific attention will be given to the geotechnical FEM program

Plaxis, its main constitutive models, several FEM tunnel modelling methods and

noteworthy remarks concerning results obtained with Plaxis.

5.1 Working principles The working principle is immediately explained in function of geotechnical applications.

The finite element method is a method of discretization to obtain results in a

beforehand chosen number of points. In most engineering applications the goal is to

determine the strains and stresses trough the deformations in these points, as is also the

case for geotechnical applications. The deformation theory is utilized to obtain the

desired values. The deformation theory is based on the basic equations for the static

deformation of soil bodies within the framework of continuum mechanics (Brinkgreve et

al., 2014). Afterwards the continuum is divided into soil volume elements, consisting of

a number of nodes. Different elements exist with their own field of use. The degrees of

freedom of each node correspond to the displacement components and form the

unknowns that need to be solved according to the deformation theory. Interpolation

functions are used to provide results that approximate the reality as much as possible in

other points than the calculation points.

5.2 Constitutive models Several constitutive models exist to model the soil behavior. Each model is developed to

provide more accurate results for certain situations and soil conditions in combination

Chapter 5. Finite element method - Plaxis

18

with a minimal computation time. The three most commonly used soil constitutive

models for tunnelling projects are the Mohr-Coulomb (MC) model, the hardened strain

(HS) model and the hardened strain model with small strain stiffness (HSsmall).

5.2.1 Mohr-Coulomb model (MC)

The linear elastic perfectly plastic model is generally known as the Mohr-Coulomb

model. As the name illustrates the model makes use of a fixed yield surface. When the

stress state is represented by a point on the yielding surface, plastic yielding occurs.

Points lying within the yield surface behave purely elastic, meaning all strains are

reversible. The principle of elastoplasticity applies. The strains and strain rates are thus

decomposed into elastic and plastic parts. The fixed yield surface is determined by the

Mohr-Coulomb yield condition. The condition ensures that the Mohr-Coulomb friction

law is respected along all planes. The five main parameters are the Oedometer modulus

(E415), the Poisson ratio (m), the cohesion (c), the effective friction angle (hi) and the dilatancy angle (j). The dilatancy angle makes it possible to model positive plastic volumetric strain. Values of other parameters are related to these five parameters, but can also be specified manually. The shear modulus (G) is an example. The soil stiffness

E415 is a very important parameter, definitely settlement wise. The secant modulus 678 is generally used to more realistically model the soil stiffness in this simple model. Other

models use more complicated soil stiffness relationships as will be seen in the HS and the

HSsmall constitutive models.

5.2.2 The hardening soil model (HS)

The hardened soil model is a more advanced model compared to the Mohr-Coulomb

model. The yield surface is no longer fixed. The zone

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