Design philosophy of concrete liningsfor tunnels in soft soils

Design philosophy of concrete linings for tunnels in soft soils
Design philosophy of concrete linings for tunnels in soft soils Proefschrift
ter verkrijging van de graad van doctor
aan de Technische Universiteit Delft,
op gezag van de Rector Magnificus prof.dr.ir. J.T. Fokkema,
in het openbaar te verdedigen ten overstaan van een commissie,
door het College voor Promoties aangewezen,
op vrijdag 20 december 2002 te 16.00 uur door Cornelis Bernhard Marco Blom civiel ingenieur geboren te Rotterdam
Dit proefschrift is goedgekeurd door de promotor: Prof.dr.ir. J.C. Walraven Toegevoegd promotor: Dr.ir. C. van der Veen
Samenstelling promotiecommissie: Rector Magnificus, voorzitter Prof.dr.ir. J.C. Walraven
Technische Universiteit Delft, promotor Dr.ir. C. van der Veen
Technische Universiteit Delft, toegevoegd promotor
Prof.dr.ir. J. Blaauwendraad Technische Universiteit Delft Prof.dr.ir. J.G. Rots Technische Universiteit Delft Prof.dr.ir. F. Molenkamp Technische Universiteit Delft Prof.dr. H. Duddeck
Technische Universität Braunschweig, Deutchland Dr.ir. A.F. Pruijssers
Ex Aequo Pruijssers Management v.o.f.
Published and distributed by: DUP Science DUP Science is an imprint of Delft University Press P.O. Box 98 2600 MG Delft The Netherlands Telephone: +31 15 27 85 678 Telefax: +31 15 27 85 706
E-mail: Info@Library.TUDelft.nl ISBN 90-407-2366-4
Keywords: tunnel, design, damage
Copyright © 2002 by C.B.M. Blom All rights reserved.
No part of the material protected by this copyright notice may be produced or utilised in any
form or by any means, electronic or mechanical, including photocopying, recording or by any
information storage and retrieval system, without permission from the author. Printed in the Netherlands Acknowledgements
The research that is reported in this thesis was performed at the Civil Engineering Department of
Delft University of Technology. I would like to thank Prof. Walraven, Dr. van der Veen and all
the financiers for their unlimited graceful willingness to support this research. This thesis is financially funded by -
Holland Railconsult, Utrecht, The Netherlands. -
Ministry of Transports and Water Management, Utrecht, The Netherlands. -
TNO Building and Construction Research, Delft, The Netherlands.
I would like to thank the financiers’ representatives of the research, Freerk de Boer, Predrag
Jovanovic, Gerrit Wolsink, Klaas-Jan Bakker, Dick Hordijk and Jan Gijsbers for their supports.
I would like to thank the financiers of the full-scale test facility at the Delft University of
Technology for their support in the realisation of this great test facility. The financing parties are: - Management Group Betuweroute. - High Speed Line South. -
TNO Building and Construction Research. -
Delft University of Technology.
I would like to thank the management of Holland Railconsult for the unique opportunity to
extend the time for this research while being member of this fantastic company.
And of course I thank my colleges at the University, Holland Railconsult and the offices I have
been working. I hope you enjoyed it as much as I have.
I address special thanks to Predrag Jovanovic for his excellent contribution and guidance in my
personal development. I hope that the tandem bicycle continues. There are many tablecloths left
we can use in discussions. Also thanks to Johan Schillings from CST to take care of the
implementation of the FEM analyses. I hope your telephone bill drops now.
Mum, Dad and family, you are great. Words are inadequate to thank you for everything. Dear
Marjolein, your unprecedented support shows the miracles of life. Kees Blom Summary
This thesis deals with the design of the segmented lining of shield driven tunnels in soft soils.
It becomes clear that a collective problem in actual projects is the quality loss during the
construction of the lining, by cracking and damage of the concrete segments. The available
structural engineering models do not provide tools to analyse the damage mechanisms that occur
during the assembly. Actually this is a result of the wish to design the lining with the
requirements for the serviceability stage as governing. Therefore the basic assumption is that the
assembly should be non-normative. However, practice shows that the assembling stage is very
important with regard to eventual loss of quality.
It is obvious that quality loss through cracks and damage mainly occurs during the construction
of the lining. In the Tunnel Boring Machine (TBM) the segments are erected to form a ring. The
TBM is a very advanced machine designed by specialists in the field of mechanics and
machinery. Specialists in the field of civil engineering design the lining. It might be a
coincidence that just at the contact interface of these two fields of specialism the quality loss
occurs. On the other hand it is questionable whether or not both disciplines sufficiently
communicate with each other in order to optimise design and construction.
In literature many analytical models are published to analyse the behaviour of the lining of
shield driven tunnels. The analytical solutions in general have in common that they only involve
a single ring, mostly without explicit consideration of the rotational stiffness of the longitudinal joints.
In this thesis a new approach is described on how to implement explicitly the rotational stiffness
of the longitudinal joints and the lateral interaction between the rings for a lining system in an
elastic soil continuum. The new analytical solution for the segmented linings of shield driven
tunnels, with explicitly integrated longitudinal joints, lateral ring joint interaction and elastic soil
continuum offers a very powerful tool to calculate the lining behaviour in the serviceability
state. The solutions provide a transparent understanding of influences of parameters and
structural design values such as internal forces and deformations. It also shows that non-linear
behaviour of the longitudinal joints can be implemented in the analytical solutions.
The comparison of the new analytical solutions with well-known solutions from literature shows
a good agreement. Since solutions in literature were never presented for single rings with
explicit longitudinal joints and coupled systems ever, such a comparison can not be made.
However the direct comparison for the single homogeneous ring is made and agrees very well.
The explicit implementation of the longitudinal joints and the lateral coupling shows the
influence of these geometrical parts of the lining.
One has to remind that the predicted forces and the deformations are based on the so-called
‘beam’ analysis. This means that the force distribution over the segmental width is assumed to
be the average value over that width. It turns out that the distribution (especially important in
crack analysis) of the stresses is not equally distributed over the segmental width.
Attention is given to load cases in the serviceability stage and at the assembly. In this thesis an
additional load case, the so-called ‘uplift loading case’ is presented to invoke the consequences
of poor support that might occur during the construction stage. Analyses of FEM models of
grouting result in the uplift loading case, which is a load model that can easily be used in the lining analyses.
It shows that structural analyses of linings with full soil support (ring analyses with soil support
in the serviceability stage) do not confirm the applied lining thickness that is observed in today’s
practice. From the structural ring analyses with full soil support it follows that the application of
thicker linings is of poor influence on the safety and costs. The uplift loading case (that involves
grout loading on the lining in the assembling stage) shows that the soil support is of major
influence on the safety of the lining and that therefore the grout material specification and
pressure should be considered very carefully.
The structural analysis of the lining includes the question what the actual ULS of the lining
means in relation to the acting forces. Geometrically and physically linear and non-linear
analyses show that the geotechnical structure of the lining in soil requires an alternative
approach of the ULS. The ULS is not reached by the excess of the tangential bending capacity of
the lining and radial deformations, but more by excess of the normal force capacity of the lining.
Two additional failure mechanisms are distinguished: local buckling and snap through. These
mechanisms should also be checked when analysing the structure for the ULS.
A comparison is made between the new analytical solution and the results of the full-scale test
carried out at the Delft University of Technology. Two main cases are considered: the all in one
test and the sequential loading test. In the all in one test the total system of three rings is loaded
in radial and axial direction at once. In the sequential load case in the first instance only two of
the three rings are loaded in radial direction. In the second instance the third ring is loaded in
radial direction in presence of the axial forces.
The results of the analytical solution for the loading at once case show very good agreement for
the radial deformations and the tangential stresses. The analytical solution is fully confirmed by
the results from the laboratory test in this case.
The comparison with the sequential loading case involves some complications. It is concluded
that the loading of a ring results in redistribution of the acting forces when ring interaction can
occur. In the case of the full-scale test about 60% of the acting loading is migrating to adjoining
rings. The direct adjoined ring dissipates 40% of the acting loading, while the next adjoining
ring dissipates 20%. These values are confirmed by 3D FEM analyses. Further it turns out that
only ovalisation loading is migrating through the lateral joints. The uniform pressure does not
migrate. As a consequence the loading in the analytical model is adapted to this migration hypothesis.
With the special consideration of the migration of acting forces, the results of the sequential
loading in the full-scale testing can be compared. The results of the several types of calculation
models, like analytical solution, frame analysis and 3D FEM analysis, show a very good
agreement with the measured values in the full-scale test.
The analysis shows that the subsequent loading influences the deformations and the internal
forces in the adjoining rings. The lateral joint interaction capacity is very important from this
point of view. It has turned out that due to the sequential loading the integrated forces in a ring
are not influenced by the coupling forces. Locally the coupling forces will result in highly disturbed stress spots.
A comparison is made between the results of the calculations and the measurements of real
tunnel linings in practice. The comparison is focused on the tangential components of the
internal forces. It becomes clear that the influence of the axial forces on the tangential
components is especially visible in the tangential stresses and the tangential normal forces. The
contribution of the axial forces to these tangential components is established by the involvement
of the lateral contraction. The tangential bending moments do not show this influence.
Nevertheless the influence of the couplings in the lateral joints is visible.
The comparison of the calculated results with the measurement data of the Botlek Railway
Tunnel (BRT) holds the conclusion that the uplift loading case with incomplete grouting has
occurred. The comparison of the tangential stresses, the tangential normal forces and the
tangential bending moments confirms a very good agreement with the calculation results based
on the incomplete grouting in the uplift loading case.
From the measurements it becomes clear that tangential stresses are not uniformly distributed
over the segmental width. An analysis of the several stages in the assembly shows that,
especially when the ring is within the TBM or just leaves the rear of the TBM, the distribution
of the tangential stresses is highly non-uniform. This is of special interest when crack analyses
are carried out. It is also observed that in these stages the amplitudes of values occur which
exceed the values in later stages.
The comparison of the model results with the measured data at the Second Heinenoord Tunnel
(SHT) holds the conclusion that the load conditions at the assembly should be due to the uplift
loading case with complete grouting or just the normal loading case without the tangential
components. It is obvious that the internal forces in the lining develop in time.
The goal of the ideal assembling process is to build a perfectly round ring without any initial
stresses, well closed joints and equal supports of all segments. Design of the segments and ring
layout intends a perfect system of segments with a perfectly round shape of the ring. It becomes
clear that there are many causes that might result in the quality loss. The causes might result in
quality loss by themselves, but the causes might also act simultaneously.
Examples are given of mechanisms that contribute to the stresses in the segments. These
mechanisms are mostly not implemented in the so-called ring models. Therefore additional
analyses have to be carried out to analyse these mechanisms. It turns out that the additional
mechanisms might result in high tensile stresses that cause cracks in the concrete. The
mechanisms result in the crack direction that is often observed in practice. The mechanisms,
mostly three-dimensional problems, give the understanding why cracks so easily occur during
the assembly of the lining. Since the mechanisms so easily result in cracking, the best solution is
to avoid the occurrence of the mechanisms. Main driving forces for the cracks are torsional
moments, additional tangential moments, shear forces and the high axial forces.
The design approach should always have the boundary condition that the serviceability stage is
normative. To fulfil this condition basic assumptions are made to the assembling stage. It has to
be proved that these basic assumptions are valid in design, construction and exploitation. In case
that the assembling stage is at least as normative as the serviceability stage, in respect to the
lining, economical loss in optimum occurs because the assembling stage is only a minor period in the lifetime of the lining.
A design philosophy is described that includes the analysis of the lining behaviour at the
assembly. The optimal design is actually the following: -
The lining is designed in the serviceability stage without any consideration of the assembly. -
Consequently the construction method is determined such that it does not result in any
aggravating addition to the serviceability stage. Samenvatting
Dit manuscript handelt over het ontwerp van de lining van geboorde tunnels in slappe grond.
Een collectief probleem in de hedendaagse tunnelbouw is het kwaliteitsverlies aan de
gesegmenteerde betonnen lining, dat optreedt tijdens de bouw van de tunnel. De beschikbare
engineeringmodellen zijn niet geschikt om de optredende schademechanismen te analyseren.
Eigenlijk is dit het resultaat van de wens om de tunnel te ontwerpen voor een maatgevende
gebruiksfase. Het uitgangspunt in het ontwerp is dat de bouwfase niet maatgevend mag zijn.
Toch laat de hedendaagse bouwpraktijk zien dat de bouwfase heel belangrijk is in het kader van kwaliteitsverliezen.
Het is duidelijk dat kwaliteitsverlies door schade en scheuren voornamelijk tijdens de bouwfase
optreedt. In de TunnelBoorMachine (TBM) worden segmenten samengesteld tot een ring. De
TBM is een geavanceerde machine die wordt ontworpen door gespecialiseerde
werktuigbouwkundigen. Specialisten uit de Civiele Techniek ontwerpen de betonnen lining. Het
kan toeval zijn dat juist op het raakvlak tussen deze disciplines kwaliteitsverlies optreedt. Aan
de andere kant is het de vraag of deze disciplines voldoende communiceren om de ontwerpen en
de uitvoering te optimaliseren.
In de literatuur zijn veel analytische modellen gepubliceerd om het gedrag van de lining van
boortunnels te analyseren. Over het algemeen beschrijven de modellen een enkele ring, zonder
expliciete bijdrage van rotatiestijfheid van langsvoegen.
In dit manuscript wordt een analytisch model beschreven met expliciete bijdrage van
rotatiestijfheid in de langsvoegen en koppelingen in de ringvoegen, waarbij het gehele systeem
in een bedding ligt. Dit nieuwe model blijkt een krachtig middel om het lininggedrag in de
gebruiksfase te analyseren. Het model geeft een verhelderend inzicht in de invloed van
parameters op de resultaten, zoals snedenkrachten en vervormingen. Tevens kan niet-lineair
rotatiegedrag van langsvoegen worden geanalyseerd.
Omdat de modellen uit de literatuur slechts analyses van enkele ringen bevatten, zonder
expliciete implementatie van rotatiestijfheden, kan een vergelijking voor dubbele ringen met
expliciete rotatiestijfheid in de langsvoegen en koppelingen in de ringvoegen niet worden
gemaakt. Toch levert de vergelijking voor de enkele ring analyse zeer goede overeenkomsten op.
De expliciete rotatiestijfheden in de langsvoegen en de ringvoeginteractie in het nieuwe model
laten de invloed van deze parameters, ten opzichte van de enkele ring modellen, duidelijk zien.
Bedacht moet worden dat de ringmodellen gebaseerd zijn op een zogenaamde ‘staaf’ analyse.
Dat betekent dat de spanningsverdeling over de breedte van segmenten gelijkmatig verdeeld
wordt verondersteld. Het blijkt dat de spanningen niet gelijkmatig verdeeld zijn. Dat is
belangrijk voor de analyses van scheuren en schade.
Aandacht wordt gegeven aan belastinggevallen in de gebruiksfase en tijdens de bouwfase. In dit
manuscript wordt een nieuw belastinggeval onderzocht, de zogenaamde ‘uplift loading case’,
om de invloed van de mogelijk slechte grondondersteuning, door het grouten, tijdens de
bouwfase te analyseren. Analyses van EEM modelberekeningen van het groutproces hebben
geresulteerd in de uplift loading case. Deze belasting is vervolgens relatief eenvoudig te modelleren in ringmodellen.
Het blijkt dat berekeningen van de lining in een volledige grondondersteuning (gebruiksfase) de
in de praktijk toegepaste liningdikte niet bevestigt. Bij een toename van de segmentdikte blijkt
dat niet alleen de kosten te stijgen, maar tevens dat de constructieveiligheid afneemt. De uplift
loading case (inachtneming van het grouten) laat zien dat de grondondersteuning van enorm
belang is en dat daarom de specificatie van het groutmateriaal en de injectiedrukken speciale aandacht vragen.
De analyse van het lininggedrag omvat de vraag wat de ULS betekent in relatie tot de
optredende snedekrachten. Geometrisch en fysisch niet-lineaire berekeningen leiden tot een
afwijkende overweging van de ULS. De ULS wordt uiteindelijk niet bereikt door het eenvoudig
overschrijden van een maatgevende normaalkracht-moment combinatie, maar door het niet meer
kunnen opnemen van de tangentiële normaalkracht. Daarnaast worden nog twee
faalmechanismen geanalyseerd: lokaal uitknikken en het doorslagverschijnsel.
Een vergelijking wordt gemaakt tussen het nieuwe analytische model en de resultaten van de
full-scale testen die zijn uitgevoerd in het Stevin II laboratorium van de Technische Universiteit
Delft. Twee belangrijke testgevallen worden onderzocht: de ‘all in one’ test en de sequentiële
test. In de all in one test worden drie ringen zowel radiaal als axiaal tegelijkertijd belast. In de
sequentiële test worden eerst twee ringen in radiale richting belast waarna de derde ring in
radiale richting wordt belast, terwijl een axiale belasting aanwezig is.
De resultaten van het analytische model en de all in one test komen zeer goed overeen voor
zowel vervormingen als tangentiële spanningen. De analytische oplossing wordt volledig bevestigd door de test.
De vergelijking van het analytische model met de sequentiële test brengt enige complicaties met
zich mee. Het blijkt dat door ringinteractie het belasten van een ring leidt tot herverdeling over
de aangrenzende ringen. In het geval van de full-scale test blijkt dat 60% van de ovaliserende
belasting wordt doorgegeven aan de aangrenzende ringen, waarvan 40% in de direct
aangrenzende ring en 20% in de daarop volgende ring. Deze waarden worden bevestigd door 3D
EEM analyses. Verder blijkt dat alleen de ovaliserende belasting migreert, maar de uniforme
belasting niet. Op basis van deze bevindingen kan de belasting in de analytische modellen
worden aangepast voor de sequentiële belasting met de bijbehorende migratie.
Met speciale aandacht voor migratie van de belastingen kunnen de meetresultaten uit de
sequentiële test worden vergeleken met modelresultaten. Deze vergelijking resulteert in goed overeenkomende waarden.
Analyses laten zien dat de sequentiële belasting de vervormingen en interne krachten in de
naastliggende ringen beïnvloedt. Daarom is de ringvoegconfiguratie erg belangrijk. Het blijkt
dat de gemiddelde krachten over verschillende ringen niet worden beïnvloed, maar lokaal
worden krachten erg beïnvloed door krachtinleiding over de ringvoegen.
Ook is een vergelijking gemaakt tussen modelresultaten en praktijkmetingen. De vergelijking
richt zich voornamelijk op de tangentiële krachtcomponenten. De bijdrage van de axiale
krachten aan de tangentiële componenten wordt in rekening gebracht door dwarscontractie. Het
is duidelijk dat de axiale krachten hoofdzakelijk zichtbaar zijn in de tangentiële spanningen en
de tangentiële normaalkrachten. De invloed van dwarscontractie op de tangentiële momenten is
beperkt, maar door krachtinleiding over de ringvoegen worden de tangentiële momenten toch beïnvloed.
De vergelijking van de modellen met de full-scale test- en praktijkresultaten leidt tot de
conclusie dat bij de praktijkmetingen van de Botlek Spoortunnel (BRT) de zogenaamde uplift
loading case opgetreden kan zijn. Een vergelijking van de modelresultaten op basis van de uplift
loading case belastingen met de praktijkmetingen, resulteert in zeer goed overeenstemmende
waarden voor de tangentiële spanningen, tangentiële normaalkrachten en momenten.
Vanuit de metingen wordt het duidelijk dat spanningen niet gelijkmatig verdeeld zijn over de
segmentbreedte. Analyse van de verschillende stadia in de bouwfase laat zien dat, zeker als de
ring binnen de TBM is of net de TBM verlaat, spanningen in hoge mate niet uniform verdeeld
zijn. Dit is erg belangrijk in het geval van spanningsanalyse voor scheurvorming. Het blijkt ook
dat dan spanningsniveaus kunnen optreden die maatgevend zijn boven spanningen in de gebruiksfase.
Vergelijking van modelresultaten met metingen van de Tweede Heinenoord Tunnnel leidt tot de
conclusie dat daar een volledig groutproces heeft plaatsgevonden of dat al heel snel de normale
grondbelastingen aangrijpen. Het is duidelijk dat de interne krachten veranderen in de tijd.
Het doel van de ideale assemblage van de tunnel is het bouwen van een perfect ronde ring, met
goed gesloten voegen op gelijkmatig verdeelde opleggingen voor alle segmenten. Hierop is ook
het ontwerp van segmenten gebaseerd. Het blijkt dat er vele oorzaken zijn voor kwaliteitsverlies
die elk op zich kunnen leiden tot schade, maar zeker ook tegelijkertijd kunnen optreden.
Voorbeelden worden uitgewerkt van schademechanismen die bijdragen aan extra spanningen in
de segmenten. Deze extra mechanismen zijn niet geïmplementeerd in de zogenaamde
ringmodellen. Daarom moeten aanvullende analyses worden uitgevoerd om deze mechanismen
te beschouwen. Het blijkt dat juist deze mechanismen kunnen leiden tot hoge spanningen in de
segmenten die schade kunnen veroorzaken. De gevonden scheurpatronen worden vaak
geobserveerd in de praktijk. De aanvullende mechanismen, die meestal driedimensionaal zijn,
laten zien waarom scheurvorming eenvoudig kan optreden. Het beste is dan ook ervoor te
zorgen dat deze mechanismen niet optreden. De belangrijkste parameters in de aanvullende
mechanismen zijn torsiemomenten, aanvullende tangentiële momenten, dwarskrachten en hoge axiale belastingen.
Het uitgangspunt van het ontwerp moet altijd zijn dat de gebruiksfase maatgevend is. Daarom
worden randvoorwaarden gesteld aan de bouwfase. Het dient aangetoond te worden dat die
randvoorwaarden gelden, zowel in het ontwerp als de uitvoering en de exploitatie. In het geval
dat de bouwfase minstens zo maatgevend is als de gebruiksfase zal voor de lining geen
economisch optimaal ontwerp gemaakt worden, omdat de bouwfase slechts een hele korte
levensfase is in vergelijking tot de gehele levensduur van de tunnel.
Een ontwerpfilosofie is opgesteld die de analyse van de lining bevat, ook tijdens de bouwfase.
Het optimale ontwerp volgt uit: -
De lining wordt ontworpen op basis van een maatgevende gebruiksfase, zonder inachtneming van de bouwfase. -
De bouwfase wordt zodanig vastgesteld en uitgevoerd dat dit niet resulteert in enige
negatieve invloed op het ontwerp van de lining in de gebruiksfase. CONTENTS SUMMARY NOTATIONS 1
INTRODUCTION ................................................................................................................1 2
STATE OF THE ART .........................................................................................................3 2.1
CONTRACTS.................................................................................................................3 2.2
DESIGN AND METHODS ................................................................................................4 2.3
APPLIED ENGINEERING MODELS...................................................................................8 2.3.1
Ring models..................................................................................................8 2.3.2
Structural behaviour in axial direction .......................................................11 2.4
JACK FORCE INTRODUCTION IN THE LINING ................................................................11 2.5
THE OBJECTIVE OF DOWEL AND SOCKET ....................................................................12 2.6
THE OBJECTIVE OF THE MASONRY LAYOUT OF THE SEGMENTED LINING .....................12 2.7
QUALITY LOSS BY CRACKING.....................................................................................13 2.8
ASSEMBLY PROTOCOL ...............................................................................................14 2.9
PLACEMENTS OF THE KEY SEGMENT ..........................................................................14 2.10
ECCENTRIC POSITIONING OF TBM JACKS...................................................................15 2.11
UNEVENNESS OF THE LATERAL JOINT.........................................................................15 2.12
TOLERANCES OF THE SIZES OF THE SEGMENTS ...........................................................16 2.13
LEARNING EXPERIENCES............................................................................................16 2.14
CONCLUSIONS ...........................................................................................................17 3
PROBLEM DEFINITION AND OBJECTIVE...............................................................19 3.1
THE PROBLEM DESCRIPTION.......................................................................................19 3.2
PROBLEM DEFINITION: THE ASSEMBLY OF THE LINING ...............................................20 3.3
THE OBJECTIVE TO CLARIFY THE ASSEMBLY OF THE LINING .......................................21 3.4
THE FRAME OF THE SOLUTION APPROACH ..................................................................21 4
ANALYTICAL SOLUTIONS FOR COUPLED RINGS IN SOIL ...............................23 4.1
INTRODUCTION ..........................................................................................................23 4.2
GEOMETRY AND LOADING .........................................................................................23 4.3
SOLUTION STRATEGY.................................................................................................28 4.4
A SINGLE RING...........................................................................................................29 4.5
DEFORMATIONS DUE TO ROTATION IN LONGITUDINAL JOINTS ....................................30 4.6
COMBINING BENDING STIFFNESS, LONGITUDINAL JOINTS AND SOIL............................32 4.7
COUPLED RINGS.........................................................................................................35 4.8
COUPLED RINGS AND ELASTIC SOIL CONTINUUM........................................................38 4.9
APPLICATION OF THE ANALYTICAL SOLUTIONS ..........................................................39 4.10
CONCLUSIONS ...........................................................................................................39 5
INTERPRETATION OF THE ANALYTICAL MODELS ...........................................41 5.1
THE NON-LINEAR ROTATIONAL STIFFNESS OF THE LONGITUDINAL JOINTS ..................41 5.2
STRATEGY FOR CALCULATING WITH NON-LINEARITY IN LONGITUDINAL JOINTS .........43 5.3
ANALYSES OF THE LINING WITH LINEAR AND NON-LINEAR ROTATIONAL STIFFNESS
IN THE LONGITUDINAL JOINTS ....................................................................................46 5.4
CONCLUSIONS ON NON-LINEAR LONGITUDINAL JOINT BEHAVIOUR ............................50 5.5
INTRODUCTION OF NON-LINEAR BEHAVIOUR FOR BENDING MOMENTS .......................50 5.5.1
Single ring with bending stiffness and longitudinal joints .........................51 5.5.2
Coupled ring system ...................................................................................52 5.5.3
Conclusions on the analytical solution related to the reducing
tangential bending moments.......................................................................54 5.6
COMPARING THE ANALYTICAL SOLUTIONS WITH THEORIES FROM LITERATURE ..........54 5.7
THE EQUIVALENT BENDING STIFFNESS OF HOMOGENEOUS RINGS TO PREDICT
DEFORMATIONS..........................................................................................................57 5.8
CONCLUSIONS FROM THE BACKGROUND DOCUMENT .................................................58 5.9
CONCLUSIONS ...........................................................................................................59 6
SEGMENTED LINING MODELS IN SOIL: GENERAL LOADING
COMPONENTS AND CONSIDERATION OF THE ULS............................................61 6.1
THE NORMAL LOAD CASES: LOADING FROM THE SOIL ................................................61 6.1.1
General .......................................................................................................61 6.1.2
Transformations of loading to the radial and tangential component ..........62 6.1.3
Approach 1: Reduction of the vertical soil pressure ..................................63 6.1.4
Approach 2: Equal vertical effective soil pressure.....................................63 6.1.5
Approach 3: Transformation to omit the ‘floating component’ .................64 6.2
EXAMPLE COMPARING THE LOAD CASES ....................................................................66 6.2.1
Determination of the radial loading............................................................66 6.2.2
Results from the different loading approaches...........................................68 6.2.3
Conclusions with regard to the different approaches for the radial
loading ........................................................................................................69 6.3
THE UPLIFT LOADING CASE ........................................................................................69 6.3.1
Introduction to the behaviour of the grout.................................................69 6.3.2
Introduction of the uplift loading case........................................................70 6.3.3
The application of the uplift loading case in a FEM model .......................72 6.3.4
The influence of the overburden.................................................................77 6.3.5
Conclusions for the uplift loading case ......................................................81 6.4
CONSEQUENCES OF THE UPLIFT LOADING CASE IN RELATION TO THE SEGMENTAL
THICKNESS .................................................................................................................82 6.5
TAIL VOID INJECTION MATERIAL ................................................................................84 6.6
EARLY AGE CONSIDERATIONS OF THE TANGENTIAL LOADING COMPONENT................84 6.7
NON-LINEAR CALCULATIONS FOR THE RING WITHOUT SOIL INTERACTION..................85 6.8
NON-LINEAR CALCULATIONS FOR THE RING WITH FULL SOIL SUPPORT.......................86 6.9
THE ULTIMATE LIMIT STATE (ULS) CONSIDERATION................................................87 6.10
THE LOCAL STABILITY PROBLEM OF THE LINING ........................................................87 6.11
THE SNAP THROUGH PROBLEM...................................................................................90 6.12
CONCLUSIONS ...........................................................................................................91 7
COMPARISON OF FULL-SCALE TESTS WITH ANALYTICAL SOLUTIONS ...93 7.1
GEOMETRY ................................................................................................................93 7.2
LOADING AT ONCE .....................................................................................................94 7.2.1
Deformations due to ovalisation.................................................................94 7.2.2
Longitudinal joints ...................................................................................100 7.2.3
Tangential stresses in segments................................................................102 7.3
SEQUENTIAL LOADING AND THE MIGRATION OF FORCES ..........................................104 7.4
DEFORMATIONS AND TANGENTIAL STRESSES DUE TO SEQUENTIAL LOADING.
MIGRATION OF THE ACTING FORCES ........................................................................105 7.5
THE DIRECTION OF COUPLING FORCES DUE TO SEQUENTIAL LOADING ......................108 7.6
CONCLUSIONS .........................................................................................................110 8
MEASUREMENTS AND CALCULATIONS OF ASSEMBLING STRESSES AT
THE BRT AND THE SHT ..............................................................................................113 8.1
INTRODUCTION ........................................................................................................113 8.2
THE CONVERSION OF MEASURED STRAINS TO STRESSES...........................................115 8.3
THE NORMAL LOAD CASE AND THE EQUIPPED RING FAR FROM THE TBM.................119 8.4
THE UPLIFT LOADING CASE AT THE BRT..................................................................121 8.5
NON-UNIFORMITY OF THE TANGENTIAL STRESSES....................................................124 8.6
THE EVOLUTION OF THE STRESSES DURING THE ASSEMBLY......................................126 8.7
THE ASSEMBLING STRESSES.....................................................................................128 8.8
THE INFLUENCE OF TIME ON THE CALCULATED STRESSES FROM MEASURED
STRAINS ...................................................................................................................129 8.9
THE MEASUREMENTS OF THE SHT ...........................................................................131 8.10
CONCLUSIONS .........................................................................................................132 9
OBSERVATION OF THE ASSEMBLY OF THE LINING........................................133 9.1
INTRODUCTION ........................................................................................................133 9.2
THE GENERAL ASSEMBLING PROCESS.......................................................................134 9.3
THE OBSERVED DAMAGE AND CRACK PATTERNS .....................................................135 9.4
CAUSES OF DAMAGE AND CRACK PATTERNS ............................................................136 9.4.1
Configuration of the lining and TBM jacks .............................................136 9.4.2
Subsequent loading and misalignments during the assembly ..................139 9.4.3
Consequences of the assembling process .................................................143 9.4.4
Long term issues.......................................................................................145 9.5
CONCLUSIONS FROM MEASUREMENTS AND OBSERVATIONS OF BUILT TUNNELS
AND THE FULL-SCALE TEST ......................................................................................146 9.5.1
Hypotheses due to the measurements from the SHT................................146 9.5.2
Observations of the SHT ..........................................................................148 9.5.3
Observations of the BRT..........................................................................148 9.5.4
Results from the lining in the full-scale test.............................................150 9.6
CONCLUSIONS .........................................................................................................151
10 EXAMPLES OF THE ADDITIONAL DAMAGE MECHANISMS...........................153 10.1
THE TORSION OF SEGMENTS.....................................................................................153 10.1.1
Torque mechanism ...................................................................................153 10.1.2
Torque mechanism including the influence of axial jack forces. .............156 10.2
THE UNEVEN SUPPORTS OF THE SEGMENTS IN THE LATERAL JOINTS .........................158 10.2.1
Uneven support at one side of the segment ..............................................158 10.2.2
Uneven support in the middle of the segment ..........................................162 10.2.3
Conclusion on uneven support crack mechanisms...................................166 10.3
THE FORCED PLACEMENT OF THE KEY SEGMENT ......................................................166 10.3.1
Analytical rotation model description of the pushed key segment...........166 10.3.2
Example of a forced placement of the key segment .................................168 10.3.3
Results of the frame analysis....................................................................169 10.3.4
Results of the full-scale test and the comparison with other models .......171 10.3.5
Conclusions to the forced placement of the key segment ........................172 10.4
DISCUSSION OF OTHER DAMAGE MECHANISMS ........................................................173 10.4.1
Jack force introduction .............................................................................173 10.4.2
Local introduction of forces .....................................................................173 10.5
CONCLUSIONS .........................................................................................................174
11 DESIGN PHILOSOPHY .................................................................................................175 11.1
THE BASIC CONSIDERATIONS OF THE DESIGN PHILOSOPHY .......................................175 11.2
DESIGN PARAMETERS FOR A SEGMENTED CONCRETE LINING....................................177 11.3
QUALITATIVE INFLUENCE OF PARAMETERS ..............................................................178 11.4
DESIGN PHILOSOPHY................................................................................................179
12 CONCLUSIONS...............................................................................................................183 REFERENCES LITERATURE
APPENDIX A: MEASURED STRAINS
APPENDIX B: THEORETICAL COMPARISON BETWEEN THE LINING OF THE BRT AND THE GHT
APPENDIX C: THE LOCAL FAILURE OF THE SOIL SUPPORT OF THE LINING
APPENDIX D : THE LINEAR SOIL SPRING REDUCTION FACTOR BASED ON ELASTIC CONTINUUMS CURRICULUM VITAE Notations A = concrete surface Ec = Young’s modulus of concrete Es = soil elasticity EA = normal stiffness EI = bending stiffness G = shear modulus of concrete It = torsional moment of inertia K0 = neutral soil coefficient Mi =
tangential bending moment in longitudinal joint i Mij =
tangential bending moment at angle ij Mu = ultimate bending moment N = normal force Pi =
radial interaction force between adjoining rings through the lateral joint at position i T = torsional moment Wt =
elastic section modulus for torsion W =
elastic section modulus for bending b = (half) segmental width cri =
rotational stiffness in the longitudinal joint at position i d = segmental thickness ks = system stiffness of the lining kv = coupling stiffness lt =
contact area height in the longitudinal joint r = radius of the lining u = total deformation u0 = uniform compression u2EI =
ovalisation by bending of the segments u2lj =
ovalisation by rotation of the longitudinal joints uc = compressive deformation ut = tangential displacement Įj =
stress correction factor for the soil stresses ȕi =
angle to longitudinal joint i (ȕ = 0 at the top of the ring) ǻıs = soil reaction stress ǻui =
deformation difference of the coupling at position i ij =
rotation angle around the ring centre axial axis (ij = 0 at the top of the ring) γsd = dead weight of saturated soil γsw =
dead weight of unsaturated soil ζ =
reduction factor for bending stiffness of homogeneous rings ȣ =
poisson coefficient of concrete ıh = horizontal soil pressure ır = radial stress ıt = tangential stress ır,side =
radial stress at the side of the ring ır.top =
radial stress at the top of the ring ıv = vertical soil pressure ıvc =
vertical stress at the centre of the lining ıv,eff =
effective vertical soil pressure ıw = water pressure ır.top = radial stress at the top ı0 =
uniform radial compression stress ı1 = floating stress component ı2 = radial ovalisation stress τ = shear stress τT = shear stress due to torsion și =
rotation in the longitudinal joint i ș ’t = torsion rotational angle BRT = Botlek Railway Tunnel GHT = Green Heart Tunnel SHT = Second Heinenoord Tunnel SRT = Sophia Railway Tunnel WST = Westerschelde Tunnel EPB = earth pressure balance TBM = tunnel boring machine LDesign =
frame analysis software specially developed for the analysis of the lining of tunnels