BORED RAILWAYTUNNELS INTHENETHERLANDS

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BORED RAILWAY TUNNELS IN THE NETHERLANDS

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Bored Railway Tunnels in The Netherlands

Study of literature:Structural analyses and design methodsfor bored tunnels in soft ground

Eerste oplage van de eerste druk 1994

Copyright <01995 "Holland Railconsult", The Netherlands

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Hclland RalkOOsultVabfdelini: Civicle Tecl:u1iekProduktgroep Tmmols

Project: Bored Railway Tunnels in The Netherlands

Project nr.: 00010.79.1.1319Document nr.: 0001076.r.p.9503

Study of literature:Structural analyses and design methods

for bored tunnels in soft ground

By order of "NS Railinfrabeheer,Projectbureau Havenspoorlijn/Betouweroute/Twentelijn"

ing. J.H. Jonker

ir. P. Jovanovic

Written by: Checked by:

ing. F. Vable

dateAugust

1995

dateSeptember

1995

Approved by:

ir. H.C.W. Duurland

dateSeptember

1995

Railway Tunnels / Study of literature: Structural analyses and design methods for bored tunnels 1

8--Holland RallconsultVabfdeling Civiele Teclmiok

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Railway Tunnels! Study of literature: Structural analyses and design methods for bored tunnels 2

----.-Holland RallconsultVabfdeling Cividc TecbniekProdubpoep Tunnels

Study of literature:Structural analyses and design methods

for bored tunnels in soft ground

Some additional aspects in review of structuralanalysis and design methods for the bored tunnels in soft ground


8-Holland RallconsultVabfdcliog Civiele Teclmick

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Railway Tunnels / Study of literature: Structural analyses and design methods for bored turmels 4

--------.Holland RaIlconsultVabfdc.liDg Civie1e TeclmIek

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Content: Page

1. Introduction 9

1.1. General considerations1.2. Basic assumptions for structural design of tunnels

912

2. Basic theory of soft soil conditions for tunnelling 14

2.1. Generalized Hook's law2.2. Applicability of Hook's law to soil2.3. Young's modulus, Poisson's ratio and modulus of subgrade reaction2.4. Stresses and displacements associated with tunnel excavation

14172024

3. Review of some general design considerations for tunnels in soft ground 25

3.1. Tabular review of design models3.2. Methods based on subgrade reaction

2635

3.2.1. Continuum models 35

3.2.1.1.3.2.1.2.3.2.1.3.3.2.1.4.

MorganMuir- WoodCurtisPeck - semi-empirical approach

36373940

3.2.2. Bedded - Beam model (Action - reaction model) 41

3.2.2.1. Shulz/Duddeck3.2.2.2. Wayss & Freytag3.2.2.3 . Yamaguchi

414345

3.2.3. Nonlinear effects 47

3.2.3.1.3.2.3.2.3.2.3.3.3.2.3.4.3.2.3.5.

Non-linear ground behaviourPlasticityBucklingCreepLining with hinges

4747484949

3.3. Relative stiffness solution 50

3.3.1.3.3.2.

Einstein & SchwartzPender

5053

3.4. Convergence - confinement method of modelling 57


8-.

Holland RallconsultVabfdeling Chicle TcdmiekProduktgroep Ttmncls

page

3.5. Finite element models

3.5.1.3.5.2.3.5.3.3.5.4.

59

General considerationsFEM model after Dr. ing. J. ErdmannFEM model after Dr. ing. P. JanBenShort review of some available FEM software

59626364

3.5.4.1. PLAXIS3.5.4.2. DIANA3.5.4.3. ANSYS

646769

4. Double - tube tunnels 73

4.1. The structural problem4.2. Two-dimensional analysis4.3. Three-dimensional analysis

737474

5. Guidelines for the design of tunnels 75

5.1. Scope of the Guidelines5.2. Outline of general approaches

5.2.1.5.2.2.5.2.3.5.2.4.5.2.5.

7576

General procedure in designing a tunnel 76Elements of the structural design model for tunnels 77Different approaches based on ground conditions and tunnelling methods 78Site investigations, structural analysis and In-Situ monitoring 80Design criteria and evaluating structural safety 81

5.3. Site investigations and ground probing

5.3.1.

5.3.2.5.3.3.

82

Geological data and ground parameters 82

5.3 .1.1. Tunnels in rock5.3 .1.2. Tunnels in soil

8284

Evaluation of parameters by ground probing and laboratory testsInterpretation of test results and documentation

8485

5.4. On structural design models for tunnelling

5.4.1.5.4.2.5.4.3.5.4.4.5.4.5.5.4.6.

86

Alternative design modelsContinuum or discontinuum modelBedded-Beam model, Action-Reaction modelEmpirical approachObservational methodSpecial design features

868888909191

5.4.6.1. Ground improvement techniques5.4.6.2. Unusual ground behaviour

9192


--------Holland RallconsultVakafdcliogCivieleTeclmiet

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page

5.5. In-Situ monitoring 92

5.5.1.5.5.2.5.5.3.

Purpose on In-Situ measurementsMonitoring methodsInterpreting results of In-Situ monitoring

929393

5.6. Guidelines for structural detailing of the lining 94

6. Conclusion 96

7. References 101


~.-Holland RallconsultVabfdding Civicle TccbnietProduktgroep1'unne1s

Railway Tunnels I Study of literature: Structural analyses and design methods for bored tunnels 8

-------Holland RailconsultVabfdcling CiYide Tc:clmiot

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1. Introduction

1.1. General considerations

"London tunnel collapses", ENR (McGraw Hill), October 31, 1994: "A report is expected thisweek on why the first attempt to apply the New Austrian Tunnelling Method (NATM) in Londonclay, hit trouble when about 40 meters of tunnel collapsed under Heathrow International Air-port...Fison believes the collapse started in one platform tunnel near the shaft, triggering failureacross the whole station width. Engineers believed failure was total but there was anothercollapse in the adjacent section 24 hours later...The company had considered stopping work afterthe Munich collapse but thought conditions dissimilar."

"Police probe repeat Munich tunnel breach", Construction today (Thomas Telford House), Octo-ber, 1994.: "Work on the DM156M second phase of Munich's U-Bahn U2 undergroundextension has been suspended pending an ... The New Austrian Tunnelling Method was beingused by contracting consortium when the collapse occurred at 6pm Tuesday 27 September,leaving a hole about 20 m. wide and 18,5 m deep. The accident bore all the hallmarks of a verysimilar collapse in the same city in 1980 The tunnel affected was one of twin running tunnelsbeing driven west during 24 hour working from a central access shaft. NA TM was being used ina strata of flinty marl, overline by some 15,5 m. of ground water bearing gravel."

To avoid these accidents it is very important to understand all the approaches and theoriesdealing with structural analyses and design of tunnels. Failures had happened in the past not onlyby applying NA TM and not only in soft soil. Thus, it results in a necessity to think carefullyabout the methods, models, theories and approaches that should be applied in structural analysesand design of tunnels.

The need for the scientific understanding of the behaviour of tunnels and the effects on thesurrounding ground has arisen due to occurring tunnel failures and the unfamiliar nature of thetunnelling environments. This has led to a decrease in tunnel failures, support optimisation and avastly improved understanding of the processes which occur in the earth as a result of excavationor drilling.

Soft soil tunnelling design is recognised as a completely different philosophy from rocktunnelling and therefore requires a separate explanation. A lot of work in this field has been doneby many authors so the knowledge of the structural design of tunnels in soft ground is widelyavailable.

Analytical methods were first applied in a design with a limited range of premises but withexplicit understandable solutions. Many of the more sophisticated numerical methods, such asfinite element analyses, can handle a high complexity of soil, tunnel, their mutual interaction andtheir general behaviour in continuum. This however, requires a proper information input.Empirical methods bypass this detailed information input by directly relating the supportrequirements to easy measurable ground properties.

Every approach has application possibilities but a design method has to meet three criteria:1. Simplicity in using2. Ability to model the most significant effects such as: soil properties, forces, stresses,

support geometry and its properties.3. Ability to model correctly the loading conditions and ground-structure interaction


-------Holland RallconsultVakafdeliDa: Civiele TcdmiekProduttgroep Tunnels

Engineers must rely on a design model of a tunnel which has to provide a suitable, safe andeconomical structure. To translate reality and the logic behaviour of structures into a mechanical-mathematical engineering model is still difficult, even if there are answers and solutions to theproblem and they are correct. But the most important question is whether the assumptions areappropriate.

This resulted in a need to methodize, organise and arrange structural analysis and design of thetunnels into various types of approaches. The working group of the International TunnellingAssociation established at the General Assembly in Tokyo 1978, directed by Prof. Dr.H.Duddeck[37], started a difficult task to summarize the information from each of the member nations,dealing with the design models used at present and determining the supporting elements oftunnelling such as: concrete thickness, reinforcement, anchors, bolts, etc. (The design model isshown in fig. 1).

In 1985 as a continuation of that work, Prof. Dr. H. Duddeck and Dr. ing. J. Erdmann [35]presented the results of the investigation into design models for soft ground tunnels and acomparative review of the progress to date in this field. The main differences in the assumptionsregarding the different models are staged. Only the circular cross-section was investigated but toa great extent the results can also be valid for noncircular cross-sections and more refinednumerical analyses.

Generally, the models for soft ground conditions are fairly well defined internationally and aremore developed than the others. Muller-Salzburg, REinstein, Craig and many others haveapplied a wide approach to all of the complex aspects of tunnelling, including different designmodels.

GEOLOGY site investigationline and ~rientation

PROBING AND

*ROCK MEeD.

EXPERIENCEESTIMATION

MECHANICALMODEL

fI)rI.)

a:

~

VERIFICATIONOF TUNNELDESIGN

fig. 1

* - Translation of reality into models


Hiilland RalkODsultVabfdeling Civiele TeclmickProduktgroep Tuanels

Among the many questions which have to be answered, few of them lead to the point:

1. Which basic assumptions are applied in order to derive a model?2. Which assumptions are generally agreed upon and which are different?3. Which design criteria is most favourable (displacement, forces, moments, safety, etc.)?

Generally simple circular tunnel geometry is applied with little interactive complications betweentunnel and the soil. This is the most important reason why, worldwide, the design model for softground tunnelling is so well developed. Certain conclusions were achieved and almost the entirefield of theoretical work has been covered, such as: creep, effect of hinges, nonlinearities etc.

This study shall not present the concept of the "The New Austrian Tunnelling Method, (NA TM)"in the full option, because it needs more space and certain considerations. " The NA TM is basedon a concept whereby the ground (rock or soil) surrounding an underground opening becomes aload bearing structural component through activation of a ring-like body of supporting ground".The material is published by the authors of NATM i.e. L.Rabcewicz, L. Muller and F.Pacher [4],and translated into ten languages.

The scope of this study will be within the borders of general international approvedconsiderations and assumptions for structural analyses and design of tunnels in soft ground.


8--Holland RallconsultVabfdeling CiYiele Teclmiek

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1.2. Basic assumptions (ITA) [37]

General agreements are based on the following basic assumptions:

a. To consider only a cross-section for the design model of the linings it might be sufficientassuming plane-strain conditions for the lining and the ground. Hence, all three dimensionalstress-strain effects close to the tunnel face are neglected, especially those of a lasting pre-decompression of the ground at the tunnel face before the lining is activated.(see fig.2)

b. The cross-section is circular. The stiffuess of the lining is considered as a constant along thecircumference. Complete or restrained structural hinges mayor may not be considered. Due tothe circular cross-section, analytical solutions are achieved and parametrical design charts arepossible.

c. The active soil pressures on the lining are assumed to be equal to the primary stresses in theundisturbed ground because the ground is soft. Hence, it is assumed that for the final stage (yearsafter construction), the ground will eventually return to the same condition as before thetunnelling, except for the passive stresses due to the deflection of the lining.(see fig.3)

Changing ground water levels, traffic vibrations, etc., may be the cause of this. For the future,monitoring results may offer the opportunity to ascertain, in which cases (e.g. type of soil anddepth of tunnel) this assumption is too conservative. Intermediate situations influenced by thedriving procedure and the placing of the supporting elements are neglected.

°v = Y H[[[[[[[IJ]]I[J]

u 0r

[[[[[[[IJ]]I[J]y -volume weight

radialdisplacement

bendinJl partof radial load

fig.2

N M

maxN No maxM

normalforces

bendingmoment


------.-Holland RallconsultVabfdcliDg Civie1e TecluUclr:

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d. Between the lining and the ground exist a bond, either for radial and tangential deformationsor for radial deformations only. With this assumption, the model complies with both equilibriumconditions and compatibility conditions at the boundary between lining and soil. This is quitedifferent from the concept of introducing a lining resistance, expressed in terms of force, whereonly equilibrium conditions are considered.

Ov= YH u a =K UB r N M

llinJJ K = const., r

Mu

°h= K~U'v

[IIIII]- Ovradialclisplacement

ground reactionpressure

normalforces

bendingmoment

fig.3

e. Owing to the bond between lining and ground, deformations of the lining result in reactionstresses in the ground. A continuum model includes these effects automatically. For a beammodel, bedding springs with appropriate bedding moduli have to be applied. Bonding at everyplace around the lining results in reduction of loading ground pressure where the lining deflectsinwards. If such load reductions are not intended, the bedding (and equivalent of this for thecontinuum model) has to be neglected in those parts of the cross-section where inward deforma-tions occur, i.e. principally at the crown. The bedding moduli should be defined so that fullcorrespondence is achieved between a continuum model and a bedded beam model.

f. The material behaviour of ground and lining are generally assumed to be elastic. More refinedtheories may also include nonlinear and plastic material laws, which, however, in most casesrequire the applications of a numerical method (e.g. Finite Element Method).

All of these assumptions are not completely covering the real behaviour of the tunnel and groundbut they are the most important points in general design approach.

To understand the essential concepts of structural analysis and design of a tunnel we must startfirst with a basic theory of soil mechanics.


8-Holland RallconsultVabfdeIiDg Civicle Teehoi'*Produktgroep Tunnels

2. Basic theory of soft ground conditions for tunnelling

The basic principles of soil mechanics applicable to the behaviour of slopes, foundations andretaining walls, apply equally to the stability of tunnels in soft ground and to the settlementscaused by tunnelling.

Recently a number of calculations have been developed in accordance with the basic principlesof soil mechanics but it is not always obvious which calculation is applicable to a particularpractical tunnelling problem. So this chapter will only deal with well known basic determinationsof soil properties which are applied in various approaches of tunnel design.

2.1. Generalized Hook's law

External forces are acting on a deformable body as body forces and surface forces.The magnitude of the surface force per unit area is called stress. Thus, stresses perpendicular tothe areas are normal components (crx,cry,crJand the shearing components are.xy,.xz,.yx,.yz,.zx,.zy.The stress conditions of the body at one point are then determined by thetotality of nine values. Only six of these nine components are not interdependent (see figA).

Zi,oz

Ox x-..

y ..°y, components of stress

figA

Under those stresses the distance between the particles will change. With the u, v and wcomponents of displacement in x, y and z direction and with the assumption of relative smalldeformations, the linear strains of an element length will be:

au . av ,E =- E =-x ax' Y ay'aw

Ez = az

However, the state of strain of a body is also determined by the rotation. This deformation iscalled shear strain:

av au aw au av awy =-+-'y =-+-'y =-+-xyax ay' xz ax az'

yzaz ay

If the stresses in the body are of a such magnitude that Yxy= Yxz= Yyz= 0, then the deformation isaccompanied only by a change in volume. From this follows the relative change in volume:

e = Ex + Ey + Ez


8-Holland RallconsultVabfde!iDg Civide Tec:hniekProduk1groep Ttmnels

If ex = ey = ez = 0 , then the deformation leads to the sliding of some elements and the

volume will not change.

The generalized Hooke's law for homogeneous isotropic bodies could be formulated as follows:

° =Ae+2I1ex r x

°y = Ae + 2 ~ ey

Oz = Ae + 2~ez

'yx = ~Yxy; 'zx = ~Yxz; 'zy = ~Yyz

where A and ~ are elastic constants, called Lame's constants.

More than two elastic constants characterize anisotropic bodies.

Assuming the elongation induced by uniform stress cr occurs in the direction of the z axis, weobtain for the stress components:

0 =0' 0 = 0 'x 'y Oz = 0

'yx = 'zx =. = 0zy

Yxy = Yxz = Yyz = 0

Substituting the normal stresses for the first three equations, we obtain:

Ae+2~ex=0

Ae + 2 ~ ey = 0

Ae + 2 ~ ez = 0

From these equations follows:

e= A+~ o"e=e=- A°z

~(3A + 2~), x y

2~(3A + 2~)


---------Holland RaIlconsultVabfdding CiYiele Techniek...............-

The quantity which defines the relationship between a tensile or compressive stress and theelongation or compression caused by this stress, is called the normal modulus of elasticity orYoung's modulus of elasticity.

E = 1-1(3A.+ 21-1)

A. +1-1

The ratio between the relative lateral contraction and the relative axial elongation which does notdepend on the shape of the cross-section is called Poisson's ratio.

ex ey A.V=-=-=-

ez ez 2(A. + 1-1)

Solving those two equations we obtain:

A. =vE

(1 + v)(1 - 2v)

E= G1-1=2(1+v)

Young's modulus of elasticity and Poisson's ratio are the two principal quantities defining theelastic properties of materials.


.-------Holland RailconsultVabfdcling Civide TecbniekProdubgroep Tunnds

2.2. Applicability of Hook's law to soil, J.E. Bowles [28]

Some soils, such as sands, clays with sands and clays, consist of particles of different materialssurrounded by air or by a film of capillary water containing a solution of various salts and gases.The rigidity of separate particles is much higher than that of soil in general. Therefore in theinvestigation of elastic deformations of soils, the particles composing the soil may be consideredto be absolutely rigid.

Soil particles are distributed at random. Therefore the elastic properties of soil are the same in alldirections, and soil may be considered as isotropic space. The only exception is presented bylayered systems of soils in which separate layers are characterized by different properties. In suchcases a soil may be considered to be isotropic only within the boundaries of a layer.

The generalized Hooke's law is based on the assumption that stresses and deformations in theinitial state are equal to zero but in reality they are not. If considerable initial stresses arepresented, then the initial deformations cannot be considered to be small, and the principlesuperpositions cease to be valid in relation to deformations. Therefore it is not possible to applyconventional methods and the nonlinear analysis takes its place. This means that we must apply anonlinear theory of elasticity operating with nonlinear differential equations. To find the explicitsolution for this problem is almost impossible without the aid of numerical methods such as theFinite Element Method.

Almost all natural behaviour of soil is anisotropic and nonhomogeneous. The anisotropy isproduced as a result of a combination of particle placement during formation and overburdenpressures. Anisotropy is an important consideration in finite element analysis of soils, sinceelastic properties are input parameters.

As early as 1944 the property of anisotropy was discovered by Casagrande and Carrillo, but onlyin more recent times attempts have been made to quantify the effects (Young and Silvestry, Lawand Lo, Yamada and Ishihara, 1979).

Figure 5. illustrates anisotropy and the possible range in strength which occurs when the stressorientation is at certain angle with respect to the bedding plane.

mo.o_o iX.-;;;;---o-__m_mo omo mo O.OiXm:>-oo-m_.o...o.o.o m o mo__«.o.o;;;o.090-0.0.0...0.0.0.0

~~:~~~~~~~~~~~:;~~~~~~~~o~:~o~~~~~~~:~~~~~~~~~i~~~~:~~~:~~~~~o~:~:~~~~~~:~~~~::~~:~:~:~:~:~~~~~~:~

a

S~- - - - -. - - - - - - - - - - - - - -. - -. - - -~- - - - - - - - - - - - - - - - R- -=.- - - - UV... - - - - - - - - - - - - - - - - - - - - - - --

Suhp".".".".".".".".".".".".".".".".".".".".".".".".".".".".-'."."."."."."."."."."."."."." ,.,...'..."'.".".".".00."." ,........................

Suu = Suh [l+(R-l) cos2cx]

fig.5


8-Holland RallconsultVabfdeling Civiele TcclmieJc

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For isotropic material only two elastic constants define the stress-strain relationship. Therefore,five constants are required when a homogeneous soil is deposited in layers, so that one canassume symmetry about a vertical axis. A soil deposit which meets this criterion is termed cross-anisotropic. Actually, soil is not cross-anisotropic because of depth variations, but this is asimplification which does not introduce serious computational problems. This simplification hasthe effect of reducing 21 general elastic constants to 7.

Generalized Hook's law for cross-anisotropic material takes the following form:

Ox °y Ozex = E - J.12E - J.11

Eh v h

°y Ox Ozey =

E- J.13

E- J.13

Ev h h

Oz Ox °yez = E - J.11 E - J.12E

h h v

Y-.XY.

Y-'xz.

Y-'yz

XY-G' xz-G' YZ-Gv h v

For problems of plane strain when ez = Yxz = Yyz = 0 then:

EhOz = J.11ox + J.12EOy

v

ex = Aox + Boy

ey = Box + Cay

'xyYxy -

Gv

where:

A =1 - J.1~ .

EhB =

J.12 + J.11 J.12

Ev


~.-Holland RaIlconsultVabfde!ing Civic1e TcdmiekProduktgtoep Tlmnels

c =1 - n1-1~. n -

Eh .E '

- -E 'v v

EhG =

2 (1 + 1-11)

In which are:

Ey

Eh

stress-strain modulus in vertical directionstress-strain modulus in horizontal plain, i.e., in the plain of isotropy

I) -ez

1'"1 - -ex

- when the applied stress is ax

ex1-12 = -;-

y- when the applied stress is ay

e1-13 = -1

ex- when the applied stress is ax

GhGy

shear modulus in the horizontal planeshear modulus in the vertical plane

Thus, the four constants (A,B,C,G) required to solve the plain-strain problems of cross-anisotrop-ic soil can be obtained from three sets of plain-strain triaxial tests. The first test is on soilsamples with the plain isotropy horizontal, the second vertical and the third at an angle of 45° tothe horizontal. If the correct evaluation of each of the four constants is not possible, the soilshould be treated as an isotropic material.


",.,-------Holland RallconsultVabfdeling Civiele TccbnietProduktgroep Tunnels

2.3. Young's modulus, Poisson's ratio and modulus of subgrade reaction

As mentioned before it is seen that the modulus of elasticity depends on the normalpressure 0". With an increase of pressure, the modulus of elasticity increases also.The magnitude of Poisson's ratio is not constant. Ifthe normal stresses are small, then the valueof u is close to the value of 8x18Zfor elastic space for which Hooke's law is valid.

B

az

,,1/

a

4Ez

..,

/I

II A/1 Lola

/ II

I

/ I1 1

/ do

daks=

do

D

r--"'--------------I

-I

IIII

II

III

1I

II

IEI x I

~unit

ax~

~t"7

Ex

v= - ~ 0E

zPoisson's ratio

modulus of sub gradereaction

fig.6

The Young's modulus of elasticity and Poisson's ratio are of use in evaluating the foundation orstructure settlements as well as determining the subgrade reaction and shear modulus. The shearmodulus G is used in soil dynamics problems to compute amplitudes of vibrations.

Both of them are dependent on:

1. Method of performing the compression tests (unconfined, confined, compression, extension)2. Confining cell pressure 0"3'E tends to increase nonlinear with the increase in confining

pressure3. Overconsolidation ratio OCR4. Soil density - E increase with particle packing5. Water content of soil - lower water contents give higher values. Brittle uactures at low

strains occur with low water contents.6. Strain rate - at low strain rates the modulus value can be lowered by a factor of 2 or more

compared with the value obtained at a high test rate (Richardson and Whitman)7. Sample disturbance


8-Holland RailconsultVakafde.lingCiviclcTechnickProdulrtgroep Tunnels

The use of the values E and u for numerical design needs consideration. Schmidt has remarkedthat u is not over-sensitive in numerical designs within the range 0,3 to 0,4. The choice of thevalue for E is one of the most important thing because in granular soils it is not possible toobtain undisturbed samples for laboratory testing and the modulus will vary in stress level andloading direction.

In undrained clays, the modulus is related to the undrained shear strength, the overconsolidationratio and plasticity index.

In general, laboratory values are too low and the appropriate value is that of the long termmodulus which is basically unknown. The sensitivity of the analyses relating to E and thedifficulties encountered in obtaining a representative value dictate that a single modulus valuecannot be used. It is necessary to vary the value of E in the design of tunnels.

More about the applied tests and values for Young's modulus of elasticity can be found in"Funderingsadvies voor spoortunnel" from Holland Railconsult.

In principle, the modulus of subgrade reaction is a relationship between soil pressure anddeflection. The basic equation when using the plate-load test is:

k =q

5 -0

Nowadays, instead of using the concept of modulus of subgrade reactions, engineers are using Esand Poisson's coefficient u, especially in Finite Element Analyses. A major problem is toestimate the numerical value of ks' Hereby are mentioned only a few approaches to define amodulus of subgrade reaction.

1. Terzaghi (1955) [28], proposed ks to be obtained from plate-load test using the followingequation:

ks = k1 Bt

where k1 - value from 1 x 1 ft. squareplate-load test

2. Vesic (1961) [28], proposed that the modulus of subgrade reaction could be computed usingstress-strain modulus Es and Poisson's coefficient u:

Esks =

B ( 1 - V2 )

Approximations are often quite satisfactory if the computed deflection can be tolerated for anyreasonable value. So from the allowable bearing capacity qa the author proposed the following:

ks = 40 F qa

The equation is based on reasoning that qa is based on the ultimate soil pressure divided bysafety factor F.


-------Holland RallconsultVabfdeliDg CiYide ToclmiekProduktgroopTusullds

3. The most general form for either a horizontal or vertical modulus of subgrade reaction is:

k = A + BZns

where:ABZ

- constant for either horizontal or vertical members- coefficient of depth- depth of interest below ground- exponent to give ks the best fit (if it is load-test or other data)n

4. Schulze/Duddeck [7] proposed that if the reacting ground is replaced by bedding springs thenthe structure can be analyzed as a beam and the radial modulus of subgrade reaction is taken as:

Es Ek (1 - v)k = - =s R R (1 + v)(1 - 2v)

where a complete transition to the continuum model for the cos2<p-mode is given for fullbonding

k = 0 6Es

s ,-R

and for tangential slip

k = 0 5Es

s ,-R

The distribution of the "k" value around the tunnel depends on the author's assumption. Aconstant value is assumed for a deep tunnelling and for average tunnelling a certain function ofdistribution:

a > 2D~ H>D a < D; H<D r;-

\1\ "I',

''''''1

""

k - krl(con:~:';'r" ""';"'k~"~:;:Y) *fig.7

A review of ks by several other authors is given in tab.! [35]


------.-Holland RailconsultVabfdeling Cvie1e Te:clmiet~..........

table. I

Author kg

AhrensLindner

Luxk,o = 0,75

Ek

R

k'2 = 0,9Ek

R

kt2 = -0,45Ek

R

kr2 = 0,75Ek

R

HainHorst C, = (0,790 +0,798)

EkR

ECt = -(0,349+0,392) ;

FleckSklivanos CLV, = 0,353

Eg

R

CLVt = 0,58Eg

R

FleckSonntag

kso = 0,75Ek

R

ks2 = 0,75Ek

R

Rodriguez RoaOn 2

ks = tgSj= K,Yw(-) ; 1:s< On tgoPa

On tgo .ks = tgS, = 2, 1:s = On tgo

I1s


0,0 0,5 1,0 1,5 2,0 2,5 3,0 3,5 O'hK=-

0'v

500I"

1500+ 0,5

h

1000,32000 I +

hI

2500

~-Holland RallconsultVlkafdeliogCivideTcclmid:Produbgroop

"'""""

2.4. Stresses and displacements associated with excavation of tunnels

The stress field is a highly variable natural phenomenon which is related to depth below thesurface, the geological history, tectonic movements and structural geological features. The stressfield is close to the surface in the depth range relating to soil deposits and encompassing manycivil engineering applications. It is dominated by gravity loads due to the weight of the overlyingmaterial. The vertical stress component crvis commonly calculated from such a consideration.

n

°v = LYihi - Ow

i=1

The horizontal stress component is written as:

°h = Ko °v

The earth pressure coefficient Ko is directly dependent on Poisson's coefficient u:

vKo=(1=v)

Terzaghi investigated the coefficient of lateral earth pressure in different soils by comparing themagnitudes of forces which had to be applied to steel bands. These bands are inserted in verticaland horizontal positions into a consolidometer, in order to be able to remove them later on. As aresult of these investigations he came to the conclusion that the coefficient of lateral earthpressure has a constant value for each soil, for sands this is 0,42 and for clays 0,70 to 0,75.

Brown and Hoek [22], have collected the results of stress measurements taken around the world.On fig.8 we can see the relationship between Ko and depth.

fig.8The values of Ko which are commonly found are less and equal to 1.0, but overconsolidatedclays can exceed unity. It is very difficult to generalize these rules.Therefore, local geotechnical investigations have to give us a necessary value for Ko.


H<illand RalkOOsultVabfdeliDg Cividc Tcdmiek

-"""""

3. Reviews of some general design considerations for tunnels in soft ground

3.1. Tabular review of design models

The ITA working group [37] researched the problem of tunnel design, among others, in soft soil.The results are applied in many countries. The general questions were about the following items:

How are the dimensions of lining determinated? Maybe it comes from experience, logicderivation or just guessing.

What kind of ground characteristics should be drawn by site investigations, needed fordesign?

What kind of structural calculation model will provide an adequate behaviourprognosis?

What kind of safety criteria should be chosen in the planning phase?

Which of the design parameters should be supplied with safety margins, globalor partial safety factors?

In table.2 a review is given of the items for tunnel design, which are applied by engineers indifferent countries: Australia, Austria, Germany (D), France, Japan, China, United Kingdom andUnited States of America.

The items considered in table.2 are:

1. Site investigations and ground parameters2. Loads3. Structural system4. Safety concept and safety factors5. Distance between the tunnels

* - shows that item is applied


table.2 Description AA A D F J C UK USA

1. Site investigations andground characteristics

1.1 Sampling, boreholes with in- * * * * * * * *situ lab.test

1.2 Trial shafts * *

1.3 Electrical resistance * *

1.4 Prestressed anchorage and * *pump

1.5 Cone penetrometer * * * * * *

1.6 Ground water level * * * * * *

1.7 Seismic survey *

1.8 Borings per 1000m

1.8.1 5 - 10 *

1.8.2 3 - 10 *

1.8.3 5 - 20 *

1.8.4 10 - 20 * *

1.8.5 Variable * * *

1.9 Particle size grading * * * * *

1.10 Density * * * * * * *

1.11 Angle of friction * * * * * *

1.12 Pore pressure *

1.13 Coefficient of stiffness *

1.14 Cohesion * * * * * *

1.15 Shear strength * *

1.16 Modulus of elasticity * * *

1.17 Modulus of deformation * * *

1.18 Saturation, porosity * * * * *

1.19 Permeability * * * * * * *

1.20 Chemical composition of * * * * * *ground water

1.21 Boring logs *

1.22 Longitudinal profile of tun- *nel axis

H~and RaI~SUItVabfdeliDJ Civicle TcdmiekProduktgroep Tunnels

Railway Tunnels! Study of literature: Structural analyses and design methods for bored tunnels 26

Description AA A D F J C UK USA

1.23 Unconfined + confined * * * * *strength

1.24 Anisotropy *

1.25 Time yield *

1.26 Consistency *

1.27 Coefficient of soil reaction *

1.28 Soil modulus * * * * *

1.29 Coefficient of lateral pres- *sure Ko

1.30 Poisson's ratio *

1.31 Soil classification *

1.32 Moisture contents *

1.33 Sensitivity *

1.34 Expansive action *

1.35 Adjustment with the labora- *tory test

1.36 Lower values of ground * *characteristics are chosen fordesign

1.37 Medium values of ground * * * * *characteristics are chosen fordesign

1.38 Higher values of groundcharacteristics are chosen fordesign

1.39 Primary stress field *full overburden

°v = y h

horizontal pressure

°h = ). °v; ). =

from 0,4 to 0,6

H~and RalkOOsultVabfde1iDa: CiYielc Tccbniek

""""",,",,""""



1.40 Primary stress field * *full overburden

°y = y h

horizontal pressure

°h = ). Oy; ). = 0,5

1.41 Primary stress field *full overburden

°y = y h

horizontal pressure

°h = ). Oy; ). =

from 0,4 to 0,5

1.42 Primary stress field * * *full overburden

°y = y h

horizontal pressure

°h = ). Oy; ). =

from experience

1.43 Primary stress fieldfull overburden

°y = y h

horizontal pressure

°h = ). Oy; ). = Ko

1.43 Primary stress field *full overburden + super load

/°y = y h

horizontal pressure

/ / ). = Ko°h = ). °y ;

.--------Holland RailconsultVabfdeliog Civicle TechDiek

-"-"



2. Loadings * * * * * * * *

2.1 Vertical earth pressure * * * * * * * *

2.2 Horizontal earth pressure * * * * * * * *

2.3 Water pressure * * * * * * * *

2.4 Own weight of lining * * * * * * * *

2.5 Surface load * * * * * * * *

2.6 Passive earth pressure

2.7 Ground reaction *

2.8 Interval loads *

2.9 Temporary loads during con- *struction

2.10 Grout pressure * * *

2.11 Earthquake effects *

2.12 Ground settlement *

2.13 Effects of adjacent tunnel *

2.14 Shield ram loads * * * * *

2.15 Jack force * *

2.16 Air pressure * * *

2.17 Slurry pressure *

2.18 Temperature * * * * *

2.19 Creep and shrinkage * * * * *

2.20 Live load * * * * * *

2.21 Impact load *

2.22 Special ground movements *

2.23 Loose loads in excavation *faze

2.24 Handling stresses *

--------Holland RailconsultVabfdcIiDg Civide Tcdmick

-"-"



3. Structural system

3.1 Action and reaction models * * * * * *(bedded rings), in which thestructure is submitted todirect loads independent ofring deformations and reac-tion forces which are depen-dent of ring deformation

3.2 Continuum models in which *the behaviour of the groundand lining ( or support) isconsidered as unity, usinge.g. finite element method

3.3 "Convergence-confinement" *models (Pacher-Fennercurves), in which the radialdisplacement of the groundis compared with the radialconfinement load providedby lining or support

3.4 Muir Wood - Curtis method * *

3.5 Empirical or semi-empirical * *model

3.6 Temporary supports * *

3.7 Modulus of subgrade * *reaction

Esc=-

R

3.8 Modulus of subgrade reac- *tion

E/K=

s

R (1 + v)

3.9 Modulus of subgrade reac- * *tion by plate bearing test

3.10 Modulus of subgrade reac- *tion by back-calculationfrom deformation

8-.Holland RailconsultVIIkafdelinsCivieleTcclmiekProduk1groep Tunnels



3.11 Modulus of subgrade reac- *tion based on previous moni-toring of lining in similarcircumstances

3.12 Theory of second order, buc- *kling

3.13 Bond condition - friction *

3.14 Bond condition - completely * *fixed

3.15 Stiffness of the constructive * * * *members as full stiffness

3.16 Stiffness of the constructive *members as a long termstiffness

3.17 Stiffness of the constructive * * *members as effective stiff-ness related to full liningadjusted by joint effects

3.18 *Stiffness proportional

EJ-R3

3.19 Total stiffness: *

'tot = 'lining(4)2 + 'jOintn

3.20 Uniform stiffness for bolted *metal segmental lining withstaggered joint

3.21 Large deformations

3.22 Nonlinear behaviour of * * *structural elements

3.23 Nonlinear behaviour of * *ground

3.24 Plasticity

3.25 Rheology

------.-Holland RallconsultVakafdeliDgCivie1eToc.bnickProduk1groep1'tmDebl



3.26 Criteria for the calcula-tions for determining thesupporting members

3.26.1 Moment and forces * * * * * * * *

3.26.2 Deformations * * * * *

3.26.3 Buckling stability *

3.26.4 Collapse mode * *

3.27 Stresses * * *

3.28 Three-dimensional effects in * *calculations

H;;lland RaI~SUItVabfdt1inB Civide TedmiekProduktgroep Tunnels



4. Safety concept

4.1 Criteria for deciding whe-ther the constructive mem-bers are sufficiently strong

4.1.1 Allowable stresses * * * * * * * *

4.1.2 Allowable strains *

4.1.3 Ultimate moments and nor- *mal forces

4.1.4 Maximum shear

4.1.5 Limited deformations * * * * *

4.1.6 Ultimate stresses *

4.1.7 Finite element test *

4.1.8 Observation *

4.1.9 Crack control *

4.2 Safety factors

4.2.1 One global factor * *

4.2.2 Global factor for lining *materials

4.2.3 Global factor for working *stress methods

4.2.4 Partial factors for ultimate *design methods

4.2.5 Partial factors for soil *

4.2.6 Partial factors for outer * * *action and inner strength

4.2.7 Partial factors in allowable *stresses

4.2.8 Partial factors on strength of *lining

4.2.9 Partial factors *

4.2.10 Different safety margins for * * * *different states

-------Holland RaIlconsultV8bfde1ing Civicle TecbDiek

-""""'"



5. Distance between the tun-nels

5.1 0,5 D between the tunnels

5.2 1 D between the tunnels * *

5.3 2 D between the tunnels *

5.4 1,5 D between the axes *

5.5 2 D between the axes * *

5.6 2,5 D between the axes *

5.7 3 D between the axes *

------.-Holland RallconsultVabfdeling Civiele TecbaiekProduktgrocp Tunnels


.--------Holland RailconsultVakafdcling Civiek Tecbniek

ProdukIgroop""""'"

3.2. Methods based on subgrade reactions

Authors who contributed to the development of the plain-strain models (fig.9) are listed belowbut a more comprehensive review is given by Dr.ing. J. Erdmann [35].

VoellmyEngelbrethMorganSchulze- DuddeckWindelsWindelsPeckMuir WoodCurtisEinstein-SchwartzAhrensYamaguchiDuddeck

- soil-lining interaction ( crt= 0 ), 1937- close from continuum, 1957- elliptical incomplete mode, 1961- partially bedded beam, full solution, 1964- second order theory, partially bedded beam, 1966- complete continuum solution, 1967- like Windels, ( crt= 0 ), 1969- like Windels with var. crt effects, 1975- completing Muir Wood solution, 1976- simplified continuum solution, 1979- investigation comparing different models- partially bedded double ring, 1985- guidelines for design of tunnels, 1988

A design approach will be presented in this work, in short crucial points, written by some of theauthors mentioned above.

3.2.1. Continuum models

Explicit formula of the continuum model is given by Dr. ing. J. Erdman [35]. The modelassumes full elasticity with expression through deformations and stresses in relation to thestiffness of lining and ground. For EA = 00,the relation between radial and tangential displace-ment for the bending terms of the primary stress approach: max ~ = 2 max v2.

°v - Y H U

11111I11111111111 0 - Ko°

N M0 rNomaxN maxM

11111111 i 111I1111y . volume weight ~~cement :;n:n.u:.

Dorma]forces

beodingmoment

fig.9


------Holland RailconsultVabfdclingCivieleTectudek!'roduhgroop

"""""

Ahrens, Lindner and Lux were given a following equation in which can be evaluated bothcontinuum model and bedded beam model:

[

or

]

1-2v Es[

5-6v -4+6V

][

U2

]° t

=(1 - V ) ( 3 - 4 V ) R -4 + 6 V 5 -6 V V2

E = 1-v Es (1 - 2v ) ( 1 + v)C

Some more approaches will be given in further text with the short, essential characteristics ofeach theory.

3.2.1.1. Morgan [63]

This method of analysis has been applied by many authors for tunnels in soft ground conditionand weak rocks. The technique involves the loading of the lining due to the passive grounddeformation and active radial loading.

A total bending moment is:

Po '02 E/, (1 + V c)

= - M crownMaxis =6E/, (1+ vc) + 2'02Ec

Similarly, equations for the normal force (hoop force) are:

Po'0 4).,0 '0Ncrown = (3) + ( ,.. ) + (Pw'o)

2 Po'0 2 ).,0 '0Ncrown = (-s) + ( ,.. ) + (Pw'o)

3Ec)., =

'0(1 + Vc)

where:

Po = Pv - PhPv - Initial vertical stress at tunnel axisPw - Pressure due to waterEc - Young's modulus of the groundEl - Young's modulus of the liningII - Moment of inertia of the liningDc - Poisson's ratio of the groundro - radius of tunnel to lining extradosA - coefficient of ground reaction8 - lining deflection


--------Holland RallconsultVabfdeliq: Civie1e Tec.baiek

""""""-"""'"

The term Pw has been added by Craig and Muir Wood and consequently is not included in theoriginal analysis of Morgan.

Morgan also presents equations for assessing the effects of consolidation and swelling of clay onthe ultimate condition of lining.

Morgan's equation for the bending moment of several Young moduli of elasticity of the groundis shown on fig. IO.

M kNm

400

E c kN/m2

... 300;! .E!0~ 200101) .

.S!"CI;! 100=

0

0 Iff'

fig.! 0

The graph done by Lyons and Reed (Morgan's equation) illustrates the role of the groundparameters and their influence with the line behaviour. According to the Morgan theory, thetransfer of bending moments at joints in terms of damage to the flanges has to be carefullyconsidered for soft ground conditions.

3.2.1.2. Muir Wood [64]

The assumptions in Morgan's theory that plane strain leads to plane stresses were corrected bythe work of Muir Wood. Another equation for coefficient of ground reaction was produced:

3EcA. =

(1 + vc) (5 - 6 vc) '0

When compared to Morgan's definition for A, for values of Dc= 0,5 and 0,35, A increases byfactor 3 and 2 resp.

The difference also appears in the application of shear resistance between the ground - lininginterface. The analysis is also based on several years of observation in practice which havehighlighted the need for further development of the original Morgan's theory.


-------Holland RaIlconsultVabfdding Civiele TochnictProduktgroepTuao.eI8

The radial closures around the tunnel:

Uo = Vo cos26

where is U 0 maximum radial closureThe bending moment is given by:

1P. 2 2 FR

MMaxis = - 0"'0 = - crown6 1 + FR

Flexibility ratio (FR):

FR = 9E/'/

A,,3 ,~

The effects of shear forces between the ground and the lining is analyzed, since the neglect ofsuch forces will lead to a conservative solution. The result of this consideration is to give a newexpression for A:

3(P + 51) EcA =

C

c = '0(1 + V c) [( 5 - 6 vc) P + 2 (13 - 15 vc) T]

with:

T - The shear stress at the tunnel axisP - Maximum value of:!: ( P - p' ) where p is the radial ground loading at any point around

the tunnel periphery

The radial and tangential stresses around the excavation which are transmitted to the lining are:

q ( '02 In,o - ,2 In,)a =,

2 k( 1 - v c)

q ( 1 - ,; In,o+ ,2 In' + ,2 )a =e D

D = 2 k( 1 - v c) ,2


8-Holland RallconsultVlkafdelingCivie1eTechniek

-"""""

where are:k - Permeability of the groundq - Discharge of water per unit area of ground in unit timer - General radius

If the permeability of the lining is less than that of the ground than the lining needs to resist thefull hydrostatic pressures.

The lining stiffness is suggested with an effective value of II:

I,,,,, = Ij + ( 4)2 .nI, < 1" n > 4""

in which are:

Ij - Effective value of I at the jointn - number of joints

Actually the full values of stresses Pv and Ph are used in conservative approach:

p = Pv - 0,5 Po (1 - cos2e)

Muir Wood suggested the other stress relaxation:

p = 0,5 [ Pv - 0,5 Po (1 - cos 2e) ]

Other authors suggested even 0,3 instead of 0,5.The hoop loads and stresses can be calculated as given by Morgan.

3.2.1.3. Curtis [65]

Curtis extended the method of Muir Wood and developed equations for M and N around thetunnel lining for the conditions of no shear between the ground and the lining.

For "no shear" conditions:

2Po'o (3 - 4vc) cos2e

M=-2 5 - 6 vc + 4 O2

M = - Po'o2

(3 - 4v c) cos2e

5-6vc+402

3E 1 '0c -O2 = E, 1 + vc 12/,


-----.-Holland RallconsultVabfdeliog Civielc TeclmiekProdubgrocp 1'u!IM1s

Under condition of shear:

Po'0Mmax= :t

O2 (3 - 2 v c) ]4 [ 1 +3 - 4v c

Po'0Nmax= :t

2 v c O2 ]2 [ 1 +(3 - 4v c) (1 + O2)

Lyons has commented on the use of Curtis' equations which take into account the ground liningshear forces and has remarked that they are currently accepted as being the most realisticequations for use in ring design.

It should be noted that there is no absolute solution to the design problem but Curtis' solutionprobably represents the best available method.

The Muir Wood and Curtis equations have found use worldwide as reported by Lyons and theyare presently used by tunnel designers and lining manufacturers (1974).

3.2.1.4. Peck - semi-empirical approach [66]

A semi empirical method of tunnel design is based on data taken from previous projects. Thecalculation is given through four steps:

1. The provision for absorbing adequate hoop stresses

2. Adequate flexibility to control the likely induced bending moments resulting from liningdeflections.

3. Prevention of buckling lining failure

4. Provision against additional external loads induced in the lining

The lining hoop stress equation assumes that no radial deformation occurs:

N=YZo'o(1 +~)

2= Pav '0

where P -Pv + P

av--h2

is the axis depth.

In fact, the radial deflection of lining takes place and hoop stress reduces.

Peck has presented a large amount of measured data for bending moments in variety of differentlinings. The problem of buckling is solved by providing adequate grouting procedures during theconstruction. Peck considered that no lining failures have been reported as a result of buckling,arising from earth pressure when the grouting perfectly provided a complete contact betweenground and lining.


8-Holland RallconsultVabfdeling Civiele Tcclmidc

-"""""

Peck also showed in his work that the ring loads can increase up to the full overburden pressureas a result of interaction with a subsequently driven tunnel.

With respect to additional bending moments resulting from interaction, a lining of increasedflexibility is suggested with the erection of rigid secondary supports being delayed. The increasedflexibility will also allow the accommodation of asymmetrical deflections to occur commonlydue to interaction.

3.2.2. Bedded beam models

3.2.2.1. Schultz- Duddeck [67]

Ifthe ground round the tunnel is replaced by bedding springs, (see fig. 11), a tunnel lining can beanalyzed in accordance to the theory of the beam on elastic foundation. The radial beddingmodulus is taken as:

K -Es

, --R

The relationship with the continuum model for the cos 2<pis given by the following transitions:

1. For full bonding K = 0 6Es, ,-R

2. For tangential slip K = 0 5Es

, ,-R

The following diagrams assumes Poisson's ratio \) = 0,3 and the value for the coefficient oflateral pressure is 0,5. Those values are characteristic for sand and hard clays. As it wasmentioned in chapter 2.1.1 we must carefully consider what exactly occurs in weak ground withthe Poisson's ratio between 0,4 to 0,5 and Ko between 0,6 to 0,9.

As a matter of fact in the model of Schultz!Duddeck the distribution of the primary stressesaround the lining depends on the ratio H/R, cover depth. Therefore hoop forces vary with thedepth ratio. In practice the bedded beam model and the continuum model vary between -4% and11%.

The bending moments for the bedded beam model in comparison with the continuum solution arepresented by H.Duddeck and J.Erdmann [39] (fig.11, fig.12 and fig.l3).

Ov= Y H U °B=KrU N M

~°h= K~Ov

[LLLLld- Ov

mm1K~OO$Mu

radial ground reactiondisplacement pressure

normalforces

bendingmoment

fig. 11


....--------Holland RallconsultVabfde1ing Civicle TcclmieJcProduktgrocIpTunnels

In the case of full bonding, the partially bedded beam (without springs at the crown) gives largermoments up to 16% from the continuum model and also when ex= 10. The linings with smallerbedding stiffness EI and larger ex, the moments ITom the continuum model are larger because thetension bedding of the continuum model influences the result.

Bedded beam modelSchulze I Duddeck

continuum model

m maxM=mR2u v

HjR- ..

0.12

0.10HjR-8 Beam Continuum full bond

0.08HjR-4

BeR3Ct--

El

200

fig. 12

Neglecting the tangential component of the ground pressure, the beam model deforms only withregard to different radial pressures at the crown and at the shoulders, whereas in the continuummodel (Pt=O), the lining is forced into that deflection into which the continuum contour deformsby including the tangential stress component.

For the assumption of the tangential slip, the deformations of the model do not comply with eachother. The moments of the bedded beam are smaller than in the case of full bonding. Exactly forH/R = 4 ; ex = 10 ; m = 0,25 ; it is about 50% less than for Pt 7=0

0.14 m M- 2

'max - m R Uv

---""""""""""""""""

continuummodel----'....

" -',",

HjR-

..

Bedded beam modelSchulze I Duddeck

Beam Continuum full bond

0.08

HjR-80.06

0.04HjR-4

Be;(t--

El

fig. 13

The bedded beam model coincides with the Muir-Wood solution, only considering radial groundpressures. For smaller bending stiffness of the lining or stiffer ground, the relative differencesbetween the moments of the other theories are large. Nevertheless, we must take into accountthat slip may be affected by grouting, ground water, temperature shrinkage etc. Moments are ofsecondary significance compared to hoop forces (normal forces) if the lining is capable ofdeveloping plastic hinges.


8--Holland RaIlconsultV.bfdeling Civie1e TcdmicJr.- TuuDoJo

3.2.2.2. Wayss & Freytag [15]

The structural analysis of the Wayss & Freytag model assumes a system of straight beammembers which are forming one lining segment. The joints can be designed either as a total fulljoint or with the possibility of certain bending stiffness. The supports of the rings are presumedto be resilient members in radial direction (see fig.14).

X !

y

n=5

fig.14

As the tunnel rings are connected longitudinally by bolts the design approach is based on twotunnel rings connected by scattered joints in a three-dimensional space.

The loading of the tunnel is given by earth and water pressures. In the standards for calculatingthe lining for shield driven tunnels the pressure of the undisturbed ground around the tunnel isapplied. The vertical earth pressure is not reduced and the water pressure is taken as full pressurewhich mainly results in favourable axial forces.

Pv = yH

mmmn

ffimmmn

H

~I

J!

- --1>-

I

-_\

Ph =(H+R)y~

fig. 15

Comparing different structural systems in analysis and design of tunnel lining, this model hasshown the adequate solution for practical problems. The computed deflection was about 10 to 20mm. which corresponds with the measurements on site (see fig.16). It was concluded that thestiffness of the system is directly dependent on the thickness of the lining and the number ofsegments in the ring. By raising the number of segments from 6 to 8 per ring, the bendingmoment will be reduced by more than 50% for a single ring. On the other hand the deflectionwill rise by 50%.


H~and RallOODsultVabfdding Civic.le Tcclmielr.Produktgroep Tunnels

maxM[kNm] 200

maxW[mm]

150 60

100 I 40

50 20

0 4

I

D1IDlber

ot segm.

5 6 9 1087

fig.16

The described system has been used by Wayss & Freytag for solving problems in 15 km oftunnel in ground-water. The main opinion about this system is security and proof in practice for aspecific case.

3.2.2.3. Yamaguchi

In Japan shield driven tunnelling has been well developed in the last 10 years, especially in verysoft and water-bearing ground. For instance, for a very soft cohesive soil, horizontal soilreactions are close to 0 and the coefficient of lateral pressure enriches the values of 0,65 to 0,75.It was necessary to strengthen the joints to avoid large deformations of rings. However, it is notpossible to have the same rigidity of joints and segments, so the calculations of the continuumring gives an underestimated bending moment of the ring.

Kubo & Yuki (1968), Yamamoto (1976) and Murakami & Koizumi (1978) proposed structuralmodels of segmental lining joints with flexural springs. Those models didn't take into account therelative displacement between the rings. Yamaguchi [71] (1978), proposed a new model whichwas later developed by Hanaya (1985) by adding a secondary inner lining. This model couldestimate member forces and also shear forces between the linings.(see fig.17)

Yamaguchi's model Hanaya's model

fig. 17


~.--Holland RallconsultVabfde.liog Civiele Tec.hnick

-"""""

The loading conditions are related to specific cases and sort of soil. The basic parameters,important for the structural analysis, are vertical and horizontal earth pressure, soil reaction,modulus of rigidity. For instance Japan Tunnel Association gives the following disposition forloadings. (see fig.I8)

Po

h '/"""""'-'-'-'-'-'-'-""'"

//B \,JI

;

\/

PvI!\

!

L ! ! I PHI!' I!!.

H H

~.

fig.I8

Hereby for cohesive soil are:

Pv1 = Po + y H

PHt = Pv1 + Ka .PH2 = Ka ( Pv1 + y2R)

and for sandy water-branded soil:

Pv1 = Po + y ( H Hw) + yl Hw + Pw1

PH1 = Ka [ Po + y ( H - Hw) + yl Hw] + Pw1

PH2 = Ka [ Po + y ( H - Hw) + yl ( Hw + 2 R )] + Pw2

where PH3 is passive earth pressure.

Additional loads that should be considered in structural analysis of the tunnel lining are:

1. The reaction of the shield trust2. Backfill grouting pressure3. Soil pressure just after the shield tail is pulled off4. Lateral forces generated by a second tunnel driving5. In earthquake regions, it is also necessary to access the possible effects of seismicity.

The complete review is given in chapter 3.1. of this work.


Type of soil Coefficient of Soil reaction N (SPT)horizontal earth [N/m3]

pressure

Well-solidified sandy soil N>30

Solidified cohesive soil0,35-0,45 30-50

N>25

compacted sandy soil 15<N<30

Hard cohesive soil10-30

0,45-0,55 8<N<25

Medium cohesive soil 5-10 4<N<8

Loose sandy soil 0,50-0,60 0-10 N<15

Soft cohesive soil 0,55-0,65 0-5 2<N<4

Very soft cohesive soil 0,65-0,75 0 N<2

---------Holland RailconsultVaImfdeliDgCivie1eTcc:bnie.k

"""""""'''''''''''

Coefficients of horizontal earth pressure and soil reaction after Japan Society of Civil Engineers

3.2.3. Nonlinear effects

Certain considerations about nonlinearities in structural analysis and design of tunnels are givenby H. Duddeck and J. Erdmann in "On structural design models for tunnels in soft soil", Tunnels& Deep Space, Underground Space, (1985). The range of nonlinear effects is quite wide so onlyfew of them, which are the most important for analysis, will be considered.

3.2.3.1. Non-linear ground behaviour

When the lining is stiff in comparison with the ground the effects of the nonlinear groundproperties have minor influence on the stresses in lining. This was proved by many calculationswith finite element method. Of course, this statement is not valid for tunnels in rock, because theground itself absorbs the stress redistribution caused by tunnelling.

Therefore, in situations involving soft ground tunnelling it is sufficient to design the lining,assuming some average values for the ground stiffness parameters. It will be sufficient when theE modulus is chosen which represents the reloading stress-strain behaviour. This should bewithin the stress level of the actual ground stresses at the lateral part of the tunnel, including thebedding reaction stresses.

3.2.3.2. Plasticity

In the ultimate state design, the load capacity is exhausted when the structure fails by a collapsemode. With the nonlinear analysis the ultimate load may be reached by increasing the groundpressure as well as by decreasing the strength parameters. This means that in the first approxima-tion it is possible to assume split safety factors.

The authors (Duddeck & Erdmann) were analyzing a tunnel concrete lining of 20 em. inthickness and a 2,65 m radius with plastic material behaviour. The conclusion was obvious forthe almost unchangeable state of normal forces, but the moments are decreasing considerably.(seefig. 19).


------Holland RailconsultVabfdeling Civiele TeclmicJc

"'"""""'"

1'uonok

120%

100%

GeO:1TI..non1in.ear :!'vI

theorie II ord. :!'vII1near .rovI.

:!'vI. N. U

150%

theorie II ord. Ngeo:1TI..non..1in.ear N

lin.ear N

-' ~ --.-..... <p

0180

lin.ear lJtl:1eor1e 11 or~.

geo:1TI..non1in.ear lJ

fig.19

If the stress-strain curve of the lining is nonlinear for cast iron then the concept of allowablestresses is an unsuitable design criterion. The stresses calculated by Bernoulli's hypothesis maybe far from reality. It can be shown that deviations of 30% of the maximum stresses are easilyevaluated by considering nonlinear stress-strain curves.(see fig.20)

M,Ngeom.nonlinear M

67 %""-'- '...,

",

""

"",

";."\...

linear M

physic.nonlinear

0180 <p

fig.20

Fig.20 shows an example of ductile material with an employed plastic analysis. As loads increasethe plastic hinges move crownwards but also regain elastic behaviour. The example includes alsogeometrical nonlinearity.

3.2.3.3. Buckling

In 1966 Windels presented a bedded beam model with design charts, including the geometricallynonlinear effects. The hoop forces did not change significantly with bending deformations. Aslong as the deformation mode does include the buckling mode of least energy, the second ordertheory also covers the instability problem.

For tunnels with a diameter up to 6,0 m., especially if the lining is thicker, the elastic nonlineareffects are negligible. For a larger diameter and steel or cast-iron linings the nonlinear effects caneasily be analyzed. As an example, the results of the slender lining of the Elbe tunnel inHamburg are shown on fig.21.


Hcilland RalkODsultVabfdc1ing Civiele Teclmick.

"""""'-"""'"


8-Holland RallconsultVabfdeling Civiele Tec.hmek

-"""'""

2max v=2,32 4 5

6,............................................

2

maxv plastic hinges

plastic zones

~~

5 10 15Wf

fig.21

If only the bending deformations are considered, the maximum moment amounts to 120%. Thedeflections at the crown correspond to these values, whereas the ring forces N are insensitive todeformation effects.

3.2.3.4. Creep

Singh and Mitchell (1969) proposed a model related with creep strain to elapsed time and stress:

Eaeop = Ae"D (t; r

where:A - Strain rate at time t1a - Slope of linear portion of plot of lOgEversus 10gD at constant timeD - Normalised stress level, deviator stress divided by stress at failuret - Timem - Negative slope of plot of log-E versus log-t

Current tunnelling literature and observation of tunnelling design practice, indicate that creepbehaviour is not generally regarded as a standard consideration for soft ground tunnel design forinstance in the United Kingdom. Researches into various aspects of creep behaviour is well docu-mented in tunnelling literature by Murayama, Ladanyi and Mayer. It would seem then that theimportance of long term creep behaviour with respect to soft ground tunnelling has beenrecognized but not adopted as a standard design practice.

3.2.3.5. Lining with hinges

Lining can be erected with permanent hinges with either full or restrained rotation capacity. Theexample with 6 hinges shows that moments of a lining are considerably reduced and hoop forceswill not change (see fig.22).


-------Holland RallconsultVabfdcJ.jq: CiYie1e Techniek

"""""

~ technical region

0,1

a. no hinges

b. 6 hinges

4L (...~ ~13= ~~

I8

360

%

fig.22

The investigation of hinged linings shows clearly that the bending moments are the secondpriority for design. The close lining provides an equilibrium by the hoop forces alone. The safetymargins can be smaller for bending moments than for normal forces. However, the bendingmoments could be decisive quantities when water-tightness is important.


H&land RalkODsultVabfdeJioa; CMde Te:clmi.ekProduktgroep Tunnell

3.3. Relative stiffness solution

3.3.1. Einstein - Schwartz [12]

The original relative stiffness solution is given by Bums and Richard for buried culverts underone dimensional blast overloads. The principle characteristic of this method is the considerationthat a tunnel support under the influence of the ground stresses will contract and change theshape, so these support deformations will in turn affect the behaviour of the ground. The uniformcontraction and change in shape of the support depend on the relative stiffness of the support andthe ground.

Characteristic curves (Rabcewicz, Peck, Lombardi) show the effects of different ground andsupport stiffness on the behaviour of the tunnel support. (see fig.23)

C Support

~Equilibrium

Ground

Ground

ps

"~

r1{I~PSupport

k Ground stiffnessg

k S,pport stiffnesss

u0 us

fig.23

The method of relative stiffness considers the ground as infinite, elastic, homogenous isotropicmaterial with initial vertical stress P and horizontal stress KP. The tunnel support is treated as anelastic thick walled shell in which both flexural and circumferential deformations are presented.

The relative stiffness of the ground of the tunnel support is incorporated into the solution bycompressibility ratio C* and flexibility ratio F*.

2

C* =ER ( 1 - Vs )

EsAs ( 1 - v2 )

F* =ERa (1 - v; )

Es's (1 - v2 )


--------Holland RailconsultVakafdelinJ Civic1c Tedmiek

"""""""''''''''''''

in which:

EU

Es

- Young's modulus of elasticity of the ground- Poisson's ratio for the ground- Young's modulus of elasticity of the support- Poisson's ratio for the support- The average cross-sectional area of the support per unit length of tunnel- The moment of inertia of the tunnel support per unit length of tunnel- The tunnel radius

Us

As

IsR

The derivation of the revised relative stiffness solution follows three basic steps:

1. Derivation of the initial displacement field in the ground mass due to in-situ stresses:

The stresses existing in the ground before tunnelling:

pa, = - [(1 + K) - (1 - K)cos2e ]

2

pa a = - [( 1 + K) + (1 - K) cos 2 e ]

2

p",a = - (1 - K)cos2e2

The stress-strain displacement relations:

e = au =~[(1 -v2)a,-v(1 +v)ao],ar E

e = au + av =~[(1 -v2)aa-v(1 +v)a,],ar rae E

From those equations expressions for the initial ground displacement (u, v) are obtained.

2. Derivation of stress and incremental displacement fields in the ground after excavation andcontact stresses at ground-support interface.

The stresses in the ground mass can be expressed through Michell's stress function ~.:

1 a<j> 1 a2<j>a =--+--,

r ar r2 ae2

-a2<j> .

- a 1 a<j>aa -a r2 ' "',a - -

a r( r as)


a. Full slip: a, = aR; ",a=O; U = Us

b. No slip: a, = aR; ",a = "Ra; U = us; V = Vs

---------.Holland RallconsultVabfcWing CiYide TcdmiekProduktgroep Tunnels

The boundary conditions at the ground-support interface must be introduced for full slip and noslip:

Combining those equations under boundary conditions for full slip and no slip, authors presentedequations for stresses and displacement.

3. Computation of the internal support forces induced by contact stresses at ground-supportinterface:

For full slip case:

L = .1 ( 1 + K) ( 1 - 80* ) + .1 (1 + K) (1 - 2 a2* ) cos 2 ePR 2 2

M 1PR2

=2

(1 -K) (1 - 2~* ) cos2e

For no slip case:

T =.1 ( 1 + K) ( 1 - 80* ) + .1 ( 1 - K) ( 1 + 2a2* ) cos2ePR 2 2

~ = .1 (1 -K) (1 - 2~* + 2b2* ) cos2ePR2 4

The authors varied the parameters in order to investigate the effects of ground and supportcharacteristics. As a result they produced a few very useful graphics which can be of use in thecalculations. It was found that for very low support stiffness the tunnel is actually unsupportedand the net displacement is inward. As the relative support stiffness increases the support beginsto resist the inward ground movement. "Ovalling" of the support will also occur when K;t:I insupport form as ellipse when the net displacement is outward. Further support stiffness increaseare accompanied by increase of the bending stiffness. Finally, for an ideal rigid support nodisplacements and maximum thrust and moment occur.

The effects of the relative stiffness variations proved the statements made by Peck and theintuitive predictions in extreme cases.

The relative stiffness solution shows clearly how the design parameters for tunnel supportschange with variations of the ground and support characteristics and indicate the ranges overwhich these characteristics have an important effect on the design.

For more detailed calculations by the relative stiffness solution method, it is necessary to applycorrection factors for effects which are not considered by basic solutions.


--------Holland RailconsultVabftiing CiYicle Tecbaid::

"""""""'........

3.3.2. Pender [52]

The displacement of the tunnel lining and surroundings depends on the predictions of boundaryconditions. The geotechnical literature does not make clear when and where these variousboundary conditions are applied. An elastic solution for a deep circular tunnel is presented byM. J. Pender (1980), Technical Notes, Civil Engineering department, University of Auckland.

In text books the theory of elasticity is usually presented as applicable to an unstressed medium.In reality the tunnel is excavated in an already prestressed medium so thedisplacements are due to the release of the in situ stresses around the tunnel periphery.

The horizontal total stress is given by:

°h = Nov

The coefficient of earth pressure gives:

I I°h = Koov

For a soil deposit with a water table at the surface and bulk density p:

N = Ko -P W ( Ko - 1 )P

The in situ stresses in polar c.s. which are acting on a circular boundary:

1 1or = - (a v + a h) - - (a v - a h) cos 2 6

2 2

1 1°e = - (ov + °h) + - (ov - °h) cos262 2

11:r,e = 2

(a v - a h) sin 2 6

The elastic problem is solved by means of the following Airy stress function ( Timoshenco andGoodier, 1970 ):

<I> = Alogr + Br2 + [ Cr2 + Dr4 + E,-2 + F] cos28

The stresses are then obtained from:

a = 1 a<l>+ 1.- &<1>

= ~ + 28 + [ -2C - 6E,-4 - 4E,-2 ]cos26r r ar r2 a62 r2


-------Holland RallcoDsultVabfdeling Civicle Tec.hniekProduk1grocp Tunnels

a'"

&<1>'"

~ + 28 + [ 2C + 120,2 + 6E,-4 ]cos28e a,2 ,2

'"~ a<l> - 1 &<1>

'"[ 2C + 6D,2 - 6E,-4 - 2F,-2 ]sin28't"e ,2 ae , a,ae

When plane-strain is assumed, then the stress in the longitudinal direction is:

az '" v ( a, + ae )

The elastic stress-strain relation are then:

EE, '"( 1 + v ) [ (1 - v ) a, - vae ]

EEe '"( 1 + v ) [ ( 1 - v ) ae - va, ]

Radial and circumferential strain are defined as:

au .-- ,E, - a,

u 1 avE "'-+--e , , ae

The detailed analysis of the stresses applied at a distant boundary is given by Obert and Duvall(1967) and Jaeger and Cook (1962) and the solution is presented by Poulos and Davis (1974). Ingeneral the problem was to analyze the stresses and displacement distribution in a plate with ahole. The stresses in an infinite plate are:

1(

a2

)

1(

3a4 4a2

)a, '" 2"

(a v + a h) 1 - ---;2 -2"

(a v - a h) 1 + ---;4 - -;2 cos2e

1(

a2

)

1(

3a4 4a2

)ae"'-(av+ah) 1 +- +-(av-ah) 1 +-+- cos2e

2 ,2 2 ,4,2

- 1(

3a4 2a2

)

.'t ',e -

2(a v - a h) 1 - - + - Sin 2 e,4 ,2

The crucial point is that those formulas are valid when the stresses in the ground are changedafter the tunnel excavation.

When the tunnel is bored, the radial and shear stresses relieved at the tunnel periphery and thisincremental change in stress fades out at some distance from the tunnel. Thus constants A to Fare found from the following:

11a, '" 11a e '" 11 't r,e '" 0 as '-+00


....-------Holland RailconsultVabfdcliq Civiele Teclmiek

I'rodu>!groop"""'"

At r = a follows:

1 1/!,.a, = - - (a y + a h) + - (a y - a h) cos 2 e

2 2

/!,. . ',e = -~

(a y - a h) sin2e

The solution for the incremental stresses are:

1

(

a2

)1

(

3a4 4a2

)/!"a,=--(ay+ah) - --(ay-ah) --- cos2e

2 ,2 2 ,4,2

1(

a2

)

1(

3a4

)ae=-(ay+ah) - +-(ay-ah) - cos2e

2 ,2 2 ,4

1(

3a4 2a2

)

./!,.."e = -- (ay - ah) - - - sm2e

2 ,4,2

The result obtained is the same for both boundary conditions, when the equations are solved withan adequate substitution.

The interaction between a tunnel lining and the ground has also been analyzed. Under the actionof a symmetric external pressure the lining ring will deform in axil compression without bendingand under the asymmetric pressure in bending. To perform this interaction analysis the deforma-tion of the ground has to be related to the radial pressure applied to the periphery of the tunnel.The radial loading is given by:

( a,) a = 50 + 51 cos 2 e

Here it is assumed that (tre)a=O, but as shown by Muir Wood (1975) and Curtis (1976) thepresence of shear stress at the tunnel periphery can be incorporated easily. As r - 00 andO"r=O"e='tre=O, the stresses are:

a, = 5,( ~ r - 5,

[( ~r - 2( ~r ]

00528

a e = - 50 ( ~ r + 51( ~ r cos 2 e


~.--Holland RallconsultVabfdeliDg Civie1e Tcclmiek

~ ,.

-", = -8, [( ~r - (~r] sin2e

The minus sign for So reflects the sign convention adopted herein. It also indicates that outwardradial displacements are negative.

Concluded was that displacement depends considerably on boundaries. The author also concludedthat in the lining-ground interaction is relevant to predict no shear stresses at the interface, so itcan be extended to include the presence of shear at the interface.


--------Holland RaIlconsultVabfdeling Civiek TechaictProduk1groep Tunnels

3.4. Convergence - confinement method

With an excavation of a tunnel in prestressed soil the stresses undergo some changes resulting indisplacement of the soil mass. As a matter of fact, the stresses acting on the tunnel lining will belower than the original stresses. Many engineers and investigators have tried to estimate andcalculate the deformations which occur in the space around the tunnel lining. Among them,Ranken and Ghaboussi [68] (1975), who defined the total radial displacement which occursbefore reaching a ground lining equilibrium.(see fig.24)

°1() Ground response curve

Ground

0 r

Of

0

Support reaction curve

~Or

- (ffi -Support

~/

Ur

{f Uu Ug UII 1 1

fig.24

Vf

Vu- Radial displacement occurring ahead of the face of the tunnel- Radial displacement occurring between the face and the point of installation

of the liner (deformation along unsupported length)- Radial displacement occurring at the point of activation before the gap is filled

Radial displacement of the tunnel liner under loadVg

VI

Eisenstein and Negro [69] (1985), presented a method for estimating the radial displacement atthe face of shallow tunnels. This calculation was performed with the Finite Element Analysis andthe expression for the unlined tunnel radial strain is given as:

U =U, Eti

D (J,oIn which are:

DVrEti

- Tunnel diameter- Radial strain- Initial tangent modulus after Duncan and Chang (1970)- Initial radial stress at the specific pointaro

The convergence confinement method is a procedure in which the interaction between groundand lining behaviour is analyzed independently. With this method it is easy to calculate thepressure applied to the support by intersection of two characteristic curves of radial stress as afunction of radial strain.


H~and Raik;msultVabfdeliDg CiYie1e Tedmiek

ProduIagroop""""""

The radial stress - radial deformation curve (see fig.19), characterizes the behaviour of theunlined tunnel due to reduction in the radial stresses which act on the unlined tunnel wall. Thesupport reaction curve is defined by the relationship between the uniform radial pressure which isapplied to lining and corresponding change in diametral displacement. The close form solution ofthis approach is limited by the following restrictions (EI-Nahhas [70], 1980):

1. The use of this approach is limited to only the circular cross-section of the tunnel which isexcavated in homogeneous, isotropic continuous ground;

2. Both, the soil and the lining behave in an axisimetrical mode. It does not take into account thedevelopment of bending moments in the lining and the effects of joints;

3. Use of this method is restricted to deformations in the tunnel surrounding. This means noconsideration of movement near the ground surface.

Eisenstein, Negro and Ahmed (1991) have proposed the coupling of three convergence curvesrepresenting the crown, invert and spring line in order to avoid the limitations of the closedsolution.

The main considerations in their analysis are excavation stage and ground lining interaction. Inthe first phase the ground deformations were associated with the tunnelling operation where thestress level is equal to "zero stress condition". Presuming the soil ground interaction was themost significant factor in the complete analysis.

Deformations which occurred as a result of ground movements due to tunnelling, have beendeterminated by analyzing the unlined tunnel from the stress level equal to the initial "in-situ"stresses. The relationship between the unloading of radial stresses for different points, located onthe boundaries of the excavation surface and the radial movement, was computed in the form ofa ground reaction curve. The final ground movements are expressed by total movements from thedeformation associated with the tunnelling process and the ground movements after lining untilthe equilibrium conditions are reached.

The results of their study show that the hyperbolic stress strain model gives higher soil deforma-tions than the model of hyperbolic nonlinear volume change. The results of the case they haveobserved (calculations and measurements), for a deep tunnel (-27.0 m, clay), show a largertunnelling deformations in the surrounding ground. The reason for this was a higher stress level.Radial displacements occur in all points of the lining and the values of the normal forces aretwice as big as the values measured.


-------Holland RallconsultVabfdeling Civicle TeclmietProduktgroep Ttmnela

3.5. Finite element models

3.5.1. General considerations

Classical linear theory of structures which is based on the assumptions of small displacementsand the elastic material behaviour gives us the following relationships between: deformations-displacement, internal- external forces and stress-strain. Those equations with boundaryconditions are determinated as a complete stress - strain state of structure. If only one equation,from a group of equations mentioned here above, is not linear then it has to be applied in thestructural analysis and design a nonlinear theory.

The basic relationship of a nonlinear theory by Finite Element Method is given as:

E = L U + EN(U). U = u*

L T (J + (JN( u, (J) + F = 0

(J ji A..= p.* ."J I'

j = 1,2,3

(J = D( u, (J) E

Where the vectors are shown as:

E

EN*u,u

LaaNFPi>

D

Deformations

- Nonlinear deformations- Differential continual displacements

Operational matrixStresses

- Nonlinear part of stresses- Volume forces

External forcesConstitution matrix

The solution of those equations is only possible when numerical methods are applied. One of themost effective and used method nowadays is a Finite Element Method.

The Finite Element Method (FEM) analysis has been applied by many authors in solvingtunnelling problems in various ground conditions. Nonlinear, elasto-visco-plastic, anisotropicnonhomogeneous materials for tunnel lining and soil could be well represented by a differentkind of applied finite elements.

For instance, the continuum model or action - reaction model with slip or "no slip" state can beanalyzed in two-dimensional or three-dimensional space. (see fig.25 and fig.26). Both of themare made in order to explain the closest and realistic behaviour of a tunnel. There is a possibilityto make models with all parameters included, but time and capacity of hardware take animportant role in the whole process. Therefore, a model has to be made which will represent anoptimization of the problem under certain circumstances.


--------.Holland RallconsultVUafdelingCivieleTecluJjctProduhpoop

""""'"

Ek=O

Ek- 0

fig.25

This technique can be used to simulate the standard loadings as well as the investigation of theeffects from the adjunct tunnel. Finite element analysis is a primary tool for research designwhich needs thorough knowledge of FEM principles and procedures. Computer programs areclassified into two groups: "older generation" (until 1985) and "new generation" (after 1985).

EF ='"

RPt

,,0 pR = 0t

fig.26

Below a short review of computer software up to now is presented:

1. The first commercial program was STRESS (Structural Engineering System Solver). Theprogram is developed at the Massachusetts Institute of Technology, 1964.

2. The program SAP IV (Structural Analysis Program) was developed in 1973 at the BerkeleyUniversity of San Francisco, California. It was a general FEM program for static and dynamicanalysis of structures. At the same time it was the most applicable program for linear struc-tural analysis and design.

3. The program NONSAP (Static and Dynamic Geometric and Material Nonlinear Analysis) wasdeveloped almost at the same time as SAP IV in 1974.


.---------Holland RallconsultVabfdeling Civie1e Tochniek

-"""".

4. The program ADINA (Automatic Dynamic Incremental Nonlinear Analysis) was developed atADINA Engineering by Prof. Dr. Klaus Jiirgen Bath in 1975. It was one of the programswhich could deal with problems of nonlinear analysis.

5. The program MSC/NASTRAN was developed by MacNeal-Schwendler Corporation, LosAngeles in 1970. With possibilities for static and dynamic linear/nonlinear analysis.

6. The program ANSYS (Engineering Analysis System) developed by Swanson Analysis Systemin Pennsylvania 1970, for general application of FEM in engineering.

7. The other programs where the result of university researches or the products of softwarecompanies as: ABACUS, ASKA, ASAS, MARC, ICS STRUDL, STAAD, PAFEC,PLUTO DIANA, PLAXIS,... etc

The Finite Element Analysis program which is used by "Holland Railconsult (formerly NSEngineering Department) is ANSYS 5.0a. How to apply this program in structural analysis anddesign of tunnels will be explained hereafter.

The application of FEM in structural analysis and design of tunnelling took place in the earlyseventies. The relative solution of the accurate problems had been assumed to be a numericalcheck of analytical approaches. Analyzing tunnel behaviour, separately but at the same time fordifferent projects, many authors came to similar conclusions resulting from structural analysisand tunnel design by applying finite element modelling.

The three-dimensional approach is more detailed and sophisticated but also more expensive thanthe two-dimensional approach. Therefore, few authors have tried to provide for a practical 2-dimensional design of tunnels which gives an equivalent for three dimensional. This problem waspresented by S. Keilbassa and H. Duddeck called "Stress-strain fields at the tunnelling face -Three-dimensional analysis for two-dimensional technical approach (for tunnels in rock, r.a.)", inRock Mechanics and Rock Engineering 24, p/115-132. The visualisation of the problem is givenin the following figure, where only the effective ground pressure is relevant for the design oflining.

>2D

D

>2D

+

P: ~p~

fig.27


.--------Holland RailconsultVabfdcling Civiek TechaickProduktgroep Tunnels

The "One step" plane model assumes the load which is equal to primary ground stresses. Inaccordance with this we obtain for vertical and horizontal loads:

Pv =(Jprim .

v Ph = (J~rim = ko.Pv

For the "Two steps" plane models these loads are split into two parts. Those models arepublished by Baudendistel (1979) and Schikora (1982) and used in practical applications asshown by Haberl and Haugeneder (1984), Bauman (1985) and others.

The main conclusion is that if the ground is stiffer the approach is more relevant.

3.5.2. FEM model after Dr. ing. J. Erdman [35], (1983)

The author presented a model of a tunnel as a cylinder ground space with a radius of 45,0 m.and length of 50,0 m. The diameter of the tunnel ring was 10,0 m. (see fig.28 and fig.29).

X2

D

Xl > 2D

+50m.

*fig.28

X2X2

x

U2U1soil element

c

dxl

Dm2

1X

X2B

A

XlA

1X

lining element

fig.29

Railway Tunnels / Study of literaiure: Struciural analyses and design methods for bored iunnels 62

ELASTICI '"

19,5

I

PLASTIC ~Ko

-- I

0,5 1,0

fig.3 1

HcllandRal~sultVabfdeling Civiele TcdmickI'n><IukIgroop TuonoJo

3.5.3. FEM model after Dr. ing. P. JanBen [24], (1983)

The model is made with certain assumptions such as:- The modulus of subgrade reaction is given by the following:

Es Es Esk, = 0,6- ; k, = 1,0- ; kt = -0,3-

R R R

and the stiffness matrix as: K = kef + KB + KNL , where KB is part of the stiffness matrix from

the subgrade reaction and KNLfrom the second order effect.

Loadings were assumed in the form of:

P, = PrO + p,2cos2<1> Pt = pt2sin 2 <I>

The model is shown in the following figures:

Ei

X2U2

B,,-/ NB U2B

A::J>\! MB q>

MA cP \2

QBB

A Xu

! \0 A loca12-

wZ"- Q IA UA A X U X I

I Uglobal

'Y""'"

I

Ei~

Ei\0

N

fig.30

q> gr.


-------.Holland RallconsultVabfdeliDg Civicle TedmiekProduktgroep 'l\mnels

3.5.4. Short review of some available software

3.5.4.1. PLAXIS

The development of PLAXIS began in early 1987 at the Delft University of Technology. Plaxiswas intended to connect soil engineering and scientific theory through an easy-to-use computa-tional procedure.

The soil or rock is subdivided into 15 nodded triangles which provide a cubic distribution ofstrain and stresses within each element. As a result the calculations could be obtained forcollapse loads and failure mechanisms with stress distribution.

Interface elements:These joint elements with values of interface friction and adhesion can be assigned.

Walls, Plates and Shells:Special line elements are used to model the bending of walls, plates or shells. The behaviour ofthese elements is defined using a flexural rigidity and normal stiffness. Beam elements used incombination with interface elements may be used to make realistic predictions for a large rangeof geotechnical structures.

Anchor elements:A special elastoplastic spring is used with a normal stiffness and a maximum force

Excess pore pressures:PLAXIS is designed to accept the differences between undrained and drained soils.

Mohr-Coulomb model:This nonlinear model is used also for axisymetric problems and it is based on soil parameterswhich are known in most practical situations.

Soil models:PLAXIS offers a variety of models in addition to linear elasticity and the Mohr-Coulomb model.The advanced Mohr-Coulomb model is available in case a stress dependent shear modulus isused within an elastic region. Also the Carn-Clay or cap model is used especially for soft clayswhich are normally consolidated or lightly overconsolidated.

Consolidation analysis:Pore pressure decay with time can be computed using two-dimensional consolidation analysis.

Tunnels:PLAXIS offers a convenient option to generate complete circular tunnels, including beamelements to simulate the lining (with or without joints), and interface elements to model theinteraction with the surrounding soil. A special remeshing program optimizes the finite elementmesh around the tunnel. Fully isoparametric elements are used to model the curved boundarieswithin the mesh. A contraction can be applied in the calculation to simulate the ground losseswhich occur during construction.


-------Holland RallcoDSUltVabfdeling CiYielc Tcclmick

~"""""

Some of the characteristic output plots are given in figures hereafter.

P I CIne Str"

i n

ME'S h IN I t. ~1 ma t e r

TypWdry W~..t T

"n~ R

-

,

n'

"

<JE+D3 0 30

"DE.O:J 0OIl;]

PL.AXIS Tur1nel dr Iver1 Culvert Aar le-Rixtel

Ri jkswaterstaat BouwdienstPc <, f.. ~ S I

0"a I

AARLEi=lIX Step 10V""",

on S 3D

fig.32

Plane 51.r"

1 n

I ; ~ I f ~ t;f *+fnt~; t~~ t t : I ; i

I vepr I nc I pa 1st r esses

1 4 SE+

02 un I t ~

PLAXIS Tunnel dr iven Culvert Aar le-R, xtel

Ri Jkswater';taat BouwdienstPc

", e,"S' on"- IAARLERIX Step 20Ver", on 5 30

fig.33

0 I sp I /lcement S

42

[*10]

Deformed meSh sea I ed up [down)

2 52E-

02 un i t <;

Tunrlel Culvert Aarle-Rlxtel

AARlERIX Step 20 Ri jkswaterstaat Bouwdienst

fig.34


8--Holland RailconsultVabfde!ina: Civic1e TocImickProduktgroep Tuancls

PI ",,,e Str"

I n1

[*10]

Mom",n!";n beam chao' n 2

Ex t'-eme

momen t 2 67E+O 1 un its

PLAXIS Tunnel driven Culvert Aarle-Rixtel

Ri Jkswa.terstaat Bouwdrenstprof

e"SI

on"I

AARLERIX Step 20V r",,on S Jll

fig.35

PI..ne 5tr"

I n1

10 15 [+10]

Effect; ve n,,(malst'"eSSeS In ,nter-fdce cha In 1

Ext remenOrrn'"

I S

'-

ress 7 53E+D 1 un Its

PLAXIS Tunnel dr Iven Cui vert Aar le-Rlxtel

Ri jkswaterstaat BouwdrenstPc 01"55 IOn" I

Var""""

S 30 AARLEI=1IX Step 20

fig.36

PI ",ne 5t r

'"

i n1

12 [*1[] ]

Norma I for ces I n beam cha I n 1

Ex t r erne for ce 2 13E+02 un, ts

PrO,,,""5")"'"

Culvert Aar le-Ri xtelPLAXISV.,. r~. ,

"n "30 Ri jkswaterstaat Bouwdienst

fig.3?


-------Holland RallconsultVabfdcling Civie1e TechnickProduktgn>op-

3.5.4.2. DIANA

DIANA (Displacement method Analyzer) was developed in 1972 at TNO (Dutch organization forapplied scientific research) in Delft. The possibilities of this software for structural analysis are:

I. Every kind of structure can be analyzed. A huge number of line, plate and block elements areavailable.

2. Different types of loadings can be applied (static or dynamic loadings).

3. A large scope of problems related to analysis of concrete, e.g.:

- Failure and postfailure behaviour of reinforced, pre- and post-tensioned concrete structures;- Analysis of temperature development and the collapse of concrete walls due to fire load;- Deformation of sub-soil tunnel segments;- Calculation of reinforcement stresses during design stages;- Time-dependent deformations in bridge engineering;- Lines and planes of influence for railway bridges;

4. Nonlinear analysis as plasticity, creep and shrinkage or temperature influence on materialproperties with their combination:

- Temperature dependence, cracking, plasticity and creep;- Temperature dependence, cracking and visco-elasticity;- Geometrical (Total and Updated Lagrange) and physical nonlinearities;- Continuum and interface nonlinearities;

5. Dynamic analysis:

- Eigenvalue analysis;- Steady state analysis (modal analysis and direct solution technique);- Transient analysis (linear and nonlinear);

6. Structure stability and large deformations in combination with material nonlinearities.

7. Graphic representation of a model and output files.

The basic calculation modules for analysis of concrete are:A. BASIC, EIGENVALUEB. NONLINEAR, DYNAMICSC. FLOW, HEAT CONDUCTION, GROUND WATER FLOWD. STABILITY, EULER

fig.38


--------.Holland RailconsultVabfdeliog Civiele TedmiekProduktgroep Tunnels

Only the basic element types can be mentioned because of the elaborate element library:

1. Stress elements:

1. Truss elements (discrete reinforcement elements),2. Beam elements,3. Plane-stress elements,4. Plain-strain elements,5. Axisymetric elements,6. 3D solid elements,7. Plate and Shell elements,8. Interface elements,9. Spring elements.

2. Flow elements:

1. 2D / 3D elements,2. Boundary elements,3. Cool pipe elements.

To solve the system of equilibrium equations, DIANA provides a direct solution procedure anddifferent types of iterative solution procedures (Conjugate Gradient Method, Generalized MinimalResidual Method). For the control of nonlinear analysis several iteration schemes, self adaptiveloading algorithms and convergence criteria can be used.

- Linear stiffness, constant stiffness, Modified Newton-Raphson, Regular Newton-Raphson,Secant stiffness (BFGS, Broyden, Crisfield),

- Arc length control (linearized and quadratic), load control, displacement control,- Automatic load control (constant energy increments, number of iterations),- Automatic loading / unloading,- Continuation method,- Eigenvalue checks,- Non-symmetric solver for non-associated plasticity,- Convergence criteria: force, displacement, energy,- Stop criteria: total load, incremental load, sign change of load vector.

The stress situation of the structure can be important as a starting condition for a nonlinearcalculation. These stresses can be introduced into the model as:

- Initial (pre)stresses as input,- Initial stress as a result of linear analysis.

In general the program is perfectly designed for scientific research with linear or nonlinearanalysis of structures or spaces under different kind of loads.


--------Holland RallconsultVabfdding CiYide TeclmiekProduktpoep TuaDeIs

3.5.4.3. ANSYS

ANSYS (Engineering Analysis System) developed by Swanson Analysis System, Pennsylvania,1970, for general application of FEM in engineering has the following capabilities:

1. Every kind of structure can be analyzed. A huge number of line, plate and block elements areavailable.

2. Different types of loadings can be applied. (static or dynamic loadings and temperature).

3. The possibility to simulate composite materials: combined material properties of concrete andsteel, prestressed cables, nets, crack control, etc.

4. Nonlinear analysis such as: geometric, material, slider, frictional and other nonlinearities.

The scope of only material nonlinearities gives the following features in analyzing:

- Rate - independent plasticity is characterized by irreversible instantaneous straining whichoccurs in any material;

Rate - dependent plasticity allows the plastic-strain to develop over a time interval. This isalso termed viscoplasticity;

Creep is also an irreversible straining that occurs in material and which is rate-dependent,so the strains develop over time;

- Nonlinear elasticity allows a nonlinear stress-strain relationship to be specified;

Hyperelasticity is defined by a strain energy density potential that characterizes elastomericand foam-type materials;

- Visco-elasticity is a rate-dependent material characterization that includes a viscouscontribution to the elastic straining;

Concrete materials include cracking and crushing capability;

Swelling allows materials to enlarge in the presence of a neutron flux.

5. Dynamic analysis includes:

Eigenvalues and eigenvectors determination;Structure response to harmonic loadings;Spectrum analysis.

6. Structure stability and large deformations in combination with material nonlinearities.

7. Graphic representation of a model and output files.


." 8-.Holland RailconsultVabfdeling Civiele TccImiet

-"""""

Some basic element types are presented below:

1. Contact elements:2. Volume elements:3. Shell elements:

CaNT AC 12,26,48,49,52SOLID65,92,95SHELL41,43,57,91,93

The program is perfectly designed for scientific research with linear or nonlinear analyses ofstructures or spaces under different kinds of loads.

At Holland Railconsult (formerly NS Engineering Department) F. Vahle and P. Jovanovicdeveloped (1994) two and three-dimensional models of a tunnel lining (see fig. 39). One of themodels presented here, is a model of subgrade reaction named two-dimensional action-reactionmodel.

In this abstract the most important points of a design approach will be shown.

Bedded beam modelwith the segments

Continuum solid model

IIII

ItIIII

i ~~""1!=::"

I/'

,\,

I /~~~ \--~;1t

I/-::(-/ ~:t~~1

I/.~~:;;/ /-;;;:;> /,?'"

~ ,.,,,::::

//

;-! j;{"" /"~------------

// -,--P'//

---.

/'/'"1/ /"

,/"

"

fig.39

The disposition of the tunnel model is shown in fig.40. Contact or interface elements can bevarious in order to optimize the simulation of contact behaviour between concrete lining, groutshield and soil.

mvwI0.00

dSOIL 1

Hn-dwJ H I Hin

~x

SOIL "1",..----------------------------------.

SOIL N

d

h~INTERFACE elements

SOIL Z

fig.40 fig.41


Yn~j 1 ~Y=DI

~S--I

---,.-

II

II

. iCONTAC12 ~X

-------Holland RailconsultVabfdding CivieJ.e Techniek

""""",,",,"""""

Loading is applied directly on the tunnel lining through contact elements:

mvd Eq>K uEG y

c1 1 °1 1 k1 k 1 U 1

Eq>K uEG yCj i 0 j j k i k j U j

0.00

Hn-dwd H I Hinl

""' + """"':" ""------------------------------------------,

E q> K u E G ky

cn nOn n kn nUn

Ph

EC q> Ko u Ek G k Yz z z z z z Uz

X

fig.42

Variation in the type of contact elements are shown in the following figures:

J JZ

~ .LL\~i" Y

I

- II~IitII

IL J

LINK 10 dement

CONTAC 48

x

FX~//1\

/1 1\/I 1\

I /I 1\ k

~ j

M

~I \\

I \\I

"/ \ \ k 1

i~CONTAC49

fig.43 fig.44

Element type of the tunnel lining (precast concrete segments) and the soil is given as a SHELL43or SOLID65 element:

x

K

>y

(})

fig.45


Hiilland RalkODsultVabfdcling Civie1c Teclmiek

""""""""""",,,,,

Rules in coordinate system orientations are given in the following figures:

zMz

Fz Fx Mxy

Nodal coordinate system

fig.46

Z

1

Moments FxNormal forcesShear forces /-

~z y

Fy Mvx'/ //~) t--Yn--

F~--

~y /yx / dx.

~ lr(/,

.

-;6"-- -- . . / /X My /

- -x /

Global coordinate systemr- ,.x dv //

/

fig.47

Z ~ StressesSxt

~

~y

/

--L-Syt //

//Syb / dx

/

Global coordinate system--L

dy //,/

fig.48


----.-Holland RallconsultVabfdeliog Civie1c Tcclmick

""""'-

,."...,.

4. Double tube tunnels

4.1. The structural problem

E. Soliman, H.Duddeck and H.Ahrens [11] (1993), have been investigating the problem ofdouble-tube tunnels. They compared the results from three-dimensional and two-dimensionalfinite element analysis in order to optimize the solution of the problem.

When the tunnel is driven the stress state in the tunnel face is released. The stresses in the liningdepend directly on the time which elapses after the drive and on the distance from the face whenthe lining is settled as a support. H. Duddeck and Keilbasa (1991) presented a report in whichthey state that only a three-dimensional analysis yields realistic stress-deformation fields.

If the ground is soft and the support of the lining acts very close to the face (as in shield driving)a two dimensional approach may be justified (Schulze and Duddeck, 1964; Duddeck andErdmann, 1985).

tD

Jca

fD

-1:

h

a = y hz

ax = Koaz

fig.49

When the second tunnel is driven, primary stresses are influenced around the first tunnel. Theground-lining interaction for the second tunnel lining is different from the first one. The stiffnessis not axisimetrical, so the model must be designed on a different bases than the first tunnel. Twomodels are developed to determine the stresses and deformations for a double-tube tunnel inanalogy to a single tunnel analysis

A plain strain model, see figure 50a, may be sufficient in cases involving soft ground and stiffsegmental lining. A three-dimensional model, see fig.50b, may be valid, e.g. when a TBM isemployed or when shotcrete is used for support.


H~and RalkODsultVabfdc:ling Civic1e TeclmiekProduktgroep~1s

4.2. Two-dimensional analysis

The Finite Element Analysis proceeds in two steps. The first step considers the simulation of thefirst drive under the stress conditions in radial direction equal to zero. The second step assumesthat the results from the first step are taken as a primary stress-field for a second tube. The finiteelement solution of a single-tube tunnel are taken as reference values.

The results which are obtained show clearly that the generally hoop forces are 18% larger andthe bending moments are smaller than those of a single tunnel. The displacement of innershoulders are significantly different from those valid for a single tunnel. For stiffer ground thedeflections at the crown differ only slightly.

0

a. two-dimensional model b. three-dimensional model

fig.50

4.3. Three-dimensional analysis

If stress release at the tunnelling face, prior to the lining support is taken into account, then athree-dimensional analysis approach is necessary. Assuming homogeneous ground and equalexcavation procedures, the stresses and deformation fields which are moving with the advancingtunnelling face through the ground converge towards stationary patterns.

The finite stress-deformation field is the sum of incremental values at the fixed point (either inthe ground or in the lining), calculated for each excavation round. For closely spaced doubletunnels, the numerical procedure of the three-dimensional model follows the two-dimensionalmodel in two steps. The single-tunnel solution is of primary importance, followed by the double-tube solution.

The stresses and deformations of a single tunnel drive are determined by primary stresses in theground. The two-dimensional finite element analysis assumes that the tunnelling stresses aredistributed simultaneously to the lining and the ground.

After the excavation of the first tunnel, as mentioned above, the stress field in the ground ischanges completely. The lateral deformations of the first tunnel caused by driving the second oneare much larger than those of the single tunnel. Obviously the hoop forces are not so muchaffected as the bending moments in the lining by driving the second tunnel.


--------Holland RailconsultVabfdeling Civiele TeduUcJcProduk1groep Tunnels

5. Guidelines for the Design of Tunnels( Complete text is taken from: Tunnelling and Underground Space Technology, Vol.3, Nr.3, pp.237-249, 1988, printed in U.K., edited by Heinz Duddeck)

ITA Working Group on General Approaches to the Design of Tunnels

AbstractThis second report by the ITA Working Group on General Approaches to the Design of Tunnelspresents international design procedures for tunnels. In most tunnelling projects, the groundactively participates in providing stability to the opening. Therefore, the general approach to thedesign of tunnels includes site investigations, ground probings and in-situ monitoring, as well asthe analysis of stresses and deformations. For the latter, the different structural design modelsapplied at present-including the observational method-are presented. Guidelines for thestructural detailing of the tunnel lining and national recommendations on tunnel design are alsogiven. It is hoped that the information herein, based on experiences from a wide range oftunnelling projects, will be disseminated to tunnel designers throughout the world.

5.1. Scope of the guidelines

The International Tunnelling Association (ITA) Working Group on General Approaches to theDesign of Tunnels was established in 1978. As its first project, the group developed aquestionnaire aimed at compiling information about structural design models used in differentcountries for tunnels constructed prior to 1980. A synopsis of the answers to the questionnairewas published by the International Tunnelling Association in 1982 (ITA 1982).As a continuation of that first report, the working group herein presents guidelines thatattempt to condense the various answers from the first report and include additional experi-ence in the general approaches to the design of tunnel structures. These guidelines fulfil oneof the main objectives of the International Tunnelling Association, namely, to disperseinformation on underground use and underground structures throughout the world by crossingnational borders and language barriers.

Those interested in the subject of tunnel design should also consult published reports of otherITA working groups, e.g. the recent ITA report on contractual sharing of risk (see T-UST 3:2)and ITA recommendations on maintenance of tunnels (see T-UST 2:3). Furthermore, anumber of national and international organizations, such as the International Society on RockMechanics, have published recommendations on related subject, such as field measurementsand laboratory testings for rock and ground. Some of these publications and reports are listedin the Appendix.

In tunnelling, most often the ground actively participates in providing stability to the opening.Therefore, the design procedure for tunnels, as compared to aboveground structures, is muchmore dependent on such factors as the site situation, the ground characteristics, and theexcavation and support methods used. Recommendations on tunnel design naturally arelimited with regard to their consistency and applicability because each tunnelling project isaffected by special features that must be considered in the design Nevertheless, it is hopedthat the general outline provided in these guidelines, based on the experience gained frommany tunnelling projects, may be of some help for those starting project.


e--Holland RallconsultVabfde.ling Civie1e Tec:linkikProdubgroep Tunnels

5.2. Outline of general approaches

5.2.1. General Procedure in Designing a Tunnel

Planning a tunnelling project requires the interdependent participation of the followingdisciplines, at a minimum:

* Geology

* Geotechnical engineering* Excavation technology e.g. machine tunnelling

* Design of the supporting structural elements, including long-therm behaviour of materials.* Contract principles and law

Although the experts in each of these disciplines may be responsible only for their specificarea of knowledge, the decision on the main design features should be the outcome of thecooperative integration of all the disciplines. Only thus can it be ensured that the project, inall its details, has been developed in unity, and not as the consecutive addition of the separatework of each of the experts.

The basics s for tunnel design should include on cover:

* The geological report presenting the results of the geological and geophysical survey.

* The hydrogeological report.

* The geotechnical report on site investigations, including the interpretation of the results ofsite and laboratory tests with respect to the tunnelling process, soil and rock classificationetc ..

* Information on line, cross-section, drainage, and structural elements affecting later use ofthe tunnel.

* Plans for and a description of the projected excavation or driving procedure, including thedifferent cross-sections related to different ground conditions.

* Design s for the types of excavation methods and tunnel supports likely to be applied,considering, e.g. excavation advance and face support (types and number of anchors,shotcrete strength, closure length, etc.).

* The program for the in-situ monitoring of the tunnel by field measurements.

* The analysis of stresses and deformations (for unlined tunnels as well as for single-ordouble-lined tunnels), and the dimensioning of the tunnel support for intermediate phasesand final linings.

* The design for waterproofing or drainage.

* Structural s for the final designing of the tunnel project, including the detailing.

* During and after the excavation, reports on the field measurements and interpretation oftheir results with respect to the response of the ground and the structural safety of thetunnel.

* action of the problems encountered during the excavation and measures applied, e.g.strengthening the ground or changing the projected type of support, based on monitoringresults.

The above sequence of these basic s also provides the general outline of the design procedure.


"".., 8-Holland RaIlconsultVabfdcliag Civicle Tcclmict

-"""""

5.2.2. Elements of the Structural Design Model for Tunnels

In planning, designing, analyzing and detailing a structure, engineers promise that thestructure will neither suffer structurally nor collapse during its projected lifetime.Thus, models of the reality are necessary for analysis in order to predict the behaviour of atunnel during the excavation and during its lifetime. Models are also needed for bidding onprojects.The following main elements involved in the design procedure are shown as a flow-chart inFig.51.

(1) Geology and site investigations must confirm the line, orientation, depth, etc., of theopening, e.g. a cavern.Ground probing and soil or rock mechanics must be applied to determine the groundcharacteristics, e.g. primary stresses, soil or rock strength, faults, water conditions.Experience and preliminary estimates or calculations are used to determine the cross-section required and the choice of the excavation method or the tunnel. driving machineto be used, as well as the methods of dewatering the ground and the selection of thesupporting structural elements.

(2)

(3)

GEOLOGY site investigation.

line and orientation

PROBING AND

*ROCK MEeH.

EXPERIENCEESTIMATION

MECHANICALMODEL

rnrn;;i:;

VERIFICATIONOF TUNNELDESIGN

fig.51

(4) After steps (1)-(3) are completed, the tunnelling engineer must derive, or even invent, astructural model. By applying equilibrium and compatibility conditions to the model, theengineer has to arrive at those criteria that are factors in deciding whether or not thedesign is safe. Different models may be used for each excavation phase, for thepreliminary and the final tunnel lining, or for different ground behaviour, e.g. indiscontinuous rock or homogeneous soft soil. Modelling of the geometric features mayvary greatly, depending on the desired intensity of the analysis.


-------Holland RailconsultVabfdding Civiele TcchnietProduktgroop-

(5) A safety concept drawn from failure hypotheses may be based on criteria such asstrains, stresses, deformation, or failure modes.

The bypass in fig.51 indicates that for many underground structures, as in mining or in self-supporting hard rock, no design models at all are applied. In such cases, past experiencesalone may be sufficient.

Risk assessment by the contractors as well by the owner is needed at the time of contractnegotiations. Risks involve possible structural failures of the tunnel support and lining,functional failures after completion of work, and financial risks. The contractual aspects alsoinclude risk sharing and risk responsibilities.

In-situ monitoring can be applied only after the tunnelling has begun. If the displacementsstop increasing over time, it generally may be assumed that the structure is designed safely.Yet monitoring provides only part of the answer to the question of safety, for it does not tellhow close the structure may be to sudden collapse or nonlinear failure modes. The results offields measurements and experiences during excavation may compel the engineer to changethe design model by adjusting it to real behaviour.

An iterative, step-by-step approach is characteristic of the design of structures in the groundthat employ the participating strength of the ground (see loops in Fig.51). The designer maybegin by applying estimated and simple behaviourial models. Adjustments based on actualexperiences during the tunnelling excavation (such as excavating the initial section in thesame ground conditions or driving a pilot tunnel) will bring the model closer to reality asrefine it (if refinement is consistent with the overall accuracy attainable). The interpretationsof in-situ measurements (and some back analyses) also may assist designers in making theseadjustments.

All of the elements of the structural design model in Fig.51 should be considered an interact-ing unity. Scattering of parameters or inaccuracy in one part of the model will affect theaccuracy of the model as a whole. Therefore, the same degree of simplicity or refinementshould be provided consistently through all the elements of the design model. For example, itis inconsistent to apply very refined mathematical tools simultaneously with rough guesses ofimportant ground characteristics.

5.2.3. Different Approaches Based on Ground Conditions and Tunnelling Methods

The response of the ground to excavation of an opening can vary widely. Based on the typeof ground in which tunnelling takes place, four principal types of tunnelling may be defined:

(1) for cut-and-cover tunnelling, in most cases the ground acts only passively as a dead loadon a tunnel structure erected like any aboveground engineering structure.

(2) In soft ground, immediate support must be provided by a stiff lining (as, for example, inthe case of shield-driven tunnels with tubbings for ring support and pressurized slurryfor face support). In such a case, the ground usually participates actively by providingresistance to outward deformation of the lining.


H&land RalkOOsultVabfdeling Civielc TccJmjck

-""""

(3) In medium-hard rock or in more cohesive soil, the ground may be strong enough toallow a certain open section at the tunnel face. Here, a certain amount of stress releasemany permanently be valid before the supporting elements and the lining begin actingeffectively. In this situation only a fraction of the primary ground pressure is acting onthe lining.

(4) When tunnelling in hard rock, the ground alone may preserve the stability of theopening so that only a thin lining, if any, will be necessary for surface protection. Thedesign model must take into account the rock around the tunnel in order to predict andverify safety considerations and deformations.

Especially in ground conditions that change along the tunnel axis, the ground may bestrengthened by injections, anchoring, draining, freezing, etc.. Under these circumstances, case(2) may be improved, at least temporarily, to case (3).

The characteristic stress release at the tunnel face (Erdmann 1983) is shown in Figs 52 andfig. 53. The relative crown displacement w is plotted along the tunnel axis, where w/wo = 1.0represents the case of an unsupported tunnel. In medium stiff ground nearly 80% of thedeformations have already taken place before the lining (shown here as shotcrete) is stiffenough to participate.

~~1_~!.?.~ ._1.~=O,5 D

D I L-EB

f~~:-~~ L:~~~~ miliom

w0 without lining

w/wo

EB = 0

fig.52

For a simplified plane model with no stress release, when the full primary stresses areassumed to act on a lined opening the displacement may be only 0.4 of that occurring in theunsupported case. The corresponding stress release is shown in Fig.53. The simplifiedexample, considering only the constant part of radial pressure, yields the values shownfor the ring stiffness of E0 = 15,000 x 0.3 = 4500 MN/m and a ground deformation modulesof Ek = 1000 MN/m2.

Even in the unrealistic case when the full primary stress a... simultaneously on the groundopening and the lining on 55% of the stress is taken by the lining; in the case of E0 = 2250MN/m, only 38% is taken by the lining. If an section of 0.25 of the tunnel diameter is leftwithout lining support, the lining takes only 25% of the primary stresses; .. Lu = 0.5 D, ittakes only 12% of the primary stresses.


-------Holland RallconsultVabfdeling Civielc TcclmidcProduJqroep 1'unne1s

For very soft ground requiring immediate support (as in the case of very shallow tunnels),almost 100% of the primer stresses are acting on the lining. The values change, of cors withother stiffness relationships and other stress distributions than those shown in Fig.53, withother cross-section and other tunnelling methods.

I

00 tnL=O,5D ~ /

%,%tunnel axis

-. .-..

a !. /

1,0. 0/ %D = 10 m I EB

d"'30 Ctn. ~100%

\ ,,"" '....

"I' """"'''''' ""....

'....

""---------

% -yH ~2

K - Oh0 - - 0 5

0 'v

100 1000

fig.53

5.2.4. Site Investigations, Structural Analysis and In-Situ Monitoring

An adequate intensity of site exploration, from which geological and hydrological mappingand ground profile are derived, is most important for choosing the appropriate tunnel designand excavation method. A well-document.. geological report should provide as muchinformation as obtainable about the physical features along the tunnel axis and in the adjacentground. The amount of information should be much greater than the information required f...entering directly into a structural analysis.

The results of an analysis depend very much on the assumed model and the values of thesignificant parameter. The main purposes of the structural analysis are to provided the designengineer with:

(1) a better understanding of the ground-structure interaction induced by the tunnellingprocess;knowledge of what kinds of principal risks a involved and where they are located; anda tool for interpreted the site observations and the in-situ measurements.

(2)(3)

The available mathematical methods of analysis are much more refined than are the propertiesthat constitute the structural model. Hence, in most cases it is more appropriate to investigatealternative possible properties of the model, even different models, than to aim for a morerefined model. For most cases, it is preferable that the structural model employed and theparameters chosen for the analyses lower-limit cases that may prove that even forunfavourable assumptions, the tunnelling precess and the final tunnel a sufficiently safe. Ingeneral, the structural design model do not try to represent exactly the very actual conditionsin the tunnel, although it covers these conditions.


8-Holland RallconsultVabfdcIiDg Civie.le TecbnickProduhgroep Tunnels

In-situ monitoring is important and should be an integer part of the design procedure,especially in cases when stability of the tunnel depends on the ground properties. Deforma-tions and displacements generally can be measured with much more accuracy than stresses.The geometry of the deformations and their development over time are more significant forthe interpretation of the actual event. However, in-situ monitoring evaluates only the verylocal and actual situation in the tunnel. Therefore, in general the conditions taken into accountby the design calculations not coincide with theconditions that are monitored. Only relating measurement results and possible failuremodes

'"''

safety margins.In many cases exploratory tunnelling may be rewarding because of the information it yieldson the actual response the ground to the proposed methods for drainage,excavation.

TBM driving, support, etc. In important cases a pilot tunnel may be driven; such a tunnel mayeven be enlarged to the full final tunnel cross-section in the most representative ground alongthe tunnel axis. For lager projects, it may be useful to excavate a trial tunnel prior tocommencing the actual work. More intensive in-situ monitoring of the exploratory tunnelsections should check the design approach by numerical analysis.

5.2.5. Design Criteria and Evaluating Structural Safety

An underground structure may lose its serviceability or its structural safety in the followingcases:

- The structure loses its watertightness.- The deformations are intolerably large.- The tunnel is insufficiently durable for its projected life and use.- The material strength of the structural elements is exhausted locally, necessitating repair.- The support technique (for example, in erecting segmental linings) fails or causes damage.- Exhaustion of the material strength of the system causes structural failure, although the

corresponding deformations develop in a restrained manner over time.- The tunnel collapses suddenly because of instability.

The structural design model should yield criteria related to failure cases, against which thetunnel should be designed safely. These criteria may be:

* Deformations and strains.* Stresses and utilization of plasticity.* Cross-sectional lining failure.

* Failure of ground or rock strength.

* Limit-analysis failure modes.

In principle, the safety margins may be chosen differently for each of the failure cases listedabove. However, in reality the evaluation of the actual safety margins is most complex andvery much affected by the scattering of the involved properties of the ground and the structureand, furthermore, by the interacting probabilistic characteristics of these properties.


Hclland RalkOOsultVabfdeling Civiele TecImie.k

""""""-

........

Therefore, the results of any calculation should be subject to critical reflection on theirrelevance to the actual conditions.

National codes for concrete or steel structures may not always be appropriate for the design oftunnels and the supporting elements. Computational safety evaluations should always becomplemented by overall safety considerations and his assessments employing criticalengineering judgment, which may include the following aspects:

* The ground characteristics should be considered in light of their possible deviations fromaverage values.

* The design model itself and the values of parameters should be discussed by the designteam, which includes all of the experts involved (see Section 2.1, "General Procedure inDesigning a Tunnel, " above).

* Several and more simple calculation runs with parametric variations may uncover thescattering of the results. In general, this approach is much more informative than a singleover-refined investigation.

* The in-situ measurements should be used for successive adjustment of design models.

* Long-term measurement of deformations via extrapolation may reveal to a large extent thefinal stability of the structure, although sudden collapse may not be announced in advance.


-------Holland RallconsultVabfdclins Civide Tcclmiek

"""""

5.3. Site investigations as ground probing

5.3.1. Geological Data and Ground Parameters

The appropriate amount of ground investigations on site and in laboratories may varyconsiderably from project to project. Because the types of ground explorations and probingsdepend on the special features of the tunnelling project, its purpose, excavation method, etc.,they should be chosen by the experts team, especially in consultations with the designengineer. The intensity of the ground explorations will depend on the homogeneity of theground, the purpose of the tunnelling, the cost of boring, e.g. for shallow or deep cover, andother factors.The geological investigations should include the following basic geotechnical information (seealso ISRM Commission on Classification of Rocks and Rock Masses 1981).

5.3.1.1. Tunnels in rock

Zoning. The ground should be divided in geotechnical units for which the design characteris-tics may be considered uniform. However, relevant characteristics may display considerablevariations within a geotechnical unit. The following aspects should be considered for thegeological description of each zone:

* Name of the geological formation in accordance with a genetic classification.

* Geologic structure and fracturing of the rock mass with strike and dip orientations.

* Colour, texture and mineral composition.

* Degree of weathering.

Parameters of the rock mass e.g. in five classes of intervals, including:

* Thickness of the layers.* Fracture intercept.* Rock classification.

* Core recovery.

* Uniaxial compressive strength of the rock, derived from laboratory tests.

* Angle of friction of the fractures (derived from laboratory direct shear tests).

* Strength of the ground in on-site situations.* Deformation properties (modulus).* Effect of water on the rock quality.

* Seismic-velocity.

Primary stressfield of the ground For larger tunnel projects, tests evaluating the naturalstresses in the rock mass may be recommended. For usual tunnel projects one should leastestimate the stress ratio a/a. at tunnel level, where ah is the lateral ground pressure and ahthe major principal stress (usually in the vertical direction), for which the weight of theoverlying rock generally may be taken. Tectonic stresses should be indicated.

Water conditions. Two types of information about water conditions are required:1. Permeability, as determined by:

Coefficient k (m/s) (from field tests).Lugeon unit (from tests in boreholes).

2. Water pressure:At the tunnel level (hydraulic head).At piezometric levels in boreholes.


.-------Holland RaIiCODsultVabfddiDg Civielc TecluUek

"""""""''"-''

Deformability of the rock mass. In-situ tests are required to derive the two different defonna-tion moduli, which can be determined either from static methods (dilatometer tests inboreholes, plate tests in edits, or radial jacking tests in chambers), or from dynamic methods(wave velocity by seismic-refraction or by geophysical logging in boreholes).Engineering judgment should be exercised in choosing the value of the modulus mostappropriate for the design-for instance, by the relevant tangent of the pressure-defonnation curve at the primary stress level in the static method.

Properties for which infonnation is needed when tunnel boring machines are to be employedinclude:

- Abrasiveness and hardness.- Mineral composites, as, e.g. quartzite contents.- Homogeneity.

Swelling potential of the rock. The presence of sulphates, hydroxides, or clay minerals shouldbe investigated by mineralogical testing. A special oedometer test may be used to detenninethe swell test-curve of a specimen subjected first to a load-unload-reload cycle in a dry state,and then unloaded with water.

The following ground water conditions should be given:- Water levels, piezometric levels, variations over time, pore pressure measurements in

confined aquifers.- Water chemistry.- Water temperatures.- Expected amount of water inflow.

5.3.2.1. Tunnels in soil

The geotechnical description should primarily follow the recommendationsrock. Additional special features for soil include:1. Soil identification (laboratory testing):

* Particle size distribution.

* Atterberg Limits TIJj, TIJp'

* Unit weights, 'Y, 'Yd, 'YZ.

* Water content TIJ.* Penneability k.* Core recovery.

given above for

2. Mechanical properties determined by laboratory testing:

* Friction angle <l>u,<1>.

* Cohesion Cu' c.

* Compressibility mv, Cv'

3. Mechanical properties determined by field testing:

* Shear strength 7v (Vane-test).

* Penetration N (Standard Penetration Test).

* Deformability E (Plate bearing, Dilatometer).

4. Ground water condition (in addition to those listed in 3.1.1.): penneability, as detenninedby pumping tests.


8--Holland RaI1consultVabfdc.ling Civiele TeclmickProduktgroep Tunnels

5.3.2. Evaluation of Parameters by Ground Probing and Laboratory Tests

The properties of the ground that are relevant for the tunnel design should be evaluated ascarefully as possible. In-situ tests, which cover larger ground masses, generally are moresignificant than are laboratory tests on small specimens, which often are the better preservedparts of the coring.

The natural scattering of ground properties requires an appropriate number of parallel tests-atleast three tests for each property (see also the corresponding ISRM recommendations).

Results of laboratory tests must be adjusted to site conditions. The size of specimen, theeffects of ground water, the inhomogeneity of the ground on site, and the effects of scatteringmust be considered. The conclusions drawn from tests also should take into considerationwhether the specimens were taken from disturbed or undisturbed ground.

In may cases, the first part of the tunnelling may be interpreted as a large-scale test, theexperiences from which may be drawn upon not only for the subsequent excavations but alsofor predicting ground behaviour. In certain cases, long horizontal boreholes may facilitateground probing ahead of the face, or a pilot tunnel may serve as a test tunnel that at the sametime provides drainage. The on-site investigations provide valuable results for checking thecorrelation of large-scale in-situ tests with laboratory tests.

Special tests that correspond directly to the proposed tunnelling method may be required, e.g.for the sufficient preservation of a membrane at the face of a bentonite shield. The evaluationof the parameters should indicate the expected scattering. From probabilistic consideration ofnormally distributed quantities it can be deduced that a mean value or a value correspondingto a moderately conservative fractiously of a Gaussian distribution is more appropriate thanthe world case value.

A set of all the parameters describing the ground behaviour of one tunnel section with regardto tunnelling should be seen as a comprehensive unit and should be well-balanced in relationto each of the parameters. For example, a small value of ground deformation modulesindicates a tendency to plastic behaviour, to which corresponds a ration of lateral to verticalprimary stress that is closer to 1.0. Hence, for alternative investigations some complete,balanced sets of parameters should be chosen instead of considering each parameter alone,unrelated to the others.

The available methods for ground probing and laboratory tests, their applicability andaccuracy are given in the Appendix.

5.3.3. Interpretation of Test Results and Documentation

The fields and laboratory tests should be given in well documented reports, in the form ofactual results. Based on these reports, an interpretation of the tests that is relevant to theactual tunnelling process and the requirements of the design models for the structural analysisis necessary. At the time the tests are planned, the team of experts referred to in Section 5.2.1should decide which ground properties and ground characteristics are necessary for thegeneral geotechnical description of the ground and for the projected design model. Thus, acloser relationship may be achieved between ground investigations and tunnelling design, andbetween the amount and refinement of tests and the tunnelling risks.


8-Holland RallconsultVakafckling Civie1e TecbDiek1'rodukIpoop-

The documents should lay open the rational interpretational way in which design values arederived dorm test results. This method has proven to be especially useful in the tenderingprocess, because it condenses the relevant data for the description of the ground and for thedesign of the tunnel on an band along the tunnel axis beneath a graphical representation of thetunnel profile.

Such condensed tables may be prepared first for tendering and the preliminary design, andthen improved through experience gained and incoming monitoring results. However, itshould be clearly stated, especially in the contract papers, that much relevant information islost or oversimplified in such tables, and that therefore the geotechnical reports and othercomplete documents should be considered the primary documents.


--------Holland RallconsultVabfddiDg Civicle TcclmieltProduktgroep Tunnels

5.4. On structural design models for tunnelling

5.4.1. Alternative Design Models

The excavation of a tunnel changes the primary stress field into a three-dimensional pattern atthe tunnelling face. Farther form the face, the stress field eventually will return to anessentially two-dimensional system. Therefore, the tunnel design may consider only two-dimensional stress-strain fields as first approximations.

The design of a tunnel should take into account the interaction between ground and lining. Inorder to do so, the lining must be placed in closest possible bond with the ground. Topreserve its natural strength, the ground should be kept as undisturbed as possible. Thedeformations resulting from the tunnelling process (see Fig.52) reduce the primary groundpressure and create stresses in the lining corresponding to that fractional part of the primarystresses in the ground which act on the sustaining lining. The stresses depend on the stiffnessrelationship of the ground to the lining, as well as on the shape of the tunnel cross-section.The latter should be selected such that an arching action in the ground and the lining maydevelop.

2

+"ED H H

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I

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II

,

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,

-

_

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_

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_

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- --.

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~o -K 0h 0 y

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fig.54

4

! ! ! !

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Figure 54 presents four different structural models for a plane-strain design analysis. Thecross-sections need not be circular. These four models are explained more explicitly below.In soft ground, immediate support is provided by a relatively stiff lining.

For tunnels at shallow depth (as for underground railways in cities), it is agreed that a two-dimensional cross-section may be considered, neglecting the three-dimensional stress releaseat the face of the tunnel during excavation. In cases (I) and (2) in Fig.54, the groundpressures acting on the cross-section are assumed to be equal to the primary stresses in theundisturbed ground.


~.-Holland RailconsultVabfdeling CiYie1eTeclmiek

""""","",'-"

Hence, it is assumed that in the final state (some years after the construction of the tunnel),the ground eventually will return to nearly the same condition as before the tunnelling.Changes in ground water levels, traffic vibrations, etc., may provoke this "readjustment".

In case (1), for shallow tunnels and soft ground, the full overburden is taken as load.Hence, no tension bedding is allowed at the crown of the tunnel. The ground reaction issimplified by radial and tangential springs, arriving at a bedded-beam model.

In case (2), for moderately stiff ground, the soil stiffness is employed by assuming a two-dimensional continuum model and a complete bond between lining and ground. As in case(1), stress release due to predeformations of the ground is neglected. Inward displacementsresult in a reduction of the pressure on the lining.

Case (3) assumes that some stress release is caused by deformations that occur before thelining participates. In medium-hard rock or in highly cohesive oil, the ground may be strongenough to allow a certain unsupported section at the tunnel face (see Fig.52). Also, for tunnelshaving a high overburden, a reduction of the acting crown pressure (represented in Fig.54 byh<H) is taken into account.

In case (4), the ground stresses acting on the lining are determined by an empirical approach,which may be based on previous experiences with the same ground and the same tunnellingmethod, on in-situ observations and monitoring of initial tunnel sections, on interpretation ofthe observed data, and on continuous improvements of the design model.

fig.55

If a plane model is not justified - as is the case for caverns, for more complicated geometriesof underground structures, or for an investigation directly at the tunnelling faze - a three-dimensional model may be necessary (see Fig.55). The three-dimensional model also may beconceived as consisting of discontinuous masses (block theory) or acontinuum with discrete discontinuous fissures of faults.


--------Holland RallconsultVabfdcliDg Civiele TochDict

-""""'"

5.4.2. Continuum or Discontinuum Model

For structural design models such as those in Fig.55, the ground may be modelled ashomogeneous or heterogeneous, isotropic or anisotropic; as a two-dimensional, i.e. allowingsone stress release before the lining is acting, or a three-dimensional stiff medium. The liningmay be modelled either as a beam element with bending stiffness or as a continuum.Plasticity, viscosity, fracture of the rock, non-linear stress-strain and deformation behaviour,etc., may be covered by special assumptions for material laws.

The design criteria are computed by numerical solutions. From their origins, the finite-elementmethod and the boundary-element method are basically continuum methods. Thus, homogene-ous media and stress-strain fields are evaluated best. In general, discontinue such as rock withfissures and faults, and failure modes, which are initiated by local rupture, shear failure, orfull collapse, cannot be covered by continuum methods.

A continuum or discontinuum model is appropriate for tunnel structures where the groundprovides the principal stability of the opening (as in hard rock) or where the geometricalproperties of the underground opening can be modelled only by numerical analysis, e.g. in thecase of closely spaced twin tunnels.

5.4.3. Bedded-Beam Model (Action-Reaction Model)

If the stiffness of the ground is small compared to the stiffness of the lining, a design modelsuch as that shown in Fig.56 may be employed. In such a case, the active ground pressuresare represented by given loads and the passive reaction of the ground against deformations issimulated by constant bedding moduli. The model may be particularly well-suited to thedesign of linings of shield-driven tunnels. As to applicability, the stiffness ratio r3may besmaller than 200:

r3 = E.fl'/EJ<200,where:

EsREJ

is the representative deformation stiffness modulus of the ground,is the radius of the tunnel cross-section or its equivalent for non-circular tunnels,is the bending stiffness of the lining.

A more correct solution for the bedding is given by a nonzero stiffness matrix for all elementswith regard to radial and tangential displacements.

However, in most cases and in view of the unavoidable approximations based on the otherassumptions, a simpler approach may be sufficient. Such an approach considers only radial(and, eventually, tangential) bedding, neglecting the interdependence of radial and tangentialdisplacements and beddings. For non-circular cross-sections, the continuum solution revealsthat bedding may be increased at comer sections of the lining, with smaller radius of thecurvature.

The bedded-beam model may be adjusted to more complex cases, e.g. by reducing the crownload in accordance with stress release at the tunnel face (see Fig.53) or, for deep tunnels, byassuming bedding also at the crown.

For articulated effective hinges in linings the bending moments are smaller; the deformationsmay be larger, depending on the ground stiffness. For hinged linings the limit of r3givenabove is not valid.


H~and RalkODsultVabfdeling Civiclc Tcdmiek

~"""""

(Jy= Y H u a =K UB r N M

rr-r-rr-n Kr = const.

~(Jh = K~(Jy

[LLLLLd- (Jy

~$radial around reactiondisplacement pressure

normalforces

bendiogmoment

fig.56

The analysis of the bedded beam yields ring forces, bending moments and deformations asdesign criteria for the lining. If the lining ring is completed closed, the bending moments maybe considered less important than the ring forces for providing equilibrium (a smaller safetyfactor may be justified for the bending moments). Allowances also may be made for a plasticrotation capacity of the lining segments.

For tunnels with very pronounced stress release due to inward deformations, e.g. for deeptunnels in rock, a simple approach to design considerations is given by the convergence-confinement model, which is based only on the interaction of the radial inward displacementand the support reaction to these deformations by resisting ring forces and the correspondingoutward pressure (see Fig.57).

The primary stresses 0"0in the ground are released with progressive inward displacements. Theacting pressure may even increase when rock joints are opening with larger displacements. Inself-supporting rock, the ground characteristic in Fig.57 meets the w-axis; because the primarystresses are released completely, a supporting lining is not necessary. Before the supportingmembers are installed, it is unavoidable -even desirable- that decompression associated withthe predeformation Wowill occur. The stiffness of the lining determines where both curves(characteristic lines) will intersect. At this point, equilibrium as well as compatibilityconditions are fulfilled. If the ground characteristic is known, e.g., by in-situ monitoring, thepredeformation Woand the stiffness of the lining (including its development over time and astunnelling advances), and even its plastic properties are very decisive for the actual stresses inthe lining. Both curves in Fig.57 mary varyconsiderable.

In its usual analytical form, the convergence-confinement model assumes constant groundpressure along a circular tunnel lining. Consequently, it yields only ring forces and no bendingmoments at all. However, it may be extended to cover ground pressure that vary along thetunnel lining (Gesta 1986).

The model may also be applied as a first approximation for non-circular tunnel cross-sections,although the support reaction curve is distinctly different, e.g. for horseshoe-type crosssections. Therefore, it may be helpful to use the convergence-confinement model in combina-tion with a continuum model and in-situ measurements.

Although the convergence-confinement approach is primarily a tool for the interpretation offield measurements, it also may be applied in support of the empirical approach.


-------Holland RallconsultV.bfdeling CiYiele Tecbn.iClkProduktgroep TunneIB

0- prim. pressure

Ground response curve 0 g

Ground

0

dO0

Support reaction curve Os

---'fiiJfUr~-I

E/

,0

~(('i;~:'PPori'~--L---:/---,../~

--

d 00 - stress release

Wo - predecompression

Ur

i ~ WA

~

fig. 57

5.4.4. Empirical Approach

The structural elements and the excavation procedure, especially for the preliminary supportof the tunnel, may be selected mainly based on experience and empirical considerations thatrely more on direct observations than on numerical calculations.This procedure may be especially reasonable if experiences from a successful tunnellingproject can be applied to a similar, new one yet to be designed. Such a transfer of informationis justified only when:

. The ground conditions, including those of the ground water, are comparable.

. The dimensions of the tunnel and its cross-sectional shape are similar.. The depths of overburden are approximately the same.. The tunnelling methods to be employed are the same.. In-situ monitoring yields results comparable to those for the preceding tunnellingproject.

One disadvantage of prolonged application of the empirical approach is that, lacking anincentive to apply a more appropriate tunnelling design via a consistent safety assessment, thestructure may be designed over conservatively, resulting in higher construction costs. Thesimple empirical approach contributes little to the advancement of the state of the art intunnelling.

The empirical approach to tunnel design may also be applied to larger projects in only slightlychanging ground if provision is made (especially in the tender) for initial experiences to beextrapolated to the subsequent sections along the tunnel axis. Such a situation justifies ameasurement programme that is more intensive for the first sections, in order to gain experi-ence.

5.4.5. Observational Method

By combining analytical methods with the empirical approach and the immediate interpreta-tions of in-situ measurements, a tunnelling design procedure that is adjustable as the tunnelexcavation proceeds may be applied. In this approach, the field measurements of groundmovements, displacements and stresses in the lining are used on an ongoing basis to verify ormodify the design of the tunnel. More intensively instrumented sections at the early stages ofthe tunnelling provide the data for these procedures.


------Holland RallconsultVabfdcliDg Civiele Teclmiek

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The interpretation of the measured data yields insight into the ground behaviour as a reactionto tunnelling procedure.

In applying the observational method, the following conditions must be met:

. The chosen tunnelling process must be adjustable along the tunnel line.. Owner and contractor must agree in advance on contractual arrangements that allow formodifications of the design on an ongoing basis during the project.. The field measurements should be interpreted on the basis of a suitable analyticalconcept relating measurement data to design criteria.. The interpretation of particular instrumented section must be used to draw conclusionsabout the other sections of the tunnel. Hence, the experiences are restricted to thosetunnel sections that are comparable with respect to ground conditions, ground cover, etc.(see Section 4.4 "Empirical Approach").. Field measurement should be provided throughout the entire length of the tunnel inorder to check its assumed behaviour.

5.4.6. Special Design Features

Special considerations may be necessary if unusual ground behaviour is expected or is causedby ground improvements. Some special design features and considerations are discussedbelow.

5.4.6.1. Ground improvement techniques

Grouting and injections. Intensive grouting or injections of the ground may improve theground characteristics considered in the design model. Although in most cases grouting isapplied only for closing discontinuities in rock or for strengthening soft ground, in both casesthe goal is to achieve better homogeneity.

Drainage and compressedair. Usually the ground is stabilized by dewatering it and byavoiding inflows of water. Ground failure may be avoided if the pore water pressure isminimized. The assumed ground characteristics may be valid only if successful drainage ispossible or if water inflow is prevented, as in tunnelling under compressed air.

Groundfreezing. Improving the ground by freezing changes the ground properties. The time-dependent stress strain behaviour of frozen ground can be significant. Freezing draws watertoward the lining, causing an increase in water volume and heave at the surface. Concretingon frozen ground delays the strength development of the concrete.

5.4.6.2. Unusual ground behaviour

Swelling ground Stress release due to tunnelling and/or ground water influx may causeswelling and a corresponding increase in pressure on the lining. In these cases, a circularcross-section or at least an invert arch is recommended. The swelling resulting from achemical reaction, as in anhydride generally is much more pronounced than that due to thephysical absorption of water, as in clay.


-------Holland RailconsultVabfdeling Civie1e TedWekProduktgroep Tunnels

Underground erosion, mining subsidence and sinkholes. Tunnelling in ground that is subjectto settlements, as in the case of gypsum erosion or mining subsidence, requires special designconsiderations. A flexible lining that follows the ground movements by utilizing its plasticdeformation capacity is more suitable in these cases than is too-ridged or brittle, failure-pronelining. If the ground has sinkholes potentials, a tunnel structure that can be repaired easilymay be more economical than a structure designed to allow the bridging of the sinkholes.


ValWdeliDg CiYide Technic!!:_Tum>ob

------.-HollandRallconsult

5.5.

5.5.1.

In-situ monitoring

Purpose of In-Situ Measurements

In-situ monitoring during the excavation and at longer intervals after the tunnel is completedshould be regarded as an integral part of the design not only for checking the structural safetyand the applied design model but also for verifying the basic conception of the response ofthe ground to tunnelling and the effectiveness of the structural support.The main objectives of in-situ monitoring are:

5.5.2.

1) To control the deformations of the tunnel, including securing the open tunnel profile.The time-history development of displacements and convergence may be consideredone safety criterion, although field measurements do not yield the margins thestructure can endure before failing.

2) To verify that the appropriate tunnelling method was selected.

3) To control the settlements at the surface, e.g. in order to obtain information on thedeformation pattern in the ground and on that part of settlements caused by loweringthe water level.

4) To measure the development of stresses in the structural members, indicatingsufficient strength or the possibility of strength failure.

5) To indicate progressive deformations, which require immediate action for ground andsupport strengthening.

6) To furnish evidence for insurance claims, e.g. by providing results of levelling thesettlements at the surface in town areas.

Monitoring Methods

A programme for monitoring the deformations and stresses during the excavation maycomprise the following measurements:

1) Levelling the crown (at the least) inside the tunnel as soon as possible. With regardto interpretation of the data, Fig.52 reveals that often only a small fraction of theentire crown movement can be monitored because a larger part occurs before the boltcan be set. For difficult tunnelling, the distance between two crown readings may beas close as 10-15 m. Levelling of the invert is recommended for rock havingswelling potentials.

2) Convergence readings (in triangular settings) should be the standard method for earlyinformation. They are easily applied and are accurate to within 1 mm.

3) In a few cross-sections, the lining may be equipped with stress cells for reading theground pressures and ring forces in the lining.

4) Stress cells also should be installed in a few sections of the final second lining iflong-term readings are desired after the tunnel has been completed.


-------.Holland RailCODsuitVabfcleliq Civide Tecbaiek

ProduJdgroop""",""

5) Surface levelling along the tunnel axis and perpendicular to it yield settlements andthe correlation to measurements inside the tunnel (see Fig.52).

6) Extensometer, inclinometers, gliding micrometers may be installed from the surfacewell ahead of the tunnelling face, yielding deformation measurements within theground. Monitoring of the ground deformations is especially appropriate for checkingand interpreting the design model. Therefore, the installation should be combinedwith convergence readings and stress cells in the same cross-section.

The frequency of the readings depends on how far from the tunnelling face the measurementsare taken, and on the results. For example, readings may be performed initially two times aday; then be reduced to one reading per week four diameters behind the face; and end withone reading per month if the time-data curves justify this reduction in measurement readings.

5.5.3. Interpreting Results of In-Situ Monitoring

The results of in-situ monitoring should be interpreted with regard to the excavation steps, thestructural support work, and the structural design model in conjunction with safety consider-ations.

The actual readings normally show a broad scatter of values. Expectations of reliability maynot be met, especially for pressure cells, because stresses and strains are very local character-istics. Deformation and convergence readings are more reliable obtainable because displace-ments register integral along a larger section of the ground.

The in-situ measurements should be interpreted in consideration of the following:

. The results should verify whether the tunnelling method is appropriate.. Graphed time-history charts may reveal a decreasing rate of deformation, or uncoverdanger of collapse.. Large discrepancies between the theoretically predicted and actually observed deforma-

tions may force revisions of the design model. However, measurements are valid onlyfor the actual state at the time and the place where they are taken. Long-term influencessuch as rising water level, traffic vibrations, and long-term creep are not registeredduring excavation.. The readings may promote visual understanding of the structural behaviour of groundand support interaction.. The readings may cover only a fraction of the actual phenomena if bolts and stress cellsare installed too late (see Fig.52).. The tunnel may be considered stable when all the readings cease to increase. However,a safety margin against failure -especially sudden collapse- cannot be deduced frommeasurement, except by extrapolation.


Vabfdeling Civielc TedmietProduktgroep Tunnels

H;.Iand RallWnsult

5.6. Guidelines for the structural detailing of the lining

On design aspects with regard to maintenance the reader is referred to other recommendationsof the ITA (see T&UST 2:3). For concrete linings, the following structural design specifica-tions are suggested:

1) The thickness of a second lining of cast-in-place concrete may have a lower limit of25-30 cm to avoid concrete placing problems such as under compaction or honey-combing of concrete. The following lower limits may be recommended:

20 cm, if lining is not reinforced;- 25 cm, if lining is reinforced;

30 cm for watertight concrete.

2) Reinforcement may be desirable for crack control, even when it is not required forcovering inner stresses. On the other hand, reinforcement may cause concrete-placingproblems or long-term durability problems due to steel corrosion. If reinforcement inthe second lining is provided for crack control, a closely-spaced steel mesh reinforce-ment may have the following cross-sections in both directions:

. At the outer surface, at least 1.5 cm3/m of steel;. At the inner surface, at least 3.0 cm3/m of steel.

3) The recommended minimum cover of reinforcement is:

3.0 cm5.0 cm-6.0 cm

At the outer surface if a waterproof membrane is provided;At the outer surface if it is directly in contact with the ground andground water;At the inner tunnel surface;For the tunnel invert and where water aggressive.

- 4.0 cm-5.0 cm5.0 cm

4) For lining segments, specifications 1), 2) and 3) .(n.r.) are not valid, especially if thesegmented tunnel ring is .(n.r.) outer preliminary lining. For detailing the tunnelsegments special attention should be given to avoiding damage during transport anderection.

5) Sealing against water (waterproofing sheets) may be necessary under the followingconditions:

. When aggressive water action threatens to damage concrete and steel;. When the water pressure level is more than 15 m above the crown;. When there is a possibility of freezing of ingressing water along the tunnel sectionclose to the portals;. When the inner installations of the tunnel must be protected.

6) In achieving watertightness of concrete, special specifications of the concretemixture, avoidance of shrinkage stresses and temperature gradients during setting,and the final quality of the concrete are much more important than theoreticalcomputations of crack widths.


8-Holland RallconsultVabfdeling Civide TeclIIIiclr.

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7) Temperature effects (tension stresses) may be somewhat controlled by working joints(as close as 5 m at the portals) and by additional surface reinforcement in concreteexposed to low temperatures.

8) An initial lining of shotcrete may be considered to participate in providing stabilityof the tunnel only when the long-term durability of the shotcrete is preserved.Requirements for achieving long-term durability include the absence of aggressivewater, the limitation of concrete additives for accelerating the setting (liquid acceler-ators), and avoiding shotcrete shadows behind steel arches and reinforcements.


--------Holland RallconsultVabfdding Civiele TedlDiclr:_To-.

6. Conclusion

6.1 General considerations

The need for scientific understanding of tunnel behaviour and the effects on the surrounding soilrose due to the occurrence of damage and the unfamiliar nature of the tunnelling environment.This led to a decrease in tunnel failures, support optimisation and an improved understanding ofthe processes which occurs in the soil as a result of excavation or boring. Tunnel design in softsoil is recognised as a completely different philosophy from rock tunneling and requires aseparate approach. A huge number of works in this field were performed by many authors andthe knowledge of the structural design of tunnels in soft soils is available everywhere.

Worldwide three different, global methods of structural analysis and design of tunnel lining areused: analytical, empirical and numerical methods.Analytical methods were first applied in a design using certain premises, but regardless of thoseassumptions, they gave explicit understandable solutions. Many of the more sophisticatednumerical methods, such as finite-element analysis, can handle the complexity of the soil and thetunnel, their mutual interaction through the contact surface and the general behaviour in acontinuum, but they need proper information input.

Empirical methods bypass this detailed information input by directly relating the support require-ments to soil properties which can easily be measured.

For the structural analysis and design of the tunnel lining it is possible to apply any of thoseapproaches but it is quite undeterminated which one will give the most realistic lining behaviour.

All approaches would satisfy three criteria:

1. Simplicity in using;2. Ability of modelling the most significant effects such as ground material properties,

forces, stresses, support geometry and properties;3. Ability of correct modelling of loading conditions and ground-structure interaction.

Engineers must be able to rely on a design model for tunnels which provides a suitable, safe andeconomical structure. To translate the reality of the structure into a mechanical-mathematicalengineering-model is difficult, even when correct solutions are given in literature. Duringmodelling the most important thing is whether the assumptions are valid in all cases (see fig. 1).

As a result it is necessary to sort and organise the various types of approaches in structuralanalysis and design of the tunnels. The working group of the International Tunnelling Association(established at the General Assembly in Tokyo 1978) led by Prof. Dr. H.Duddeck, started adifficult task. It summarised the information from each of the member nations about the designmodels used at the moment, in order to determine the relevant parameters of the tunnelling suchas concrete thickness, reinforcement, anchors, bolts, etc. The design model is shown in fig.7.

In 1985 Prof. Dr. H. Duddeck and Dr. ing. J. Erdmann presented the results of their investigationon design models for tunnels in soft soil, a comparative review of the progress in this field. Themain differences in the assumptions of the distinguished models are summarized. Although onlythe circular cross-section was investigated, the results are assumed to be also valid for non-circular cross-sections.


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According to the general conclusions from the investigations mentioned above, the models fortunnels in soft soil condition are internationally fairly well defined and are more developed thanthe models for tunnels in rocks.

The most important questions which still need to be answered are:

1. Which basic assumptions are applied to derive a model?2. Which basic assumptions are generally agreed upon and which are not?3. Which design criteria are relevant (displacement, forces, moments, safety, etc.)?

One of the most important reasons why, worldwide, the design model for soft soil tunnelling isso well developed, is that it uses a circular tunnel geometry with a simple interaction between thetunnel and the soil. Certain conclusions were drawn and almost the entire field of theoreticalwork was considered, such as: creep, shrinkage, effect of hinges, buckling, etc.

In 1988 the working group on "General Approaches to the Design of Tunnels" of the Interna-tional Tunnelling Association (of which The Netherlands are a member ), presented internationaldesign procedures for tunnels titled: "Guidelines for the Design of Tunnels".

In accordance with the "Guidelines for the Design of Tunnels", the definition of the procedurefor the structural analysis and design of tunnel lining depends on project specifications andcircumstances under which the tunnel has to be constructed. However the "Guidelines for theDesign of Tunnels" only gives us a general presentation of experience and knowledge.

The structural analysis and design of the tunnel lining, as we saw before, depends directly onspecific soil conditions in specific regions. Most of the design approaches are verified bymeasurements (in-situ) and laboratory tests, therefor the results and the procedures can be used inany specific analysis in tunnelling design.

International experience gives us a large number of differently constructed tunnels, each one forits own specific soil circumstances. A huge number of parameters which are important instructural analysis and design of tunnel lining differ widely from country to country. Therefor itis almost impossible to say which are generally valid.

In the enormous amount of existing world literature of tunnelling many useful data can be found,but it is mostly presented in general considerations with its own restrictions.

There is a broad pallet of structural systems available which are in accordance with the differentapproaches in structural analysis and design of tunnels in soft soil. They are mentioned below:


H&land RallWnsultVabfdeling Civiele Teclmiek--

1. The methods based on subgrade reaction:

Continuum models which are developed by Morgan, Muir Wood, Curtis, Peck etc., aredealing with both the circular cross section of the tunnel lining and the ground. The modelsconsider the loading of the lining caused by the passive soil deformation and active radialloading (see p.3.2.1; fig.9).

Bedded - Beam models or Action/Reaction models which are developed by a number ofGerman and Japanese authors (Duddeck,Yamaguchi,etc.). In the action-reaction model thestructure is submitted to direct loads, independent of ring deformations with the assumption ofa bond caused by friction.

For engineering the models are very simple to use; they clearly show the tunnel behaviour insand and the results from the calculations are close to in-situ measurements. The mainpossibly crucial disadvantage is the lack of experience in using these models for tunnel liningin the specific soft soil as found on the sites in the Netherland. However, basic calculations oftunnel lining could generally be performed following the "simplicity desired versus accuracyrequired" (p.3 .2.2.1; fig. 11).

2. Method based on relative stiffness solution (Einstein& Schwartz, Pender, etc.)The principle characteristic of this method is the consideration that the tunnel support, by theinfluence of the soil stresses, contracts and changes the shape. In turn support deformationswill affect the behaviour of the soil (p.3.3.1.; fig.23).

3. Convergence - confinement approachThe convergence confinement method is a procedure in which the interaction betweenthe ground and the lining behaviour is analyzed independently. The disadvantage of thisapproach is that it is only valid for circular cross sections of tunnels excavated in homogene-ous, isotropic and continuous soils (p.3.4.; fig.24).

4. Finite Element Method of modellingWith the Finite Element Method (PLAXIS, ANSYS, DIANA) it is possible to predict thetunnel behaviour in a soft soil package with a high probability and to control in detail othercalculations. The disadvantages of the Finite Element analysis are complexity and costs.Compared with the other models the final results are the most realistic (p.3.S.).

5. Observational methodWhen this method is applied modifications in the design of the tunnel lining is directly depen-dent on in-situ measurements. In combination with analytical and empirical methods, theobservational method takes corrections of in-situ results into account (p.S.4.S).

All approaches could be applied in the structural analysis and design of the bored railway tunnelsin the Netherland. At first the kind of problems which should be solved have to be defined.


8--Holland RailconsultVabfdeling Civielc Tcdmiok

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6.2. Problem definition

Generally, the soil properties at the sites of the bored railway tunnels in the Netherland are wellknown and they are obviously different from those in Germany, USA, Japan, France, etc. Ofcourse it is possible to find similarities of the soil properties here and abroad in a few parts alongthe lining.

The problem occurring in the structural analysis and design of the bored railway tunnel lining isthe fact that the tunnel is bored and constructed in two completely different types of soil:

1. Pleistocene sand; variable sand package (H > 2D )2. Holocene sand; variable soft soil package ( H < 2D ), in which:

H- Tunnel depth (measured from the top of the tunnel to the surface)D- Tunnel diameter

The general behaviour of the tunnel lining in the sand package is known from the literature. Themain question is how the tunnel behaves in the typical Dutch soft soil package. As can be seenin the research rapport and laboratory tests the Young's modulus of elasticity of the soil rangesfrom 500 to 3000 Knlm2. Considering the fact that E in sand is between 25000 to 50000 Kn/m2 itis logic that the results obtained by the same design method should be carefully treated. Most ofthe available models consider the cross section of the tunnel without accent on the longitudinaldirection.

There are only a few articles in the world literature, dealing with this problem. Probably, therewas no need for analyzing because of the available positive experience with the lining in theground with average stiffer ground characteristics and more homogeneous package constellations.

The essential difficulty of some locations in the Netherland is that the tunnel lies in bothpackages, which could behave, during the years, absolutely different from each other. Theinfluence of water level changing, ground embankment, free support settlements etc., couldprovoke different deformations of each soil package together with the tunnel lining in bothdirections.

The ground stresses change as well as their redistribution on the lining in longitudinal direction.If the average difference between the deformations is high, then the solution should be con-sidered carefully. Usually the second parallel tunnel has, in accordance with the availableexperience and the world literature, a favourable influence on the first one, but in this case itmight result negative effects to both of them.

Most of the available structural models analyze the tunnel as a single circular cross section ordouble coupled rings connected with the joints in the length direction. Solutions obtained fromthose models are not representing the response of the lining to the changing ground stress andinfluences mentioned here above therefor the ring forces, moments and deformations shouldprobably be changed too. As a matter of fact, the capacity of the tunnel lining segments and theability of joints to connect them are the most important parameters in lining behaviour.As a result serious research has to be done on the problem of the joints shape between thesegments in both directions. The forces in couple ring joints, caused by the influences mentionedhere above, could be so high that the standard existing type of joint, which have been successful-lyapplied on many projects, is not an appropriate measure for the bored tunnels in the Netherla-nd. The realistic behaviour mechanism of the tunnel lining has to be investigated, this alsoincludes the complexity of the realistic behaviour mechanism in longitudinal direction.


~.-Holland RailconsultVakafdelingCivit1cTcclmiekProduktgroep Tunnels

6.3. Possible solutions

Possible solutions to the difficulties mentioned are:

1. To bore the tunnels deeper in relative better soil conditions.2. To substitute the soft parts under the tunnels by a better one.3. To apply an exact, proper type of lining with adequate joints between the segments which

could respond on all influences.

It is also possible to divide the complete lining in longitudinal direction in a few parts, each withspecial flexible joints. The critical part of the lining should consist of e.g tangentially fixed orloose segments. The other part, in sand, should have a standard joint type.

Of course those solutions are more expensive in comparison with the available standard options.In the following chapter general points which are most important for design procedure as aconclusion of the whole literature study, will be discussed in short.


~.-Holland RallconsultVabfdeling Civicle Tcclmielr.

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6.4. The design procedure

6.4.1. Ground parameters and primary stress field

The ground parameters playa very important role in tunnel design. The various ways in usingthe parameters in different countries show, that they have to be chosen very carefully by theexperts and especially in consultation with the responsible design engineer. Site investigationsand ground characteristics vary from country to country, but in general (the necessary features ofsoils are given in chapters: 2.; 5.3.1.1; 5.3.2.1. and in table.2.) some of them are unavoidable:

unit weights y,- Poisson's coefficient u,

Friction angle <p,Cohesion c,Shear strength t,Young's modulus of elasticity Es.Stress ratio (Jh/(JyParticle size distribution

Those parameters mentioned here above are determined in accordance with the country standardswhere the tunnel has been drilled. This means, that a complete balanced set of parameters, inaccordance with the "Nederlandse norm (NEN)", should be taken as a close realistic package forthe structural analysis and design of the bored tunnels in the Netherland.

For instance, the vertical stresses or vertical ground pressure, were generally referred to as a fulloverburden by many authors in their analysis of tunnelling (p.2.4.; p.3.2.2. and table.2):

Oy = Y H

The difference appears in assuming a horizontal ground pressure and coefficient Ko (relationbetween vertical and horizontal ground pressure).

0 h = Ko °y

vKo = 1-= v

-(Jy - vertical ground pressure-(Jh - horizontal ground pressure

-Ko - the relationship between them

Mostly, Ko which has a crucial influence on the results, takes a value between 0,3 and 0,5 andsometimes 1,0 or greater. This should be considered properly in the analysis in accordance withthe available "Nederlandse Norm".

6.4.2. Structural system

Duddeck's [37] bedded beam model with and without hinges could be applied as a structuralsystem for the tunnel linning. This is the action-reaction model in which the structure issubmitted to direct loads, independent of ring deformations assuming the bond condition asfriction. It is very simple to use this model for engineering purposes.


8-.Holland RallconsultVabfdeliDg Civit1c TcclmieJcProduktgroep TuDDeIB

It shows the tunnel behaviour in sand and the results from the calculations are close to in-situmeasurements (See p.1.2.; p.3 .2.2.; p.3 .2.3.; [37]).

The main problem is that no experience was gained by using this model for tunnel lining in softweak ground as can be found in The Netherlands. However, basic calculations of tunnel liningcould be done following the "simplicity desired versus accuracy required" method.

a = yHv @] ~=KrUI

[E]CInIrJ Kr = var. or c~nst.

I / I

~Mu

a =K'a'h 0 v

[IIIIJ]- avradialdisplacement

ground reactionpressure

normalforces

bendingmoment

fig.58

The distribution of the bedding constant is given on fig.7 (p.2.3.4.) and the value should be:

Eks = seq

R

where:Eseq - equivalent "oedometer" modulus of elasticityR - tunnel radius

Simultaneous calculation should be performed with the Wayss & Freytag model [15] (p.3.2.2.2,fig. 14) as an additional prove analysis. This model for a tunnel in sand, gives the best compara-tive results between calculations and on-situ measurements. Three-dimensional effects of tunnellining through 2 coupled rings, can be analyzed but with some restrictions. As we can see in theliterature, a model gives the results which are very close to the measurement data, but only insand, not in a weak variable soil package.

The tunnel lining in weak soil package should be calculated by Finite Element Method (e.i.:PLAXIS, ANSYS 5.0, p.3.5.4.1., p.3.5.4.3.) to approve, correct and to control the resultsobtained by the analysis mentioned here above. The reasons why tunnels in a soft weak soil haveto be analyzed are obvious, because there is no experience yet with "Boortunnels" in TheNetherlands (see paragraphs: 2.2.; 3.5.; 4.; 5.4.1. and further 6.2.8.). With Finite Element Methodit is possible to predict the realistic tunnel behaviour in a soft weak soil package and to control indetail other calculations. The disadvantage of Finite Element analysis is its complexity and costsbut in comparison with the other models the final results are closer to reality.


HOlland RaIk;mSUItVllklfdcJiDa:Cividc Tcclmiek

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6.4.3 . Loadings ( p.1.2.; p.2.4; p.3.; p.5.4; )

There are many variations possible in assuming the type of load that should be applied intunnelling design. The crucial, main loads considered for structural analysis and the design oftunnels by almost all authors are:

1. Vertical earth pressure,

p = y Il'

I

-'-'-:::-

n'-'-'~:~:~::'-'

'-"'"max.

/::::::::::::~:~._. :~:

::::::::::

.1./ P/~r

{UiL__-".

","

"""

""',

" -'_,1

','III

''"'

H

D

fig.59

2. Horizontal earth pressure,[The active soil pressures on the lining are assumed to be equal to the primarystresses (p.1.2.c.)],Water pressure,Own weight of lining,Surface load,Live load.

3.4.5.6.

The other types of loads are applied in accordance with the specific project requirements in acountry where the tunnel was drilled. Additional loadings, according to many authors, which areimportant for segmental lining in detailed analysis are listed below:

1.2.3.4.5.67.8.9.10.11.12.

Grout pressure,Shield ram loads,Jack force,Air pressure,Temperature,Creep and shrinkage,Dead load, fulling ("bed"),Impact load,Interval loads,Special ground and water movement,Effects of adjacent tunnel,Fire influence.

For some of these loads the values and influences are given in literature (i.e. 11, 12), but for therest detailed information is not available.(see p.4. and [27])


-------Holland RailconsultVabfdeling Civie1e TccboiekProduktgroepTuluJeIs

6.4.4. Calculation criteria for determining the lining (p.7)

Most of the authors agree on the calculation criteria for determining the tunnel lining. They are:

1.2.3.4.

Moments and forces,Deformations (global and local),Stresses,Three-dimensional effects (segments).

Dimensioning of lining segments were done all around the world in accordance with the differentnational standards. There is no special recommendation for lining dimensions so, it could be donefor the bored tunnels in the Netherland following the Dutch Standards [Nederlandse Norm(NEN)] and the Guidelines Dutch Railway (Richtlijnen Nederlandse Spoorwegen).

6.4.5. Safety concept (p.7; p.3.; table.2)

Some of the authors assumed a global safety factor for tunnelling, some of them a partial safetyfactor, but most of them were following their own national standards.

In most cases the allowable stresses, limited deformations and rotations are the criteria fordeciding whether the constructive segments in tunnel lining are sufficiently strong and safe.

6.4.6. Distance between the tunnels (p.4.)

To provide stability and to avoid unexpected behaviour of tunnels the distance between thetunnel axis should be 2 tunnel diameter. This is the conclusion in many analyses, which weredone for specific projects, in different countries and under different ground conditions. It seemsthat when the distance between the tunnels is less than one tunnel diameter, the redistribution ofthe bedding constant should be considered carefully. This is because during the drilling of asecond tunnel the horizontal stresses are going to increase and disturbed soil around the tunnelscould not provide the expected uniform reaction. One of the possible redistributions of thebedding constant is shown in fig.60.

Some research has been done by Duddeck and Soliman, but again for tunnels in sand. There isno information on tunnels in soft, weak, soil package. The problem should be analyzed by usingthe Finite Element Method with carefully determined ground parameters.

+--E. Ia<D. I D

h<D

k = E&/R

a. = y h

ax = Koaz

Ko'" 1

fig.60


8--Holland RailconsultVabfdelina: CiYide Tcdmick

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6.4.7. Additional effects on tunnel lining (p.3.2.3.)

Large deformations, nonlinear behaviour of ground and lining, plasticity, rheology wereconsidered in basic calculations in a few countries. The influence of those effects should beanalyzed in further calculations to predict the unexpected behaviour of tunnel lining.

6.4.8. Three dimensional Finite element analysis (p.3.5.4.3.)

This is a very important part of structural analysis and the design of tunnel lining. Through thissort of calculation it is possible to analyze and to obtain some more detailed results which areprobably closer to the realistic behaviour of tunnel lining. To know how the lining is going tobehave in a soft, weak soil package is very important, because there is still no informationavailable.

The scope of results that could be obtained by three-dimensional Finite Element Analysis is quitelarge. In general, with one part of FEM modelling we can find the following answers to:

1.2.3.4.5.6.7.8.9.10.11.12.13.14.15.

Forces in segments and joints,Deflections and deformations,Influence from imperfections of segments and their placement,Shape of joints,Type of bolts,Behave of axial and tangential connections at the same time,Type and behave of waterstop,Optimization the number of segments,Segments behaviour under the asymmetric loadings,Nonlinear effects,Influence of adjunct tunnel,Lining behave in longitudinal direction,Lateral connections,Start effects,etc ..

The main consideration, based on the existing available literature on structural analysis anddesign of tunnels, leads to the conclusion that first simple models should be applied with allnecessary parameters and then control and justify the obtained results with more detailedanalyses.

Important points for attention are how the linings behave and which philosophy should beapplied in a structural analysis and design. This to predict the kind of influences the tunnels aresubmitted to when large diameters are applied in the typical Dutch soil.

This gives a flavour to the projects of bored railway tunnels in the Netherland which can lead tonew dimensions in approach for boring tunnels in these particular circumstances. Manyinvestigations, studies and researches have to be done to predict the tunnel lining behaviour andto avoid unexpected failures.

Of course this does not imply that the most expensive solution is the best one. If the existingmodels are applicable to the Dutch soil, then we have another verification of existing theoriesand available approaches. The research could show that there is something which we should payattention to and (anyhow) will be an additional step forward in the general design approaches.


-------Holland RallconsultVabfdcling Civide T~ekProduktgroep Tunnels

A tunnel lining is the final product of a complicated process to meet the users demands. In someprojects the costs of the lining reach the sum of more than 35% of the total costs. Because of theinterrelation of so many influences there is an existential need to consider the problems of tunnellining design with special care. It is obvious that an effective and unique philosophy can not beestablished for all types of tunnels in all kinds of soil, but it is clear that some of the theories andcombinations give an appropriate background and a practical orientation to find an optimalsolution in a specific case. Experience still is of considerable importance but new knowledgegained by the numerical approach rise to the idea that tunnel behaviour can be predicted.


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Hiilland RalkODsultVabideling Civiele TcclmiekProdukt.groep1'ua1M1s


--------Holland RallconsultVabfdding CiYiele TechojekProduktgroep1'uDno1s

Appendix.1

7. References


--------Holland RaIlconsultVabfdeliDg Civie1e TecbaiekProduk!groep Tunnels


-------Holland RallconsultVabfdeling CiYicle TcclmiekProdukIgroq> 1'um>eh

7. References

International Recommendations on Structural Design of Tunnels

1. - Views on structural design models for tunnelling: Advances in tunnelling technologyand subsurface use (1982)

- ISRM recommendations on site investigation techniques (1985)

- ISRM committee on field tests,- document nr. 1 - Suggested method for determining shear strength- document nr. 2 - Suggested method for rock bolt testing

- ISRM committee on laboratory tests; ISRM committee on swelling rocks- document nr. 1 - Suggested methods for determining the uniaxial compressive strength

of rock materials and point load strength index- document nr. 2 - Suggested methods for determining water content, porosity, density,

absorbtion and related properties, swelling and slake durability index propertiesInternational society for rock mechanics

2. - Australian standard 1726 - S.A.A. Site investigation code- Australian standard 1289 - Methods of testing soils for engineering purposes

Australia

3. - ONORM B 2203 - Untertagebaunorm, richtlinien und vertragsbestemmungenrkvertragsnorm

- Projektierungsrichtlinien fur geotechnische arbeiten. RVS 9240 u. 9241,Forschungsges. Srassenwesen (1977)Austria

4. - Recommendations for design of underground openings in rock. Tunnelbau- Taschenbuch1980, Gluckauf-verlag, Essen (1980), pp. 157-239

- Recommendations for the analyses of tunnels in soft ground (1986). Bautechnik 10 (1980),Berlin, pp. 349-356

- Recommendations for the concrete lining of tunnels in soft ground (1986). Bautechnik 10,(1980), Berlin, pp. 331-338Germany

5. - Usual calculation methods for the design of tunnel linings- Presentation of the tunnel construction method with immediate support by shotcrete

and bolting- Recommendations for conditions of use of bolting

Tunnels et ouvrages souterrains, special issue (1982), pp. 32-123- Recommendations for use of convergence - confinement method.

Tunnels et ouvrages souterrains 73, (1986), pp. 18-38- Recommendations for the selection of tunnel support

Tunnels et ouvrages souterrains, (1985), pp. 80-97France


--------.Holland RallconsultVabfdeliJlg Civiele Teclmielr:ProduJrtgroep1'unno1a

6. - Standard specifications for tunnels:- Mountain tunnelling method, 1986- Shield tunnelling method, 1986- Cut-and-cover method, 1986

Tunnel engineering committee, Japan society of civil engineering, Japan tunnellingassociationJapan

7. - Recommendation SIA nr. 199: Etude du massif rocheux pour les travaux souterrain. 1975- Norme SIA nr.198: Travaux souterrains (advancement a l'explosif) 1975- Recommendation SIA nr. 1988/1: Construction de tunnels et de galeries en rocher au

moyen de tunneliers 1985Switzerland

8. - British standard 1377. Methods of test for soils for civil engineering purposes, 1975- British standard 5930. Code of practice for site investigation, 1981

British Standard Institution

- Craig, R. N. and Muir, A. M. A review of tunnel lining practice in the United Kingdom.TRRT Supplementary rapport nr. 335, 1978

- Tunnelling waterproofingCIRIA rapport nr. 81, 1979

- Dumbelton M. J. and West G. A. A guide to site investigation procedures for tunnelsTRRT laboratory report nr. 740, 1976United Kingdom

9. - Guidelines for tunnelling design.O'Rourke. ASC Technical Committee on tunnel lining design. Technical council onresearch.American society of civil engineersU.S.A.


IReferences

I I

[:]Title

I

Author

I

Editor

I

YOM

I

1 De boortunnel dichtbij. Samenvat- J.Jonker Nederlandse Spo- 1991ting studies NS Schildboortunnel orwegen

2 Some consideration for tunnel Dr.ing.F .Rodriguez Rapport, Catholicdesign, p(353-356) Roa University of

Chile, Santiago

3 The present and future of Dr.ing.G.Fukuchi Tunnelling and 1991mechanized tunnel works in soft underground spaceground p(175-183) technology, vo1.6

Pergamon

4 Gibt es eine NOT? Fehlkonzepte Prof.Dr.K.Kovari Vortag anHisslich 1993der Neuen Osterreichischen Tun- des Rabcewicz-nelbauweise, p(l6-25) Geomechanik

Kolloquium inSalzburg

5 Tunnelling using earth pressure ba- G.R.Flint Tunnelling and 1992lance (EPB) for the Boulac Spine underground spaceSewers of the Greater Cairo waste- technology, vol.4water project, p(415-424) Pergamon

6 Tunnel excavation with the world K.Hashimoto Rapport, Publiclargest slurry shield, p(45-51) T.Takayama Works Bureau,

Osaka, Japan

7 Analysis of lining for shielddriven Prof.Dr.H.Duddeck Rapport, Instituttunnels, p(235-243) rur Statik, TU

Braunschweig

8 Tunnelling machines in soft Dr.ing. Tunnelling and 1991ground: a comparison of slurry and S.Babendererde underground spaceEPB Shield Systems, p(l69-17 4) technology, vo1.6

Pergamon

9 Statische Berechnung erdiiberdeck- W.Backes Bauingenieur, 1994ter Beigesteifer Rohre mit Defor- nr.69mationsschicht, p(231-235)

10 Tunnelauskleidungen mit Stahlbet- Dr.ing. T.Baumann Bautechnik 69 1992ontiibbingen, p(lI-20)

II Two- and three-dimensional ana- E.Soliman Tunnelling and 1993lysis of closely spaced double-tube H.Duddeck underground spacetunnels, p( 13-18) H.Ahrens technology, vol.8

Pergamon

8-.HollandRailconsultVabfdcling Civiele Teclmiek

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1'uDDdo


nr. Title Author Editor Year

12 Simplified analysis for tunnel Sup- Prof.Dr .H.Einstein Journal of the 1979ports, p(499- 518) Mr. C.W.Schwartz geotechnical engi-

neering division

13 Interaction of tunnel linings and Dr.F .El-Nahhas Tunnelling and 1992soft ground, p(33-43) F.El-Kadi underground space

technology, vol. 7Pergamon

14 Calculating the support load of Dr.ing.M.Kopf Tunnel 1990deep-seated tunnels and roads withthe aid of the silo formula,p(92-1 02)

15 Reinforced concrete segments as H.H.Lingenfelser Wayss&Freytagone-pass lining for shield-driventunnels, p(251-253)

16 Statik der Tunnel im Lockergest- Prof.Dr.H.Duddeck Bauingenieur 58 1983einein Vergleich der Berechnungs- Dipl.ing.J.Erdmannmod.p(407-414)

17 Empfehlungen zur Berechnung von Prof.Dr.H.Duddeck Die Bautechnik 10 1980Tunneln im Lockergestein (1980),p(349-356)

18 Zur Dimensionierung von Tunne- Prof.Dr.H.Ahrens Die Bautechnik 9 1982lausbauten nach den "Empfehlun- Dr.ing.E.Lindnergen zur Berechnung von Tunneln Dr.ing.K.H. Luxim Lockergestein (1980), p(303-311)

19 Soil mechanics aspects of soft J.H.Atkinson Ground Enginee- 1981ground tunnelling, p(20-26) R.J.Mair rmg

20 Shield tunnels R.S.Mayo Tunnel enginee- 1982ring handbook

21 The art of tunnelling Prof. Dr. .K. Szechy Akademia Kiado, 1967Budapest

22 -Tunnelling methods: soft ground B.N. Whittaker Tunnelling 1990conditions, p(69-92) R.C. Frith The Institution of-Stresses and displ.associated with Mining and Me-excavation of tunnels, p(36l-378) tallurgy-Design of tunnels: soft ground,p(379-405)

23 Booren van tunnels voor rail-en werkgroep KIVI, Tunneltech- 1993wegverbindingen niek ondergronde

bouwen

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24 Tragverhalten yon P.JanBen Dissertation, TU 1983Tunnelausbauten mit BraunschweigGelenktii bbings

25 Water leakages in subsurface Dr.ing.A.Hack Tunnelling and 1991facilities:required watert- underground spaceightness,contr.matt.end methods of technology, vol.6redevelopment, p(273-286) Pergamon

26 Convergence-confinement method Prof.Z.Eisenstein Tunnelling and 1992in shallow tunnels, p(343-346) Dr.P.Branco underground space

technology, vol.7Pergamon

27 Structural analysis for tunnels Prod.Dr.H.Duddeck Tunnelling and 1992exposed to fire temperatures, Dr.ing.H.Ahrens underground spacep(19-24) technology, vol. 7

Pergamon

28 Foundation analysis and design Prof.Dr.J.Bowles McGraw-Hill 1982Book Co.

29 De geprefabriceerde tunnelseg- Cement nr.8 1979menten voor Antwerpse metrop(459-461)

30 Geboorde tunnel onder Hartelka- Cement nr.6 1988naal, p(12-20)

31 Design en construction of Seg- J.A.Richards Tunnelling and 1979mental Lining for a Machinebo- F.Remmer underground spaceredtunnel:Delivery tunnel north, J.C.Sharp technology, vol.9Lesotho Highlands Water Project, Pergamonp(91-99)

32 Structural analysis and design Geilord & Geilord McGraw-Hill 1988Book Co.

33 Technische grondslagen voor bou- Nederlands normali- CUR 1990wconstructies, TGB 1990 satie instituut

34 Ondergronds overwegen en onder- Prof.ir.J.Stuip Civiele Techniek 1994gronds bouwen, p(8-11) nr.2

35 Vergleich ebener und Entwicklung J.Erdmann Dissertation, TU 1983raumlicher Berechnungsverfahren Braunschweigfur Tunnel

36 Betrag zur statischen Berechnung Prof.Dr.J. Spang Die Bautechnik 11 1980yon Tunnelauskleidungen, Dr. ing.H.Fleckp(361-367) Prof.Dr.G.Sonntag

u-Holland RallconsultVabfdelina: Chie1e Tcchniek

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37 Views on structural design models Prof.Dr.H.Duddeck International 1982for tunnelling, p(153-228) with working group tunnelling

association

38 Guidelines for the design of tun- Prof.Dr.H.Duddeck Tunnelling and 1988nels underground space

technology, vo1.3Pergamon

39 On structural design models for Prof.Dr.H.Duddeck Underground 1985tunnels in soft soil Dr.ing.J.Erdmann space

40 Design of Storrebelt Railway Tun- A. Odgard Tunnelling and 1994nel G. Bridges Underground

S. Rostam space technology,vol9, nr.3Pergamon

41 Principles of tunnel lining design T.R. Kuesel Tunnels & 1987Tunnelling, April

42 Boston Harbor Outfall Tunnel: An R.G. Sherman Tunnelling and 1994Environmental Imperative M. Gay Underground

W. van Ast space technology,K.S. Chin vol9, nr.3

Pergamon

43 Prefabricated linings for metro- P. Lunardi Options for 1993politan underground railway tun- E.M. Pizzaroti tunnelling 1993nels constructed using mechanized G. Cassani H. Burgershields M. Rivoltini

44 Dowelled segments for tunnel H. Wagner Options for 1993linings tunnelling 1993

H. Burger

45 Beispie1e zum Stand der B. Mandl TIS 12/90 and 1991Schildvortriebstechnik in D. Handke 1/91Deutschland, I, II

46 Premetro, Koncept en uitvoering A. Wittemans Het Ingenieursb-van Antwerps Linkeroeverprojekt E. Hemerycks lad

K. MeuwesJ. Maertens

47 NEN 6071 - Rekenkundige bepali- Nederlandse Nor- 1991ng van de brandwerendheid van malisatie Instituutbouwdelen

48 Tunnelauskleidungen mit Stahlbet- T. Baumann Bautechnik 1992, 1992ontiibingen HI, Sl1

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49 Stahlfaserpumpbeton, erstmalige R. Hoffmann Eisenbahningeni- 1992Anwendung des neuen Baustoffes G. Wilhelm eur, H.5bei der DB im LiitgendortmunderS-Bahn-Tunnel

50 Nouveau terminus our maggaly La vie du rail, 1994nr.2464

51 Eindrapportage studiereis Japan Ministerie van 1993Verkeer en Water-staat, ProvincieZeeland

52 Tunnelling in a soft ground W.H. Waard General report 1981M.J. Pender from 10th SSMFE

congres, Stocholm

53 Tunnelling '91 G.E. Pearce ITA, BTS 1991D.R. Donaldson International sym-Dr. J. Temporal posiums, Inst. of

Mining and Me-tallurgy, ElsevierApplied Science

54 Stress-strain fields at the S. Keilbassa Rock Mechanics 1991tunnelling face-three-dimensional H. Duddeck and rock engineer-analysis for two-dimensional tech- mgnical approach

55 Tunnel engineering handbook J.O. Bickel Van no strand rein- 1982T.R. Keusel hold company

56 Principles of tunnel lining design T.R. Keusel Tunnels and 1987tunnelling

57 Earth pressure acting on shield A. Inokuma ISOUC 1994driven tunnels in soft ground T. Ishimura New Delhy

58 Aanleg van een geboorde duiker Grondmechanica Rapport 1994te Aarle-Rixter Delft CO-312870

59 Inventarisatie geotechnische ont- Grondmechanica Rapport 1994werpaspecten boortunnels Delft CO-348670

60 Towards new worlds in tunnelling L.Vietez-Utesa Proceeding of the 1992L.Montanez-Cartaxo international cong-

res towards newworlds in tunn-elling, Accapu1co

8--Holland RallconsultVabfdeling CiYie1e Teclmict

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61 Police probe repeat Munich tunnel Construction 1994breach Today, October 94

Thomas Telford

62 London tunnel collapses Engineerings news 1994record, McGraw-Hill constructionweekly, Oct.31

63 A contribution to the analysis of H.D Morgan Geotechnique 11 1961stress in a circular tunnel, or. 1pp(3 7-46)

64 The circular tunnel in elastic A.M. Muir Wood Geotechnique 25 1975ground, pp(115-l27) or. 1

65 Correspondence on Muir Wood, D.l Curtis Geotechnique 26 1976A.M.: The circular tunnel in elas-tic ground, pp(231-237)

66 State of the art of soft ground R.B. Peck RETC Proceed- 1972tunnelling, pp(260-286) A.J. Hendron ings, vo1.1, Illinois

B. Mohraz

67 Spannungen in schildvorgetrieben- H. Schulze Beton und Stahlb- 1964en Tunneln, pp(169-175) H. Duddeck etonbau

68 Tunnel design consideration: Ana- R. E. Ranken Raport for U.S. 1975lysis of stresses and deformations J. Ghaboussi Dept. of transpor-around advancing tunnels tation, UILU-

ENG75-2016

69 Comprehensive method for shal- z. Eisenstein Proceedings of a 1985low tunnels, pp(375-39l) A. Negro conf. on Under-

ground structuresin urban areas,voll, CSSR

70 The behaviour of tunnel in stiff F. El-Nahhas Ph.D. Thesis, Dept. 1980soil of CE Univ. of

Alberta EdmontonCanada

71 Comparison of design methods for Y. Yamaguchi Collective reports 1978segmential ring H. Kawata of structural

M. Yamazaki design office 55,Japan nationalrailways

72 Design recomendations for University of US Department of 1983concrete tunnel linings, Vol.l&2 Illinois Transportation

8-Holland RallconsultVabfdcling Civiek Tc:clmieJr:Produkt.groep TunnmK


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