Madrid Tunel

8/17/2019 Madrid Tunel

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Prediction and analysis of subsidence induced by

shield tunnelling in the Madrid Metro extension

Manuel Melis, Luis Medina, and José Ma Rodríguez

Abstract: The development of tunnelling projects under heavily populated cities has been rapidly increasing around theworld during the last decades. Since tunnel construction can have disastrous effects on buildings, structures, and utili-ties near the excavation, construction methods have necessarily to provide maximum safety inside and outside the tun-nel. To predict and correct dangerous ground movements due to the tunnelling works, the authors developed anumerical model to simulate the earth pressure balance (EPB) excavation procedure and injection to complement somedeficiencies found in previous analytical or empirical subsidence estimating procedures. This model takes into accountthe full excavation sequence and has been validated by a large amount of monitoring data from the previous MadridMetro extension. In the present paper, several predictive methods are used to predict the ground movements generatedduring a new Madrid Metro extension project consisting of 48 km of tunnel (1999–2003). At the end of the works theresults will be compared with data from monitored sections placed in all five cities linked by the extension. Conclu-sions about the applicability and accuracy of the methods will be established with the aim of helping researchers and

engineers in their future projects.Key words: ground movements, monitoring, numerical modelling and analysis, settlement, tunnels.

Résumé : Le développement de projets de creusage de tunnels sous des villes densément peuplées s’est accru rapide-ment dans le monde au cours des dernières dizaines d’années. Mais la construction de tunnels peut avoir des effets dé-sastreux sur les bâtiments, structures et équipements près des excavations, et en conséquence, les méthodes deconstruction ont nécessairement progressé pour fournir un maximum de sécurité à l’intérieur et à l’extérieur du tunnel.Afin de prédire et corriger les mouvements dangereux de terrain dus aux travaux de creusage de tunnel, les auteurs ontdéveloppé un modèle numérique pour simuler la procédure EPB d’excavation et d’injection pour compenser certainsdéfauts trouvés dans les procédures antérieures d’évaluation analytique ou empirique de l’affaissement. Ce modèleprend en compte la pleine séquence de construction et a été validée par une énorme quantité de données de mesuresprovenant de la prolongation antérieure du métro de Madrid. Dans le présent article, plusieurs méthodes de prédictionont été utilisées pour prédire les mouvements de terrain générés au cours du projet de prolongation du métro de Ma-drid sur 48 km de tunnel (1999–2003). À la fin des travaux, les résultats vont être comparés avec les données de sec-

tions instrumentées placées dans les cinq sites reliés par la prolongation. On propose des conclusions sur l’applicabilitéet la précision des méthodes dans le but d’aider les chercheurs et les ingénieurs dans leurs projets futurs.

Mots clés : mouvements de terrain, mesures, modélisation et analyse numériques, tassement, tunnels.

[Traduit par la Rédaction] Melis et al. 1287

Introduction

A vast amount of tunnelling work that has taken placearound the world in recent decades is related to mass transpor-tation projects in overpopulated cities. Los Angeles, New York,Boston, London, Paris, Madrid, Rome, Amsterdam, Cairo, Sin-gapore, Hong Kong, Beijing, Tianjin, Algiers, Sao Paulo, Bue-

nos Aires, Mexico City, Caracas, and many others are just asmall sample of the cities that are extending or creating theirunderground transportation network. This trend is very recent,and it is foreseeable that in the next decades undergroundtransportation projects will increase to levels still unknown.

On the other hand, high speed railway transportation is alsoincreasing around the world. The success of the first line, To-kyo–Osaka in Japan in 1964, even with its relatively lowspeed of 200 km/h, brought the Paris–Lyon TGV, leading tothe construction of the European high speed network, whichincludes countries such as France, England, Spain, Belgium,Holland, Germany, and Italy. The layouts of these new 300–

350 km/h railways, with their low longitudinal slopes (1.5%)and enormous radii (7–9 km), necessitates the construction of long base tunnels in order to cross the mountains or the sea(e.g., the recent tunnels of La Manche (50 km) between Eng-land and France; the Guadarrama near Madrid (30 km); the

Can. Geotech. J. 39 : 1273–1287 (2002) DOI: 10.1139/T02-073 © 2002 NRC Canada

1273

Received 11 May 2001. Accepted 15 May 2002. Published on the NRC Research Press Web site at http://cgj.nrc.ca on6 November 2002.

M. Melis1 and L. Medina. Department of Geotechnical Engineering, University of La Coruña, La Coruña, Spain.J.Ma. Rodríguez. Department of Geotechnical Engineering, Madrid Polytechnical University, Madrid, Spain.

1Corresponding author (e-mail: [email protected]).


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future Vignemale (40 km) crossing the Pyrinees from Spainto France; the new St. Gotthard in Switzerland (57 km); orthe new Loetschberg also in Switzerland (42 km)). In sum-mary, the authors believe that tunnelling projects will have anever-increasing importance in the near future. Pollution-freemass transportation and the reduction of surface traffic, aswell as new sewage and water supply projects, are forcing

city administrations to use more of these solution types. How-ever, designing and building tunnels, especially in soils andsoft rocks, is one of the most difficult geotechnical projects toundertake. Tunnels are usually located under densely popu-lated zones, and their construction can have disastrous effectson the buildings above. There are many recent examples of collapses and accidents due to the construction of tunnellingprojects, and the last report of the Health and Safety Execu-tive of England (HSE 2000) summarized 154 collapses, witha high number of human lives lost.

The first tunnelling shield machine with full face protec-tion, i.e., a slurry machine, is believed to have been designedby John Bartlett, from Mott-Hay-Anderson of England inMarch 1965 and used in a water supply tunnel project under

the Thames. Further developments of this idea were made inGermany, where Wayss-Freytag developed the so-calledHydroshield system, which was used successfully in Ham-burg, Berlin, and Amberes. Earth pressure balance (EPB)machines first appeared in Japan in the late 1970s and wereintroduced to the geotechnical community by Abe et al.(1978) and Endo and Miyoshi (1978). In the last 30 yearsthe concept of tunnelling design and construction haschanged drastically, and today most of the tunnelling pro-

jects, either in hard rock, in soft rock, or in soils, are beingdesigned and built using this new type of shield, with eitherthe slurry or EPB technologies.

In some sectors of the geotechnical community there isstill, however, a fierce resistance to the use of shields in tun-nelling projects. The supporters of methods such as the NewAustrian Tunnelling Method (NATM), the precuttingmethod, or others, such as the ADECO method (acronym of the Italian for analysis controlled deformation in rocks andsoils), are still insistent on their safety, low cost, and speed.

The Regional Government of Madrid successfully de-signed and built 38 km of 9.4 m diameter tunnels in softground and 38 stations for the Madrid Metro extension in

just 40 months, between September 1995 and February1999, at a cost of 44 million $US per km without any acci-dent or collapse. This was achieved using EPB machines be-cause the NATM or other open face tunnelling methods wereabsolutely prohibited.

This absolute prohibition, perhaps the first case ever, wasspecified by the senior writer responsible for the technicaland economical aspects of the project. During the same pe-riod, other cities using the open face methods of tunnellingfor similar projects spent in excess of 44 million $USper km, needed more than 10 years for the design and con-struction of tunnel lengths less than 20 km, and some of them reported a heavy record of collapses and accidents. InNovember 1999 the World Bank described this project ashaving an “evidently superb manner of procurement and im-plementation.”

After the 1995–1999 extension, the Madrid Metro net-work had reached a total length of 176 km with 197 stations.

Another huge extension (METROSUR) was decided upon in1999 by the Regional Government (Comunidad de Madrid),consisting of a further 48 km with a 9.4 m diameter tunnelconnecting five cities southwest of Madrid. The design of these tunnels, also located under heavily populated urban ar-eas, necessitates the prediction of the subsidence that willoccur during construction, so that the stability of the build-

ings and other construction located above the tunnels can beproperly studied, analyzed, and guaranteed.This work consists of two parts. The first part deals with

the prediction of the soil movements caused by the tunnel-ling works of the 1999–2003 Madrid Metro extension (thispaper). The second part, to be published after the tunnellingworks are finished, hopefully in 2003, will compare mea-sured soil movements with those predicted in this paper.

The METROSUR extension project

METROSUR was designed as a new underground circularline some 40.5 km in length (Fig. 1) that will connect fivecities located southwest of Madrid (Alcorcón, Móstoles,

Fuenlabrada, Getafe, and Leganés). The tunnel will pass un-der urban areas, where 27 new stations are being built, sothat the system will be used as local underground transportin each city.

The ring established by METROSUR is 40.5 km in lengthand will be linked with the present Madrid Metro networkthrough the extension of Line 10 up to Alcorcón, where theconnection between both lines will be placed. In each citythe new circular line connects through interchange stationswith the regional railway network of commuter trains. Thus,other cities, like Parla or Pinto, may join the METROSURsystem. The location of the stations takes into account notonly the service of the most populated areas but also the po-sition of the university zones, hospitals, and shopping cen-tres. It is foreseen that 140 000 passengers per day will usethe system during the first year of service.

Selected subsidence prediction methods

It is difficult to use most subsidence estimation methodsfor prediction purposes. In fact, they employ several parame-ters that are not always easy to estimate before the start of tunnelling works

(1) ε (radial strain), α (a parameter), and ρ (relativeovality) in Sagaseta’s and Verruijt’s methods;

(2) Ψ (an empirical parameter) and η (a parameter) inOteo’s method;

(3) g (undrained gap parameter) in Loganathan’s method;(4) V S (volume loss) and i (position of the point of inflec-tion in the normal distribution curve) in Peck’s method; and

(5) K 0 (coefficient of earth pressure at rest) and the soilchamber pressure on the tunnel face in the Romo (Romo1997) and Medina-Melis methods.

When a lot of field data is available (V S values for exam-ple), an important part of this is either contradictory or doesnot allow for easy extraction of accurate values. Further-more, in most cases they were obtained from very diverseconstruction techniques, geotechnical conditions, tunnel ge-ometries, etc. (and are also different from those correspond-ing to the analyzed problem). As a consequence, a wide

© 2002 NRC Canada

1274 Can. Geotech. J. Vol. 39, 2002


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range of possible settlement predictions may be obtainedfrom each method.

The settlement estimation corresponding to this paper willbe made with the following methods.

(1) The Sagaseta methodThis method is based on the analytical solution of the sub-

sidence given by Sagaseta (1987) and later extended bySagaseta (1988) and Uriel and Sagaseta (1989). The surfacesettlements are given by the following expressions:

[1] δπz

S( ) x V H x H

=+2 2

[2] δπz

S( ) y V

H

y

y H = +

+

2

12 2

where δz( x ) is the vertical soil movement in the orthogonalplane to the tunnel axis, x is the distance to the centre line,δz( y) is the vertical soil movement in the longitudinal plane,and y is the distance to the tunnel face. Finally, V S is the vol-ume loss (ratio of the volume of the surface settlement

trough per metre run to the excavated area, usually ex-pressed as a percentage), and H is the tunnel axis depth.

Later improvements to the method were proposed byGonzález and Sagaseta (2001)

[3] δ ε ρα

αz( )

( ) x R

R

H x

x

x =

+ + −

+

−

2 11

1 11

2 1

2

2

2

where R is the radius of the tunnel, ε is the radial strain, x isthe relative distance to the tunnel axis ( x / H ), α is a parame-ter, and ρ is the relative ovality

© 2002 NRC Canada

Melis et al. 1275

Fig. 1. METROSUR extension project.


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[4] ρ δε

=

where δ is the ovality. All of these parameters depend on thesoil and the excavation process. When α and ρ are equal to 1,this expression converts into eq. [1].

The soil movement distribution is defined by three param-eters (ε, α, ρ). To obtain them from the surface settlementprofile we should make an adjustment at three points.

Sagaseta proposes that α = 1 in clayey soils and values of this parameter depend on the tunnel axis depth in granularsoils (α = 2 when H < 2 D and α = 1 when H > 4 D).

The value of ρ ranges between 0 and 1 and may be greaterthan 1 if grouting is used to fill the gap.

As a first approach, ε (in %) can be obtained from V S asfollows:

[5] ε = V S2

assuming undrained conditions (the volume loss, V S, is equalto the ground loss at the tunnel, V 0).

(2) The Verruijt-Booker methodThe Verruijt-Booker method (Verruijt and Booker 1996) is

a generalization of Sagaseta’s solution for compressible soils(arbitrary values of Poisson’s ratio); it includes the effect of ovality

[6] δ ε ν δz( ) ( ) ( )

( ) x R

H

x H R

H x H

x H = −

+ − −

+4 1 22

2 2

22 2

2 2 2

where ν is Poisson’s ratio. For the undrained case, δ = 0 and ν = 0.5, and eq. [6] converts into eq. [1].

The total area ( A) of the settlement trough is found by in-tegrating eq. [6] from –∞ to +∞. The result is

[7] A = 4(1 – ν) επ R2

Thus

[8] ε ν π ν

=−

=−

A

R

V

4 1 4 12( ) ( )

S

(3) The Peck methodThis method is based on the famous work by Professor

Peck (1969), with later corrections such as those of Atkinsonand Potts (1977) and Clough and Schmidt (1981). It is basedon the former observed data and does not include consider-ation of the effects associated with the recent developmentof shield techniques. As a result, the ground deformationpredicted by this method is larger than the measurement dataobserved in recent shield excavations.

[9] δπ

z,maxS S= ≅V

i

V

i2 2 5.

[10] δπ

δz S z,maxe e( ) x V

i

x

i

x

i= =−

−

2

2

2

2

22 2

where δz,max is the maximum settlement over the tunnel axis,and i is the position of the point of inflection in the normaldistribution curve.

Peck provided graphical empirical correlations betweenV S and the stability number, N , where the stability number isdefined as(after Broms and Bennermark 1967)

[11] N c

= −σ σv Tu

where σ v is the total vertical stress at the tunnel axis level,σT is the internal support pressure, and cu is the undrainedshear strength of the soil. Because of the difficulty in esti-mating these parameters and the vagueness of the graphicalcorrelations, V S values have been obtained from monitoringdata corresponding to the last Madrid Metro extension, asexplained later.

It was also difficult to estimate the position of the point of inflection, i. Graphical correlations between i and H (like thatfrom Peck, for example) are imprecise and the ranges of pos-

© 2002 NRC Canada


Fig. 2. Longitudinal settlement profile (after De la Fuente and Oteo 1996).


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sible values are too wide. In the present study eq. [13] hasbeen used to determine the i values needed by Peck’s method.

(4) The Oteo method

This semiempirical method is based on Oteo’s works overthe last 30 years (Oteo and Moya 1979; Sagaseta et al. 1980).

[12] δ γ ν)z e= −−

Ψ D E

x

i2

20 85

2

2

( .

where ν and γ are Poisson’s ratio and the total unit weight of the soil, respectively; D is the tunnel diameter; Ψ is an em-pirical parameter to be obtained from monitoring data analy-

© 2002 NRC Canada

Melis et al. 1277

Fig. 3. Finite difference mesh, global co-ordinate system, and construction process.

Fig. 4. Mesh dimensions and position of the section for soil movement control.


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sis; and E is the extension Young’s modulus. The position of the point of inflection, i, corresponding to the surface subsi-dence profile is obtained from Sagaseta et al. (1980)

[13] i

R

H

D= −

η 1 05 0 42. .

where η is a parameter that depends on the properties of thesoil.

(5) The De la Fuente and Oteo methodThis method (De la Fuente and Oteo 1996) is based on the

finite element analysis. The model allows an easy and quick estimation of the longitudinal subsidence curve (Fig. 2). Soilsurface settlements that start at a distance of 0.85 H ahead of the tunnel face are in the order of ∆δmax over the tunnel faceand stabilize at α D metres behind it. The point of inflection

is proposed to be at a distance of ε D behind the tunnel face.The maximum settlement, δmax, may be obtained fromeq. [12]. Values for α, ε, and ∆ are given in Fig. 2.

(6) The Loganathan-Poulos analytical prediction methodIn this method (Loganathan and Poulos 1998)

[14] δ νz e( ) ( ) ( ).

( ) x

H

x H gR g

x

H R= −+

+−

+

1 42 2

2

1 38 2

2

where g is the undrained gap parameter, which can be esti-mated as follows:

[15] g = Gp + U 3D + ω where Gp is the physical gap that represents the geometricclearance between the outer skin of the shield and the lining(if grouting is employed to fill the physical gap, the value of Gp is assumed to be in the order of 0.07–0.1 times its origi-nal value); U 3D is the equivalent three-dimensional (3D)elastoplastic deformation at the tunnel face; and ω takes intoaccount the quality of the workmanship.

When using EPB machines elastoplastic 3D strains at thetunnel face may be neglected with relation to Gp. Besides, if good quality construction conditions are considered ω ≅ 0; thusthe gap parameter is equal to the physical gap (i.e., g ≅ Gp).

(7) The Medina-Melis methodThis is a numerical method based on the FLAC3D finite

difference code (Medina 2000). This model takes into ac-

count the full excavation sequence as described below.

Numerical simulation

IntroductionThe numerical simulation of EPB tunnel excavation in

Madrid has been carried out with the FLAC3D finite differ-ence code (Itasca 1997) to account for deformations aheadof the face and the effect of the shield. The full excavationsequence, as detailed later, has been simulated, including theoverexcavation (the void between the ground and the shield),the gap (the tailpiece void between soil and liner), and thegrouting process behind the shield tail. The buildings placednear the tunnel axis have not been included in the model.

According to the authors’ experience with more than 37kilometres of big diameter tunnels, displacements due toshield excavations depend mainly on construction sequencesand EPB parameters. In the present study, special care hasbeen taken of the following aspects (Medina 2000): ( i) soilchamber pressures (top, centre, and bottom) on the tunnelface; (ii) void space between soil and shield (overexcavation);(iii) tailpiece void between soil and lining (gap parameter);(iv) injection grout pressure; and (v) lining behaviour.

A 3D model allows a more accurate analysis of the con-struction effects on the soil and the repercussions of somekey parameters, such as the injection grout and chamberpressures. In order to take into account the 3D effects in thevicinity of the tunnel face, 2D models should make hypothe-

ses about stress release or inward soil movements along theperimeter of the tunnel as the successive excavation stagesare taking place (Lee et al. 1992; Hashimoto et al. 1999;Benmebarek and Kastner 2000).

Geometrical and mechanical modelThe adopted mesh and global coordinate system x , y, z,

are represented in Fig. 3. The mesh dimensions have beenobtained from sensitivity analyses (Fig. 4). All movementsin the model are measured at one diameter distance from theorigin of the mesh to avoid boundary effects caused by theplane y = 0 m.

© 2002 NRC Canada


Elastic and Mohr-Coulomb models Modified Cam clay model

Material

Fines

content (%)

Cohesion

(kPa)

Friction

angle (°)

Compression elastic

modulus (MPa) ν λ κ M N

Man-made fills 15–80 5 28 10 0.35 0.11 0.02 1.11 2.16

Arena de miga

(loamy sand)

0–25 10 35 80 0.30 0.08 0.01 1.42 1.92

Arena tosquiza

(clayey sand)

25–40 15 33 100 0.28 0.10 0.02 1.33 2.11

Tosco arenoso

(sandy clay)

40–60 25 32 130 0.30 0.11 0.03 1.29 2.20

Tosco (brown

clay)

60–85 40 30 170 0.30 0.14 0.05 1.20 2.39

Peñuela (blue,

plastic clay)

85–95 60 28 220 0.28 0.21 0.07 1.11 3.00

Table 1. Classification and characteristic geotechnical properties of Madrid soils.


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According to present theories and knowledge about thegeological history of Madrid soils, they have experienced animportant overconsolidation process. The past maximum ele-vation of Madrid ground surface is believed to have been inthe order of 725 m and today varies between 600 and 700 m.Measurements of the coefficient of earth pressure at rest, K 0,done during the last decades in Madrid soils provided K 0values in some cases higher than 1, and as high as 1.6. Theauthors are currently undertaking a new series of measure-ments to ascertain the value of this parameter. In this work,K 0 values were obtained from Alpan (1967)

[16] K 0 = K 0NC OCRff

where K 0NC is the coefficient of earth pressure at rest fornormally consolidated soils; OCR is the overconsolidationratio; and ff is a parameter depending on the soil. The values

for these parameters may be inferred from the followingequations:

[17] ff PI

= × −

0 54 10 281. (Alpan 1967)

[18] K 0NC = 1 – sin ϕ′ (Jaky 1948)

where PI is the plasticity index and ϕ′ is the friction angle(Table 1). The OCR value corresponding to each element isobtained from its current depth and elevation.

Three different soil constitutive models have been selectedfor analysis as follows:

(1) The linear elastic model. Here K (tangential bulkmodulus) and G (shear modulus) are supposed to be con-stant. This is a very simplified hypothesis, but its predictionsare acceptable in many cases because Madrid soils are verystiff, and plasticity effects are not very important for the pur-pose of predicting subsidence (Medina 2000).

(2) The Mohr-Coulomb elastoplastic model. The main ad-vantage with respect to the elastic model is that plastic de-formations are taken into account. Construction difficultiessuch as steering and alignment problems can cause over-excavation and remolding of adjacent soils. Usually duringtunnelling, a significant disturbed zone is induced around thetunnel. Therefore, it is expected that the use of a linear elas-tic model coupled with modelling overexcavation processdoes not reliably represent the soil behaviour in the problem

of tunnelling. Besides, the mechanical parameters neededare well known in the case of Madrid soils.

(3) The modified Cam clay model. It offers the followingadvantages with respect to the preceding models:

(a) The elastic parameters, K and G, are obtained from thefollowing expressions:

[19] K p

= ν

κ

[20] G

p

=

−

+

3 1 2

2 1

νκ

ν

ν

( )

( )

where v is the specific volume, p is the mean stress and κ isthe slope of the swelling lines.

As the equations for the normal consolidation line andswelling lines are different, different values for K and G areemployed to calculate elastic deformations along these paths.

(b) Furthermore, these parameters are not constant alongthe normal consolidation line and the swelling lines, but they

depend on the current strain state in each element ( p).(c) Soil overconsolidation is considered by the model notonly as an initial stress state but also as a factor determiningthe pre-failure and post-failure mechanical soil behaviour.When working with the preceding models, the original stressstate may be introduced by means of initial conditions, butthese do not reflect the stress history, and the over-consolidation effects on the soil response are not taken intoaccount.

EPB excavation process modelA discontinuous advance of the shield has been studied:

soil cylinders, whose length is equal to the lining ringlength, are instantaneously excavated. After each cylinder

excavation, stress balance is allowed. The FLAC3D largestrain option has been adopted (the deformed mesh geome-try is taken into account). The EPB frustum conic shape hasalso been modelled. For each excavation step the followingsequence of operations is applied (Fig. 3):

(1) Removal of face elements.(2) Interface generation on the new soil surfaces created.

Shield and soil meshes are independent and may deform in-dependently. This interface, with the appropriate mechanicalproperties, avoids penetration of the soil into the EPB meshand allows contact forces to be applied between them whereand when they contact each other.

(3) Shield displacement for a length equal to the removedsoil cylinder length. The linear elastic constitutive modelwas used for the EPB elements. Their unit weight is the ratiobetween the total shield weight and its apparent volume. Be-cause of the overexcavation (the difference between shieldand tunnel diameters), small steel plates are welded to thelower half of the EPB to maintain the alignment of the tun-nel and the machine axis. These plates were modelled withthe same mechanical properties as the EPB.

(4) Grout pressure application, after EPB passage, on tun-nel surfaces. To reduce the volume loss, V S , and the surfacesettlement, the gap between the soil and the lining is filledwith grout. Close to the shield tail, the grout has still nothardened; thus, soil pressure cannot be applied to the lining.

© 2002 NRC Canada

Melis et al. 1279

Fig. 5. Volume loss, V S, versus H / D. Madrid Metro extension(1995–1999).


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A hydrostatic pressure distribution is believed by the authorsto be the most realistic approach to model the effect of thegrout on the ground. Grouting pumps in Madrid EPBs cangive up to 6000 kPa pressure, and pressure at the end of thelines has been kept normally as high as 250 kPa.

(5) Generation of grouted elements. Injection hardens12 m away from the shield tail because the grouting material

is designed to harden 12 h after it is applied, and the meanshield speed is 1 m/h (Melis 1997). The linear elastic modelis employed to simulate these elements.

(6) Generation of lining ring elements. After the grouthardening, soil pressures may be sustained by the lining, soring elements are also created 12 m away from the shieldtail. The linear elastic model has been used to model liningmechanical behaviour. Behind the shield, lining rings settleinto the fluid grout injection. However, they do not reach thebottom of the excavation because of the 140 mm separationdue to the shield wall plus the guidance steel profiles and thebolts linking them with both the ring inside the shield andthe preceding rings surrounded by hardened grout.

(7) Soil chamber pressure application on the tunnel face.

In most cases, the EPB shield is operated so that the rate of excavation is less than the rate of the machine advance, forc-ing the soil away from its face causing small initial heave.This initial heave will reduce the amount of final settlement,especially in hollow tunnels or when soft soils are excavated(sometimes it can even be removed). As in the numericalmodel the rates of excavation and machine advance are thesame, this effect may be taken into account by varying thesoil chamber pressure. The values of this parameter areavailable from the files recorded from the shields during theexcavation of the tunnels. Madrid EPBs work under normalcircumstances with 60 to a maximum of 100 kPa pressure atthe upper cell in the soil chamber and as high as 270–300 kPa at the bottom cells.

(8) Finally, the weight of the back-up is applied on thecorresponding lining rings.

Technical parameters referring to EPBs, lining rings, andinjection grout are as follows:

(1) EPB parameters. (a) EPB shield external diameter is9.33 m in the Mitsubishi machines. The cutting wheel diam-eter, as related to the peripherical bits is 9.38 m. Thus, theoverexcavation is normally equal to 25 mm excluding thecurves, where the copy-cutters increase slightly the horizon-tal diameter, thus providing an elliptical cross-section in theexcavation in order for the shield to be able to build thecurve. (b) The total length is 10 800 mm. An intermediate ar-ticulation allows up to 2.5° relative tilt between the front andthe tail part of the shield. The thickness is 80 mm with aconicity of 0.01 m/m. (c) The weight is 9750 kN. (d ) Theback-up length is 115 m. (e) The back-up weight is 5050 kN.

(2) Lining ring parameters. (a) A universal ring was se-lected for the 9.38 m diameter machines, although excellentresults were also obtained with the right-left ring in the7.4 m diameter EPB from LOVAT. (b) The inner diameter is8.43 m. (c) The thickness is 0.32 m. Several analysis werecarried out to determine the appropriate value for this pa-rameter. Different load hypotheses were considered: storageand transport of dowels and ground pressures on the liningwhen varying the tunnel axis depth (Melis 1997). (d ) Thelength is 1.5 m.

© 2002 NRC Canada


P e c k

O

t e o

V e r r u i j t - B o o k e r

L o g a n a t h a n - P o u l o s

S a g a s e t a

i ( m )

V S

( % )

η

γ ( k N / m 3 )

i ( m )

Ψ

E (

k P a )

ν

ε ( % )

ρ

δ ( % )

ν

g

( m )

ν

ε ( % )

ρ

α

( % )

S e c t i o n I

6 . 3

0 . 5

0

1

. 1 3

2 0 . 2

6 . 3

0 . 3

4 6 7

0 . 3

0

0 . 1

8

1 . 3

0 . 2

3

0 . 3

0

0 . 0

1 2

0 . 3

0

0 . 1

8

1 . 3

1

S e c t i o n I I

7 . 5

0 . 3

5

1

. 0 7

2 0 . 1

7 . 5

0 . 3

4 2 0

0 . 3

1

0 . 1

3

1 . 3

0 . 1 7

0 . 3

1

0 . 0

1 2

0 . 3

1

0 . 1

3

1 . 3

1

S e c t i o n I I I

9 . 5

0 . 2

3

1

. 1 3

2 0 . 4

9 . 5

0 . 3

3 7 4

0 . 2

9

0 . 0

8

1 . 3

0 . 1

0

0 . 2

9

0 . 0

1 2

0 . 2

9

0 . 0

8

1 . 3

1

S e c t i o n I V

4 . 5

0 . 7

0

1

. 3 0

2 0 . 2

4 . 5

0 . 7

6 0 0

0 . 2

9

0 . 2

5

1 . 3

0 . 3

3

0 . 2

9

0 . 0

1 2

0 . 2

9

0 . 2

5

1 . 3

1

S e c t i o n V

4 . 5

0 . 2

5

1

. 2 4

2 0 . 3

4 . 5

0 . 3

5 5 1

0 . 3

0

0 . 0

9

1 . 3

0 . 1

2

0 . 3

0

0 . 0

1 2

0 . 3

0

0 . 0

9

1 . 3

1

T a b l e

2 .

A d o p t e d v a l u e s f o r r e q u i r

e d p a r a m e t e r s i n t h e p r e d i c t i v e m e t h o d s .


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(3) Injection grout parameters. (a) Pressure at the shieldtail, end of grouting pipes is 200–600 kPa. (b) Young’smodulus (when hardened) is 2.57 GPa. (c) Poisson’s ratio(when hardened) is 0.286.

Results

In October–November 2000, six EPBs had started tunnel-ling in the areas where the predictions of this paper havebeen made. It is foreseen that by the end of year 2002 alltunnels will have been constructed.

Five sections have been analyzed in this work by meansof each of the seven estimation methods detailed herein.These sections cover a wide range of both geotechnical pro-files and tunnel depths.

All sections analyzed have been fully instrumented. Thegeotechnical instrumentation of each control section consistsof (a) seven leveling points, (b) three sliding micrometers,(c) one trivec, and (d ) one inclinometer.

© 2002 NRC Canada

Melis et al. 1281

Fig. 6. Stratigraphic profile. Section I (Fuenlabrada, chainage 0+305).

Fig. 7. Predicted transversal settlement profile by the numericalmethod (elastic, Mohr-Coulomb, and Cam clay models). SectionI (Fuenlabrada, chainage 0+305).

Fig. 8. Predicted transversal settlement profile by different meth-ods. Section I (Fuenlabrada, chainage 0+305).

Fig. 9. Predicted longitudinal settlement profile by differentmethods. Section I (Fuenlabrada, chainage 0+305).


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Once all of the measurements are collected, the results of the predicted and measured surface movements will be pub-lished. In the present work the results of the soil movement

estimation will cover the following items: (a) maximumsettlement at the surface above the tunnel axis; (b) point of inflection of the subsidence curve; (c) volume loss in thesection; (d ) the shape of the transversal subsidence curve;and (e) the shape of the longitudinal subsidence curve.

The adopted values, in the numerical method, for the param-eters of the EPB tunnelling machine are as follows: (a) earthpressure in the face chamber (hydrostatic distribution in depth):50 and 200 kPa on the upper and lower cells, respectively; and(b) grouting pressure at the shield tail: 100 and 220 kPa on thetop and the bottom of the tunnel, respectively.

The main properties corresponding to the Madrid soils, asrequired by the numerical method, are summarized in Ta-ble 1. Elastic and Mohr-Coulomb parameters have been ob-tained from several hundred soil tests from the last MadridMetro extension (Medina 2000), while Cam clay parametershave been inferred from the following empirical correlations(Wood 1990):

[21] λ ρ= ≅PI PIs100 000 100

0 006ln( )

.

© 2002 NRC Canada


Fig. 10. Stratigraphic profile. Section II (Fuenlabrada, chainage 1+114).

Fig. 11. Predicted transversal settlement profile by the numericalmethod (elastic, Mohr-Coulomb, and Cam clay models). SectionII (Fuenlabrada, chainage 1+114).

Fig. 12. Predicted transversal settlement profile by differentmethods. Section II (Fuenlabrada, chainage 1+114).

Fig. 13. Predicted longitudinal settlement profile by differentmethods. Section II (Fuenlabrada, chainage 1+114).


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[22] M = ′− ′

63

sinsin

ϕϕ

[23] Γ = + +1100000

0 3ρs LL PI( . )

where λ is the slope of the normal compression line in the

ν– ln p′ plane, PI is the plasticity index, ρs is the density of the soil particles, expressed in kg/m3, M is the shape factorfor the Cam clay ellipse–slope of the critical state line, LL isthe liquid limit, and Γ is the value of the specific volume onthe critical state line at a mean effective stress p′ = 1 kPa.

This later expression can be combined with the followingone obtained from 178 soil samples (Medina 2000):

[24] LL = 1.422 PI + 9.581

The following relationship between N , PI, λ , and κ is ob-tained:

[25] N = + −Γ ( ) lnλ κ 2

[26] N = 1.25 + 0.045 PI + 0.693(λ κ − )

where N is the value of the specific volume on the normalcompression line at a mean effective stress p′ = 1 kPa, and κ is the slope of the unloading–reloading line in the ν– ln p′plane.

The preconsolidation pressure, pc0, is obtained in each fi-nite difference element from

[27] p p q

M pc0 max

max

max

= +2

2

where pmax and qmax are the maximum previous p and q

[28] pmaxv, max h,max= +σ σ2

3

[29] qmax v,max h,max= −σ σ

and σv,max and σh,max are the maximum vertical and horizon-tal stresses, respectively, corresponding to each element.They are obtained from the current depth and elevation of

© 2002 NRC Canada

Melis et al. 1283

Fig. 14. Stratigraphic profile. Section III (Getafe, chainage 7+385).

Fig. 15. Predicted transversal settlement profile by differentmethods. Section III (Getafe, chainage 7+385).

Fig. 16. Predicted longitudinal settlement profile by differentmethods. Section III (Getafe, chainage 7+385).


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each element, the past maximum elevation of Madrid groundsurface, and eq. [16].

To be able to compare the results from the different meth-ods, the same V S values have been used with those methodsthat need it (i.e., Sagaseta, Verruijt-Booker, and Peck meth-ods). These values have been obtained from Fig. 5, whichshows data from several instrumented sections in the MadridMetro extension (1995–1999).

Most of the V S values are within the range 0.1 and 0.6%.If we consider that V S ≈ (0.7–1.0)V 0 (Medina 2000), and theoverexcavation (a circular ring 15 mm thick) represents0.64% of the tunnel cross section, it is possible that most of the ground loss, V 0, is due to this overexcavation. Thus, afterthe passage of the shield, grouting and lining rings avoid ad-ditional ground loss.

The values of the parameters employed in the analyzed sec-tions for each predictive method are summarized in Table 2.

Section IThis section is located in the city of Fuenlabrada (chain-

age 0+305, overburden 9.5 m). The stratigraphic profile isformed, from top to bottom, by 3.5 m of man-made fills,8 m of brown clay, and several strata of clayey sand, sandyclay, and brown clay randomly distributed (Fig. 6).

The subsidence profiles from the numerical simulation areshown in Fig. 7. As said before, three different constitutivemodels have been used: the linear-elastic model, the Mohr-Coulomb elastoplastic model, and the critical state Cam claymodel.

Settlements predicted by the Mohr-Coulomb model areslightly higher than those obtained from the elastic model. Thisis a consequence of the ring of plasticized soil around the exca-vation. Soil movements from the Cam clay model estimationare between those corresponding to the two other ones.

The most reliable predictions are believed to be those fromthe Mohr-Coulomb model because (i) it takes into account theplasticity phenomenon, as explained before; and (ii) its corre-sponding parameters are better known than those of the criti-cal state model obtained from empirical correlations.

Results from all of the prediction methods correspondingto the transversal and longitudinal troughs are shown in

© 2002 NRC Canada


Fig. 17. Stratigraphic profile. Section IV (Alcorcón, chainage 7+505).

Fig. 18. Predicted transversal settlement profile by differentmethods. Section IV (Alcorcón, chainage 7+505).

Fig. 19. Predicted longitudinal settlement profile by differentmethods. Section IV (Alcorcón, chainage 7+505).


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Figs. 8 and 9, respectively. Because of the above-mentionedreasons, the represented numerical prediction (Medina-Melismethod) corresponds to the Mohr-Coulomb model resultsshown in Fig. 7.

The maximum settlement, over the tunnel axis, ranges be-tween 6.2 (Oteo’s method) and 32.3 mm (Peck’s method).

With respect to the longitudinal subsidence profile, similar

results have been obtained with the Medina-Melis and De laFuente methods. In this case, the Sagaseta model predicts afinal maximum movement greater than the others.

Section IIThis section is also located in the city of Fuenlabrada

(chainage 1+114, overburden 10.3 m). The stratigraphic pro-file is formed, from top to bottom, by 4.5 m of man-madefills and several strata of clayey sand, sandy clay, brownclay, and loamy sand randomly distributed (Fig. 10).

The subsidence profiles from the numerical simulation(Medina-Melis method) are shown in Fig. 11.

As happened in section I, settlements predicted by theMohr-Coulomb model are a bit higher than those obtainedfrom the elastic model. In this case, the Cam clay model es-timates greater movements than the other two models andthey are very close to the elastoplastic prediction.

As explained before, the most reliable predictions arethose from the Mohr-Coulomb model. Because of the simi-larity between the estimations from the different constitutivemodels, only the Mohr-Coulomb results have been presentedin the next two figures.

Results from all of the prediction methods correspondingto the transversal and longitudinal troughs are shown inFigs. 12 and 13, respectively.

The maximum settlement, over the tunnel axis, oscillatesbetween 6.8 (Oteo’s method) and 22.1 mm (Peck’s method).

With respect to the longitudinal subsidence profile, similarresults have been obtained with the Sagaseta and De laFuente methods. In this case, the Medina-Melis model pre-dicts a final maximum movement much greater than theother methods.

© 2002 NRC Canada

Melis et al. 1285

Fig. 20. Stratigraphic profile. Section V (Alcorcón, chainage 8+770).

Fig. 21. Predicted transversal settlement profile by differentmethods. Section V (Alcorcón, chainage 8+770).

Fig. 22. Predicted longitudinal settlement profile by differentmethods. Section V (Alcorcón, chainage 8+770).


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Section IIIThis section is located in the city of Getafe (chainage

7+385, overburden 12.8 m). The stratigraphic profile isformed by 2.4 m of man-made fills and several strata of sandy clay and high plasticity clays (Fig. 14).

Results from all the prediction methods corresponding tothe transversal and longitudinal troughs are shown inFigs. 15 and 16, respectively. The numerical prediction cor-responds to the Mohr-Coulomb model.

The final settlement over the tunnel axis ranges between4.6 (Sagaseta’s method) and 11.1 mm (Peck’s method).

Similar shapes for the longitudinal subsidence profile

have been obtained by means of the employed methods, al-though each of them predicts a different final settlement.

Section IVThis section is located in the city of Alcorcón (chainage

7+505, overburden 6.3 m). The stratigraphic profile isformed by several alternate strata of loamy sand, sandy clay,and clayey sand, as shown in Fig. 17.

Results for transversal and longitudinal troughs are repre-sented in Figs. 18 and 19, respectively. The numerical pre-diction corresponds to the Cam clay model. In hollowtunnels ( H < 1.5 D) this model seems to fit field data betterthan the others (Medina 2000).

The maximum settlement ranges between 11.5 and

56.5 mm, as predicted by Oteo and Peck, respectively.Similar shapes for the longitudinal subsidence profile

have been obtained using the employed methods, althoughfinal movements are quite different.

Section VThis section is located in the city of Alcorcón (chainage

8+770, overburden 15.2 m). The stratigraphic profile isformed, from top to bottom, by 3 m of man-made fills,4.5 m of loamy sand, 3 m of clayey sand, and several alter-nated strata of sandy clay, loamy sand, and brown clay asshown in Fig. 20.

Results for transversal and longitudinal profiles are repre-sented in Figs. 21 and 22, respectively. The numerical pre-diction corresponds to the Mohr-Coulomb model.

The maximum settlement ranges between 4.5 and 9.5 mm,as predicted by Sagaseta and Peck, respectively.

Similar shapes for the longitudinal subsidence profilehave been obtained using the employed methods, althougheach of them predicts a different final settlement; in thiscase, the Medina-Melis method gives an estimation higherthan the others.

As a final summation of this point, results from the fiveanalyzed sections are gathered in Table 3. It refers to the

maximum settlement, δmax, the position of the point of in-flection, i, and the volume loss, V S.The positions of the point of inflection given by Peck’s

method are smaller to the positions from the other methods.Nevertheless, in most cases the maximum settlements arepredicted by Peck’s method. Thus, the volume loss valuesfrom this method are similar to the values from the others.

In general, the minimum vertical movements are obtainedfrom Sagaseta’s method.

Conclusions

Although a few methods have been proposed to predictthe deformations in numerical, statistical, and empiricalways, it is difficult to say whether these methods can beused in confidence.

To convert analytical methods into a practical predictivetool, it would be of great interest to establish easy ways toestimate their parameters. Much help could be found in allof the available data from the Madrid Metro extensions.

Empirical methods are very useful and easy to handle toolsfor estimating ground settlements. However, tunnelling engi-neers would be grateful for them if they provided more specificvalues to be used for their parameters in each kind of problem.

Numerical methods are very flexible and may be adoptedto solve a specific problem taking into account geometrical

© 2002 NRC Canada


Section I Section II Section III Section IV Section V

Medina-Melis δmax (mm) 7.7 9.9 17.2 16.4 6.6i (m) 6.0 9.5 7.4 3.5 10.0V S (%) 0.12 0.26 0.32 0.18 0.26

Peck δmax (mm) 32.3 11.1 22.1 56.6 9.5

i (m) 6.2 8.3 6.3 4.9 10.5V S (%) 0.50 0.23 0.35 0.69 0.25Oteo δmax (mm) 6.2 7.9 6.8 11.5 5.3

i (m) 6.2 8.3 6.3 4.9 10.5V S (%) 0.10 0.16 0.11 0.14 0.14

Loganathan δmax (mm) 11.0 9.0 10.4 14.5 7.9i (m) 7.5 7.0 9.0 5.0 10.5V S (%) 0.23 0.23 0.22 0.24 0.22

Verruijt δmax (mm) 15.0 5.5 10.0 26.8 5.3i (m) 7.0 6.5 8.5 4.5 8.0V S (%) 0.34 0.16 0.24 0.48 0.17

Sagaseta δmax (mm) 12.8 4.6 8.6 22.7 4.5i (m) 7.0 6.5 8.0 4.3 7.5V S (%) 0.25 0.12 0.18 0.35 0.13

Table 3. Estimated values for δ max, i, and V S corresponding to the analyzed sections.


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and geotechnical variables and the construction process.They provide much more information than analytical or em-pirical methods. However, the incorrect choice of the consti-tutive model, the inaccuracy in the values of the parametersemployed, the improper understanding of the constructionprocess, etc., may lead to wrong results. Numerical modelsshould be verified and validated with the help of analytical

and empirical models and field data.After the completion of the tunnelling works correspond-ing to the METROSUR Extension Project, a comparison be-tween the predicted settlements presented in this paper andthe monitoring data will be made. The accuracy of each pre-dictive method will be assessed with reference to the soilmovements measured at the five analyzed sections.

An improved fitting of the variables involved in the pre-sented methods and a further knowledge about their applicabil-ity to specific situations will be inferred from this future study.

Acknowledgements

The authors wish to thank Professor Jiménez Salas, sadly

no longer with us, for his invaluable contribution to theworld of geotechnical engineering and in particular to that inSpain.

References

Abe, T., Sugimoto, Y., and Ishihara, K. 1978. Development and ap-plication of environmentally acceptable new soft ground tunnel-ling method. In Tunnelling under difficult conditions:Proceedings of the international tunnel symposium, Tokyo 1978.Pergamon Press, NY, pp. 315–320.

Alpan, I. 1967. The empirical evaluation of the coefficient K 0 andK 0R. Soils and Foundations, 7(1): 31–40.

Atkinson, J.H., and Potts, D.M. 1977. Subsidence above shallow

tunnels in soft ground. Journal of the Geotechnical EngineeringDivision, ASCE, 103(GT4): 307–325.

Benmebarek, S., and Kastner, R. 2000. Modélisation numériquedes mouvements de terrain meuble induits par un tunnelier. Ca-nadian Geotechnical Journal, 37: 1309–1324.

Broms, B.B., and Bennermark, H. 1967. Stability of clay at verticalopenings. Journal of the Soil Mechanics and Foundations Divi-sion; Proceedings of the American Society of Civil Engineers,93(SM1): 71–95.

Clough, G.W., and Schmidt, B. 1981. Design and performance of excavation and tunnels in soft clay. In Soft clay engineering(Chapter 8). Elsevier, Amsterdam, pp. 569–634.

De la Fuente, P., and Oteo, C. 1996. Theoretical research on thesubsidence originated by the underground construction in urban

areas. In Proceedings of the Danube International Symposium,Rumania, 1996.Endo, K., and Miyoshi, M. 1978. Closed type shield tunnelling

through soft silt layer and consequent ground behaviour. In Tun-nelling under difficult conditions: Proceedings of the interna-tional tunnel symposium, Tokyo 1978. Pergamon Press, NY,pp. 329–334.

González, C., and Sagaseta, C. 2001. Patterns of soil deformationsaround tunnels. Application to the extension of Madrid Metro.Computers and Geotechnics, 28: 445–468.

Hashimoto, T., Nagaya, J., and Konda, T. 1999. Prediction of ground deformation due to shield excavation in clayey soils.Soils and Foundations, 39(3): 53–61.

HSE. 2000. The collapse of NATM tunnels at Heathrow Airport.The Health and Safety Executive (HSE), HSE Books, Suffolk,U.K., C45 7/00.

Itasca Consulting Group. 1997. FLAC3D Fast Lagrangian analysisof continua in 3-D. Version 2.0. Minneapolis, MN.

Jaky, J. 1948. Pressure in silos. In Proceedings of the 2nd Interna-tional Conference on Soil Mechanics and Foundation Engi-neering, Rotterdam, Vol. 1, pp. 103–107.

Lee, K.M., Rowe, R.K., and Lo, K.Y. 1992. Subsidence owing totunnelling. I. Estimating the gap parameter. Canadian Geo-technical Journal, 29: 929–940.

Loganathan, N., and Poulos, H.G. 1998. Analytical prediction fortunnelling-induced ground movements in clays. Journal of Geo-technical and Geoenvironmental Engineering, 124(9): 846–856.

Medina, L. 2000. Estudio de los movimientos originados por laexcavación de túneles con escudos de presión de tierras en los

suelos tosquizos de Madrid. Ph.D. thesis. University of LaCoruña, La Coruña, Spain.Melis, M. 1997. Selection and specifications of the EPB tunnelling

machines for the Madrid Metro extension. Jornadas Técnicas sobrela ampliación del Metro de Madrid. Fundación Agustín deBethencourt y Comunidad de Madrid. Madrid, Vol. I. (In Spanish.)

Oteo, C., and Moya, J.F. 1979. Evaluación de parámetros del suelo deMadrid con relación a la construcción de túneles. In Proceedings of the 7th European Conference on Soil Mechanics and FoundationEngineering, Brighton, Paper f13, Vol. 3, pp. 239–247.

Peck, R.B. 1969. Deep excavations and tunnelling in soft ground. In Proceedings of the 7th International Conference on Soil Me-chanics and Foundation Engineering, Mexico, Vol. 4 (State of the Art), pp. 225–290.

Romo, P. 1997. Soil movements induced by slurry shield tunnel-ling. In Proceedings of the 14th International Conference onSoil Mechanics and Foundation Engineering, Hamburgo, 6–12September. A.A. Balkema, Rotterdam. Vol. 3, pp. 1473–1481.

Sagaseta, C. 1987. Analysis of undrained soil deformation due toground loss. Géotechnique, 37(3): 301–320.

Sagaseta, C. 1988. Discussion on: Sagaseta, C.: Analysis of un-drained soil deformation due to ground loss. Author’s reply toB. Schmidt. Géotechnique, 38(4): 647–649.

Sagaseta, C., Moya, J.F., and Oteo, C. 1980. Estimation of groundsubsidence over urban tunnels. In Proceeding of the 2nd Confer-ence on Ground Movement and Structures, Cardiff, pp. 331–344.

Uriel, A.O., and Sagaseta, C. 1989. Selection of design parametersfor underground construction. In Proceedings of the 12th Inter-national Congress on Soil Mechanics, Río de Janeiro, 13–18

August, General report, Discussion session. A.A. Balkema, Rot-terdam. Vol. 9, pp. 2521–2551.Verruijt, A., and Booker, J.R. 1996. Surface settlements due to de-

formation of a tunnel in an elastic half plane. Géotechnique,46(4): 753–757.

Wood, D.M. ( Editor ) 1990. Soil behaviour and critical state soilmechanics. Cambridge University Press, Cambridge.

Melis et al. 1287

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