Ground Loss and Static Soil–Structure Interaction During Urban Tunnel Excavation: Evidence from the Excavation of the Athens Metro

infrastructures

Article Ground Loss and Static Soil–Structure Interaction during Urban Tunnel Excavation: Evidence from the Excavation of the Athens Metro

Villy Kontogianni 1,* and Stathis C. Stiros 2 1 Hellenic Survey for Geology and Mineral Exploration (HSGME—former IGME), Sp. Loui 1, Olympic Village, 13677 Acharnes, Greece 2 Department of Civil Engineering, Patras University, 26500 Patras, Greece; [email protected] * Correspondence: [email protected]

Received: 23 June 2020; Accepted: 28 July 2020; Published: 31 July 2020

Abstract: Ground settlement above urban tunnels is a threat for nearby buildings, because it may lead to their differential settlement, tilting, and damage, depending on their structural characteristics, on ground conditions, and on the excavation procedure. Still, for few cases only details on ground settlement are known. In this article we analyze ground subsidence data during the excavation of Lines 2 and 3 of the Athens Metro. Based on this evidence, and in comparison with previous studies, we show that observations of elevation changes and of tilting of buildings may underestimate the amount of ground loss; this is because part of the ground deformation may be compensated by the stiffness of buildings or accommodated by internal deformation of sizeable buildings hosting measuring benchmarks. This effect can be described as static soil–structure interaction (sSSI), in analogy to the dynamic SSI produced during earthquakes. sSSI can produce bias in monitoring data above an advancing tunnel front, leading to skew and not to symmetric subsidence curves if observations are made on one side on buildings and on the other side in open spaces (‘greenfields’). Furthermore, we show that ‘bowls’ of increased subsidence are observed along subsidence troughs during excavation; such ‘bowls’, not infrequently underestimated because of sSSI, may conceal a potential for sinkholes and other types of failure. Isolated towers on the contrary describe well ground subsidence and tilting.

Keywords: ground settlement; geodetic monitoring; tunnel excavation; building damage; soil structure interaction

1. Introduction Tunnels represent important civil infrastructures, tend to be excavated in increasingly adverse conditions, and their construction is not without problems. The reason is that tunnel excavation produces a rearrangement of stresses around the void produced by the excavation and deformation of its surrounding rock mass, usually reaching the ground surface and known as ‘ground loss’. In terms of topography, ground loss takes the form of a subsidence trough, with maximum above the axis of a shallow (up to 30 m deep) tunnel and attenuating away from it, at distances usually 2–3 times the tunnel diameter [1]. Such ground deformation is obviously a threat for overlying buildings, and for this reason, since the experience gained by the excavation of the Chicago Metro by Karl Terzaghi (see [2]), a main task during tunnel excavation is to model, observe, control, and minimize surface ground subsidence, including time-dependent deformation. In fact, there are numerous examples of structural deformation and damage especially of ﬂexible masonry buildings during excavation of nearby tunnels [3,4], even in the case of small ground movements [5]. The eﬀects of tunneling are even more apparent at high, slender structures, such as towers, chimneys, or minarets. The most known

Infrastructures 2020, 5, 64; doi:10.3390/infrastructures5080064 www.mdpi.com/journal/infrastructures Infrastructures 2020, 5, 64 2 of 13 example is the controlled tilting of the Big Ben Clock Tower in London during the excavation of the Jubilee Metro Line extension, passing at a distance of 30 m from the Clock Tower [6]. Still, modeling and prediction of ground loss proved not easy. Theoretical modeling by closed functions proved not successful, numerical models are limited by the uncertainty and variability of ground strength parameters in urban environment, while the quasi-empirical model of a Gauss-type curve proposed by Peck in 1969 [1], or its variations [7], remains the most popular method for ground loss modeling. On the other hand, despite the large number of tunneling projects combined with geodetic measurements of ground subsidence [4,6,8–14], the available information on the ground loss is limited. This is due to two reasons: (1) in each project, the amount and distribution of monitoring points is limited, usually confined to buildings at risk (Figure1a), mainly for cost-suppression and practical reasons (for example benchmarks on the ground above or near the tunnel axis are frequently destroyed during the project) and (2) monitoring data are rarely available because of their legal and financial implications in case of failure (cf. [15]). Such limitations are reflected in two critical, interrelated problems. First, measurements of ground subsidence of large buildings usually indicate moderate amounts of subsidence and tilting [4,14,16], but on the contrary, measurements on benchmarks on free-field (or greenfields), on posts and fences, and on isolated towers show higher, even extreme amounts of tilting and conspicuously of ground subsidence (Figure1b; [ 6]). This was clearly detected during excavation of the Athens Metro at the Gazi area indicating a complex pattern of surface ground deformation and tilting of up to 0.75% of the two 30 m high old brick chimneys at the site (Figure2,[ 17]), in ≈ contrast, minor deformation was recorded at adjacent massive buildings. This contrast, however, is not limited to tunneling, but it tends to indicate a more general effect: for example, in Venice, widespread differential ground subsidence produces important tilting to isolated towers, but not to nearby massive buildings (Figure1c). Second, in several cases of tunneling, observations on buildings provided evidence of moderate ground deformation and absence of structural damage in buildings, but sinkholes have been produced in open, nearby spaces, mostly roads. Such an example is an 8 m-wide sinkhole in Ottawa city in 2016, during the construction of the light rail tunnel through weak ground [18]. A similar sinkhole had been reported much earlier during the Athens Metro construction (Figure3,[ 19]). Such effects in many cases probably indicate accumulation of ground deformation not identified by monitoring on nearby buildings [20]. Hence, studies of ground loss based on observations on bulky buildings tend to underestimate the true ground loss, because of the potential of buildings to affect their deformation, as a result of the stiffness or of the internal deformation of the structures. In analogy to soil–structure interaction (SSI) in earthquake engineering (for example [21]), this effect can be regarded as static Soil-Structure Interaction, sSSI [3,22]; a complicated, geotechnical effect, with high impacts for tunneling. In this article we present and analyze monitoring data from different projects of the excavation of Lines 2 and 3 of Athens Metro about 15 years ago. These data, until recently confidential, can provide not only a qualitative, but also a quantitative approach to the role of sSSI and of the associated greenfield (free-field) effect in the modeling of ground loss during tunnel excavation. Infrastructures 2020, 5, 64 3 of 13

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FigureFigure 1. 1.The The static static soil–structure soil–structure interactioninteraction (sSSI) and and th theee ‘greenfield‘greenfield ‘greenfield effect’effect’ effect’ manifestedmanifested manifested asas as contrastcontrast contrast ininin the thethe amplitude amplitudeamplitude of ofof tilting tiltingtilting between betwbetweeneen wholewholewhole buildingsbuildings (ground (ground lossloss loss anan andd tilting tilting partly partly concealed) concealed) and and isolatedisolatedisolated towers towerstowers (local (local(local tilting tiltingtilting evident): evident):evident): ((aa)) monitoring monitoring pointspoints points (indicated(indicated (indicated byby by circles)circles) circles) inin inthethe the facadesfacades facades ofof of AmsterdamAmsterdam buildings buildings for for the the metro metro excavationexcavation study. 2-D2-D displacementdisplacement displacement onlyonly only (settlement(settlement (settlement andand and tiltingtilting tilting down-to-the-street)down-to-the-street) can can be be recorded, recorded, butbut notnot tilting parallel parallel to to the the street street because because it itis iscompensated compensated bybyby adjacent adjacentadjacent buildings. buildings.buildings. ( b((b))) Evidence EvidenceEvidence ofofof groundgroundground subsidence subsidence onon on thth theee roadroad road pavementpavement pavement andand and onon on aa stonestone a stone wallwall wall (fence)(fence)(fence) at theatat thethe plain plainplain of Thessaly, ofof Thessaly,Thessaly, Greece, Greece,Greece, due duedue to water toto water overpumping. overpumping. The rigidThe rigid wall wall responded responded to ground to subsidencegroundground subsidencesubsidence with some withwith hysteresis; somesome hysteresis;hysteresis; on the contrary, onon thethe thecontrary,contrary, building thethe made buildingbuilding with mademade stiff concretewithwith stiffstiff foundations concreteconcrete showedfoundationsfoundations no significant showedshowed nono evidence significantsignificant of damageevidenceevidence (afterofof damagedamage [20]). (after(after (c) Regional [20]).[20]). ((cc)) RegionalRegional ground subsidencegroundground subsidencesubsidence in Venice producesinin VeniceVenice limited producesproduces tilting limitedlimited in massive tiltingtilting in buildingsin massivemassive (palazzos buildbuildingsings and(palazzos(palazzos churches), andand churcheschurches but high),), tiltingbutbut highhigh in belltiltingtilting towers inin (campanile),bellbell towerstowers such (campanile),(campanile), as that of suchsuch San asas Giorgio thatthat ofof SanSan dei GreciGiGiorgioorgio (tilting deidei GreciGreci indicated (tilting(tilting by indicatedindicated red arrow). byby redred arrow).arrow).

FigureFigure 2. 2.Contrasting Contrasting evidence evidence of of ground ground loss loss during during the thee excavation excavationexcavation of ofof the thethe Athens AthensAthens Metro MetroMetro Line LineLine 3in 3in3in the Gazithethe area GaziGazi from areaarea buildings fromfrom buildinbuildin andgsgs chimneys, andand chimneys,chimneys, based on basedbased geodetic onon geodeticgeodetic monitoring. monitoring.monitoring. (a) Benchmarks ((aa)) BenchmarksBenchmarks on buildings onon buildings (black and red symbols) indicate limited ground loss, but benchmarks on the 30 m-high (blackbuildings and red(black symbols) and red indicate symbols) limited indicate ground limited loss, ground but benchmarksloss, but benchmarks on the 30 on m-high the 30 chimneysm-high chimneys indicate a 3-D deformation, summarized in (d), (e) and tilting up 0.75%. The tunnel path is indicatechimneys a 3-D indicate deformation, a 3-D deformation, summarized summarized in (d), (e) in and (d), tilting (e) and up tilting 0.75%. up The0.75%. tunnel The tunnel path is path shaded, is shaded, and the predicted influence limits are shown by purple and green lines. (b) Aerial view of andshaded, the predicted and the predicted influence influence limits are limits shown are by shown purple by and purple green and lines. green ( blines.) Aerial (b) viewAerial of view the Gaziof the Gazi area (map of the Hellenic Cadastre) of the area in (a). The excavation route is marked by areathe (map Gazi ofarea the (map Hellenic of the Cadastre) Hellenic ofCadastre) the area of in the (a). area The in excavation (a). The excavation route is marked route is by marked two yellow by two yellow curves. (c) A simplified sketch of the area around chimneys K1 and K2 showing the curves.two yellow (c) A simplifiedcurves. (c) sketchA simplified of the areasketch around of the chimneys area arou K1nd andchimneys K2 showing K1 and the K2 advancement showing the of advancement of the tunnel front. Predicted limits of the tunnel influence zone are marked by theadvancement tunnel front. of Predicted the tunnel limits front. of thePredicted tunnel limits influence of the zone tunnel are marked influence by zone continuous are marked and dotted by continuous and dotted lines. (d,e) Summary of observations of movement of the center of gravity of lines.continuous (d,e) Summary and dotted of observationslines. (d,e) Summary of movement of observations of the center of movement of gravity of ofthe chimneys center of gravity K1, K2 of near chimneys K1, K2 near their top. (f) Side view of the K2 chimney; in the background, some of the theirchimneys top. (f )K1, Side K2 view near of their the K2top. chimney; (f) Side view in the of background, the K2 chimney; some in of the the background, buildings which some providedof the buildingsbuildings whichwhich providedprovided evidenceevidence ofof minimalminimal susubsidence.bsidence. BasedBased onon [17][17] andand unpublishedunpublished data.data. evidence of minimal subsidence. Based on [17] and unpublished data. Infrastructures 2020, 5, 64 4 of 13 Infrastructures 2020, 5, 64 4 of 13

(a) (b)

Figure 3. The problem ofof conﬁdentialityconfidentiality inin tunneltunnel excavation excavation data: data: ( a()a) A A sinkhole sinkhole 8 8 m m wide wide and and 12 12 m mdeep deep opened opened up up at at the the construction construction site site of of Ottawa’s Ottawa’s light light rail rail tunnel tunnel in in2016 2016 [[18].18]. ((b)) AΑ 10 m wide and 15 m deep sinkhole opened up during tunnelin tunnelingg beneath beneath Doukissis Doukissis Plaken Plakentiastias Ave., Ave., Athens for thethe Metro Metro Line Line 3 3 in 2003 [19]. [19]. In In both both cases cases poor poor gr groundound conditions have have been been reported reported but but no other technicaltechnical information information is available.

2. Theoretical Theoretical Modeling Modeling of of Ground Ground Loss Loss The simplestsimplest and and most most eﬃ efficientcient way way to describe to describe ground ground loss was loss proposed was proposed by Peck [1by]. APeck settlement [1]. A settlementtrough is predicted trough is on predicted the ground on the surface ground along surf theace tunnel along axis.the tunnel The 2-D axis. deformation The 2-D deformation of the ground of thesurface groundSv(x surface) in a section Sv(x) in normal a section to the normal tunnel to axisthe tunnel is described axis is by described Equation by (1): Equation (1):

2 ! x 2 Sv(x) = Svmax exp x  (1) S (x ) = S ·⋅ exp−2 i2  v v max  2  (1)  2·⋅ i  whereas Svmax is the maximum settlement above the tunnel axis, x is the horizontal distance from the whereastunnel axis, Svmax and is thei is amaximum parameter settlement defining the above shape the of tunnel the subsidence axis, x is the curve horizontal in analogy distance to the from standard the tunneldeviation axis, of theand normal i is a distribution.parameter defining Parameters the Sshapevmax and of itheare subsidence unknown and curve can in be analogy computed to from the standardinversion deviation of observations of the ofnormal ground distribution. subsidence. Parameters A characteristic Svmax ofand this i curve,are unknown shown inand Figure can 3bea, computedis its symmetry, from ainversion point to be of discussed observations in a laterof ground section, subsidence and describes. A nearly characteristic ideal conditions, of this curve, with a shownuniform in distribution Figure 3a, is of its observations symmetry, fora point a tunnel to be excavated discussed at in nearly a later uniform section, geotechnical and describes conditions. nearly idealExperience conditions, from various with a tunnels uniform indicates distribution that Equation of observations (1) describes for ground a tunnel loss excavated well. A characteristic at nearly uniformexample isgeotechnical shown in Figure conditions.3b, from Experience the Budapest from metro, various a traditional tunnels and indicates representative that Equation example (1) of describestunneling ground [23]. Leveling loss well. data A indicate characteristic a trough exam of theple ground, is shown but in the Figure two parameters 3b, from the describing Budapest it, metro,Svmax and a traditionali, are not constant,and representative because ground example conditions of tunneling in urban [23]. environment Leveling data are indicate variable a (troughSvmax for of theexample ground, vary but by 50%the two in nearby parameters points). describing it, Svmax and i, are not constant, because ground conditions in urban environment are variable (Svmax for example vary by 50% in nearby points). 3. Static Soil Structure Interaction (sSSI) 3. StaticIn the Soil case Structure of Budapest Interaction metro (Figure (sSSI)4 b), the distance between tunnel axis and the nearest facades of buildings is nearly constant and subsidence is typically derived from observations on benchmarks In the case of Budapest metro (Figure 4b), the distance between tunnel axis and the nearest in building facades. In certain cases, however, usually when the tunnel axis was crossing areas with facades of buildings is nearly constant and subsidence is typically derived from observations on buildings on one side and greenfields on the other, benchmarks were established either on building benchmarks in building facades. In certain cases, however, usually when the tunnel axis was facades, or directly on the ground. The outcome of these studies was that the symmetric pattern of crossing areas with buildings on one side and greenfields on the other, benchmarks were Figure4a was violated and in the side of the tunnel proximal to buildings, subsidence was smaller in established either on building facades, or directly on the ground. The outcome of these studies was amplitude and in extension than in the sides of greenfield areas (Figure5). that the symmetric pattern of Figure 4a was violated and in the side of the tunnel proximal to buildings, subsidence was smaller in amplitude and in extension than in the sides of greenfield areas (Figure 5). Infrastructures 2020, 5, 64 5 of 13

(a) (b) Infrastructures 2020, 5, 64 5 of 13 InfrastructuresFigure 4.2020 (a,) 5Idealized, 64 pattern of ground loss, which can be approximated by a Gaussian curve,5 of 13 defined by two parameters, Svmax and i; (b) typical subsidence trough during the excavation of the Budapest Metro (after [23], modified). Subsidence follows the pattern of Equation (1), but along the trough, the amplitude of subsidence (shown by contours, in cm) is variable and ‘bowls’ of increased subsidence are formed.

The explanation proposed for this ‘greenfield effect’ was that buildings absorbed some of the ground deformation, either because of their stiffness, or because of internal deformation (see [24]). This effect, thereafter static Soil Structure Interaction(sSSI), has been investigated on the grounds of numerical modeling. Several studies on modeling the response of specific buildings to tunneling have been made, and their output is that the interaction between building, ground, and tunnel is particularly difficult to (model,a) requiring various a priori assumptions. For(b instance,) sSSI is regarded as a FigureFigure2-D problem 4.4.( a()a Idealized) Idealized [5], buildings pattern pattern of groundofare ground simulated loss, loss, which whichas can beams be can approximated be [25], approximated or the by aeffects Gaussian by a Gaussianof curve, shear deﬁned curve,walls are assumedbydefined two to parameters, beby minortwo parameters, [26].Svmax Therefore,and Siv;(maxb )and typical numerical i; (b subsidence) typical analyses subsidence trough cannot during trough constrain the du excavationring sSSI the excavationwell of the [27]. Budapest However,of the thereMetro Budapestare also (after studiesMetro [23], (after modiﬁed). including [23], modified). Subsidenceevidence Subsidence from follows monito the follows patternring therecords of pattern Equation that of ledEquation (1), to but the along(1), conclusion but the along trough, thatthe the soil–structurethetrough, amplitude the interactionamplitude of subsidence of maysu (shownbsidence reduce by (shown contours, the bypred incontours, cm)icted is variable intendency cm) andis variable ‘bowls’of a and ofbuilding increased ‘bowls’ toof subsidence increasedsuffer high settlementsaresubsidence formed. and are damage formed. during tunneling (see for instance [28,29]).

Figure 5.5. Geodetic observations of ground loss and tiltingtilting (benchmarks on building and on ground) indicateindicate symmetricsymmetric subsidence subsidence troughs troughs if buildings if build existings atexist both at sides both of thesides tunnel of the (top tunnel), but asymmetric (top), but ifasymmetric buildings areif buildings on one side are andon one a greenﬁeld side and ona greenfield the other (onbottom the other). (bottom).

4. EvidenceThe explanation from the Athens proposed Metro for this Line ‘greenfield 2 effect’ was that buildings absorbed some of the ground deformation, either because of their stiffness, or because of internal deformation (see [24]). This effect, thereafter static Soil Structure Interaction(sSSI), has been investigated on the grounds of numerical modeling. Several studies on modeling the response of specific buildings to tunneling have been made, and their output is that the interaction between building, ground, and tunnel is particularly difficult to model, requiring various a priori assumptions. For instance, sSSI is regarded as a 2-D problem [5], buildings are simulated as beams [25], or the effects of shear walls are assumed to be minor [26]. Therefore, numerical analyses cannot constrain sSSI well [27]. However, there are also studies including evidence from monitoring records that led to the conclusion that the soil–structure Figure 5. Geodetic observations of ground loss and tilting (benchmarks on building and on ground) interactionindicate may symmetric reduce thesubsidence predicted troughs tendency if build ofings a building exist at to both suff ersides high of settlementsthe tunnel ( andtop), damagebut duringasymmetric tunneling if (seebuildings for instance are on one [28 side,29]). and a greenfield on the other (bottom).

4. Evidence from the Athens Metro Line 2 Infrastructures 2020, 5, 64 6 of 13

4. Evidence from the Athens Metro Line 2 Certain geodetic monitoring data from the Athens Metro excavation have been recently classified as non-confidential and are available for our research. These data represent the official CSV files of repeated measurements of elevations of benchmarks using geodetic instruments, such as different direct leveling techniques (optical, electronic, and hydraulic leveling) and indirect leveling techniques (using total stations and robotic theodolites). The data cover wider areas above the tunnel sections analyzed, before and long after the excavation of the tunnel and beyond the influence zones of the excavation. There is also available information for the tunnel front advancement, topographic maps with the precise location of the benchmarks, as well as metadata, such as information on the measuring techniques, replacement of benchmarks, etc. These data were evaluated for errors and completeness and were processed. Cases of interaction of double tunnels were excluded. The final product of this preliminary analysis presented in this article is contours of elevation changes of the total subsidence recorded because of a single tunnel line, relative to nearby stable areas. The output of this analysis (input data) is summarized in Figures6 and7 and covers sections of two different lines of the Athens Metro Line 2, between Sepolia and Aghios Antonios station (Kifissos Ave. site) excavated in 2001–2002 at 40 m depth in loose Quaternary deposits and between Peristeri ≈ and Anthoupoli stations in 2002–2003 (Panagi Tsaldari Ave. site) using an Open Face Shield TBM in a Neogene formation of marls at about 20–25 m depth of the tunnel, respectively. In these graphs, the projection of the tunnel section and nearby buildings are also shown in order to understand the effect of the asymmetry in the distribution of buildings and greenfields around tunnels. In these cases, no structural failure in buildings was observed. The pattern of ground deformation derived from Figures6 and7 is roughly consistent with that predicted by Equation (1), especially since it corresponds to a subsidence trough along the tunnel axis, locally disturbed by bowls of increased local ground deformation (compare points S1 to S4 in Figure7 with Figure4b). Still, the data of Figures6 and7 covering tunneling through fully built areas and greenfields, show two main differences in comparison to the model of Figure4b. First, in the case of Budapest Metro excavation, the differences in the maximum amplitude of subsidence along the trough (Svmax) range up to 30% (18–24 mm), while the differences in the width of the trough differ by a factor of 2 (Figure4b). On the contrary, in the cases of the Athens Metro in Figure6, measured subsidence ranges between 5 and 225 mm, i.e., a di fference of 450%, while the width of the trough ranges between 15 and 100 m, a difference of up to 600%. Second, the model of Figure4a and Equation (1) are characterized by symmetry in the deformation along the tunnel axis, but not the cases of Figures6 and7. Asymmetry is mainly reflected in the increase of the width of the side of the subsidence trough in greenfield areas. More specifically, geological reports from the construction site at Panagi Tsaldari Ave. suggest no significant variations of the geological and hydrogeological conditions in the study area, nor in the front advancement rate. The excavation was based on OFS (Open Face Shield) TBM excavation through a fair rock mass (GSI values between 25 and 35). This information, along with details on the excavation and its associated risks, was publicized by [30]. A representative cross section of the tunnel is given in Figure8 (based on [ 31]). Furthermore, according to the official records, the excavation front progress was at a constant rate of 5 m per day and no changes to the support measures or any other ≈ modifications to the excavation procedure were reported. Infrastructures 2020, 5, 64 7 of 13 Infrastructures 2020, 5, 64 7 of 13 Infrastructures 2020, 5, 64 7 of 13

0 20 m 0 20 m

Figure 6. Settlement contours during the excavation of the Athens Metro near Kifissos Ave. FigureFigure 6. Settlement 6. Settlement contours contours during theduring excavation the excavation of the Athens of the Metro Athens near KiﬁssosMetro Ave.near AsymmetriesKifissos Ave. Asymmetries in the subsidence trough (ground loss) due to scattering of buildings on the top in theAsymmetries subsidence trough in the (ground subsidence loss) trough due to scattering(ground lo ofss) buildings due to scattering on the top of signify buildings observations on the top on signify observations on buildings underestimate subsidence due to sSSI. For significant results, only buildingssignify underestimate observations subsidenceon buildings due underestimate to sSSI. For signiﬁcantsubsidence results,due to sSSI. only For settlements significant above results, 10 mmonly settlements above 10 mm are examined. are examined.settlements above 10 mm are examined.

0 40 m 0 40 m

Figure 7. Settlement contours during the excavation of the Athens Metro Line 2 in the Panagi Figure 7. Settlement contours during the excavation of the Athens Metro Line 2 in the Panagi FigureTsaldari 7. AvenueSettlement area contours superimposed during on the Google excavation Map background. of the Athens High Metro subsidence Line 2 contours in the Panagi are Tsaldari Avenue area superimposed on Google Map background. High subsidence contours are Tsaldarishown Avenueby increased area color superimposed grading. White on Google dashes Mapindicate background. areas in which High monitoring subsidence benchnmarks contours are shown by increased color grading. White dashes indicate areas in which monitoring benchnmarks shownwere bydestroyed increased and color replaced, grading. and observations White dashes were indicate discarded areas because in which they monitoring record only benchnmarks part of the were destroyed and replaced, and observations were discarded because they record only part of the wereground destroyed deformation. and replaced, Asymmetries and observations in the subsidence were trough discarded (ground because loss) theyrelated record to the only distribution part of the ground deformation. Asymmetries in the subsidence trough (ground loss) related to the distribution groundof buildings deformation. and greenfield Asymmetries areas insuggest the subsidence that observations trough (groundon buildings loss) underestimate related to thedistribution subsidence of of buildings and greenfield areas suggest that observations on buildings underestimate subsidence buildingsdue to sSSI. and For greenﬁeld significant areas results, suggest only that settle observationsments above on 10 buildings mm are underestimateexamined in this subsidence article. due to due to sSSI. For significant results, only settlements above 10 mm are examined in this article. sSSI. For signiﬁcant results, only settlements above 10 mm are examined in this article. Infrastructures 2020, 5, 64 8 of 13 Infrastructures 2020, 5, 64 8 of 13

Figure 8.8. AA sketchsketch ofof the the tunnel tunnel cross cross section section beneath beneat Panagih Panagi Tsaldari Tsaldari Ave Ave (geology (geology taken taken from from [31]). [31]).The excavated The excavated diameter diameter is 9.5 mis 9.5 and m crown and crown is at 15–20 is at 15–20 m below m below ground ground surface. surface.

5. Discussion Discussion Figures6 6and and7 indicates 7 indicates that inthat greenfields in greenfields the width the ofwidth recorded of recorded subsidence subsidence above an advancing above an advancingtunnel is much tunnel higher is much than higher in the proximitythan in the of proximity various types of various of buildings, types of either buildings, bulky either buildings bulky of buildingslarge dimensions of large ordimensions even smaller or even old brick smaller houses. old brick Thus, houses. it is evident Thus, thatit is subsidenceevident that at subsidence built areas atnormally built areas forms normally a much forms narrower a much trough narrower profile. trou Theregh areprofile. two There possible are explanations two possible for explanations that; either forthat that; ground either subsidence that ground is reduced subsidence at the is ground reduce surfaced at the or ground that because surface of theor interactionthat because between of the interactionground and between structures ground local and strain structures is partly local concealed. strain is The partly first concealed. alternative The can first be rejected alternative in most can becases, rejected because in most ground cases, loss because is a relatively ground deeploss is e ffa ect,relatively affecting deep the effect, rock/ soilaffecting mass the above rock/soil/around mass the above/aroundtunnel, until the the ground tunnel, surface, until whilethe ground foundations surface, of buildings while foundations are usually of shallow buildings and observationsare usually shalloware based and on benchmarksobservations on are the based buildings. on benchmarks In a few cases on only, the forbuildings. example Ιn in a Amsterdam few cases oronly, Venice, for examplebuilding foundationsin Amsterdam include or Venice, relatively building long pilesfoundations and can include make an relatively exception. long The piles second and alternative can make anis thatexception. sSSI leads The to second a smoother alternative trough beneathis that sSSI structures leads to related a smoother to the higher trough sti beneathffness of structures the mixed relatedsystem to of groundthe higher and stiffness structure. of the Still, mixed the situation system is,of however,ground and more structure. complicated. Still, the As situation is analyzed is, however,below, ground more deformation complicated. derived Αs is analyzed from observations below, ground on benchmarks deformation on bulkyderived structures from observations is recorded onwith benchmarks some hysteresis, on bulky and onlystructures after it is exceeds recorded a certain with some threshold. hysteresis, These obscureand only the after pattern it exceeds of “true” a certainground threshold. deformation. These obscure the pattern of “true” ground deformation.

5.1. Amount and Timing of Recorded Ground Deformation 5.1. Amount and Timing of Recorded Ground Deformation Bulky buildingsbuildings modifymodify the the pattern pattern and and amplitude amplitude of groundof ground deformation deformation either either because because of their of theirstiffness stiffness or of internalor of internal strain. strain. For this For reason, this reason, in Figure in 9Figure the original 9 the original ground surfaceground (1)surface would (1) take would the takeform the of curve form (3) of in curve greenfield, (3) in but greenfield, monitoring but stations monitoring on the stations buildings on testify the buildings to a settlement testify trough to a settlementdefined by trough curve (2).defined The troughby curve pattern (2). isThe further trough aff ectedpattern by is the furt facther that affected monitoring by the targets fact that are monitoringplaced mostly targets on structures are placed of interest mostly and on not structur acrosses the of whole interest tunnel and influence not across zone; the so, whole the available tunnel influencedata are confined zone; so, to the specific available areas data and troughsare confined across to the specific tunnel areas axis areand designed troughs withacross interpolation the tunnel axistechniques are designed using limitedwith interpolation data. techniques using limited data.

Infrastructures 2020, 5, 64 9 of 13 Infrastructures 2020, 5, 64 9 of 13

5.2. Uncertainties in Observations Observations of subsidence derive either from various types of leveling (leading to direct or indirect measurement of vertical movements), and/or and/or indirectly from tilting, in combination with models suchsuch as as that that of Equationof Equation (1). Furthermore,(1). Furthermore, all measurements all measurements are characterized are characterized by an uncertainty by an (error,uncertainty noise) (error, typically noise) between typically one between and a few one millimeters. and a few millimeters. This uncertainty is convenient to be regarded in terms of SNR (signal-to-noise ratio), i.e., of the ratio betweenbetween mean mean amplitude amplitude of displacement of displacement to the meanto the amplitude mean ofamplitude uncertainty of inuncertainty measurements. in measurements.For example, leveling For example, measurements leveling close measurements to the ground close surface to the are ground inﬂuenced surface by atmospheric are influenced eﬀects by (lowatmospheric SNR) and effects their (low quality SNR) is much and their lower quality than in is higher much levelslower (higher than in SNR). higher Similarly, levels (higher the accuracy SNR). Similarly,of estimation the ofaccuracy tilting increases of estimation with theof tilting height increases of studied with structure, the height and isof low studied for a structure, typical fence and but is lowhigh for for a a typical tower (highfence SNR).but high Similarly, for a tower at the (high edges SNR) or at. theSimilarly, early stages at the of edges formation or at the of a early subsidence stages oftrough formation (for instance of a subsidence at the edges trough of the (for troughs instance of Figureat the 5edges), the amplitudeof the troughs of dislocation of Figure and 5), itsthe amplitudeSNR are small of dislocation and do not and describe its SNR precisely, are small even and they do may not notdescribe detect precisely, the “true” even dimensions they may of not the detectimpact. the Hence “true” the dimensions extent of the of subsidencethe impact. troughHence tendsthe extent to be of underestimated. the subsidence Thetrough implications tends to be of underestimated.this situation are The summarized implications in Table of this1. situation are summarized in Table 1.

Figure 9. A conceptual model to explain ground loss: ( 1)) original ground surface; ( 2) ground surface derived from subsidence of benchmarks (marked by solid circles) mainly on buildings.buildings. Dashed line indicates troughtrough designed designed by by interpolation interpolation (due (due to limitation to limitation in recording in recording data); (data);3) predicted (3) predicted ground groundsurface atsurface greenﬁeld, at greenfield, following following the Gaussian the Gaussian curve introduced curve introduced by Peck [by1]; Peck (4) formation [1]; (4) formation of sinkhole of (daylightsinkhole (daylight failure). failure). 5.3. Implications for Modeling of the Subsidence Curve and Unexpected Failures 5.3. Implications for Modeling of the Subsidence Curve and Unexpected Failures The problem with sSSI, however, is not limited to the amount of subsidence but extends also to The problem with sSSI, however, is not limited to the amount of subsidence but extends also to its timing [32,33]. Small amounts of subsidence may be concealed because of the combined eﬀect of its timing [32,33]. Small amounts of subsidence may be concealed because of the combined effect of SNR and SSI and evidence of ground subsidence and tilting may appear only after the true ground SNR and SSI and evidence of ground subsidence and tilting may appear only after the true ground deformation exceeds a certain threshold which depends on the ground characteristics and the inertial deformation exceeds a certain threshold which depends on the ground characteristics and the properties of structures. For this reason, early (and critical) phases of deformation may remain inertial properties of structures. For this reason, early (and critical) phases of deformation may unnoticed. This may have destructive implications: monitoring for ground loss based on benchmarks remain unnoticed. This may have destructive implications: monitoring for ground loss based on on buildings may not identify early phases of deformation of buildings or of the ground, which may in benchmarks on buildings may not identify early phases of deformation of buildings or of the fact fail without previous notice. ground, which may in fact fail without previous notice. Infrastructures 2020, 5, 64 10 of 13

Table 1. Signal-to-noise ratio (SNR) for the recorded subsidence at various cases of the surface above tunneling.

Width of Half Part SNR of Subsidence Trough (Signal to Noise Ratio) Precisely estimated. Depending on subsidence amplitude. Free ﬁeld zone (but underestimated if subsidence (SNR proportional to subsidence amplitude is small). amplitude). Isolated tower Precisely estimated. High. Underestimated subsidence. Bulky building Strains partly accommodated by Small. building stiﬀness.

This is perhaps the explanation for some ‘unexplained’ sinkholes. For example, during the excavation of the Athens Metro line 1, a 10 m wide and 15 m deep (until the tunnel roof) sinkhole occurred at the excavation site of Doukissis Plakentias Ave. in January 2003 (see Figure3), but for this event no formal technical information is available. A possible scenario for this last sinkhole is that it occurred in an area with few structures close to the tunnel axis and hence with very few monitoring benchmarks. The tunnel advance was stopped for the New Year’s Day holidays permitting accumulation of deformation due to relaxation of the ground. When the excavation resumed in early January, the (unnoticed) deformation of the soil above the tunnel exceeded a critical threshold, indicating widening of the plastic zone around the tunnel, and possibly in combination with a local eﬀect (possibly an abandoned buried well, among those often met at this area) and/or because of additional deformation induced by the resumed tunnel excavation (cf. [2]), produced the sinkhole.

5.4. Pattern of Ground Subsidence The model of Figure3a describes a 2-D e ffect, but, because of the gradual advancement of the tunnel excavation front, the ground deformation becomes a 3-D effect [11,13,17]. Still, monitoring points, especially on the facades of buildings, usually parallel to the tunnel axes (see Figure1a) can only record tilting down-to-the tunnel axis, i.e., a 2-D effect. This is because the component of ground tilting parallel to the tunnel axis (and to the facades of the buildings) is counteracted and masked by the interaction of adjacent buildings (Figure1a). This limitation does not cover slender structures with small, isolated foundations, such as those of Figures1c and2f (see [17]). In order to further investigate the pattern of the ground subsidence perpendicular to the tunnel at built areas, first we explored the asymmetry of the subsidence troughs (Figure5) and considered sections along the tunnel axis for Panagi Tsaldari Ave. and Kifissos Ave. with symmetric and asymmetric troughs normal to the axis (Figures6 and7). For all nine sections we measured the distance left and right of the tunnel axis from the closest building (dl and dr, respectively; indicating left and right of the tunnel axis) and the corresponding width of the subsidence trough up to the contour of 10 mm, `l and `r, respectively. We also divided these sections in three classes, depending on the background of monitoring points: ‘building-to-building’ (B-B) for both dl and dr < 2.5D (D: tunnel diameter, i.e., the mean width of the tunnel influence zone; [1]), ‘greenfield-to-building’ (G-B) for dl or dr > 2.5D (D: tunnel diameter) and ‘greenfield-to-greenfield’ (G-G), if both dl and dr > 2.5D (i.e., the width of the tunnel influence zone). To compare the sections, we calculated the environs asymmetry ratio E (i.e., asymmetry in building distance) and the skewness of the trough ratio S as follows:

E = dl/dr (2)

S= `l/`r (3) selecting l, r in each section so that dl > dr and `l > `r. Infrastructures 2020, 5, 64 11 of 13 Infrastructures 2020, 5, 64 11 of 13 All these data are summarized in Table 2. In Figure 10, we plotted the ratio of environs asymmetry E as a function of the skewness of the subsidence trough S. A striking contrast between observationsAll these of data tunnel are summarized influence inzone Table in2 .un Iniform Figure 10environment, we plotted the(B-B, ratio G-G) of environs and non-uniform asymmetry environmentE as a function (G-B) of the is skewnessobserved. of This the subsidencecontrast inde troughed indicatesS. A striking a bias contrast in observations between observations of tunnel influenceof tunnel zone influence because zone of in sSSI, uniform which environment is not evident (B-B, G-G)in observations and non-uniform in uniform environment environmental (G-B) is conditionsobserved. (B-B). Thiscontrast indeed indicates a bias in observations of tunnel influence zone because of sSSI, which is not evident in observations in uniform environmental conditions (B-B). Table 2. Nine representative sections drawn along the metro tunnel axis at Panagi Tsaldari Ave., Table 2. Nine representative sections drawn along the metro tunnel axis at Panagi Tsaldari Ave., marked as PT1 to PT6, and Kifissos Ave., marked as K1 to K3 (shown in Figure 4). Distance of marked as PT1 to PT6, and Kifissos Ave., marked as K1 to K3 (shown in Figure4). Distance of tunnel tunnel axis up to the closest building at left and right and the corresponding trough width are axis up to the closest building at left and right and the corresponding trough width are measured. measured. Environs asymmetry ratio E and trough skewness ratio S are calculated using Equations Environs asymmetry ratio E and trough skewness ratio S are calculated using Equations (2) and (3). (2) and (3). Section type (B-B, G-B, or G-G) is marked. Section type (B-B, G-B, or G-G) is marked.

DistanceDistanceDistance to Trough Trough Trough Trough Distance to to to EnvironsEnvirons TroughTrough Building at WidthWidth at at WidthWidth atat Type of TypeSv ofmax SBuilding atBuilding Building AsymmetryAsymmetry SkewnessSkewness SectionSection vmax Right Side LeftLeft Side Side RightRight Side Section Section(mm) Left(mm) Side (m)at Left at Right RatioRatio RatioRatio (m) (m)(m) Side(m) (m) dl Side (m) Side (m) E E S S dr ℓl `l `ℓrr d dr PT1 B-B 24 14 l 14 13 9 1 0.69 PT2 PT1B-B B-B11 24 14 14 14 14 6 13 9 7 1 1 0.69 0.86 PT3 PT2B-B B-B220 11 6 14 14 14 8 6 107 1 0.57 0.86 0.8 PT4 PT3G-B B-B58 220 14 6 25 14 7 8 10 14 0.57 1.78 0.8 2 PT4 G-B 58 14 25 7 14 1.78 2 PT5 G-G 78 25 25 26 28 1 0.93 PT5 G-G 78 25 25 26 28 1 0.93 PT6 G-B 20 25 14 23 15 1.78 1.53 PT6 G-B 20 25 14 23 15 1.78 1.53 K1 G-B 18 25 8 13 8 3.12 1.62 K1 G-B 18 25 8 13 8 3.12 1.62 K2 K2G-B G-B15 15 25 25 10 10 12 12 7 7 2.5 2.5 1.71 1.71 K3 K3B-B B-B12 12 15 15 12 12 8 8 5 5 0.8 0.8 0.62 0.62

3 K1 K2 2 PT6 PT4 PT1 PT2 1 PT5 PT3 Environs assymetry E K3 0 0 0.5 1 1.5 2 2.5

Trough skewness S FigureFigure 10. 10. EnvironsEnvirons asymmetry asymmetry ratio ratio EE (distance(distance to to buildings) buildings) as as a a fu functionnction of of the the subsidence subsidence trough trough skewnessskewness ratio ratio SS.. Data Data as as in in Table 2 2.. SkewnessSkewness ratio ratio SS isis minimumminimum in in uniform uniform greenfield greenfield areas areas (PT5, (PT5, in ingreen) green) and and maximum maximum insections in sections with with buildings buildings at one at side one of theside tunnel of the axis tunnel (Building-Greenfield, axis (Building- Greenfield,i.e., PT4, PT6, i.e., K1, PT4, K2 PT6, shown K1, inK2 red). shown in red). 6. Conclusions 6. Conclusions Analysis of monitoring data from the Athens Metro lines permit to investigate the problem of Analysis of monitoring data from the Athens Metro lines permit to investigate the problem of sSSI during urban tunneling. Observations on benchmarks in greenfields and on isolated towers are sSSI during urban tunneling. Observations on benchmarks in greenfields and on isolated towers are usually free of the sSSI impacts and offer an unbiased estimation of the “true” ground loss. On the usually free of the sSSI impacts and offer an unbiased estimation of the “true” ground loss. On the contrary, observations of ground settlement of urban tunnels are usually based on benchmarks on contrary, observations of ground settlement of urban tunnels are usually based on benchmarks on buildings and tend to present a biased pattern of the subsidence curve: underestimation of subsidence, buildings and tend to present a biased pattern of the subsidence curve: underestimation of masking of its 3-D character, and an apparent skewness in subsidence curves because much of the subsidence, masking of its 3-D character, and an apparent skewness in subsidence curves because local ground surface deformation is concealed due to sSSI. Hence, it seems likely that failures such as much of the local ground surface deformation is concealed due to sSSI. Hence, it seems likely that Infrastructures 2020, 5, 64 12 of 13 damage in buildings, and to sinkhole development are related to underestimation of the “true” ground loss. This result is important for the planning of future projects, for the interpretation of monitoring data during tunnel excavation, as well as for the interpretation of certain cases of failure related to tunnel excavation for which no information exists.

Author Contributions: Conceptualization, V.K.; methodology, V.K. and S.C.S.; formal analysis, V.K. and S.C.S.; resources, V.K. and S.C.S.; data curation, V.K. and S.C.S.; writing—original draft, V.K. and S.C.S.; writing—review and editing, V.K.; visualization, V.K. All authors have read and agreed to the published version of the manuscript. Funding: This research received no external funding. Acknowledgments: Attiko Metro SA and M. Novak in particular are thanked for valuable information and monitoring data. This paper benefited from comments of two anonymous reviewers. These results do not mean that Attiko Metro endorses our views or that it recognizes any legal impacts from this publication. Conflicts of Interest: The authors declare no conflict of interest.

References

1. Peck, R.B. Advantages and limitations of the observational method in applied soil mechanics. Geotechnique 1969, 19, 171–187. [CrossRef] 2. Kontogianni, V.; Psimoulis, P.; Pytharouli, S.; Stiros, S. Geodetic monitoring of underground excavations: 70 years after Terzaghi’s innovative techniques at the Chicago subway tunnels. In Proceedings of the 5th International Symposium of the International Society for Soil Mechanics and Geotechnical Engineering, Amsterdam, The Netherlands, 15–17 June 2005; pp. 31–36. 3. Burland, J.B.; Standing, J.R.; Jardine, F.M. Building Responses to Tunneling—Case studies from Construction of the Jubilee Line Extension; Thomas Telford: London, UK, 2001; Volume 1. 4. Ritter, S.; Giardina, G.; DeJong, M.J.; Mair, J. Influence of building characteristics on tunnelling-induced ground movements. Géotechnique 2017, 67, 926–937. [CrossRef] 5. Giardina, G.; DeJong, M.J.; Mair, R.J. Interaction between surface structures and tunnelling in sand: Centrifuge and computational modelling. Tunn. Undergr. Space Technol. 2015, 50, 465–478. [CrossRef] 6. Harris, D.I. Building Response to Tunnelling—The Clock Tower and The Palace of Westminster; Thomas Telford: London, UK, 2002; Chapter 28. 7. Kavvadas, M. Monitoring ground deformation in tunnelling: Current practice in transportation tunnels. Eng. Geol. 2005, 79, 93–113. [CrossRef] 8. Finno, R.; Bryson, L. Response of building adjacent to stiff excavation support system in soft clay. J. Perform. Constr. Facil. 2002, 16, 10–20. [CrossRef] 9. Kaalberg, F.J. Advanced Modeling to Support Innovative Developments in Tunneling for Amsterdam North/South Line. In Finite Elements in Civil Engineering Applications, Proceedings of the Third DIANA World Conference on Finite Elements in Civil Engineering Tokyo, 9–11 October 2002; A.A. Balkema Publisher: Tokyo, Japan, 2002. 10. Finno, R.; Voss, F.; Rossow, E.; Blackburn, T.J. Evaluating Damage Potential in Buildings Affected by Excavations. J. Geotech. Geoenviron. Eng. 2005, 131, 1199–1210. [CrossRef] 11. Finno, R.; Blackburn, J.T.; Roboski, J. Three-dimensional effects for supported excavations in clay. J. Geotech. Geoenviron. Eng. 2007, 133, 30–36. [CrossRef] 12. Son, M.; Cording, E. Responses of buildings with different structural types to excavation-induced ground settlements. J. Geotech. Geoenviron. Eng. 2011, 137, 323–333. [CrossRef] 13. Namazi, E.; Mohamad, H. Assessment of building damage induced by three-dimensional ground movements. J. Geotech. Geoenviron. Eng. 2013, 139, 608–618. [CrossRef] 14. Farrell, R.; Mair, R.; Sciotti, A.; Pigorini, A. Building response to tunnelling. Soils Found. 2014, 54, 269–279. [CrossRef] 15. Bjureland, W.; Spross, J.; Johansson, F.; Prästings, A.; Larsson, S. Reliability aspects of rock tunnel design with the observational method. Int. J. Rock Mech. Min. Sci. 2017, 98, 102–110. [CrossRef] 16. Van Hasselt, D.R.S.; Hentschel, V.; Hutteman, M. Amsterdam’s north/south metroline. Tunn. Undergr. Space Technol. 1999, 14, 191–210. [CrossRef] Infrastructures 2020, 5, 64 13 of 13

17. Papastamos, G.; Stiros, S.; Saltogianni, V.; Kontogianni, V. 3-D strong tilting observed in tall, isolated brick chimneys during the excavation of the Athens metro. Appl. Geomat. 2015, 7, 115. [CrossRef] 18. Science Alert. This Gigantic Sinkhole in Ottawa Just Took Out a 4-Lane Road. 2016. Available online: www.sciencealert.com/gigantic-sinkhole-in-canada-s-capital-ottawa-may-have-been-caused-by- quick-clay (accessed on 30 July 2020). 19. Kathimerini Newspaper. 2003. Available online: www.kathimerini.gr/139341/article/epikairothta/ellada/h- trypa-sto-metro-ek8eteiergolavoys-kai-mhxanikoys (accessed on 30 July 2020). (In Greek). 20. Kontogianni, V.; Pytharouli, S.; Stiros, S. Ground subsidence, quaternary faults and vulnerability of utilities and transportation networks in Thessaly, Greece. Environ. Geol. 2007, 52, 1085–1095. [CrossRef] 21. Mair, R.J.; Taylor, R.N.; Burland, J.B. Prediction of Ground Movements and Assessment of Risk of Building Damage Due to Bored Tunneling. In Proceedings of the International Symposium on Geotechnical Aspects of Underground Construction in Soft Ground, London, UK, 15–17 April 1996; pp. 713–718. 22. Maravas, A.; Mylonakis, G.; Karabalis, D. Dynamic Soil-Structure Interaction for SDOF Structures on Footings and Piles. In Proceedings of the Geotechnical Earthquake Engineering and Soil Dynamics IVGSP181, Sacramento, CA, USA, 18–22 May 2008. [CrossRef] 23. Szechy, K. The Art of Tunneling; Hungarian Academy of Sciences: Budapest, Hungary, 1973. 24. Franzius, J.N.; Potts, D.M.; Burland, J.B. The response of surface structures to tunnel construction. Proc. Inst. Civ. Eng. Geotech. Eng. 2006, 159, 3–17. [CrossRef] 25. Pickhaver, J.A.; Burd, H.J.; Houlsby, G.T. An equivalent beam method to model masonry buildings in 3D ﬁnite element analysis. Comput. Struct. 2010, 88, 1049–1063. [CrossRef] 26. Goh, K.H.; Mair, R.J. Response of framed buildings to excavation-induced movements. Soils Found. 2014, 54, 250–268. [CrossRef] 27. Franza, A.; Marshall, A.; Haji, T.; Abdelatif, A.O.; Carbonari, S.; Morici, M. A simpliﬁed elastic analysis of tunnel-piled structure interaction. Tunn. Undergr. Space Technol. 2017, 61, 104–121. [CrossRef] 28. Burd, H.J.; Houlsby, G.T.; Augarde, C.E.; Liu, G. Modelling tunnelling-induced settlements of masonry buildings. Proc. Inst. Civ. Eng. Geotech. Eng. 2000, 143, 17–29. [CrossRef] 29. Bilotta, E.; Paolillo, A.; Russo, G.; Aversa, S. Displacements induced by tunnelling under a historical building. Tunn. Undergr. Space Technol. 2017, 61, 221–232. [CrossRef] 30. Marinos, P.; Marinos, V.; Stoumpos, G.; Novak, M.; Korkaris, K.; Benissi, M. Behaviour of the “Athenian schist” in excavation by an open face shield boring machine extension line to peristeri of the metropolitan railway of Athens. Bull. Geol. Soc. Greece 2004, 36, 1790–1795. [CrossRef] 31. Kynigalaki, M.; Nikolaou, N.; Karfakis, J.; Koutsouveli, A.; Poyiadji, E.; Pyrgiotis, L.; Konstantopoulou, G.; Bellas, M.; Apostolidis, E.; Loupasakis, K.; et al. Digital engineering geological map of the Athens Prefecture area and related Database Management System. Bull. Geol. Soc. Greece 2010, 43, 1619–1626. [CrossRef] 32. Kontogianni, V.; Psimoulis, P.; Stiros, S. What is the contribution of time-dependent deformation in tunnel convergence. Eng. Geol. 2006, 82, 264–267. [CrossRef] 33. Sulem, J.; Panet, M.; Guenot, A. Closure analysis in deep tunnels. Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 1987, 24, 145–154. [CrossRef]

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