Predictions of ground deformations in shallow tunnels in clay

Ž.Tunnelling and Underground Space Technology1720023᎐19Predictions of ground deformations in shallow tunnels in clayWei-I.Chou a,Antonio Bobet b,Ua Professional Ser¨ice Industries,Inc.,Indianapolis,IN,USAb Purdue Uni¨ersity,West Lafayette,IN,USAReceived7May2001;received in revised form15October2001;accepted1November2001AbstractTwenty-eight tunnels are used to evaluate predictions from an analytical solution for shallow tunnels in saturated ground.The solution assumes plane strain conditions at any cross-section perpendicular to the tunnel axis and poroelastic behavior of the ground and elastic behavior of the liner.Stresses and deformations are obtained with this method for short-and long-term conditions anywhere in the continuum.Of particular interest to this study are the short-term surface settlements at the ground parisons between predictions and observations from actual tunnels show good agreement,generally within15%Ž.difference.The analyses show that:1most of the ground movements are caused by the gap parameter,which is a measure of the three-dimensional deformations at the tunnel face,the physical gap between the liner and the perimeter of the excavation,Ž.and of the workmanship;2most of the ground deformations take place within a distance of three to four radii around the Ž.tunnel;3the bottom boundary of zero vertical deformation should be placed at a distance of two tunnel diameters below theŽ.tunnel center line,or at the location of a stiff soil layer,whichever comesfirst;4the horizontal movements around the tunnelŽ.are relatively smaller than the vertical movements;and5the analytical solution tends to underpredict the maximum soil deformations and overestimate the settlement trough;however,with an appropriate estimation of the gap parameter and small soil yield,the differences between predictions and observations are small.ᮊ2002Elsevier Science Ltd.All rights reserved.Keywords:Tunnels;Analytical solution;Saturated ground1.IntroductionDue to recent city developments with limited avail-able land to build on,more and more public facilities are developed under the ground plex un-derground constructions may cause serious damage to existing structures if predictions do not forecast the ground behavior during excavation.Surface settlements are often estimated using empirical methods such asŽ. the Schmidt᎐Peck method Peck,1969;Schmidt,1969, where it is generally assumed that the surface settle-U Corresponding author.Tel.:q1-765-494-5033;fax:q1-765-496-1364.Ž.E-mail address:bobet@ A.Bobet.ment trough can be approximated by the normal probability curve or error function:x2Ž. S s S exp y1 max2ž/2iIn the equation,S is settlement,S is the maxi-maxmum settlement above the tunnel centerline,‘x’is the horizontal distance from the tunnel centerline in the transverse direction,and‘i’is the distance from the tunnel centerline to the inflexion point of the curve. Other empirical or quasi-empirical methods haveŽbeen proposed recently Verruijt and Booker,1996;.Loganathan and Poulos,1998that show good correla-tions between observations from actual tunnels and predictions.Empirical methods,however,have signifi-0886-7798r02r$-see front matterᮊ2002Elsevier Science Ltd.All rights reserved.Ž.PII:S0886-77980100068-2()W.Chou,A.Bobet r Tunnelling and Underground Space Technology 1720023᎐194Ž.cant shortcomings:1they have been developed or Ž.have been validated from a limited number of cases;2they should be applied only to tunnels that fall within the scope of the cases from which the method was Ž.developed;3only few soil and geometry parameters Ž.are taken into account;4they do not consider con-Ž.struction methods;and 5they cannot give the com-plete solution of a tunnel with support.Empirical methods are still widely used;however,predictions of ground movements based on such meth-ods are insufficient for most practical applications.There are a limited number of analytical and numerical tools that can be used to predict ground deformations,but there is a growing demand for developing practical rational methods for tunnel design.This paper focuses on the applicability of one of the recently proposed Ž.rational methods Bobet,2001for shallow tunnels in saturated ground.Although the method is based on elasticity and does not fully account for the behavior of the soil,the predictions are quite good when compared with actual cases,and the solution may be used for preliminary design.2.The analytical solutionThe solution of a shallow tunnel in a saturated Ž.ground has been obtained by Bobet 2001,with the Ž.Ž.following assumptions see Fig.1:a circular cross-Ž.section with radius r ;b plane strain conditions in a o direction perpendicular to the cross-section of the tun-Ž.nel;c frictionless interface between the ground and Ž.Ž.the liner e.g.shield driven tunnels ;d depth to radius Ž.ratio larger than 1.5;e homogeneous and isotropic Ž.ground;f poroelastic behavior of the ground and Ž.Želastic liner;g small thickness of the liner i.e.linerFig.1.Shallow tunnel..Ž.thickness,t <r ;and g permeability of the ground o small enough such that no excess pore pressures dissi-Žpate during construction i.e.undrained conditions ap-.ply .Of particular interest to this study is the short-term Ž.i.e.immediately after construction ground movements of a shallow tunnel in a saturated ground with or without application of air pressure during construction.The following is a summary of the most relevant equa-tions needed for the analysis.Further details can be Ž.found in Bobet 2001.The solution must satisfy the equilibrium equations,the strain compatibility equations,and the boundary conditions.A general solution has been proposed by Ž.Timoshenko and Goodier 1970,in the form of the Airy function,␾:␾s a ln r q b r 2q c r 2ln r q d r 2␪q a Ј␪0000013y 1Ž.q a r ␪sin ␪q b r q a Јr q b Јr ln r cos ␪1111213y 1Ž.y c r ␪cos ␪q d r q c Јr q d Јr ln r sin ␪11112ϱn n q 2y n y n q 2Ž.q a r q b r q a Јr q b Јr cos n ␪Ýn n n n n s 2ϱn n q 2y n y n q 2Ž.qc r qd r q c Јr q d Јr sin n ␪Ýn n n n n s 2Ž.2where the parameters a ,b ,c ,etc.,are determined 000from the boundary conditions.The complete solution is obtained by decoupling the liner and the ground and imposing compatibility of deformations and stresses at the interface between the ground and the liner.The following boundary conditions apply:<<␶s U s 0␪s "␲r 2␪s "␲r 2r ␪␪ground <liner <U s U y w r s r r s r r r o o ground <liner <Ž.␴s ␴3r s r r s r r r o oground <liner <Ž.␶s ␶s 0smooth interface r s r r s r r ␪r ␪o o <Ž.Ž.␴sy ␥q ␥h y y r ªϱy b w <Ž.␴s k ␴Јq ␥h y y r ªϱx y w w where x ,y are the Cartesian coordinates with origin atthe center of the tunnel and r ,␪are the corresponding polar coordinates;␴,␴,␶,U ,U ,are the total r ␪r ␪r ␪stresses and displacements in polar coordinates;␴,␴x y()W.Chou,A.Bobet r Tunnelling and Underground Space Technology 1720023᎐195Žare the total stresses in Cartesian coordinates ␴Јis for .effective stresses ;w is the gap parameter,which is the magnitude of the radial soil displacements that occur before the liner provides support;␥and ␥are the b w buoyant unit weight of the ground and the unit weight of the water,respectively;k is the coefficient of earth pressure at rest;h and h are the depth of the tunnel w below the ground surface and below the water table Ž.Ž.Fig.1.Note that the far field stresses i.e.for y ªϱcorrespond to the geostatic stresses in a half-space continuum.Because of the assumption of short-term analysis Ž.i.e.excess pore pressures do not dissipate ,the ground Ž.cannot change volume i.e.␧s 0.For a poroelastic vol material,this requires:Ž.␴Јq ␴Јs 04r ␪The stress ᎐displacement relations for the liner are Ž.Flugge,1966:¨2linerlinerŽ2.dU dU C 1y ␯␪r liner qsyr ␶o r ␪2d ␪Ed ␪dU liner d 4U liner d 2U linerC␪r r liner liner q U q q 2q U r r 42ž/d ␪Fd ␪d ␪Ž2.C 1y ␯linerŽ.s r ␴5o r EC and F are the compressibility and flexibility ratios,respectively,defined as:Ž2.3Ž2.Er 1y ␯Er 1y ␯o s o s Ž.C s ;F s622Ž.Ž.E A 1y ␯E I 1y ␯s s s s where E ,␯are the Young’s modulus and Poisson’s ratio of the ground;E ,␯are the Young’s modulus s s and Poisson’s ratio of the liner;A ,I are the area and s s moment of inertia of the cross-section of the liner per Ž.unit length of tunnel Fig.1.2.1.Short-term analysis of a tunnel in saturated ground ()no air pressure Ž.Ž.The solution of Eqs.2᎐6determines the stresses Žand displacements anywhere in the continuum i.e.for .both ground and liner .The ground displacements are of particular interest,and are given by:a c Ј1q ␯1o 1U sy q q c ln r sin ␪r 12½E r 2r a Јb Јc Јd Ј2233q 2q 2cos2␪q 3q 3sin3␪3425r r r r c Ј1q ␯11Ž.U sy y c 1q ln r cos ␪␪12½E 2r a Јc Јd Ј233Ž.q 2sin2␪y 3q cos3␪73425r r r withw Ž.x Ž2.␥h 1q k q 2␥h 1y ␯CFb w w Ž.Ž.q 2E C q F w r r 1o 2a s r 0o22Ž.Ž.Ž.C q F 1q ␯q 1y ␯CFŽ.2c sy ␥q ␥r 1b w o14Ž.c Јsy ␥1y k r 1b o8Ž.11y ␯F q 34Ž.Ž.a Јsy␥h 1y k r 82b o4Ž.1y ␯F q 6Ž.121y ␯F q 32Ž.b Јs␥h 1y k r 2b o4Ž.1y ␯F q 6Ž.11y ␯F q 126Ž.c Јs␥1y k r 3bo12Ž.1y ␯F q 24Ž.11y ␯F q 84Ž.d Јsy␥1y k r 3bo8Ž.1y ␯F q 242.2.Short-term analysis of a tunnel in saturated ground with air pressureThe stresses and displacements of the ground and liner are obtained for the following construction process:1.The tunnel is excavated under air pressure,p .a2.The liner is installed and the air pressure released.During excavation the opening is created and,at the same time,an internal air pressure,p ,is applied.To a prevent water inflow into the tunnel,the value of the air pressure is generally taken as the magnitude of the water pressure at the invert of the tunnel.Ž.Ž.P s ␥h q r 9a w w o Once the excavation is completed,the liner is in-stalled and the air pressure released.At the end of this()W.Chou,A.Bobet r Tunnelling and Underground Space Technology 1720023᎐196Ž.construction process,the solution is given by Eq.7with:122Ž.Ž.a s␥h 1q k r q ␥h y p r 0bo w w a o 2Ž2.Ž.Ž.1y ␯CFp q C q F E w r r a o 2q ro2Ž.Ž.Ž.1q ␯C q F q 1y ␯CF Ž.2c sy ␥q ␥r 1b w o14Ž.c Јsy ␥1y k r 1b o814Ž.Ž.a Јsy ␥h 1y k r 102b o412Ž.b Јs␥h 1y k r 2bo 216Ž.c Јs␥1y k r 3bo 1214Ž.d Јsy ␥1y k r 3b o8Ž.As it can be observed in Eq.7,the analytical solution predicts an increase of displacements with the logarithm of the radial distance.While this is a mathe-Žmatical consequence of the assumptions made i.e.semi-infinite,elastic,isotropic,homogeneous medium,.and infinitely long tunnel ,it has no physical basis.In reality,the soil conditions are not homogeneous and the soil does not extend to an unlimited depth.At a certain distance below the tunnel there will be a stiff Ž.layer e.g.bedrock where the vertical displacements should be zero.In addition,other factors such as an increase of the stiffness of the soil with depth,weight Ž.Žof the Tunnel Boring Machine TBM and liner not .considered in the analytical solution ,and not uniform tail gap around the excavation will reduce at the invert the soil displacements towards the excavation.Hence a correction should be made to the above formulation such as at a certain distance below the tunnel center-line the vertical displacements are zero.Hence,corrected analyticalsolutiontopof stiff layerŽ.U s U y U 11y y y The boundary of zero vertical displacement is chosen Ž.at a depth which is the smallest of:a the depth of Žbedrock or stiff layer a soil layer can be considered stiff when its Young’s modulus is approximately 100times larger than that of the soil where the tunnel is .Ž.excavated ;and b two times the tunnel diameter below the tunnel centerline;this is an empirical ap-proximation obtained from actual case studies and is related to the zone of influence of the excavation.Once this correction is done,the solution recovers physical meaning in that displacements decrease as the distance Ž.from the tunnel increases Bobet,2001.Note that horizontal displacements do not need correction.Ž.Soil displacements,as defined by Eq.7,are very sensitive to the gap parameter,w ,since small variations of w may have a large effect on soil settlements.The gap parameter represents the soil deformations that occur before the soil gets in contact with the liner.Hence,this parameter is a measure not only of the physical gap between the liner and the ground,but also of the soil deformations ahead of the excavation and of Ž.the quality of the workmanship overcutting .The rela-tive importance of this parameter can be evaluated by Žlooking at the maximum settlements at the surface i.e..for ␪s 90Њ,y s h .With typical ground and liner properties the flexibility ratio,F ,is very large.An approximate solution for some tunnels can be obtained Ž.assuming a very flexible F s ϱand incompressible Ž.liner C s 0.If the water table is at the surface,and for a tunnel without air pressure,the maximum settle-Žments,␦,are no corrections for stiff layer are max .used :wr 1q ␯1o 2␦syq y ␥r ln h max o ½h E 235r r r 31o o oŽ.q ␥h 1y k r y qyb o ž/ž/5h 4h 4h Ž.12For a tunnel excavated under air pressure:wr 1q ␯1o 2Ž␦syq y ␥r ln h q ␥h 3max o b ½h E 235r r 31oo2.Ž.y k r q ␥h 1y k r yo b ož/ž/4h4h 2r o Ž.q ␥hr 13w ož/5hŽ.Ž.Eqs.12and 13show that for a very flexible and incompressible liner the maximum settlements on the Ž.surface are due to two terms:1a geometric term that Ž.involves the gap parameter;and 2a term that in-volves the ground stiffness,E .The relative importance that each term has on the total settlement depends on the geometry of the tunnel and on the ground stiffness.It is clear that as the stiffness of the ground increases,the gap parameter becomes very important.For other Ž.types of liners i.e.relatively flexible and compressible the stiffness of the liner may have a substantial effect on settlements,particularly the compressibility of the()W.Chou,A.Bobet r Tunnelling and Underground Space Technology1720023᎐197liner since as the parameter C becomes larger theŽsettlements increase note that at the limit,Cªϱ,the.tunnel behaves as if there was no liner.Ž.Ž.A comparison between Eq.12and Eq.13also shows that the ground displacements at the surface are larger for a tunnel excavated under air pressure than without air pressure.This is due to the construction process assumed,where the ground is initially sup-ported only with the air pressure.The definition of the gap parameter necessarily in-troduces some uncertainty on its determination;how-ever,it can be estimated from one of the following two methods:Ž.Ž.1Direct estimation Lee et al.,1992.Ž. w s G q U q workmanship14 p3Dwhere G is the physical gap between the liner and the pperimeter of the excavation and includes the thickness of the TBM tailskin and the clearance required forerection of the liner;U is a measure of the soil3Dmovements ahead of the face of the tunnel;and the workmanship is a measure of the overcutting as theŽTBM is steered Lee et al.,1992,provide details on how to obtain each of the three components of the gap .parameter.Ž.2Back-calculation from the estimated or measured ground loss.22Ž.␲r q w y␲r2wo oŽ. Ground loss s(152r␲r oowhere the ground loss should also include workman-ship.3.Case studiesŽ.A total of14tunnels including28tunnel sections have been investigated.They comprise different con-struction techniques including compressed air,have ground conditions that range from soft to stiff clay,and coefficients of earth pressure at rest ranging from0.5 to1.5.Some of the cases have been investigated by previous researchers and are well documented,and thus they are very well suited to make comparisons with the analytical solution and assess its applicability to actual tunnels.Table1summarizes characteristic soil properties, geometry of the tunnels,and construction methods. Most of the parameters are taken from published re-sults;in a few cases,however,some of the data needed for the analytical solution are not available and have been estimated from other parameters;for example the Poisson’s ratio of the soil,if not available,is taken as 0.2,and the soil Young’s modulus,if not given,is estimated from undrained shear strength S,standardu penetration tests,or from cone penetration tests.If the properties of the liner are not reported in the litera-ture,they are taken as E s25000MPa and␯s0.3,s s which correspond to a typical support.Table1also gives the stability number N at the face of the excava-tion;the stability number is defined as:␥h y␴iŽ. N s16 Suwhere␥h is the total vertical stress at the tunnel axis,␴is the support pressure at the face of the tunnel,and iS is the undrained shear strength of the soil.uFive cases are reviewed in detail in this paper and are used to compare the predictive capabilities of the analytical solution with actual measurements.Three of thefive tunnels are excavated without compressed air, and two with compressed air.The conclusions obtained from the cases presented are thought to be representa-tive and applicable to the rest of the tunnels.3.1.Tunnels without compressed air3.1.1.London Transport Fleet Line,Green Park UndergroundThe Green Park Underground Tunnel was shield driven in stiff heavily overconsolidated London clay. The tunnel was excavated by hand with a 4.146-m diameter shield at a depth of approximately29m.A seven-segment cast-iron lining4.07-m external diame-ter and0.6-m width was erected inside the shield tailskin and water᎐cement grout was injected into the cavity between the liner ring and the excavated soil.A simplified soil profile of the construction site consisted from top to bottom of a layer of sand and gravel down to a depth of2m;underneath there was a very thick layer of stifffissured clay where most of the tunnel was Ž.excavated Attewell and Farmer,1974.The ground-water level was found at a depth of approximately2m. The undrained shear strength of the stiff clay,obtained from unconsolidated undrained triaxial tests,is taken for the analyses as270kPa which is consistent with the reported stability number N of2.2.The elastic modu-Ž. lus of the clay is estimated as50MPa Lo et al.,1984, and the coefficient of lateral earth pressure at rest K0 is1.5,which is typical of London clay.The physical gap between the perimeter of the excavation and the liner is the sum of the size of the bead,6.5mm,and the tail void,76mm.Lo et al.have suggested a gap parameter, w,equal to23mm,based on their evaluation of the physical gap,grouting of the tail void,and face move-()W.Chou,A.Bobet r Tunnelling and Underground Space Technology 1720023᎐199ments;this is the magnitude of the gap parameter taken for the analytical solution.Fig.2shows a comparison between predictions from the analytical solution and observed movements.Fig.3shows observed and predicted soil settlements above the tunnel centerline.The comparisons are quite good.As observed in the figures both the analytical solution and the observed settlements resemble a Gauss probability function.Another interesting observation is that,as shown in Fig.3,most of the soil deformations occur within an area very close to the tunnel,of the order of three to four radii.3.1.2.Bangkok Sewer Tunnel,ThailandThe tunnel is a sewer tunnel built for the Metropoli-tan Water Works Authority in Bangkok.The tunnel was driven at a depth of approximately 18m;it has a total length of 10.5km,and a diameter of 2.67m Ž.Phienwej,1997.Three earth-pressure balanced shields were used to excavate the tunnel and each shield had a diameter of 2.8m and a length of 6.2m.Depending on the ground conditions,the ground control features of the machines ranged from closeable flood door or Ž.stable ground to full earth pressure balance EPB support for unstable ground.The primary support con-sisted of 150-mm-thick and 1-m-long bolted concrete segments with secondary grouting to backfill the annu-lar space behind the segmental rings.Bangkok is situated on a thick series of marine and alluvial soil deposits.Down to 35-m depth the subsoil profile is relatively uniform.A thick soft marineclayFig.2.Green Park Underground Tunnel.Surface settlements.layer with undrained shear strength of 10᎐15kPa and water content 70᎐120%extends from the ground sur-face to a depth of 12᎐15m.Underneath there is a uniform and impervious stiff clay with thickness rang-ing between 5and 15m.A fine to medium dense sand layer appears under the stiff clay with a total thickness ranging between 8and 16m.The undrained Young’s modulus of the stiff clay is approximately 20MPa.The water table is found within the soft marine clay approx-imately 2m below thesurface.Fig.3.Green Park Underground Tunnel.Subsurface settlements above centerline.()W.Chou,A.Bobet r Tunnelling and Underground Space Technology 1720023᎐1910Fig.4.Bangkok Sewer Tunnel.Surface settlements.A gap parameter of 37mm is taken for the analysis,based on the estimated ground loss 3᎐5%and tunnel Ž.geometry Phienwej,1997.The bottom boundary is set at a depth of 23m where a dense sand layer is found.Figs.4᎐6show predicted and observed soil deforma-tions.Fig.4is a plot of surface settlements;Fig.5is a plot of subsurface settlements with depth,and Fig.6shows actual and predicted horizontal displacements at a vertical cross-section perpendicular to the tunnel,4m from the tunnel centerline.Surface settlements and Ž.horizontal displacements Figs.4and 6are predicted reasonably rger differences are observed inFig.Fig.5.Bangkok Sewer Tunnel.Subsurface settlements above centerline.() W.Chou,A.Bobet r Tunnelling and Underground Space Technology1720023᎐1911Fig.6.Bangkok Sewer Tunnel.Subsurface horizontal displacements4m from centerline.5between predictions and measurements,particularly close to the crown of the tunnel.Observed settlements are much larger than predicted settlements;this may be caused by the large deformations that are necessary in the soil tofill the physical gap between the liner and the excavation.Such large deformations are likely to produce plastic deformations in the soil which may account for some of the discrepancies.Another reason for the differences is the layered nature of the soil; although the tunnel is excavated in the stiff clay,there is a thick soft clay deposit near the surface.The influ-ence of this deposit can be noticed on the horizontal displacements depicted in Fig.6,where the slope of the observed settlement curve increases significantly on the top10m of the soil,where the soft deposit is encoun-tered.3.1.3.London Transport Fleet Line,Regent’s ParkTwo tunnels with4.146m diameter were constructed with expanded concrete lining at depths of20.1mŽ.Ž. northbound and34.1m southbound at Regent’s Park,London,as part of the Fleet Line of the LondonŽ. Underground Barratt and Tyler,1976.The vertical distance between the Northbound and the Southbound tunnel centerlines is14m,and the horizontal distance is18m.Both tunnels were shield driven with a3-mm bead and were hand excavated;the southbound tunnel was constructedfirst.Precast concrete segments were used as the primary support and the concrete lining was expanded against the ground immediately after erection.The tunnels were excavated in London Clay,which can be characterized as a stiff,fissured,overconsoli-dated clay.The undrained shear strength of the clay, S,obtained from unconsolidated undrained triaxial utests is230kPa.The Young’s modulus is taken as32 MPa for the northbound tunnel and56MPa for theŽ. southbound tunnel,after Lee et al.1992;the coeffi-cient of lateral earth pressure is1.5,which is typical of London clay.The groundwater table was found at a depth of approximately4m.The ground loss for both tunnels was 1.3᎐1.4%.Ž. Although the tail void was quite small3mm the gap parameter is taken as17mm for the northbound tunnel and23mm for the southbound to account forŽface deformations and workmanship after Lo et al., .1984.Figs.7᎐9show comparisons between the analytical solution and actual measurements.All comparisons are reasonably good.Fig.7is a plot of surface settlements for both the northbound and southbound tunnels.Since the distance between the two tunnels is quite large,it is expected that the construction of thefirst tunnel Ž.southbound should not affect the settlements caused by the construction of the second tunnel;this is shown in thefigure.Fig.8is a plot of the subsurface settle-ments above the centerline of the northbound tunnel. The soil deformations are larger above the crown of the tunnel and decrease as the distance from the tunnel increases;in fact beyond a distance of approxi-mately three tunnel radii the settlements do not in-crease significantly.A similar observation can be made()W.Chou,A.Bobet r Tunnelling and Underground Space Technology 1720023᎐1912Fig.7.Regent Park Underground.Surface settlements.Ž.for the southbound tunnel Fig.9.The settlements of the southbound tunnel above the crown are larger than the northbound tunnel even though the southbound tunnel rests on a relatively stiffer clay compared to the northbound tunnel;this is a result of the larger gap parameter,and for this case is an indication of the relative importance of this parameter compared to the geometry of the tunnel or to the soil properties.3.2.Tunnels with compressed air3.2.1.Belfast Sewer Scheme,Sydenham,BelfastThe tunnel is a sewer tunnel constructed in Belfast;it is 450m long and has a circular cross-section of 2.74m in diameter.The tunnel is rather shallow,with an average depth of 4.85m below the groundsurface.Fig.8.Regent Park Underground.Northbound tunnel.Surface settlements above centerline.Fig.9.Regent Park Underground.Southbound tunnel.Surface settlements above centerline.Considerable settlements were experienced by previ-ous cut and cover excavations.Since the route of the culvert ran close to housing and industrial buildings,it was decided to construct the culvert in the tunnel to reduce surface settlements and minimize damage to the above buildings.The tunnel was shield-driven and was supported by precast concrete rings.The shield had a3-mm bead and a1-m-long tailskin.The rings were composed offive bolted segments0.6m long, which were erected within the tailskin of the shield. Grouting was directly injected into the rear of the tailskin after each shove to reduce settlement.The tunnel was excavated below the groundwater table, which was located at a depth of1.2᎐1.5m below the ground surface.To keep water out of the tunnel and to help stabilize the weak face,the tunnel was constructed2Žwith compressed air at a pressure of48kN r m41 2.kN r m at an earlier stage.This air pressure lowered the stability number N of the face from8.35to3.60. The tunnel was built in an alluvial deposit with sandy layers with variable clay and organic content.Below the surface there was afill deposit between2and3m thick;underneath there was a soft gray silty clay5᎐6m thick followed by a thick stiff brown clay.The tunnel was excavated within the soft silt deposit,under the water table.The silty clay deposit showed highly vari-able engineering properties,with undrained shear strength ranging from8to20.5kN r m2.The gap parameter is obtained from the ground loss,Ž.1.8᎐2.1%,Glossop and Farmer,1977,and ranges between23and28mm.Figs.10and11show predictions and measurementsŽ.at two control locations arrays A and B.As shown in thefigures the predictions are reasonably good.At array A,the settlement trough had a maximum settle-ment of16mm and a width of approximately14m, while at array B the maximum settlement was20mm and the width20m.The difference between the two sites is due to a thicker surfacefill layer at array B,to the variability of the soil properties,and to a different Ž. axial depth 4.55m at array A and4.35m at array B.3.2.2.Central Interceptor Tunnel,Mexico CityThe tunnel was driven with an open face shield6.28 m in diameter and6.37m long at an average depth ofŽ23m through soft clay Schmitter et al.,1981;Schmit-.ter and Rendon,1981.Excavation was full-face hand mined under compressed air.The air pressure applied ranged between127.4and117.6kPa.The air pressure was kept constant within the pressurized chamber until the secondary lining was started.The primary lining consisted offive precast concrete segments,75cm long and25cm thick,which were assembled within the shield.A void of7cm was left between the liner and the excavated soil and wasfilled with pea gravel and grout.There were six instrumented sections to measure soil deformations.Thefirstfive sections were located at depths of approximately23.5m and the sixth section was located at a depth of27m.The soil profile,as an average,consisted of a layer of silty sandy soil and clay down to a depth of5m below the surface.Underneath there was a soft,compressible clay,down to a depth of25m;interspersed within this layer at different depths there were sandy silt and silty。