Art-Predictions of ground deformations in shallow tunnels in clay.pdf

Ž .Tunnelling and Underground Space Technology 17 2002 3�19

Predictions of ground deformations in shallow tunnels in clay

Wei-I. Choua, Antonio Bobetb,�

aProfessional Ser�ice Industries, Inc., Indianapolis, IN, USAbPurdue Uni�ersity, West Lafayette, IN, USA

Received 7 May 2001; received in revised form 15 October 2001; accepted 1 November 2001

Abstract

Twenty-eight tunnels are used to evaluate predictions from an analytical solution for shallow tunnels in saturated ground. Thesolution assumes plane strain conditions at any cross-section perpendicular to the tunnel axis and poroelastic behavior of theground and elastic behavior of the liner. Stresses and deformations are obtained with this method for short- and long-termconditions anywhere in the continuum. Of particular interest to this study are the short-term surface settlements at the groundsurface. Comparisons between predictions and observations from actual tunnels show good agreement, generally within 15%

Ž .difference. The analyses show that: 1 most of the ground movements are caused by the gap parameter, which is a measure ofthe three-dimensional deformations at the tunnel face, the physical gap between the liner and the perimeter of the excavation,

Ž .and of the workmanship; 2 most of the ground deformations take place within a distance of three to four radii around theŽ .tunnel; 3 the bottom boundary of zero vertical deformation should be placed at a distance of two tunnel diameters below the

Ž .tunnel center line, or at the location of a stiff soil layer, whichever comes first; 4 the horizontal movements around the tunnelŽ .are relatively smaller than the vertical movements; and 5 the analytical solution tends to underpredict the maximum soil

deformations and overestimate the settlement trough; however, with an appropriate estimation of the gap parameter and smallsoil yield, the differences between predictions and observations are small. � 2002 Elsevier Science Ltd. All rights reserved.

Keywords: Tunnels; Analytical solution; Saturated ground

1. Introduction

Due to recent city developments with limited avail-able land to build on, more and more public facilitiesare developed under the ground surface. Complex un-derground constructions may cause serious damage toexisting structures if predictions do not forecast theground behavior during excavation. Surface settlementsare often estimated using empirical methods such as

Ž .the Schmidt�Peck method Peck, 1969; Schmidt, 1969 ,where it is generally assumed that the surface settle-

� Corresponding author. Tel.: �1-765-494-5033; fax: �1-765-496-1364.

Ž .E-mail address: [email protected] A. Bobet .

ment trough can be approximated by the normalprobability curve or error function:

x 2Ž .S�S exp � 1max 2ž /2 i

In the equation, S is settlement, S is the maxi-maxmum settlement above the tunnel centerline, ‘x ’ is thehorizontal distance from the tunnel centerline in thetransverse direction, and ‘i’ is the distance from thetunnel centerline to the inflexion point of the curve.

Other empirical or quasi-empirical methods haveŽbeen proposed recently Verruijt and Booker, 1996;

.Loganathan and Poulos, 1998 that show good correla-tions between observations from actual tunnels andpredictions. Empirical methods, however, have signifi-

0886-7798�02�$ - see front matter � 2002 Elsevier Science Ltd. All rights reserved.Ž .PII: S 0 8 8 6 - 7 7 9 8 0 1 0 0 0 6 8 - 2

( )W. Chou, A. Bobet � Tunnelling and Underground Space Technology 17 2002 3�194

Ž .cant shortcomings: 1 they have been developed orŽ .have been validated from a limited number of cases; 2

they should be applied only to tunnels that fall withinthe scope of the cases from which the method was

Ž .developed; 3 only few soil and geometry parametersŽ .are taken into account; 4 they do not consider con-Ž .struction methods; and 5 they 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 numericaltools that can be used to predict ground deformations,but there is a growing demand for developing practicalrational methods for tunnel design. This paper focuseson the applicability of one of the recently proposed

Ž .rational methods Bobet, 2001 for shallow tunnels insaturated ground. Although the method is based onelasticity and does not fully account for the behavior ofthe soil, the predictions are quite good when comparedwith actual cases, and the solution may be used forpreliminary design.

2. The analytical solution

The solution of a shallow tunnel in a saturatedŽ .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 ao

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 radiusŽ .ratio larger than 1.5; e homogeneous and isotropic

Ž .ground; f poroelastic behavior of the ground andŽ . Želastic liner; g small thickness of the liner i.e. liner

Fig. 1. Shallow tunnel.

. Ž .thickness, t� r ; and g permeability of the groundosmall 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-termŽ .i.e. immediately after construction ground movementsof a shallow tunnel in a saturated ground with orwithout 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 boundaryconditions. A general solution has been proposed by

Ž .Timoshenko and Goodier 1970 , in the form of theAiry function, �:

��a ln r�b r 2 �c r 2 ln r�d r 2 ��a ��0 0 0 0 0

1 3 �1Ž .� a r�sin�� b r �a �r �b �r ln r cos�1 1 1 121 3 �1Ž .� c r�cos�� d r �c �r �d �r ln r sin�1 1 1 12

�n n�2 �n �n�2Ž .� a r �b r �a �r �b �r cosn�Ý n n n n

n�2�

n n�2 �n �n�2Ž .� c r �d r �c �r �d �r sin n�Ý n n n nn�2

Ž .2

where the parameters a , b , c , etc., are determined0 0 0from the boundary conditions. The complete solution isobtained by decoupling the liner and the ground andimposing compatibility of deformations and stresses atthe interface between the ground and the liner. Thefollowing boundary conditions apply:

� �� U �0�� 2 �� 2r � �

ground � liner �U �U �wr�r r�rr ro o

ground � liner � Ž .� �� 3r�r r�rr ro o

ground � liner � Ž .� �� 0 smooth interfacer�r r�rr � r �o o

� Ž .Ž .� �� h�yr ��y b w

� Ž .� �k� �� h �yr ��x y w w

where x, y are the Cartesian coordinates with origin atthe center of the tunnel and r, � are the correspondingpolar coordinates; � , � , � , U , U , are the totalr � r � r �

stresses and displacements in polar coordinates; � , �x y

( )W. Chou, A. Bobet � Tunnelling and Underground Space Technology 17 2002 3�19 5

Žare the total stresses in Cartesian coordinates �� is for.effective stresses ; w is the gap parameter, which is the

magnitude of the radial soil displacements that occurbefore the liner provides support; and are theb wbuoyant unit weight of the ground and the unit weightof the water, respectively; k is the coefficient of earthpressure at rest; h and h are the depth of the tunnelwbelow the ground surface and below the water tableŽ . Ž .Fig. 1 . Note that the far field stresses i.e. for y��correspond to the geostatic stresses in a half-spacecontinuum.

Because of the assumption of short-term analysisŽ .i.e. excess pore pressures do not dissipate , the ground

Ž .cannot change volume i.e. �0 . For a poroelasticvolmaterial, this requires:

Ž .� �� 0 4r �

The stress�displacement relations for the liner areŽ .Flugge, 1966 :¨

2 liner liner Ž 2 .d U dU C 1�� r liner� �� r �o r �2 d� Ed�

dU liner d4U liner d2U linerC� r rliner liner�U � �2 �Ur r4 2ž /d� F d� d�

Ž 2 .C 1�� liner Ž .� r � 5o rE

C and F are the compressibility and flexibility ratios,respectively, defined as:

Ž 2 . 3 Ž 2 .Er 1�� Er 1��o s o s Ž .C� ; F� 62 2Ž . Ž .E A 1�� E I 1��s s s s

where E, � are the Young’s modulus and Poisson’sratio of the ground; E , � are the Young’s moduluss sand Poisson’s ratio of the liner; A , I are the area ands smoment 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 � 6 determines the stressesŽand displacements anywhere in the continuum i.e. for

.both ground and liner . The ground displacements areof particular interest, and are given by:

a c �1�� 1o 1U � � � � c ln r sin�r 12½E r 2r

a � b � c � d �2 2 3 3� 2 �2 cos2�� 3 �3 sin3�3 4 2 5rr r r

c �1�� 11 Ž .U � � � c 1� ln r cos�� 12½E 2r

a � c � d �2 3 3 Ž .�2 sin2�� 3 � cos3� 73 4 2 5r r r

with

� Ž . �Ž 2 . h 1�k �2 h 1�� CFb w wŽ .Ž .�2 E C�F w�r1 o 2a � r0 o22 Ž .Ž . Ž .C�F 1�� 1�� CF

Ž . 2c �� r1 b w o

1 4Ž .c �� 1�k r1 b o8

Ž .1 1�� F�3 4Ž . Ž .a �� h 1�k r 82 b o4 Ž .1�� F�6

Ž .1 2 1�� F�3 2Ž .b �� h 1�k r2 b o4 Ž .1�� F�6

Ž .1 1�� F�12 6Ž .c �� 1�k r3 b o12 Ž .1�� F�24

Ž .1 1�� F�8 4Ž .d �� 1�k r3 b o8 Ž .1�� F�24

2.2. Short-term analysis of a tunnel in saturated groundwith air pressure

The stresses and displacements of the ground andliner are obtained for the following constructionprocess:

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 thesame time, an internal air pressure, p , is applied. Toaprevent water inflow into the tunnel, the value of theair pressure is generally taken as the magnitude of thewater pressure at the invert of the tunnel.

Ž . Ž .P � h � 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


Ž .construction process, the solution is given by Eq. 7with:

1 2 2Ž . Ž .a � h 1�k r � h �p r0 b o w w a o2

Ž 2 . Ž . Ž .1�� CFp � C�F E w�ra o 2� ro2Ž .Ž . Ž .1�� C�F � 1�� CF

Ž . 2c �� r1 b w o

1 4Ž .c �� 1�k r1 b o8

1 4Ž . Ž .a �� h 1�k r 102 b o4

1 2Ž .b �� h 1�k r2 b o2

1 6Ž .c �� 1�k r3 b o12

1 4Ž .d �� 1�k r3 b o8

Ž .As it can be observed in Eq. 7 , the analyticalsolution predicts an increase of displacements with thelogarithm 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. Inreality, the soil conditions are not homogeneous andthe soil does not extend to an unlimited depth. At acertain distance below the tunnel there will be a stiff

Ž .layer e.g. bedrock where the vertical displacementsshould be zero. In addition, other factors such as anincrease 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 invertthe soil displacements towards the excavation. Hence acorrection should be made to the above formulationsuch as at a certain distance below the tunnel center-line the vertical displacements are zero. Hence,

corrected analytical solution top of stiff layer Ž .U �U �U 11y y y

The boundary of zero vertical displacement is chosenŽ .at a depth which is the smallest of: a the depth of

Žbedrock or stiff layer a soil layer can be consideredstiff 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 diameterbelow the tunnel centerline; this is an empirical ap-

proximation obtained from actual case studies and isrelated to the zone of influence of the excavation. Oncethis correction is done, the solution recovers physicalmeaning in that displacements decrease as the distance

Ž .from the tunnel increases Bobet, 2001 . Note thathorizontal displacements do not need correction.

Ž .Soil displacements, as defined by Eq. 7 , are verysensitive to the gap parameter, w, since small variationsof w may have a large effect on soil settlements. Thegap parameter represents the soil deformations thatoccur before the soil gets in contact with the liner.Hence, this parameter is a measure not only of thephysical gap between the liner and the ground, but alsoof 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 ��90�, y�h . With typical ground and liner

properties the flexibility ratio, F, is very large. Anapproximate solution for some tunnels can be obtained

Ž .assuming a very flexible F�� and incompressibleŽ .liner C�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 aremax

.used :

wr 1�� 1o 2 �� r ln hmax o½h E 2

3 5r r r3 1o o oŽ .� h 1�k r � � �b o ž / ž / 5h 4 h 4 hŽ .12

For a tunnel excavated under air pressure:

wr 1�� 1o 2 Ž �� r ln h� h 3max o b½h E 2

3 5r r3 1o o2. Ž .�k r � h 1�k r �o b o ž / ž /4 h 4 h

2ro Ž .� hr 13w o ž / 5h

Ž . Ž .Eqs. 12 and 13 show that for a very flexible andincompressible liner the maximum settlements on the

Ž .surface are due to two terms: 1 a geometric term thatŽ .involves the gap parameter; and 2 a term that in-

volves the ground stiffness, E. The relative importancethat each term has on the total settlement depends onthe 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 compressiblethe stiffness of the liner may have a substantial effecton settlements, particularly the compressibility of the


liner since as the parameter C becomes larger theŽsettlements increase note that at the limit, C��, the

.tunnel behaves as if there was no liner .Ž . Ž .A comparison between Eq. 12 and Eq. 13 also

shows that the ground displacements at the surface arelarger for a tunnel excavated under air pressure thanwithout air pressure. This is due to the constructionprocess 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 twomethods:Ž . Ž .1 Direct estimation Lee et al., 1992 .

Ž .w�G �U �workmanship 14p 3D

where G is the physical gap between the liner and thepperimeter of the excavation and includes the thicknessof 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 theworkmanship is a measure of the overcutting as the

ŽTBM is steered Lee et al., 1992, provide details onhow to obtain each of the three components of the gap

.parameter .Ž .2 Back-calculation from the estimated or measured

ground loss.

2 2Ž .� r �w �� r 2wo o Ž .Ground loss� � 152 r� r oo

where the ground loss should also include workman-ship.

3. Case studies

Ž .A total of 14 tunnels including 28 tunnel sectionshave been investigated. They comprise different con-struction techniques including compressed air, haveground conditions that range from soft to stiff clay, andcoefficients of earth pressure at rest ranging from 0.5to 1.5. Some of the cases have been investigated byprevious researchers and are well documented, andthus they are very well suited to make comparisonswith the analytical solution and assess its applicabilityto actual tunnels.

Table 1 summarizes 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 neededfor the analytical solution are not available and havebeen estimated from other parameters; for example thePoisson’s ratio of the soil, if not available, is taken as0.2, and the soil Young’s modulus, if not given, is

estimated from undrained shear strength S , standardupenetration tests, or from cone penetration tests. If theproperties of the liner are not reported in the litera-ture, they are taken as E �25 000 MPa and � �0.3,s swhich correspond to a typical support. Table 1 alsogives the stability number N at the face of the excava-tion; the stability number is defined as:

h��i Ž .N� 16Su

where h is the total vertical stress at the tunnel axis,� is the support pressure at the face of the tunnel, andiS is the undrained shear strength of the soil.u

Five cases are reviewed in detail in this paper andare used to compare the predictive capabilities of theanalytical solution with actual measurements. Three ofthe five tunnels are excavated without compressed air,and two with compressed air. The conclusions obtainedfrom the cases presented are thought to be representa-tive and applicable to the rest of the tunnels.

3.1. Tunnels without compressed air

3.1.1. London Transport Fleet Line, Green ParkUnderground

The Green Park Underground Tunnel was shielddriven in stiff heavily overconsolidated London clay.The tunnel was excavated by hand with a 4.146-mdiameter shield at a depth of approximately 29 m. Aseven-segment cast-iron lining 4.07-m external diame-ter and 0.6-m width was erected inside the shieldtailskin and water�cement grout was injected into thecavity between the liner ring and the excavated soil. Asimplified soil profile of the construction site consistedfrom top to bottom of a layer of sand and gravel downto a depth of 2 m; underneath there was a very thicklayer of stiff fissured clay where most of the tunnel was

Ž .excavated Attewell and Farmer, 1974 . The ground-water level was found at a depth of approximately 2 m.The undrained shear strength of the stiff clay, obtainedfrom unconsolidated undrained triaxial tests, is takenfor the analyses as 270 kPa which is consistent with thereported stability number N of 2.2. The elastic modu-

Ž .lus of the clay is estimated as 50 MPa Lo et al., 1984 ,and the coefficient of lateral earth pressure at rest K0is 1.5, which is typical of London clay. The physical gapbetween the perimeter of the excavation and the lineris the sum of the size of the bead, 6.5 mm, and the tailvoid, 76 mm. Lo et al. have suggested a gap parameter,w, equal to 23 mm, based on their evaluation of thephysical gap, grouting of the tail void, and face move-

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Table 1

Geometry and soil conditions of the tunnels investigated

Tunnel Reference Depth Water Diameter E soil Su Ko Soil unit Gap Maximum Stability Soil type Construction method2 2Ž . Ž . Ž . Ž . Ž .Ž .Ž .Ž .m table m MPa kN�m weight w Settlement number b m kN�m mm mm N

Green Park Attewell and Farmer, 28.9 2.3 4.15 50 270 1.5 19 23 6.1 2.2 London clay Hand-excavated with1974 cast iron segments

Thunder Bay Belshaw and Palmer, 19781978Belshaw and Palmer,1979

Array-1 10.7 1.5 2.47 13 35 1 18 156 51 4.80 Soft silty clay TBMArray-2 10.5 1.3 2.47 13 35 1 18 120 49 4.80 Soft silty clay TBMBangkok Phienwej, 1997 18.0 2.2 2.67 20 15 1 17 37 12 3.20 Soft to stiff clay EPB TBMMississauga Delory et al., 1979 13.1 6.0 4.28 140 360 0.9 24 10 2.2 0.86 Dense glacial till Shield drivenTyneside Attewell and Farmer 7.5 0.0 2.02 15 75 1 19 19 7.9 1.96 Laminated clay Shield driven

1975Frankfurt Schmidt, 1974 14.6 5.6 6.5 70 130�550 1 19 60 32 0.50�2.0 Frankfurt clay Shield with bolted

marl concrete segmentsMilwaukee Ilsley et al., 1991CT-8-1 16.0 4.0 3.2 20 35 0.5 19 320 114 4.70 Stiff clayey silt EPB, bolted, precast

concrete segmentsNS-10-U 7.93 4.0 2.25 20 35 0.5 19 324 84 4.10 Medium stiff Slurry, jacked concrete pipe

organic siltNS-10-R 7.6 5.0 2.25 20 35 0.5 19 78 55 3.90 Medium stiff Slurry, jacked

organic silt concrete pipeCT-8-2 12.81 4.0 3.0 20 35 0.5 19 196 70 7.70 Medium stiff EPB shield

organic siltCT-5�6 10.74 8.0 3.23 20 35 0.5 19 98 39.6 3.90 Soft-medium EPB shield, grouted at

organic silt the end of 8-h shiftCT-7 7.44 4.0 3.57 20 35 0.5 19 103 56 4.50 Soft-medium EPB shield

organic siltManuel Tinajero and Vieitez, 11.7 2.5 2.96 4 35 1 17 288 105 5.00 Plastic lacustrine Shield with cutters, steel

Gonzales 1971 clay lining and dewateringRegent Park Barratt and Tyler

Northbound 1976 20.1 4.3 4.14 32 230 1.5 19 17 7 1.70 London clay Hand-excavated withconcrete segments

Southbound 34.1 4.3 4.14 56 280 1.5 19 23 5.5 2.40 London clay Hand-excavated withconcrete segments

Barcelona Ledesma and Romero 10.0 0.0 8.0 25 75 1 18 31 24 2.30 Stiff clay with gravelSubway 1997

BART Lower Kuesel, 1972 19.0 6.0 5.66 10 50 0.45 16.5 116 36 4.60 San Francisco Bay Shield with cutters and groutedMarket Mud, soft and plastic segments with compressed air

Haycroft Glossop and O’ReillyArray A 1982 8.0 5.0 3.0 20 12 0.7 19 118 77 5.90 Marine warp Hand-excavated with

segments with compressed airArray B 5.3 2.3 3.0 6 12 0.7 19 66 48 3.95 Marine warp Hand-excavated with

segments with compressed airArray C 6.5 3.5 3.0 6 12 0.7 19 84 61 5.62 Marine warp Hand-excavated with

segments with compressed airBelfast Glossop and Farmer,

Array A 1977 4.85 1.45 2.74 4 10 0.7 15 23 16 3.64 Soft saturated silt Shield with precast concretesegments with compressed air

Array B 4.4 1.2 2.74 4 10 0.7 15 30 20 3.64 Soft saturated silt Shield with precast concretesegments with compressed air

Central Schmitter et al., 1981;Interceptor, Schmitter and Rendon,Mexico City 1981

Section-1,2 23.5 3.5 6.28 6 11 0.7 15 100 Soft clay with silt Precast segments withcompressed air

Section-3 23.5 3.5 6.28 5 11 0.7 15 100 Soft clay with silt Precast segments withcompressed air



Section-6 27.0 2.0 6.28 5 11 0.7 15 80 122 4.00�5.0 Soft clay with silt Compressed air


ments; this is the magnitude of the gap parametertaken for the analytical solution.

Fig. 2 shows a comparison between predictions fromthe analytical solution and observed movements. Fig. 3shows observed and predicted soil settlements abovethe tunnel centerline. The comparisons are quite good.As observed in the figures both the analytical solutionand the observed settlements resemble a Gaussprobability function. Another interesting observation isthat, as shown in Fig. 3, most of the soil deformationsoccur within an area very close to the tunnel, of theorder 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 tunnelwas driven at a depth of approximately 18 m; it has atotal length of 10.5 km, and a diameter of 2.67 mŽ .Phienwej, 1997 . Three earth-pressure balanced shieldswere used to excavate the tunnel and each shield had adiameter of 2.8 m and a length of 6.2 m. Depending onthe ground conditions, the ground control features ofthe machines ranged from closeable flood door or

Ž .stable ground to full earth pressure balance EPBsupport for unstable ground. The primary support con-sisted of 150-mm-thick and 1-m-long bolted concretesegments with secondary grouting to backfill the annu-lar space behind the segmental rings.

Bangkok is situated on a thick series of marine andalluvial soil deposits. Down to 35-m depth the subsoilprofile is relatively uniform. A thick soft marine clay

Fig. 2. Green Park Underground Tunnel. Surface settlements.

layer with undrained shear strength of 10�15 kPa andwater content 70�120% extends from the ground sur-face to a depth of 12�15 m. Underneath there is auniform and impervious stiff clay with thickness rang-ing between 5 and 15 m. A fine to medium dense sandlayer appears under the stiff clay with a total thicknessranging between 8 and 16 m. The undrained Young’smodulus of the stiff clay is approximately 20 MPa. Thewater table is found within the soft marine clay approx-imately 2 m below the surface.

Fig. 3. Green Park Underground Tunnel. Subsurface settlements above centerline.


Fig. 4. Bangkok Sewer Tunnel. Surface settlements.

A gap parameter of 37 mm is taken for the analysis,based on the estimated ground loss 3�5% and tunnel

Ž .geometry Phienwej, 1997 . The bottom boundary is setat a depth of 23 m where a dense sand layer is found.

Figs. 4�6 show predicted and observed soil deforma-tions. Fig. 4 is a plot of surface settlements; Fig. 5 is a

plot of subsurface settlements with depth, and Fig. 6shows actual and predicted horizontal displacements ata vertical cross-section perpendicular to the tunnel, 4 mfrom the tunnel centerline. Surface settlements and

Ž .horizontal displacements Figs. 4 and 6 are predictedreasonably well. Larger differences are observed in Fig.

Fig. 5. Bangkok Sewer Tunnel. Subsurface settlements above centerline.


Fig. 6. Bangkok Sewer Tunnel. Subsurface horizontal displacements 4 m from centerline.

5 between predictions and measurements, particularlyclose to the crown of the tunnel. Observed settlementsare much larger than predicted settlements; this maybe caused by the large deformations that are necessaryin the soil to fill the physical gap between the liner andthe excavation. Such large deformations are likely toproduce plastic deformations in the soil which mayaccount for some of the discrepancies. Another reasonfor the differences is the layered nature of the soil;although the tunnel is excavated in the stiff clay, thereis a thick soft clay deposit near the surface. The influ-ence of this deposit can be noticed on the horizontaldisplacements depicted in Fig. 6, where the slope of theobserved settlement curve increases significantly on thetop 10 m of the soil, where the soft deposit is encoun-tered.

3.1.3. London Transport Fleet Line, Regent’s ParkTwo tunnels with 4.146 m diameter were constructed

with expanded concrete lining at depths of 20.1 mŽ . Ž .northbound and 34.1 m southbound at Regent’sPark, London, as part of the Fleet Line of the London

Ž .Underground Barratt and Tyler, 1976 . The verticaldistance between the Northbound and the Southboundtunnel centerlines is 14 m, and the horizontal distanceis 18 m. Both tunnels were shield driven with a 3-mmbead and were hand excavated; the southbound tunnelwas constructed first. Precast concrete segments wereused as the primary support and the concrete liningwas expanded against the ground immediately aftererection.

The tunnels were excavated in London Clay, whichcan be characterized as a stiff, fissured, overconsoli-dated clay. The undrained shear strength of the clay,S , obtained from unconsolidated undrained triaxialutests is 230 kPa. The Young’s modulus is taken as 32MPa for the northbound tunnel and 56 MPa for the

Ž .southbound tunnel, after Lee et al. 1992 ; the coeffi-cient of lateral earth pressure is 1.5, which is typical ofLondon clay. The groundwater table was found at adepth of approximately 4 m.

The ground loss for both tunnels was 1.3�1.4%.Ž .Although the tail void was quite small 3 mm the gap

parameter is taken as 17 mm for the northboundtunnel and 23 mm for the southbound to account for

Žface deformations and workmanship after Lo et al.,.1984 .

Figs. 7�9 show comparisons between the analyticalsolution and actual measurements. All comparisons arereasonably good. Fig. 7 is a plot of surface settlementsfor both the northbound and southbound tunnels. Sincethe distance between the two tunnels is quite large, it isexpected that the construction of the first tunnelŽ .southbound should not affect the settlements causedby the construction of the second tunnel; this is shownin the figure. Fig. 8 is a plot of the subsurface settle-ments above the centerline of the northbound tunnel.The soil deformations are larger above the crown ofthe tunnel and decrease as the distance from thetunnel 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


Fig. 7. Regent Park Underground. Surface settlements.

Ž .for the southbound tunnel Fig. 9 . The settlements ofthe southbound tunnel above the crown are larger thanthe northbound tunnel even though the southboundtunnel rests on a relatively stiffer clay compared to thenorthbound tunnel; this is a result of the larger gapparameter, and for this case is an indication of therelative importance of this parameter compared to thegeometry of the tunnel or to the soil properties.

3.2. Tunnels with compressed air

3.2.1. Belfast Sewer Scheme, Sydenham, BelfastThe tunnel is a sewer tunnel constructed in Belfast;

it is 450 m long and has a circular cross-section of 2.74m in diameter. The tunnel is rather shallow, with anaverage depth of 4.85 m below the ground surface.

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 theculvert ran close to housing and industrial buildings, itwas decided to construct the culvert in the tunnel toreduce surface settlements and minimize damage tothe above buildings. The tunnel was shield-driven andwas supported by precast concrete rings. The shieldhad a 3-mm bead and a 1-m-long tailskin. The ringswere composed of five bolted segments 0.6 m long,which were erected within the tailskin of the shield.Grouting was directly injected into the rear of thetailskin after each shove to reduce settlement. Thetunnel was excavated below the groundwater table,which was located at a depth of 1.2�1.5 m below theground surface. To keep water out of the tunnel and tohelp stabilize the weak face, the tunnel was constructed

2 Žwith compressed air at a pressure of 48 kN�m 412 .kN�m at an earlier stage . This air pressure lowered

the stability number N of the face from 8.35 to 3.60.The tunnel was built in an alluvial deposit with sandy

layers with variable clay and organic content. Below thesurface there was a fill deposit between 2 and 3 mthick; underneath there was a soft gray silty clay 5�6 mthick followed by a thick stiff brown clay. The tunnelwas excavated within the soft silt deposit, under thewater table. The silty clay deposit showed highly vari-able engineering properties, with undrained shearstrength ranging from 8 to 20.5 kN�m2.

The gap parameter is obtained from the ground loss,Ž .1.8�2.1%, Glossop and Farmer, 1977 , and ranges

between 23 and 28 mm.Figs. 10 and 11 show predictions and measurements

Ž .at two control locations arrays A and B . As shown inthe figures the predictions are reasonably good. Atarray A, the settlement trough had a maximum settle-ment of 16 mm and a width of approximately 14 m,while at array B the maximum settlement was 20 mmand the width 20 m. The difference between the twosites is due to a thicker surface fill layer at array B, tothe variability of the soil properties, and to a different

Ž .axial depth 4.55 m at array A and 4.35 m at array B .

3.2.2. Central Interceptor Tunnel, Mexico CityThe tunnel was driven with an open face shield 6.28

m in diameter and 6.37 m long at an average depth ofŽ23 m through soft clay Schmitter et al., 1981; Schmit-

.ter and Rendon, 1981 . Excavation was full-face handmined under compressed air. The air pressure appliedranged between 127.4 and 117.6 kPa. The air pressurewas kept constant within the pressurized chamber untilthe secondary lining was started. The primary liningconsisted of five precast concrete segments, 75 cm longand 25 cm thick, which were assembled within theshield. A void of 7 cm was left between the liner andthe excavated soil and was filled with pea gravel andgrout. There were six instrumented sections to measuresoil deformations. The first five sections were located atdepths of approximately 23.5 m and the sixth sectionwas located at a depth of 27 m.

The soil profile, as an average, consisted of a layer ofsilty sandy soil and clay down to a depth of 5 m belowthe surface. Underneath there was a soft, compressibleclay, down to a depth of 25 m; interspersed within thislayer at different depths there were sandy silt and silty


Fig. 10. Belfast Sewer Tunnel. Array A. Surface settlements.

sand layers with thicknesses between 0.2 and 1 m; it iswithin the soft clay layer where the tunnel was located.Underneath the soft clay there was a hard clay layerdown to depths of 25�30 to 30�34 m. A soft clay layerwas found underneath down to 34�40 m. Below therewas a sandy silt and dense silty sand. The groundwatertable was found 2 m below the surface.

The physical gap between the soil and the lining was140 mm; however, during the excavation the gap de-creased to 70 mm before grouting of the tail void. Thegap parameter is taken as 100 mm for all sectionsexcept section 6, where due to a better tunnelingexperience, the gap parameter is reduced to 80 mm.

The boundary of zero vertical displacement is set at

Fig. 11. Belfast Sewer Tunnel. Array B. Surface settlements.


Fig. 12. Central Interceptor Tunnel. Section 6. Surface settlements.

a depth of 35 m which corresponds to the depth of thehard clay layer. Figs. 12�14 plot observed settlementsand predictions from the analytical solution. Specifi-cally, Fig. 12 shows the surface settlements at section 6,Fig. 13 the settlements at 6 m below the surface, andFig. 14 the settlements at 12 m below the surface. Asone can observe, predictions and measurements relatequite well.

4. Discussion

Table 2 shows the maximum observed settlementsŽ .above the tunnel centerline for all 28 tunnels, thepredicted settlements based on the analytical solution,and the error obtained with the predictions comparedwith the field measurements. The errors are generally

Fig. 13. Central Interceptor Tunnel. Section 5. Settlements 6 m below surface.


Fig. 14. Central Interceptor Tunnel. Section 5. Settlements 12 m below surface.

Žsmaller than 15%. There are few tunnels Green Park,.Mississauga, Regent Park Southbound where the er-

rors are large but the settlements are small; the errorsare large because small differences are compared with

Žsmall values i.e. the magnitude of the total settlement.compares well with measurements .

ŽFor four of the tunnels Milwaukee NS-10-U and.NS-10-R, Haycroft Array C, and Central Interceptor

the analytical solution does not predict well the soildeformations. The reasons for that are non-uniform orlayered soil, soft soil conditions, or deficient construc-tion procedures. The Milwaukee tunnels were all exca-vated with earth pressure balance machines, except forcontract NS-10 where a slurry machine was used. Asobserved in Table 2, predictions for the EPB tunnelsare quite good, but not so for the tunnels excavatedwith the slurry machine. The reason for the largeerrors may be a poor prediction of the gap parameterdue to improper design pressure in the NS-10 contract.The large error for array C of the Haycroft tunnel isbecause of the plastic deformations that occurred inthe soft marine clay where the tunnel was excavated.

Although the discrepancies highlight the limitationsof the analytical solution, they also emphasize theimportance of the construction methods for the estima-tion of the soil deformations. It has to be noted thatthe analytical solution provides reasonable predictionsfor the other 24 tunnels.

The analytical solution shows that one of the mostimportant parameters to predict soil deformations isthe gap parameter. This can also be shown from field

observations, as illustrated in Fig. 15, which is a plot ofmaximum surface settlements with the ratio of the gap

Ž .and the tunnel radius w�r . The figure shows quite aobit of scatter for the lower w�r ratios, but a definiteotrend of increasing settlements with increasing gapratio. The line drawn in the figure is obtained fromlinear regression and it should be considered only as ageneral trend to illustrate the importance of the gapparameter, rather than a best fit.

As already mentioned, the gap is the result of threeŽ .factors: 1 three-dimensional deformations at the face

Ž .of the excavation; 2 the physical gap between theŽ .liner and the soil; and 3 the quality of the workman-

ship which is reflected on the steering of the shield andconstruction details. Good construction proceduresobviously decrease the workmanship but they can alsodecrease the physical gap by quickly grouting the voidbetween the liner and the soil. Also, the level of theface support is critical to decrease the 3-D gap factor.This is illustrated in Fig. 16 which is a plot of themaximum surface settlements with the stability numberN. As observed in the figure, for stability numbers lessthan approximately 4, the surface settlements are mostlybelow 25�30 mm. For stability numbers greater than 4the scatter is larger but also the maximum settlementsare larger.

5. Conclusions and recommendations

Twenty-eight tunnels, 11 excavated with compressed


Table 2Comparison between observations and predictions for the tunnels investigated

Tunnel Depth Diameter S K Gap Stability Observed Predicted Erroru o2Ž . Ž . Ž . Ž . Ž .m m kN�m w mm number settlement settlement %

Ž . Ž .N mm mm

Green Park 28.9 4.15 270 1.5 23 2.20 6.1 7.4 21.3Thunder Bay

Array-1 10.7 2.47 35 1 156 4.80 51 48 �5.9Array-2 10.5 2.47 35 1 120 4.80 49 51.8 5.7

Bangkok 18.0 2.67 15 1 37 3.20 12 11.3 �5.8Mississauga 13.1 4.28 360 0.9 10 0.86 2.2 3.4 54.5Tyneside 7.5 2.02 75 1 19 1.96 7.9 7.83 �0.9Frankfurt 14.6 6.5 130�550 1 60 0.50�2.0 32 28.12 �12.1Milwaukee

CT-8-1 16.0 3.2 35 0.5 320 4.70 114 105.37 �7.6NS-10-U 7.93 2.25 35 0.5 324 4.10 84 118.1 40.6NS-10-R 7.6 2.25 35 0.5 78 3.90 55 35.6 �35.3CT-8-2 12.81 3.0 35 0.5 196 7.70 70 68 �2.9CT-5�6 10.74 3.23 35 0.5 98 3.90 39.6 38.1 �3.8CT-7 7.44 3.57 35 0.5 103 4.50 56 48.6 �13.2

Manuel Gonzales 11.7 2.96 35 1 288 5.00 105 110.9 5.6Regent Park

Northbound 20.1 4.14 230 1.5 17 1.70 7 6.4 �8.6Southbound 34.1 4.14 280 1.5 23 2.40 5.5 7.3 32.7

Barcelona 10.0 8.0 75 1 31 2.30 24 21.51 �10.4Subway

BART Lower 19.0 5.66 50 0.45 116 4.60 36 30.3 �15.8Market

HaycroftArray A 8.0 3.0 12 0.7 118 5.90 77 74.2 �3.6Array B 5.3 3.0 12 0.7 66 3.95 48 49.1 2.3Array C 6.5 3.0 12 0.7 84 5.62 61 81 32.8

BelfastArray A 4.85 2.74 10 0.7 23 3.64 16 17.11 6.9Array B 4.4 2.74 10 0.7 30 3.64 20 16.56 �17.2

Central InterceptorSection-1,2 23.5 6.28 11 0.7 100Section-3 23.5 6.28 11 0.7 100Section-4 23.5 6.28 11 0.7 100Section-5 23.5 6.28 11 0.7 100Section-6 27.0 6.28 11 0.7 80 4.00�5.0 122 149 22.1

air, in stiff to soft clay below the water table have beenused to evaluate an analytical solution for shallowtunnels in saturated clay immediately after construc-

Ž .tion Bobet, 2001 . The following conclusions wereobtained:

1. The analytical solution provides a rational methodfor the design of tunnels since all relevant parame-ters are considered in the formulation. However, itshould be restricted to those cases that fall within

Žthe scope of the analysis e.g. limited ground yield-.ing .

2. The analytical solution gives reasonable predictionsfor shield driven tunnels in medium to stiff clays, orin soils and soft rocks where plastic deformationsaround the tunnel are small.

3. One of the most important parameters for theŽmaximum surface settlements i.e. at the tunnel

.centerline is the gap parameter.

4. An effective control of the face support and a goodconstruction quality are very effective in minimiz-ing soil movements.

5. Most of the ground deformations take place withina distance of three to four radii around the tunnel.

6. The location of the bottom boundary of zero verti-cal deformation is critical to predict vertical defor-mations of the ground. This boundary should belocated at a distance of two tunnel diameters belowthe tunnel center line, or at the location of a stiffsoil layer, whichever comes first.

7. The horizontal movements around the tunnel arerelatively smaller than the vertical movements. Thisis confirmed by the analytical solution and by fieldobservations.

8. Because the analytical solution is based on theassumption of elasticity, it tends to underpredictmaximum soil deformations and overestimate thesettlement trough. With an appropriate estimation


Fig. 15. Correlation between maximum surface settlement and gapratio.

of the gap parameter and small soil yielding, pre-dictions can compare quite well with field observa-tions.

9. For tunnels excavated with compressed air, soilmovements produced after the air pressure is shut-off are not smaller than for tunnels without airpressure. A pressurized tunnel cannot significantlyreduce the ground settlements, but can slightlydecrease the width of the settlement trough.

Fig. 16. Correlation between maximum surface settlement and stabil-ity number.

In summary, although the analytical solution pre-sented in this paper is limited in scope, it can be usedfor a preliminary design of tunnels in medium to stiffclays. The comparisons presented show good correla-tions between observed soil displacements and predic-tions. However, this solution cannot substitute detailednumerical analyses where realistic ground propertiesand construction procedures should be modeled indetail.

As already mentioned one of the most importantparameters to estimate ground deformations is the gap.No attempt has been made in this study to evaluate thisparameter; there is quite uncertainty on how to predictits magnitude because it depends on the quality of theconstruction and may vary from section to section.What it has been shown is that with reasonable esti-mates of the gap, the analytical solution predicts quitewell the magnitude and distribution of the groundsettlements at different locations and depths.

The comparisons presented in this paper are usefulto evaluate and understand the relation between soiland liner, tunnel geometry, and construction proce-dure. This is an important advantage of a rational overan empirical method since all variables can be takeninto consideration.

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