f. hage chehade_ i. shahrour -- numerical analysis of the interaction between twin-tunnels- influen

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Technical note

Numerical analysis of the interaction between twin-tunnels: Influenceof the relative position and construction procedure

F. Hage Chehade a, I. Shahrour b,*

a Institut Universitaire de Technologie, UniversiteLibanaise, BP 813 Saida, Lebanonb Laboratoire de Mecanique de Lille, Universitedes Sciences et Technologies de Lille, Polytech-Lille, 59 655 Villeneuve dAscq, France

Received 21 August 2006; received in revised form 28 January 2007; accepted 19 March 2007Available online 4 May 2007

Abstract

The development of transportation in large cities requires the construction of twin-tunnels or the construction of new tunnels close tothe existing ones. Since, both the relative position of tunnels and the construction procedure affect the soil movement and internal forcesin the lining, it is of major interest to study the influence of these factors on the tunnel design. This paper presents analysis of this issuewith a particular interest for the optimization of both the relative position of the twin-tunnels and the construction procedure. For thisconcern, a parametric study is conducted for the investigation of the influence of these two factors on the soil settlement and internalforces resulting from the tunnel construction. The paper presents successively the numerical model and then analyses conducted for threeconfigurations of the twin-tunnels: aligned-horizontally, vertically and inclined. It shows that the construction procedure affects the soilsettlement and internal forces. The construction of upper tunnel at first leads to both higher settlement and bending moment. The highestsoil settlement is obtained for vertical aligned tunnels, while horizontal aligned tunnels cause the lowest settlement. 2007 Elsevier Ltd. All rights reserved.

Keywords: Bending moment; Construction procedure; Finite element; Plasticity; Settlement; Tunnel design; Twin-tunnels; Thrust

1. Introduction

The development of large cities requires the use theunderground area for the construction of transportationinfrastructures and facilities. In some cities, the geotechni-cal and underground conditions impose the construction ofnew tunnels close to existing ones. In other cases, the solu-tion of twin-tunnels presents major advantages, such the

reduction of the both the tunnel diameter and the soilmovement resulting from the tunnel construction.Both numerical modeling and in situ observations were

used to analyze the interaction between twin-tunnels (Soli-man et al., 1993; Kawata and Ohtsuka, 1993; Perri, 1994;Saitoh et al., 1994; Yamaguchi et al., 1998; Shahrour andMroueh, 1997). Results show that in some configurations,

the interaction could largely affect the soil settlement andthat the design of twin-tunnels requires numerical analysesassociated to monitoring during the tunnel construction.

This paper concerns the design phase. It presents analy-sis of the interaction between twin-tunnels with a particularinterest for the optimization of both the relative position ofthe twin-tunnels and the construction procedure. For thisconcern, a parametric study is conducted for the investiga-

tion of the influence of these two factors on the soilsettlement and internal forces resulting from the tunnelconstruction. The paper presents successively the numericalmodel and then analyses conducted for three configura-tions of twin-tunnels: aligned-horizontally, vertically andinclined (Fig. 1).

2. Numerical modeling

Analyses are conducted using the finite element method.The soil behavior is described using an elastic perfectly

0886-7798/$ - see front matter 2007 Elsevier Ltd. All rights reserved.

doi:10.1016/j.tust.2007.03.004

* Corresponding author.E-mail addresses: [email protected] (F. Hage Chehade), Isam.

[email protected] (I. Shahrour).

www.elsevier.com/locate/tust

Tunnelling and Underground Space Technology 23 (2008) 210214

Tunnelling and

Underground Space

Technologyincorporating Trenchless

Technology Research
mailto:[email protected]:Isam.%[email protected]:Isam.%[email protected]:Isam.%[email protected]:Isam.%[email protected]:[email protected]


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plastic constitutive relation based on the non associatedMohrCoulomb criterion. The Youngs modulus of the soilE is supposed to increase with depth according to the fol-lowing expression:

Ez E0Pm=P00:5

wherePmdenotes the mean stress at the depth z;E0is con-stitutive parameter, which corresponds to the YoungsModulus at the mean pressure Pm= P0. This expression

takes into account the variation of the Youngs moduluswith the mean pressure, which increases with depth dueto the soil self-weight. The behavior of the lining is as-sumed to be linear-elastic.

The finite element modeling of the construction of twin-tunnels is carried out as follows:

(i) Construction of the first tunnel using the conver-gence-confinement method with a stress release factorb= 0.5. This factor corresponds to the ratio of thestress release before the lining installation.

(ii) Construction of the second tunnel using also the con-vergence-confinement method, as for the first tunnelwith a stress release factor b= 0.5. This factor isapplied to the stresses exercised around the tunnelafter the excavation of the first tunnel.

Finite element analyses were conducted using the finiteelement program PLAXIS. Fig. 2 shows the mesh usedfor the analysis of horizontally aligned tunnel with a ratiospacingSx/D= 2(D,Sxdenote the tunnel diameter and thedistance between tunnel axes, respectively). It contains2036 triangular 6-nodes elements. The soil layer is under-lined by a stiff one at a depth H= 8D. The lateral extensionof the soil mass is equal to 20D. This extension ensures theabsence of lateral boundary effect on the numerical model-ing of the tunnel construction.

Concerning the boundary conditions, the displacementsare constrained in both directions at the bottom, while zerohorizontal displacement is imposed at lateral boundaries(Fig. 2).

Table 1summarizes the properties of the soil and the lin-ing used in this study. The soil corresponds to mediumsand. The coefficient of the lateral stress (K0) is equal to0.5. The thickness of the lining is equal to 0.5 m.

Sx Sx

Sy

Tunnels with horizontal alignment Tunnels with inclined alignment

Sy

Tunnels with vertical alignment

Fig. 1. Configurations considered in the analysis of the interaction between twin-tunnels.

Fig. 2. Mesh used in the analysis of tunnels with horizontal alignment.

Table 1Properties of both the soil ratio and lining materials

Material E0(MPa)

Poissonsratio

Cohesion(kPa)

Frictionangle

()

Dilancyangle

()

Unitweight

kN/m3

Soil 30 0.3 3 33 7 18Lining 35000 0.25 25

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3. Result of analyses

Analyses are conducted for the following configurations(Fig. 1,Table 2):

tunnels with horizontal alignment

tunnels with vertical alignment tunnels with inclined alignment

3.1. Tunnels with horizontal alignment

Analyses were conducted for fives values of the tunnelspacing ration Sx/D (2, 2.5, 3, 4 and 5) (Fig. 3a). Fig. 3bshows the settlement pattern at the ground surface at theend of construction of the second tunnel. It shows thatboth the settlement pattern and amplitude depend on thedistance between tunnels. The maximum soil settlement isobserved for the configuration with close tunnel (Sx/D= 2). In this case, the maximum soil settlement is

induced between the two tunnels, it attains about 50 mm.The increase in the distance between tunnels induces adecrease in the settlement in the central part of the twin-tunnels and leads to a stabilization in the settlement aboveeach tunnel. Beyond the distance (Sx= 3D), the construc-tion of the first tunnel does not affect the second one.The non-symmetry of the settlement results from the asym-metry of the plasticity induced in the soil mass as illustratedinFig. 4.

Fig. 3c and d show the distribution of the bendingmoment and the thrust in the right tunnel, respectively. Itcan be observed that the both the tunnels spacing and con-

struction do not affect the internal forces in the tunnel.

3.2. Tunnels with vertical alignment

Fig. 5a shows the tunnel configuration considered in thissection. The upper tunnel center is located at 2.5D belowthe soil surface; the distance between the tunnel axes isequal to 2D (Fig. 5a). Two analyses were carried out. Inthe first one, the upper tunnel is constructed at first (refer-ence case), while in the second analysis, the lower tunnel isconstructed first (inverted case). Results are presented atthe achievement of the construction of tunnels. Fig. 5b, cand d illustrate the influence of the construction procedureon the soil settlement, bending moment and thrust, respec-tively. It shows that the construction of the upper tunnel atfirst leads to higher settlement and internal forces com-pared to that obtained by the construction of the lower

tunnel at first. The maximum settlement (Fig. 5b) in thefirst case is about 12% higher than that in the second case,while the bending moment in the first case is higher by

about 23% than that induced in the second case (Fig. 5c);

Table 2Configurations of twin-tunnels analyzed in this paper

Configuration Sx/D Sy/D Inclination angle (a) ()

Horizontal alignment 2, 2.5, 3, 4 5 0 0Vertical alignment 0 2 90

Inclined alignment 2, 2.5 2 45, 39

-700

-600

-500

-400

-300

-200

0 50 100 150 200 250 300 350 400

Radial Angle

Thrust(kN)

2 D

2.5 D

3 D

4 D

5 D

-700

-600

-500

-400

-300

-200

0 50 100 150 200 250 300 350 400

Radial Angle

Thrust(kN)

2 D

2.5 D

3 D

4 D

5 D

-700

-600

-500

-400

-300

-200

0 50 100 150 200 250 300 350 400

Radial Angle

Thrust(kN)

2 D

2.5 D

3 D

4 D

5 D

Thrust in the right tunnel

Geometric configuration

-50

-40

-30

-20

-10

0

-30 -20 -10 0 10 20 30X/D

Settlementatthesoilsurface(mm)

2D

2.5 D

3D

4D

5D

Soil settlement induced by the construction of the twin-tunnel

-300

-200

-100

0

100

200

300

0 50 100 150 200 250 300 350 400

Radial Angle

Bendingmomentintheliningofrighttunnel2(KNm)

2 D

2.5 D

3 D

4 D

5D

Bending moment in the right tunnel

2.5 DSx

2.5 DSx

a

b

c

d

Fig. 3. Tunnels with horizontal alignment: Influence of the constructionprocedure and configurations on the soil settlement and internal forces.

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Plasticity after the excavation of the first tunnel Plasticity after the excavation of the second tunnel

a b

Fig. 4. Plasticity in horizontal alignment tunnels (Sx= 2D).

-80

-70

-60

-50

-40

-30

-20

0 50 100 150 200 250 300 350 400

Radial angle

Thrust(kN)

alpha = 45 (reference case)

alpha = 45 (invertedcase)



-800

-700

-600

-500

-400

-300

-200

0 50 150 350

Thrust(kN)





Thrust in the upper tunnel at the end of construction


-60

-40

-20

0

-10 -5 0 5 10X/D

Settlementatthesoilsurface(mm)


alpha = 45 (inverted case)



Settlement induced at the achievement of the construction

-400

-200

0

200

400

0 50 100 150 200 250 300 350 400

Radial angleBendingmomentintheliningofuppertunnel

(kNm)


alpha = 45 (inverted case)alpha = 39 (reference case)


Bending moment in the upper tunnel at the end of construction

2.5 DSx

Sy

a

b

c

d

Reference case: upper tunnel constructed at firstInverted case: lower tunnel constructed at first

Fig. 6. Tunnels with inclined alignment: Influence of the constructionprocedure and tunnels configuration on the soil settlement and internal

forces.


-60

-40

-20

0

-25 -20 -15 -10 -5 0 5 10 15 20 25

X/D

Settlementatthesoilsurface(m

m)

reference case

inverted case

Soil settlement induced by the construction of the twin-tunnels

-300

-200

-100

0

100

200

300

0 50 100 150 200 250 300 350 400

Radial angle

Bendingmomentintheliningoftunnel2(kNm)

reference case

invertedcase

Bending moment in the lower tunnel

2.5 D

2 D

-1200

-1000

-800

-600

-400

0 50 100 150 200 250 300 350 400

Radial angle

Thrust(kN)

reference case

inverted case

-1200

-1000

-800

-600

-400

0 50 100 150 200 250 300 350 400

Radial angle

r

reference case

inverted case

Thrust in the lower tunnel

a

b

c

d

Reference case: upper tunnel constructed at first

Inverted case: lower tunnel constructed at first

Fig. 5. Tunnels with vertical alignment: Influence of the construction

procedure on the soil settlement and internal forces.

F. Hage Chehade, I. Shahrour / Tunnelling and Underground Space Technology 23 (2008) 210214 213


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the thrust in the reference case is higher by about 10% than

that obtained in the inverted case (Fig. 5d).

3.3. Tunnels parallel inclined

Two configurations were analyzed (Fig. 6a). The verti-cal distance between the tunnel axes is equal to Sy= 2D.In the first configuration, the horizontal distance betweenthe tunnel axes is equal to Sx= 2D(a= 45); in the secondconfiguration Sx= 2.5D(a= 39). Fig. 6bd shows theinfluence of both the tunnel configuration and construc-tion procedure on the soil settlement and internal forcesin the upper tunnel. It can be observed that the construc-

tion of the lower tunnel at first (inverted case) leads tohigher soil settlement than that induced when the uppertunnel is first constructed (Fig. 6b). This result is similarto that obtained with vertical aligned tunnels. Both thebending moment (Fig. 6c) and thrust (Fig. 6d) in the uppertunnel are moderately affected by the order of constructionof the tunnels.

The influence of the construction order on the plasticitydistribution is illustrated in Figs. 7a and 7b. It shows thatthe construction order affects the distribution of plasticityinduced around the tunnels. A lower plasticity level isobserved around the tunnel constructed first.

4. Conclusion

This paper included a numerical analysis of the con-struction of twin-tunnels with a particular focus on theinfluence of both the construction procedure and geometricconfiguration on the soil settlement and internal forces dueto tunnels construction. The comparative study shows thatthe construction procedure (order of construction of tun-

nels) affects the soil settlement and bending moment. The

construction of the upper tunnel at first leads to higher set-tlement and bending moment, compared to that obtainedby the construction of the lower tunnel at first. The highestsoil settlement is obtained for vertical aligned tunnels,while horizontal aligned tunnels cause the lowest settle-ment, but with a larger lateral extension of the settlement.The design of twin-tunnels must take into considerationother constraints related to the environment and to theunderground congestion. The numerical modeling helpsin considering such constraints to find an optimal solutionfor the construction of twin-tunnels.

References

Kawata, T., Ohtsuka, M., 1993. Observational construction of large-

scaled twin road tunnels with minimum interval. In: Reith, J.L. (Ed.),

Infrastructures Souterraines de Transports. Balkema, Rotterdam.

Perri, G., 1994. Analysis of the effects of the new twin-tunnels excavation

very close to a big diameter tunnel of Caracas Subway. In: Salam,

Abdel (Ed.), Tunnelling and Ground Conditions. Balkema, Rotter-

dam, pp. 523530.

Saitoh, A., Gomi, K., Shiraishi, T., 1994. Influence forecast and field

measurement of a tunnel excavation crossing right above existing

tunnels. In: Salam, Abdel (Ed.), Tunnelling and Ground Conditions.

Balkema, Rotterdam, pp. 8390.

Shahrour, I., Mroueh, H., 1997. Three-dimensional non linear analysis of

a closely twin tunnels. In: Sixth International Symposium on Numer-ical Models in Geomechanics (NUMOG VI), vol. 2. Montreal,

Quebec, Canada, pp. 481487.

Soliman, E., Duddeck, H., Ahrens, H., 1993. Two and three-dimensional

analysis of closely spaced double-tube tunnels. Tunelling Underground

Space Technol. 8 (1), 1318.

Yamaguchi, I., Yamazaki, I., Kiritani, K., 1998. Study of ground-tunnel

interactions of four shield tunnels driven in close proximity, in relation

to design and constructions of parallel shield tunnels. Tunelling

Underground Space Technol. 13 (3), 289304.

After the excavation of the upper tunnel After the excavation of the lower tunnel

Fig. 7a. Plasticity in inclined alignment tunnels (a= 45) (Reference case).

After the excavation of the lower tunnel After the excavation of the upper tunnel

Fig. 7b. Plasticity in inclined alignment tunnels (a= 45) (Inverted case).

214 F. Hage Chehade, I. Shahrour / Tunnelling and Underground Space Technology 23 (2008) 210214

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