FINITE ELEMENT INVESTIGATION ON THE INTERACTION BETWEEN SHALLOW AND DEEP EXCAVATED TWIN TUNNELS

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1 VOL. 13, NO. 1, JANUARY 18 ISSN Aian Reearch Publihing Network (ARPN). All right reerved. FINITE ELEMENT INVESTIGATION ON THE INTERACTION BETWEEN SHALLOW AND DEEP EXCAVATED TWIN TUNNELS Adel A. Al-Azzawi 1, Khalida A. Daud 1 and Halah A. Daud 1 College of Engineering, Al-Nahrain Univerity, Baghdad, Iraq Minitry of Higher Education and Scientific /Science and Technology, Baghdad, Iraq dr_adel_azzawi@yahoo.com ABSTRACT In the twin tunnel, the pacing between tunnel or pillar width i an important iue for tability, becaue the mutual interference between tunnel depend on it during the contruction equence. It mut be calculated with repect to tunnel ize, oil condition, foundation type, contruction method, and contruction equence. The tunnel and oil around it repone are alo dependent on the clear ditance between tunnel. Therefore, enough clear ditance between tunnel mut be maintained to enure the tunnel tability. Sometime, the urface movement and the interaction with exiting foundation are required to be calculated. The hallow and deep twin tunnel in the preent reearch are analyzed uing PLAXIS finite element oftware. The analyi reult obtained from finite element are compared with experimental tet reult and analytical olution obtained by other reearcher. The preent tudy how that the interaction between twin tunnel can be ignored for tunnel ditance greater than the diameter of tunnel multiplied by 4. Keyword: clay oil, deep and hallow, pillar width, ettlement, oil -tructure interaction, twin tunnel. INTRODUCTION The need for contructed tunnel in Arab countrie, mainly for tranportation purpoe are increaed in recent year. Sometime, it i required to build new tunnel in cloe to exiting contructed tunnel and the contruction proce ha to be carried without cauing any expected damage either to the exiting building or to uburface infratructure. Therefore, it i required to predict poible interaction effect before reaching the deign tage. The urface oil ettlement, S in the exiting of a ingle tunnel built beneath in oft oil are aumed to obey an inverted Gauian curve defined by Peck (1969) and examined by different ite invetigation and meaurement [Mair et al. (1993)]. The propoed equation are given by: S S S max exp x / i V 1. i max 5 VLR i where x i the normal or perpendicular ditance from the tunnel centerline axi, S max (1) i the maximum oil urface ettlement (above the tunnel axi),, i i the ettlement trough width, V i the volume lo, V i the percentage of ground lo if oil i incompreible ( VL V /( R ) and R i the tunnel radiu) [Attewell and Farmer (1975)]. Thee ettlement are developed due to the lo in volume which happen at the tunnel. It may be defined a the additional volume of excavated oil over the final lining volume. During excavation and a it proceed, the oil around the tunnel face are unloaded and tend to move inward. Loe may happen behind the tunnel face due to L the nature or type of the tunnel hield. Many ite or field tudie have checked and confirmed that Equation 1 i acceptable for Green-field ite [Mairet al.(1993); Atkinon and Mair (1981)] but where building tructure are preent, a in citie, Equation 1 i aumed to be no longer valid. For multiple intalled tunnel, the ettlement from each are determined by uing Equation 1 and accumulated. Thi equation neglect the tunnel interaction during the intallation or contruction of each one. It i clear that the oil diturbance due to tunnel contruction will change the urrounding oil propertie, or reditribute the effect of a ubequent tunneling intallation through that zone of oil. Auming multiple tunneling ytem, with two parallel tunnel i conidered. Due to intallation of the econd new tunnel, the firt old tunnel and the oil urrounding move a a rigid body. The reditribution of oil tree develop arching around the new tunnel. Thi give a gradual load removal from the tunnel. If the new or econd tunnel i intalled cloe to the firt tunnel, the lining of firt tunnel will ditorted and ha diplacement. The minimum expected clear ditance between the tunnel to prevent interaction effect depend on the poition and oil propertie. Superpoition method i propoed in cae of multiple tunnel which i baed on Gau ditribution a follow Mair et al. (1993) S Smax(1) exp Smax() exp () i(1) i() S 1 ( x T / ) ( x T / ) 6

2 VOL. 13, NO. 1, JANUARY 18 ISSN Aian Reearch Publihing Network (ARPN). All right reerved. where S 1 = for no interaction and T i the tunnel pacing. If the two tunnel have the ame diameter and the ground lo, then Smax( 1) Smax( ) and i( 1) i(). Finally the ground ettlement i S ( x T / ) ( x T / ) exp S max() exp (3) i i Smax Previou reearcher have been carried out the tudy uing both experimental and finite element model to imulate the tunnel interaction. Ghaboui and Ranken (1977) carried out analyi baed on linear plane train finite element of multiple intalled tunnel auming the oil to be elatic. They howed that tunnel interaction effect were leer for a clear pace between the outide of two tunnel (pillar width) equal to tunnel diameter (1D). However, for a pillar width larger than D there wa no ignificant tunnel interaction. Therefore the tunnel are conidered a independent and ettlement calculated accordingly. Kim (1996) tudied the effect of hield tunnel contruction on the developed and induced diplacement that are formed in the lining of exiting cloe old tunnel through. The author carried out experimental model tet in which the tunnel were intalled uing a miniature hield tunneling machine. The experimental model were imulated with few number of two-dimenional plane finite element. The adopted model are choen to be imilar to the model that mentioned by Ghaboui and Ranken (1977). The difference wa that pecial finite element treatment were ued to imulate the oil boundary movement related to tunnel intallation. A et of five experiment have been made uing kaolin clay ample conolidated in the tank with plane train hown in Figure-1. In ingle clay oil ample, three tunnel were ued and intalled to carry out two interaction tet. One of thee experiment wa for a far tunnel (tunnel centerline pacing of.d) and the other wa for a near' tunnel (tunnel center-line pacing of 1.4D) where D i the tunnel diameter. The plane train condition conited of a rectangular tank with internal dimenion 1 mm by 3 mm in plan and 6 mm in depth. Two 5 mm thick perpex wall were ued having three hole (correponding to the intallation poition of the model tunnel). Figure-1. Layout of plane train tank. A et of additional experimental tet were carriedout by Kim (1996) in which the tunnel were put normal rather than parallel. A farther detail and dicuion of thee tet are given by Kim (1996). The oil propertie and geometry of the plane train experimental tet are pecified in Table-1. Table-1. Specification of the tet carried by Kim (1996). Tet H/D Su (kpa) OCR t (mm) P (kpa) PS PS PS PS3R PS where u = Undrained hear trength of clay, P = Surcharge preure, t = Liner thickne 63

3 VOL. 13, NO. 1, JANUARY 18 ISSN Aian Reearch Publihing Network (ARPN). All right reerved. The clay oil ample were prepared by a kaolin lurry conolidation within the tet rig itelf. The ued tet oil ample were clay of either normally conolidated or over- conolidated with a value of approximately 3 for OCR. Thi value of OCR wa choen to repreent real condition in London Clay. All tet ample had approximately the ame hear trength of oil (about kpa). The 7 mm diameter plain teel tube are ued a tunnel liner. The tube thicknee are elected to obtain the correct tunnel lining tiffne FINIE ELELMENT ANALYSIS The tudy of interaction problem between contructed tunnel i complicated and cannot be fully invetigated through uing prototype model teting becaue it i required many tudy parameter. The finite element modeling of uch problem are carried out to check the obtained reult, it i firt neceary to develop realitic modeling procedure. The finite element have alo been ued to invetigate ome of the modeling aumption inherent in the phyical tet. The analyi i limited to the cae of the undrained condition to model interaction behavior immediately after tunnel contruction. A platicity oil model adopting Mohr- Coulomb yield criterion i ued in the analyi of model. Fifteen node triangular continuum element are ued to imulate the oil and hell element are ued to model the tunnel liner. Figure- how the ued meh in finite element model analyi. The material propertie of the lining and the oil are preented in Table and 3. Figure-.Finite element meh. Table-. Material propertie of the lining. Parameter Name Value Unit Norma tiffne EA 58 N/mm Flexural rigidity EI 3 N/mm /mm Thickne d.54 mm Poion' ratio.3 - Table-3. Material propertie of the oil. Parameter Name Value Unit Dry oil weight dry 15e-6 N/mm Wet oil weight at 18e-6 N/mm Permeability k.1 mm/day Young' modulu Poion' ratio E 6.8 N/mm.3 Coheion c. N/mm Friction angle. Dilatancy angle. Effective tre K ratio o.64 The tunnel excavation wa modeled numerically through deactivating the oil element inide the tunnel [Augarde et al. (1995)]. In thee analye, it wa important to imulate the void between the oil and tunnel liner a a reult of the tunnel overcutting. Thi wa done by applying to the inide of the tunnel liner a uitable hydrotatic uction in order to reduce it circumference. Thi method or procedure i expected to produce varying hoop force or tre value. The following procedure were ued for modeling the contruction of each tunnel in the analye. a) Apply initial tree to oil with tunnel hell element deactivated. The expreion.64 OCR i aumed to give K o value. b) Remove excavated oil element inide the tunnel. c) Activate tunnel hell element to model tunnel liner in tunnel poition to be intalled. d) Apply internal preure to imulate ground lo. Three eparate calculation procedure were adopted for comparion with experimental work a given below. a) Single tunnel intallation or contruction in poition 1. b) After intallation or contruction of tunnel in poition 1, the tunnel at poition i intalled. c) Tunnel intallation or contruction in poition 3 after tunnel are contructed or intalled at poition 1 and. Cae 1, and 3 were intended to repreent the procedure adopted in the experimental model tet carried by Kim (1996) 64

4 VOL. 13, NO. 1, JANUARY 18 ISSN Aian Reearch Publihing Network (ARPN). All right reerved. VERFICATION WITH PREVIOUS TEST RESULTS The reult preented in thi article are concerned with the comparion between the tet reult of PS3 ample that wa carried by Kim (1996) and the preent tudy finite element. In general, the reult of the experimental model tet how that tunnel interaction effect are larger for the pillar pring-line and old tunnel crown. Figure-3[a] and [b] how typical diplacement reult of the old tunnel liner due to the addition of two new twin tunnel in poition and 3 for the Kim (1996) experimental model and the preent tudy numerical model. The obtained finite element reult how acceptable agreement with the data obtained from experimental model tet. The reult how alo that greater outward diplacement of the pillar pring-line occurred if a new tunnel wa added. In each cae the tunnel crown diplaced downward; however movement of the invert wa negligible. Similar general diplacement pattern for tunnel intalled at ditance of.d and 1.4D (from each other) i obtained with greater magnitude for the near tunnel. [a] Tunnel intalled at poition (Spacing =. D) [b] Tunnel intalled at poition 3 (Spacing =1.4 D) Figure-3. Additional diplacement of the exiting or old tunnel liner for PS3. The tunnel deformation are hown through the value of horizontal diameter change at pring-line level and vertical diameter change. The exiting tunnel immediate diameter change after the contruction of the new tunnel i drawn together with the tunnel pacing and hown in Figure-4. Thi figure how the previou experimental reult are plotted together with the preent numerical analyi reult. Figure-4 indicate acceptable agreement between the reult obtained from phyical and numerical model. Thee reult how that the tunnel interaction effect are mall for tunnel pacing exceed 4 D. Tunnel diameter change (mm) Exp(vertical dip.)[kim (1996)] Exp(horizontal dip)[kim (1996)] FE(vertical dip) FE (horizontal dip) Tunnel pacing to diameter ratio (T/D) Figure-4.Tunnel diameter change againt Tunnel pacing for PS3. Figure 5 and 6 how the bending moment at each increment developed in the intrumented liner due to the exiting of the nd and 3rd tunnel. In thee figure M i the moment at each increment obtained in the intalled tunnel after contructing the additional tunnel. The value obtained from the preent tudy analyi and meaured by 65

5 VOL. 13, NO. 1, JANUARY 18 ISSN Aian Reearch Publihing Network (ARPN). All right reerved. Kim (1996) are drawn in thee figure. The reult how that ignificant value of bending moment were developed in the intalled tunnel due to the intallation of the new tunnel. Through the two ued method (the numerical and experimental teted model) the reult i found to be agreed. A, the new tunnel are contructed cloe to an exiting or tunnel, the increment in the moment developed at the pillar pring-line of the exiting or old tunnel liner become larger. Inremental bending moment (N.mm/mm) Expermental tudy[kim (1996)] Finite element analyi Tunnel ection angle ( degree) Figure-5. Additional Bending Moment (PS3) due to Tunnel intallation at poition (Spacing=. D). Inremental bending moment (N.mm/mm) Expermental tudy[kim (1996)] Finite element analyi Tunnel ection angle ( degree) Figure-6. Additional Bending Moment (PS3) due to Tunnel intallation at poition 3 (Spacing=1.4 D). SETTLEMENT DUE TO TUNNEL INTERACTION Thi numerical tudy give guidance on the poible ground ettlement induced by one and two twin tunnel. The interaction and tunnel depth are tudied a variable parameter. A hown in Figure-7, a finite element analyi model i ued for olving the problem uing the material propertie and model dimenion for (PS1) problem. The effect of ground loading (urcharge) and water table are neglected here. In general before excavation of the tunnel the oil ytem wa in equilibrium. When the tunnel are excavated in oil, the oil equilibrium i diturbed and the oil move to the boundarie of the tunnel. Figure 8 and 9 compare urface ettlement induced by one tunnel and two tunnel. Superpoition method (equation 3) without interaction i alo plotted for comparion. For one and two tunnel the numerical reult agree with the analytical olution obtained by Mair et al (1993) with a percentage of 3%. 66

6 VOL. 13, NO. 1, JANUARY 18 ISSN Aian Reearch Publihing Network (ARPN). All right reerved. H / D 3 D 7mm T D Figure-7. Tunnel model for finite element analyi.. Surface ettlement (mm) Emperical equation Mair et al (1993) Finite element analyi Ditance from tunnel centre (mm) Figure-8. Comparion of urface ettlement for one tunnel. 67

7 VOL. 13, NO. 1, JANUARY 18 ISSN Aian Reearch Publihing Network (ARPN). All right reerved.. Surface ettlement (mm) Emperical equation Mair et al (1993) Finite element analyi Ditance from tunnel centre (mm) Figure-9. Comparion of urface ettlement for two tunnel. Figure-1 how the interaction i an important index to the urface ettlement. When the ditance between tunnel pacing i greater than 4D, the interaction effect can be ignored and reduced value of urface ettlement are obtained. Maximum urface ettlement to tunnel diameter ratio (Smax/D) Finite element analyi (two tunnel) Finite element analyi (one tunnel) Tunnel pacing to diameter ratio (T/D) Figure-1. Effect of tunnel pacing on the maximum urface ettlement (H/D=3). Figure-11 how the effect of tunnel depth i a major factor on the urface ettlement. When the depth of tunnel i large, the urface ettlement value i reduced. 68

8 VOL. 13, NO. 1, JANUARY 18 ISSN Aian Reearch Publihing Network (ARPN). All right reerved. Maximum urface ettlement to tunnel diameter ratio (Smax/D) Finite element analyi (two tunnel) Finite element analyi (one tunnel) Tunnel depth to diameter ratio (H/D) Figure-11. Effect of tunnel depth on the maximum urface ettlement (T/D=). Figure-1 how the effect of tunnel thickne on ground urface and tunnel ettlement. A the tunnel thickne increaed, the oil urface and tunnel ettlement decreaed. The effect wa found to be greater on urface ettlement. Maximum ettlement to tunnel diameter ratio (Smax/D) Surface ettelement Tunnel ettelement Tunnel thickne to diameter ratio (t/d) Figure-1. Effect of tunnel thickne on the maximum for ingle tunnel. CONCLUSIONS The numerical analyi through finite element how that for tunnel paced cloely, the ettlement and moment of tunnel are conidered to be important. The main concluion obtained from the preent reearch are a follow: a) Finite element analyi give reult that in acceptable agreement with the previou model tet reult carried out by Kim (1996) and the previou cloed form olution. b) It i obviou that the tunnel interaction i neglected for the ditance between the tunnel center i le than or equal to the value of tunnel diameter multiplied by 4. c) The effect of tunnel depth i a major factor on the urface ettlement. When the depth of tunnel i large 69

9 VOL. 13, NO. 1, JANUARY 18 ISSN Aian Reearch Publihing Network (ARPN). All right reerved. (the tunnel diameter multiplied by 4), the urface ettlement value i reduced. d) When the tunnel thickne increaed, the urface of oil ettlement and alo tunnel ettlement are decreaed. The obtained effect wa greater on urface ettlement. REFERENCES Attewell P.B. and Farmer I.W Ground ettlement above hield driven tunnel in clay. Tunnel and Tunnelling, January. pp Attkinon J.H. and Mair R.J Soil mechanic apect of oft ground tunnelling, Ground Engineering. Vol.14, pp. -4. Augarde C.E., Burd H.J. and Houlby G.T A threedimenional finite element model of tunnelling. Numerical Model in Geomechanic - NUMOG V, Pande and Pietruzczak (ed). pp Duncan J.P. and Buchignani A.L An engineering manual for ettlement tudie. Geotech.Eng. Report, Dept. of Civil Eng., Univ. of California at Berkeley. pp. 94. Ghaboui, J and Ranken, R.E Interaction between two parallel tunnel. International Journal for Numerical and Analytical Method in Geomechanic. 1: Kim S. H Model teting and analyi of interaction between tunnel in clay. D. Phil. Thei, Oxford Univerity, UK. Mair, R.J., Taylor, R.N. & Bracegirdle A Suburface ettlement profile above tunnel in clay, Geotechnique. 43(): Peck R. B Deep excavation and tunneling in oft ground. Proceeding of the 7 th Conference on Soil Mechanic and Foundation Engineering. pp