Analysis of Leakage Paths Induced by Longitudinal Differential Settlement of the Shield-driven Tunneling

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1 2016 rd International Conferene on Engineering Tehnology and Appliation (ICETA 2016) ISBN: Analysis of Leakage Paths Indued by Longitudinal Differential Settlement of the Shield-driven Tunneling Yin Liu* Shanghai Key Laboratory of Engineering Struture Safety, Shanghai Researh Institute of Building Sienes, Shanghai, China Department of Geotehnial Engineering, Tongji University, Shanghai, China Hongbo Zhou Shanghai Key Laboratory of Engineering Struture Safety, Shanghai Researh Institute of Building Sienes, Shanghai, China ABSTRACT: It is a lear simplifiation to onsider the tunnel lining as uniformly permeable. In reality, it is more likely that there are speifi leaks, assoiated with segmental lining joints. In the ase of the in situ onrete linings, onstrution joints an provide leakage paths, espeially aounting for most of the water leakage. For transportation tunnels in saturated soils below water table, different settlements will lead to ring offsets and hanges in joint opening near the edges where the gaskets are loated and may signifiantly affet the sealant potential of the lining. In this paper, taking the metro line No.1 in Shanghai as an example, the development of joint opening and ring offset was set up based on the mehanial model of segment joint. Based on the magnitude of the joint opening or ring offset, the ourring of water leaking into the tunnel through the joint system an be judged. This analysis not only helps us realize the leakage paths of the segmental linings, but also provides the guidane for waterproof design and protetion measures of the shield tunnel. Keywords: leakage paths; segment joint; joint opening; ring offset 1 INTRODUCTION The shield-driven tunneling method has been widely adopted for onstrution of urban underground tunnels in soft ground. In Shanghai, a vast network of underground mass transit systems has been strutured with this method. Jointed segmental preast onrete linings onneted by steel bolts are ommonly used in most shield driven tunnels. Due to the existene of joints, the joint openings will have important influene on tunnel leakage [1]. Aording to preliminary investigation of Shanghai Metro Tunnel, substantial proportion of shield tunnel setions features water leakage in different degrees. This is one of the most important diseases for shield tunnel in soft grounds, affeting the stability of tunnel struture, the durability of segment, failities in subway and ground settlement [2]. *Corresponding author: liu009yin@16.om So for tunnels in saturated ground below water table, ontrol of leakage is one of the most important problems to be onsidered in lining design. Considering most of the tunnel leakage taking plae at the joints, one of the most effetive solutions to this problem is to use sealant between the segments. But for the long-term operation subway, most parts of the distortions will emerge at the longitudinal joints as a result of uneven settlements of the tunnel. These struture deformations may alter joint opening and ring offset near the edges of segments where the gaskets are loated and may signifiantly affet the sealant behavior of the lining []. 2 MECHANISM OF LEAKAGE THROUGH THE JOINT OF LINING The joint gaps between segments are inevitable beause of struture of the onrete linings. Rubber gas- 896

2 kets between two adjaent segments have been used as a sealant material for water in bolted preast onrete segment linings for many years. The gasket material is ompressed by ontat pressure to prevent water leaking into the tunnel and the mehanism of segment gaskets waterproof is illustrated in Figure 1. The rubber gasket sealed is shown in Figure 2. Pr In order to waterproof tunnel segments, the magnitude of gaps between adjaent segments should be limited. For example, Shanghai Subway takes 5mm as the limit value of the joint opening and 8mm of the ring offset [6]. Otherwise leakage is expeted to take plae between two adjaent segments. LEAKAGE CAUSED BY CIRCUMFERENTIAL JOINT OPENING Pw Pr Joint gap Figure 1. Mehanism of rubber gasket sealed..1 Tunneling deformation aused by joint opening The manifestation of different settlement is in the form of bending deformation in the ase of weak bending stiffness. If the value of longitudinal urvature radius inreases, water leakage will our beause of the inreasing of joint opening, as shown in Figure. Figure. Cross setion and longitudinal deformation in the form of joint opening. Figure 2. Rubber gasket sealed. The mehanism formula proposed by a Japanese sholar is [4]: P mp (1) r w where Pr is the required total gasket ontat pressure; m is the oeffiient of rubber gaskets, whih is related with the material properties, and Pw is the water pressure. So if the joint open exeeds the required value, leakage will our between the two gaskets as a result of the ontat pressure between the two gaskets not satisfying the above formula. For a long-term operation, tunnel will deform into oval irumferentially and settle longitudinally. The longitudinal deformation is in two different forms, namely: joint opening and ring offset, whih are probably aused by the segment assembly and ompliated external geologial onditions. The former mainly suffers from bending moment while the latter from shear fore [5]. Taking one ring of lining and joint as one alulation unit ls and the orresponding rotation angle mainly from irumferential joint rotating as relative rotation of two adjaent segments, /ls is the urvature of longitudinal deformation, and M is the orresponding bending moment. As for the influene of irumferential joints, the oordination ondition and physial equilibrium an be applied to get the loation of neutral axis angle and the setion rotation supposed that the ross setion is under ideal elasti state. The stress-strain relationship of the ross setion is illustrated in Figure 4 [7,8,9] and an be written as: 1 K j1 tg 2 EA l f (2) in whih, lf=λls,λ is the relative oeffiient of the length effeted by the irumferential joint; Kj1 is the elastiity stiffness oeffiient of all vertial bolt joint; E is the elastiity modulus of onrete segment; A is the ross-setional area of onrete segment. When the length effeted by the irumferential joint is assumed to be the length of bolt, the equation (2) an be rewritten as 1 tg m 2 () 897

3 Figure 4. The stress-strain relationship of the ross setion under the elasti state. Inner diameter /m Outer diameter /m Table 1. Main struture oeffiients of the shield tunnel. Ring width /m Elasti modulus of onrete/kpa Bolt diameter /mm Bolt length /mm Bolt quantity Elasti modulus of bolt/kpa E E+08 m ne A EA b b (4) where m is the stiffness ratio of bolt to onrete segment; E is the elastiity modulus of bolt; A is the ross-setional area of onrete segment. Aording to the deformation ompatibility ondition and load equilibrium equation, the orner angle of ross setion θ an be obtained as: l f os ( / 2 )sin M (5) EI os where M is the longitudinal bending moment. Make the oeffiient of rotation rigidity of the irumferential joint to be K f os os ( / 2 )sin Equation (5) an be rewritten as (6) l f 1 M (7) EIK f Aording to the assumption of equivalent bending, the stiffness of equivalent bending of tunnel is lk s f ( EI) eq E I E I K ( l l ) l where lk s f K ( l l ) l f s f f f s f f (8) (9) Based on the above equations, the the magnitude of the joint opening an be obtained. M ls sin t ( D/2rsin ) 0 E I os Equation (10) an also be written as (10) l f sin t ( D/2rsin ) 0 (11) R os where R is the urvature radius of tunneling settlement, δt is the magnitude of the joint opening, δ0 is the initial value of δt, D is the diameter of the tunnel..2 Parameter analysis As an be seen from the analytial expression of the magnitude of the joint opening δt, the influene fators of δt inlude: the urvature radius of tunneling settlement R, the stiffness ratio of bolt to onrete segment m, the relative oeffiient of the length effeted by the irumferential joint λ; the width of lining ring ls and the diameter of the tunnel D and et. To take the influene degree of different fators into aount, the metro line No.1 in Shanghai was taken as an example. The influene of different fators was alulated and analysed. Calulating results were summarized in Table 1. Aording to equation(11), the influene of R, λ, ls and m on δt was alulated without the effet of initial joint opening δ0. The relationships between δt and R with λ = 0.1, 0.2, 0.1 and 0.8 are summarized in Figure 5. It an be seen that δt dereases obviously with R at different λ and the relationships are almost the same with different λ. This indiates that λ has almost no effet on δt. 898

4 Although λ has ertain effet on the alulating length lf and the position of neutral axis, the range of effet is small and the hange range of is also small. Figure 5. Relationships between δ t and R with different λ. Figure 6 shows the relationships between δt and R with ls =0.6, 0.8, 1.0, 1.5 and 2m. It is seen that δt inreases signifiantly with the inrease of ls at the same R. As an be seen from equation(2), the alulating length lf and the position of neutral axis inrease with ls. So δt inreases obviously with the inrease of ls. It an also be seen that δt inreases obviously with the derease of R at different ls. with m =0.005,0.010,0.020 and It an be seen that δt dereases with the inrease of m at the same R. This may be explained that the inrease of m only affets the position of neutral axis and the hange range of is small. Thus the effet of m on δt is not obviously. It an be seen from the above analysis that the urvature radius of tunneling settlement R has signifiant effet on the magnitude of the joint opening δt. Thus, R an be seleted as an important index to evaluate the normal operation and safe using of the shield tunnel. Aording to the tehnology standard of Shanghai metro protetion, R is required to be at least15000m in general. Besides, as δt is small, the initial value of δt(δ0) has signifiant influene on the final value of δt. δ0 is lose related to the prodution of segment and the onstrution quality of shield tunnel. Therefore, the leakage through joint opening an be seen as the results of the prodution of segment, the onstrution of shield tunnel and the differential longitudinal settlement of tunnel during operation. 4 LEAKAGE CAUSED BY RING OFFSET 4.1 Tunneling deformation aused by shear fore. The shear fore ating on the irumferential joint varies and beomes more ompliated along the longitudinal axis of tunnel. Generally, when the shear stiffness of tunnel is not big enough ompared to the shear fore, the longitudinal differential displaement is generated by rings offset, as shown in Figure 8. Segment Figure 6. Relationships between δ t and R with different l s. Ring offset Figure 8. Longitudinal deformation in the form of ring offsets. 4.2 Development of ring offsets. Figure 7. Relationships between δ t and R with different m. The value of m of the shield tunnel of metro line No.1 in Shanghai is aording to equation(4). Figure 7 shows the relationships between δt and R Taking the segment of Shanghai metro line 1 as an example, the length of onvex tenon of the joint is BC =127mm, AD=157mm, ompared with that of the groove B C =15mm, A D =165mm, as shown in Figure 9(a). Sine the length of groove is longer than that of onvex tenon, there is an assembly margin of 8mm whih will permit miro radial diretional sliding. The relative movement between the segments is manifested in the phenomenon of ring offset. Aording to design, the ontat length of gaskets is about 2mm when no offset ourring between the joints, as depited in Figure 10(a). Considering the 899

5 A B A' B' A A' B' B A B B' C D C' C D C' C D D' A''D' D' (a) (b) () Figure 9. Illustration shows the different segments ontat state with inreasing offset (a) (b) () Figure 10. The ompression area of the orresponding gaskets with different offsets. development of the shear fore and the struture of joint, the progress of onvex-groove ontat an be divided into the following three stages [10, 11]: 1. The magnitude of ring offset is very small, namely: 1mm 4mm and the onvex tenson and groove are not separate. In this ase, small sliding ours between joints and the onvex tenson and groove interat, as shown in Figure 9(b). In this ontext, the gaskets an also prevent water leaking into the tunnel, but the ontat area of gasket-to-gasket dereases and the amount of ompression beomes smaller, as plotted in Figure 10(b). 2. If the shear fore inreases due to the growing of different settlement, the relative deformation of the adjaent ring will inrease with the value of the offset 4mm 8mm.The joint sliding will ontinue until the side of the onvex tenson ompresses the side of groove, as shown in Figure 9(). The inreasing shear fore makes the onvex tenson and groove nearly separate,as depited in Figure 10(). In this ase, leakage will our easily as ontat pressure and amount of ompression of the waterproof gasket derease.. If the value of ring offset is larger than 8mm, whih means the onvex tenson and groove separate ompletely and the sealant gasket an t prevent leakage at this stage. 5 SUMMARY In this paper, mehanism of leakage paths indued by longitudinal different settlement of the shield-driven tunneling was investigated. From the above analysis, it was known that tunnel strutural deformation an ause joint opening and ring offset, whih affet the ompress and ontat area between the gaskets that mainly prevent water leaking into tunnel. For the long-term operation of the subway, the amount of joint opening and ring offset will grow with the inreasing uneven settlement of the tunnel. But the developments of the two struture deformation are different. The former is aused by bending moment and the longitudinal joint opening is inversely proportional to it. While the latter is aused by shear fore and the progress of onvex-groove ontat an be divided into three stages aording to the development of the shear fore and the struture of joint. In summary, water leaking between two adjaent segments will our if the longitudinal different settlement of tunnel is too large in any ase. In turn, the settlements of tunnel will be aggravated as a result of leakage, whih is an emerge viious irle. REFERENCES [1] Faisal Shalabi Behaviour of Gasketed Segmental Conrete Tunnel Lining, University of Illinois at Urbana-Champaign. [2] J.H. Liu, X.Y. Hou Shield-driven Tunnels. Beijing: China Railways Press. [] Faisal Shalabi, Edward Cording, Stanley Paul Sealant behavior of gasketed-segmental onrete tunnel lining. Proeedings of the Underground Strutures in Hot Climate Conditions. Riyadh, Saudi Arabia. 900

6 [4] Q.G. Fan Experimental study on the waterproof apability of the hydro-expansive rubber sealing ushion in shield tunnel. Underground Spae, 22(4): 5-8. [5] Z.Y. Fan Calulation Method and Longitudinal Deformation Analysis on Shield Tunnel Lining in Soft Soil, Shanghai: Tongji University. [6] Siene and Tehnology Committee of Shanghai Muniipal Constrution Commission Shanghai Metro-Line 1. Shanghai: Shanghai Sientifi and Tehnial Publishers. [7] Z.H. Huang Study on loading model of joints at longitudinal seam of lining of lining segment in shield tunnel. Underground Spae, 2(): [8] H. Murakanu, A. Koiumi Study of load-bearing apaity and mehanis of shield segment ring. In Proeedings of JSCE, 272. [9] S.M. Liao, F.L. Peng Analysis of shearing effet on tunnel indued by load transfer along longitudinal diretion. Tunnelling and Underground Spae Tehnology, 2: [10] R.L. Wang Longitudinal deformation analysis for Shanghai subway tunnel onstruted. Underground Engineer and Tunnels, 4: 1-6. [11] Z.L. Wang Researh on Deformation Charateristis and Strutural Properties for Operating Metro, Shanghai: Tongji University. 901