- Email: [email protected]
Mechanical behavior of two kinds of prestressed composite linings: A case study of the Yellow River Crossing Tunnel in China
Tunnelling and Underground Space Technology 79 (2018) 96–109
Contents lists available at ScienceDirect
Tunnelling and Underground Space Technology journal homepage: www.elsevier.com/locate/tust
Mechanical behavior of two kinds of prestressed composite linings: A case study of the Yellow River Crossing Tunnel in China
T
⁎
Fan Yang, Sheng-rong Cao , Gan Qin State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, Wuhan 430072, China School of Water Resources and Hydropower Engineering, Wuhan University, Wuhan 430072, China
A R T I C LE I N FO
A B S T R A C T
Keywords: Shield tunnel 3D finite element method Prestressed composite lining Water conveyance Yellow River Crossing Tunnel
This paper presents the mechanical behavior of two innovative prestressed composite linings in shield tunnels for water conveyance. The Yellow River Crossing Tunnel of the Middle Route Project of the South-to-North Water Division Project (SNWD) is adopted in this study as a case. Three-dimensional finite element models are established to analyse the stress distribution and deformation feature of the prestressed composite lining when the tunnel is under the completed segment assembly condition (CSAC), the completed cable tension condition (CCTC) and the design water pressure condition (DWPC). The calculation and analysis results reveal that the prestressed composite lining with rebars (Model R) has an obviously combined bearing capacity, and the rebar is the key factor influencing the capacity. The prestressed composite lining with membranes (Model M) has a relatively separated bearing capacity, because the membrane can play a significant role in preventing stress transmission between the segmental ling and the secondary lining. Full circular compression can be realized for the secondary linings of both Model R and Model M when the tunnel is under the DWPC. However, the load bearing mechanism of Model M is more concise than that of Model R, the secondary lining of Model M is more secure than that of Model R because of the full use of prestresses and materials, and the membrane is beneficial to anti-seepage. By contrast, Model M is more suitable for the Yellow River Crossing Tunnel.
1. Introduction The prestressed composite lining is a kind of tunnel structure composed of an outer segmental primary lining and an inner prestressed secondary lining with circular anchor cables. The prestressed secondary lining can overcome the shortcoming of the small tensile strength of the concrete so that the concrete material can be fully utilized to withstand high internal pressures (Kang and Hu, 2005; Grunicke and Ristić, 2012). Therefore, this prestressed composite lining has more advantages over the ordinary double lining in load bearing capacity and anti-seepage capacity, and it is more suitable for application in shield tunnels with high internal pressures. According to the connection between the segmental lining and the prestressed lining, there are two types of the prestressed composite linings which are the prestressed composite lining with rebars (Model R) and the prestressed composite lining with membranes (Model M). The segmental lining and the prestressed lining of Model R are connected by rebars (Fig. 1a). The segmental lining and the prestressed lining of Model M are separated by membranes (Fig. 1b). At present, Model M has been applied to the Yellow River Crossing Tunnel of the South-to-North Water Division
⁎
Project (SNWD) in China for the first time, while Model R has not appeared in projects. The researches on the lining of the shield tunnel mainly focus on the monolayer segmental lining. The numerical models of the monolayer segmental lining mainly include the uniform ring model, multi-hinge ring model, beam-spring model, and shell-spring model (Lee et al., 2001; Ding et al., 2004; Do et al., 2013; Yang et al., 2014). In addition, three-dimensional finite element models are proposed to fully consider the three-dimensional effects of the segments (Blom et al., 1999). For the monolayer circular prestressed lining, it has been applied in some high pressure tunnels, such as the water conveyance tunnel of Geheyan Hydropower Station, the water conveyance tunnel of Tianshengqiao First Cascade Hydropower Station, and the desilting tunnel of Xiaolangdi Project in China. The common approach to considering the prestresses is to simplify them as a uniform radial pressure (Li et al., 2004). Since this simplified method cannot accurately simulate the nonuniform distribution of the prestresses along the circumferential direction and the spacing distribution of the anchor cables along the axial direction, it should be verified by three-dimensional finite element analysis or physical model experiments.
Corresponding author at: State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, Wuhan 430072, China. E-mail address: [email protected] (S.-r. Cao).
https://doi.org/10.1016/j.tust.2018.04.036 Received 9 November 2016; Received in revised form 21 April 2018; Accepted 29 April 2018 0886-7798/ © 2018 Elsevier Ltd. All rights reserved.
Tunnelling and Underground Space Technology 79 (2018) 96–109
F. Yang et al.
Fig. 1. Sketch of the prestressed composite lining: (a) Model R; (b) Model M.
simulate the two kinds of the prestressed composite linings (Model R and Model M). The performance of each component of the prestressed composite lining and the interaction between the segmental lining and the secondary lining are analysed when the tunnel is under three working conditions. The first working condition is the completed segment assembly condition (CSAC) that the segmental lining is assembled and reaches stable states. The second working condition is the completed cable tension condition (CCTC) that the secondary lining concrete is poured and the prestressed anchor cable tension is completed. The third working condition is the design water pressure condition (DWPC) that the grooves are backfilled with concrete and the lining withstands the design water pressure. According to the analyses of the numerical calculations and the experimental results, the mechanical behavior of the two prestressed composite linings is presented and compared.
The researches on the composite lining mainly focus on the ordinary double lining for shield tunnels. In the case of the double shell structure, the methods for computing the member forces of the secondary lining are generally divided into the bedded frame model method and the elastic equation method (ITA, 2000). A number of numerical calculations of the composite lining are based on the bedded frame model method. At present, the reported numerical models of the composite lining are mainly based on which the segmental lining is simulated by the two-dimensional beam-spring model or the three-dimensional shellspring model, and the interaction between the segmental lining and the secondary lining is mainly simulated by springs, beams or contact (Murakami and Koizumi, 1987; Takamatsu et al., 1992, 1993; Zhang et al., 2001; Yan et al., 2015). This ordinary composite lining is mainly applied to railway tunnels and highway tunnels, and some research results reveal that reinforcing the coupling between the segmental lining and the secondary lining can improve the bearing capacity of the ordinary composite lining (Takamatsu et al., 1992, 1993; Zhang et al., 2001). However, for the prestressed composite lining, it is a combination of the segmental lining and the prestressed lining, and it is mainly applied to shield pressure tunnels. The distribution of the prestresses along the prestressed anchor cable length direction is not uniform, and the anchor cables are equidistantly distributed along the axial direction. In addition to the external load, both the prestress and the internal pressure are borne by the prestressed composite lining. Moreover, whether the segmental lining and the prestressed lining are separated by membranes or connected by rebars, both the membranes and the rebars have a significant impact on the stress transmission between the segmental lining and the secondary lining. Therefore, the structure form, load condition and stress transmission of the prestressed composite lining are all much more complex than the ordinary double lining. The numerical models and the research results of the ordinary double lining are not applicable to the prestressed composite lining directly. The prestressed composite lining is an innovative and significant structure for the shield tunnel. This innovative technique is a desirable solution for the Yellow River Crossing Tunnel with characteristics such as poor geological conditions, high internal pressure, high anti-seepage requirements, deep buried depth, large cross section, etc. However, as it is applied for the first time in the world, there are few documented experimental, numerical or analytical results in the literature concerning this new type of the lining, and the mechanical behavior of the lining is still not clarified. Therefore, we investigate the mechanical behavior of the prestressed composite lining in a comprehensive way so that it could provide some references for the application of this typical lining in some other similar projects. In this work, the Yellow River Crossing Tunnel is adopted as a case, and detailed three-dimensional finite element models are established to
2. Case studied tunnel The SNWD is the one of the most expensive project in China. This project consists of the Eastern Route Project, the Middle Route Project and the Western Route Project. For the Middle Route Project, it has been completed since December 12, 2014. Several generations of technical personnel have carried out a large amount of survey, planning, design and research work since the 1950s. The Yellow River Crossing Project is a key project of the Middle Route Project of the SNWD, which is widely known as the most ambitious water conservancy project that crosses great rivers in the history of mankind. The Yellow River Crossing Tunnel is the largest individual project with the longest construction period, the most advanced technology and the most difficult construction in the SNWD. The total length of the Yellow River Crossing Tunnel is 3450 m, the excavation diameter is 8.7 m, and the design flow rate is 265 m3/s. The longitudinal profile of the Yellow River Crossing Project is shown in Fig. 2. The Yellow River Crossing Tunnel passes through soft soil and is constructed by the shield tunnelling method. In order to avoid large deformations of the excavation face, the precast segments are assembled timely to withstand the soil pressure and the external water pressure during the excavation. The internal water pressure in the centre of the tunnel is 0.51 MPa when the tunnel is under the DWPC. It is very important to prevent the high-pressure water from leaking out and to avoid seepage failure of the soil around the tunnel. If the internal water pressure is withstood only by the segmental lining, the segmental joints will be open sharply, resulting in water seepage. Therefore, a secondary lining is needed to improve the bearing capacity of the tunnel lining and to simultaneously improve the tunnel internal surface smoothing. As the prestressed concrete lining with circular anchor cables has advantages with respect to load bearing strengthening, high 97
Tunnelling and Underground Space Technology 79 (2018) 96–109
F. Yang et al.
Fig. 2. Longitudinal profile of the Yellow River Crossing Project (unit: m).
are listed in Table 1.
material utilization and anti-seepage strengthening, it is proposed as the secondary lining. During the preliminary design phase of the Yellow River Crossing Tunnel lining, two schemes (Model R and Model M) have been proposed. For Model R, the external load is expected to be withstood by the segmental lining, and the internal water pressure is expected to be withstood by the segmental lining and the secondary lining jointly. For Model M, the external load is expected to be withstood by the segmental lining, and the internal water pressure is expected to be withstood by the secondary lining individually.
3.3. Full-scaled experiment An outdoor full-scaled experiment is carried out, and the test site is located in the Mount Mangshan near the southern bank of the Yellow River (Niu et al., 2011; Duan et al., 2011). As shown in Fig. 6, the fullscaled experimental model consists of the lining models (Model R and Model M), plugs and shaft. The plugs can guarantee the seal of the experimental models. The water pump is placed in the shaft which is also used for transportation. The surface elevation of the test site is 172.8 m. The lining models are buried underground, and the elevation of the model centre is 155.9 m. The soil condition and the water pressure of the experiment are as the same as those of the real project. The external soil condition is simulated by backfilling sand to the elevation of 190.9 m when the construction of the experimental model is complete. The external water pressure is carried out by pouring water in the sand wrapped by the geomembrane, and the internal water pressure is carried out by elevating the water tank. Section I ∼ Section III of Model R and Section I' ∼ Section III' of Model M are observed in the experiment, respectively (Fig. 4). Fig. 3 presents the observation points of the observation section, and the numbers in the parentheses represent the dimensions of the observation section.
3. Full-scaled experiment and numerical simulation 3.1. Lining dimensions As shown in Figs. 3 and 4, the dimensions of Model R are the same as those of Model M, and each model has an axial length of 9.6 m. Segment external diameter is 8.7 m; internal diameter is 7.9 m; width is 1.6 m. The segmental lining is erected by staggered format (Fig. 1). The segments are connected by M32 straight bolts. Pre-tightening force of each bolt is 100 kN. For Model R, the concrete of the secondary lining is poured on the internal surface of the segmental lining directly, and the secondary lining and the segmental lining are connected by the rebars which are shown as blue1 lines in Fig. 3(a). The rebars are placed in the hand holes. The diameter of the rebar is 16 mm. For Model M, only the bottoms of the segmental lining and the secondary lining are bonded together, and the others are separated by the membranes which are shown as a red line in Fig. 3(b). The membranes have a total thickness of 6 × 10−3 m and annularly enclose a circumferential angle of 301.548°. The membranes compose of three layers of materials; the middle layer is a polyethylene membrane, and the others are geomembranes. The secondary lining external diameter is 7.9 m; internal diameter is 7.0 m. The secondary lining concrete is poured when the segmental lining has already withstood the external pressure and achieved stability. The prestressed anchor cable tension begins when the secondary lining concrete pour is completed and the concrete strength exceeds 75 percent of the design strength. As shown in Figs. 3 and 4, the preformed grooves are in the lower half of the secondary lining and the centre lines of the grooves are located at the angles of 96°, 134°, 226° and 264°. The distance between adjacent grooves is 0.45 m along the axial direction. Small relaxation steel wire strands of 12φj15.24, which have a design tension stress of 1395 MPa, are used as the prestressed anchor cables.
3.4. Three-dimensional finite element simulation 3.4.1. Element types Three-dimensional models of Model R and Model M are established using the 3D finite element analysis software ANSYS. The finite element models are shown in Fig. 7. Eight-node three-dimensional solid elements (SOLID45) are used for the soil, and eight-node three-dimensional solid elements (SOLID65) are used for the concrete. Two-node link elements (LINK8) are used for the prestressed anchor cables. Twonode beam elements (BEAM188) are used for the radial bolts, the circumferential bolts and the rebars. Constraint equations (CEINTF) are adopted to constrain the anchor cables with the secondary lining concrete and constrain the blot with the segmental lining concrete (Chong et al., 2014). Two-node nonlinear elastic spring elements (COMBIN39) are adopted to simulate the interaction between the rebar and the concrete. The rebar element and the concrete element are connected by COMBIN39, and its spring rigidity F-D relationship can be converted by Nilson bond stress-slip relationship (Nilson, 1972) which is given by
τ = 9.78 × 102s−5.72 × 10 4s 2 + 8.35 × 105s 3 3.2. Material properties
(1)
where τ is the bond stress (N/mm2), and s is the corresponding slip value (mm). As shown in Figs. 7 and 8, the contact surface between the segmental lining and the soil and the contact surface between the adjacent segments are simulated by the contact elements (TARGE170 and CONTA174). These “face-to-face” elements can simulate cold interface conditions transmitting only compression in the direction normal to the surfaces and shear in the tangential direction (Kim et al., 2007; Mo and
The soil above the Yellow River Crossing Tunnel is the medium granular sand, and the clay is below the tunnel. Fig. 5 presents the material properties for the soil. The material properties for the lining 1 For interpretation of color in Fig. 3, the reader is referred to the web version of this article.
98
Tunnelling and Underground Space Technology 79 (2018) 96–109
F. Yang et al.
Fig. 3. Cross section of the prestressed composite lining (unit: m): (a) Model R; (b) Model M.
Fig. 4. Groove layout along the axial direction (unit: m). Table 1 Material properties for lining. Type
Material
Young’s modulus (kN/ m2)
Poisson's ratio
Unit weight (kN/m3)
Segmental lining Secondary lining M32 Bolt Rebar Anchor cable Membrane
C50 concrete
3.45 × 107
0.167
25.5
C40 concrete
3.25 × 107
0.167
24.5
0.3 0.3 0.3 0.3
78.5 78.5 78.5 –
Steel Steel Steel Composite materials
8
2.1 × 10 2.1 × 108 1.95 × 108 1.5 × 103
Chen, 2008). A friction coefficient of 0.3 is used to simulate the tangential behavior (Chen and Mo, 2009) and the Lagrange and penalty method is used as the contact algorithm. For the finite element models of Model R and Model M, the bottoms of the segmental lining and the secondary lining are considered to be bonded completely and the relative slip is prohibited. As shown in Fig. 8, the rebar of Model R is simulated by beam elements, and the membrane of Model M is simulated by three springs: one normal spring and two shear springs. The normal spring behaves as a compression
Fig. 5. Material properties for soil.
99
Tunnelling and Underground Space Technology 79 (2018) 96–109
F. Yang et al.
Fig. 6. Profile section of the full-scaled experiment (unit: m).
Fig. 7. Finite element models: (a) soil; (b) secondary lining; (c) segments and bolts.
the tangential stiffness of a single shear spring; E is the Young’s modulus of the membrane; G is the shear modulus of the membrane; A is the corresponding area of a single spring; and t is the thickness of the membrane.
support and does not contribute to tension. The stiffnesses of the springs are calculated as follows:
kr =
E×A t
(2)
kτ =
G×A t
(3)
3.4.2. Material models The elastic-plastic constitutive model based on Drucker-Prager yield criterion is used for the soil. The yield function of the Drucker-Prager
where kr is the compression stiffness of a single normal spring; kτ is 100
Tunnelling and Underground Space Technology 79 (2018) 96–109
F. Yang et al.
Fig. 8. Interaction between segmental lining and secondary lining: (a) Model R; (b) Model M.
conditions of the Yellow River Crossing Tunnel, the calculation process is divided into three stages which are consistent with the three working conditions (CSAC, CCTC and DWPC). The load combinations of each working condition are shown in Table 2. The external water pressure in the horizontal line of the tunnel centre is 0.323 MPa. The internal water pressure in the tunnel centre is 0.51 MPa when the tunnel is under the DWPC. Separate calculations of water pressures and earth pressures can be used when the tunnel is covered by sandy soil (Mashimo and Ishimura, 2003). The external water pressures are directly applied on the segmental lining and the effective unit weight of the soil is used. Prestress loss of the anchor cables is inevitable because of the deformation of anchorages and the shrinkage of steel strands, the friction between the steel strand and the duct, the relaxation of the steel strand stresses and the shrinkage and creep of the concrete. The effective prestress of the anchor cables is equal to the design tension stress minus all of the prestress loss (GB50010, 2010; Collins and Mitchell, 1997). The effective prestresses along the circumferential angle (cumulative angle between the tensioning position and the calculation position) are shown in Fig. 10. The prestress is converted to the temperature load and applied to the anchor cable element in the model. The temperature load can be calculated by
model is defined as
αI1 +
J2 −k = 0
(4)
where I1 is the first stress invariant; J2 is the second deviatoric stress invariant; α and k are constants which depend on cohesion (c) and angle of internal friction (φ) of the material given by
α=
2 sin φ 3 (3−sin φ)
(5)
k=
6c cos φ 3 (3−sin φ)
(6)
For the concrete, the multi-linear isotropic hardening (MISO) stressstrain relationship is obtained using the model proposed by Popovics (1973) as given by
fc =
f ′c ·x·p p−1 + x p
(7)
where fc is the compressive stress at any strain εc ; εc′is the strain corresponding to the ultimate compressive strength ( fc′) of unconfined concrete; x is the ratio (εc /εc′); p is the ratio [Ec /(Ec−Esec )]; Ec and Esec are the tangential and secant modulus, respectively. Once the element's principal stress achieves the concrete compressive strength, any further application of load develops an increasing strain at a constant stress, as shown in Fig. 9a. The stress-strain relationship of steel reinforcement in tension and compression is idealized to be bilinear kinematic hardening (BKIN) with a post-yield strain hardening of 1% (Esp = 0.01Ese ), where Ese and Esp are the elastic and plastic modulus, respectively (Fig. 9b).
T=−
σpe E·α
(8)
where T is the temperature load applied to the anchor cable elements; σpe is the effective prestress of the anchor cables; E is the elastic modulus of the anchor cables; and α is the linear expansion coefficient of the anchor cables.
3.4.3. Load combinations of working conditions According to the construction processes and the operating
Fig. 9. Material constitutive models. 101
Tunnelling and Underground Space Technology 79 (2018) 96–109
F. Yang et al.
Table 2 Load combinations of working conditions. Working conditions
Gravity
Soil pressure
Bolt pre-tightening force
External water pressure
Anchor cable prestress
Internal water pressure
CSAC CCTC DWPC
√ √ √
√ √ √
√ √ √
√ √ √
√ √
√
segmental lining is further compressed. Compared with the CCTC, the compressive stresses of the segmental lining under the DWPC are decreased (Fig. 13a), and the maximum joint gap of the segments under the CCTC is increased (Fig. 11b and c). It is because the internal water pressures are transmitted to the segmental lining in the same way as the prestresses. Generally speaking, Model R has an obviously combined bearing capacity. A number of prestresses and internal water pressures can be transmitted to the segmental lining, which leads to obvious changes in the stresses and the joint gaps of the segmental lining. For Model M, the compressive stresses of the segmental lining except the bottom under the three working conditions are almost the same with each other (Fig. 13b), and the maximum joint gap under the three working conditions does not change significantly (Fig. 12). These indicate that Model M has a relatively separated bearing capacity. The prestresses and the internal water pressures have little effect on the stresses and deformations of the segmental lining, because the segmental lining and the secondary lining are separated by the membranes which can prevent stresses being transmitted from the secondary lining to the segmental lining. The stresses of the bottom of the segmental lining in Fig. 13b are similar to those in Fig. 13a. It is because the secondary lining and the segmental lining of Model M are bonded together at the bottom, which is the same with those of Model R, and the prestresses and the internal water pressures can be transmitted to the bottom of the segmental lining.
Fig. 10. Effective prestresses along the circumferential angle.
4. Results and discussion 4.1. Circumferential stresses of the segmental lining The segmental lining circumferential stresses of Model R and Model M under the three working conditions are presented in Figs. 11 and 12. Positive values represent tensile stresses and negative values represent compressive stresses. The segmental lining of Model R is exactly the same with that of Model M. The soil pressure and the external water pressure are both withstood only by the segmental lining under the CSAC. Therefore, the stress distribution of the segmental lining in Fig. 11a is the same with that in Fig. 12a. Because the deformation shapes of the segmental lining are squashed ovals under the three working conditions, circumferential tensions occur on the extrados surface of the springline, the intrados surface of the crown and the intrados surface of the bottom. Meanwhile, the radial joints of the segments are opening there, and the maximum joint gap of the segmental lining under the three working conditions are presented in Figs. 11 and 12. In order to further mutual contrast the stresses of the segmental lining under the three working conditions, the circumferential stresses of the nodes which are in the middle ring of the segmental lining section (Z = 5600) are analysed under the three working conditions (Fig. 13). For Model R, compared with the CSAC, the compressive stresses of the segmental lining under the CCTC are increased (Fig. 13a), and the maximum joint gap of the segments under the CCTC is decreased (Fig. 11a and b). It is because the prestresses are transmitted from the secondary lining to the segmental lining through the rebars and the
4.2. Deformation of the segmental lining and the secondary lining The deformations of Model R under the CCTC and the DWPC are shown in Fig. 14. The secondary lining shrinks inward under the CCTC because of the prestresses. Therefore, the interface gaps between the segmental lining and the secondary lining are open, and the maximum gap occurs at the top position is about 0.32 mm. The secondary lining expands outward under the DWPC because of the internal water pressures. Therefore, the gaps are smaller than those are under the CCTC and the maximum gap is only about 0.13 mm. The deformations of Model M under the CCTC and the DWPC are shown in Fig. 15. For Model M, the bottoms of the secondary lining and the segmental lining are bonded together, and the others are separated by the membranes. Therefore, the tensile stresses cannot be transmitted between the segmental lining and the secondary lining which are separated by the membranes. When the tunnel is under the CCTC, only the gaps above the springline of the lining are open, and the maximum gap occurs at the top position is about 2.21 mm. When the tunnel is
Fig. 11. Segmental lining circumferential stresses of Model R (unit: MPa): (a) CSAC; (b) CCTC; (c) DWPC. 102
Tunnelling and Underground Space Technology 79 (2018) 96–109
F. Yang et al.
Fig. 12. Segmental lining circumferential stresses of Model M (unit: MPa): (a) CSAC; (b) CCTC; (c) DWPC.
that the circumferential compression stresses under the DWPC are smaller than those under the CCTC because of the internal water pressures. However, full circular compression can also be realized except the backfilled concrete which is not influenced by the prestresses. The maximum circumferential tensile stress of the backfilled concrete exceeds 3 MPa. For Model M, the circumferential stress distributions of the secondary lining under the CCTC and the DWPC are shown in Fig. 17. Compared with Fig. 16, the stress distributions of Model M are similar to those of Model R. In practical projects, the grooves are filled with micro-expansive concrete. Therefore, full circular compression can be realized for the secondary linings of both Model R and Model M when the tunnel is under the DWPC. From the point of view of stresses, the two models are both feasible for the Yellow River Crossing Tunnel. However, the circumferential compression stresses in Fig. 17a are obviously larger than those in Fig. 16a. It indicates that the membrane can improve the effect of the prestresses, and the secondary lining of Model M gets much more compression stresses. Even when the internal water pressures are applied on the secondary lining, the circumferential compression stresses in Fig. 17b are still larger than those in Fig. 16b. Therefore, the secondary lining of Model M is more secure than that of Model R, since the prestresses of Model M can be fully utilized.
under the DWPC, the gaps are smaller than those under the CCTC, and the maximum gap is about 0.98 mm. As shown in Fig. 14, the secondary lining of the Model R is almost completely disengaged from the segmental lining. For the Model M, only the secondary lining above the springline is disengaged from the segmental lining (Fig. 15), and the radial compression springs below the springline of the lining are compressed. However, according to the forces of the springs, when the tunnel is under the CCTC and the DWPC, the compression stresses of the membranes are very small and the maximum compression stress is only about −0.08 MPa. Therefore, the stresses transmitted from the secondary lining to the segmental lining through the membranes are very small when the prestresses or the internal water pressures are applied on the secondary lining. The membrane can play a significant role in preventing stress transmission between the secondary lining and the segmental lining. 4.3. Circumferential stresses of the secondary lining For Model R, the circumferential stress distributions of the secondary lining under the CCTC and the DWPC are shown in Fig. 16. As shown in Fig. 16a, full circular compression is realized when the tunnel is under the CCTC. The circumferential stresses above the springline of the secondary lining are relatively uniform. The maximum circumferential compression stress occurs on the intrados surface of the springline. Because the thickness of the secondary lining bottom is increased by applying a platform there, the circumferential stresses of the bottom are relatively small. By comparing Fig. 16b with Fig. 16a, it can be seen
4.4. Bending moments and axial forces of the secondary lining The bending moments and the axial forces of the segmental lining
Fig. 13. Node stresses in the middle ring of the segmental lining: (a) Model R; (b) Model M. 103
Tunnelling and Underground Space Technology 79 (2018) 96–109
F. Yang et al.
Fig. 14. Lining deformation of Model R (amplification factor = 300): (a) CCTC; (b) DWPC.
stress is −7.45 MPa. Compared with the average stress of Model R, there is an evident increase of 35.21%. When the tunnel is under the DWPC, the compressive stresses of the observation points range from −7.91 to −1.33 MPa, and the average stress is −3.90 MPa. Compared with the average stress of Model R, there is an evident increase of 16.4%. Obviously, the compressive stresses of the secondary lining of Model M are larger than those of Model R, and the secondary lining of Model M is more secure than that of Model R.
for Model R and Model M are presented in Figs. 18 and 19, respectively. As shown in Fig. 18, the bending moment distributions of the two models are similar. For each working condition, the bending moments of the crown and bottom are larger than these of the springline. For each model, the bending moments under the DWPC are smaller than these under the CCTC. From Fig. 19 it can be seen that, for each working condition, the secondary lining axial compression forces of Model M are obviously larger than these of Model R, which further indicates that the secondary lining of Model M is more secure than that of Model R.
4.5.2. Circumferential stresses increment of the secondary lining When the two models are under the CCTC, the circumferential compressive stress increments of the secondary lining caused by the prestresses are obvious, especially below the springline (Figs. 20a and 21a). For Model M, the average compressive stress increment calculated is −7.43 MPa. Compared with the average compressive stress increment of Model R (−5.83 MPa), there is an evident increase of 27.4%. When the two models are under the DWPC, the circumferential tensile stress increments of the secondary lining are caused by the internal water pressures (Figs. 20b and 21b). For Model M, the average tensile stress increment calculated is 3.96 MPa. Compared with the average tensile stress increment of Model R (3.09 MPa), there is an evident increase of 28.2%. Therefore, compared with Model R, the secondary lining of Model M gets more prestresses and withstands more internal water pressures. The prestresses and the secondary lining material of Model R can be fully utilized. Several strain gauges are broken and several experimental observations have some errors comparing with the numerical results. That
4.5. Comparison between the numerical results and the experimental results 4.5.1. Results of the full-scaled experiment The circumferential stress of the secondary lining under the under the CCTC and DWPC are observed in the full-scaled experiment. The distribution of the observation points and the observation sections are shown in Figs. 3 and 4, respectively. The results of the full-scaled experiment are presented in Table 3. For Model R, when the tunnel is under the CCTC, the stresses of the observation points range from −8.10 to −2.94 MPa, and the average stress is −5.51 MPa. When the tunnel is under the DWPC, the compressive stresses of the observation points are decreased because of the internal water pressures. The stresses of the observation points range from −5.93 to −0.57 MPa, and the average stress is −3.35 MPa. For Model M, when the tunnel is under the CCTC, the stresses of the observation points range from −12.99 to −3.83 MPa, and the average
Fig. 15. Lining deformation of Model M (amplification factor = 200): (a) CCTC; (b) DWPC. 104
Tunnelling and Underground Space Technology 79 (2018) 96–109
F. Yang et al.
Fig. 16. Secondary lining circumferential stresses of Model R (unit: MPa): (a) CCTC; (b) DWPC.
factor influencing the stress transmission. Setting D as 12 mm, 14 mm, 16 mm, 18 mm and 20 mm, respectively, the circumferential stress increments of the nodes which are in the middle ring of the segmental lining section (Z = 5600) are analysed under the CCTC and the DWPC (Fig. 22). Both Fig. 22a and b show that D has a significant effect on the stress increments of the segmental lining. With D increasing constantly, the prestresses transmitted to the segmental lining tend to increase, which lead to the increase of the compressive stress increments (Fig. 22a). With D increasing constantly, the internal water pressures transmitted to the segmental lining tend to increase, which lead to the increase of the tensile stress increments (Fig. 22b). Therefore, increasing the diameter of the rebar can effectively improve the combined bearing capacity of Model R. However, when the diameter of the rebar exceeds 16 mm, the improvement tends to be negligible.
may be because the concrete vibrator or some other interference factors have affected the strain gauges during the construction of the experiment. However, the calculated stresses of most of the observation points approximate to the experimental results (Table 3), and the stress increments of the numerical results are roughly consistent with the experimental results (Figs. 20 and 21). 4.6. Stress transmission between the segmental lining and the secondary lining 4.6.1. Parameter analysis on the stress transmission of Model R For Model R, the concrete of the secondary lining is poured on the segmental lining directly. The secondary lining and the segmental lining are connected by the rebars. Theoretically, the bond stresses between the segmental lining and the secondary lining, the number of the rebars and the diameter of the rebars can all influence the stress transmission between the segmental lining and the secondary lining. Setting the bond stress as 0.1 MPa, 0.4 MPa, 0.6 MPa and 0.8 MPa, respectively, the sensitivity analysis of the bond stresses is carried out. However, all the calculation results indicate that the secondary lining except the bottom is invariably disengaged from the segmental lining because of the splitting effect. The number of the rebars is determined by the number of the hand holes, because the rebars are placed in the hand holes. Therefore, only the diameter (D) of the rebar is the key
4.6.2. Parameter analysis on the stress transmission of Model M Fig. 15 shows that the secondary lining of Model M below the springline squeezes the segmental lining when the tunnel is under the CCTC and the DWPC. Therefore, stresses can be transmitted from the secondary lining to the segmental lining through the membranes below the springline. According to Eqs. (1) and (2), the compression stiffness per unit area (K) of the membrane can directly affect the stiffnesses of the normal springs and shear springs. It means that K can influence the
Fig. 17. Secondary lining circumferential stresses of Model M (unit: MPa): (a) CCTC; (b) DWPC. 105
Tunnelling and Underground Space Technology 79 (2018) 96–109
F. Yang et al.
4.6.3. Stress transmission comparison between Model R and Model M The rebar is the assurance of the combined bearing capacity of Model R, and the stresses transmitted to the segmental lining are significantly affected by the diameter of the rebar. However, it is difficult to maintain the long-term combined bearing capacity of Model R. Because the secondary lining is almost completely disengaged from the segmental lining (Fig. 14), the rebars are exposed to the air and water, which can easily lead to corrosion. In case the rebars are corroded and fractured, Model R will lose the combined bearing capacity. Model M has a relatively separated bearing capacity because of the membrane, and the stresses transmitted to the segmental lining are little affected by the material properties or the geometric parameters of the membrane. Therefore, the load bearing mechanism of Model M is much more concise than Model R. The secondary lining of Model M can even be approximately considered to bear all the prestresses and internal water pressures individually, since the prestresses and the internal water pressures have little effect on the stresses of the segmental lining (Fig. 13b). In addition, the membrane has more beneficial effects on anti-seepage of the pressure tunnel. 5. Conclusions Fig. 18. Bending moments of the secondary lining.
The Yellow River Crossing Tunnel of the Middle Route Project of the SNWD is adopted in this study as a case, three-dimensional models of two kinds of the prestressed composite lining (Model R and Model M) are established by the finite element method. The performances of the segmental lining, the secondary lining and the stress transmission between the segmental lining and the secondary lining are studied, respectively. Some conclusions about the prestressed composite lining can be drawn as follows: (1) Model R has an obviously combined bearing capacity. Prestresses and internal water pressures can be transmitted to the segmental lining and obviously influence the stress distribution of the segmental lining. Model M has a relatively separated bearing capacity. The prestresses and the internal water pressures have little effect on the stress distribution of the segmental lining. (2) For Model M, the compressive stress increments caused by the prestresses is −7.43 MPa. Compared with Model R, there is an evident increase of 27.4%. For Model M, the average tensile stress increment caused by the internal water pressure is 3.96 MPa. Compared with Model R, there is an evident increase of 28.2%. Therefore, the prestresses and the secondary lining material of Model M can be more fully utilized than those of Model R. (3) The rebar is the key factor influencing the stress transmission of Model R. Increasing the diameter of the rebar can improve the combined bearing capacity, but the improvement tends to be negligible when the diameter of the rebar exceeds 16 mm. The membrane can play a significant role in preventing the stress transmission, and decreasing the compression stiffness of the membrane can improve the individual bearing capacity of Model M. Since the improvement is little when the compression stiffness ranges from 50 MN/m to 1000 MN/m, there is no need to concern too much about the effect of the material properties and the geometric parameters of the membrane on the design of Model M. (4) From the point of view of stresses, the two models are both feasible for the Yellow River Crossing Tunnel. However, the rebars are easily corroded, which is not conducive to the long-term combined bearing capacity of Model R. The load bearing mechanism of Model M is much more concise than that of Model R, and the secondary lining of Model M is more secure than that of Model R. In addition, the membranes of Model M can make a significant contribution to anti-seepage of the water conveyance tunnel. Therefore, Model M has more advantages over Model R in engineering applications.
Fig. 19. Axial forces of the secondary lining.
stress transmission. According to the material properties and the geometric parameters of the membranes applied in some other projects (Wang, 2000), setting K as 50 MN/m, 100 MN/m, 250 MN/m, 500 MN/ m and 1000 MN/m, respectively, the circumferential stress increments of the segmental lining can be seen in Fig. 23. Both Fig. 23a and b show that K affects the stress increments of the segmental lining only below the springline and above the end of the membrane. With K decreasing constantly, both the prestresses and the internal water pressures transmitted to the segmental lining tend to decrease. However, as shown in Fig. 23a and b, the decreases are relatively small, and the influence scopes are also relatively small (only below the springline and above the end of the membrane). Therefore, decreasing the compression stiffness of the membrane has an effect on preventing stress transmission and improving the separated bearing capacity of Model M, but the effect is little.
Finally, the Middle Route Project of the SNWD has been put into 106
Tunnelling and Underground Space Technology 79 (2018) 96–109
F. Yang et al.
Table 3 Results of the full-scaled simulation experiment (unit: MPa). Section
Position (°)
Model R
Model M
CCTC
DWPC
CCTC
DWPC
Experimental results
Numerical results
Experimental results
Numerical results
Experimental results
Numerical results
Experimental results
Numerical results
I-I
0 45 90 135 225 270 315
−2.94 −4.93 −4.63 −6.84 −6.93 −5.46 −4.47
−2.48 −3.10 −5.12 −6.49 −6.38 −4.65 −3.05
−0.57 −3.17 −4.20 −3.23 −4.22 −4.69 −1.13
−1.26 −1.41 −2.93 −3.72 −3.69 −4.15 −1.38
−8.02 −6.04 −5.53 −8.47 −12.99 −8.05 −5.11
−6.28 −6.20 −9.69 −8.78 −8.50 −8.06 −6.16
−2.23 −3.36 −3.50 −4.64 −7.91 −5.73 −1.99
−2.44 −2.19 −5.50 −4.98 −4.72 −4.13 −2.16
II-II
0 45 90 135 225 270 315
– −4.98 −5.00 – −8.10 −5.12 −4.66
−2.45 −3.11 −4.98 −6.41 −6.43 −5.71 −3.04
– −2.06 −4.59 – −4.83 −3.95 −1.46
−1.31 −1.41 −2.75 −3.68 −3.74 −3.48 −1.40
−7.25 −6.01 −5.20 – −11.12 −8.81 −5.75
−6.25 −6.16 −9.31 −8.75− −8.55 −10.68 −6.02
−1.33 −3.78 −3.10 – – – −3.72
−2.41 −2.16 −5.10 −4.98 −4.78 −6.48 −2.03
0 45 90 135 225 270 315 Average stress
– −4.31 −5.38 −7.15 −7.00 −6.99 −4.22 −5.51
−2.52 −3.07 −5.12 −6.54 −6.45 −3.72 −3.07 −4.47
– −2.51 −4.78 −3.92 −4.14 −5.93 −0.94 −3.35
−1.29 −1.44 −2.86 −3.82 −3.74 −0.74 −1.40 −2.45
– – −5.39 −10.89 −9.70 −3.83 −5.88 −7.45
−6.28 −6.35 −9.41 −8.82 −8.60 −4.11 −6.12 −7.52
– – −3.04 −7.16 −5.87 −1.69 −3.27 −3.90
−2.44 −2.34 −5.22 −5.04 −4.82 −1.29 −2.12 −3.68
III-III
Fig. 20. Secondary lining circumferential stress increments of Model R: (a) CCTC; (b) DWPC.
Fig. 21. Secondary lining circumferential stress increments of Model M: (a) CCTC; (b) DWPC.
large cross section, etc.
use, and the actual operation of the Yellow River Crossing Tunnel indicates that the prestressed composite lining with membranes has an ideal performance in long-term stable bearing, high material utilization and excellent anti-seepage capacity. This prestressed composite lining appears a very innovative and promising solution for the shield pressure tunnel with characteristics such as poor geological conditions, high internal pressure, high anti-seepage requirements, deep buried depth,
Acknowledgements This work is supported by the National Natural Science Foundation of China (No. 51079107) and the Fundamental Research Funds for the Central Universities (No. 5082022). Additionally, the provision of the 107
Tunnelling and Underground Space Technology 79 (2018) 96–109
F. Yang et al.
Fig. 22. Segmental lining circumferential stress increments of Model R: (a) CCTC; (b) DWPC.
Fig. 23. Segmental lining circumferential stress increments of Model M: (a) CCTC; (b) DWPC.
original data by Changjiang Institute of Survey, Planning, Design and Research are gratefully acknowledged.
GB50010, 2010. Code for Design of Concrete Structures (in Chinese). China Architecture and Building Press, Beijing. Grunicke, U.H., Ristić, M., 2012. Pre-stressed tunnel lining-pushing traditional concepts to new frontiers/Neue Grenzen für passiv vorgespannte Druckstollenauskleidungen. Geomech. Tunnel. 5 (5), 503–516. ITA, 2000. Guidelines for the design of shield tunnel lining (ITA WG 2 report). Tunn. Undergr. Space Technol. 15 (3), 303–331. Kang, J.F., Hu, Y.M., 2005. Techniques and performance of post-prestressed tunnel liner. Pract. Period. Struct. Des. Construct. 10 (2), 102–108. Kim, J., Yoon, J.C., Kang, B.S., 2007. Finite element analysis and modeling of structure with bolted joints. Appl. Math. Model. 31 (5), 895–911. Lee, K.M., Hou, X.Y., Ge, X.W., Tang, Y., 2001. An analytical solution for a jointed shielddriven tunnel lining. Int. J. Numer. Anal. Met. 25 (4), 365–390. Li, X.K., Zhao, S.B., Zhao, G.F., 2004. Design methods of prestressed concrete penstock. Eng. Mech. 21 (6), 124–130 (in Chinese). Mashimo, H., Ishimura, T., 2003. Evaluation of the load on shield tunnel lining in gravel. Tunn. Undergr. Space Technol. 18 (2), 233–241. Mo, H.H., Chen, J.S., 2008. Study on inner force and dislocation of segments caused by shield machine attitude. Tunn. Undergr. Space Technol. 23 (3), 281–291. Murakami, H., Koizumi, A., 1987. Behavior of shield segment ring reinforced by secondary lining. J. Jpn. Soc. Civ. Eng. 388, 85–94 (in Japanese). Nilson, A.H., 1972. Internal measurement of bond slip. ACI J. 69 (7), 439–441. Niu, X.Q., Fu, Z.Y., Zang, C.J., 2011. Full-scaled simulation model and experiment research on lining of tunnel crossing Yellow River. Yangtze River 42 (8), 77–87 (in Chinese).
References Blom, C.B.M., Van der Horst, E.J., Jovanovic, P.S., 1999. Three-dimensional structural analyses of the shield-driven “Green Heart” tunnel of the high-speed line south. Tunn. Undergr. Space Technol. 14 (2), 217–224. Chen, J.S., Mo, H.H., 2009. Numerical study on crack problems in segments of shield tunnel using finite element method. Tunn. Undergr. Space Technol. 24 (1), 91–102. Chong, X., Huang, J.Q., Ye, X.G., 2014. Numerical analysis on nonlinear behavior of the superimposed wall under quasi-static reversed cyclic loading. In: Proceedings of the Sustainable Development of Critical Infrastructure, Shanghai, 16–18 May, pp. 238–246. Collins, M.P., Mitchell, D., 1997. Prestressed Concrete Structures. Prentice Hall, Englewood Cliffs, NJ. Ding, W.Q., Yue, Z.Q., Tham, L.G., Zhu, H.H., Lee, C.F., Hashimoto, T., 2004. Analysis of shield tunnel. Int. J. Numer. Anal. Met. 28 (1), 57–91. Do, N.A., Dias, D., Oreste, P., Djeran-Maigre, I., 2013. 2D numerical investigation of segmental tunnel lining behaviour. Tunn. Undergr. Space Technol. 37, 115–127. Duan, G.X., Xu, H., 2011. Analysis on stress observation results of full-scaled lining simulation model of tunnel crossing Yellow River. Yangtze River 42 (8), 87–91 (in Chinese).
108
Tunnelling and Underground Space Technology 79 (2018) 96–109
F. Yang et al.
Wang, S., 2000. Simplified analysis of the effect of the elastic layer on turbine case in hydropower station. J. Hydraul. Eng. 3, 23–28 (in Chinese). Yan, Q.X., Yao, C.F., Yang, W.B., He, C., Geng, P., 2015. An improved numerical model of shield tunnel with double lining and its applications. Adv. Mater. Sci. Eng. Yang, Y.Z., Zhang, W.W., Wang, J.W., Yang, Z.H., 2014. Three-dimensional orthotropic equivalent modelling method of large-scale circular jointed lining. Tunn. Undergr. Space Technol. 44, 33–41. Zhang, H.M., Guo, C., Lu, G.L., 2001. Mechanical model for shield pressure tunnel with secondary linings. J. Hydraul. Eng. 4, 28–33 (in Chinese).
Popovics, S., 1973. A numerical approach to the complete stress-strain curve of concrete. Cement Concrete Res. 3 (5), 583–599. Takamatsu, N., Murakami, H., Koizumi, A., 1992. A study on the bending behaviour in the longitudinal direction of shield tunnels with secondary linings. In: Proceedings of the International Congress on 'Towards New World in Tunnellings', Acapulco, 16–22 May, pp. 227–285. Takamatsu, N., Murakami, H., Koizumi, A., 1993. Study on the analytical model on bending behaviour in longitudinal direction of shield tunnel with secondary lining. J. Jpn. Soc. Civ. Eng. 481, 97–106 (in Japanese).
109
Contents lists available at ScienceDirect
Tunnelling and Underground Space Technology journal homepage: www.elsevier.com/locate/tust
Mechanical behavior of two kinds of prestressed composite linings: A case study of the Yellow River Crossing Tunnel in China
T
⁎
Fan Yang, Sheng-rong Cao , Gan Qin State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, Wuhan 430072, China School of Water Resources and Hydropower Engineering, Wuhan University, Wuhan 430072, China
A R T I C LE I N FO
A B S T R A C T
Keywords: Shield tunnel 3D finite element method Prestressed composite lining Water conveyance Yellow River Crossing Tunnel
This paper presents the mechanical behavior of two innovative prestressed composite linings in shield tunnels for water conveyance. The Yellow River Crossing Tunnel of the Middle Route Project of the South-to-North Water Division Project (SNWD) is adopted in this study as a case. Three-dimensional finite element models are established to analyse the stress distribution and deformation feature of the prestressed composite lining when the tunnel is under the completed segment assembly condition (CSAC), the completed cable tension condition (CCTC) and the design water pressure condition (DWPC). The calculation and analysis results reveal that the prestressed composite lining with rebars (Model R) has an obviously combined bearing capacity, and the rebar is the key factor influencing the capacity. The prestressed composite lining with membranes (Model M) has a relatively separated bearing capacity, because the membrane can play a significant role in preventing stress transmission between the segmental ling and the secondary lining. Full circular compression can be realized for the secondary linings of both Model R and Model M when the tunnel is under the DWPC. However, the load bearing mechanism of Model M is more concise than that of Model R, the secondary lining of Model M is more secure than that of Model R because of the full use of prestresses and materials, and the membrane is beneficial to anti-seepage. By contrast, Model M is more suitable for the Yellow River Crossing Tunnel.
1. Introduction The prestressed composite lining is a kind of tunnel structure composed of an outer segmental primary lining and an inner prestressed secondary lining with circular anchor cables. The prestressed secondary lining can overcome the shortcoming of the small tensile strength of the concrete so that the concrete material can be fully utilized to withstand high internal pressures (Kang and Hu, 2005; Grunicke and Ristić, 2012). Therefore, this prestressed composite lining has more advantages over the ordinary double lining in load bearing capacity and anti-seepage capacity, and it is more suitable for application in shield tunnels with high internal pressures. According to the connection between the segmental lining and the prestressed lining, there are two types of the prestressed composite linings which are the prestressed composite lining with rebars (Model R) and the prestressed composite lining with membranes (Model M). The segmental lining and the prestressed lining of Model R are connected by rebars (Fig. 1a). The segmental lining and the prestressed lining of Model M are separated by membranes (Fig. 1b). At present, Model M has been applied to the Yellow River Crossing Tunnel of the South-to-North Water Division
⁎
Project (SNWD) in China for the first time, while Model R has not appeared in projects. The researches on the lining of the shield tunnel mainly focus on the monolayer segmental lining. The numerical models of the monolayer segmental lining mainly include the uniform ring model, multi-hinge ring model, beam-spring model, and shell-spring model (Lee et al., 2001; Ding et al., 2004; Do et al., 2013; Yang et al., 2014). In addition, three-dimensional finite element models are proposed to fully consider the three-dimensional effects of the segments (Blom et al., 1999). For the monolayer circular prestressed lining, it has been applied in some high pressure tunnels, such as the water conveyance tunnel of Geheyan Hydropower Station, the water conveyance tunnel of Tianshengqiao First Cascade Hydropower Station, and the desilting tunnel of Xiaolangdi Project in China. The common approach to considering the prestresses is to simplify them as a uniform radial pressure (Li et al., 2004). Since this simplified method cannot accurately simulate the nonuniform distribution of the prestresses along the circumferential direction and the spacing distribution of the anchor cables along the axial direction, it should be verified by three-dimensional finite element analysis or physical model experiments.
Corresponding author at: State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, Wuhan 430072, China. E-mail address: [email protected] (S.-r. Cao).
https://doi.org/10.1016/j.tust.2018.04.036 Received 9 November 2016; Received in revised form 21 April 2018; Accepted 29 April 2018 0886-7798/ © 2018 Elsevier Ltd. All rights reserved.
Tunnelling and Underground Space Technology 79 (2018) 96–109
F. Yang et al.
Fig. 1. Sketch of the prestressed composite lining: (a) Model R; (b) Model M.
simulate the two kinds of the prestressed composite linings (Model R and Model M). The performance of each component of the prestressed composite lining and the interaction between the segmental lining and the secondary lining are analysed when the tunnel is under three working conditions. The first working condition is the completed segment assembly condition (CSAC) that the segmental lining is assembled and reaches stable states. The second working condition is the completed cable tension condition (CCTC) that the secondary lining concrete is poured and the prestressed anchor cable tension is completed. The third working condition is the design water pressure condition (DWPC) that the grooves are backfilled with concrete and the lining withstands the design water pressure. According to the analyses of the numerical calculations and the experimental results, the mechanical behavior of the two prestressed composite linings is presented and compared.
The researches on the composite lining mainly focus on the ordinary double lining for shield tunnels. In the case of the double shell structure, the methods for computing the member forces of the secondary lining are generally divided into the bedded frame model method and the elastic equation method (ITA, 2000). A number of numerical calculations of the composite lining are based on the bedded frame model method. At present, the reported numerical models of the composite lining are mainly based on which the segmental lining is simulated by the two-dimensional beam-spring model or the three-dimensional shellspring model, and the interaction between the segmental lining and the secondary lining is mainly simulated by springs, beams or contact (Murakami and Koizumi, 1987; Takamatsu et al., 1992, 1993; Zhang et al., 2001; Yan et al., 2015). This ordinary composite lining is mainly applied to railway tunnels and highway tunnels, and some research results reveal that reinforcing the coupling between the segmental lining and the secondary lining can improve the bearing capacity of the ordinary composite lining (Takamatsu et al., 1992, 1993; Zhang et al., 2001). However, for the prestressed composite lining, it is a combination of the segmental lining and the prestressed lining, and it is mainly applied to shield pressure tunnels. The distribution of the prestresses along the prestressed anchor cable length direction is not uniform, and the anchor cables are equidistantly distributed along the axial direction. In addition to the external load, both the prestress and the internal pressure are borne by the prestressed composite lining. Moreover, whether the segmental lining and the prestressed lining are separated by membranes or connected by rebars, both the membranes and the rebars have a significant impact on the stress transmission between the segmental lining and the secondary lining. Therefore, the structure form, load condition and stress transmission of the prestressed composite lining are all much more complex than the ordinary double lining. The numerical models and the research results of the ordinary double lining are not applicable to the prestressed composite lining directly. The prestressed composite lining is an innovative and significant structure for the shield tunnel. This innovative technique is a desirable solution for the Yellow River Crossing Tunnel with characteristics such as poor geological conditions, high internal pressure, high anti-seepage requirements, deep buried depth, large cross section, etc. However, as it is applied for the first time in the world, there are few documented experimental, numerical or analytical results in the literature concerning this new type of the lining, and the mechanical behavior of the lining is still not clarified. Therefore, we investigate the mechanical behavior of the prestressed composite lining in a comprehensive way so that it could provide some references for the application of this typical lining in some other similar projects. In this work, the Yellow River Crossing Tunnel is adopted as a case, and detailed three-dimensional finite element models are established to
2. Case studied tunnel The SNWD is the one of the most expensive project in China. This project consists of the Eastern Route Project, the Middle Route Project and the Western Route Project. For the Middle Route Project, it has been completed since December 12, 2014. Several generations of technical personnel have carried out a large amount of survey, planning, design and research work since the 1950s. The Yellow River Crossing Project is a key project of the Middle Route Project of the SNWD, which is widely known as the most ambitious water conservancy project that crosses great rivers in the history of mankind. The Yellow River Crossing Tunnel is the largest individual project with the longest construction period, the most advanced technology and the most difficult construction in the SNWD. The total length of the Yellow River Crossing Tunnel is 3450 m, the excavation diameter is 8.7 m, and the design flow rate is 265 m3/s. The longitudinal profile of the Yellow River Crossing Project is shown in Fig. 2. The Yellow River Crossing Tunnel passes through soft soil and is constructed by the shield tunnelling method. In order to avoid large deformations of the excavation face, the precast segments are assembled timely to withstand the soil pressure and the external water pressure during the excavation. The internal water pressure in the centre of the tunnel is 0.51 MPa when the tunnel is under the DWPC. It is very important to prevent the high-pressure water from leaking out and to avoid seepage failure of the soil around the tunnel. If the internal water pressure is withstood only by the segmental lining, the segmental joints will be open sharply, resulting in water seepage. Therefore, a secondary lining is needed to improve the bearing capacity of the tunnel lining and to simultaneously improve the tunnel internal surface smoothing. As the prestressed concrete lining with circular anchor cables has advantages with respect to load bearing strengthening, high 97
Tunnelling and Underground Space Technology 79 (2018) 96–109
F. Yang et al.
Fig. 2. Longitudinal profile of the Yellow River Crossing Project (unit: m).
are listed in Table 1.
material utilization and anti-seepage strengthening, it is proposed as the secondary lining. During the preliminary design phase of the Yellow River Crossing Tunnel lining, two schemes (Model R and Model M) have been proposed. For Model R, the external load is expected to be withstood by the segmental lining, and the internal water pressure is expected to be withstood by the segmental lining and the secondary lining jointly. For Model M, the external load is expected to be withstood by the segmental lining, and the internal water pressure is expected to be withstood by the secondary lining individually.
3.3. Full-scaled experiment An outdoor full-scaled experiment is carried out, and the test site is located in the Mount Mangshan near the southern bank of the Yellow River (Niu et al., 2011; Duan et al., 2011). As shown in Fig. 6, the fullscaled experimental model consists of the lining models (Model R and Model M), plugs and shaft. The plugs can guarantee the seal of the experimental models. The water pump is placed in the shaft which is also used for transportation. The surface elevation of the test site is 172.8 m. The lining models are buried underground, and the elevation of the model centre is 155.9 m. The soil condition and the water pressure of the experiment are as the same as those of the real project. The external soil condition is simulated by backfilling sand to the elevation of 190.9 m when the construction of the experimental model is complete. The external water pressure is carried out by pouring water in the sand wrapped by the geomembrane, and the internal water pressure is carried out by elevating the water tank. Section I ∼ Section III of Model R and Section I' ∼ Section III' of Model M are observed in the experiment, respectively (Fig. 4). Fig. 3 presents the observation points of the observation section, and the numbers in the parentheses represent the dimensions of the observation section.
3. Full-scaled experiment and numerical simulation 3.1. Lining dimensions As shown in Figs. 3 and 4, the dimensions of Model R are the same as those of Model M, and each model has an axial length of 9.6 m. Segment external diameter is 8.7 m; internal diameter is 7.9 m; width is 1.6 m. The segmental lining is erected by staggered format (Fig. 1). The segments are connected by M32 straight bolts. Pre-tightening force of each bolt is 100 kN. For Model R, the concrete of the secondary lining is poured on the internal surface of the segmental lining directly, and the secondary lining and the segmental lining are connected by the rebars which are shown as blue1 lines in Fig. 3(a). The rebars are placed in the hand holes. The diameter of the rebar is 16 mm. For Model M, only the bottoms of the segmental lining and the secondary lining are bonded together, and the others are separated by the membranes which are shown as a red line in Fig. 3(b). The membranes have a total thickness of 6 × 10−3 m and annularly enclose a circumferential angle of 301.548°. The membranes compose of three layers of materials; the middle layer is a polyethylene membrane, and the others are geomembranes. The secondary lining external diameter is 7.9 m; internal diameter is 7.0 m. The secondary lining concrete is poured when the segmental lining has already withstood the external pressure and achieved stability. The prestressed anchor cable tension begins when the secondary lining concrete pour is completed and the concrete strength exceeds 75 percent of the design strength. As shown in Figs. 3 and 4, the preformed grooves are in the lower half of the secondary lining and the centre lines of the grooves are located at the angles of 96°, 134°, 226° and 264°. The distance between adjacent grooves is 0.45 m along the axial direction. Small relaxation steel wire strands of 12φj15.24, which have a design tension stress of 1395 MPa, are used as the prestressed anchor cables.
3.4. Three-dimensional finite element simulation 3.4.1. Element types Three-dimensional models of Model R and Model M are established using the 3D finite element analysis software ANSYS. The finite element models are shown in Fig. 7. Eight-node three-dimensional solid elements (SOLID45) are used for the soil, and eight-node three-dimensional solid elements (SOLID65) are used for the concrete. Two-node link elements (LINK8) are used for the prestressed anchor cables. Twonode beam elements (BEAM188) are used for the radial bolts, the circumferential bolts and the rebars. Constraint equations (CEINTF) are adopted to constrain the anchor cables with the secondary lining concrete and constrain the blot with the segmental lining concrete (Chong et al., 2014). Two-node nonlinear elastic spring elements (COMBIN39) are adopted to simulate the interaction between the rebar and the concrete. The rebar element and the concrete element are connected by COMBIN39, and its spring rigidity F-D relationship can be converted by Nilson bond stress-slip relationship (Nilson, 1972) which is given by
τ = 9.78 × 102s−5.72 × 10 4s 2 + 8.35 × 105s 3 3.2. Material properties
(1)
where τ is the bond stress (N/mm2), and s is the corresponding slip value (mm). As shown in Figs. 7 and 8, the contact surface between the segmental lining and the soil and the contact surface between the adjacent segments are simulated by the contact elements (TARGE170 and CONTA174). These “face-to-face” elements can simulate cold interface conditions transmitting only compression in the direction normal to the surfaces and shear in the tangential direction (Kim et al., 2007; Mo and
The soil above the Yellow River Crossing Tunnel is the medium granular sand, and the clay is below the tunnel. Fig. 5 presents the material properties for the soil. The material properties for the lining 1 For interpretation of color in Fig. 3, the reader is referred to the web version of this article.
98
Tunnelling and Underground Space Technology 79 (2018) 96–109
F. Yang et al.
Fig. 3. Cross section of the prestressed composite lining (unit: m): (a) Model R; (b) Model M.
Fig. 4. Groove layout along the axial direction (unit: m). Table 1 Material properties for lining. Type
Material
Young’s modulus (kN/ m2)
Poisson's ratio
Unit weight (kN/m3)
Segmental lining Secondary lining M32 Bolt Rebar Anchor cable Membrane
C50 concrete
3.45 × 107
0.167
25.5
C40 concrete
3.25 × 107
0.167
24.5
0.3 0.3 0.3 0.3
78.5 78.5 78.5 –
Steel Steel Steel Composite materials
8
2.1 × 10 2.1 × 108 1.95 × 108 1.5 × 103
Chen, 2008). A friction coefficient of 0.3 is used to simulate the tangential behavior (Chen and Mo, 2009) and the Lagrange and penalty method is used as the contact algorithm. For the finite element models of Model R and Model M, the bottoms of the segmental lining and the secondary lining are considered to be bonded completely and the relative slip is prohibited. As shown in Fig. 8, the rebar of Model R is simulated by beam elements, and the membrane of Model M is simulated by three springs: one normal spring and two shear springs. The normal spring behaves as a compression
Fig. 5. Material properties for soil.
99
Tunnelling and Underground Space Technology 79 (2018) 96–109
F. Yang et al.
Fig. 6. Profile section of the full-scaled experiment (unit: m).
Fig. 7. Finite element models: (a) soil; (b) secondary lining; (c) segments and bolts.
the tangential stiffness of a single shear spring; E is the Young’s modulus of the membrane; G is the shear modulus of the membrane; A is the corresponding area of a single spring; and t is the thickness of the membrane.
support and does not contribute to tension. The stiffnesses of the springs are calculated as follows:
kr =
E×A t
(2)
kτ =
G×A t
(3)
3.4.2. Material models The elastic-plastic constitutive model based on Drucker-Prager yield criterion is used for the soil. The yield function of the Drucker-Prager
where kr is the compression stiffness of a single normal spring; kτ is 100
Tunnelling and Underground Space Technology 79 (2018) 96–109
F. Yang et al.
Fig. 8. Interaction between segmental lining and secondary lining: (a) Model R; (b) Model M.
conditions of the Yellow River Crossing Tunnel, the calculation process is divided into three stages which are consistent with the three working conditions (CSAC, CCTC and DWPC). The load combinations of each working condition are shown in Table 2. The external water pressure in the horizontal line of the tunnel centre is 0.323 MPa. The internal water pressure in the tunnel centre is 0.51 MPa when the tunnel is under the DWPC. Separate calculations of water pressures and earth pressures can be used when the tunnel is covered by sandy soil (Mashimo and Ishimura, 2003). The external water pressures are directly applied on the segmental lining and the effective unit weight of the soil is used. Prestress loss of the anchor cables is inevitable because of the deformation of anchorages and the shrinkage of steel strands, the friction between the steel strand and the duct, the relaxation of the steel strand stresses and the shrinkage and creep of the concrete. The effective prestress of the anchor cables is equal to the design tension stress minus all of the prestress loss (GB50010, 2010; Collins and Mitchell, 1997). The effective prestresses along the circumferential angle (cumulative angle between the tensioning position and the calculation position) are shown in Fig. 10. The prestress is converted to the temperature load and applied to the anchor cable element in the model. The temperature load can be calculated by
model is defined as
αI1 +
J2 −k = 0
(4)
where I1 is the first stress invariant; J2 is the second deviatoric stress invariant; α and k are constants which depend on cohesion (c) and angle of internal friction (φ) of the material given by
α=
2 sin φ 3 (3−sin φ)
(5)
k=
6c cos φ 3 (3−sin φ)
(6)
For the concrete, the multi-linear isotropic hardening (MISO) stressstrain relationship is obtained using the model proposed by Popovics (1973) as given by
fc =
f ′c ·x·p p−1 + x p
(7)
where fc is the compressive stress at any strain εc ; εc′is the strain corresponding to the ultimate compressive strength ( fc′) of unconfined concrete; x is the ratio (εc /εc′); p is the ratio [Ec /(Ec−Esec )]; Ec and Esec are the tangential and secant modulus, respectively. Once the element's principal stress achieves the concrete compressive strength, any further application of load develops an increasing strain at a constant stress, as shown in Fig. 9a. The stress-strain relationship of steel reinforcement in tension and compression is idealized to be bilinear kinematic hardening (BKIN) with a post-yield strain hardening of 1% (Esp = 0.01Ese ), where Ese and Esp are the elastic and plastic modulus, respectively (Fig. 9b).
T=−
σpe E·α
(8)
where T is the temperature load applied to the anchor cable elements; σpe is the effective prestress of the anchor cables; E is the elastic modulus of the anchor cables; and α is the linear expansion coefficient of the anchor cables.
3.4.3. Load combinations of working conditions According to the construction processes and the operating
Fig. 9. Material constitutive models. 101
Tunnelling and Underground Space Technology 79 (2018) 96–109
F. Yang et al.
Table 2 Load combinations of working conditions. Working conditions
Gravity
Soil pressure
Bolt pre-tightening force
External water pressure
Anchor cable prestress
Internal water pressure
CSAC CCTC DWPC
√ √ √
√ √ √
√ √ √
√ √ √
√ √
√
segmental lining is further compressed. Compared with the CCTC, the compressive stresses of the segmental lining under the DWPC are decreased (Fig. 13a), and the maximum joint gap of the segments under the CCTC is increased (Fig. 11b and c). It is because the internal water pressures are transmitted to the segmental lining in the same way as the prestresses. Generally speaking, Model R has an obviously combined bearing capacity. A number of prestresses and internal water pressures can be transmitted to the segmental lining, which leads to obvious changes in the stresses and the joint gaps of the segmental lining. For Model M, the compressive stresses of the segmental lining except the bottom under the three working conditions are almost the same with each other (Fig. 13b), and the maximum joint gap under the three working conditions does not change significantly (Fig. 12). These indicate that Model M has a relatively separated bearing capacity. The prestresses and the internal water pressures have little effect on the stresses and deformations of the segmental lining, because the segmental lining and the secondary lining are separated by the membranes which can prevent stresses being transmitted from the secondary lining to the segmental lining. The stresses of the bottom of the segmental lining in Fig. 13b are similar to those in Fig. 13a. It is because the secondary lining and the segmental lining of Model M are bonded together at the bottom, which is the same with those of Model R, and the prestresses and the internal water pressures can be transmitted to the bottom of the segmental lining.
Fig. 10. Effective prestresses along the circumferential angle.
4. Results and discussion 4.1. Circumferential stresses of the segmental lining The segmental lining circumferential stresses of Model R and Model M under the three working conditions are presented in Figs. 11 and 12. Positive values represent tensile stresses and negative values represent compressive stresses. The segmental lining of Model R is exactly the same with that of Model M. The soil pressure and the external water pressure are both withstood only by the segmental lining under the CSAC. Therefore, the stress distribution of the segmental lining in Fig. 11a is the same with that in Fig. 12a. Because the deformation shapes of the segmental lining are squashed ovals under the three working conditions, circumferential tensions occur on the extrados surface of the springline, the intrados surface of the crown and the intrados surface of the bottom. Meanwhile, the radial joints of the segments are opening there, and the maximum joint gap of the segmental lining under the three working conditions are presented in Figs. 11 and 12. In order to further mutual contrast the stresses of the segmental lining under the three working conditions, the circumferential stresses of the nodes which are in the middle ring of the segmental lining section (Z = 5600) are analysed under the three working conditions (Fig. 13). For Model R, compared with the CSAC, the compressive stresses of the segmental lining under the CCTC are increased (Fig. 13a), and the maximum joint gap of the segments under the CCTC is decreased (Fig. 11a and b). It is because the prestresses are transmitted from the secondary lining to the segmental lining through the rebars and the
4.2. Deformation of the segmental lining and the secondary lining The deformations of Model R under the CCTC and the DWPC are shown in Fig. 14. The secondary lining shrinks inward under the CCTC because of the prestresses. Therefore, the interface gaps between the segmental lining and the secondary lining are open, and the maximum gap occurs at the top position is about 0.32 mm. The secondary lining expands outward under the DWPC because of the internal water pressures. Therefore, the gaps are smaller than those are under the CCTC and the maximum gap is only about 0.13 mm. The deformations of Model M under the CCTC and the DWPC are shown in Fig. 15. For Model M, the bottoms of the secondary lining and the segmental lining are bonded together, and the others are separated by the membranes. Therefore, the tensile stresses cannot be transmitted between the segmental lining and the secondary lining which are separated by the membranes. When the tunnel is under the CCTC, only the gaps above the springline of the lining are open, and the maximum gap occurs at the top position is about 2.21 mm. When the tunnel is
Fig. 11. Segmental lining circumferential stresses of Model R (unit: MPa): (a) CSAC; (b) CCTC; (c) DWPC. 102
Tunnelling and Underground Space Technology 79 (2018) 96–109
F. Yang et al.
Fig. 12. Segmental lining circumferential stresses of Model M (unit: MPa): (a) CSAC; (b) CCTC; (c) DWPC.
that the circumferential compression stresses under the DWPC are smaller than those under the CCTC because of the internal water pressures. However, full circular compression can also be realized except the backfilled concrete which is not influenced by the prestresses. The maximum circumferential tensile stress of the backfilled concrete exceeds 3 MPa. For Model M, the circumferential stress distributions of the secondary lining under the CCTC and the DWPC are shown in Fig. 17. Compared with Fig. 16, the stress distributions of Model M are similar to those of Model R. In practical projects, the grooves are filled with micro-expansive concrete. Therefore, full circular compression can be realized for the secondary linings of both Model R and Model M when the tunnel is under the DWPC. From the point of view of stresses, the two models are both feasible for the Yellow River Crossing Tunnel. However, the circumferential compression stresses in Fig. 17a are obviously larger than those in Fig. 16a. It indicates that the membrane can improve the effect of the prestresses, and the secondary lining of Model M gets much more compression stresses. Even when the internal water pressures are applied on the secondary lining, the circumferential compression stresses in Fig. 17b are still larger than those in Fig. 16b. Therefore, the secondary lining of Model M is more secure than that of Model R, since the prestresses of Model M can be fully utilized.
under the DWPC, the gaps are smaller than those under the CCTC, and the maximum gap is about 0.98 mm. As shown in Fig. 14, the secondary lining of the Model R is almost completely disengaged from the segmental lining. For the Model M, only the secondary lining above the springline is disengaged from the segmental lining (Fig. 15), and the radial compression springs below the springline of the lining are compressed. However, according to the forces of the springs, when the tunnel is under the CCTC and the DWPC, the compression stresses of the membranes are very small and the maximum compression stress is only about −0.08 MPa. Therefore, the stresses transmitted from the secondary lining to the segmental lining through the membranes are very small when the prestresses or the internal water pressures are applied on the secondary lining. The membrane can play a significant role in preventing stress transmission between the secondary lining and the segmental lining. 4.3. Circumferential stresses of the secondary lining For Model R, the circumferential stress distributions of the secondary lining under the CCTC and the DWPC are shown in Fig. 16. As shown in Fig. 16a, full circular compression is realized when the tunnel is under the CCTC. The circumferential stresses above the springline of the secondary lining are relatively uniform. The maximum circumferential compression stress occurs on the intrados surface of the springline. Because the thickness of the secondary lining bottom is increased by applying a platform there, the circumferential stresses of the bottom are relatively small. By comparing Fig. 16b with Fig. 16a, it can be seen
4.4. Bending moments and axial forces of the secondary lining The bending moments and the axial forces of the segmental lining
Fig. 13. Node stresses in the middle ring of the segmental lining: (a) Model R; (b) Model M. 103
Tunnelling and Underground Space Technology 79 (2018) 96–109
F. Yang et al.
Fig. 14. Lining deformation of Model R (amplification factor = 300): (a) CCTC; (b) DWPC.
stress is −7.45 MPa. Compared with the average stress of Model R, there is an evident increase of 35.21%. When the tunnel is under the DWPC, the compressive stresses of the observation points range from −7.91 to −1.33 MPa, and the average stress is −3.90 MPa. Compared with the average stress of Model R, there is an evident increase of 16.4%. Obviously, the compressive stresses of the secondary lining of Model M are larger than those of Model R, and the secondary lining of Model M is more secure than that of Model R.
for Model R and Model M are presented in Figs. 18 and 19, respectively. As shown in Fig. 18, the bending moment distributions of the two models are similar. For each working condition, the bending moments of the crown and bottom are larger than these of the springline. For each model, the bending moments under the DWPC are smaller than these under the CCTC. From Fig. 19 it can be seen that, for each working condition, the secondary lining axial compression forces of Model M are obviously larger than these of Model R, which further indicates that the secondary lining of Model M is more secure than that of Model R.
4.5.2. Circumferential stresses increment of the secondary lining When the two models are under the CCTC, the circumferential compressive stress increments of the secondary lining caused by the prestresses are obvious, especially below the springline (Figs. 20a and 21a). For Model M, the average compressive stress increment calculated is −7.43 MPa. Compared with the average compressive stress increment of Model R (−5.83 MPa), there is an evident increase of 27.4%. When the two models are under the DWPC, the circumferential tensile stress increments of the secondary lining are caused by the internal water pressures (Figs. 20b and 21b). For Model M, the average tensile stress increment calculated is 3.96 MPa. Compared with the average tensile stress increment of Model R (3.09 MPa), there is an evident increase of 28.2%. Therefore, compared with Model R, the secondary lining of Model M gets more prestresses and withstands more internal water pressures. The prestresses and the secondary lining material of Model R can be fully utilized. Several strain gauges are broken and several experimental observations have some errors comparing with the numerical results. That
4.5. Comparison between the numerical results and the experimental results 4.5.1. Results of the full-scaled experiment The circumferential stress of the secondary lining under the under the CCTC and DWPC are observed in the full-scaled experiment. The distribution of the observation points and the observation sections are shown in Figs. 3 and 4, respectively. The results of the full-scaled experiment are presented in Table 3. For Model R, when the tunnel is under the CCTC, the stresses of the observation points range from −8.10 to −2.94 MPa, and the average stress is −5.51 MPa. When the tunnel is under the DWPC, the compressive stresses of the observation points are decreased because of the internal water pressures. The stresses of the observation points range from −5.93 to −0.57 MPa, and the average stress is −3.35 MPa. For Model M, when the tunnel is under the CCTC, the stresses of the observation points range from −12.99 to −3.83 MPa, and the average
Fig. 15. Lining deformation of Model M (amplification factor = 200): (a) CCTC; (b) DWPC. 104
Tunnelling and Underground Space Technology 79 (2018) 96–109
F. Yang et al.
Fig. 16. Secondary lining circumferential stresses of Model R (unit: MPa): (a) CCTC; (b) DWPC.
factor influencing the stress transmission. Setting D as 12 mm, 14 mm, 16 mm, 18 mm and 20 mm, respectively, the circumferential stress increments of the nodes which are in the middle ring of the segmental lining section (Z = 5600) are analysed under the CCTC and the DWPC (Fig. 22). Both Fig. 22a and b show that D has a significant effect on the stress increments of the segmental lining. With D increasing constantly, the prestresses transmitted to the segmental lining tend to increase, which lead to the increase of the compressive stress increments (Fig. 22a). With D increasing constantly, the internal water pressures transmitted to the segmental lining tend to increase, which lead to the increase of the tensile stress increments (Fig. 22b). Therefore, increasing the diameter of the rebar can effectively improve the combined bearing capacity of Model R. However, when the diameter of the rebar exceeds 16 mm, the improvement tends to be negligible.
may be because the concrete vibrator or some other interference factors have affected the strain gauges during the construction of the experiment. However, the calculated stresses of most of the observation points approximate to the experimental results (Table 3), and the stress increments of the numerical results are roughly consistent with the experimental results (Figs. 20 and 21). 4.6. Stress transmission between the segmental lining and the secondary lining 4.6.1. Parameter analysis on the stress transmission of Model R For Model R, the concrete of the secondary lining is poured on the segmental lining directly. The secondary lining and the segmental lining are connected by the rebars. Theoretically, the bond stresses between the segmental lining and the secondary lining, the number of the rebars and the diameter of the rebars can all influence the stress transmission between the segmental lining and the secondary lining. Setting the bond stress as 0.1 MPa, 0.4 MPa, 0.6 MPa and 0.8 MPa, respectively, the sensitivity analysis of the bond stresses is carried out. However, all the calculation results indicate that the secondary lining except the bottom is invariably disengaged from the segmental lining because of the splitting effect. The number of the rebars is determined by the number of the hand holes, because the rebars are placed in the hand holes. Therefore, only the diameter (D) of the rebar is the key
4.6.2. Parameter analysis on the stress transmission of Model M Fig. 15 shows that the secondary lining of Model M below the springline squeezes the segmental lining when the tunnel is under the CCTC and the DWPC. Therefore, stresses can be transmitted from the secondary lining to the segmental lining through the membranes below the springline. According to Eqs. (1) and (2), the compression stiffness per unit area (K) of the membrane can directly affect the stiffnesses of the normal springs and shear springs. It means that K can influence the
Fig. 17. Secondary lining circumferential stresses of Model M (unit: MPa): (a) CCTC; (b) DWPC. 105
Tunnelling and Underground Space Technology 79 (2018) 96–109
F. Yang et al.
4.6.3. Stress transmission comparison between Model R and Model M The rebar is the assurance of the combined bearing capacity of Model R, and the stresses transmitted to the segmental lining are significantly affected by the diameter of the rebar. However, it is difficult to maintain the long-term combined bearing capacity of Model R. Because the secondary lining is almost completely disengaged from the segmental lining (Fig. 14), the rebars are exposed to the air and water, which can easily lead to corrosion. In case the rebars are corroded and fractured, Model R will lose the combined bearing capacity. Model M has a relatively separated bearing capacity because of the membrane, and the stresses transmitted to the segmental lining are little affected by the material properties or the geometric parameters of the membrane. Therefore, the load bearing mechanism of Model M is much more concise than Model R. The secondary lining of Model M can even be approximately considered to bear all the prestresses and internal water pressures individually, since the prestresses and the internal water pressures have little effect on the stresses of the segmental lining (Fig. 13b). In addition, the membrane has more beneficial effects on anti-seepage of the pressure tunnel. 5. Conclusions Fig. 18. Bending moments of the secondary lining.
The Yellow River Crossing Tunnel of the Middle Route Project of the SNWD is adopted in this study as a case, three-dimensional models of two kinds of the prestressed composite lining (Model R and Model M) are established by the finite element method. The performances of the segmental lining, the secondary lining and the stress transmission between the segmental lining and the secondary lining are studied, respectively. Some conclusions about the prestressed composite lining can be drawn as follows: (1) Model R has an obviously combined bearing capacity. Prestresses and internal water pressures can be transmitted to the segmental lining and obviously influence the stress distribution of the segmental lining. Model M has a relatively separated bearing capacity. The prestresses and the internal water pressures have little effect on the stress distribution of the segmental lining. (2) For Model M, the compressive stress increments caused by the prestresses is −7.43 MPa. Compared with Model R, there is an evident increase of 27.4%. For Model M, the average tensile stress increment caused by the internal water pressure is 3.96 MPa. Compared with Model R, there is an evident increase of 28.2%. Therefore, the prestresses and the secondary lining material of Model M can be more fully utilized than those of Model R. (3) The rebar is the key factor influencing the stress transmission of Model R. Increasing the diameter of the rebar can improve the combined bearing capacity, but the improvement tends to be negligible when the diameter of the rebar exceeds 16 mm. The membrane can play a significant role in preventing the stress transmission, and decreasing the compression stiffness of the membrane can improve the individual bearing capacity of Model M. Since the improvement is little when the compression stiffness ranges from 50 MN/m to 1000 MN/m, there is no need to concern too much about the effect of the material properties and the geometric parameters of the membrane on the design of Model M. (4) From the point of view of stresses, the two models are both feasible for the Yellow River Crossing Tunnel. However, the rebars are easily corroded, which is not conducive to the long-term combined bearing capacity of Model R. The load bearing mechanism of Model M is much more concise than that of Model R, and the secondary lining of Model M is more secure than that of Model R. In addition, the membranes of Model M can make a significant contribution to anti-seepage of the water conveyance tunnel. Therefore, Model M has more advantages over Model R in engineering applications.
Fig. 19. Axial forces of the secondary lining.
stress transmission. According to the material properties and the geometric parameters of the membranes applied in some other projects (Wang, 2000), setting K as 50 MN/m, 100 MN/m, 250 MN/m, 500 MN/ m and 1000 MN/m, respectively, the circumferential stress increments of the segmental lining can be seen in Fig. 23. Both Fig. 23a and b show that K affects the stress increments of the segmental lining only below the springline and above the end of the membrane. With K decreasing constantly, both the prestresses and the internal water pressures transmitted to the segmental lining tend to decrease. However, as shown in Fig. 23a and b, the decreases are relatively small, and the influence scopes are also relatively small (only below the springline and above the end of the membrane). Therefore, decreasing the compression stiffness of the membrane has an effect on preventing stress transmission and improving the separated bearing capacity of Model M, but the effect is little.
Finally, the Middle Route Project of the SNWD has been put into 106
Tunnelling and Underground Space Technology 79 (2018) 96–109
F. Yang et al.
Table 3 Results of the full-scaled simulation experiment (unit: MPa). Section
Position (°)
Model R
Model M
CCTC
DWPC
CCTC
DWPC
Experimental results
Numerical results
Experimental results
Numerical results
Experimental results
Numerical results
Experimental results
Numerical results
I-I
0 45 90 135 225 270 315
−2.94 −4.93 −4.63 −6.84 −6.93 −5.46 −4.47
−2.48 −3.10 −5.12 −6.49 −6.38 −4.65 −3.05
−0.57 −3.17 −4.20 −3.23 −4.22 −4.69 −1.13
−1.26 −1.41 −2.93 −3.72 −3.69 −4.15 −1.38
−8.02 −6.04 −5.53 −8.47 −12.99 −8.05 −5.11
−6.28 −6.20 −9.69 −8.78 −8.50 −8.06 −6.16
−2.23 −3.36 −3.50 −4.64 −7.91 −5.73 −1.99
−2.44 −2.19 −5.50 −4.98 −4.72 −4.13 −2.16
II-II
0 45 90 135 225 270 315
– −4.98 −5.00 – −8.10 −5.12 −4.66
−2.45 −3.11 −4.98 −6.41 −6.43 −5.71 −3.04
– −2.06 −4.59 – −4.83 −3.95 −1.46
−1.31 −1.41 −2.75 −3.68 −3.74 −3.48 −1.40
−7.25 −6.01 −5.20 – −11.12 −8.81 −5.75
−6.25 −6.16 −9.31 −8.75− −8.55 −10.68 −6.02
−1.33 −3.78 −3.10 – – – −3.72
−2.41 −2.16 −5.10 −4.98 −4.78 −6.48 −2.03
0 45 90 135 225 270 315 Average stress
– −4.31 −5.38 −7.15 −7.00 −6.99 −4.22 −5.51
−2.52 −3.07 −5.12 −6.54 −6.45 −3.72 −3.07 −4.47
– −2.51 −4.78 −3.92 −4.14 −5.93 −0.94 −3.35
−1.29 −1.44 −2.86 −3.82 −3.74 −0.74 −1.40 −2.45
– – −5.39 −10.89 −9.70 −3.83 −5.88 −7.45
−6.28 −6.35 −9.41 −8.82 −8.60 −4.11 −6.12 −7.52
– – −3.04 −7.16 −5.87 −1.69 −3.27 −3.90
−2.44 −2.34 −5.22 −5.04 −4.82 −1.29 −2.12 −3.68
III-III
Fig. 20. Secondary lining circumferential stress increments of Model R: (a) CCTC; (b) DWPC.
Fig. 21. Secondary lining circumferential stress increments of Model M: (a) CCTC; (b) DWPC.
large cross section, etc.
use, and the actual operation of the Yellow River Crossing Tunnel indicates that the prestressed composite lining with membranes has an ideal performance in long-term stable bearing, high material utilization and excellent anti-seepage capacity. This prestressed composite lining appears a very innovative and promising solution for the shield pressure tunnel with characteristics such as poor geological conditions, high internal pressure, high anti-seepage requirements, deep buried depth,
Acknowledgements This work is supported by the National Natural Science Foundation of China (No. 51079107) and the Fundamental Research Funds for the Central Universities (No. 5082022). Additionally, the provision of the 107
Tunnelling and Underground Space Technology 79 (2018) 96–109
F. Yang et al.
Fig. 22. Segmental lining circumferential stress increments of Model R: (a) CCTC; (b) DWPC.
Fig. 23. Segmental lining circumferential stress increments of Model M: (a) CCTC; (b) DWPC.
original data by Changjiang Institute of Survey, Planning, Design and Research are gratefully acknowledged.
GB50010, 2010. Code for Design of Concrete Structures (in Chinese). China Architecture and Building Press, Beijing. Grunicke, U.H., Ristić, M., 2012. Pre-stressed tunnel lining-pushing traditional concepts to new frontiers/Neue Grenzen für passiv vorgespannte Druckstollenauskleidungen. Geomech. Tunnel. 5 (5), 503–516. ITA, 2000. Guidelines for the design of shield tunnel lining (ITA WG 2 report). Tunn. Undergr. Space Technol. 15 (3), 303–331. Kang, J.F., Hu, Y.M., 2005. Techniques and performance of post-prestressed tunnel liner. Pract. Period. Struct. Des. Construct. 10 (2), 102–108. Kim, J., Yoon, J.C., Kang, B.S., 2007. Finite element analysis and modeling of structure with bolted joints. Appl. Math. Model. 31 (5), 895–911. Lee, K.M., Hou, X.Y., Ge, X.W., Tang, Y., 2001. An analytical solution for a jointed shielddriven tunnel lining. Int. J. Numer. Anal. Met. 25 (4), 365–390. Li, X.K., Zhao, S.B., Zhao, G.F., 2004. Design methods of prestressed concrete penstock. Eng. Mech. 21 (6), 124–130 (in Chinese). Mashimo, H., Ishimura, T., 2003. Evaluation of the load on shield tunnel lining in gravel. Tunn. Undergr. Space Technol. 18 (2), 233–241. Mo, H.H., Chen, J.S., 2008. Study on inner force and dislocation of segments caused by shield machine attitude. Tunn. Undergr. Space Technol. 23 (3), 281–291. Murakami, H., Koizumi, A., 1987. Behavior of shield segment ring reinforced by secondary lining. J. Jpn. Soc. Civ. Eng. 388, 85–94 (in Japanese). Nilson, A.H., 1972. Internal measurement of bond slip. ACI J. 69 (7), 439–441. Niu, X.Q., Fu, Z.Y., Zang, C.J., 2011. Full-scaled simulation model and experiment research on lining of tunnel crossing Yellow River. Yangtze River 42 (8), 77–87 (in Chinese).
References Blom, C.B.M., Van der Horst, E.J., Jovanovic, P.S., 1999. Three-dimensional structural analyses of the shield-driven “Green Heart” tunnel of the high-speed line south. Tunn. Undergr. Space Technol. 14 (2), 217–224. Chen, J.S., Mo, H.H., 2009. Numerical study on crack problems in segments of shield tunnel using finite element method. Tunn. Undergr. Space Technol. 24 (1), 91–102. Chong, X., Huang, J.Q., Ye, X.G., 2014. Numerical analysis on nonlinear behavior of the superimposed wall under quasi-static reversed cyclic loading. In: Proceedings of the Sustainable Development of Critical Infrastructure, Shanghai, 16–18 May, pp. 238–246. Collins, M.P., Mitchell, D., 1997. Prestressed Concrete Structures. Prentice Hall, Englewood Cliffs, NJ. Ding, W.Q., Yue, Z.Q., Tham, L.G., Zhu, H.H., Lee, C.F., Hashimoto, T., 2004. Analysis of shield tunnel. Int. J. Numer. Anal. Met. 28 (1), 57–91. Do, N.A., Dias, D., Oreste, P., Djeran-Maigre, I., 2013. 2D numerical investigation of segmental tunnel lining behaviour. Tunn. Undergr. Space Technol. 37, 115–127. Duan, G.X., Xu, H., 2011. Analysis on stress observation results of full-scaled lining simulation model of tunnel crossing Yellow River. Yangtze River 42 (8), 87–91 (in Chinese).
108
Tunnelling and Underground Space Technology 79 (2018) 96–109
F. Yang et al.
Wang, S., 2000. Simplified analysis of the effect of the elastic layer on turbine case in hydropower station. J. Hydraul. Eng. 3, 23–28 (in Chinese). Yan, Q.X., Yao, C.F., Yang, W.B., He, C., Geng, P., 2015. An improved numerical model of shield tunnel with double lining and its applications. Adv. Mater. Sci. Eng. Yang, Y.Z., Zhang, W.W., Wang, J.W., Yang, Z.H., 2014. Three-dimensional orthotropic equivalent modelling method of large-scale circular jointed lining. Tunn. Undergr. Space Technol. 44, 33–41. Zhang, H.M., Guo, C., Lu, G.L., 2001. Mechanical model for shield pressure tunnel with secondary linings. J. Hydraul. Eng. 4, 28–33 (in Chinese).
Popovics, S., 1973. A numerical approach to the complete stress-strain curve of concrete. Cement Concrete Res. 3 (5), 583–599. Takamatsu, N., Murakami, H., Koizumi, A., 1992. A study on the bending behaviour in the longitudinal direction of shield tunnels with secondary linings. In: Proceedings of the International Congress on 'Towards New World in Tunnellings', Acapulco, 16–22 May, pp. 227–285. Takamatsu, N., Murakami, H., Koizumi, A., 1993. Study on the analytical model on bending behaviour in longitudinal direction of shield tunnel with secondary lining. J. Jpn. Soc. Civ. Eng. 481, 97–106 (in Japanese).
109