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Compression-shear behavior of a scaled immersion joint with steel shear keys
Tunnelling and Underground Space Technology 70 (2017) 76–88
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Compression-shear behavior of a scaled immersion joint with steel shear keys ⁎
MARK
⁎
Wenhao Xiaoa, Haitao Yub, , Yong Yuanc, , Luc Taerwea,d, Guoping Xue a
Department of Structural Engineering, Ghent University, Ghent, Belgium Key Laboratory of Geotechnical and Underground Engineering of Ministry of Education, Tongji University, Shanghai 200092, China c State Key Laboratory for Disaster Reduction in Civil Engineering, Tongji University, Shanghai 200092, China d High-End Foreign Expert at Tongji University, Shanghai, China e CCCC Highway Consultants Co., Ltd., Beijing 100088, China b
A R T I C L E I N F O
A B S T R A C T
Keywords: Immersed tunnel Immersion joint Steel shear-key Shear stiffness Shear capacity Shear failure
The shear behavior of an immersion joint subjected to compressive-shear loads is investigated in this paper. To explore the performance of the immersion joint a scaled specimen, according to a specific protocol of a real project, is designed. A quasi-static shear force is applied horizontally while a constant compression force is maintained on the joint. A hysteresis effect is observed during the test and the area of the hysteretic loop increases with the shear force. An envelope curve of the shear force-displacement of the joint is obtained and divided into four stages based on the observed shear behavior of the joint. The shear stiffness of the immersion joint is calculated, showing a non-linear change with the shear displacement. The shear capacity of the model immersion joint and that of a single steel shear key are evaluated. It is found that the capacity of the joint is smaller than the sum of the capacities of all shear keys. This shows that the shear keys are not activated at the same time. The failure mode of the joint consists of a brittle shear failure in the single shear keys and a step-bystep failure way of the complete joint.
1. Introduction An immersion joint is the connecting part between two adjacent elements of an immersed tunnel. Compared to the stiffness of the concrete elements, the stiffness of the immersion joint is relatively small. When it is subjected to shear actions, whether resulting from foundation settlement or horizontal earthquake movements, the shear resistance of the joint is one of the main concerns for a safe and reliable water-proof design, which is as important as the longitudinal response which has been analyzed by Xiao et al. (2015). As mentioned in available literature (Akimoto et al., 2002; Baber et al., 2011; Hung et al., 2009), the immersion joint is a vital part not only for the connection between elements but it is also critical for the water tightness. A flexible immersion joint, which normally consists of a rubber seal and shear keys, is a common solution in practice. The way in which the shear keys and the rubber seal behave together in the joint is of vital importance to a thorough understanding of the shear behavior of the joint. However, very few experiments on the shear behavior of immersed joints are available in the literature although flexible joints have been used in practice for more than 50 years already. Kiyomiya et al. (1992) carried out both a 3-dimensional experiment ⁎
and a finite element analysis of a new type of a flexible joint referred to as the Crown Seal. The results indicated that this new type of joint can be used in practice due to the effective reduction of lateral deformation. However, the test only focused on the “rubber seal” and didn’t take the shear keys into account. A simplified linear model was found in the numerical simulation analysis in the paper of Anastasopoulos et al. (2008) who describe the behavior of the shear keys, assuming that the stiffness of the shear keys tends to infinity. However, this model was not supported by subsequent literature and the effect of the rubber seal was ignored. As an improvement, a three-dimensional nonlinear stiffness mechanical model was developed by Ding and Liu (2014) to analyze the axial and shear structural performance of the immersion joint by considering different working modes of the joint. However, both the simplified and improved models of the joint behavior rely on the input parameters of the stiffness of the seal and the shear keys. This means that if different stiffnesses are selected, different results are obtained. Therefore, the selected parameters as well as the models themselves need numerical and experimental verification. The shear capacity of concrete shear keys in segmental joints was discussed by Van Oorsouw (2010) by considering the influence of both the reinforcement in the keys and the friction between the segments. Although some suggestions
Corresponding authors at: Department of Geotechnical Engineering, Tongji University, 1239 Siping Road, 200092, China. E-mail addresses: [email protected] (H. Yu), [email protected] (Y. Yuan).
http://dx.doi.org/10.1016/j.tust.2017.07.007 Received 16 December 2015; Received in revised form 12 July 2017; Accepted 12 July 2017 0886-7798/ © 2017 Elsevier Ltd. All rights reserved.
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as such, the initial compression force varies from the water depth where the joint is located. Hence, the compression force is constant for a specific joint and it is mainly transferred by the primary rubber seal. Under seismic excitation, horizontal and vertical ground displacements caused by S-waves may occur, resulting in horizontal and vertical bending in the tunnel which is also referred as ‘snaking effect’. The resulting bending moments lead to a reciprocal shear effect arising in the joints. Also, differential settlements may occur between adjacent elements, resulting in vertical shear effects. All of these shear forces are transferred from element to element through the joint with the contribution of the shear keys. It should be note that the shear keys only resist shear force rather than compression force. Based on that, both the compression and shear force need to be taken into account at the same time and the compression-shear behavior of the joint will be examined by means of the experiment.
were given, the shear behavior of the concrete shear keys was not discussed in depth and the calculated shear capacity was not considered to be accurate as the model was not verified. To obtain a thorough understanding of the behavior of the joint, large-scale experiments were done by Kiyomiya et al. (1992) and Xiao et al. (2015) but only the axial and flexural behavior of the joint were considered but not the shear behavior. Although the shear-keys play an important role in an immersion joint, no published reports on experiments concerning their mechanical behavior are found. In a numerical analysis of a joint under shear actions, the shear keys are always modelled as simplified linear or bilinear springs in the shear direction by lack of experimental data. Moreover, the shear capacity of the joint and how the rubber and the shear keys interact was never considered and neither was the shear failure mode of the shear keys or the joint. Hence, the shear behavior of the joint needs more attention in a comprehensive way, taking the shear stiffness, the shear capacity and the failure mode into account. To clarify the mechanical behavior of an immersion joint under shear action, this paper presents the results of a large-scale experimental investigation. Compression-shear quasi-static loading was applied to a flexible immersion joint, with a geometric scale of 1/10 with respect to an actual design. The loading protocol in compression-shear was designed according to the axial water pressure, to which the joint would be subjected during its service life at typical buried depths, and to transverse shear movements due to seismic actions. The shear forces are applied reciprocally at increasing amplitude in the horizontal plane until the joint fails. Measuring devices were installed systematically to record the applied loads, the extension and closure of the joint. Through observed load-deformation curves, both the shear stiffness and the failure mode of the scaled joint are obtained and the results are discussed in detail.
2.2. Geometric scale As shown in Fig. 1, the cross-sectional dimensions of the prototype tunnel are 37.95 m by 11.40 m, which is oversize and exceeds the loading capacity of the lab. Hence the dimensions of the model specimen need to be scaled down. In consideration of the available loading capacity, a geometric scale of 1/10 is selected. As the same materials as the prototype are used, the same elastic modulus, the density and strain in the model are obtained. Based on the dimensional analysis, the scale of the stress, area and force can be obtained as follows:
Cσ =
σm =1 σp
CA =
Am ⎛ lm ⎞ = ⎜ ⎟ = 1/100 Ap ⎝ lp ⎠
(2)
2.1. Flexible joint
CF =
Fm A = m = 1/100 Fp Ap
(3)
2.1.1. Prototype design As the rubber seal becomes more common, flexible immersion joints have been widely used around the world. A typical cross-section of an immersion joint from an actual project, as well as its dimensions, are shown in Fig. 1(a). The cross-section is 37.95 m in width and 11.40 m in height with chamfered upper corners. There are two middle walls inside the tunnel, forming two traffic bores apart and one middle gallery. The joint mainly involves a primary rubber seal, a secondary rubber seal and shear keys, as can be seen in Fig. 1(b). The primary rubber seal is installed on the steel shell around the external perimeter of the joint, acting as the permanent water-tightness proof. When the immersed tunnel is being installed, the element is pulled towards the previously installed one. Then the primary rubber seal between the elements is pressed tightly and sealed completely due to hydrostatic pressure. After that, the secondary rubber seal is placed. If the primary rubber seal fails, the secondary rubber seal will be activated to work to avoid leakage. Steel shear keys are box sections mounted on an embedded plate secured to the end of the concrete tunnel element by studs and steel bars as shown in Fig. 2. The steel box is a hollow box strengthened with stiffening ribs inside. The box-type steel shear keys are connected to the embedded plate by bolts going through the steel box. The dimensions of the steel box are 2400 mm × 760 mm × 550 mm. The diameter of the bolts ranges between 56 mm and 64 mm, depending on the position.
where CA,CF ,Cσ ,A,F ,σ and l represent the scale of the area, scale of the force, scale of the stress, the area, the force, the stress and the length respectively. The subscripts m and p represent model and prototype respectively. Hence, the dimensions and the area of the scaled model are one tenth and one hundredth of the prototype respectively. In this case, the model has the same structural shape, structural form and reinforcement ratio as the prototype. The input loading and the capacity are scaled down as well, based on the obtained scale.
(1) 2
2. Scaled model of immersion joint
2.3. Scaled model 2.3.1. Model tunnel element Shear deformations of an immersion joint can happen both in the vertical or horizontal direction. However, the horizontal and vertical shearing of the joint are basically the same from a mechanical point of view. The difference is the influence of the rubber due to its different lengths along the horizontal and vertical sides. Moreover, gravity needs to be considered for vertical loading, resulting in one more difficulty with the application of shear loading. Therefore, only a horizontal shear force will be considered as well as only the horizontal shear keys. Due to the negligible contribution to the horizontal shear behavior of the joint, the cross-sectional profile of the model element was simplified as a rectangle and the middle walls, which are present in the actual tunnel (see Fig. 1(a)), were not provided. Fig. 3 also provides the dimensions of a single tunnel element with a width of 3800 mm, a height of 1150 mm, and a length of 1250 mm, as well as a 150 mm-thick concrete slab. Referring to the Chinese Code for concrete structure (GB50010-2010), the types of concrete and reinforcement are C50 and HRB335 respectively. The reinforcement ratio
2.1.2. Compression-shear force in the joint Due to the unique construction method of an immersed tunnel, an initial compression force caused by hydraulic static pressure always exists in the joint and consequently the joint is compressed and completely sealed. The hydraulic pressure depends on the water depth and 77
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Fig. 1. A typical immersion joint.
(a) Cross-section of a joint
(b) Details of A-A cross-section test. Also the dimensions and the photos of the model rubber seal are displayed and the physical parameters of the used rubber are listed in Table 1. Fig. 4(d) shows the comparison of the target load–compression curves and the curve from the model rubber seal, which are provided by the producers and own tests respectively. Two curves basically follow the same trend. At 2500 kN, the maximum compressions for these two curves are 19.0 mm and 20.4 mm respectively and there is only 7% difference between them. Therefore, the model rubber seal can be considered to be representative for the actual rubber under compression. A detailed view of the rubber seal after installation is shown in Fig. 4(c) (see Table 2).
for the model is the same as that of the prototype. There are two tunnel elements in this test, Element A and Element B as indicated in Fig. 3(b) and (c). The difference of these two elements is the different position of the shear keys.
2.3.2. Model rubber seal in immersion joint The model immersion joint basically follows the design of the real project and its detailed design is presented in the following section. The steel shell and second rubber seal are not adopted in this model joint due to the negligible of contribution to the shear behavior of the immersion joint. The model rubber seal is designed and manufactured especially for this experiment. As can be seen in Fig. 4, the GINA profile is used in this
Fig. 2. Prototype steel shear keys.
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Fig. 3. Model tunnel: position of joint and dimensions (a) and indication of shear keys (b and c) [mm]
(a) Model tunnel
(b) Element A
(c) Element B
Fig. 4. Model rubber seal in immersion joint.
(a) Dimensions of the model rubber seal [mm]
(b) Profile of model rubber seal
(c) Detailed view of model rubber seal after installation
(d) Comparison of the target load–compression curve and the curve from model rubber seal 79
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immersion joint is assumed to be the sum of the shear capacities of the four shear keys, which is 720 kN. Moreover, it should be noted that in the test, a gap of around 5 mm ( ± 3 mm) exists and the keys are not activated at the very beginning. Fig. 5(c) and (d) shows the photos of HSK1 and HKS2 respectively.
Table 1 Mechanical characteristics of the model rubber seal (Provided by producers). Characteristic
Value
Hardness Breaking Tenacity Extensibility Allowable Compressive Strength Shear Modulus Friction Coefficient
55–60 Shore A 14 MPa > 450% 10 MPa 0.98–1.47 MPa Steel:0.2; Concrete:0.3
3. Compression-shear test 3.1. Test set-up 3.1.1. Loading system In this experiment a combination of axial and shear load is applied. Fig. 6 shows the load application points (L1-L5) in the experiment. The axial force is applied by the four hydraulic jacks at the end of Element B. The four load application points (L1-L4) are loaded symmetrically in the vertical plane to make sure that the total axial force is exerted centrically. The shear force is provided by one actuator along the area L5 in Fig. 6, providing an approximate uniform linear shear load to the element. To achieve it, a round steel bar with a diameter of 50mm was placed in the loading connection, which can be seen in Fig. 7(d). Although the area L5 is as close as possible to the joint, an expected maximum bending moment of 180 kN·m in the joint is generated, resulting in a compression of only 0.3 mm at each side of the joint (Xiao et al., 2015). However, the influence of this bending moment is deemed to be negligible in this test. To achieve this, one tunnel element (Element A) is fixed horizontally while the other one (Element B) is movable in two horizontal directions, allowing compression and shear deformations of the immersion joint. As illustrated in Fig. 7, the tunnel elements are placed on supports resting on a reaction floor, and are kept in position with the loading frames which are installed against an L-shaped reaction wall. Each part of the loading frame is marked in a different color depending on its function. Two horizontal frames (light-blue) provide the axial reaction when the model tunnel is subjected to a compressive force by the 4 hydraulic jacks (dark blue1) installed on the reaction wall. There are two vertical frames placed next to the immersion joint. One frame (orange) is used to fix one element of the model tunnel, while the other one (green) provides a reciprocal shear force to the other element. Moreover, to avoid friction between the elements and the reaction floor, several column-supports with a spherical hinge bearing on top (red) are installed before the elements are positioned. As mentioned, the axial forces are applied to Element B and then transferred to the joint. Fig. 7(a) demonstrates the 4 loading points (dark blue) for the axial force. Four hydraulic jacks (dark blue) are situated between Element B and the reaction wall. The jacks are controlled synchronically to avoid rotation of Element B. The shear force is applied by an actuator (yellow), connecting to the element with a column and a round steel bar with diameter of 50 mm (Fig. 7(d)). There is also a steel plate between the steel bar and the concrete element to avoid stress concentration. The actuator can pull and push the element in this way and hence, the shear force can be reciprocal with varying amplitudes.
Table 2 Mechanical characteristics of materials in shear keys [MPa] Item
Tension/Compression Strength
Shear Strength
Steel Plate Weld Bolts
310 310 170
180 180 140
2.3.3. Model shear keys in immersion joint As mentioned, only the horizontal shear keys are considered as they are installed in both the roof and bottom slabs. The design of the steel shear keys is based on the actual project. In the actual project, a three-part shear key is required to resist the horizontal movement in both directions. There are two types of shear keys, HSK1 and HSK2 respectively. One single shear key (HSK1) is fixed to one tunnel element and the other two shear keys (HSK2) to the other element. The two types of shear keys are staggered in the different elements, making that HSK1 s are loaded in two directions while HSK2 s are loaded in only one direction. It can be seen from Fig. 2 that the possible failure mode for a single shear key could be (1) the failure of the shear box; (2) the failure of the bolts; and (3) the failure of the embedded plate or surrounding concrete. As for design, the shear box and the embedded plate are normally strong enough and the bolts are expected to fail. In this experiment, the model shear keys basically follow the actual design: (1) There are two types of model shear keys with staggered installation as shown in Fig. 5(a); (2) The dimensions of the shear box are scaled down by 1/10 (the geometric scale of the test) and the shape of the shear box is the same as the actual one (Shown in Fig. 5(b)); (3) The number and diameters of the bolts in the model are also reduced due to the geometric scale. For the model shear key, the bolts are also expected to fail during the test. Moreover, a bending moment may occur in the shear key when it is subjected to a shear force. However, the lever arm is very small (around 0.06 m), only introducing a small tensile force in the bolt. Based on that, it is assumed that the shear capacity of the shear key is provided by the shear capacity of the bolts and the friction force between the shear box and the tunnel element. Then the shear capacity of one shear key can be approximately calculated by Eq. (4).
RSK =
∑
RB + RF
(4)
where RSK and RB represent the resistances of a shear key and a bolt respectively while RF represents the friction force between the shear box and the element. It should be noted that there is no normal force on the shear box nor an extra preload on the bolts, which means that the friction force is small. Therefore, it is assumed that the friction force can be ignored in the analysis of the test results. According to the geometric scale, 8 bolts with a diameter of 12 mm and 2 bolts with a diameter of 8 mm are selected for each HSK1 while each HSK2 has 4 bolts with a diameter of 10 mm and 4 bolts with a diameter of 6 mm. The bolts are fixed with the sleeve welded to the embedded plate. The design capacity of one model shear key (HKS2) is approximately calculated as 180 kN while the capacity of the complete
3.1.2. Measurement of the joint displacement The shear displacement is measured while the joint is being loading during the test. As shown in Fig. 8, 4 transducers (Number 1 to 4) are placed near the corners of the cross-section of the joint. The transducers are positioned parallel to the shear force to obtain the relative displacement of the joint along this direction. Also, another 4 transducers (Number 5 to 8) are placed perpendicularly to the cross-sectional plane of the joint to measure the axial deformation. In order to observe the shear keys in the joint during the test, video1 For interpretation of color in Fig. 7, the reader is referred to the web version of this article.
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Fig. 5. Model steel shear keys.
(a) Staggered installation of two types of shear keys
(b) Details of the model shear keys
(c) HSK1
(d) HSK2 excitation. As each element of the immersed tunnel will be located at different water depths, the pressure acting on an immersion joint will vary with its location. The scaled-down axial forces corresponding to the minimum and the maximum water depths are 440 kN and 1760 kN. In this experiment, only one axial force is considered, referring to the water depth of the final joint in the actual project. Based on calculations, the axial force selected is 850 kN. As the horizontal shear action is mainly due to a seismic loading, a quasi-static loading mode for the shear force is applied (Fig. 10). In order to obtain the complete force-displacement behavior of the joint, the actuator is servo-controlled as a combination of force control and displacement control. Force control is used in the first part of the test because the joint is displacement-sensitive as the stiffness is high. However, in the second part of the test, the joint is force-sensitive due to the possible occurrence of plastic behavior or sudden brittle failure of the shear keys. Therefore, during the test, a force-control is adopted, followed by a displacement-control. First, reciprocal loading is applied in force-control until the shear force reaches a value of 400 kN, which is about 50% of the designed shear capacity as recommended by Chinese code (JGJ/T 101-2015). Then, the loading mode is switched and the actuator applies a reciprocal shear displacement at increasing amplitude until the joint fails. As shown in Fig. 10, the test does not stop as the loading mode is switched and the first point of input shear displacement corresponds to the last point of the input shear force. It should be noted that the loading and displacement rates are 1 kN/s and 0.1 mm/s respectively. The expected deformation mode of the joint subjected to combined compression and shear force is shown in Fig. 11. When both axial and shear forces are applied to element B, a compression occurs as well as a
Fig. 6. Load application points in the experiment.
recording cameras are used as displayed in Fig. 9(a). The real-time images captured by the cameras are shown on the monitor. The cameras are installed in the joint (Fig. 9(b)) and each camera focuses on one group of shear keys. If a shear key fails, it can be found on the monitor and then the failure can be recorded. Fig. 9(c) shows an example of shear keys captured by a camera.
3.2. Loading protocol As aforementioned, the combination of a shear force and an axial force is considered. First, the constant axial force is applied at a design value to simulate the initial water pressure in an actual joint at a specific water depth. After that, a reciprocal shear force, instead of a monotonic shear force, is applied horizontally to account for seismic actions, while the axial force remains constant. A reciprocal load means that first a load in the ‘positive’ direction is applied, followed by unloading. Then the loading and unloading in the ‘negative’ direction are applied. Such reciprocal load is applied repeatedly with increasing amplitude after each cycle to simulate the gradually increasing seismic 81
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lateral deformation. 4. Shear performance of the immersion joint 4.1. Recorded shear displacement The recorded compression is 9.31 mm at the axial force of 850 KN. Data of the relative shear displacement from the 4 transducers via a data recording acquisition system are plotted in Fig. 12. The numbers 1 till 4 in the legend represent the transducers #1 till #4 respectively in Fig. 8. It shows that the data from the four transducers are nearly in accordance with each other during the whole loading process, except for the last part of the test. Hence, the shear displacement of the joint can be taken as the average of the values measured by the four transducers.
(a) Plan view
4.2. Hysteretic curves during reciprocal loading The shear force versus shear displacement is shown in Fig. 13, in which “positive” and “negative” represent the loading directions. It can be seen that under quasi-static reciprocal loading, the joint behaves hysteretically. As long as the displacement of the joint ranges between 0 and 2.50 mm, a linear elastic behavior and minor residual displacement can be observed. The deformation of the joint is restored to its initial position. As the shear displacement increases up to around 7 mm, the rate of increase of the peak shear force starts to slow down gradually. Then the test switches to displacement-control. The shear force no longer increases with the displacement and it starts to go up and down, the maximum basically remaining around 500 kN. The hysteretic loop starts after the shear displacement exceeds 2.50 mm and from then on the hysteresis effect keeps growing until the end of the test.
(b) Front view
4.3. Shear force-displacement curves The envelop shear force-displacement curve of the joint is derived by selecting the peak point if each hysteretic loop from Fig. 13. Consecutive points are connected by a line, resulting in Fig. 14, in which both the Positive and Negative envelope curves are placed in the first quadrant for the ease of comparison. Based on the obtained shear performance of the joint, the complete behavior of the joint can be divided into 4 stages.
(c) Side view
• Stage I: At the beginning of the test, from 0 mm to 0.50 mm, it is • •
(d) SchemaƟc of the shear loading connecƟon Fig. 7. Set-up of testing system.
•
Fig. 8. Measurement lay-out.
clear that the positive behavior of the joint is in accordance with the negative behavior, indicating that the same behavior occurs in both directions. The steepest part of the curves can be found in this stage, while the shear displacement is relatively small. Stage II: As the test continues, the slope of the envelope curves starts to reduce slightly with small differences between both directions. The two curves clearly split after the shear displacement increases up to around 2.50 mm, indicating a difference between the behavior in the two directions. Stage III: In this stage the first damage within the joint occurs (details will be discussed in Section 5.1), resulting in the separation of both curves. From a displacement of about 3 mm on, both curves remain almost parallel until the negative curve reaches its peak value at a shear displacement of about 7 mm. Stage IV: The shear force fluctuates around 500 kN as mentioned above. The curves go up and down and the joint entered into a state of increasing displacement without much increase of the shear force in the ‘Positive’ curve but decrease of the shear force in the ‘Negative’ curve. This corresponds to failure of the shear keys and the rubber seal (Discussed in Section 5.1). It can be seen that the positive and negative behavior of the joint are
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Fig. 9. Observation of the shear keys.
Monitor Camera
(a) Layout of the system
(b) Cameras in the joint
(c) An example of the photo for one shear key taken by a camera
Fig. 10. Loading patterns for shear force.
Fig. 11. Compression-shear action in a joint.
basically in accordance with each other, though there are some differences found in Stage IV. In other words, the joint almost behaved synchronously at the beginning of the test and then, when the joint entered the last stage, an anti-synchronous behavior occurs, due to the failure of the shear keys, which influences the displacements in the
Fig. 12. Data of shear displacement recorded by transducers #1-#4.
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obtained, which is the slope of the secant line at that point:
kis =
Qi di
(5)
where Qi and di are the shear force and the shear displacement of the joint respectively at step i of the test. The calculated stiffnesses for both directions are shown in Fig. 15. The curve is divided into the same four stages as mentioned before. It can be seen that, as the shear displacement increases, the shear stiffnesses from the two curves are completely different at Stage I. For the positive direction, the curve fluctuates at around 250 kN/mm while the stiffnesses in the ‘negative’ curve are relatively large (maximum: 2489 kN/mm). At this stage, the shear displacements are very small (< 0.5 mm). The installation inaccuracies of the reaction frame may be of the same order of magnitude as the shear displacement in this stage, which results in significant fluctuations and dissimilarities in the value of kis . Both curves of the stiffness start to drop in Stage II, in which the value ranges decreases from 200 to 100 kN/mm, showing a degradation of the joint characteristics. In Stage III, the stiffness keeps decreasing but more slowly. The shear stiffness drops down to around 60 kN/mm before the joint enters into the final failure Stage IV. In this situation, the stiffness of the joint decreases and eventually tends to be constant value at around 25 kN/mm. It should be noted that the calculated shear stiffness of the model reinforcement concrete element is 21,610 kN/ mm. This means that the shear stiffness ratio between the model element and the model joint ranges from about 54 to 864 at the given compressive force. Since the shear stiffness ratio is a non-dimensional value, it is more applicable than the obtained shear stiffness of the joint in further numerical analyses due to its scale-independent character.
Fig. 13. Shear force-displacement curves.
4.5. Failure of the joint 4.5.1. General process As aforementioned, the shear keys are the key component in the shear capacity of the immersion joint. Once complete failure of the shear keys occurs, there is no limitation for the shear displacement, resulting in complete destruction of the joint. So far, no literature on the failure of immersion joints and the shear keys is available. Before discussing the failure mode, the definition of “failure” needs to be addressed. In this paper failure of the shear keys means that the shear keys lose their shear capacity completely. In the test, if the shear keys in the top slab fall down or the shear keys at the bottom slab lose contact with the tunnel element, the shear keys are no longer fixed to the concrete element and the failure state is reached. Fig. 16 shows an example of the ‘failure’ of shear keys in the joint. Fig. 16(a) displays a HSK2 fallen from the roof during the test while Fig. 16(b) shows a damaged HSK2, which has lost contact with the element. In both cases, all the bolts in the HSK2s are broken and the keys have lost their shear capacity. Moreover, through the camera observations, it can be noticed that all the HSK2s and not the HKS1s, are damaged one after another. For the HSK1s, the main bodies are basically preserved, and they remain in their initial position. After the test, some damage is found in the rubber as well. Details are discussed in Sections 4.5.2 and 4.5.3 respectively.
Fig. 14. Envelope curve of the shear behavior of the joint.
‘positive’ and ‘negative’ direction in a different way. 4.4. Shear stiffness of the joint The shear stiffness is an important parameter in the evaluation of the shear performance of the joint. Under the axial force of 850 kN, from equation (5) the shear stiffness k s at each loading step i is
4.5.2. Tearing of the rubber seal Damage also occurred in the rubber seal. Different types and levels of damage can be found only when the two elements are separated after the test. It should be noted that the rubber is fixed on element A and the rubber has contact with element B. The rubber seal in the side walls suffers the most serious damage, which is shown in Fig. 17(a). It can also be observed that broken bolts have fallen from the embedded steel plate and that the steel strips were hardly fixed to the rubber seal any more. Local damage of the rubber is shown in Fig. 17(b). Such damage over a small distance may be caused by many factors, such as initial imperfections, fallen dust and so on. When the rubber is subjected to a
Fig. 15. Relationship between shear stiffness and shear displacement.
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Fig. 16. Observed failure of the shear keys.
Lost contact
(a) A HKS2 fallen from the roof
(b) A damaged HSK2 in the bo om slab
(a) Broken bolts and loose steel strips on side wall
Fig. 18. Almost intact HSK1 at the bottom slab.
shear force, such initial imperfection or other factors may cause force concentrations, resulting in local damage in the rubber. On the element B, the black mark of the rubber is left on the surface of the concrete because the rubber scraps adhere to the concrete (Fig. 17(c)). This is because the rubber seal was highly compressed and large shear displacements of the joint cause a frictional sliding between rubber and concrete. However, such sliding has not been measured in this test.
4.5.3. Damage of the steel shear keys All the HSK2 steel shear keys are found to have failed one by one as aforementioned. Instead, the HSK1’s are well preserved and no serious deformation nor cracks are observed. The final shear displacement amounted to 21 mm, being 0.5% of the width of the tunnel segment in the lateral direction. One of the almost intact HSK1’s is shown in Fig. 18. The HSK1 is still connected firmly to the tunnel element. From the square grid marked on the surface, it can be seen that neither plastic deformations nor cracks occurred. On the contrary, the HSK2’s suffered serious damage. After failure of the bolts, no plastic elongation of the bolts is observed and all the bolts were cut by the shear force. The fracture surfaces are
(b) Local damage of the rubber sea on roof slabl
Fracture surface of the bolts
(c) Rubber scraps adhering to concrete element B Fig. 17. Damage observed in the rubber seal.
Fig. 19. Sheared-off cross-section of a shear key.
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Table 3 Detailed information on the failure points. Failure Point
Shear displacement [mm]
Relative Shear Force [%]
Positive P1 P2 P3 P4
2.84 8.00 10.01 17.16
38.9 68.1 71.5 67.4
Negative N1 N2 N3 N4
9.19 12.30 19.26 23.06
73.3 70.6 67.4 71.5
2.3.2. For example, when the P2 shear key fails, the shear force corresponds to only 68.1% of the design value. It can be seen that besides the first damaged shear keys, the rest of the shear keys all fail in Stage IV and the corresponding shear force is around 500 kN. The corresponding maximum and minimum shear forces when the rest of the shear keys fail are 528 kN and 485 kN respectively. The corresponding relative shear forces are 73.3% and 67.4%. It can be found that the shear force corresponding to failure of the shear key varies from each other, but the occurring differences of the shear capacities of the shear keys are deemed to be in an acceptable range. As discussed, except for the first damage occurring at shear key P1, damage to the shear keys starts to occur when the joint reaches the peak shear in the Negative curve. It can be easily found from Fig. 20 that the damage occurs at different times, which means that the shear keys in the joint fail one by one, instead of all together. During the test, the first damage (P1) appears in the positive direction when the shear force is 280 kN (end of stage II) while no damage occurred in the negative direction up to then. However, the shear force keeps increasing as the test continues.
(a) Occurrence of damage points
5.2. Discussion about the shear bearing capacity of the shear keys
(b) LocaƟons of damaged keys
Given the peak value of both the positive and the negative envelope curves in Fig. 14, it can be concluded that the shear capacity of the joint is 544 kN. For a single steel shear key, the first failure, as shown in Fig. 20(a), appears when the joint is subjected to a shear force of 280 kN. At a shear displacement of 2.81 mm, the rubber seal and the steel shear key provide the shear capacity together. In order to know the behavior of the rubber seal separately, it is assumed that before the first damage, the rubber seal behaves elastically and no sliding occurred. The deformation of the rubber seal is shown in Fig. 21. A compression da and a shear displacement ds occur as well as a shear strain γ when the joint is subjected to an axial force Fa and a shear force Q. Based on the above assumptions, the shear stiffness of the rubber krubber at a shear displacement of 2.81mm can be estimated by the following Eq. (6).
Fig. 20. Damaging process of the shear keys.
even and smooth, as shown in Fig. 19. Hence, it can be concluded that the bolts failed in a brittle way. No damage is found in the main bodies of the shear keys and they are preserved quite well. This also proves that in this test, the shear capacity of the shear keys relies on the shear capacity of the bolts. 5. Shear capacity of the joint subjected to reciprocal loading 5.1. Damage and failure of the joint In Fig. 20(a) eight typical damage points of the shear keys are indicated by red stars. The location of each damage point refers to the shear keys indicated in Fig. 20(b). In the figure, P and N represent the direction Positive and Negative respectively while the following number means the order of the damage. The first failure of the shear keys occurred at a shear displacement of 2.81 mm in the positive direction. When the shear displacement reaches 8.00 mm (9.00 mm in the negative direction), the second and third damage point are found in both positive and negative direction, corresponding to shear forces of 490 kN and 528 kN respectively. As the test continues, the damage at the other shear keys occurs one after one. At a displacement of 23.00 mm, the last shear key fails resulting in complete failure of the joint. The detailed information of the damage points is listed in Table 3. The relative shear force in the table is the ratio of the shear force applied to the design value, which is 720 kN as mentioned in Section
γGA s Q GA s EA s Fa d ≈ = = = da 2(1 + λ)(d−da) ds ds d−da 2(1 + λ)(d−da) kad = 2(1 + λ)(d−da) (6)
krubber =
where Q and Fa are the shear force and axial force applied to the rubber seal. d, ds and da are the original height of rubber seal and, the shear and axial displacement respectively. λ means the Poisson ratio, which is 0.5 in this case. As is the estimated cross-sectional area of the rubber. ka represents the axial stiffness of the rubber as obtained by Xiao et al. (2015). It should be noted that this equation only works with this shear displacement and it cannot be applied to the later-on situation. Then the shear stiffness of the rubber seal can be easily calculated as 31.8 kN/mm. Hence the shear force, allocated to the rubber seal, is 86
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Fig. 21. Deformation of the rubber seal.
the behavior of the rubber separately.
Table 4 Design value of the shear capacities and test results [kN]
Design value Test results
Single shear key
Immersion joint
6. Conclusions
180 190.6
720 544
This paper presents the results of an experimental study on a scaled immersion joint subjected to compression-shear loading. Based on a real project, a level of compressive load (850 kN) is applied as well as the increasing amplitudes of the reciprocal horizontal shear force. Analysis of the experimental results leads to the following conclusions.
obtained by the product of the shear stiffness and the shear displacement, which results in a value of 89.4 kN. As the rubber seal and the shear keys resist the shear force together, the shear force acting on the shear key is 190.6 kN when the first failure occurs. At this moment, the rubber seal takes up about 32% of the total shear force of the joint. The comparison between the design value and the test results of the shear capacities is shown in Table 4. It can be seen that the designed and obtained shear capacities of a single shear key are 180 kN and 190.6 kN respectively while the designed and obtained ones of a joint are 720 kN and 544 kN respectively. It should be noted that the shear capacity of the joint was assumed to be the sum of the shear capacities of all the shear keys. In this case, the capacity of the joint is 4 times the capacity of the keys. Although the design capacity of a single shear key is only 6% more than the obtained capacity, the design capacity of the immersion joint is 33% larger than the obtained value. The shear capacity of the immersion joint (540 kN) is not equal to the sum of that of all the shear keys (720 kN), which was not expected. In conclusion, not all the steel shear keys fail at the same time, resulting in a smaller shear capacity of the joint. There are installation inaccuracies in the test set-up, which means that some of the shear keys are not perfectly installed at the target location and an error of about ± 3 mm exists. In other words, the initial gaps between the shear keys vary between each other. This means that the different groups of shear keys get in touch with one another at different shear displacements. This situation may reduce the shear capacity of the joint because not all the shear keys are activated at the same time. In the real project, rubber bearings are used to fill the gap between the shear keys to make all the shear keys work together. The shear capacity of the immersion joint is about 2.8 times that of a single steel shear key. In the last stage of the test, a large displacement in the joint is obtained as well as a large shear deformation of the rubber seal. Although the shear force of the rubber seal at a displacement of 2.81 mm is obtained by Eq. (3), afterwards its behavior remains unknown and cannot be measured and quantified. But it is a fact that parts of the total shear force are transferred by the rubber seal, which is about 32% (89.4 kN of 280 kN) of the total force when the first failure occurs. As the test continued, it is believed that the shear force taken by the rubber may also increase along with the input shear force due to the friction force. However, the shear capacity of the rubber remains unknown as the coefficient of friction is unclear and impossible to measure in this test. Also, the unpredictable failure behavior of the shear keys add a complexity in this issue. From the view of the designer, it tends to be more conservative due to the contribution of the rubber as such contribution is never considered in actual design. Although the shear capacity of the rubber cannot be obtained, its contribution in shear direction should be taken into account in reality and further numerical analysis is required to elaborate
(1) Under a reciprocal horizontal shear force, a clear hysteretic loop is found and the area of it increases with the shear force. According to the obtained behavior of the joint, the envelope curve of the shear force-displacement of the joint can be divided into four stages based on the performance of the immersion joint corresponding to a decreasing shear stiffness. (2) It is observed that the failure mode of the immersion joint relies on the failure of the steel shear keys. Moreover, the HSK2’s are found to be damaged and they fail one after another. Based on the fracture of the bolts, the failure mode of a single shear key turns out to be a brittle shear failure. Also, damage of the rubber seal is occurring. The failure of the joint shows a step-by-step character. (3) The maximum shear capacity of the immersion joint and that of a single steel shear key are 544 kN and 191 kN respectively. The obtained capacity of the joint is lower than the designed one due to the fact that all the shear keys do not work at the same time. In an actual project, care should be seriously taken, i.e. installing bearing rubber between the shear keys, to assure that the shear forces are evenly distributed to all shear keys as practically possible. It is also found that the rubber seal has a certain contribution to the shear capacity. It should be noted that the limitation of this experiment still exist. The presented results on the shear behavior of the immersion joint rely on the material properties of the rubber seal and the shear keys, construction quality and the loading protocol. Size effect needs to be taken into account as well. A larger axial force or monotonic loading protocol may increase the shear capacity as a stiffer rubber seal is obtained or cumulative damage does not occur. Another type of the rubber seal may also influence the results. Such factors cannot be considered at the same time in this large-scale structural experiment. Moreover, the separate behavior of the rubber still remains unclear and it cannot be quantified due to the impossibility of the measurement in the test and the complex configuration of the rubber. A separate numerical and experimental analysis is required to elaborate this issue. However, the global shear behavior and the failure mode of the model immersion joint have been obtained from this test as well as the fact that the rubber seal contributes a lot to the shear resistance. Acknowledgement The authors would like to express their gratitude for the financial supports from NSFC (51678438 & 51478343), the Shanghai Rising-Star Program (17QC1400500), the Shanghai Committee of Science and 87
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Baber, J., Markey, I., Janssen, W., van Beek, R., Muller, C.P., 2011. Report of ITA Working Group 11 for Immersed and Floating Tunnels: International Tunnelling and Underground Space Association (ITA). Ding, W., Liu, P., 2014. Research on the Three Dimensional Nonlinear Stiffness Mechanical Model of Immersed Tube Tunnel Joints, Geo Shanghai. Tunnelling and Underground Construction, Shanghai, China, pp. 1–14. Hung, J., Monsees, J., Munfah, N., Wisniewski, J., 2009. Technical Manual for Design and Construction of Road Tunnels – Civil Elements. U.S. Department of Transportation Federal Highway Administration. Kiyomiya, O., Fujisawa, T., Yamada, M., Honda, M., 1992. Mechanical Properties of Flexible Joint Between Submerged Tunnel Elements (Japanese). Port and Harbour Research Institute, Yokosuka, Japan. Van Oorsouw, R.S., 2010. Behavior of segment joints in immersed tunnels under seismic loading. Master Thesis Delft University of Technology, Delft. Xiao, W., Yu, H., Yuan, Y., et al., 2015. Compression-bending behavior of a scaled immersion joint. Tunn. Undergr. Space Technol. 49 (2015), 426–437.
Technology (16DZ1200302 & 16DZ1201904) and the National Key Technology R & D Program (2011BAG07B01). The financial support from the China Scholar Council (No. 201406260199) and the High-end Foreign Expert program of Tongji University, China are also gratefully acknowledged. References Akimoto, K., Hashidate, Y., Kitayama, H., Kumagai, K., 2002. Immersed tunnels in Japan: recent technological trends. In: Proceedings at the International Symposium on Underwater Technology, Tokyo, Japan. Anastasopoulos, I., Gerolymos, N., Drosos, V., Georgarakos, T., Kourkoulis, R., Gazetas, G., 2008. Behaviour of deep immersed tunnel under combined normal fault rupture deformation and subsequent seismic shaking. Bull. Earthq. Eng. 6 (2), 213–239. http://dx.doi.org/10.1007/s10518-007-9055-0.
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Compression-shear behavior of a scaled immersion joint with steel shear keys ⁎
MARK
⁎
Wenhao Xiaoa, Haitao Yub, , Yong Yuanc, , Luc Taerwea,d, Guoping Xue a
Department of Structural Engineering, Ghent University, Ghent, Belgium Key Laboratory of Geotechnical and Underground Engineering of Ministry of Education, Tongji University, Shanghai 200092, China c State Key Laboratory for Disaster Reduction in Civil Engineering, Tongji University, Shanghai 200092, China d High-End Foreign Expert at Tongji University, Shanghai, China e CCCC Highway Consultants Co., Ltd., Beijing 100088, China b
A R T I C L E I N F O
A B S T R A C T
Keywords: Immersed tunnel Immersion joint Steel shear-key Shear stiffness Shear capacity Shear failure
The shear behavior of an immersion joint subjected to compressive-shear loads is investigated in this paper. To explore the performance of the immersion joint a scaled specimen, according to a specific protocol of a real project, is designed. A quasi-static shear force is applied horizontally while a constant compression force is maintained on the joint. A hysteresis effect is observed during the test and the area of the hysteretic loop increases with the shear force. An envelope curve of the shear force-displacement of the joint is obtained and divided into four stages based on the observed shear behavior of the joint. The shear stiffness of the immersion joint is calculated, showing a non-linear change with the shear displacement. The shear capacity of the model immersion joint and that of a single steel shear key are evaluated. It is found that the capacity of the joint is smaller than the sum of the capacities of all shear keys. This shows that the shear keys are not activated at the same time. The failure mode of the joint consists of a brittle shear failure in the single shear keys and a step-bystep failure way of the complete joint.
1. Introduction An immersion joint is the connecting part between two adjacent elements of an immersed tunnel. Compared to the stiffness of the concrete elements, the stiffness of the immersion joint is relatively small. When it is subjected to shear actions, whether resulting from foundation settlement or horizontal earthquake movements, the shear resistance of the joint is one of the main concerns for a safe and reliable water-proof design, which is as important as the longitudinal response which has been analyzed by Xiao et al. (2015). As mentioned in available literature (Akimoto et al., 2002; Baber et al., 2011; Hung et al., 2009), the immersion joint is a vital part not only for the connection between elements but it is also critical for the water tightness. A flexible immersion joint, which normally consists of a rubber seal and shear keys, is a common solution in practice. The way in which the shear keys and the rubber seal behave together in the joint is of vital importance to a thorough understanding of the shear behavior of the joint. However, very few experiments on the shear behavior of immersed joints are available in the literature although flexible joints have been used in practice for more than 50 years already. Kiyomiya et al. (1992) carried out both a 3-dimensional experiment ⁎
and a finite element analysis of a new type of a flexible joint referred to as the Crown Seal. The results indicated that this new type of joint can be used in practice due to the effective reduction of lateral deformation. However, the test only focused on the “rubber seal” and didn’t take the shear keys into account. A simplified linear model was found in the numerical simulation analysis in the paper of Anastasopoulos et al. (2008) who describe the behavior of the shear keys, assuming that the stiffness of the shear keys tends to infinity. However, this model was not supported by subsequent literature and the effect of the rubber seal was ignored. As an improvement, a three-dimensional nonlinear stiffness mechanical model was developed by Ding and Liu (2014) to analyze the axial and shear structural performance of the immersion joint by considering different working modes of the joint. However, both the simplified and improved models of the joint behavior rely on the input parameters of the stiffness of the seal and the shear keys. This means that if different stiffnesses are selected, different results are obtained. Therefore, the selected parameters as well as the models themselves need numerical and experimental verification. The shear capacity of concrete shear keys in segmental joints was discussed by Van Oorsouw (2010) by considering the influence of both the reinforcement in the keys and the friction between the segments. Although some suggestions
Corresponding authors at: Department of Geotechnical Engineering, Tongji University, 1239 Siping Road, 200092, China. E-mail addresses: [email protected] (H. Yu), [email protected] (Y. Yuan).
http://dx.doi.org/10.1016/j.tust.2017.07.007 Received 16 December 2015; Received in revised form 12 July 2017; Accepted 12 July 2017 0886-7798/ © 2017 Elsevier Ltd. All rights reserved.
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as such, the initial compression force varies from the water depth where the joint is located. Hence, the compression force is constant for a specific joint and it is mainly transferred by the primary rubber seal. Under seismic excitation, horizontal and vertical ground displacements caused by S-waves may occur, resulting in horizontal and vertical bending in the tunnel which is also referred as ‘snaking effect’. The resulting bending moments lead to a reciprocal shear effect arising in the joints. Also, differential settlements may occur between adjacent elements, resulting in vertical shear effects. All of these shear forces are transferred from element to element through the joint with the contribution of the shear keys. It should be note that the shear keys only resist shear force rather than compression force. Based on that, both the compression and shear force need to be taken into account at the same time and the compression-shear behavior of the joint will be examined by means of the experiment.
were given, the shear behavior of the concrete shear keys was not discussed in depth and the calculated shear capacity was not considered to be accurate as the model was not verified. To obtain a thorough understanding of the behavior of the joint, large-scale experiments were done by Kiyomiya et al. (1992) and Xiao et al. (2015) but only the axial and flexural behavior of the joint were considered but not the shear behavior. Although the shear-keys play an important role in an immersion joint, no published reports on experiments concerning their mechanical behavior are found. In a numerical analysis of a joint under shear actions, the shear keys are always modelled as simplified linear or bilinear springs in the shear direction by lack of experimental data. Moreover, the shear capacity of the joint and how the rubber and the shear keys interact was never considered and neither was the shear failure mode of the shear keys or the joint. Hence, the shear behavior of the joint needs more attention in a comprehensive way, taking the shear stiffness, the shear capacity and the failure mode into account. To clarify the mechanical behavior of an immersion joint under shear action, this paper presents the results of a large-scale experimental investigation. Compression-shear quasi-static loading was applied to a flexible immersion joint, with a geometric scale of 1/10 with respect to an actual design. The loading protocol in compression-shear was designed according to the axial water pressure, to which the joint would be subjected during its service life at typical buried depths, and to transverse shear movements due to seismic actions. The shear forces are applied reciprocally at increasing amplitude in the horizontal plane until the joint fails. Measuring devices were installed systematically to record the applied loads, the extension and closure of the joint. Through observed load-deformation curves, both the shear stiffness and the failure mode of the scaled joint are obtained and the results are discussed in detail.
2.2. Geometric scale As shown in Fig. 1, the cross-sectional dimensions of the prototype tunnel are 37.95 m by 11.40 m, which is oversize and exceeds the loading capacity of the lab. Hence the dimensions of the model specimen need to be scaled down. In consideration of the available loading capacity, a geometric scale of 1/10 is selected. As the same materials as the prototype are used, the same elastic modulus, the density and strain in the model are obtained. Based on the dimensional analysis, the scale of the stress, area and force can be obtained as follows:
Cσ =
σm =1 σp
CA =
Am ⎛ lm ⎞ = ⎜ ⎟ = 1/100 Ap ⎝ lp ⎠
(2)
2.1. Flexible joint
CF =
Fm A = m = 1/100 Fp Ap
(3)
2.1.1. Prototype design As the rubber seal becomes more common, flexible immersion joints have been widely used around the world. A typical cross-section of an immersion joint from an actual project, as well as its dimensions, are shown in Fig. 1(a). The cross-section is 37.95 m in width and 11.40 m in height with chamfered upper corners. There are two middle walls inside the tunnel, forming two traffic bores apart and one middle gallery. The joint mainly involves a primary rubber seal, a secondary rubber seal and shear keys, as can be seen in Fig. 1(b). The primary rubber seal is installed on the steel shell around the external perimeter of the joint, acting as the permanent water-tightness proof. When the immersed tunnel is being installed, the element is pulled towards the previously installed one. Then the primary rubber seal between the elements is pressed tightly and sealed completely due to hydrostatic pressure. After that, the secondary rubber seal is placed. If the primary rubber seal fails, the secondary rubber seal will be activated to work to avoid leakage. Steel shear keys are box sections mounted on an embedded plate secured to the end of the concrete tunnel element by studs and steel bars as shown in Fig. 2. The steel box is a hollow box strengthened with stiffening ribs inside. The box-type steel shear keys are connected to the embedded plate by bolts going through the steel box. The dimensions of the steel box are 2400 mm × 760 mm × 550 mm. The diameter of the bolts ranges between 56 mm and 64 mm, depending on the position.
where CA,CF ,Cσ ,A,F ,σ and l represent the scale of the area, scale of the force, scale of the stress, the area, the force, the stress and the length respectively. The subscripts m and p represent model and prototype respectively. Hence, the dimensions and the area of the scaled model are one tenth and one hundredth of the prototype respectively. In this case, the model has the same structural shape, structural form and reinforcement ratio as the prototype. The input loading and the capacity are scaled down as well, based on the obtained scale.
(1) 2
2. Scaled model of immersion joint
2.3. Scaled model 2.3.1. Model tunnel element Shear deformations of an immersion joint can happen both in the vertical or horizontal direction. However, the horizontal and vertical shearing of the joint are basically the same from a mechanical point of view. The difference is the influence of the rubber due to its different lengths along the horizontal and vertical sides. Moreover, gravity needs to be considered for vertical loading, resulting in one more difficulty with the application of shear loading. Therefore, only a horizontal shear force will be considered as well as only the horizontal shear keys. Due to the negligible contribution to the horizontal shear behavior of the joint, the cross-sectional profile of the model element was simplified as a rectangle and the middle walls, which are present in the actual tunnel (see Fig. 1(a)), were not provided. Fig. 3 also provides the dimensions of a single tunnel element with a width of 3800 mm, a height of 1150 mm, and a length of 1250 mm, as well as a 150 mm-thick concrete slab. Referring to the Chinese Code for concrete structure (GB50010-2010), the types of concrete and reinforcement are C50 and HRB335 respectively. The reinforcement ratio
2.1.2. Compression-shear force in the joint Due to the unique construction method of an immersed tunnel, an initial compression force caused by hydraulic static pressure always exists in the joint and consequently the joint is compressed and completely sealed. The hydraulic pressure depends on the water depth and 77
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Fig. 1. A typical immersion joint.
(a) Cross-section of a joint
(b) Details of A-A cross-section test. Also the dimensions and the photos of the model rubber seal are displayed and the physical parameters of the used rubber are listed in Table 1. Fig. 4(d) shows the comparison of the target load–compression curves and the curve from the model rubber seal, which are provided by the producers and own tests respectively. Two curves basically follow the same trend. At 2500 kN, the maximum compressions for these two curves are 19.0 mm and 20.4 mm respectively and there is only 7% difference between them. Therefore, the model rubber seal can be considered to be representative for the actual rubber under compression. A detailed view of the rubber seal after installation is shown in Fig. 4(c) (see Table 2).
for the model is the same as that of the prototype. There are two tunnel elements in this test, Element A and Element B as indicated in Fig. 3(b) and (c). The difference of these two elements is the different position of the shear keys.
2.3.2. Model rubber seal in immersion joint The model immersion joint basically follows the design of the real project and its detailed design is presented in the following section. The steel shell and second rubber seal are not adopted in this model joint due to the negligible of contribution to the shear behavior of the immersion joint. The model rubber seal is designed and manufactured especially for this experiment. As can be seen in Fig. 4, the GINA profile is used in this
Fig. 2. Prototype steel shear keys.
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Fig. 3. Model tunnel: position of joint and dimensions (a) and indication of shear keys (b and c) [mm]
(a) Model tunnel
(b) Element A
(c) Element B
Fig. 4. Model rubber seal in immersion joint.
(a) Dimensions of the model rubber seal [mm]
(b) Profile of model rubber seal
(c) Detailed view of model rubber seal after installation
(d) Comparison of the target load–compression curve and the curve from model rubber seal 79
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immersion joint is assumed to be the sum of the shear capacities of the four shear keys, which is 720 kN. Moreover, it should be noted that in the test, a gap of around 5 mm ( ± 3 mm) exists and the keys are not activated at the very beginning. Fig. 5(c) and (d) shows the photos of HSK1 and HKS2 respectively.
Table 1 Mechanical characteristics of the model rubber seal (Provided by producers). Characteristic
Value
Hardness Breaking Tenacity Extensibility Allowable Compressive Strength Shear Modulus Friction Coefficient
55–60 Shore A 14 MPa > 450% 10 MPa 0.98–1.47 MPa Steel:0.2; Concrete:0.3
3. Compression-shear test 3.1. Test set-up 3.1.1. Loading system In this experiment a combination of axial and shear load is applied. Fig. 6 shows the load application points (L1-L5) in the experiment. The axial force is applied by the four hydraulic jacks at the end of Element B. The four load application points (L1-L4) are loaded symmetrically in the vertical plane to make sure that the total axial force is exerted centrically. The shear force is provided by one actuator along the area L5 in Fig. 6, providing an approximate uniform linear shear load to the element. To achieve it, a round steel bar with a diameter of 50mm was placed in the loading connection, which can be seen in Fig. 7(d). Although the area L5 is as close as possible to the joint, an expected maximum bending moment of 180 kN·m in the joint is generated, resulting in a compression of only 0.3 mm at each side of the joint (Xiao et al., 2015). However, the influence of this bending moment is deemed to be negligible in this test. To achieve this, one tunnel element (Element A) is fixed horizontally while the other one (Element B) is movable in two horizontal directions, allowing compression and shear deformations of the immersion joint. As illustrated in Fig. 7, the tunnel elements are placed on supports resting on a reaction floor, and are kept in position with the loading frames which are installed against an L-shaped reaction wall. Each part of the loading frame is marked in a different color depending on its function. Two horizontal frames (light-blue) provide the axial reaction when the model tunnel is subjected to a compressive force by the 4 hydraulic jacks (dark blue1) installed on the reaction wall. There are two vertical frames placed next to the immersion joint. One frame (orange) is used to fix one element of the model tunnel, while the other one (green) provides a reciprocal shear force to the other element. Moreover, to avoid friction between the elements and the reaction floor, several column-supports with a spherical hinge bearing on top (red) are installed before the elements are positioned. As mentioned, the axial forces are applied to Element B and then transferred to the joint. Fig. 7(a) demonstrates the 4 loading points (dark blue) for the axial force. Four hydraulic jacks (dark blue) are situated between Element B and the reaction wall. The jacks are controlled synchronically to avoid rotation of Element B. The shear force is applied by an actuator (yellow), connecting to the element with a column and a round steel bar with diameter of 50 mm (Fig. 7(d)). There is also a steel plate between the steel bar and the concrete element to avoid stress concentration. The actuator can pull and push the element in this way and hence, the shear force can be reciprocal with varying amplitudes.
Table 2 Mechanical characteristics of materials in shear keys [MPa] Item
Tension/Compression Strength
Shear Strength
Steel Plate Weld Bolts
310 310 170
180 180 140
2.3.3. Model shear keys in immersion joint As mentioned, only the horizontal shear keys are considered as they are installed in both the roof and bottom slabs. The design of the steel shear keys is based on the actual project. In the actual project, a three-part shear key is required to resist the horizontal movement in both directions. There are two types of shear keys, HSK1 and HSK2 respectively. One single shear key (HSK1) is fixed to one tunnel element and the other two shear keys (HSK2) to the other element. The two types of shear keys are staggered in the different elements, making that HSK1 s are loaded in two directions while HSK2 s are loaded in only one direction. It can be seen from Fig. 2 that the possible failure mode for a single shear key could be (1) the failure of the shear box; (2) the failure of the bolts; and (3) the failure of the embedded plate or surrounding concrete. As for design, the shear box and the embedded plate are normally strong enough and the bolts are expected to fail. In this experiment, the model shear keys basically follow the actual design: (1) There are two types of model shear keys with staggered installation as shown in Fig. 5(a); (2) The dimensions of the shear box are scaled down by 1/10 (the geometric scale of the test) and the shape of the shear box is the same as the actual one (Shown in Fig. 5(b)); (3) The number and diameters of the bolts in the model are also reduced due to the geometric scale. For the model shear key, the bolts are also expected to fail during the test. Moreover, a bending moment may occur in the shear key when it is subjected to a shear force. However, the lever arm is very small (around 0.06 m), only introducing a small tensile force in the bolt. Based on that, it is assumed that the shear capacity of the shear key is provided by the shear capacity of the bolts and the friction force between the shear box and the tunnel element. Then the shear capacity of one shear key can be approximately calculated by Eq. (4).
RSK =
∑
RB + RF
(4)
where RSK and RB represent the resistances of a shear key and a bolt respectively while RF represents the friction force between the shear box and the element. It should be noted that there is no normal force on the shear box nor an extra preload on the bolts, which means that the friction force is small. Therefore, it is assumed that the friction force can be ignored in the analysis of the test results. According to the geometric scale, 8 bolts with a diameter of 12 mm and 2 bolts with a diameter of 8 mm are selected for each HSK1 while each HSK2 has 4 bolts with a diameter of 10 mm and 4 bolts with a diameter of 6 mm. The bolts are fixed with the sleeve welded to the embedded plate. The design capacity of one model shear key (HKS2) is approximately calculated as 180 kN while the capacity of the complete
3.1.2. Measurement of the joint displacement The shear displacement is measured while the joint is being loading during the test. As shown in Fig. 8, 4 transducers (Number 1 to 4) are placed near the corners of the cross-section of the joint. The transducers are positioned parallel to the shear force to obtain the relative displacement of the joint along this direction. Also, another 4 transducers (Number 5 to 8) are placed perpendicularly to the cross-sectional plane of the joint to measure the axial deformation. In order to observe the shear keys in the joint during the test, video1 For interpretation of color in Fig. 7, the reader is referred to the web version of this article.
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Fig. 5. Model steel shear keys.
(a) Staggered installation of two types of shear keys
(b) Details of the model shear keys
(c) HSK1
(d) HSK2 excitation. As each element of the immersed tunnel will be located at different water depths, the pressure acting on an immersion joint will vary with its location. The scaled-down axial forces corresponding to the minimum and the maximum water depths are 440 kN and 1760 kN. In this experiment, only one axial force is considered, referring to the water depth of the final joint in the actual project. Based on calculations, the axial force selected is 850 kN. As the horizontal shear action is mainly due to a seismic loading, a quasi-static loading mode for the shear force is applied (Fig. 10). In order to obtain the complete force-displacement behavior of the joint, the actuator is servo-controlled as a combination of force control and displacement control. Force control is used in the first part of the test because the joint is displacement-sensitive as the stiffness is high. However, in the second part of the test, the joint is force-sensitive due to the possible occurrence of plastic behavior or sudden brittle failure of the shear keys. Therefore, during the test, a force-control is adopted, followed by a displacement-control. First, reciprocal loading is applied in force-control until the shear force reaches a value of 400 kN, which is about 50% of the designed shear capacity as recommended by Chinese code (JGJ/T 101-2015). Then, the loading mode is switched and the actuator applies a reciprocal shear displacement at increasing amplitude until the joint fails. As shown in Fig. 10, the test does not stop as the loading mode is switched and the first point of input shear displacement corresponds to the last point of the input shear force. It should be noted that the loading and displacement rates are 1 kN/s and 0.1 mm/s respectively. The expected deformation mode of the joint subjected to combined compression and shear force is shown in Fig. 11. When both axial and shear forces are applied to element B, a compression occurs as well as a
Fig. 6. Load application points in the experiment.
recording cameras are used as displayed in Fig. 9(a). The real-time images captured by the cameras are shown on the monitor. The cameras are installed in the joint (Fig. 9(b)) and each camera focuses on one group of shear keys. If a shear key fails, it can be found on the monitor and then the failure can be recorded. Fig. 9(c) shows an example of shear keys captured by a camera.
3.2. Loading protocol As aforementioned, the combination of a shear force and an axial force is considered. First, the constant axial force is applied at a design value to simulate the initial water pressure in an actual joint at a specific water depth. After that, a reciprocal shear force, instead of a monotonic shear force, is applied horizontally to account for seismic actions, while the axial force remains constant. A reciprocal load means that first a load in the ‘positive’ direction is applied, followed by unloading. Then the loading and unloading in the ‘negative’ direction are applied. Such reciprocal load is applied repeatedly with increasing amplitude after each cycle to simulate the gradually increasing seismic 81
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lateral deformation. 4. Shear performance of the immersion joint 4.1. Recorded shear displacement The recorded compression is 9.31 mm at the axial force of 850 KN. Data of the relative shear displacement from the 4 transducers via a data recording acquisition system are plotted in Fig. 12. The numbers 1 till 4 in the legend represent the transducers #1 till #4 respectively in Fig. 8. It shows that the data from the four transducers are nearly in accordance with each other during the whole loading process, except for the last part of the test. Hence, the shear displacement of the joint can be taken as the average of the values measured by the four transducers.
(a) Plan view
4.2. Hysteretic curves during reciprocal loading The shear force versus shear displacement is shown in Fig. 13, in which “positive” and “negative” represent the loading directions. It can be seen that under quasi-static reciprocal loading, the joint behaves hysteretically. As long as the displacement of the joint ranges between 0 and 2.50 mm, a linear elastic behavior and minor residual displacement can be observed. The deformation of the joint is restored to its initial position. As the shear displacement increases up to around 7 mm, the rate of increase of the peak shear force starts to slow down gradually. Then the test switches to displacement-control. The shear force no longer increases with the displacement and it starts to go up and down, the maximum basically remaining around 500 kN. The hysteretic loop starts after the shear displacement exceeds 2.50 mm and from then on the hysteresis effect keeps growing until the end of the test.
(b) Front view
4.3. Shear force-displacement curves The envelop shear force-displacement curve of the joint is derived by selecting the peak point if each hysteretic loop from Fig. 13. Consecutive points are connected by a line, resulting in Fig. 14, in which both the Positive and Negative envelope curves are placed in the first quadrant for the ease of comparison. Based on the obtained shear performance of the joint, the complete behavior of the joint can be divided into 4 stages.
(c) Side view
• Stage I: At the beginning of the test, from 0 mm to 0.50 mm, it is • •
(d) SchemaƟc of the shear loading connecƟon Fig. 7. Set-up of testing system.
•
Fig. 8. Measurement lay-out.
clear that the positive behavior of the joint is in accordance with the negative behavior, indicating that the same behavior occurs in both directions. The steepest part of the curves can be found in this stage, while the shear displacement is relatively small. Stage II: As the test continues, the slope of the envelope curves starts to reduce slightly with small differences between both directions. The two curves clearly split after the shear displacement increases up to around 2.50 mm, indicating a difference between the behavior in the two directions. Stage III: In this stage the first damage within the joint occurs (details will be discussed in Section 5.1), resulting in the separation of both curves. From a displacement of about 3 mm on, both curves remain almost parallel until the negative curve reaches its peak value at a shear displacement of about 7 mm. Stage IV: The shear force fluctuates around 500 kN as mentioned above. The curves go up and down and the joint entered into a state of increasing displacement without much increase of the shear force in the ‘Positive’ curve but decrease of the shear force in the ‘Negative’ curve. This corresponds to failure of the shear keys and the rubber seal (Discussed in Section 5.1). It can be seen that the positive and negative behavior of the joint are
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Fig. 9. Observation of the shear keys.
Monitor Camera
(a) Layout of the system
(b) Cameras in the joint
(c) An example of the photo for one shear key taken by a camera
Fig. 10. Loading patterns for shear force.
Fig. 11. Compression-shear action in a joint.
basically in accordance with each other, though there are some differences found in Stage IV. In other words, the joint almost behaved synchronously at the beginning of the test and then, when the joint entered the last stage, an anti-synchronous behavior occurs, due to the failure of the shear keys, which influences the displacements in the
Fig. 12. Data of shear displacement recorded by transducers #1-#4.
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obtained, which is the slope of the secant line at that point:
kis =
Qi di
(5)
where Qi and di are the shear force and the shear displacement of the joint respectively at step i of the test. The calculated stiffnesses for both directions are shown in Fig. 15. The curve is divided into the same four stages as mentioned before. It can be seen that, as the shear displacement increases, the shear stiffnesses from the two curves are completely different at Stage I. For the positive direction, the curve fluctuates at around 250 kN/mm while the stiffnesses in the ‘negative’ curve are relatively large (maximum: 2489 kN/mm). At this stage, the shear displacements are very small (< 0.5 mm). The installation inaccuracies of the reaction frame may be of the same order of magnitude as the shear displacement in this stage, which results in significant fluctuations and dissimilarities in the value of kis . Both curves of the stiffness start to drop in Stage II, in which the value ranges decreases from 200 to 100 kN/mm, showing a degradation of the joint characteristics. In Stage III, the stiffness keeps decreasing but more slowly. The shear stiffness drops down to around 60 kN/mm before the joint enters into the final failure Stage IV. In this situation, the stiffness of the joint decreases and eventually tends to be constant value at around 25 kN/mm. It should be noted that the calculated shear stiffness of the model reinforcement concrete element is 21,610 kN/ mm. This means that the shear stiffness ratio between the model element and the model joint ranges from about 54 to 864 at the given compressive force. Since the shear stiffness ratio is a non-dimensional value, it is more applicable than the obtained shear stiffness of the joint in further numerical analyses due to its scale-independent character.
Fig. 13. Shear force-displacement curves.
4.5. Failure of the joint 4.5.1. General process As aforementioned, the shear keys are the key component in the shear capacity of the immersion joint. Once complete failure of the shear keys occurs, there is no limitation for the shear displacement, resulting in complete destruction of the joint. So far, no literature on the failure of immersion joints and the shear keys is available. Before discussing the failure mode, the definition of “failure” needs to be addressed. In this paper failure of the shear keys means that the shear keys lose their shear capacity completely. In the test, if the shear keys in the top slab fall down or the shear keys at the bottom slab lose contact with the tunnel element, the shear keys are no longer fixed to the concrete element and the failure state is reached. Fig. 16 shows an example of the ‘failure’ of shear keys in the joint. Fig. 16(a) displays a HSK2 fallen from the roof during the test while Fig. 16(b) shows a damaged HSK2, which has lost contact with the element. In both cases, all the bolts in the HSK2s are broken and the keys have lost their shear capacity. Moreover, through the camera observations, it can be noticed that all the HSK2s and not the HKS1s, are damaged one after another. For the HSK1s, the main bodies are basically preserved, and they remain in their initial position. After the test, some damage is found in the rubber as well. Details are discussed in Sections 4.5.2 and 4.5.3 respectively.
Fig. 14. Envelope curve of the shear behavior of the joint.
‘positive’ and ‘negative’ direction in a different way. 4.4. Shear stiffness of the joint The shear stiffness is an important parameter in the evaluation of the shear performance of the joint. Under the axial force of 850 kN, from equation (5) the shear stiffness k s at each loading step i is
4.5.2. Tearing of the rubber seal Damage also occurred in the rubber seal. Different types and levels of damage can be found only when the two elements are separated after the test. It should be noted that the rubber is fixed on element A and the rubber has contact with element B. The rubber seal in the side walls suffers the most serious damage, which is shown in Fig. 17(a). It can also be observed that broken bolts have fallen from the embedded steel plate and that the steel strips were hardly fixed to the rubber seal any more. Local damage of the rubber is shown in Fig. 17(b). Such damage over a small distance may be caused by many factors, such as initial imperfections, fallen dust and so on. When the rubber is subjected to a
Fig. 15. Relationship between shear stiffness and shear displacement.
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Fig. 16. Observed failure of the shear keys.
Lost contact
(a) A HKS2 fallen from the roof
(b) A damaged HSK2 in the bo om slab
(a) Broken bolts and loose steel strips on side wall
Fig. 18. Almost intact HSK1 at the bottom slab.
shear force, such initial imperfection or other factors may cause force concentrations, resulting in local damage in the rubber. On the element B, the black mark of the rubber is left on the surface of the concrete because the rubber scraps adhere to the concrete (Fig. 17(c)). This is because the rubber seal was highly compressed and large shear displacements of the joint cause a frictional sliding between rubber and concrete. However, such sliding has not been measured in this test.
4.5.3. Damage of the steel shear keys All the HSK2 steel shear keys are found to have failed one by one as aforementioned. Instead, the HSK1’s are well preserved and no serious deformation nor cracks are observed. The final shear displacement amounted to 21 mm, being 0.5% of the width of the tunnel segment in the lateral direction. One of the almost intact HSK1’s is shown in Fig. 18. The HSK1 is still connected firmly to the tunnel element. From the square grid marked on the surface, it can be seen that neither plastic deformations nor cracks occurred. On the contrary, the HSK2’s suffered serious damage. After failure of the bolts, no plastic elongation of the bolts is observed and all the bolts were cut by the shear force. The fracture surfaces are
(b) Local damage of the rubber sea on roof slabl
Fracture surface of the bolts
(c) Rubber scraps adhering to concrete element B Fig. 17. Damage observed in the rubber seal.
Fig. 19. Sheared-off cross-section of a shear key.
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Table 3 Detailed information on the failure points. Failure Point
Shear displacement [mm]
Relative Shear Force [%]
Positive P1 P2 P3 P4
2.84 8.00 10.01 17.16
38.9 68.1 71.5 67.4
Negative N1 N2 N3 N4
9.19 12.30 19.26 23.06
73.3 70.6 67.4 71.5
2.3.2. For example, when the P2 shear key fails, the shear force corresponds to only 68.1% of the design value. It can be seen that besides the first damaged shear keys, the rest of the shear keys all fail in Stage IV and the corresponding shear force is around 500 kN. The corresponding maximum and minimum shear forces when the rest of the shear keys fail are 528 kN and 485 kN respectively. The corresponding relative shear forces are 73.3% and 67.4%. It can be found that the shear force corresponding to failure of the shear key varies from each other, but the occurring differences of the shear capacities of the shear keys are deemed to be in an acceptable range. As discussed, except for the first damage occurring at shear key P1, damage to the shear keys starts to occur when the joint reaches the peak shear in the Negative curve. It can be easily found from Fig. 20 that the damage occurs at different times, which means that the shear keys in the joint fail one by one, instead of all together. During the test, the first damage (P1) appears in the positive direction when the shear force is 280 kN (end of stage II) while no damage occurred in the negative direction up to then. However, the shear force keeps increasing as the test continues.
(a) Occurrence of damage points
5.2. Discussion about the shear bearing capacity of the shear keys
(b) LocaƟons of damaged keys
Given the peak value of both the positive and the negative envelope curves in Fig. 14, it can be concluded that the shear capacity of the joint is 544 kN. For a single steel shear key, the first failure, as shown in Fig. 20(a), appears when the joint is subjected to a shear force of 280 kN. At a shear displacement of 2.81 mm, the rubber seal and the steel shear key provide the shear capacity together. In order to know the behavior of the rubber seal separately, it is assumed that before the first damage, the rubber seal behaves elastically and no sliding occurred. The deformation of the rubber seal is shown in Fig. 21. A compression da and a shear displacement ds occur as well as a shear strain γ when the joint is subjected to an axial force Fa and a shear force Q. Based on the above assumptions, the shear stiffness of the rubber krubber at a shear displacement of 2.81mm can be estimated by the following Eq. (6).
Fig. 20. Damaging process of the shear keys.
even and smooth, as shown in Fig. 19. Hence, it can be concluded that the bolts failed in a brittle way. No damage is found in the main bodies of the shear keys and they are preserved quite well. This also proves that in this test, the shear capacity of the shear keys relies on the shear capacity of the bolts. 5. Shear capacity of the joint subjected to reciprocal loading 5.1. Damage and failure of the joint In Fig. 20(a) eight typical damage points of the shear keys are indicated by red stars. The location of each damage point refers to the shear keys indicated in Fig. 20(b). In the figure, P and N represent the direction Positive and Negative respectively while the following number means the order of the damage. The first failure of the shear keys occurred at a shear displacement of 2.81 mm in the positive direction. When the shear displacement reaches 8.00 mm (9.00 mm in the negative direction), the second and third damage point are found in both positive and negative direction, corresponding to shear forces of 490 kN and 528 kN respectively. As the test continues, the damage at the other shear keys occurs one after one. At a displacement of 23.00 mm, the last shear key fails resulting in complete failure of the joint. The detailed information of the damage points is listed in Table 3. The relative shear force in the table is the ratio of the shear force applied to the design value, which is 720 kN as mentioned in Section
γGA s Q GA s EA s Fa d ≈ = = = da 2(1 + λ)(d−da) ds ds d−da 2(1 + λ)(d−da) kad = 2(1 + λ)(d−da) (6)
krubber =
where Q and Fa are the shear force and axial force applied to the rubber seal. d, ds and da are the original height of rubber seal and, the shear and axial displacement respectively. λ means the Poisson ratio, which is 0.5 in this case. As is the estimated cross-sectional area of the rubber. ka represents the axial stiffness of the rubber as obtained by Xiao et al. (2015). It should be noted that this equation only works with this shear displacement and it cannot be applied to the later-on situation. Then the shear stiffness of the rubber seal can be easily calculated as 31.8 kN/mm. Hence the shear force, allocated to the rubber seal, is 86
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Fig. 21. Deformation of the rubber seal.
the behavior of the rubber separately.
Table 4 Design value of the shear capacities and test results [kN]
Design value Test results
Single shear key
Immersion joint
6. Conclusions
180 190.6
720 544
This paper presents the results of an experimental study on a scaled immersion joint subjected to compression-shear loading. Based on a real project, a level of compressive load (850 kN) is applied as well as the increasing amplitudes of the reciprocal horizontal shear force. Analysis of the experimental results leads to the following conclusions.
obtained by the product of the shear stiffness and the shear displacement, which results in a value of 89.4 kN. As the rubber seal and the shear keys resist the shear force together, the shear force acting on the shear key is 190.6 kN when the first failure occurs. At this moment, the rubber seal takes up about 32% of the total shear force of the joint. The comparison between the design value and the test results of the shear capacities is shown in Table 4. It can be seen that the designed and obtained shear capacities of a single shear key are 180 kN and 190.6 kN respectively while the designed and obtained ones of a joint are 720 kN and 544 kN respectively. It should be noted that the shear capacity of the joint was assumed to be the sum of the shear capacities of all the shear keys. In this case, the capacity of the joint is 4 times the capacity of the keys. Although the design capacity of a single shear key is only 6% more than the obtained capacity, the design capacity of the immersion joint is 33% larger than the obtained value. The shear capacity of the immersion joint (540 kN) is not equal to the sum of that of all the shear keys (720 kN), which was not expected. In conclusion, not all the steel shear keys fail at the same time, resulting in a smaller shear capacity of the joint. There are installation inaccuracies in the test set-up, which means that some of the shear keys are not perfectly installed at the target location and an error of about ± 3 mm exists. In other words, the initial gaps between the shear keys vary between each other. This means that the different groups of shear keys get in touch with one another at different shear displacements. This situation may reduce the shear capacity of the joint because not all the shear keys are activated at the same time. In the real project, rubber bearings are used to fill the gap between the shear keys to make all the shear keys work together. The shear capacity of the immersion joint is about 2.8 times that of a single steel shear key. In the last stage of the test, a large displacement in the joint is obtained as well as a large shear deformation of the rubber seal. Although the shear force of the rubber seal at a displacement of 2.81 mm is obtained by Eq. (3), afterwards its behavior remains unknown and cannot be measured and quantified. But it is a fact that parts of the total shear force are transferred by the rubber seal, which is about 32% (89.4 kN of 280 kN) of the total force when the first failure occurs. As the test continued, it is believed that the shear force taken by the rubber may also increase along with the input shear force due to the friction force. However, the shear capacity of the rubber remains unknown as the coefficient of friction is unclear and impossible to measure in this test. Also, the unpredictable failure behavior of the shear keys add a complexity in this issue. From the view of the designer, it tends to be more conservative due to the contribution of the rubber as such contribution is never considered in actual design. Although the shear capacity of the rubber cannot be obtained, its contribution in shear direction should be taken into account in reality and further numerical analysis is required to elaborate
(1) Under a reciprocal horizontal shear force, a clear hysteretic loop is found and the area of it increases with the shear force. According to the obtained behavior of the joint, the envelope curve of the shear force-displacement of the joint can be divided into four stages based on the performance of the immersion joint corresponding to a decreasing shear stiffness. (2) It is observed that the failure mode of the immersion joint relies on the failure of the steel shear keys. Moreover, the HSK2’s are found to be damaged and they fail one after another. Based on the fracture of the bolts, the failure mode of a single shear key turns out to be a brittle shear failure. Also, damage of the rubber seal is occurring. The failure of the joint shows a step-by-step character. (3) The maximum shear capacity of the immersion joint and that of a single steel shear key are 544 kN and 191 kN respectively. The obtained capacity of the joint is lower than the designed one due to the fact that all the shear keys do not work at the same time. In an actual project, care should be seriously taken, i.e. installing bearing rubber between the shear keys, to assure that the shear forces are evenly distributed to all shear keys as practically possible. It is also found that the rubber seal has a certain contribution to the shear capacity. It should be noted that the limitation of this experiment still exist. The presented results on the shear behavior of the immersion joint rely on the material properties of the rubber seal and the shear keys, construction quality and the loading protocol. Size effect needs to be taken into account as well. A larger axial force or monotonic loading protocol may increase the shear capacity as a stiffer rubber seal is obtained or cumulative damage does not occur. Another type of the rubber seal may also influence the results. Such factors cannot be considered at the same time in this large-scale structural experiment. Moreover, the separate behavior of the rubber still remains unclear and it cannot be quantified due to the impossibility of the measurement in the test and the complex configuration of the rubber. A separate numerical and experimental analysis is required to elaborate this issue. However, the global shear behavior and the failure mode of the model immersion joint have been obtained from this test as well as the fact that the rubber seal contributes a lot to the shear resistance. Acknowledgement The authors would like to express their gratitude for the financial supports from NSFC (51678438 & 51478343), the Shanghai Rising-Star Program (17QC1400500), the Shanghai Committee of Science and 87
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Baber, J., Markey, I., Janssen, W., van Beek, R., Muller, C.P., 2011. Report of ITA Working Group 11 for Immersed and Floating Tunnels: International Tunnelling and Underground Space Association (ITA). Ding, W., Liu, P., 2014. Research on the Three Dimensional Nonlinear Stiffness Mechanical Model of Immersed Tube Tunnel Joints, Geo Shanghai. Tunnelling and Underground Construction, Shanghai, China, pp. 1–14. Hung, J., Monsees, J., Munfah, N., Wisniewski, J., 2009. Technical Manual for Design and Construction of Road Tunnels – Civil Elements. U.S. Department of Transportation Federal Highway Administration. Kiyomiya, O., Fujisawa, T., Yamada, M., Honda, M., 1992. Mechanical Properties of Flexible Joint Between Submerged Tunnel Elements (Japanese). Port and Harbour Research Institute, Yokosuka, Japan. Van Oorsouw, R.S., 2010. Behavior of segment joints in immersed tunnels under seismic loading. Master Thesis Delft University of Technology, Delft. Xiao, W., Yu, H., Yuan, Y., et al., 2015. Compression-bending behavior of a scaled immersion joint. Tunn. Undergr. Space Technol. 49 (2015), 426–437.
Technology (16DZ1200302 & 16DZ1201904) and the National Key Technology R & D Program (2011BAG07B01). The financial support from the China Scholar Council (No. 201406260199) and the High-end Foreign Expert program of Tongji University, China are also gratefully acknowledged. References Akimoto, K., Hashidate, Y., Kitayama, H., Kumagai, K., 2002. Immersed tunnels in Japan: recent technological trends. In: Proceedings at the International Symposium on Underwater Technology, Tokyo, Japan. Anastasopoulos, I., Gerolymos, N., Drosos, V., Georgarakos, T., Kourkoulis, R., Gazetas, G., 2008. Behaviour of deep immersed tunnel under combined normal fault rupture deformation and subsequent seismic shaking. Bull. Earthq. Eng. 6 (2), 213–239. http://dx.doi.org/10.1007/s10518-007-9055-0.
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