# Study on Deformation Characteristics of Segment Joints of the Immersed Tunnel in Hong Kong-Zhuhai-Macau Bridge

Authors: Yapeng Niu; Yongli Xie; Hongguang Zhang; Xiabing Yue; Yingguang Han; Zhinan Hu
Journal: Advances in Materials Science and Engineering
 (2022)

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## Abstract

The segmental joints are the weak parts of the immersed tunnel structure, and their deformation characteristics are closely correlated with the waterproof behavior and structural safety of the whole tunnel. In order to study the deformation characteristics of the segmental joints of immersed structure, in this paper, the E13 pipe section in the natural foundation section of an immersed tunnel in the Hong Kong-Zhuhai-Macao Bridge is taken as the research object, and the model test of the immersed tunnel is carried out. The similarity ratio of the model to the prototype is determined according to the actual engineering scale and the capability of the model test system, and the plexiglass is selected as the model material of the immersed tunnel according to the similarity of elastic modulus and density. In the test, various working conditions, including back-silting load and different prestress control values, are analyzed, and the influence of settlement and opening of the immersed tunnel is obtained, along with the stress-strain characteristics of the segment joints. Results show that the increase of the back-silting load will increase the element settlement and the expansion of the segment joints, but the application of prestress increases the overall stiffness of the element, which can effectively restrain the settlement of element and the expansion of joints. Furthermore, based on the model test conditions, a finite element model is established to simulate the mechanical behavior of the immersed tunnel. The settlement curve and stress-strain curve of the numerical analysis are found to be similar to those obtained from the model test, which verifies the reliability of the model test.


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## Body

## 1. Introduction

As a large underwater transportation tunnel crossing rivers and straits, the immersed tube tunnel has the advantages of large cross-section area, high utilization rate, small environmental disturbance, good adaptability to the foundation, and short construction period [1–6]. Therefore, it is increasingly favored by engineering applications. However, there are still some problems limiting the applications of the immersed tunnel; for example, although the multisection immersed tunnel structure is more suitable for uneven foundation settlement [7–11], it also produces a large number of element joints and segment joints. While the stiffness of these joints is much smaller than that of the concrete main structure, thus, they become the weak part of the whole structure. Under the influence of uneven back-silting at the top of the tunnel, the construction errors of the crushed stone cushion, and uneven foundation settlement, the joints are easy to occur displacement and open mouths, which may reduce or totally destroy the waterproofing effect of joint and even cause the shear key damage of segment joint. Therefore, the research on the deformation characteristics of segment joints is of great significance to structural waterproofing and the structural design of the immersed tunnel.At present, a number of studies have been carried out through the model test and numerical simulations on the mechanical performances of the segment joints. For the studies by model tests, Zhang et al. [12] analyzed the seismic performance of the immersed tunnel by using the model test and found that strong seismic action would cause tensile rupture of the tunnel at the joint. Besides, Hu et al. [13] studied the spatial distribution of shear forces of the segment joints of the immersed tunnel through a 1:4.69 large-scale model test. The results found that the distribution laws of segment joint shearing stress along with differential settlement and immersed tunnel cross sections. In addition, through centrifugal model tests, Yue et al. [14] revealed the stress distribution and deformation characteristics of immersed tunnels during the natural foundation excavation rebound and backfill recompression processes. It was found that the stress distribution in the base was saddle-shaped. Moreover, Yuan et al. [15] studied the deformation characteristics of the shear key of the element joint under the action of axial force and bending moment through a 1:10 model test, and they found that the local warping failure and tension failure in the root of the tenon are regarded as the failure model of the concrete shear keys. Furthermore, Qian et al. [16] established an analytical model for calculating the shear bond of element joints based on comparative analysis with the photoelastic model test. For the research on practical engineering, Hans et al. [17] studied the mechanical behaviors of the Busan-Geoje immersed tunnel during the butt joint process, which also adopted model tests. For the studies using a numerical model, Zhou et al. [18] established a three-dimensional finite element model to analyze the mechanical performances of prestressed anchor cables with segment joints, and the results showed that the prestressed anchor cable can effectively control the relative displacement between the segment joints. Similarly, Dai et al. [19] also used the finite element software to study the influence of the shear of the prestressed tendons of an immersed tunnel on the structure. Besides, Zhang et al. [20] used finite element software to perform numerical analysis on each part of the segment joint under various working conditions and obtained the relevant optimal parameters of each part of the joint. In addition, by adopting finite element software, Liu et al. [21] simulated the force of the joint segment in detail and found that the shear force borne by the concrete shear key was larger than that of the steel shear key. The above-mentioned researches on element joints mainly focus on the mechanical behaviors of the segment joints, but few studies are conducted on their deformation characteristics, especially those considering the influence of the prestressing and degree of back-silting on the deformation characteristics of segment joints.According to the above problems, in this work, the deformation characteristics of segment joints of the E13 section of the immersed tunnel in the Hong Kong-Zhuhai-Macao Bridge are studied by adopting a model test (HZMB). The effects of back-silting load and prestress control value on the settlement of immersed tunnels and the opening of segment joints are simulated, and the distribution characteristics of compressive stress at the base of the immersed tunnel and the strain characteristics of tunnel structure are revealed. Furthermore, finite element simulations are conducted to verify the model test results and compensate for test data. Through the numerical model, the influences of prestress tension on settlement, joint deformation, and joint internal force of the immersed tunnel under the action of back-silting load are further analyzed. The present work provides a basis for theoretical research, engineering construction, and design of the segment joint of the immersed tunnel.


## 2. General Engineering Situation

The immersed tunnel of the Hong Kong-Zhuhai-Macau Bridge is located in a marine environment with complex geological conditions and harsh weather conditions, such as deep waters and rapid sea conditions. The total length of the immersed tunnel is about 5.659 km and consists of 33 elements, which is the longest undersea tunnel in the world, and the tunnel length from east to west is 90 m + 90 m + 180 m × 30 m + 79 m. The section studied in this work is 37.95 m long and composed of 8 segments, as shown in Figure1 [22]. Due to the long longitudinal length of the tunnel and the long time of construction period, after the elements are settled to the designated position, the prestressed tendons are easy to be relaxed, and thus, the mutual constraints between the segments are weakened before the completion of the tunnel. In addition, the underwater environment of the tunnel is relatively complex; the back siltation is serious; and the section safety issues are prominent. In this test, the E13 element in the natural foundation section of the immersed tunnel with large back siltation is taken as the prototype. The foundation soil layers consist of 10.6 m of silty soil, 26.7 m of clay, and 35 m of gravel-bearing sand from top to bottom. Among them, the gravel cushion is well-graded with moderate material particle size, containing no debris, and the mud content is no more than 3%; besides, the maximum particle size is not more than 31.5 mm. The parameters of foundation soil are shown in Table 1.Figure 1
Geological and foundation profile of the HZMB tunnel (m) [22].Table 1
Soil parameters.
Soil layerES/MPaγ′/kN/m3c/kPaφ/°ϑH/mMucky clay2.686.80960.4310.60Clay soil10.788.4026210.4026.70Clay and soft sand73.7011.8016330.3035.00The segment joints of the immersed tunnel are composed of concrete shear keys, steel plate sealing strips, OMEGA water stops, and prestressed anchor cables.


### 2.1. Similarity Theory

The geometric similarity scale of this model test was 1:100 [22], and similarity criteria were obtained by the dimensional analysis method of the similarity theory and based on the similarity constant. In the model test, such physical quantities as geometric length (L), elastic modulus (E), Poisson’s ratio (μ), load (F), stress (σ), strain (ε), unit weight (γ), accelerated velocity (α), moment of inertia (I), linear displacement (ω), and angular displacement (φ) were mainly considered. Generally, the dimensionless quantities such as Poisson’s ratio, strain, angular displacement, accelerated velocity, and so on were assumed to be 1. Therefore, using the other six physical quantities to derive the similarity criterion and taking the elastic modulus and length as the basic physical quantities, the remaining four similarity criteria could be obtained. The dimensional matrix was as follows:(1)a1a2a3a4a5a6a7ωσFγILEL1−2−2−341−2F0111001.Depending on the above matrix, a linear equation set could be obtained:(2)L:a1−2a2−2a3−3a4+4a5+a6−2a7=0F:a2+a3+a4+a7=0.Then, theπ matrix could be described as follows:(3)a1a2a3a4a5a6a7ωσFγILEπ110000−10π2010000−1π3001000−1π4000101−1π500001−40.The similarity criteria were(4)π1=L−1ω,π2=E−1σ,π3=E−1F,π4=E−1γL,π5=L−4I.In this paper, plexiglass was used as the model material. The elastic modulus of plexiglass was 5.67 GPa. Since the elastic modulus of the immersed tube tunnel prototype reinforced concrete can be controlled to 34.5 GPa, the dimensional analysis method based on a similar theory could easily deduceCE=6.08.


### 2.2. Model Test

#### 2.2.1. Production of the Model Box

The model box is made of a steel plate and plexiglass. The size of the model box is 3 m (length) × 1.2 m (width) × 0.6 m (height), and the size of the plexiglass is 3 m (length) × 1.2 m (width) × 0.45 m (high), as shown in Figure2. From this figure, it can be seen that the plexiglass plate is 0.15 m away from the top of the model box. This part of the gap is used by the CCD to monitor the deformation image during the test, as shown in Figure 3. The friction between the inner wall of the soil box and the model foundation has a certain influence on the model test; therefore, in order to guarantee the reliability and authenticity of the model test, the influence of the boundary effect on the model test should be reduced, and the inner wall of the model box is smeared with petroleum jelly.Figure 2
Model box.Figure 3
Monitoring of the deformed image.


#### 2.2.2. Tunnel Model Making

Considering the mechanical characteristics of segment joints, similarity relationship of test, and size of the model box of the immersed tunnel under longitudinal bending conditions, the plexiglass is selected as the tunnel model material. Due to the fact that the contribution of the horizontal shear key to shearing is small, only four sets of vertical shear keys are retained in the model test, and the horizontal shear keys and other waterproof structures are not included. The prestress is simulated by controlling the tension of the prestressed steel strands at both ends of the element. The cross section of the segment joint is shown in Figure4; the size of the element model is 1.8 m (length) × 0.3795 m (width) × 0.114 m (height), as shown in Figure 5.Figure 4
Cross section of the segment joint (mm).Figure 5
Pipe joint model.


#### 2.2.3. Fabrication of the Foundation Soil Model

The prototype foundation soil contains three layers, namely, silty soil, clay, and rough sand. The equivalent substitution method is adopted to substitute a single layer of soil, and considering the site conditions and the size of the model box, comprehensively, the compression modulus is selected as the control parameter. Through calculation, the compression modulus of the foundation model after equivalent substitution isES=37.51MPa [23], and according to similarity theory, the compressive modulus of the foundation soil in the model test is Es = 6.17 MPa. A mixture of commercial sand and EPS particles was used to simulate the foundation soil, and the particle size and proportion of commercial sand are 6.6% (of total mass) of 1∼2mm, 33.1% of 0.5∼1mm, 0.25∼0.5mm of 44.9%, and 0.075∼0.25mm of 13.6%, while the particle size less than 0.075 mm accounts for 1.8% of the total mass. The physical and mechanical indexes are shown in Table 2, and the particle gradation is shown in Figure 6.Table 2
Soil parameter of model foundation.
Soil sampleρ/g⋅cm−3ω/%E/MPac/MPaφ/°Foundation soil1.454.16.1710.528.1Figure 6
Grain distribution curve of test sand.


#### 2.2.4. Layout of Monitoring Components

The test data acquisition system is mainly used to measure and record the test data of pressure and strain gauges. Specifically, the original data are measured by a micro earth pressure sensor (LY-350) and strain gauges, which are then transmitted through the static strain gauge data acquisition system (TDS-530), and the errors of the monitoring instruments are all less than 0.5% FS (full span). The subsidence observation data are transmitted through a noncontact measuring instrument data acquisition system (DIC), which is composed of a tripod, an industrial camera, a controller, and an image display device, as shown in Figure7. The industrial camera adopts RMOD-71-TEC rolling shutter CCD camera; the lens adopts a focal length of 16 mm; the pixel size is 3.1 × 3.1 μm; the pixel resolution 10,000 (H) × 7,094 (V); the effective image size is 31 × 22 mm; and the dynamic range is 64 db.Figure 7
Schematic diagram of the measuring instrument: (a) noncontact precision measurement systems and (b) static strain gauge.
(a)(b)This test mainly studies the vertical settlement of the element and the deformation characteristics of the section joint, and the layout position of the monitoring instruments and the schematic diagram of the noncontact measuring instruments are shown in Figures8(a) and 8(b). In these figures, S1–S7 represent the earth pressure sensors arranged along the transverse trench bottom layout, while the high-sensitivity strain gauges are arranged on the bottom and each side of the immersed tunnel to measure the strain change of the immersed tunnel during the test, as displayed in Figure 8(b). White and black matte paints are sprayed on the side walls of the longitudinal sections of the element to form speckles, and ZJ1–ZJ17 are selected as settlement observation points, as displayed in Figure 8(a).Figure 8
Layout of monitoring gauges: (a) observation point of longitudinal settlement of the element and (b) stress and strain observation point on the end face of J4.
(a)(b)


### 2.3. Loading System

#### 2.3.1. Load Loading Method

In the model test, a self-balancing air pressure positive pressure loading device is used; first place the airbag above the sunk immersed tunnel model, then connect the airbag to the air pump, close the top cover of the model box, and finally apply the air pressure in stages to simulate the silt load, as shown in Figure9. The schematic diagram of the load applied by the airbag is shown in Figure 10.Figure 9
Self-balancing loading device: (a) airbag and (b) the top cover of the model box is closed.
(a)(b)Figure 10
The schematic diagram of the loading device.


#### 2.3.2. Prestress Loading Method

The prestressed steel strands in the standard element of the prototype immersed tunnel are only distributed on the top and bottom plates, with a total of 60 holes. The 100% prestressing force of the standard strength of each hole is 6510 kN. Prestressed anchor cables are used to increase the positive pressure at the joints of the segments and the frictional resistance at the joints. Taking into account the purpose and implementation difficulty of the test, the model similarity theory is adopted for the model test. A self-made prestressed loading device (clip anchor, prestressed steel strand, and tensioning equipment) is used to simulate the application of the prestress of the structural model (Figure11), with axial force as the control variable. The prestress arrangement is shown in Figure 12.Figure 11
Prestressed loading device: (a) anchor, (b) prestressed steel strand, and (c) prestressed tensioning equipment.
(a)(b)(c)Figure 12
Schematic diagram of the prestress layout.


#### 2.3.3. Experimental Research Contents

In the model test, five working conditions under the prestress tension values of 0, 0.2, 0.4, 0.6, and 0.8 kN were carried out. The test conditions are shown in Table3. All of these test conditions are conducted under the most unfavorable back-silting load. According to the most unfavorable back-silting load on the pipe joint, the load applied in the test was reduced by 1:6.08, with the final load of about 20 kPa. In the test, the influence of the prestress control on the settlement of the immersed tunnel, the opening of the segment joints, and the deformation characteristics of the joints under the back-silting load are studied. The testing procedures are as follows:(1)
Preliminary Preparations. First, the equipment used for testing are calibrated and debugged to ensure normal use. Then, the side walls of the element are sprayed with a matte paint to from speckles and marks. Before filling the soil, the Vaseline is smeared on the inner wall of the model box to reduce the friction effect on the side wall. Finally, the foundation soil with the designed thickness is laid into the model box in layers.(2)
Prestress Tension. At one end of the element, the prestressed tendon is fixed by the anchor, and the prestressed loading device, tension and pressure sensor, and prestressed steel strand are connected at the other end. The prestress is applied to the prestressed steel strand through the loading device until it reaches the design value. Finally, the tensioning device is removed.(3)
Loading Measurement. The noncontact measuring instrument device (DIC) and the static strain gauge are first to be debugged. After the model is settled, the airbag is placed, and the cover plate of the model box is closed. The step-by-step loading method is adopted to pressurize the airbag to simulate the back-silting load on the element until the loading is complete. At the same time as hierarchical loading, the DIC image acquisition instrument and static strain gauge are used to collect data from the observation points. After the readings of each measurement point become stable, the next loading level is performed.(4)
Uninstall. After the reading of settlement becomes stable, unloading was carried out. In this process, the element model is lifted; the foundation soil is loosened and leveled again; and the next set of working condition tests is conducted.(5)
Data from each measurement system in the test process are extracted and processed.Table 3
Test conditions.
Prestress tension degree0%20/%40/%60/%80/%Prestress tension value (kN)00.20.40.60.8


### 2.4. Finite Element Calculation

#### 2.4.1. Establishment of the Finite Element Model

The immersed element consists of eight segments, which are connected by longitudinal prestressed anchor cables and shear keys. In this paper, ABAQUS software is used to numerically simulate the foundation soil, segments, and prestress components. A three-dimensional solid calculation model of a segmental element composed of eight segments (S1∼S8) is established, as shown in Figure11. The calculation model is the same as the test model (the length of the foundation soil model is 3 m, the width is 1.2 m, the length of the tunnel model is 1.8 m, the width is 0.38 m, and the height is 0.115 m). It is assumed that the foundation soil layer is a homogeneous and isotropic medium and conforms to the Mohr–Coulomb criterion.The tunnel structure adopts a solid element; the element type is C3D8R; the material is C50 concrete; and the elastic constitutive relation is used to approximately characterize the stress of the pipe section structure, which ignores the effect of concrete plasticity on calculation results. The overall mesh size of the pipe structure is 0.5 m, and the meshing is encrypted at the joint. The three-dimensional mechanical model of the pipe joint is shown in Figures13 and 14, and the model parameters are shown in Table 4.Figure 13
Finite element analysis model.Figure 14
Grid partition schematic diagram.Table 4
Calculation parameters of numerical simulation.
Material nameMaterial propertiesParameterUnitFoundation modelWeight (γ)14.2(kN/m3)Elastic modulus (E)6.17(MPa)Cohesion (c)10.5(kPa)Friction angle (φ)28.1(°)Dilation angle (ψ)0(°)Tunnel modelWeight (γ)11.61(kN/m3)Elastic modulus (E)5670(MPa)Prestressed anchor cableElastic modulus (E)32072(MPa)


#### 2.4.2. Boundary Conditions

The lateral boundary of the foundation soil model is constrained in theX direction; the longitudinal boundary is constrained in the Y direction; and the bottom is constrained in the Z direction. A segment is added at each end of the pipe joint model to apply pressure and weight, which can reduce the influence of boundary effects on the deformation characteristics of segment joints.


#### 2.4.3. Definition of Contact Relationship

The calculation model includes the element-foundation soil contact surface and the segment-joint contact surface. In the mechanical model of the segment-joint contact surface, the normal mechanical model adopts the hard contact, and the tangential mechanical model adopts the penalty function for simulation. Besides, the element-soil interface is simulated by a penalty function.


#### 2.4.4. Simulation of the Prestressed Anchor Cable

The segment joints of Hong Kong-Zhuhai-Macau immersed tunnels use longitudinal prestressed anchor cables to increase the positive pressure and frictional resistance, thereby improving the shear stiffness. In the finite element model, the truss element is used to simulate cable; the element type is T3D2; and the elastic constitutive relation is used to approximately present mechanical characteristics of the prestressed anchor cable. When calculation, the model adopts the “initial stress method,” at the beginning of the calculation, the initial stress of the element is defined, and prestress is applied.


#### 2.4.5. Analysis of Working Conditions

In this paper, the prestress control value is set to 0, 0.2, 0.4, 0.6, and 0.8 kN as the model calculation conditions, and 20 kPa is taken as the final load of back silting (note: the actual back-silting height corresponding to the final load is 20m). The specific back siltation is simulated by staged loading of 5, 10, 15, and 20 kPa, respectively.


### 2.5. Analysis and Verification of Test Results

#### 2.5.1. Analysis of the Impact of Immersed Tube Tunnel Settlement

It can be seen from Figure15 that under the action of back-silting load, the settlement distribution of the immersed tunnel with different prestress control values are all bent downward along the longitudinal direction of the element.Figure 15
Settlement-load distribution curve: (a) 5 kPa, (b) 10 kPa, (c) 15 kPa, and (d) 20 kPa.
(a)(b)(c)(d)With the increase in the back-silting load, the settlement of the element increases. When the prestress is large, it decreases with the increase of the prestress control value. It is worth noting that the maximum settlement of each measurement line appears at the joint of the middle section of the pipe section. When the prestress control value increases from 0 to 0.8 kN, the settlement at the middle section of the pipe section under the action of the back-silting load of 5 kPa decreases from8.375×10−1mm to 7.375×10−1mm, with a reduction of 12%. And the settlement of the middle section of the element under the action of the back-silting load of 20 kPa decreases from 2.2 mm to 2.09 mm, with a decrease of 1.05 times. When the back-silting load increases from 5 kPa to 20 kPa, the settlement of the middle section of the element with the prestress control value of 0 increases by 2.63 times, and that of the element with a prestress control value of 0.8 kN increases by 2.83 times, indicating that the presence of prestress increases the overall height of the element and improves the settlement of element, but the increase of the back-silting load will increase the settlement of element.Figure16 compares the prediction results from numerical simulation and measurement results from the test. Although the experimental data are larger than the simulated data, the two settlement curves follow the same trend and are close to each other, which indicates that the numerical simulation can reflect the main settlement behavior characteristics of the model test, and the difference may be due to the simplification of the model and the complexity of the model test.Figure 16
Comparison of measured settlements and finite element analysis settlements.


#### 2.5.2. Influence Analysis of Segment Joint Opening

It can be seen from Figure17 that at the end face of J4 in the middle of the element, the opening amount of the segment joint decreases with the increase of the prestress control value and increases with the increase of the back-silting load. When the prestress control value increases from 0 to 0.8 kN, the joint opening of the segment under the action of back-silting load of 5 kPa decreases from 1.37×10−1mm to 3.622×10−2mm, which is reduced 3.78 times. Under the action of the back-silting load of 20 kPa, the joint opening of the segment reduces from 3.192×10−1mm to 8.6×10−2mm, which is reduced by 3.71 times. When the back-silting load increases from 5 kPa to 20 kPa, the joint opening of the segment increases from 1.37×10−1mm to 3.192×10−1mm, which is increased by 2.32 times. Under the action of a prestress of 0.8 kN, the opening amount of the segment joints increases from 3.622×10−2mm to 8.6×10−2mm, which is increased by 2.37 times. The result coincides that the increase of the prestress control value improves the friction and shear stiffness of the segment joints, which significantly reduces the expansion of the segment joints.Figure 17
Relationships between segment joint opening and prestress control value.


#### 2.5.3. Compressive Stress of the Segment Joint

It can be seen from Figure18 that under the action of back-silting load and prestress tension, the base stress at the end face of J4 in the middle of the element is in a saddle-shaped distribution. The base stress of the partition wall and side wall of the immersed structure increases with the increase of back siltation and decreases with the increase of the prestress control value. Besides, the base stress of the carriageway increases with the increase of the back siltation and also the prestress control value. When the prestress control value increases from 0 to 0.8 kN, the base stress of the carriageway under the back-silting load of 5 kPa increases from 6.68 kPa to 8.22 kPa, with an increase of 23%, and the base stress of the partition wall decreases from 9.34 kPa to 8.85 kPa, with a decrease of 5.2%, while the base stress of the side wall reduces from 12.01 kPa to 9.31 kPa, with a decrease of 22.5%. Under the action of a resulting load of 20 kPa, the base stress of the carriageway increases from 14.56 kPa to 18.77 kPa, with an increase of 28.9%, and the base stress of the partition wall decreases from 22.38 kPa to 19.32 kPa, with a decrease of 13.7%, while the base stress of the side wall decreases from 32.32 kPa to 21.67 kPa, with a decrease of 33%. When the back-silting load increases from 5 kPa to 20 kPa, the base stress of the element carriageway, partition wall, and side wall under the prestress control value of 0 kN increases by 1.18, 1.4, and 1.69 times, respectively, and the element under the prestress control value of 0.8 kN increases by 1.18, 1.4, and 1.69 times, while the base stress of the section carriageway, the partition wall, and the side wall increases by 1.28, 1.17, and 1.25 times, respectively. It shows that the application of prestress increases the vertical reaction force of the element joints and produces a homogenizing effect on the base stress.Figure 18
Distribution curve of base stress: (a) 5 kPa, (b) 10 kPa, (c) 15 kPa, and (d) 20 kPa.
(a)(b)(c)(d)Figure19 shows the stress distribution curve of the J4 basement at the segment joint under the back-silting load of 20 kPa. It can be seen that the test curve is in good agreement with the numerical calculation curve. Specifically, the bottom of the segment joint is saddle-shaped along the horizontal direction of the stress distribution, and the stress values of the sidewalls, the partition wall, and the base of the driveway decrease sequentially. With the increase of the prestress control value, the stress value in the direction of the substrate decreases, and the stress amplitude changes smoothly.Figure 19
Comparison of measured stresses and finite element analysis stresses.


#### 2.5.4. Analysis of Strain Changes

It can be seen from Figure20 that under the action of back-silting load and prestress tension, the strain curve of the bottom plate of the immersed structure at the end face of J4 presents a saddle-shaped distribution. The strain value of the carriageway was positive, meaning that the part of the carriageway is under stretched, and the strain value of the side wall and the partition wall of the immersed tunnel are negative, meaning that the bottom is under compressed. From the results data, when the prestress control value increases from 0 to 0.8 kN, the strain of the immersed floor under the back-silting load of 5 kPa decreases from 7.7×10−3mm to 3.2×10−3mm, reduced by 58.4%, and the strain of the central partition wall decreases from 3.4×10−3mm to 1.75×10−3mm, reduced by 48.5%, while the strain of the side wall reduces from 11.6×10−3mm to 4.2×10−3mm, with a reduction of 63.8%. Under the action of the back-silting load of 20 kPa, the strain of the immersed floor reduces from 1.6×10−2mm to 8.9×10−3mm, with a reduction of 44.4%, and the strain of the partition wall reduces from 1.56×10−2mm to 9.5×10−3mm, with a reduction of 39.1%, while the strain of the side wall reduces from 3.24×10−2mm to 1.56×10−2mm, with a decrease of 51.9%. When the back-silting load increases from 5 kPa to 20 kPa, the strain values of the element floor carriageway, middle partition wall, and side wall under the prestress control value of 0 increase by 1.08, 3.59, and 1.79 times, respectively; the element joint floor carriageway, middle partition wall with the prestress control value of 0.8 kN, and the strain value of the side wall increases by 1.78, 4.4, and 2.71 times, respectively; which shows that due to the special structure of the immersed tunnel, the back-silting load causes a certain deformation of the immersed tunnel. Therefore, to reduce the deformation of the immersed tunnel and ensure the deformation coordination, it is necessary to adopt reasonable tunnel wall thickness.Figure 20
Strain distribution curve of the immersed tunnel bottom plate: (a) 5 kPa, (b) 10 kPa, (c) 15 kPa, and (d) 20 kPa.
(a)(b)(c)(d)Figure21 compares the numerical prediction results and the experimental results. It can be found that the curve of the numerical calculation result is similar to that of the model test, and the overall test values are greater than the calculated ones. After back-silting, the vertical strain curve of the bottom plate is saddle-shaped under the action of the soil. The strain value of the carriageway is positive, and the strain direction is upward (tension state), but the strain values of the sidewall and the partition wall of the immersed tunnel are negative (compression state). From the results data, it can be seen that with the increase of the prestress control value, the strain value is decreasing, which indicates that the increase of the prestress control value can improve the stiffness and strength of the element and reduce the deformation of the joint.Figure 21
Immersed tunnel strain curve.


## 2.1. Similarity Theory

The geometric similarity scale of this model test was 1:100 [22], and similarity criteria were obtained by the dimensional analysis method of the similarity theory and based on the similarity constant. In the model test, such physical quantities as geometric length (L), elastic modulus (E), Poisson’s ratio (μ), load (F), stress (σ), strain (ε), unit weight (γ), accelerated velocity (α), moment of inertia (I), linear displacement (ω), and angular displacement (φ) were mainly considered. Generally, the dimensionless quantities such as Poisson’s ratio, strain, angular displacement, accelerated velocity, and so on were assumed to be 1. Therefore, using the other six physical quantities to derive the similarity criterion and taking the elastic modulus and length as the basic physical quantities, the remaining four similarity criteria could be obtained. The dimensional matrix was as follows:(1)a1a2a3a4a5a6a7ωσFγILEL1−2−2−341−2F0111001.Depending on the above matrix, a linear equation set could be obtained:(2)L:a1−2a2−2a3−3a4+4a5+a6−2a7=0F:a2+a3+a4+a7=0.Then, theπ matrix could be described as follows:(3)a1a2a3a4a5a6a7ωσFγILEπ110000−10π2010000−1π3001000−1π4000101−1π500001−40.The similarity criteria were(4)π1=L−1ω,π2=E−1σ,π3=E−1F,π4=E−1γL,π5=L−4I.In this paper, plexiglass was used as the model material. The elastic modulus of plexiglass was 5.67 GPa. Since the elastic modulus of the immersed tube tunnel prototype reinforced concrete can be controlled to 34.5 GPa, the dimensional analysis method based on a similar theory could easily deduceCE=6.08.


## 2.2. Model Test

### 2.2.1. Production of the Model Box

The model box is made of a steel plate and plexiglass. The size of the model box is 3 m (length) × 1.2 m (width) × 0.6 m (height), and the size of the plexiglass is 3 m (length) × 1.2 m (width) × 0.45 m (high), as shown in Figure2. From this figure, it can be seen that the plexiglass plate is 0.15 m away from the top of the model box. This part of the gap is used by the CCD to monitor the deformation image during the test, as shown in Figure 3. The friction between the inner wall of the soil box and the model foundation has a certain influence on the model test; therefore, in order to guarantee the reliability and authenticity of the model test, the influence of the boundary effect on the model test should be reduced, and the inner wall of the model box is smeared with petroleum jelly.Figure 2
Model box.Figure 3
Monitoring of the deformed image.


### 2.2.2. Tunnel Model Making

Considering the mechanical characteristics of segment joints, similarity relationship of test, and size of the model box of the immersed tunnel under longitudinal bending conditions, the plexiglass is selected as the tunnel model material. Due to the fact that the contribution of the horizontal shear key to shearing is small, only four sets of vertical shear keys are retained in the model test, and the horizontal shear keys and other waterproof structures are not included. The prestress is simulated by controlling the tension of the prestressed steel strands at both ends of the element. The cross section of the segment joint is shown in Figure4; the size of the element model is 1.8 m (length) × 0.3795 m (width) × 0.114 m (height), as shown in Figure 5.Figure 4
Cross section of the segment joint (mm).Figure 5
Pipe joint model.


### 2.2.3. Fabrication of the Foundation Soil Model

The prototype foundation soil contains three layers, namely, silty soil, clay, and rough sand. The equivalent substitution method is adopted to substitute a single layer of soil, and considering the site conditions and the size of the model box, comprehensively, the compression modulus is selected as the control parameter. Through calculation, the compression modulus of the foundation model after equivalent substitution isES=37.51MPa [23], and according to similarity theory, the compressive modulus of the foundation soil in the model test is Es = 6.17 MPa. A mixture of commercial sand and EPS particles was used to simulate the foundation soil, and the particle size and proportion of commercial sand are 6.6% (of total mass) of 1∼2mm, 33.1% of 0.5∼1mm, 0.25∼0.5mm of 44.9%, and 0.075∼0.25mm of 13.6%, while the particle size less than 0.075 mm accounts for 1.8% of the total mass. The physical and mechanical indexes are shown in Table 2, and the particle gradation is shown in Figure 6.Table 2
Soil parameter of model foundation.
Soil sampleρ/g⋅cm−3ω/%E/MPac/MPaφ/°Foundation soil1.454.16.1710.528.1Figure 6
Grain distribution curve of test sand.


### 2.2.4. Layout of Monitoring Components

The test data acquisition system is mainly used to measure and record the test data of pressure and strain gauges. Specifically, the original data are measured by a micro earth pressure sensor (LY-350) and strain gauges, which are then transmitted through the static strain gauge data acquisition system (TDS-530), and the errors of the monitoring instruments are all less than 0.5% FS (full span). The subsidence observation data are transmitted through a noncontact measuring instrument data acquisition system (DIC), which is composed of a tripod, an industrial camera, a controller, and an image display device, as shown in Figure7. The industrial camera adopts RMOD-71-TEC rolling shutter CCD camera; the lens adopts a focal length of 16 mm; the pixel size is 3.1 × 3.1 μm; the pixel resolution 10,000 (H) × 7,094 (V); the effective image size is 31 × 22 mm; and the dynamic range is 64 db.Figure 7
Schematic diagram of the measuring instrument: (a) noncontact precision measurement systems and (b) static strain gauge.
(a)(b)This test mainly studies the vertical settlement of the element and the deformation characteristics of the section joint, and the layout position of the monitoring instruments and the schematic diagram of the noncontact measuring instruments are shown in Figures8(a) and 8(b). In these figures, S1–S7 represent the earth pressure sensors arranged along the transverse trench bottom layout, while the high-sensitivity strain gauges are arranged on the bottom and each side of the immersed tunnel to measure the strain change of the immersed tunnel during the test, as displayed in Figure 8(b). White and black matte paints are sprayed on the side walls of the longitudinal sections of the element to form speckles, and ZJ1–ZJ17 are selected as settlement observation points, as displayed in Figure 8(a).Figure 8
Layout of monitoring gauges: (a) observation point of longitudinal settlement of the element and (b) stress and strain observation point on the end face of J4.
(a)(b)


## 2.2.1. Production of the Model Box

The model box is made of a steel plate and plexiglass. The size of the model box is 3 m (length) × 1.2 m (width) × 0.6 m (height), and the size of the plexiglass is 3 m (length) × 1.2 m (width) × 0.45 m (high), as shown in Figure2. From this figure, it can be seen that the plexiglass plate is 0.15 m away from the top of the model box. This part of the gap is used by the CCD to monitor the deformation image during the test, as shown in Figure 3. The friction between the inner wall of the soil box and the model foundation has a certain influence on the model test; therefore, in order to guarantee the reliability and authenticity of the model test, the influence of the boundary effect on the model test should be reduced, and the inner wall of the model box is smeared with petroleum jelly.Figure 2
Model box.Figure 3
Monitoring of the deformed image.


## 2.2.2. Tunnel Model Making

Considering the mechanical characteristics of segment joints, similarity relationship of test, and size of the model box of the immersed tunnel under longitudinal bending conditions, the plexiglass is selected as the tunnel model material. Due to the fact that the contribution of the horizontal shear key to shearing is small, only four sets of vertical shear keys are retained in the model test, and the horizontal shear keys and other waterproof structures are not included. The prestress is simulated by controlling the tension of the prestressed steel strands at both ends of the element. The cross section of the segment joint is shown in Figure4; the size of the element model is 1.8 m (length) × 0.3795 m (width) × 0.114 m (height), as shown in Figure 5.Figure 4
Cross section of the segment joint (mm).Figure 5
Pipe joint model.


## 2.2.3. Fabrication of the Foundation Soil Model

The prototype foundation soil contains three layers, namely, silty soil, clay, and rough sand. The equivalent substitution method is adopted to substitute a single layer of soil, and considering the site conditions and the size of the model box, comprehensively, the compression modulus is selected as the control parameter. Through calculation, the compression modulus of the foundation model after equivalent substitution isES=37.51MPa [23], and according to similarity theory, the compressive modulus of the foundation soil in the model test is Es = 6.17 MPa. A mixture of commercial sand and EPS particles was used to simulate the foundation soil, and the particle size and proportion of commercial sand are 6.6% (of total mass) of 1∼2mm, 33.1% of 0.5∼1mm, 0.25∼0.5mm of 44.9%, and 0.075∼0.25mm of 13.6%, while the particle size less than 0.075 mm accounts for 1.8% of the total mass. The physical and mechanical indexes are shown in Table 2, and the particle gradation is shown in Figure 6.Table 2
Soil parameter of model foundation.
Soil sampleρ/g⋅cm−3ω/%E/MPac/MPaφ/°Foundation soil1.454.16.1710.528.1Figure 6
Grain distribution curve of test sand.


## 2.2.4. Layout of Monitoring Components

The test data acquisition system is mainly used to measure and record the test data of pressure and strain gauges. Specifically, the original data are measured by a micro earth pressure sensor (LY-350) and strain gauges, which are then transmitted through the static strain gauge data acquisition system (TDS-530), and the errors of the monitoring instruments are all less than 0.5% FS (full span). The subsidence observation data are transmitted through a noncontact measuring instrument data acquisition system (DIC), which is composed of a tripod, an industrial camera, a controller, and an image display device, as shown in Figure7. The industrial camera adopts RMOD-71-TEC rolling shutter CCD camera; the lens adopts a focal length of 16 mm; the pixel size is 3.1 × 3.1 μm; the pixel resolution 10,000 (H) × 7,094 (V); the effective image size is 31 × 22 mm; and the dynamic range is 64 db.Figure 7
Schematic diagram of the measuring instrument: (a) noncontact precision measurement systems and (b) static strain gauge.
(a)(b)This test mainly studies the vertical settlement of the element and the deformation characteristics of the section joint, and the layout position of the monitoring instruments and the schematic diagram of the noncontact measuring instruments are shown in Figures8(a) and 8(b). In these figures, S1–S7 represent the earth pressure sensors arranged along the transverse trench bottom layout, while the high-sensitivity strain gauges are arranged on the bottom and each side of the immersed tunnel to measure the strain change of the immersed tunnel during the test, as displayed in Figure 8(b). White and black matte paints are sprayed on the side walls of the longitudinal sections of the element to form speckles, and ZJ1–ZJ17 are selected as settlement observation points, as displayed in Figure 8(a).Figure 8
Layout of monitoring gauges: (a) observation point of longitudinal settlement of the element and (b) stress and strain observation point on the end face of J4.
(a)(b)


## 2.3. Loading System

### 2.3.1. Load Loading Method

In the model test, a self-balancing air pressure positive pressure loading device is used; first place the airbag above the sunk immersed tunnel model, then connect the airbag to the air pump, close the top cover of the model box, and finally apply the air pressure in stages to simulate the silt load, as shown in Figure9. The schematic diagram of the load applied by the airbag is shown in Figure 10.Figure 9
Self-balancing loading device: (a) airbag and (b) the top cover of the model box is closed.
(a)(b)Figure 10
The schematic diagram of the loading device.


### 2.3.2. Prestress Loading Method

The prestressed steel strands in the standard element of the prototype immersed tunnel are only distributed on the top and bottom plates, with a total of 60 holes. The 100% prestressing force of the standard strength of each hole is 6510 kN. Prestressed anchor cables are used to increase the positive pressure at the joints of the segments and the frictional resistance at the joints. Taking into account the purpose and implementation difficulty of the test, the model similarity theory is adopted for the model test. A self-made prestressed loading device (clip anchor, prestressed steel strand, and tensioning equipment) is used to simulate the application of the prestress of the structural model (Figure11), with axial force as the control variable. The prestress arrangement is shown in Figure 12.Figure 11
Prestressed loading device: (a) anchor, (b) prestressed steel strand, and (c) prestressed tensioning equipment.
(a)(b)(c)Figure 12
Schematic diagram of the prestress layout.


### 2.3.3. Experimental Research Contents

In the model test, five working conditions under the prestress tension values of 0, 0.2, 0.4, 0.6, and 0.8 kN were carried out. The test conditions are shown in Table3. All of these test conditions are conducted under the most unfavorable back-silting load. According to the most unfavorable back-silting load on the pipe joint, the load applied in the test was reduced by 1:6.08, with the final load of about 20 kPa. In the test, the influence of the prestress control on the settlement of the immersed tunnel, the opening of the segment joints, and the deformation characteristics of the joints under the back-silting load are studied. The testing procedures are as follows:(1)
Preliminary Preparations. First, the equipment used for testing are calibrated and debugged to ensure normal use. Then, the side walls of the element are sprayed with a matte paint to from speckles and marks. Before filling the soil, the Vaseline is smeared on the inner wall of the model box to reduce the friction effect on the side wall. Finally, the foundation soil with the designed thickness is laid into the model box in layers.(2)
Prestress Tension. At one end of the element, the prestressed tendon is fixed by the anchor, and the prestressed loading device, tension and pressure sensor, and prestressed steel strand are connected at the other end. The prestress is applied to the prestressed steel strand through the loading device until it reaches the design value. Finally, the tensioning device is removed.(3)
Loading Measurement. The noncontact measuring instrument device (DIC) and the static strain gauge are first to be debugged. After the model is settled, the airbag is placed, and the cover plate of the model box is closed. The step-by-step loading method is adopted to pressurize the airbag to simulate the back-silting load on the element until the loading is complete. At the same time as hierarchical loading, the DIC image acquisition instrument and static strain gauge are used to collect data from the observation points. After the readings of each measurement point become stable, the next loading level is performed.(4)
Uninstall. After the reading of settlement becomes stable, unloading was carried out. In this process, the element model is lifted; the foundation soil is loosened and leveled again; and the next set of working condition tests is conducted.(5)
Data from each measurement system in the test process are extracted and processed.Table 3
Test conditions.
Prestress tension degree0%20/%40/%60/%80/%Prestress tension value (kN)00.20.40.60.8


## 2.3.1. Load Loading Method

In the model test, a self-balancing air pressure positive pressure loading device is used; first place the airbag above the sunk immersed tunnel model, then connect the airbag to the air pump, close the top cover of the model box, and finally apply the air pressure in stages to simulate the silt load, as shown in Figure9. The schematic diagram of the load applied by the airbag is shown in Figure 10.Figure 9
Self-balancing loading device: (a) airbag and (b) the top cover of the model box is closed.
(a)(b)Figure 10
The schematic diagram of the loading device.


## 2.3.2. Prestress Loading Method

The prestressed steel strands in the standard element of the prototype immersed tunnel are only distributed on the top and bottom plates, with a total of 60 holes. The 100% prestressing force of the standard strength of each hole is 6510 kN. Prestressed anchor cables are used to increase the positive pressure at the joints of the segments and the frictional resistance at the joints. Taking into account the purpose and implementation difficulty of the test, the model similarity theory is adopted for the model test. A self-made prestressed loading device (clip anchor, prestressed steel strand, and tensioning equipment) is used to simulate the application of the prestress of the structural model (Figure11), with axial force as the control variable. The prestress arrangement is shown in Figure 12.Figure 11
Prestressed loading device: (a) anchor, (b) prestressed steel strand, and (c) prestressed tensioning equipment.
(a)(b)(c)Figure 12
Schematic diagram of the prestress layout.


## 2.3.3. Experimental Research Contents

In the model test, five working conditions under the prestress tension values of 0, 0.2, 0.4, 0.6, and 0.8 kN were carried out. The test conditions are shown in Table3. All of these test conditions are conducted under the most unfavorable back-silting load. According to the most unfavorable back-silting load on the pipe joint, the load applied in the test was reduced by 1:6.08, with the final load of about 20 kPa. In the test, the influence of the prestress control on the settlement of the immersed tunnel, the opening of the segment joints, and the deformation characteristics of the joints under the back-silting load are studied. The testing procedures are as follows:(1)
Preliminary Preparations. First, the equipment used for testing are calibrated and debugged to ensure normal use. Then, the side walls of the element are sprayed with a matte paint to from speckles and marks. Before filling the soil, the Vaseline is smeared on the inner wall of the model box to reduce the friction effect on the side wall. Finally, the foundation soil with the designed thickness is laid into the model box in layers.(2)
Prestress Tension. At one end of the element, the prestressed tendon is fixed by the anchor, and the prestressed loading device, tension and pressure sensor, and prestressed steel strand are connected at the other end. The prestress is applied to the prestressed steel strand through the loading device until it reaches the design value. Finally, the tensioning device is removed.(3)
Loading Measurement. The noncontact measuring instrument device (DIC) and the static strain gauge are first to be debugged. After the model is settled, the airbag is placed, and the cover plate of the model box is closed. The step-by-step loading method is adopted to pressurize the airbag to simulate the back-silting load on the element until the loading is complete. At the same time as hierarchical loading, the DIC image acquisition instrument and static strain gauge are used to collect data from the observation points. After the readings of each measurement point become stable, the next loading level is performed.(4)
Uninstall. After the reading of settlement becomes stable, unloading was carried out. In this process, the element model is lifted; the foundation soil is loosened and leveled again; and the next set of working condition tests is conducted.(5)
Data from each measurement system in the test process are extracted and processed.Table 3
Test conditions.
Prestress tension degree0%20/%40/%60/%80/%Prestress tension value (kN)00.20.40.60.8


## 2.4. Finite Element Calculation

### 2.4.1. Establishment of the Finite Element Model

The immersed element consists of eight segments, which are connected by longitudinal prestressed anchor cables and shear keys. In this paper, ABAQUS software is used to numerically simulate the foundation soil, segments, and prestress components. A three-dimensional solid calculation model of a segmental element composed of eight segments (S1∼S8) is established, as shown in Figure11. The calculation model is the same as the test model (the length of the foundation soil model is 3 m, the width is 1.2 m, the length of the tunnel model is 1.8 m, the width is 0.38 m, and the height is 0.115 m). It is assumed that the foundation soil layer is a homogeneous and isotropic medium and conforms to the Mohr–Coulomb criterion.The tunnel structure adopts a solid element; the element type is C3D8R; the material is C50 concrete; and the elastic constitutive relation is used to approximately characterize the stress of the pipe section structure, which ignores the effect of concrete plasticity on calculation results. The overall mesh size of the pipe structure is 0.5 m, and the meshing is encrypted at the joint. The three-dimensional mechanical model of the pipe joint is shown in Figures13 and 14, and the model parameters are shown in Table 4.Figure 13
Finite element analysis model.Figure 14
Grid partition schematic diagram.Table 4
Calculation parameters of numerical simulation.
Material nameMaterial propertiesParameterUnitFoundation modelWeight (γ)14.2(kN/m3)Elastic modulus (E)6.17(MPa)Cohesion (c)10.5(kPa)Friction angle (φ)28.1(°)Dilation angle (ψ)0(°)Tunnel modelWeight (γ)11.61(kN/m3)Elastic modulus (E)5670(MPa)Prestressed anchor cableElastic modulus (E)32072(MPa)


### 2.4.2. Boundary Conditions

The lateral boundary of the foundation soil model is constrained in theX direction; the longitudinal boundary is constrained in the Y direction; and the bottom is constrained in the Z direction. A segment is added at each end of the pipe joint model to apply pressure and weight, which can reduce the influence of boundary effects on the deformation characteristics of segment joints.


### 2.4.3. Definition of Contact Relationship

The calculation model includes the element-foundation soil contact surface and the segment-joint contact surface. In the mechanical model of the segment-joint contact surface, the normal mechanical model adopts the hard contact, and the tangential mechanical model adopts the penalty function for simulation. Besides, the element-soil interface is simulated by a penalty function.


### 2.4.4. Simulation of the Prestressed Anchor Cable

The segment joints of Hong Kong-Zhuhai-Macau immersed tunnels use longitudinal prestressed anchor cables to increase the positive pressure and frictional resistance, thereby improving the shear stiffness. In the finite element model, the truss element is used to simulate cable; the element type is T3D2; and the elastic constitutive relation is used to approximately present mechanical characteristics of the prestressed anchor cable. When calculation, the model adopts the “initial stress method,” at the beginning of the calculation, the initial stress of the element is defined, and prestress is applied.


### 2.4.5. Analysis of Working Conditions

In this paper, the prestress control value is set to 0, 0.2, 0.4, 0.6, and 0.8 kN as the model calculation conditions, and 20 kPa is taken as the final load of back silting (note: the actual back-silting height corresponding to the final load is 20m). The specific back siltation is simulated by staged loading of 5, 10, 15, and 20 kPa, respectively.


## 2.4.1. Establishment of the Finite Element Model

The immersed element consists of eight segments, which are connected by longitudinal prestressed anchor cables and shear keys. In this paper, ABAQUS software is used to numerically simulate the foundation soil, segments, and prestress components. A three-dimensional solid calculation model of a segmental element composed of eight segments (S1∼S8) is established, as shown in Figure11. The calculation model is the same as the test model (the length of the foundation soil model is 3 m, the width is 1.2 m, the length of the tunnel model is 1.8 m, the width is 0.38 m, and the height is 0.115 m). It is assumed that the foundation soil layer is a homogeneous and isotropic medium and conforms to the Mohr–Coulomb criterion.The tunnel structure adopts a solid element; the element type is C3D8R; the material is C50 concrete; and the elastic constitutive relation is used to approximately characterize the stress of the pipe section structure, which ignores the effect of concrete plasticity on calculation results. The overall mesh size of the pipe structure is 0.5 m, and the meshing is encrypted at the joint. The three-dimensional mechanical model of the pipe joint is shown in Figures13 and 14, and the model parameters are shown in Table 4.Figure 13
Finite element analysis model.Figure 14
Grid partition schematic diagram.Table 4
Calculation parameters of numerical simulation.
Material nameMaterial propertiesParameterUnitFoundation modelWeight (γ)14.2(kN/m3)Elastic modulus (E)6.17(MPa)Cohesion (c)10.5(kPa)Friction angle (φ)28.1(°)Dilation angle (ψ)0(°)Tunnel modelWeight (γ)11.61(kN/m3)Elastic modulus (E)5670(MPa)Prestressed anchor cableElastic modulus (E)32072(MPa)


## 2.4.2. Boundary Conditions

The lateral boundary of the foundation soil model is constrained in theX direction; the longitudinal boundary is constrained in the Y direction; and the bottom is constrained in the Z direction. A segment is added at each end of the pipe joint model to apply pressure and weight, which can reduce the influence of boundary effects on the deformation characteristics of segment joints.


## 2.4.3. Definition of Contact Relationship

The calculation model includes the element-foundation soil contact surface and the segment-joint contact surface. In the mechanical model of the segment-joint contact surface, the normal mechanical model adopts the hard contact, and the tangential mechanical model adopts the penalty function for simulation. Besides, the element-soil interface is simulated by a penalty function.


## 2.4.4. Simulation of the Prestressed Anchor Cable

The segment joints of Hong Kong-Zhuhai-Macau immersed tunnels use longitudinal prestressed anchor cables to increase the positive pressure and frictional resistance, thereby improving the shear stiffness. In the finite element model, the truss element is used to simulate cable; the element type is T3D2; and the elastic constitutive relation is used to approximately present mechanical characteristics of the prestressed anchor cable. When calculation, the model adopts the “initial stress method,” at the beginning of the calculation, the initial stress of the element is defined, and prestress is applied.


## 2.4.5. Analysis of Working Conditions

In this paper, the prestress control value is set to 0, 0.2, 0.4, 0.6, and 0.8 kN as the model calculation conditions, and 20 kPa is taken as the final load of back silting (note: the actual back-silting height corresponding to the final load is 20m). The specific back siltation is simulated by staged loading of 5, 10, 15, and 20 kPa, respectively.


## 2.5. Analysis and Verification of Test Results

### 2.5.1. Analysis of the Impact of Immersed Tube Tunnel Settlement

It can be seen from Figure15 that under the action of back-silting load, the settlement distribution of the immersed tunnel with different prestress control values are all bent downward along the longitudinal direction of the element.Figure 15
Settlement-load distribution curve: (a) 5 kPa, (b) 10 kPa, (c) 15 kPa, and (d) 20 kPa.
(a)(b)(c)(d)With the increase in the back-silting load, the settlement of the element increases. When the prestress is large, it decreases with the increase of the prestress control value. It is worth noting that the maximum settlement of each measurement line appears at the joint of the middle section of the pipe section. When the prestress control value increases from 0 to 0.8 kN, the settlement at the middle section of the pipe section under the action of the back-silting load of 5 kPa decreases from8.375×10−1mm to 7.375×10−1mm, with a reduction of 12%. And the settlement of the middle section of the element under the action of the back-silting load of 20 kPa decreases from 2.2 mm to 2.09 mm, with a decrease of 1.05 times. When the back-silting load increases from 5 kPa to 20 kPa, the settlement of the middle section of the element with the prestress control value of 0 increases by 2.63 times, and that of the element with a prestress control value of 0.8 kN increases by 2.83 times, indicating that the presence of prestress increases the overall height of the element and improves the settlement of element, but the increase of the back-silting load will increase the settlement of element.Figure16 compares the prediction results from numerical simulation and measurement results from the test. Although the experimental data are larger than the simulated data, the two settlement curves follow the same trend and are close to each other, which indicates that the numerical simulation can reflect the main settlement behavior characteristics of the model test, and the difference may be due to the simplification of the model and the complexity of the model test.Figure 16
Comparison of measured settlements and finite element analysis settlements.


### 2.5.2. Influence Analysis of Segment Joint Opening

It can be seen from Figure17 that at the end face of J4 in the middle of the element, the opening amount of the segment joint decreases with the increase of the prestress control value and increases with the increase of the back-silting load. When the prestress control value increases from 0 to 0.8 kN, the joint opening of the segment under the action of back-silting load of 5 kPa decreases from 1.37×10−1mm to 3.622×10−2mm, which is reduced 3.78 times. Under the action of the back-silting load of 20 kPa, the joint opening of the segment reduces from 3.192×10−1mm to 8.6×10−2mm, which is reduced by 3.71 times. When the back-silting load increases from 5 kPa to 20 kPa, the joint opening of the segment increases from 1.37×10−1mm to 3.192×10−1mm, which is increased by 2.32 times. Under the action of a prestress of 0.8 kN, the opening amount of the segment joints increases from 3.622×10−2mm to 8.6×10−2mm, which is increased by 2.37 times. The result coincides that the increase of the prestress control value improves the friction and shear stiffness of the segment joints, which significantly reduces the expansion of the segment joints.Figure 17
Relationships between segment joint opening and prestress control value.


### 2.5.3. Compressive Stress of the Segment Joint

It can be seen from Figure18 that under the action of back-silting load and prestress tension, the base stress at the end face of J4 in the middle of the element is in a saddle-shaped distribution. The base stress of the partition wall and side wall of the immersed structure increases with the increase of back siltation and decreases with the increase of the prestress control value. Besides, the base stress of the carriageway increases with the increase of the back siltation and also the prestress control value. When the prestress control value increases from 0 to 0.8 kN, the base stress of the carriageway under the back-silting load of 5 kPa increases from 6.68 kPa to 8.22 kPa, with an increase of 23%, and the base stress of the partition wall decreases from 9.34 kPa to 8.85 kPa, with a decrease of 5.2%, while the base stress of the side wall reduces from 12.01 kPa to 9.31 kPa, with a decrease of 22.5%. Under the action of a resulting load of 20 kPa, the base stress of the carriageway increases from 14.56 kPa to 18.77 kPa, with an increase of 28.9%, and the base stress of the partition wall decreases from 22.38 kPa to 19.32 kPa, with a decrease of 13.7%, while the base stress of the side wall decreases from 32.32 kPa to 21.67 kPa, with a decrease of 33%. When the back-silting load increases from 5 kPa to 20 kPa, the base stress of the element carriageway, partition wall, and side wall under the prestress control value of 0 kN increases by 1.18, 1.4, and 1.69 times, respectively, and the element under the prestress control value of 0.8 kN increases by 1.18, 1.4, and 1.69 times, while the base stress of the section carriageway, the partition wall, and the side wall increases by 1.28, 1.17, and 1.25 times, respectively. It shows that the application of prestress increases the vertical reaction force of the element joints and produces a homogenizing effect on the base stress.Figure 18
Distribution curve of base stress: (a) 5 kPa, (b) 10 kPa, (c) 15 kPa, and (d) 20 kPa.
(a)(b)(c)(d)Figure19 shows the stress distribution curve of the J4 basement at the segment joint under the back-silting load of 20 kPa. It can be seen that the test curve is in good agreement with the numerical calculation curve. Specifically, the bottom of the segment joint is saddle-shaped along the horizontal direction of the stress distribution, and the stress values of the sidewalls, the partition wall, and the base of the driveway decrease sequentially. With the increase of the prestress control value, the stress value in the direction of the substrate decreases, and the stress amplitude changes smoothly.Figure 19
Comparison of measured stresses and finite element analysis stresses.


### 2.5.4. Analysis of Strain Changes

It can be seen from Figure20 that under the action of back-silting load and prestress tension, the strain curve of the bottom plate of the immersed structure at the end face of J4 presents a saddle-shaped distribution. The strain value of the carriageway was positive, meaning that the part of the carriageway is under stretched, and the strain value of the side wall and the partition wall of the immersed tunnel are negative, meaning that the bottom is under compressed. From the results data, when the prestress control value increases from 0 to 0.8 kN, the strain of the immersed floor under the back-silting load of 5 kPa decreases from 7.7×10−3mm to 3.2×10−3mm, reduced by 58.4%, and the strain of the central partition wall decreases from 3.4×10−3mm to 1.75×10−3mm, reduced by 48.5%, while the strain of the side wall reduces from 11.6×10−3mm to 4.2×10−3mm, with a reduction of 63.8%. Under the action of the back-silting load of 20 kPa, the strain of the immersed floor reduces from 1.6×10−2mm to 8.9×10−3mm, with a reduction of 44.4%, and the strain of the partition wall reduces from 1.56×10−2mm to 9.5×10−3mm, with a reduction of 39.1%, while the strain of the side wall reduces from 3.24×10−2mm to 1.56×10−2mm, with a decrease of 51.9%. When the back-silting load increases from 5 kPa to 20 kPa, the strain values of the element floor carriageway, middle partition wall, and side wall under the prestress control value of 0 increase by 1.08, 3.59, and 1.79 times, respectively; the element joint floor carriageway, middle partition wall with the prestress control value of 0.8 kN, and the strain value of the side wall increases by 1.78, 4.4, and 2.71 times, respectively; which shows that due to the special structure of the immersed tunnel, the back-silting load causes a certain deformation of the immersed tunnel. Therefore, to reduce the deformation of the immersed tunnel and ensure the deformation coordination, it is necessary to adopt reasonable tunnel wall thickness.Figure 20
Strain distribution curve of the immersed tunnel bottom plate: (a) 5 kPa, (b) 10 kPa, (c) 15 kPa, and (d) 20 kPa.
(a)(b)(c)(d)Figure21 compares the numerical prediction results and the experimental results. It can be found that the curve of the numerical calculation result is similar to that of the model test, and the overall test values are greater than the calculated ones. After back-silting, the vertical strain curve of the bottom plate is saddle-shaped under the action of the soil. The strain value of the carriageway is positive, and the strain direction is upward (tension state), but the strain values of the sidewall and the partition wall of the immersed tunnel are negative (compression state). From the results data, it can be seen that with the increase of the prestress control value, the strain value is decreasing, which indicates that the increase of the prestress control value can improve the stiffness and strength of the element and reduce the deformation of the joint.Figure 21
Immersed tunnel strain curve.


## 2.5.1. Analysis of the Impact of Immersed Tube Tunnel Settlement

It can be seen from Figure15 that under the action of back-silting load, the settlement distribution of the immersed tunnel with different prestress control values are all bent downward along the longitudinal direction of the element.Figure 15
Settlement-load distribution curve: (a) 5 kPa, (b) 10 kPa, (c) 15 kPa, and (d) 20 kPa.
(a)(b)(c)(d)With the increase in the back-silting load, the settlement of the element increases. When the prestress is large, it decreases with the increase of the prestress control value. It is worth noting that the maximum settlement of each measurement line appears at the joint of the middle section of the pipe section. When the prestress control value increases from 0 to 0.8 kN, the settlement at the middle section of the pipe section under the action of the back-silting load of 5 kPa decreases from8.375×10−1mm to 7.375×10−1mm, with a reduction of 12%. And the settlement of the middle section of the element under the action of the back-silting load of 20 kPa decreases from 2.2 mm to 2.09 mm, with a decrease of 1.05 times. When the back-silting load increases from 5 kPa to 20 kPa, the settlement of the middle section of the element with the prestress control value of 0 increases by 2.63 times, and that of the element with a prestress control value of 0.8 kN increases by 2.83 times, indicating that the presence of prestress increases the overall height of the element and improves the settlement of element, but the increase of the back-silting load will increase the settlement of element.Figure16 compares the prediction results from numerical simulation and measurement results from the test. Although the experimental data are larger than the simulated data, the two settlement curves follow the same trend and are close to each other, which indicates that the numerical simulation can reflect the main settlement behavior characteristics of the model test, and the difference may be due to the simplification of the model and the complexity of the model test.Figure 16
Comparison of measured settlements and finite element analysis settlements.


## 2.5.2. Influence Analysis of Segment Joint Opening

It can be seen from Figure17 that at the end face of J4 in the middle of the element, the opening amount of the segment joint decreases with the increase of the prestress control value and increases with the increase of the back-silting load. When the prestress control value increases from 0 to 0.8 kN, the joint opening of the segment under the action of back-silting load of 5 kPa decreases from 1.37×10−1mm to 3.622×10−2mm, which is reduced 3.78 times. Under the action of the back-silting load of 20 kPa, the joint opening of the segment reduces from 3.192×10−1mm to 8.6×10−2mm, which is reduced by 3.71 times. When the back-silting load increases from 5 kPa to 20 kPa, the joint opening of the segment increases from 1.37×10−1mm to 3.192×10−1mm, which is increased by 2.32 times. Under the action of a prestress of 0.8 kN, the opening amount of the segment joints increases from 3.622×10−2mm to 8.6×10−2mm, which is increased by 2.37 times. The result coincides that the increase of the prestress control value improves the friction and shear stiffness of the segment joints, which significantly reduces the expansion of the segment joints.Figure 17
Relationships between segment joint opening and prestress control value.


## 2.5.3. Compressive Stress of the Segment Joint

It can be seen from Figure18 that under the action of back-silting load and prestress tension, the base stress at the end face of J4 in the middle of the element is in a saddle-shaped distribution. The base stress of the partition wall and side wall of the immersed structure increases with the increase of back siltation and decreases with the increase of the prestress control value. Besides, the base stress of the carriageway increases with the increase of the back siltation and also the prestress control value. When the prestress control value increases from 0 to 0.8 kN, the base stress of the carriageway under the back-silting load of 5 kPa increases from 6.68 kPa to 8.22 kPa, with an increase of 23%, and the base stress of the partition wall decreases from 9.34 kPa to 8.85 kPa, with a decrease of 5.2%, while the base stress of the side wall reduces from 12.01 kPa to 9.31 kPa, with a decrease of 22.5%. Under the action of a resulting load of 20 kPa, the base stress of the carriageway increases from 14.56 kPa to 18.77 kPa, with an increase of 28.9%, and the base stress of the partition wall decreases from 22.38 kPa to 19.32 kPa, with a decrease of 13.7%, while the base stress of the side wall decreases from 32.32 kPa to 21.67 kPa, with a decrease of 33%. When the back-silting load increases from 5 kPa to 20 kPa, the base stress of the element carriageway, partition wall, and side wall under the prestress control value of 0 kN increases by 1.18, 1.4, and 1.69 times, respectively, and the element under the prestress control value of 0.8 kN increases by 1.18, 1.4, and 1.69 times, while the base stress of the section carriageway, the partition wall, and the side wall increases by 1.28, 1.17, and 1.25 times, respectively. It shows that the application of prestress increases the vertical reaction force of the element joints and produces a homogenizing effect on the base stress.Figure 18
Distribution curve of base stress: (a) 5 kPa, (b) 10 kPa, (c) 15 kPa, and (d) 20 kPa.
(a)(b)(c)(d)Figure19 shows the stress distribution curve of the J4 basement at the segment joint under the back-silting load of 20 kPa. It can be seen that the test curve is in good agreement with the numerical calculation curve. Specifically, the bottom of the segment joint is saddle-shaped along the horizontal direction of the stress distribution, and the stress values of the sidewalls, the partition wall, and the base of the driveway decrease sequentially. With the increase of the prestress control value, the stress value in the direction of the substrate decreases, and the stress amplitude changes smoothly.Figure 19
Comparison of measured stresses and finite element analysis stresses.


## 2.5.4. Analysis of Strain Changes

It can be seen from Figure20 that under the action of back-silting load and prestress tension, the strain curve of the bottom plate of the immersed structure at the end face of J4 presents a saddle-shaped distribution. The strain value of the carriageway was positive, meaning that the part of the carriageway is under stretched, and the strain value of the side wall and the partition wall of the immersed tunnel are negative, meaning that the bottom is under compressed. From the results data, when the prestress control value increases from 0 to 0.8 kN, the strain of the immersed floor under the back-silting load of 5 kPa decreases from 7.7×10−3mm to 3.2×10−3mm, reduced by 58.4%, and the strain of the central partition wall decreases from 3.4×10−3mm to 1.75×10−3mm, reduced by 48.5%, while the strain of the side wall reduces from 11.6×10−3mm to 4.2×10−3mm, with a reduction of 63.8%. Under the action of the back-silting load of 20 kPa, the strain of the immersed floor reduces from 1.6×10−2mm to 8.9×10−3mm, with a reduction of 44.4%, and the strain of the partition wall reduces from 1.56×10−2mm to 9.5×10−3mm, with a reduction of 39.1%, while the strain of the side wall reduces from 3.24×10−2mm to 1.56×10−2mm, with a decrease of 51.9%. When the back-silting load increases from 5 kPa to 20 kPa, the strain values of the element floor carriageway, middle partition wall, and side wall under the prestress control value of 0 increase by 1.08, 3.59, and 1.79 times, respectively; the element joint floor carriageway, middle partition wall with the prestress control value of 0.8 kN, and the strain value of the side wall increases by 1.78, 4.4, and 2.71 times, respectively; which shows that due to the special structure of the immersed tunnel, the back-silting load causes a certain deformation of the immersed tunnel. Therefore, to reduce the deformation of the immersed tunnel and ensure the deformation coordination, it is necessary to adopt reasonable tunnel wall thickness.Figure 20
Strain distribution curve of the immersed tunnel bottom plate: (a) 5 kPa, (b) 10 kPa, (c) 15 kPa, and (d) 20 kPa.
(a)(b)(c)(d)Figure21 compares the numerical prediction results and the experimental results. It can be found that the curve of the numerical calculation result is similar to that of the model test, and the overall test values are greater than the calculated ones. After back-silting, the vertical strain curve of the bottom plate is saddle-shaped under the action of the soil. The strain value of the carriageway is positive, and the strain direction is upward (tension state), but the strain values of the sidewall and the partition wall of the immersed tunnel are negative (compression state). From the results data, it can be seen that with the increase of the prestress control value, the strain value is decreasing, which indicates that the increase of the prestress control value can improve the stiffness and strength of the element and reduce the deformation of the joint.Figure 21
Immersed tunnel strain curve.


## 3. Conclusion

(1)
Under the action of back-silting load and different prestress control values, the settlement of element is in a downward bending posture, with a large value appearing in the middle and a small value appearing at both ends. The settlement and the segment joint openings decrease with the increase of the prestress control value and show a linear increasing trend with the increase of back-silting load. It shows that the increase of the back-silting load will increase the element settlement and the expansion of the segment joints, but the application of prestress increases the overall stiffness of the element, which can effectively restrain the settlement of element and the expansion of joints. Therefore, in the long-term stable design of the immersed tunnel, prestress should be applied to the immersed element structures to ensure their relative stability. During the operation period, the silt should be cleaned regularly to reduce the impact of back siltation on the immersed pipe structure and further ensure the safety of segment joints.(2)
The prestress control values have a significant influence on the stress and strain distribution of immersed structure. Under the action of prestress control, the base stress of immersed structure and the strain curve of immersed bottom plate distributes in a saddle shape. When the prestress control value increases from 0 to 0.8 kN, the base stress of the carriageway increases by 23%∼28.9%, and the strain value decreases by 44.4%∼58.4%, and the base stress of the partition wall and the side wall decreases by 5.2%∼13.7% and 22.5%∼33%, respectively, while the strain values decrease by 39.1%∼48.5% and 51.9%∼63.8%, respectively; It is indicated that the application of prestress improves the stiffness of the tube section, enables the tube section to bear the external load, and allows the external load to be transmitted along the longitudinal direction of the tube section so that the stress curve distribution of the tunnel foundation is smooth. At the same time, the prestress increases the vertical reaction force of the tube section, makes the base stress become even, controls the relative displacement of the section joint effectively, and reduces the deformation capacity of the immersed tube structure.(3)
The settlement curve and stress-strain curve obtained by the finite element show the same trend and similar values to the measured values of the model test, which further verifies the reliability of the model test.(4)
Since this article mainly studies the deformation characteristics of the segment joints under the back-silting load and prestress tension, in the next stage of the study, the dispersion of foundation stiffness, uneven back siltation, and uneven loss of prestress should be considered comprehensively. The model test conducted in the present work studied the mechanical performances of the segmental joints and the effect of corresponding influencing factors.



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*Source: 7152132-2022-06-10.xml*