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(1a.State Key Laboratory of Hydraulic Engineering Simulation and Safety;b.School of Civil Engineering,Tianjin University,Tianjin 300072,China;2.The Second Engineering Co.,Ltd.of CCCC First Harbor Engineering Co.,Ltd.,Qingdao 266071,China;3.CCCC First Harbor Engineering Co.,Ltd.,Tianjin 300461,China;4.CCCC Highway Consultant Co.,Ltd.,Beijing 100007,China)

Abstract:During the immersion operation of an immersed tunnel element,the immersed tunnel element is always hung by vertical lines and then connected to the immersion installation vessel.It is difficult to accurately determine the force of the vertical lines and the motion state of the immersed tunnel element due to the action of high-intensity ocean currents in the process of hoisting.Experimental investigation on motion responses of an immersed tunnel element under the action of waves and highintensity ocean currents was carried out.The forces on the vertical lines,mooring line and installation cable were collected and the influence of waves and high-intensity ocean currents on the forces was analyzed.The displacement in six directions of the immersed tunnel element during the process of sinking was recorded in real time and the displacement data were used to achieve high precision installation of the immersed tunnel element.The numerical simulation of the sinking of the immersed tunnel element was carried out.Comparison of the experimental results with the numerical simulation results shows that the experimental results are in good agreement with the simulation ones.The numerical analysis method can be used to simulate similar engineering operations.

Key words:immersed tunnel;immersion;mooring cable force;installation cable system;mechanical value

0 Introduction

The development of the world’s immersed tunnel technology for transportation began in 1910.More than 150 immersed tunnels have been built around the world since that time.With the development of science and technology and the accumulation of construction experience,more and more attention has been paid to the key parameters of the construction process of the immersed tube tunnel.The study of sinking construction(e.g.,?resund immersed tunnel in Europe,the Busan-Geoje immersed tunnel in South Korea,the Bosphorus Marmaray Tunnel)makes it necessary to carry out hydrodynamic tests[1-2].During the immersed tunnel construction process,the influence of the dynamic response on the sinking process also changes with the water depth and environmental conditions.An immersed tunnel element weighs around 20 000～80 000 tons,which can be regarded as a super-large component.The technical parameters of the dynamic response during the sinking process are essential for constructability and safety,especially for maintaining the cable force of immersion rigs and the movement of tunnel elements in precise sinking operations.Also,the dynamic response of an immersed tube is also very sensitive to the environmental conditions[3].Therefore,the success of the immersed tube installation and the entire project depends on the dynamic response of the immersed tunnel construction,especially the influence of the ship motions on the movement of the submerged tube element when the installation ship is in its coupled state of suffering from the fluid force over and under the sea surface.Hence,the dynamic response of the system is the key to the construction of the immersed tunnel[4-5].

A review of the relevant literatures indicates that very little information is available on the force of the vertical lines and motions of the immersed tunnel element due to the action of high-intensity ocean currents in the process of hoisting.It has become increasingly evident that accurate determination of cable force and immersed tunnel element displacement are two major factors contributing to installation accuracy of an immersed tunnel element under water.Therefore,based on the hydrodynamic analysis method,multi-directional flow in fluid mechanics and ship-tube cable coupling,a finite element model based on the immersed tunnel works of the Hong Kong-Zhuhai-Macao Bridge was established to analyse the force on the vertical lines,mooring lines,installation cables and the displacement in six directions of the immersed tunnel elements during the process of sinking.The simulation results are compared with the actual test results.

1 Construction parameters

1.1 General descriptions

The Hong Kong-Zhuhai-Macao Bridge(HZMB),situated at the waters of Lingdingyang of Pearl River Estuary,is a large sea crossing linking the Hong Kong Special Administrative Region(HKSAR),Zhuhai City of Guangdong Province and Macao Special Administrative Region.The island-and-tunnel section,a key part of the main bridge,consists of two artificial islands and an immersed tunnel,the latter of which is one of the most challenging constructions.The immersed tube section in the open sea is 5 664 m long,consisting of 33 tunnel elements.A typical tunnel element is 180 m long,37.95 m wide and 11.4 m high,with a mass of approximately 80 000 t.The deepest water depth for immersion is around 46 m.

Combined with the measured data of the environmental conditions around the project area,when an immersed tunnel element is in the mooring state,the following conditions are most representative:(1)the angle between the direction of wave action and the axis of the immersed tunnel element is 90 degrees;(2)the wave height is 0.8 m,and the flow rate is 0.6 m/s;(3)the angle between high-intensity ocean currents under water and the axis of the immersed tunnel element is 90 degrees.

1.2 Technical parameters

The main technical parameters governing tunnel installation are sea state parameters and sinking depth of an immersed tunnel element[1].These parameters are selected by a combined consideration of availability of weather and marine conditions,sea water density and the ability of construction facilities.

The mooring and sinking processes of an immersed tunnel element are shown in Fig.1.The technical parameters of an immersed tunnel element installation vessel are shown in Tab.1.

Tab.1 Technical parameters of immersion installation vessel

Fig.1 Schematic diagram of immersion installation vessel

The negative buoyancy of the immersed tunnel element was controlled at 1.5% of the total weight of the immersed tunnel element[2],or 12 000 kN in the study.

The immersed tunnel element was lifted at four lifting points,each undertaking an average force of 3 000 kN.

Mooring lines were used to resist the forces from waves and currents[3].Eight cables(M1-M8,as shown in Fig.2)were deployed on the sinking barge to keep the positions of the tunnel element and the immersion rigs and to resist the currents in the field;five installation cables(H1-H5,as shown in Fig.2)were used to assist the installation of the tunnel elements.

Fig.2 Layout of the cable system of an immersed tunnel element in mooring state

2 Numerical analysis

2.1 Numerical model

The immersed tunnel element and the immersion installation vessel were modeled using the software of Deep C.The dynamic analysis in time domain was performed using the software of OrcaFlex.The immersed tube sinking model is shown in Fig.3.

Fig.3 Immersed tube sinking model

The sign conventions are as follows:Xis positive from the stern,perpendicular to the bow;Yis positive from the ship centerline to the port side;andZis positive upward from the baseline.A three-dimensional potential flow model was generated in AQWA,with additional data,including the added mass coefficients,damping coefficients and wave forces obtained in a hydrodynamic analysis and directly imported into the Orcaflex program.

The sinking process of the immersed tunnel element was simulated according to the actual operation duration,which was more than 6 hours.The typical working conditions(waveHs=0.8 m,waveTp=0.6 s,flow rate=0.6 m/s,env.dir.=90°)and time history of sinking tunnel element were shown in Fig.4.

Fig.4 Typical working condition and time history of sinking tunnel element

2.2 Results and analysis

In the sinking process of the immersed tunnel element,the force acting on the immersed tunnel element was more complicated due to the fact that there was no restoring force in the heave direction when the area in the waterline was zero[4].In order to find out the characteristics of the heave and roll responses of the immersed tunnel element,a parametric analysis was performed.

Fig.5 and Fig.6 show the RAO curves of the heave and roll of the immersed tunnel element under the cross-wave condition.It can be seen that as the immersion depth of the immersed tunnel element increases,the responses of the heave and roll become smaller[5].The reason is that the circular motion of the water particle decreases exponentially along the depth.When the wave period is below 6 s(the frequency is greater than 1 rad/s),the heave and roll responses of the tunnel elements are very small and stable[6],and the hanging cable load is mainly influenced by the response of the immersion rigs.

Fig.5 Heave RAO curve in different drafts

Fig.6 Roll RAO curve in different drafts

The cable force and movement results of the immersed tunnel element during the waiting and installation are shown in Tab.2.

Tab.2 Working conditions of immersed tunnel element installation

3 Physical model test analysis

3.1 Principal dimension and similarity of the test model

The scale between the model and prototype is 1:40,and the principal dimensions are shown in Tab.3.The sea state parameters for irregular waves test are given in Tab.4.The base groove model test conditions are shown in Tab.5.

Tab.3 Immersed tunnel element principal dimensions

Tab.4 Sea state parameters for irregular waves test

Tab.5 Base groove model test conditions

3.2 Test results

Under the combined effects of waves and currents,the motion response of the immersion installation vessel and the tunnel element in working conditions is relatively small[7],and the motion response of the immersed tunnel element is more gradual than that of the installation vessel.For the full-amplitude motion response,the deeper the sinking depth,the more intense the response of the immersion installation vessel,and the smaller the tunnel element motion response.With the measurement accuracy of the non-contact measuring system taken into consideration,under the three working conditions,the motion response gap of the immersion installation vessel is very small,and that of immersed tunnel element is also small.In addition,the motion response value of the immersed tunnel element itself is small while the installed non-contact measuring system has a certain displacement from the center of gravity of the immersed tunnel element.The measurement error will be further amplified during the conversion process,resulting in the motion response value of the immersed tunnel element to be larger than the actual value.

When the immersed tunnel element enters the water(C1 condition),the motion response of the immersion installation vessel is the smallest.The displacement under the conditions of a surge of 0.17 m,a sway of 0.39 m,a heave of 0.30 m,a pitch of 0.21°,a roll of 0.51° and a yaw of 0.18° is the largest.The immersion installation vessel has the maximum response when the immersed tunnel element reaches the seabed(C3 condition).The displacement of immersion installation vessel under the conditions of a surge of 0.24 m,a sway of 0.39 m,a heave of 0.47 m,a pitch of 0.23°,a roll of 0.95°and a yaw of 0.20°is the largest.

When the immersed tunnel element enters the water,it has the largest response.The motion response of the immersed tunnel element is the smallest when it reaches the seabed(C3 condition).

Tab.6 shows the statistical values of the six-degree-of-freedom motion responses of the immersed tunnel element in the three conditions(C1-C3).The six-degree-of-freedom motion responses of the immersed tunnel element under the conditions of C1-C3 are shown in Tab.7.

Tab.6 Statistical motion response values of the immersed tunnel element under various working conditions

Tab.7 Maximum and minimum tension forces of the immersed tunnel element under C1-C3 conditions

Tab.7(Continued)

4 Test and calculation results with engineering application analysis

According to the results of the numerical simulation calculation and the physical model test,at the time when the immersed tunnel element sank,the cable forces obtained are shown in Tab.8.

Tab.8 Statistical comparison results between numerical simulation calculations and physical model test

According to the analysis results,under the combined effects of waves and currents,the sixdegree-of-freedom motion responses of the immersion installation vessel and the immersed tunnel element are small in its working state,and the motion response of immersed tunnel element is smaller than that of the immersion installation vessel.In addition,it should be noted that the immersed tunnel element has a small motion response value,and the installed non-contact measuring system has a certain displacement from the center of gravity for the immersed tunnel element.The system measurement tolerance will be further amplified during the conversion process,resulting in the motion response value of the immersed tunnel element higher than the actual situation.Under different base groove forms,the deeper the sinking depth,the greater the peak value of the tension in each hanging vertical lines and the handling line.In different groove forms,generally the deeper the immersed tunnel element,the greater the peak tension of each suspension cable and installation cable.

Based on the data obtained from these results,the numerical values of mooring anchors,mooring lines,and lifting lines of a sinking barge are determined.Combined with a physical model test and numerical simulation calculation,the maximum values of the immersed tunnel element lifting force from the numerical calculations and the physical model test are 4 115 kN and 4 262 kN,respectively,and the minimum values are 308 kN and 218 kN,respectively.The maximum difference between experimental results and the simulation results is 147 kN,with a deviation of 3.4%,and the minimum difference between experimental results and the simulation results is 90 kN,with a deviation of 29%.The maximum value of the mooring cable force according to experimental results and the simulation results are 878 kN and 955 kN,respectively,and the maximum difference is 77 kN,with a deviation of 8.1%.

By deviation analysis,the above values are all within the control range,but for the minimum value of the hanging force while sinking,the control point should be determined by the situation in which the immersed tunnel element and the immersion installation vessel are not detached.According to the above analysis,the vertical lines should be selected when the control value of the total lifting force is 4 262 kN and the control value of the mooring cable force is 955 kN.The safety of the immersed tunnel element can be guaranteed during the sinking process of the immersed tunnel element.Upon concluding the above numerical analysis research,the sinking and mooring equipment were determined and prepared.The effect and real diagram of the immersed tunnel element installation is shown in Fig.7.

Fig.7 Effect and real diagram of immersed tunnel element installation

During the sinking process,the data of the displacement in three directions of the immersed tunnel element were tested.The slope of an immersed tunnel element was marked with 4 points according to the reaching seabed position at the bottom of the immersed tunnel element.

From May,2013 to March,2017,the research results were validated by the construction of the immersed tunnel construction of the Hong Kong-Zhuhai-Macao Bridge,where 33 large-scale immersed tunnel elements were successfully installed.The sinking and docking time of an immersed tunnel element was controlled to be approximately 12 h.The monitored underwater motion data of the immersed tunnel element were consistent with the predicted results.

5 Conclusions

After verification and validation among the model test,the numerical simulation analysis and engineering application,some conclusions are derived as follows:

(1)The positioning methods of different immersed tunnel elements during mooring and sinking are explored.By means of numerical simulation and physical model test,using the coupling principle of the immersed tunnel element and the immersion installation vessel under hydrodynamic action,the total control value of the sinking lifting force is 4 262 kN,with a deviation of 3.4%,and the control value of the mooring cable force is 955 kN,with a deviation of 8.1%.Both of the deviations were controlled within 10%.

(2)According to the test and field monitoring data,the motion response of the immersion installation vessel is the lowest when the immersed tunnel element enters the water.

(3)The immersion rig has the maximum coupling motion response when the immersed tunnel element comes close to the seabed.The immersed tunnel element has the largest motion response when it enters the water.The immersed tunnel element has the minimum motion response when it reaches the seabed.

(4)Through the field application validation,the numerical results obtained by the combination of numerical simulation and physical model tests provide both a better understanding of the immersion system of an immersed tunnel and a guidance for further studies.

(5)The results in the paper have great significance to effectively decrease risks,which include economic loss,safety issues and other unpredictable concerns during large-scaled immersed tunnel construction.These factors will certainly affect the quality and period of engineering construction.Undoubtedly,expericences of the test and numerical simulation in the paper can be applied to similar design and engineering construction of underwater component sinking equipment in port engineering,ocean engineering and other related fields,as well as the Shenzhen-Zhuhai tunnels and other immersed tunnel projects.