A long and large suspended tunnel two-way fluid-solid coupling calculation method under wave environment

Abstract

The application relates to a long and large suspended tunnel bidirectional fluid-structure coupling calculation method under a wave environment, and belongs to the field of marine engineering suspended tunnel structure design. In view of the problems of low calculation efficiency, neglect of structure disturbance to a flow field and incapability of processing complex topography of the existing method, a modeling strategy based on a two-dimensional potential flow wave tank group is provided: key sections are divided along a tunnel axis to establish independent water tanks, section wave loads are obtained by parallel solving of mathematical models of the water tanks, full pipe body load distribution is calculated by interpolation, and dynamic interaction of fluid motion and pipe body vibration is realized by bidirectional coupling iteration. The application efficiently processes kilometer-level suspended tunnel fluid-structure coupling calculation, significantly improves wave load precision, can simulate multidirectional waves and complex seabed topography, comprehensively outputs section forces and moments, is excellent in numerical stability, and provides a reliable analysis means for suspended tunnel engineering design.

Description

A Two-Way Fluid-Structure Coupling Calculation Method for Long Suspended Tunnels in Wave Environment Technical Field

[0001] This invention belongs to the field of marine engineering suspended tunnel structure design, and relates to a two-way fluid-structure interaction calculation method for long suspended tunnels in wave environments. Background Technology

[0002] Suspended tunnels, as a novel type of transportation structure spanning waterways, possess advantages such as large spanning capacity, strong adaptability to deep-water construction, all-weather operation, and excellent environmental and economic benefits, and are considered the most promising underwater transportation solution of the 21st century. However, due to the incomplete understanding of the interaction mechanism between the tunnel body and the fluid in the complex marine environment, especially the insufficient research on the fluid-structure interaction dynamic response characteristics of long suspended tunnel bodies under wave loads, there is still a lack of practical engineering application cases worldwide.

[0003] In traditional methods, the Morrison equation is commonly used to calculate wave loads on suspended tunnels. However, this method is based on semi-empirical theory, assuming that the disturbance of the structure to the wave field is negligible. Its calculation accuracy is highly dependent on the hydrodynamic coefficient of the cross section, requiring pre-calibration through physical or numerical experiments, a cumbersome process with poor universality. Furthermore, the Morrison equation cannot account for the influence of seabed topography on the flow field, nor can it calculate the torque effect of fluid loads on the cross section, severely limiting its applicability in complex marine environments and the analysis of large-scale flexible tube structures. On the other hand, while computational fluid dynamics methods can achieve full flow field simulation, their computational resource consumption is enormous, making it difficult to meet the efficiency requirements of fluid-structure interaction analysis for kilometer-scale suspended tunnels.

[0004] Therefore, how to efficiently handle the two-way fluid-structure interaction problem of long suspended tunnels in wave environments while ensuring computational accuracy, accurately predicting the dynamic response of the tunnel body, and simultaneously being compatible with complex seabed topography and multi-directional wave conditions has become a technical bottleneck restricting the engineering application of suspended tunnels. The shortcomings of existing methods in terms of computational efficiency, accuracy, and applicability urgently necessitate the development of a novel fluid-structure interaction calculation method. Summary of the Invention

[0005] In view of this, the purpose of this invention is to provide a calculation method for bidirectional fluid-structure interaction of long suspended tunnels in wave environments, which solves the calculation problem of bidirectional fluid-structure interaction of suspended tunnels in wave environments.

[0006] To achieve the above objectives, the present invention provides the following technical solution:

[0007] A method for bidirectional fluid-structure interaction calculation of long suspended tunnels in a wave environment includes the following steps:

[0008] Step 1: Divide the suspended tunnel axis into multiple sections, and establish a two-dimensional potential flow wave tank at each section location to form a tank group. The two-dimensional potential flow wave tank is based on the ideal fluid potential flow theory to simulate the wave field.

[0009] Step 2: Solve the mathematical model of each two-dimensional potential flow wave tank to obtain the velocity potential function of each section. The mathematical model includes the governing equations, boundary conditions and initial conditions.

[0010] Step 3: Calculate the wave load at each section based on the velocity potential function, and obtain the overall wave load distribution of the suspended tunnel through the interpolation function;

[0011] Step 4: Update the pipe motion state according to the wave load, and simultaneously update the surface boundary conditions of the water tank. Perform time step progression to realize fluid-structure interaction iterative calculation.

[0012] Furthermore, the spacing between the multiple sections in step one is determined based on the flexible vibration characteristics of the suspended tunnel tube, and the spacing between adjacent sections is no greater than 1 / 4 of the characteristic wavelength of the incident wave.

[0013] Furthermore, in step two, the two-dimensional potential flow wave tanks are independent of each other, and the wave incident conditions of each tank are set independently, allowing for the specification of different incident wave parameters and seabed topography parameters.

[0014] Furthermore, the boundary conditions in step two include inlet boundary conditions:

[0015]

[0016] Export boundary conditions:

[0017]

[0018] in, Let U be the incident wave velocity potential function. o R is the velocity potential function of the emitted wave. m S is a buffer function. l and S r These are the entrance and exit boundaries, respectively.

[0019] Furthermore, the buffer function is defined as follows:

[0020]

[0021] Among them, T m The buffer period is set to twice the characteristic period of the incident wave.

[0022] Furthermore, the wave load calculation in step three employs a high-order difference scheme based on the body derivative:

[0023]

[0024] Where Δt is the time step, and t0, t1, t2, and t3 are four consecutive time nodes.

[0025] Furthermore, the time progression in step four adopts a fourth-order explicit Adams scheme:

[0026]

[0027] Where Y is a state vector containing the position vector of the free surface nodes and the velocity potential.

[0028] Furthermore, in step two, the boundary element method is used to solve the governing equations. The Laplace equations are transformed into integral equations and then discretized using quadratic isoparametric elements to form a system of algebraic equations:

[0029] [A]{ψ}={b}

[0030] Where [A] is the coefficient matrix, {b} is the augmented coefficient, and {ψ} is the unknown quantity at the boundary node.

[0031] Furthermore, the expression for calculating the wave load distribution in step three is as follows:

[0032]

[0033] Among them, F w (x,t) represents the wave load distribution vector of the suspended tunnel pipe at position x and time t; x is the position coordinate along the pipe's axis; t is the time variable; g u g w g θ F represents the interpolation functions for the horizontal, vertical, and torsional directions, respectively. tuS (t) Horizontal wave load at the s-th section; F twS (t) Vertical wave load at the s-th section; F tθS (t) The torsional wave moment about the centroidal axis of the s-th section, where the counterclockwise direction is positive.

[0034] Furthermore, the method includes a wave height detection and verification step: a detection point is set in front of the structure, and the wave height time history curves calculated by potential flow theory and CFD are compared. The calculation is deemed valid when the error of the height of five consecutive wave peaks is less than 5%.

[0035] The beneficial effects of this invention are as follows:

[0036] The proposed two-way fluid-structure interaction calculation method for long suspended tunnels in wave environments can efficiently and accurately handle the dynamic response calculation problem of long suspended tunnels in wave environments. Compared with the current mainstream CFD simulation and Morison equation calculation methods, its significant advantages are:

[0037] (1) The modeling method based on two-dimensional potential flow wave flume group significantly reduces the consumption of computing resources by ignoring fluid viscosity and adopting a parallel solution strategy for key sections, breaking through the efficiency bottleneck of traditional computational fluid dynamics methods in full-basin simulation, and realizing efficient analysis of the dynamic response of kilometer-level suspended tunnels.

[0038] (2) The two-way fluid-structure interaction iterative algorithm is adopted to dynamically update the boundary conditions of the object surface in each time step, fully reflecting the disturbance effect of the structure motion on the flow field, overcoming the inherent defect of the Morrison equation ignoring the influence of the structure on the flow field, and making the wave load calculation more in line with the actual physical process.

[0039] (3) Each two-dimensional potential flow wave tank supports independent setting of incident wave parameters and seabed topography, which can simulate complex working conditions such as multi-directional irregular waves and local topographical changes. It breaks through the traditional method's assumption of uniform wave field and flat terrain, and expands the engineering applicability of suspended tunnel design.

[0040] (4) The horizontal force, vertical force and torque of the cross section can be directly solved by integrating the pressure on the structural surface, avoiding the limitation of the Morrison equation in calculating torque, and providing more complete load input conditions for the design of the suspended tunnel anchor cable system.

[0041] (5) By combining the high-order volume derivative difference scheme with the fourth-order explicit Adams time-progression method, numerical oscillations caused by free surface grid distortion are effectively suppressed while ensuring computational accuracy, thus ensuring the stability of ultra-long time domain simulation.

[0042] (6) The shape of the object surface boundary is flexibly defined by the discretization of the quadratic isoparametric element, which can accurately describe the fluid load distribution of complex cross-sections such as circles, ellipses, and polygons, providing a reliable analysis tool for the design of irregular cross-section suspended tunnels.

[0043] Other advantages, objectives, and features of the invention will be set forth in part in the description which follows, and in part will be apparent to those skilled in the art from the following examination, or may be learned from practice of the invention. The objectives and other advantages of the invention can be realized and obtained through the following description. Attached Figure Description

[0044] To make the objectives, technical solutions, and advantages of the present invention clearer, the preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings, wherein:

[0045] Figure 1 shows a typical suspended tunnel structure and a schematic diagram of the coordinate system of this method;

[0046] Figure 2 is a schematic diagram of the two-way fluid-structure interaction calculation model for a suspended tunnel;

[0047] Figure 3 is a schematic diagram of a two-dimensional potential flow wave flume model;

[0048] Figure 4 is a schematic diagram of the discretization of the quadratic boundary element;

[0049] Figure 5 shows the construction of the equally spaced high-order difference scheme for the volume derivative;

[0050] Figure 6 is a flowchart of the two-way fluid-structure interaction calculation for a suspended tunnel;

[0051] Figure 7 shows the wave height time history at the detection point 40m in front of the structure;

[0052] Figure 8 shows the time history diagram of wave load;

[0053] Figure 9 shows a comparison of the peak horizontal and vertical displacements and wave loads under stable vibration conditions. Detailed Implementation

[0054] The following specific examples illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of the present invention. Unless otherwise specified, the following embodiments and features can be combined with each other.

[0055] The accompanying drawings are for illustrative purposes only and are schematic diagrams, not actual pictures. They should not be construed as limiting the invention. To better illustrate the embodiments of the invention, some parts in the drawings may be omitted, enlarged, or reduced, and do not represent the actual product dimensions. It is understandable to those skilled in the art that some well-known structures and their descriptions may be omitted in the drawings.

[0056] In the accompanying drawings of the embodiments of the present invention, the same or similar reference numerals correspond to the same or similar components. In the description of the present invention, it should be understood that if terms such as "upper," "lower," "left," "right," "front," and "rear" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the drawings, they are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, the terms used to describe positional relationships in the drawings are only for illustrative purposes and should not be construed as limiting the present invention. For those skilled in the art, the specific meaning of the above terms can be understood according to the specific circumstances.

[0057] Figure 1 shows a schematic diagram of a typical suspended tunnel structure, with the coordinate system as shown. The origin of the world coordinate system is located on the still water surface, the length direction of the tube is the X-axis, and the Z-axis is perpendicular to the water surface and upwards. A right-handed coordinate system is used, and the cross-section at the left revetment end of the tube is coplanar with the YZ plane. The displacement components of each position of the tube are represented by u(x,t), w(x,t), and θ(x,t), respectively, in the horizontal, vertical, and torsional directions around the centroidal axis of the cross-section. u and w are taken as positive in the positive directions of the Y and Z axes, respectively, and θ is taken as positive in the counterclockwise rotation shown in the figure.

[0058] A method for bidirectional fluid-structure interaction calculation of long suspended tunnels in a wave environment includes the following steps:

[0059] Step 1: Establish a two-dimensional potential flow wave tank assembly.

[0060] First, several sections are divided along the axis of the suspended tunnel, as shown in Figure 2. A two-dimensional potential flow wave tank is then constructed at each section to form a two-dimensional potential flow wave tank group. The two-dimensional potential flow wave tank is a mathematical model simulating fluid motion in the tank based on the potential flow theory of ideal fluids. By solving this mathematical model, the horizontal, vertical, and torsional fluid loads on the pipe sections can be calculated. Finally, after calculating the wave loads on all the divided pipe sections, the wave loads at other locations are calculated using interpolation methods and applied to the pipe as distributed forces. The calculation expression for the fluid loads is as follows:

[0061]

[0062] In the above formula, F wu F ww and F wθ These represent the fluid load distribution in three directions; g u g w and g θ These represent the interpolation functions in the three directions; F tus F tws and Ftθs These represent the wave loads in three directions at the s-th cross-section of the tube at a certain moment.

[0063] It is important to note that the two-dimensional potential flow wave tanks in this computational model are independent of each other. That is, the fluids in each tank do not affect each other's motion. The motion of the fluid in each tank is coupled only to the motion of the pipe cross-section. The position and velocity of each point on the pipe cross-section are transmitted to the potential flow tank as boundary conditions. Because of this characteristic, the solutions for each potential flow tank can be calculated in parallel within a single sub-loop calculation at the same time step, with thread or process synchronization only required when calculating the fluid distribution load. This significantly improves computational efficiency.

[0064] Step 2: Solve the mathematical model of the two-dimensional potential flow wave tank.

[0065] The two-dimensional potential flow wave tank is a mathematical model based on potential flow theory to simulate fluid motion in a tank, as shown in Figure 3. The width of the tank is b, the width of the water tank is d, and the bottom boundary of the tank is S. d The free water surface boundary is S u The left end is the entrance boundary S l The right end is the exit boundary S r The surface boundary of the structure is S b The entire flume region is denoted as Ω, and the flume is located on the YZ plane. Waves propagate from the left end to the right end, and wave-absorbing zones, also known as artificial beaches, are set at the left and right boundaries to absorb incident waves propagating to the outlet boundary and reflected waves reflected from the structure surface to the inlet and outlet boundaries, eliminating the influence of secondary wave reflections on the dynamic response calculation of the structure. Potential flow wave flumes treat the fluid within the flume as an inviscid, irrotational, incompressible fluid, and have been widely used in marine engineering, especially in the study of wave-structure interactions. The fundamental unknown in potential flow theory is the velocity potential function. According to the assumption of irrotational flow, the gradient of the velocity potential function is the velocity vector in the flow field, that is:

[0066]

[0067] In the above formula, Let be the Nabla differential operator, and u be the velocity vector function of the flow field. In a two-dimensional potential-flow wave tank, the differential governing equations (Laplace equations) satisfied by the velocity potential function are as follows:

[0068]

[0069] In the above formula, t represents time, η is the free water surface height function; z0 is the initial water surface position; X = (y, z) is the position vector of the fluid particles on the free water surface; D / Dt is the volume derivative (mass derivative) differential operator, i.e.:

[0070]

[0071] n is the unit outward normal vector of the boundary, pointing to the region outside the computational domain Ω; V is the velocity vector of the wall point; Let be the velocity potential function of the incident wave; The velocity potential function of the outgoing wave is usually specified as the velocity potential function of the water flow or still water region; and These are the free surface height function and the velocity potential function of the incident wave, respectively; and Let μ1 and μ2 be the free surface height function and velocity potential function of the outgoing wave, respectively, and let μ1 and μ2 be the damping functions of the inlet and outlet boundaries, respectively. Their expressions are as follows:

[0072]

[0073] In the above formula, α d and β d The damping coefficient is typically taken as 1.0; ω w and L w y1 and y2 represent the characteristic frequency and characteristic wavelength of the incident wave, respectively; y1 and y2 are the starting positions of the left and right wave-damping relaxation regions. To ensure the wave-damping effect, the distance from the starting position of the wave-damping relaxation region to the boundary is at least one characteristic wavelength. Since the velocity potential function and gradient of the entire flow field are usually set to 0 at the initial moment, the sudden addition of non-zero boundary conditions will cause numerical discontinuities. To ensure the stability of numerical calculations, buffer functions need to be added at the inlet and outlet boundaries and the free surface boundary.

[0074]

[0075] Among them, T m The buffer period is typically twice the characteristic period of the incident wave.

[0076] This invention solves the velocity potential control equation using the boundary element method. Based on the fundamental theory of the boundary element method, the Laplace equation satisfied by the velocity potential is first transformed into an integral equation using the second Green's formula. Then, the boundary element is discretized using quadratic isoparametric elements, as shown in Figure 4. Finally, the integral equation is transformed into an algebraic equation for solution.

[0077] [A]{ψ}={b} (7)

[0078] In the above formula, [A] is the coefficient matrix; {b} is the augmented coefficient, and {ψ} is the unknown quantity to be solved at each boundary node.

[0079] Step 3: Calculation of wave load on pipe section

[0080] After solving the velocity potential governing equations, it is necessary to calculate the pressure on the structure surface. The pressure can be calculated using the Bernoulli equations:

[0081]

[0082] In the above formula, ρ is the fluid density; p is the fluid pressure; and the reference pressure at the water surface is denoted as 0. The local derivative of the velocity potential is indirectly calculated using the volume derivative difference method, and is expressed as a volume derivative:

[0083]

[0084] In the above formula, V represents the moving velocity of the object surface node. To improve the calculation accuracy of the volume derivative, Figure 5 shows the construction of the equally spaced higher-order difference scheme for the volume derivative. This paper constructs the higher-order difference scheme for the volume derivative using the velocity potential of the object surface node at four consecutive time points, as shown in Figure 9. The velocity potential of the same node on the object surface at four consecutive time points t0, t1, t2, and t3 is known to be... and If the time interval between the four moments is Δt, then the body derivative of the nodal velocity potential at time t3 can be expressed as:

[0085]

[0086] The above format uses velocity potential data from four consecutive points and has third-order accuracy. After obtaining the body derivatives of the surface nodes, the local derivatives of the surface nodes are calculated using equation (9), and then the pressure at the surface nodes is calculated using equation (8). Finally, the wave loads (F) in the horizontal, vertical, and torsional directions of the pipe section are calculated using the surface integral of the pressure. y ,F z ,F θ ):

[0087]

[0088] In the above formula, n y and n z Let n be the coordinate components of the boundary unit outward normal vector n, (y c ,zc () represents the coordinates of the centroid of the pipe section;

[0089] After calculating the wave load of each cross section of the water tank pipe using equation (11), the wave load distribution of the entire pipe at the current moment is calculated using equation (1).

[0090] Step 4: Update the water tank boundary

[0091] After calculating the wave load at the current moment, time advancement is required. First, the wave surface needs to be updated. Nodes on the free surface boundary will move with the wave surface. The motion of the surface nodes is controlled by the kinematic and dynamic boundary conditions of the water surface, which can be considered as first-order governing differential equations of the node position vector and velocity potential. Given the initial conditions for each node, explicit time advancement is performed using numerical methods. This paper uses the fourth-order explicit Adams scheme in the linear multistep method to calculate the position vector and velocity potential of the wave surface nodes at the next moment. The first-order differential equations can be uniformly expressed as:

[0092]

[0093] In the above formula, Y is the function vector to be determined, and Y0 is the initial value of the function vector. Then, the fourth-order Adams display format can be expressed as:

[0094]

[0095] In the above formula, the subscript i represents the time node, and Δt represents the time step. It is easy to see that when using the above formula for time advancement, the values ​​of dY / dt for the first four time nodes are needed. In the wave flume problem, dY / dt for the first three time nodes can be set to 0, and the solution calculation starts from the fourth time node. Therefore, after solving the Laplace equation, the velocity potential gradient of the surface nodes can be calculated, thereby calculating the body derivatives of the surface node position vector and velocity potential. The position vector and velocity potential of the surface nodes at the next time step can then be predicted using the Adams scheme. For the suspended tunnel problem, although the structure is underwater and the contact between the surface nodes and the structure does not need to be considered, the movement of the surface nodes will cause deformation of the surface mesh. To improve the stability of the calculation, after calculating the position vector and velocity potential of the surface nodes at the next time step, the horizontal coordinates of each surface node need to be restored to their initial positions. The isoparametric coordinates are then calculated using the interpolation expression of the type function, and the vertical coordinates corresponding to the initial horizontal coordinates of each node and the velocity potential of the node are then calculated.

[0096] After updating the water surface nodes, the inlet and outlet boundary conditions need to be updated based on the velocity potential functions of the incident and outgoing waves. Simultaneously, the pipe's structural motion solver predicts the displacement and velocity of each section of the pipe at the next moment based on the wave loads on the pipe, thereby updating the surface boundaries.

[0097] Figure 6 shows the calculation flowchart for all the above steps. It should be noted that the pipe motion solver may need to perform multiple sub-loop iterations within each time step. To ensure computational efficiency, the strategy adopted in this invention is to update the free surface boundary and the inlet / outlet boundary once at the beginning of each time step, and then update only the surface boundary in subsequent sub-loop iterations to ensure that the fluid motion state and the pipe motion state are fully coupled, thereby improving computational stability.

[0098] Example 1

[0099] To verify the accuracy of the proposed method, a two-dimensional viscous numerical wave flume model was established using the CFD open-source package OpenFOAM. Wave forces on an underwater fixed structure were calculated, and the differences between the viscous and inviscid models in calculating large-scale structural wave loads dominated by inertial forces were examined. The flume was 220m high, the water depth was 200m, and the structure was 750m from the flume inlet. The cross-section was circular with a diameter of 15m, and the center was located 40m below the still water surface. Wave-dissipating relaxation zones of 300m and 250m were set at the inlet and outlet, respectively. The target wave height was 6.2m, the wave period was 12.69s, and linear wave theory was used. Figure 7 shows the wave height time history at the detection point 40m in front of the structure, and Figure 8 shows the wave load time history (left: horizontal load; right: vertical load). From the wave generation effect, for the 710m wave height detection point, due to the difference between the wave dissipation method and the inlet buffer calculation method, the wave height calculated by the potential flow theory was lower than that calculated by the CFD for the first four wave peaks. For the 5th to 11th wave peaks, the two methods were basically equal, with wave heights around 6.2m. However, because the CFD used viscous theory and the wave tank was too large, the height of subsequent wave peaks continued to dissipate and decrease. In contrast, the potential flow theory used in this simulation platform did not have energy dissipation, and the wave height remained at 6.2m. This shows that the wave generation capability of this simulation platform is strong. Figure 8 shows the wave load time history diagram, with horizontal load on the left and vertical load on the right. It is clear from Figure 8 that the magnitude of the wave force is positively correlated with the wave height. Whether it is horizontal or vertical wave force, the wave loads calculated by the potential flow theory and the viscous theory are basically consistent at the 6th to 8th peaks, and the wave heights above the structure are also roughly the same. This shows that the proposed method is accurate and reliable in calculating wave loads.

[0100] Example 2

[0101] To further verify the accuracy of the proposed method, this example will use the method proposed in this invention to calculate a typical working condition of the dynamic response of a suspended tunnel in a linear wave environment. At the same time, the calculation results will be compared with existing frequency domain theories to verify the accuracy of the two-way flow graph coupling calculation. Table 1 gives the basic structural parameters of the suspended tunnel under the typical working condition.

[0102] Table 1

[0103]

[0104]

[0105] Figure 9 shows a comparison of the peak horizontal and vertical displacements and wave loads under stable vibration conditions of the pipe. It is evident that the peak horizontal and vertical displacements calculated using the time-domain method proposed in this invention are in excellent agreement with the results calculated using the frequency-domain method. The vertical displacement calculated using the frequency-domain method shows a slight fluctuation compared to the time-domain method, possibly because the frequency-domain method employs the assumption of an elastic foundation beam. The horizontal wave load across the entire span is slightly lower in the time-domain method than in the frequency-domain method, while the vertical wave load is slightly higher, possibly because the time-domain method does not fully achieve a stable state, but the overall difference is less than 5%. The above analysis demonstrates that the proposed method is also accurate and reliable for calculating bidirectional fluid-structure interaction.

[0106] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A two-way fluid-structure interaction calculation method for long suspended tunnels in a wave environment, characterized in that: The process includes the following steps: Step 1: Divide the suspended tunnel axis into multiple sections, and establish a two-dimensional potential flow wave tank group at each section location. The two-dimensional potential flow wave tank simulates the wave field based on the ideal fluid potential flow theory; Step 2: Solve the mathematical model of each two-dimensional potential flow wave tank to obtain the velocity potential function of each section. The mathematical model includes governing equations, boundary conditions, and initial conditions. The two-dimensional potential flow wave tanks are independent of each other, and the wave incident conditions of each tank are set independently, allowing the specification of different incident wave parameters and seabed topography parameters; Step 3: Calculate the wave load of each section based on the velocity potential function, and obtain the overall wave load distribution of the suspended tunnel through an interpolation function; the wave load calculation adopts a high-order difference scheme of the body derivative. in For time step, For four consecutive time points; This represents the velocity potential at a node on the surface of the object at time t0. This represents the velocity potential at a node on the surface of the object at time t1. This represents the velocity potential at a node on the surface of the object at time t2. This represents the velocity potential at a node on the surface at time t3; Step 4: Update the pipe's motion state according to the wave load, synchronously update the surface boundary conditions of the water tank, and perform time-step progression to achieve fluid-structure interaction iterative calculation; the time progression adopts the fourth-order explicit Adams scheme: Where Y is a state vector containing the position vector of the free surface nodes and the velocity potential.

2. The method for calculating bidirectional fluid-structure interaction in long suspended tunnels under wave conditions according to claim 1, characterized in that: The spacing between the multiple sections in step one is determined based on the flexible vibration characteristics of the suspended tunnel tube, and the spacing between adjacent sections is no greater than 1 / 4 of the characteristic wavelength of the incident wave.

3. The method for calculating bidirectional fluid-structure interaction in long suspended tunnels under wave conditions according to claim 1, characterized in that: The boundary conditions in step two include the inlet boundary conditions: Export boundary conditions: in, Let be the incident wave velocity potential function. Let be the velocity potential function of the outgoing wave. For buffer functions, and These are the entrance and exit boundaries, respectively.

4. The method for calculating bidirectional fluid-structure interaction in long suspended tunnels under wave conditions according to claim 3, characterized in that: The buffer function is defined as follows: in, The buffer period is set to twice the characteristic period of the incident wave.

5. The method for calculating bidirectional fluid-structure interaction in long suspended tunnels under wave conditions according to claim 1, characterized in that: In step two, the boundary element method is used to solve the governing equations. The Laplace equations are transformed into integral equations and then discretized using quadratic isoparametric elements to form a system of algebraic equations. in The coefficient matrix, For augmentation coefficients, For unknown quantities at boundary nodes.

6. The method for calculating bidirectional fluid-structure interaction in long suspended tunnels under wave conditions according to claim 1, characterized in that: The expression for calculating the wave load distribution in step three is as follows: in, The wave load distribution vector of the suspended tunnel pipe at position x and time t; x is the position coordinate along the pipe's axis; t is the time variable. These are interpolation functions for the horizontal, vertical, and torsional directions, respectively. Horizontal wave load at the s-th section; Vertical wave load at the s-th section; The torsional wave moment about the centroidal axis of the s-th cross section, where the counterclockwise direction is positive.

7. The method for calculating bidirectional fluid-structure interaction in long suspended tunnels under wave conditions according to claim 1, characterized in that: The method includes a wave height detection and verification step: a detection point is set in front of the structure, and the wave height time history curves calculated by potential flow theory and CFD are compared. The calculation is deemed valid when the height error of five consecutive wave peaks is less than 5%.

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