Shield tunnel segment floating simulation method based on direct force immersion boundary method

Abstract

The invention is suitable for the technical field of simulation, and relates to a shield tunnel segment floating simulation method based on a direct force immersion boundary method, which comprises the following steps: carrying out grid division on a flow field area, generating a control volume number and a center coordinate, and setting a flow field boundary condition; initializing flow field parameters and calculating parameters; updating the surface speed of the current time step flow field control body; discretizing the flow field control equation, and iteratively solving the flow field speed and pressure; utilizing a segment motion control equation to update boundary discrete point speed and position coordinates; utilizing an interpolation function to obtain the speed of a boundary discrete point, and utilizing a direct force method to calculate the force borne by the boundary discrete point; dispersing the force generated by the boundary discrete points to the whole drainage basin; and transmitting the boundary discrete point speed calculated in the current time step, the force applied to each unit of the flow field, the force applied to the boundary discrete point and the updated slurry viscosity to the next time step, and iterating to specified time. According to the invention, the floating of the shield tunnel segment can be quickly and accurately simulated.

Description

Technical Field

[0001] The invention belongs to the field of simulation technology, and in particular relates to a shield tunnel segment floating simulation method based on a direct force immersed boundary method. Background Art

[0002] During shield tunneling construction, due to the existence of the shield shell, a circle of gaps will be formed between the segments that have been assembled and removed from the shield tail and the stratum, namely the shield tail gap. If it is not filled in time, it will cause stratum instability, segment dislocation and other problems. The shield tail synchronous grouting fills the shield tail gap by injecting cement slurry into the gap. After the shield tail grouting, before the slurry solidifies, the segment is surrounded by a circle of liquid slurry. Since the segment is hollow inside and its thickness is relatively small relative to the outer diameter, the segment gravity is less than the buoyancy, which will cause the segment to float. Problems such as segment misalignment, water leakage at the joints, and axis deviation caused by the floating of synchronous grouting segments in shield tunnels are becoming increasingly prominent. If these problems are not taken seriously, they will seriously endanger construction safety.

[0003] At present, the simulation method of pipe segment floating mainly uses the equivalent layer to simulate the slurry filling gap at the shield tail, and simulates the synchronous grouting process of the shield tail by changing the equivalent layer modulus. This method is essentially to simulate the fluid by reducing the modulus of the solid unit, which cannot simulate the pipe segment floating process well, and it is also impossible to study the pressure distribution of the slurry during the pipe segment floating process, and cannot reveal the pipe segment floating mechanism more realistically; another way is to use CFD software to study the pipe segment floating mechanism, but because the solid moves during the pipe segment floating simulation process, it is necessary to use dynamic grid technology, and the grid needs to be constantly re-divided during the simulation process. And because the shield tail gap is relatively small, the grid size needs to be divided very finely, which greatly increases the simulation cost and is prone to non-convergence. The patent with announcement number CN109684716B discloses a periodic interval optimization method for the multi-layer deposition process of metal droplets, which is also unable to simulate the floating of shield tunnel pipe segments, and has the same disadvantages as the prior art.

[0004] Therefore, how to provide a method for simulating the floating of shield tunnel segments, accurately and quickly simulate the floating of shield tunnel segments and output the results, is an urgent problem to be solved by personnel in this technical field. Summary of the invention

[0005] In view of the shortcomings of the prior art, the purpose of the present invention is to provide a shield tunnel segment floating simulation method based on the direct force immersed boundary method, so as to solve the problems of low accuracy and high cost of the shield tunnel segment floating simulation method in the prior art.

[0006] In order to solve the above technical problems, the present invention adopts the following technical solutions:

[0007] The present invention provides a shield tunnel segment floating simulation method based on a direct force immersed boundary method, comprising the following steps:

[0008] S10. Grid the flow field area according to the orthogonal control volume of the predetermined size, generate the control volume number and center coordinates, and set the flow field boundary conditions; S20. Discretize the contact boundary between the slurry and the pipe segment, obtain the boundary discrete point information, initialize the flow field parameters and calculation parameters; S30. Update the surface velocity of the flow field control volume in the current time step; S40. Discretize the flow field control equations using the same grid finite volume method according to the force on the flow field unit in the previous time step, and iteratively solve the flow field velocity and pressure; S50. Update the velocity and position coordinates of the boundary discrete points using the pipe segment motion control equation according to the force on the boundary discrete points in the previous time step; S60. Obtain the velocity of the boundary discrete points using the interpolation function, and calculate the force on the boundary discrete points using the direct force method; S70. Discretize the force generated by the boundary discrete points to the entire flow basin using the interpolation function; S80. Pass the boundary discrete point velocity, the force on each unit of the flow field, the force on the boundary discrete points and the updated slurry viscosity calculated in the current time step to the next time step until the external iteration reaches the specified time.

[0009] Furthermore, the step S10 specifically sets the flow field solution domain size, i.e., a predetermined size, according to the outer diameter of the shield tunnel segment and the thickness of the shield tail gap, grids the flow field area with the predetermined size to form a square grid, numbers the control bodies, generates and stores the center coordinates of the control bodies, and sets the flow field boundary as the wall boundary.

[0010] Furthermore, in step S20, the flow field parameters include fluid initial velocity, fluid initial pressure, fluid density, fluid viscosity, time step and calculation time, and the calculation parameters include segment thickness, segment inner diameter, segment outer diameter, segment density, number of boundary discrete points and coordinates of boundary discrete points.

[0011] Furthermore, in step S30, the specific formula is as follows:

[0012]

[0013] Where i and j represent the control volume index along the x and y directions respectively, and u f represents the velocity of the control volume wall in the x direction, v f represents the velocity of the control body wall in the y direction, u represents the velocity of the control body in the x direction, and v represents the velocity of the control body in the y direction. When the wall of the control body is the boundary, the wall velocity of the control body is 0.

[0014] Furthermore, in step S40, the control equation is:

[0015]

[0016] Among them, u n+1 is the flow velocity at time step n+1, u n is the velocity of the flow field in n time steps, Δt is the time step length, and p n+1 is the flow field pressure at n+1 time steps, ρ is the flow field density, μ is the dynamic viscosity of the flow field, and f n is the force on the control body at position x in the flow field at time step n.

[0017] Furthermore, in step S50, the segment motion control equation is:.

[0018]

[0019] Among them, U c is the velocity vector of the segment mass center, F K is the force on the Kth discrete boundary point, Δx and Δy are the control volume sizes in the x and y directions, N is the total number of discrete boundary points, Q is the segment buoyancy, Q r is the anti-buoyancy force of the segment, I c is the segment moment of inertia, ω c is the segment angular velocity, X K is the position vector of the Kth discrete boundary point, X c is the position vector of the segment center.

[0020] Furthermore, in step S50, the velocity and position coordinates of the discrete boundary points are calculated by the following formula:

[0021]

[0022] in, is the position vector of the segment center in the n+1 time step, is the position vector of the segment center in n time steps, is the velocity vector of the centroid of the segment in n+1 time steps, is the segment angular velocity in the n+1 time step, θ n is the rotation angle of the pipe segment in n time steps, θ n+1 is the rotation angle of the tube in the n+1 time step, X n+1 is the position vector of the discrete point on the boundary of the n+1 time step, X n+1 is the x-direction position of the discrete point on the boundary of the n+1 time step, Y n+1 is the y-direction position of the discrete point on the boundary of the n+1 time step, U n+1 (X) is the velocity vector of the discrete boundary point at position X at time step n+1.

[0023] Furthermore, in step S60, the velocity of the discrete boundary points is calculated by the following formula:

[0024]

[0025] in, is the intermediate velocity vector of the discrete point at the boundary of the x position, u(x) is the velocity vector of the control body at the x position, x is the position vector of the control body, and x n is the position vector of the discrete point on the boundary of n time steps, (xX n ) is the Dirac function.

[0026] Furthermore, in step S60, the force on the discrete points of the boundary is calculated using the direct force method by the following formula:

[0027]

[0028] Among them, F(X, t) is the force on the discrete point of the boundary at position X at time t, and U(X, t) is the velocity vector of the discrete point of the boundary at position X at time t, which is obtained through the segment motion control equation. is the intermediate velocity vector of the discrete points on the X position boundary at time t, obtained by interpolating the control volume velocity.

[0029] Furthermore, in step S70, the calculation formula is as follows:

[0030]

[0031] Among them, f n+1 (x) represents the force on the control volume at position x at time step n+1.

[0032] Compared with the prior art, the shield tunnel segment floating simulation method based on the direct force immersed boundary method provided by the present invention has at least the following beneficial effects:

[0033] The existing segment floating simulation method cannot simulate the segment floating process well, and it is also impossible to study the pressure distribution of slurry during the segment floating process, and it cannot reveal the segment floating mechanism more realistically. In addition, it also greatly increases the simulation cost and is prone to non-convergence. The present invention has a simple process, convenient operation, and low cost. The flow field control equation is discretized by the same grid finite volume method, the flow field velocity and pressure are iteratively solved, and the boundary discrete point velocity and position coordinates are updated by the segment motion control equation. The boundary discrete point velocity is obtained by the interpolation function, and the force generated by the boundary discrete point is calculated by the direct force method. The force generated by the boundary point is discretized to the entire flow basin by the interpolation function. Finally, the boundary discrete point velocity calculated in the current time step, the force received by each unit of the flow field, the force received by the boundary discrete point and the updated slurry viscosity are passed to the next time step until the external iteration reaches the specified time, so as to realize the rapid and accurate simulation of the shield tunnel segment floating and output the results. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] In order to more clearly illustrate the scheme of the present invention, a brief introduction is given below to the figures required for use in the description of the embodiments. Obviously, the figures described below are some embodiments of the present invention. For ordinary technicians in this field, other figures can be obtained based on these figures without paying any creative work.

[0035] Figure 1 A flow chart of a shield tunnel segment floating simulation method based on a direct force immersed boundary method provided in an embodiment of the present invention;

[0036] Figure 2 A diagram of segment buoyancy simulation results of a shield tunnel segment buoyancy simulation method based on a direct force immersed boundary method provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0037] In order to facilitate the understanding of the present invention, the present invention will be described more fully below with reference to the relevant drawings. The preferred embodiments of the present invention are given in the drawings. However, the present invention can be implemented in many different forms and is not limited to the embodiments described herein. On the contrary, the purpose of providing these embodiments is to make the understanding of the disclosure of the present invention more thorough and comprehensive.

[0038] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as those commonly understood by those skilled in the art of the present invention. The terms used in the specification of the present invention herein are only for the purpose of describing specific embodiments and are not intended to limit the present invention.

[0039] The present invention provides a shield tunnel segment floating simulation method based on a direct force immersed boundary method, which is applied to the simulation process of shield tunnel segment floating. The shield tunnel segment floating simulation method based on the direct force immersed boundary method comprises the following steps:

[0040] S10. Grid the flow field area according to the orthogonal control volume of the predetermined size, generate the control volume number and center coordinates, and set the flow field boundary conditions; S20. Discretize the contact boundary between the slurry and the pipe segment, obtain the boundary discrete point information, initialize the flow field parameters and calculation parameters; S30. Update the surface velocity of the flow field control volume in the current time step; S40. Discretize the flow field control equations using the same grid finite volume method according to the force on the flow field unit in the previous time step, and iteratively solve the flow field velocity and pressure; S50. Update the velocity and position coordinates of the boundary discrete points using the pipe segment motion control equation according to the force on the boundary discrete points in the previous time step; S60. Obtain the velocity of the boundary discrete points using the interpolation function, and calculate the force on the boundary discrete points using the direct force method; S70. Discretize the force generated by the boundary discrete points to the entire flow basin using the interpolation function; S80. Pass the boundary discrete point velocity, the force on each unit of the flow field, the force on the boundary discrete points and the updated slurry viscosity calculated in the current time step to the next time step until the external iteration reaches the specified time.

[0041] The present invention can quickly and accurately simulate the floating of shield tunnel segments.

[0042] In order to enable those skilled in the art to better understand the solutions of the present invention, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings.

[0043] The present invention provides a shield tunnel segment floating simulation method based on the direct force immersed boundary method, which is applied to the simulation process of shield tunnel segment floating. Figure 1 and Figure 2 In this embodiment, the shield tunnel segment floating simulation method based on the direct force immersed boundary method includes the following steps:

[0044] S10, meshing the flow field region according to orthogonal control volumes of predetermined sizes, generating control volume numbers and center coordinates, and setting flow field boundary conditions.

[0045] Specifically, in this embodiment, step S10 includes:

[0046] The size of the flow field solution domain, i.e., the predetermined size, is set according to the outer diameter of the shield tunnel segment and the thickness of the shield tail gap. The flow field area is gridded with the predetermined size to form a square grid. The control bodies are numbered, the center coordinates of the control bodies are generated and stored, and the flow field boundary is set as the wall boundary.

[0047] S20, discretizing the contact boundary between the slurry and the pipe segment, obtaining the discrete point information of the boundary, and initializing the flow field parameters and calculation parameters.

[0048] Specifically, in this embodiment, the flow field parameters include the initial velocity of the fluid, the initial pressure of the fluid, the fluid density, the fluid viscosity, the time step and the calculation time, and the calculation parameters include the thickness of the pipe segment, the inner diameter of the pipe segment, the outer diameter of the pipe segment, the pipe segment density, the number of boundary discrete points, and the coordinates of the boundary discrete points.

[0049] S30, updating the surface velocity of the flow field control volume at the current time step.

[0050] Specifically, the specific formula of step S30 is as follows:

[0051]

[0052] Where i and j represent the control volume index along the x and y directions respectively, and u f represents the velocity of the control volume wall in the x direction, v f represents the velocity of the control body wall in the y direction, u represents the velocity of the control body in the x direction, and v represents the velocity of the control body in the y direction. When the wall of the control body is the boundary, the wall velocity of the control body is 0.

[0053] S40. According to the force on the flow field unit in the previous time step, the flow field control equation is discretized using the co-located grid finite volume method, and the flow field velocity and pressure are solved iteratively.

[0054] Specifically, in this embodiment, the control equation of step S40 is as follows:

[0055]

[0056] Among them, u n+1 is the flow velocity at time step n+1, u n is the velocity of the flow field in n time steps, Δt is the time step length, and p n+1 is the flow field pressure at n+1 time steps, ρ is the flow field density, μ is the dynamic viscosity of the flow field, and f n is the force on the control body at position x in the flow field at time step n.

[0057] S50. According to the force applied to the discrete boundary points in the previous time step, the segment motion control equation is used to update the velocity and position coordinates of the discrete boundary points.

[0058] Specifically, in this embodiment, the segment motion control equation in step S50 is:

[0059]

[0060] Among them, U c is the velocity vector of the segment mass center, F K is the force on the Kth discrete boundary point, Δx and Δy are the control volume sizes in the x and y directions, N is the total number of discrete boundary points, Q is the segment buoyancy, Q ris the anti-buoyancy force of the segment, I c is the segment moment of inertia, ω c is the segment angular velocity, X K is the position vector of the Kth discrete boundary point, X c is the position vector of the segment center.

[0061] Furthermore, in this embodiment, the velocity and position coordinates of the discrete boundary points are calculated by the following formula:

[0062]

[0063] in, is the position vector of the segment center in the n+1 time step, is the position vector of the segment center in n time steps, is the velocity vector of the centroid of the segment in n+1 time steps, is the segment angular velocity in the n+1 time step, θ n is the rotation angle of the pipe segment in n time steps, θ n+1 is the rotation angle of the tube in the n+1 time step, X n+1 is the position vector of the discrete point on the boundary of the n+1 time step, X n+1 is the x-direction position of the discrete point on the boundary of the n+1 time step, Y n+1 is the y-direction position of the discrete point on the boundary of the n+1 time step, U n+1 (X) is the velocity vector of the discrete boundary point at position X at time step n+1.

[0064] S60. Obtain the velocity of the discrete boundary points using an interpolation function, and calculate the force acting on the discrete boundary points using a direct force method.

[0065] Specifically, in this embodiment, the velocity of the discrete boundary points in step S60 is calculated by the following formula:

[0066]

[0067] in, is the intermediate velocity vector of the discrete point at the boundary of the x position, u(x) is the velocity vector of the control body at the x position, x is the position vector of the control body, and x n is the position vector of the discrete point on the boundary of n time steps, (xX n ) is the Dirac function, and its specific form is as follows:

[0068]

[0069] Among them, Φ(r) is a continuous function about r, and the continuous function is:

[0070]

[0071] Where h is the grid width.

[0072] Furthermore, in this embodiment, the force on the discrete points of the boundary is calculated using the direct force method by the following formula:

[0073]

[0074] Among them, F(X, t) is the force on the discrete point of the boundary at position X at time t, and U(X, t) is the velocity vector of the discrete point of the boundary at position X at time t, which is obtained through the segment motion control equation. is the intermediate velocity vector of the discrete points on the X position boundary at time t, obtained by interpolating the control volume velocity.

[0075] S70. Use an interpolation function to discretize the force generated by the discrete points on the boundary to the entire flow basin.

[0076] Specifically, in this embodiment, the calculation formula in step S70 is as follows:

[0077]

[0078] Among them, f n+1 (x) represents the force on the control volume at position x at time step n+1.

[0079] S80, passing the boundary discrete point velocity, the force on each unit of the flow field, the force on the boundary discrete point and the updated slurry viscosity calculated in the current time step to the next time step until the external iteration reaches the specified time.

[0080] Specifically, in this embodiment, the slurry viscosity model formula is as follows:

[0081] μ(t)=μ0e ξt

[0082] Among them, μ(t) represents the slurry viscosity at time t, μ0 represents the initial viscosity of the slurry, and ξ represents a parameter related to the slurry properties.

[0083] Embodiment 1

[0084] Taking the shield tunnel segment of Zhengzhou Metro Line 12 as an example, in this embodiment, S10 is specifically: the outer diameter of the shield tunnel segment is 6.2m, the inner diameter of the segment is 5.5m, the segment thickness is 0.35m, the shield tail gap thickness is 0.2m, the segment density is 2450 kilograms per cubic meter, the control body is an orthogonal control body with a size of 0.05m, the control body is numbered, the center coordinates of the control body are generated and stored, and the flow field boundary is set to the wall boundary.

[0085] In this embodiment, S20 is specifically: the flow field parameters include the initial velocity of the fluid, the initial pressure of the fluid, the density of the fluid, the viscosity of the fluid, the time step and the calculation time, and the calculation parameters include the thickness of the segment, the inner diameter of the segment, the outer diameter of the segment, the density of the segment, the number of discrete points on the boundary, and the coordinates of the discrete points on the boundary. In this embodiment, the initial velocity of the flow field is 0, the initial pressure of the fluid is one standard atmospheric pressure, the density of the fluid is 1830 kilograms per cubic meter, the time step is 0.02s, the calculation time is 10 hours, the outer diameter of the segment is 6.2m, the inner diameter of the segment is 5.5m, the thickness of the segment is 0.35m, the thickness of the shield tail gap is 0.2m, the density of the segment is 2450 kilograms per cubic meter, the number of discrete points on the boundary is 389, and the initial coordinates of the discrete points on the boundary are calculated according to the following formula:

[0086]

[0087] In this embodiment, S30 is specifically:

[0088]

[0089] Where i and j represent the control volume index along the x and y directions respectively, and u f represents the velocity of the control volume wall in the x direction, v f represents the velocity of the control body wall in the y direction, u represents the velocity of the control body in the x direction, and v represents the velocity of the control body in the y direction. When the wall of the control body is the boundary, the wall velocity of the control body is 0.

[0090] In this embodiment, S40 is specifically:

[0091]

[0092] Among them, u n+1 is the flow velocity at time step n+1, u n is the velocity of the flow field in n time steps, Δt is the time step length, and p n+1 is the flow field pressure at n+1 time steps, ρ is the flow field density, μ is the dynamic viscosity of the flow field, and f n is the force on the control body at position x in the flow field at time step n.

[0093] In this embodiment, S50 is specifically:

[0094] The segment motion control equation is:

[0095]

[0096] Among them, U c is the velocity vector of the segment mass center, F K is the force on the Kth discrete boundary point, Δx and Δy are the control volume sizes in the x and y directions, N is the total number of discrete boundary points, Q is the segment buoyancy, Q ris the anti-buoyancy force of the segment, I c is the segment moment of inertia, ω c is the segment angular velocity, X K is the position vector of the Kth discrete boundary point, X c is the position vector of the segment center.

[0097] The velocity and position coordinates of the discrete boundary points are calculated by the following formula:

[0098]

[0099] in, is the position vector of the segment center in the n+1 time step, is the position vector of the segment center in n time steps, is the velocity vector of the centroid of the segment in n+1 time steps, is the segment angular velocity in the n+1 time step, θ n is the rotation angle of the pipe segment in n time steps, θ n+1 is the rotation angle of the tube in the n+1 time step, X n+1 is the position vector of the discrete point on the boundary of the n+1 time step, X n+1 is the x-direction position of the discrete point on the boundary of the n+1 time step, Y n+1 is the y-direction position of the discrete point on the boundary of the n+1 time step, U n+1 (X) is the velocity vector of the discrete boundary point at position X at time step n+1.

[0100] In this embodiment, S60 specifically includes:

[0101] The interpolation speed of the boundary discrete points is obtained by the following formula:

[0102]

[0103] in, is the intermediate velocity vector of the discrete point at the boundary of the x position, u(x) is the velocity vector of the control body at the x position, x is the position vector of the control body, and x n is the position vector of the discrete point on the boundary of n time steps, (xX n ) is the Dirac function, and its specific form is as follows:

[0104]

[0105] Among them, Φ(r) is a continuous function about r, and the continuous function is:

[0106]

[0107] Where h is the grid width.

[0108] The force generated by the discrete points on the boundary is calculated using the direct force method by the following formula:

[0109]

[0110] Among them, F(X, t) is the force on the discrete point of the boundary at position X at time t, and U(X, t) is the velocity vector of the discrete point of the boundary at position X at time t, which is obtained through the segment motion control equation. is the intermediate velocity vector of the discrete points on the X position boundary at time t, obtained by interpolating the control volume velocity.

[0111] In this embodiment, S70 specifically includes:

[0112] The interpolation function is used to discretize the force generated by the boundary points to the entire basin and calculate it by the following formula:

[0113] f n+1 (x) = ∑F n+1 δ(xX n )ΔxΔy

[0114] Among them, f n+1 (x) represents the force on the control volume at position x at time step n+1.

[0115] In this embodiment, S80 specifically includes: transferring the boundary discrete point velocity, the force on each unit of the flow field, the force on the boundary discrete point and the updated slurry viscosity calculated in the current time step to the next time step until the external iteration reaches the specified time.

[0116] Specifically, in this embodiment, the slurry viscosity model formula is as follows:

[0117] μ(t)=2*e 0.0147t

[0118] Among them, μ(t) represents the slurry viscosity at time t, μ0 represents the initial viscosity of the slurry, and ξ represents a parameter related to the slurry properties.

[0119] After calculation, if Figure 2 From the simulation result diagram of the buoyancy of the pipe segments shown, it can be seen that with the increase of the viscosity of the slurry, the buoyancy speed of the pipe segments gradually decreases until the buoyancy of the pipe segments tends to be stable, which is consistent with the development process of the buoyancy of the pipe segments during the construction of the shield tunnel in actual projects, verifying the reliability of the simulation method disclosed in this embodiment.

[0120] The above embodiment of the shield tunnel segment floating simulation method based on the direct force immersed boundary method is compared with the prior art. The segment floating simulation method in the prior art cannot simulate the segment floating process well, and it is also impossible to study the pressure distribution of the slurry during the segment floating process, and cannot reveal the segment floating mechanism more realistically. In addition, it also greatly increases the simulation cost and is prone to non-convergence. The present invention has a simple process, convenient operation, and low cost. The flow field control equation is discretized by the same grid finite volume method, the flow field velocity and pressure are iteratively solved, and the boundary discrete point velocity and position coordinates are updated by the segment motion control equation. The boundary discrete point velocity is obtained by the interpolation function, the force generated by the boundary discrete point is calculated by the direct force method, and the force generated by the boundary point is discretized to the entire flow basin by the interpolation function. Finally, the boundary discrete point velocity calculated at the current time step, the force received by each unit of the flow field, the force received by the boundary discrete point and the updated slurry viscosity are passed to the next time step until the external iteration reaches the specified time, so as to realize the rapid and accurate simulation of the shield tunnel segment floating and output the results.

[0121] Obviously, the embodiments described above are only preferred embodiments of the present invention, rather than all embodiments. The preferred embodiments of the present invention are shown in the accompanying drawings, but they do not limit the patent scope of the present invention. The present invention can be implemented in many different forms. On the contrary, the purpose of providing these embodiments is to make the understanding of the disclosure of the present invention more thorough and comprehensive. Although the present invention has been described in detail with reference to the aforementioned embodiments, for those skilled in the art, it is still possible to modify the technical solutions recorded in the aforementioned specific embodiments, or to perform equivalent replacements for some of the technical features therein. Any equivalent structure made using the contents of the specification and drawings of the present invention, directly or indirectly used in other related technical fields, is also within the scope of patent protection of the present invention.

Claims

1. A shield tunnel segment floating simulation method based on direct force immersed boundary method, characterized in that: The following steps are involved: S10, meshing the flow field region according to an orthogonal control body of a predetermined size, generating a control body number and a center coordinate, and setting a flow field boundary condition; S20, discretizing the contact boundary between the slurry and the pipe segment, obtaining the discrete point information of the boundary, and initializing the flow field parameters and calculation parameters; S30, updating the surface velocity of the flow field control volume at the current time step; S40, discretizing the flow field control equations using the collocated grid finite volume method according to the force applied to the flow field unit in the previous time step, and iteratively solving the flow field velocity and pressure; S50, updating the velocity and position coordinates of the discrete boundary points using the segment motion control equation according to the force applied to the discrete boundary points in the previous time step; S60, using an interpolation function to obtain the velocity of the discrete point on the boundary, and using a direct force method to calculate the force on the discrete point on the boundary; S70, using an interpolation function to discretize the force generated by the discrete points on the boundary to the entire flow basin; S80, passing the boundary discrete point velocity, the force on each unit of the flow field, the force on the boundary discrete point and the updated slurry viscosity calculated in the current time step to the next time step until the external iteration reaches the specified time.

2. The shield tunnel segment floating simulation method based on direct force immersed boundary method according to claim 1 is characterized in that: The step S10 specifically sets the flow field solution domain size, i.e., the predetermined size, according to the outer diameter of the shield tunnel segment and the thickness of the shield tail gap, meshes the flow field area with the predetermined size to form a square grid, numbers the control bodies, generates and stores the center coordinates of the control bodies, and sets the flow field boundary to the wall boundary.

3. The shield tunnel segment floating simulation method based on direct force immersed boundary method according to claim 1 is characterized in that: In step S20, the flow field parameters include fluid initial velocity, fluid initial pressure, fluid density, fluid viscosity, time step and calculation duration, and the calculation parameters include segment thickness, segment inner diameter, segment outer diameter, segment density, number of boundary discrete points and coordinates of boundary discrete points.

4. The shield tunnel segment floating simulation method based on direct force immersed boundary method according to claim 1 is characterized in that: In step S30, the specific formula is as follows: Where i and j represent the control volume index along the x and y directions respectively, and u f represents the velocity of the control volume wall in the x direction, v f represents the velocity of the control body wall in the y direction, u represents the velocity of the control body in the x direction, and v represents the velocity of the control body in the y direction. When the wall of the control body is the boundary, the wall velocity of the control body is 0.

5. The shield tunnel segment floating simulation method based on direct force immersed boundary method according to claim 1 is characterized in that: In step S40, the control equation is: Among them, u n+1 is the flow velocity at time step n+1, u n is the velocity of the flow field in n time steps, Δt is the time step length, and p n+1 is the flow field pressure at n+1 time steps, ρ is the flow field density, μ is the dynamic viscosity of the flow field, and f n is the force on the control body at position x in the flow field at time step n.

6. The shield tunnel segment floating simulation method based on direct force immersed boundary method according to claim 1 is characterized in that: In step S50, the segment motion control equation is:. Among them, U c is the velocity vector of the segment mass center, F K is the force on the Kth discrete boundary point, Δx and Δy are the control volume sizes in the x and y directions, N is the total number of discrete boundary points, Q is the segment buoyancy, Q r is the anti-buoyancy force of the segment, I c is the segment moment of inertia, ω c is the segment angular velocity, X K is the position vector of the Kth discrete boundary point, X c is the position vector of the segment center.

7. The shield tunnel segment floating simulation method based on direct force immersed boundary method according to claim 6 is characterized in that: In step S50, the velocity and position coordinates of the discrete boundary points are calculated using the following formula: in, is the position vector of the segment center in the n+1 time step, is the position vector of the segment center in n time steps, is the velocity vector of the centroid of the segment in n+1 time steps, is the angular velocity of the tube segment in the n+1 time step, θ n is the rotation angle of the pipe segment in n time steps, θ n+1 is the rotation angle of the tube in the n+1 time step, X n+1 is the position vector of the discrete point on the boundary of the n+1 time step, X n+1 is the x-direction position of the discrete point on the boundary of the n+1 time step, Y n+1 is the y-direction position of the discrete point on the boundary of the n+1 time step, U n+1 (X) is the velocity vector of the discrete boundary point at position X at time step n+1.

8. The shield tunnel segment floating simulation method based on direct force immersed boundary method according to claim 1 is characterized in that: In step S60, the velocity of the discrete boundary points is calculated by the following formula: in, is the intermediate velocity vector of the discrete point at the boundary of the x position, u(x) is the velocity vector of the control body at the x position, x is the position vector of the control body, and x n is the position vector of the discrete point on the boundary of n time steps, (xX n ) is the Dirac function.

9. The shield tunnel segment floating simulation method based on direct force immersed boundary method according to claim 8 is characterized in that: In step S60, the force on the discrete points of the boundary is calculated using the direct force method by the following formula: Among them, F(X, t) is the force on the discrete point of the boundary at position X at time t, and U(X, t) is the velocity vector of the discrete point of the boundary at position X at time t, which is obtained through the segment motion control equation. is the intermediate velocity vector of the discrete points on the X position boundary at time t, obtained by interpolating the control volume velocity.

10. The shield tunnel segment floating simulation method based on direct force immersed boundary method according to claim 1 is characterized in that: In step S70, the calculation formula is as follows: f n+1 (x)=∑F n+1 δ(xX n )ΔxΔy Among them, f n+1 (x) represents the force on the control volume at position x at time step n+1.

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