A shield tunnel segment floating simulation method based on direct force immersed boundary method

Abstract

The application belongs to the technical field of simulation and relates to a shield tunnel segment floating simulation method based on a direct force immersed boundary method, which comprises the following steps: carrying out grid division on a flow field area, generating control body numbers and center coordinates, and setting flow field boundary conditions; initializing flow field parameters and calculation parameters; updating the surface speed of the flow field control body at the current time step; discretizing the flow field control equation and iteratively solving the flow field speed and pressure; updating the boundary discrete point speed and position coordinates by using a segment motion control equation; obtaining the boundary discrete point speed by using an interpolation function and calculating the force borne by the boundary discrete point by using a direct force method; discretizing the force borne by the boundary discrete point to the entire flow area; and transferring the boundary discrete point speed obtained at the current time step, the force borne by each unit of the flow field, the force borne by the boundary discrete point and the updated slurry viscosity to the next time step and iterating to a specified time. The application can quickly and accurately simulate the floating of a shield tunnel segment.

Description

Technical Field

[0001] This invention belongs to the field of simulation technology, and in particular relates to a simulation method for the floating of shield tunnel segments based on the direct force immersion boundary method. Background Technology

[0002] During shield tunneling, the presence of the shield shell creates a gap between the assembled tunnel segments (after they exit the shield tail) and the ground. This gap, known as the shield tail gap, can cause ground instability and segment misalignment if not filled promptly. Simultaneous grouting at the shield tail fills this gap by injecting cement grout. After grouting, before the grout solidifies, the tunnel segments are surrounded by a ring of liquid grout. Due to the hollow interior and relatively small thickness of the segments compared to their outer diameter, the weight of the segments is less than their buoyancy, causing them to float. Problems such as segment misalignment, joint leakage, and axial displacement caused by the floating of synchronously grouted tunnel segments in shield tunnels are becoming increasingly prominent. If these problems are not addressed, they can seriously jeopardize construction safety.

[0003] Currently, the main simulation method for tunnel segment floating is to use equivalent layers to simulate the grout filling in the shield tail gap. This method simulates the synchronous grouting process at the shield tail by changing the modulus of the equivalent layers. Essentially, this method simulates fluid flow by reducing the modulus of solid elements, which cannot accurately simulate the segment floating process. Furthermore, it cannot study the pressure distribution of the grout during the floating process, thus failing to reveal the floating mechanism more realistically. Another approach is to use CFD software to study the floating mechanism, but because the solids move during the simulation, dynamic meshing technology is required. This necessitates continuous re-meshing of the mesh during the simulation, and because the shield tail gap is relatively small, the mesh size needs to be very fine, significantly increasing the simulation cost and increasing the likelihood of non-convergence. Patent CN109684716B discloses a method for optimizing the periodic interval of a multi-layer deposition process of metal droplets, but it also cannot simulate the floating of shield tunnel segments, exhibiting the same drawbacks as existing technologies.

[0004] Therefore, how to provide a simulation method for simulating the floating of shield tunnel segments, accurately and quickly simulating the floating of shield tunnel segments and outputting the results, is a problem that urgently needs to be solved by people in this technical field. Summary of the Invention

[0005] To address the shortcomings of existing technologies, the purpose of this invention is to provide a simulation method for the floating of shield tunnel segments based on the direct force immersion boundary method, so as to solve the problems of low accuracy and high cost in existing simulation methods for the floating of shield tunnel segments.

[0006] To solve the above-mentioned technical problems, the present invention adopts the following technical solution:

[0007] This invention provides a simulation method for the floating of shield tunnel segments based on the direct force immersion boundary method, comprising the following steps:

[0008] S10. Mesh the flow field region according to the orthogonal control volume of the predetermined size, generate control volume number and center coordinates, and set the flow field boundary conditions; S20. Discretize the contact boundary between the slurry and the tube segment, obtain the boundary discrete point information, and 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 equation using the finite volume method with in-situ mesh according to the forces on the flow field elements in the previous time step, and iteratively solve the flow field velocity and pressure; S5. Update the velocity and position coordinates of the boundary discrete points using the tube segment motion control equation according to the forces on the boundary discrete points in the previous time step; S60. Obtain the boundary discrete point velocity using the interpolation function, and calculate the force on the boundary discrete points using the direct force method; S70. Discretize the forces generated by the boundary discrete points to the entire flow domain using the interpolation function; S8. Transfer the boundary discrete point velocity, the forces on each flow field element, the forces 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] In step S50, the velocity and position coordinates of the boundary discrete points are calculated using the following formula:

[0010]

[0011] in, Let n+1 be the position vector of the center of the tube segment. Let n be the position vector of the center of the tube segment at time step n. Let Δt be the velocity vector of the centroid of the tube segment at time step n+1, and Δt be the time step size. Let θ be the angular velocity of the tube segment at time step n+1. n Let θ be the rotation angle of the tube segment at time step n. n+1 Let X be the rotation angle of the tube segment at time step n+1. n+1 P is the position vector of the discrete point at the boundary of time step n+1. n+1 Let x be the position of the discrete point at time step n+1 in the x-direction, and y be the position of the point n+1 U represents the y-direction position of the discrete point at the boundary of time step n+1. n+1 (X) is the velocity vector of the boundary discrete point at time step X at time step n+1.

[0012] Furthermore, step S10 specifically involves setting the flow field solution domain size, i.e., the predetermined size, based on the outer diameter of the shield tunnel segment and the thickness of the shield tail gap. The flow field region is then divided into grids using the predetermined size to form a square grid. The control volumes are numbered, the center coordinates of the control volumes are generated and stored, and the flow field boundary is set as the wall boundary.

[0013] Furthermore, in step S20, the flow field parameters include the initial fluid velocity, initial fluid pressure, fluid density, fluid viscosity, time step, and calculation time, and the calculation parameters include the tube thickness, tube inner diameter, tube outer diameter, tube density, number of boundary discrete points, and coordinates of the boundary discrete points.

[0014] Furthermore, in step S30, the specific formula is as follows:

[0015]

[0016] Where i and j represent the control volume indices along the x and y directions, respectively, u f v represents the velocity of the control body wall in the x-direction. 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 control body wall is a boundary, the velocity of the control body wall is 0.

[0017] Furthermore, in step S40, the governing equation is:

[0018]

[0019] Among them, u n+1 Let u be the flow velocity at time step n+1. n Let p be the flow velocity at time step n. n+1 Let ρ be the flow pressure at time step n+1, ρ be the flow density, μ be the dynamic viscosity of the flow, and f be the flow velocity. n Let x be the force acting on the control body at position x in the flow field at time step n.

[0020] Furthermore, in step S50, the control equation for the segment motion is:

[0021]

[0022] Among them, U c Let F be the velocity vector of the segment's center of mass. K Let Δx and Δy be the force exerted on the Kth boundary discrete point, Δx and Δy be the control volume dimensions in the x and y directions respectively, N be the total number of boundary discrete points, and Q be the buoyancy of the tunnel segment. r To resist buoyancy of the tunnel segments, I c Let ω be the moment of inertia of the tunnel segment. c X is the angular velocity of the tube segment. K Let X be the position vector of the Kth discrete boundary point. c This is the position vector of the segment center.

[0023] Furthermore, in step S60, the velocity at the boundary discrete point is calculated using the following formula:

[0024]

[0025] in, Let u(x) be the velocity vector at the discrete point on the X-position boundary, u(x) be the velocity vector of the control volume at the X-position, and x be the position vector of the control volume. n Let δ(xX) be the position vector of the discrete point at the boundary at time step n. n Let be the Dirac function, and let Δx and Δy be the control volume dimensions in the x and y directions, respectively.

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

[0027]

[0028] Where F(X,t) is the force acting on the discrete point at position X at time t, and U(X,t) is the velocity vector of the discrete point at position X at time t, obtained through the control equations for the segment motion. The velocity vector at the intermediate point of the discrete boundary point at position X at time t is obtained by interpolation of the control volume velocity.

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

[0030] f n+1 (x)=∑F n+1 δ(xX n )ΔxΔy

[0031] Among them, f n+1 (x) represents the force on the control volume at position x at time step n+1, Δx and Δy are the dimensions of the control volume in the x and y directions respectively, and δ(xX) is the force on the control volume at position x. n ) is the Dirac function.

[0032] The shield tunnel segment floating simulation method based on the direct force immersion boundary method provided by this invention has at least the following advantages compared with the prior art:

[0033] Existing simulation methods for tunnel segment floating cannot accurately simulate the floating process, nor can they study the pressure distribution of the slurry during floating, thus failing to realistically reveal the floating mechanism. Furthermore, these methods significantly increase simulation costs and are prone to convergence issues. This invention offers a simple, convenient, and low-cost process. It discretizes the flow field control equations using the finite volume method with a co-located mesh, iteratively solves for flow field velocity and pressure, updates the velocity and position coordinates of boundary discrete points using the tunnel segment motion control equations, obtains the boundary discrete point velocities using interpolation functions, calculates the forces generated at the boundary discrete points using the direct force method, and discretizes these forces across the entire flow domain using interpolation functions. Finally, the boundary discrete point velocities calculated at the current time step, the forces acting on each element of the flow field, the forces acting on the boundary discrete points, and the updated slurry viscosity are passed to the next time step, until the specified time is reached. This enables rapid and accurate simulation of shield tunnel segment floating and outputs the results. Attached Figure Description

[0034] To more clearly illustrate the solution of the present invention, a brief introduction will be given to the drawings used in the description of the embodiments below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0035] Figure 1 A flowchart of a simulation method for the floating of shield tunnel segments based on the direct force immersion boundary method is provided for an embodiment of the present invention;

[0036] Figure 2 The figure shows the simulation results of the segment uplift of a shield tunnel segment based on the direct force immersion boundary method, which is provided in an embodiment of the present invention. Detailed Implementation

[0037] To facilitate understanding of the present invention, a more complete description will be given below with reference to the accompanying drawings. Preferred embodiments of the invention are shown in the drawings. However, the invention can be implemented in many different forms and is not limited to the embodiments described herein. Rather, these embodiments are provided to provide a thorough and complete understanding of the disclosure of the invention.

[0038] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. The terminology used herein in the description of the invention is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention.

[0039] This invention provides a simulation method for the floating of shield tunnel segments based on the direct force immersion boundary method, which is applied to the simulation of the floating of shield tunnel segments. The simulation method for the floating of shield tunnel segments based on the direct force immersion boundary method includes the following steps:

[0040] S10. Mesh the flow field region according to the orthogonal control volume of predetermined size, generate control volume numbers and center coordinates, and set flow field boundary conditions; S20. Discretize the contact boundary between the slurry and the tube segments, obtain boundary discrete point information, and initialize 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 finite volume method with in-situ mesh based on the forces acting on the flow field elements in the previous time step, and iteratively solve for the flow field velocity and pressure; S50. Update the velocity and position coordinates of the boundary discrete points using the tube segment motion control equations based on the forces acting on the boundary discrete points in the previous time step; S60. Obtain the boundary discrete point velocity using an interpolation function, and calculate the forces acting on the boundary discrete points using the direct force method; S70. Discretize the forces generated by the boundary discrete points to the entire flow domain using an interpolation function; S80. Transfer the boundary discrete point velocity, the forces acting on each flow field element, the forces acting 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] This invention can quickly and accurately simulate the floating of shield tunnel segments.

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

[0043] This invention provides a simulation method for the floating of shield tunnel segments based on the direct force immersion boundary method, which is applied to the simulation of the floating of shield tunnel segments, combined with... Figure 1 and Figure 2 In this embodiment, the simulation method for the floating of shield tunnel segments based on the direct force immersion boundary method includes the following steps:

[0044] S10. The flow field region is meshed according to the orthogonal control volume of the predetermined size, the control volume number and center coordinates are generated, and the flow field boundary conditions are set.

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

[0046] The solution domain size of the flow field is set according to the outer diameter of the shield tunnel segment and the thickness of the shield tail gap. The flow field region is divided into grids according to the predetermined size to form a square grid. The control volume is numbered, the center coordinates of the control volume are generated and stored, and the flow field boundary is set as the wall boundary.

[0047] S20, Discrete the contact boundary between the slurry and the tube segment, obtain the information of the discrete points of the boundary, and initialize the flow field parameters and calculation parameters.

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

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

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

[0051]

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

[0053] S40. Based on the forces acting on the flow field elements in the previous time step, the flow field control equations are discretized using the finite volume method with in-situ meshes, and the flow field velocity and pressure are solved iteratively.

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

[0055]

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

[0057] S50. Based on the forces acting on the boundary discrete points in the previous time step, update the velocity and position coordinates of the boundary discrete points using the segment motion control equations.

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

[0059]

[0060] Among them, U c Let F be the velocity vector of the segment's center of mass.K Let Δx and Δy be the force exerted on the Kth boundary discrete point, Δx and Δy be the control volume dimensions in the x and y directions respectively, N be the total number of boundary discrete points, and Q be the buoyancy of the tunnel segment. r To resist buoyancy of the tunnel segments, I c Let ω be the moment of inertia of the tunnel segment. c X is the angular velocity of the tube segment. K Let X be the position vector of the Kth discrete boundary point. c This is the position vector of the segment center.

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

[0062]

[0063] in, Let n+1 be the position vector of the center of the tube segment. Let n be the position vector of the center of the tube segment at time step n. Let Δt be the velocity vector of the centroid of the tube segment at time step n+1, and Δt be the time step size. Let θ be the angular velocity of the tube segment at time step n+1. n Let θ be the rotation angle of the tube segment at time step n. n+1 Let X be the rotation angle of the tube segment at time step n+1. n+1 P is the position vector of the discrete point at the boundary of time step n+1. n+1 Let x be the position of the discrete point at time step n+1 in the x-direction, and y be the position of the point n+1 U represents the y-direction position of the discrete point at the boundary of time step n+1. n+1 (X) is the velocity vector of the boundary discrete point at time step X at time step n+1.

[0064] S60. Use the interpolation function to obtain the velocity of the discrete boundary points, and use the direct force method to calculate the force on the discrete boundary points.

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

[0066]

[0067] in, Let u(x) be the velocity vector at the discrete point on the X-position boundary, u(x) be the velocity vector of the control volume at the X-position, and x be the position vector of the control volume. n Let δ(xX) be the position vector of the discrete point at the boundary at time step n. n Let Δx and Δy be the Dirac function, and let Δx and Δy be the control volume dimensions in the x and y directions, respectively. The specific forms are as follows:

[0068]

[0069] Where Φ(r) is a continuous function with respect to r, and the continuous function is:

[0070]

[0071] Where h is the grid width.

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

[0073]

[0074] Where F(X, t) is the force acting on the discrete point at position X at time t, and U(X, t) is the velocity vector of the discrete point at position X at time t, obtained through the control equations for the segment motion. The velocity vector at the intermediate point of the discrete boundary point at position X at time t is obtained by interpolation of the control volume velocity.

[0075] S70. Use interpolation functions to discretize the forces generated at the boundary discrete points to the entire watershed.

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

[0077] f n+1 (x)=ΣF n+1 δ(xX n )ΔxΔy

[0078] Among them, f n+1 (x) represents the force on the control volume at position x at time step n+1, Δx and Δy are the dimensions of the control volume in the x and y directions respectively, and δ(xX) is the force on the control volume at position x. n ) is the Dirac function.

[0079] S80. Pass the boundary discrete point velocity, the force on each element 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] Where 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 properties of the slurry.

[0083] Example 1

[0084] Taking the shield tunnel segments of Zhengzhou Metro Line 12 as an example, in this embodiment, S10 specifically refers to: 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 kg per cubic meter, the control volume is an orthogonal control volume with a size of 0.05m, the control volume is numbered, the control volume center coordinates are generated and stored, and the flow field boundary is set as the wall boundary.

[0085] In this embodiment, S20 specifically includes: flow field parameters such as initial fluid velocity, initial fluid pressure, fluid density, fluid viscosity, time step, and calculation duration; calculation parameters such as segment thickness, segment inner diameter, segment outer diameter, segment density, number of boundary discrete points, and coordinates of boundary discrete points. In this embodiment, the initial flow field velocity is 0, the initial fluid pressure is one standard atmosphere, the fluid density is 1830 kg / m³, the time step is 0.02 s, the calculation duration is 10 hours, the segment outer diameter is 6.2 m, the segment inner diameter is 5.5 m, the segment thickness is 0.35 m, the shield tail gap thickness is 0.2 m, the segment density is 2450 kg / m³, the number of boundary discrete points is 389, and the initial coordinates of the boundary discrete points are calculated according to the following formula:

[0086]

[0087] In this embodiment, S30 specifically refers to:

[0088]

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

[0090] In this embodiment, S40 specifically refers to:

[0091]

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

[0093] In this embodiment, S50 specifically refers to:

[0094] The control equations for the segment motion are:

[0095]

[0096] Among them, U c Let F be the velocity vector of the segment's center of mass. K Let Δx and Δy be the force exerted on the Kth boundary discrete point, Δx and Δy be the control volume dimensions in the x and y directions respectively, N be the total number of boundary discrete points, and Q be the buoyancy of the tunnel segment. r To resist buoyancy of the tunnel segments, I c Let ω be the moment of inertia of the tunnel segment. c X is the angular velocity of the tube segment. K Let X be the position vector of the Kth discrete boundary point. c This is the position vector of the segment center.

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

[0098]

[0099] in, Let n+1 be the position vector of the center of the tube segment. Let n be the position vector of the center of the tube segment at time step n. Let Δt be the velocity vector of the centroid of the tube segment at time step n+1, and Δt be the time step size. Let θ be the angular velocity of the tube segment at time step n+1. n Let θ be the rotation angle of the tube segment at time step n. n+1 Let X be the rotation angle of the tube segment at time step n+1. n+1 P is the position vector of the discrete point at the boundary of time step n+1. n+1 Let x be the position of the discrete point at time step n+1 in the x-direction, and y be the position of the point n+1 U represents the y-direction position of the discrete point at the boundary of time step n+1. n+1 (X) is the velocity vector of the boundary discrete point at time step X at time step n+1.

[0100] In this embodiment, S60 specifically refers to:

[0101] The interpolation rate at the boundary discrete points is obtained by the following formula:

[0102]

[0103] in, Let u(x) be the velocity vector at the discrete point on the X-position boundary, u(x) be the velocity vector of the control volume at the X-position, and x be the position vector of the control volume. n Let δ(xX) be the position vector of the discrete point at the boundary at time step n. nLet Δx and Δy be the Dirac function, and let Δx and Δy be the control volume dimensions in the x and y directions, respectively. The specific forms are as follows:

[0104]

[0105] Where Φ(r) is a continuous function with respect to r, and the continuous function is:

[0106]

[0107] Where h is the grid width.

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

[0109]

[0110] Where F(X,t) is the force acting on the discrete point at position X at time t, and U(X,t) is the velocity vector of the discrete point at position X at time t, obtained through the control equations for the segment motion. The velocity vector at the intermediate point of the discrete boundary point at position X at time t is obtained by interpolation of the control volume velocity.

[0111] In this embodiment, S70 specifically refers to:

[0112] The forces generated at the boundary points are discretized across the entire watershed using an interpolation function and calculated using 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, Δx and Δy are the dimensions of the control volume in the x and y directions respectively, and δ(xX) is the force on the control volume at position x. n ) is the Dirac function.

[0115] In this embodiment, S80 specifically involves: passing the boundary discrete point velocity, the force on each element of the flow field, the force on the boundary discrete point, and the updated slurry viscosity calculated at 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] Where 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 properties of the slurry.

[0119] Calculations show that, Figure 2 The simulation results of the segment float shown in the figure can be seen that as the viscosity of the slurry increases, the floating speed of the segment gradually decreases until the floating amount of the segment tends to stabilize. This is consistent with the floating development process of the segment during the actual shield tunnel construction process, which verifies the reliability of the simulation method disclosed in this embodiment.

[0120] The shield tunnel segment floating simulation method based on the direct force immersion boundary method described in the above embodiment, compared with the prior art, cannot effectively simulate the segment floating process, nor can it study the pressure distribution of the slurry during the segment floating process, thus failing to realistically reveal the segment floating mechanism. Furthermore, it significantly increases simulation costs and is prone to non-convergence. This invention, however, features a simple process, convenient operation, and low cost. It discretizes the flow field control equations using the finite volume method with a co-located mesh, iteratively solves for flow field velocity and pressure, updates the velocity and position coordinates of the boundary discrete points using the segment motion control equations, obtains the boundary discrete point velocity using an interpolation function, calculates the force generated at the boundary discrete points using the direct force method, and discretizes the force generated at the boundary points to the entire flow domain using an interpolation function. Finally, it transmits the boundary discrete point velocity calculated at the current time step, the force on each element of the flow field, the force on the boundary discrete points, and the updated slurry viscosity to the next time step, until the external iteration reaches a specified time. This achieves rapid and accurate simulation of shield tunnel segment floating and outputs the results.

[0121] Obviously, the embodiments described above are merely preferred embodiments of the present invention, and not all embodiments. The accompanying drawings illustrate preferred embodiments of the present invention, but do not limit the scope of the patent. The present invention can be implemented in many different forms; rather, these embodiments are provided to provide a more thorough and complete understanding of the disclosure of the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing specific embodiments, or make equivalent substitutions for some of the technical features. Any equivalent structures made using the content of this specification and drawings, directly or indirectly applied to other related technical fields, are similarly within the scope of patent protection of this invention.

Claims

1. A method for simulating the floating of a shield tunnel segment based on a direct force immersed boundary method, characterized in that, The method comprises the following steps: S10, grid division is performed on the flow field region according to a predetermined size of a control body, control body numbers and center coordinates are generated, and a flow field boundary condition is set; S20, a slurry and a segment contact boundary are discretized, boundary discrete point information is obtained, flow field parameters and calculation parameters are initialized; S30, a face velocity of a current time step flow field control body is updated; S40, a control equation is discretized using a collocated grid finite volume method according to forces borne by flow field units of a previous time step, and flow field velocities and pressures are iteratively solved; S50, segment motion control equations are used to update boundary discrete point velocities and position coordinates according to forces borne by the boundary discrete points of the previous time step; In the step S50, the boundary discrete point velocities and position coordinates are calculated through the following formula: wherein, is the position vector of the center of the tube segment at the n+1 time step, is the position vector of the center of the tube segment at the n time step, is the center of mass velocity vector of the tube segment at the n+1 time step, and Δt is the time step, is the angular velocity of the tube segment at the n+1 time step, and θ n is the angle of rotation of the tube segment at the n time step, and θ n+1 is the angle of rotation of the tube segment at the n+1 time step, and X n+1 is the position vector of the boundary discrete point at the n+1 time step, and P n+1 is the x-direction position of the boundary discrete point at the n+1 time step, and Y n+1 is the y-direction position of the boundary discrete point at the n+1 time step, and U n+1 is the velocity vector of the boundary discrete point at the n+1 time step at the X position. S60, an interpolation function is used to obtain the boundary discrete point velocities, and a direct force method is used to calculate the forces borne by the boundary discrete points; S70, an interpolation function is used to discretize the forces borne by the boundary discrete points to the entire flow field; S80, the boundary discrete point velocities calculated in the current time step, the forces borne by the flow field units, the forces borne by the boundary discrete points and the updated slurry viscosity are passed to a next time step until an external iteration is performed to a specified time.

2. The shield tunnel segment floating simulation method based on the direct force immersed boundary method according to claim 1, characterized in that, In the step S10, the flow field solving domain size is set according to a shield tunnel segment outer diameter and a shield tail gap thickness, that is, a predetermined size, the flow field region is grid divided according to the predetermined size, a square grid is formed, control bodies are numbered, control body center coordinates are generated and stored, and a flow field boundary is set as a wall boundary.

3. The method of claim 1, wherein the method is characterized by, In the step S20, the flow field parameters include fluid initial velocities, fluid initial pressures, fluid densities, fluid viscosities, time step lengths and calculation lengths, and the calculation parameters include segment thicknesses, segment inner diameters, segment outer diameters, segment densities, boundary discrete point numbers and boundary discrete point coordinates.

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

5. The method of claim 1, wherein the method is characterized by, In the step S40, the control equation is as follows: where u n+1 is the n + 1 time step flow field velocity, u n is the n time step flow field velocity, p n+1 is the n + 1 time step flow field pressure, p is the flow field density, m is the flow field dynamic viscosity, f n is the force experienced by the control volume at the x location in the n time step flow field.

6. The method of claim 1, wherein, In the step S50, the segment motion control equation is as follows: where U c is the centroid motion velocity vector of the segment, F K is the force on the Kth boundary discrete point, Δx and Δy are the control volume size in x and y direction respectively, N is the total number of boundary discrete points, Q is the segment buoyancy, Q r is the segment anti-buoyancy, I c is the segment moment of inertia, ω c is the segment angular velocity, X K is the position vector of the Kth boundary discrete point, X c is the position vector of the segment center.

7. The method of claim 1, wherein the method is characterized by, In the step S60, the boundary discrete point velocities are calculated through the following formula: where, is the intermediate velocity vector at the boundary discrete point for X position, u(x) is the control volume velocity vector at x position, x is the control volume position vector, X n is the position vector at the boundary discrete point for n time step, δ(x-X n ) is the Dirac function, Δx and Δy are the control volume size in x and y direction, respectively.

8. The method of claim 7, wherein the method is characterized by, In the step S60, the forces borne by the boundary discrete points are calculated through the following formula using the direct force method: Wherein, F(X, t) is the force received by the boundary discrete point at position X at time t, U(X, t) is the velocity vector of the boundary discrete point at position X at time t, which is obtained through the segment motion control equation, is the intermediate velocity vector of the boundary discrete point at position X at time t, which is obtained through the control body velocity interpolation.

9. The method of claim 1, wherein the method is characterized by, In the step S70, the calculation formula is as follows: f n+1 (x) = ∑F n+1 δ(x-X n )ΔxΔy where f n+1 (x) represents the force on the control volume at position x at time step n+1, Δx and Δy are the control volume dimensions in the x and y directions, respectively, and δ(x-X n ) is the Dirac function.

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