Pipe roofing structure deformation calculation method, system and equipment considering pipe-culvert soil mass resistance and storage medium

Abstract

The invention discloses a pipe roofing structure deformation calculation method, system and device considering pipe-culvert soil mass resistance and a storage medium. The method comprises the following steps that S1, a pipe roofing structure is simplified into an elastic thin plate; meanwhile, according to the boundary conditions, the problem is simplified into the deformation problem of the elastic thin plate which is subjected to uniform load on the Winkler elastic foundation and has fixed opposite sides and simply supported opposite sides, and a differential equation of the bending surface of the thin plate on the Winkler elastic foundation and a boundary condition expression of the thin plate are obtained; s2, determining the elastic modulus when the pipe-roofing structure is simplified into an elastic thin plate, and calculating the flexural rigidity D of the pipe-roofing structure; and S3, solving the differential equation of the bending surface of the thin plate on the Winkler elastic foundation by adopting a mixed solution of trigonometric series and a force method to obtain a deflection formula of the elastic thin plate which is arranged on the elastic foundation and is subjected to uniform load distribution. The method can accurately predict the deformation of the pipe roofing structure.

Description

Technical Field

[0001] The present invention relates to the technical field of tunnel engineering, and in particular to a method, system, equipment and storage medium for calculating deformation of a pipe curtain structure considering the resistance of soil between a pipe and a culvert. Background Art

[0002] The pipe-curtain box culvert method is widely used in underground excavation projects with strict surface control. A row of steel pipes is pre-jacked into the soil layer to be excavated to form a pre-support system, and then the box culvert is jacked under the pipe-curtain structure to reduce the disturbance of the soil during the jacking process and control the surface settlement. Considering the interaction between the steel pipe and the soil, models such as Winkler elastic foundation beam and Pasternak two-parameter elastic foundation beam are used. The above models can accurately calculate the final deformation of the pipe-curtain structure, but the deformation of the pipe-curtain structure in actual construction is a gradual process, and the above models such as Winkler elastic foundation beam and Pasternak two-parameter elastic foundation beam cannot accurately predict it. Simplifying the pipe-curtain structure into a single continuous beam for analysis is inconsistent with the actual state of the pipe-curtain structure under bidirectional force, ignoring the influence of the interaction between steel pipes on the support effect, and the analysis results tend to be conservative.

[0003] As a whole, the transverse and longitudinal deformations of the pipe-roof structure are coupled with each other, and the mechanical mechanism is more inclined to the plate. In the actual application of the pipe-roof-box culvert method, the soil between the pipe-roof structure and the box culvert will produce resistance, which will inevitably affect the support effect and construction safety of the pipe-roof structure. At the same time, the selection of steel pipe diameter, wall thickness, and steel pipe spacing is highly dependent on engineering experience. In addition, the research on the transverse and longitudinal coordinated deformation of the pipe-roof structure is still in its infancy, and there is a lack of in-depth understanding of the linkage and mutual feedback mechanism of the soil layer-pipe-roof structure system.

[0004] Therefore, it is urgent to solve the above problems. Summary of the invention

[0005] Purpose of the invention: The first purpose of the present invention is to provide a method for calculating the deformation of a pipe-roof structure taking into account the resistance of the soil between the pipe and the culvert. The calculation method fully considers the resistance of the soil between the pipe and the culvert and can accurately predict the deformation of the pipe-roof structure.

[0006] The second object of the present invention is to provide a pipe-roof structure deformation calculation system that takes into account the resistance of the soil between the pipe and the culvert.

[0007] A third object of the present invention is to provide an electronic device.

[0008] A fourth object of the present invention is to provide a computer storage medium.

[0009] Technical solution: To achieve the above purpose, the present invention discloses a method for calculating the deformation of a pipe curtain structure taking into account the resistance of the soil between the pipe and the culvert, comprising the following steps:

[0010] S1. The tube-roof structure is simplified into an elastic thin plate. At the same time, according to the boundary conditions, the problem is simplified into the deformation problem of an elastic thin plate with fixed opposite sides and simply supported opposite sides under uniform load on a Winkler elastic foundation. The differential equation of the bending surface of the thin plate on the Winkler elastic foundation and the boundary condition expression of the thin plate are obtained.

[0011] S2. Determine the elastic modulus when the tube-roof structure is simplified as an elastic thin plate, and calculate the bending stiffness D of the tube-roof structure;

[0012] S3. The differential equation of the bending surface of a thin plate on a Winkler elastic foundation is solved by a hybrid solution of trigonometric series and force method, and the deflection formula of an elastic thin plate placed on an elastic foundation and subjected to a uniformly distributed load is obtained.

[0013] Optionally, the differential equation of the bending surface of the thin plate on the Winkler elastic foundation obtained in step S1 is:

[0014]

[0015] In formula (4), D is the bending stiffness of the thin plate, w is the deflection of the plate, k is the foundation coefficient, (x, y) is the coordinate of the point on the thin plate on the mid-plane, and q(x, y) is the load perpendicular to the plate surface.

[0016] Optionally, the specific steps of obtaining the boundary condition expression of the thin plate in step S1 include:

[0017] Assuming that the two sides of the tube-roof structure are simply supported, and the two sides of the tube-roof structure are fixed in the longitudinal direction, the deformation problem of the tube-roof structure is simplified to the deformation problem of an elastic thin plate with fixed opposite sides and simply supported opposite sides placed on a Winkler elastic foundation under uniform load. The boundary condition expression of the tube-roof structure, that is, the boundary condition expression of the thin plate is as follows:

[0018] The fixed edge is parallel to the x-axis, so the deflection and slope of both sides of the plate are 0 at y=0 and y=b:

[0019] (w) y＝0 =(w) y＝b =0(5)

[0020]

[0021] The direction of the simply supported edge is parallel to the y-axis, so the deflection and bending moment on both sides of the plate at x = 0 and x = b are both 0:

[0022] (w) x＝0 =(w) x＝a =0(7)

[0023]

[0024] In formula (8), w is the deflection of the thin plate, and μ is the Poisson's ratio of the thin plate.

[0025] Optionally, the specific steps of step S3 include:

[0026] The simplified boundary conditions of the thin plate are: the opposite side in the x direction is fixed, and the opposite side in the y direction is simply supported; the boundary of the thin plate is equivalent to an elastic thin plate with four simply supported sides, and at the same time, a bending moment M(x) that changes with the x value and a bending moment M(y) that changes with the y value are applied on y = 0 and y = b, x = 0 and x = a respectively. It can be seen from formula (8) that M(y) is 0. According to the differential equation of the bending surface of the thin plate on the Winkler elastic foundation, that is, according to formula (4), the deflection w of the thin plate is solved by a double sine series:

[0027]

[0028] In formula (12), a is the transverse length of the thin plate, b is the longitudinal length of the thin plate, m and n are equal to 1, 2, 3, ...; a mn is a function of x and y. For the entire system of the elastic thin plate and the Winkler elastic foundation, when it is deformed by load, the deformation energy is composed of the deformation energy U of the elastic thin plate itself. 1 and elastic foundation deformation energy U 2 composition;

[0029] The deformation energy of the elastic thin plate itself is U 1 The calculation formula is as follows:

[0030]

[0031] Elastic foundation deformation energy U 2 The calculation formula is as follows:

[0032]

[0033] Total strain energy U:

[0034]

[0035] The slope of the elastic plate at the four sides of y = 0, y = b and x = 0, x = a can be expressed as:

[0036]

[0037] when a mn Increase to a mn +δa mn When , the strain energy increment δU is:

[0038]

[0039] External load q, bending moment M(x), and the work δT done by the bending moment M(y) are:

[0040]

[0041] Where E m and F n These are the coefficients of M(x) and M(y) when they are expanded into Fourier series:

[0042]

[0043] Formula (20) is equal to Formula (21). Combining the virtual displacement principle, we can get:

[0044]

[0045] Substitute the bending stiffness D of the tube-roof structure in step S2 into equation (24) to obtain a mn , the obtained a mn Substituting into formula (12) we can get:

[0046]

[0047] The two sides of the thin plate parallel to the y-axis are simply supported, so M(y) = 0, that is, F n =0; the two sides of the thin plate parallel to the x-axis are fixed constraints, and the rotation angle is 0. From equations (16) and (17), we can get:

[0048]

[0049] Sum the series of equation (26):

[0050]

[0051] Where:

[0052]

[0053] From formula (27), we can get:

[0054]

[0055] Substituting equation (30) into equation (25) we can obtain the deflection formula of an elastic thin plate placed on an elastic foundation and subjected to a uniformly distributed load.

[0056] Based on the same inventive concept, the present invention discloses a pipe curtain structure deformation calculation system taking into account the soil resistance between pipes and culverts, comprising:

[0057] Simplification module, used to simplify the tube-roof structure into an elastic thin plate, and simplify the problem into the deformation problem of an elastic thin plate with fixed opposite sides and simply supported opposite sides under uniform load on a Winkler elastic foundation according to the boundary conditions, and obtain the differential equation of the bending surface of the thin plate on the Winkler elastic foundation and the boundary condition expression of the thin plate;

[0058] A calculation module is used to determine the elastic modulus when the tube-roof structure is simplified into an elastic thin plate, and calculate the bending stiffness D of the tube-roof structure;

[0059] The solution module is used to solve the differential equation of the bending surface of a thin plate on a Winkler elastic foundation by using a hybrid solution of trigonometric series and force method, and obtain the deflection formula of an elastic thin plate placed on an elastic foundation and subjected to a uniformly distributed load.

[0060] Optionally, the differential equation of the bending surface of the thin plate on the Winkler elastic foundation obtained in the simplified module is:

[0061]

[0062] In formula (4), D is the bending stiffness of the thin plate, w is the deflection of the plate, k is the foundation coefficient, (x, y) is the coordinate of the point on the thin plate on the mid-plane, and q(x, y) is the load perpendicular to the plate surface.

[0063] Optionally, the boundary condition expression of the thin plate obtained in the simplified module is:

[0064] Assuming that the two sides of the tube-roof structure are simply supported, and the two sides of the tube-roof structure are fixed in the longitudinal direction, the deformation problem of the tube-roof structure is simplified to the deformation problem of an elastic thin plate with fixed opposite sides and simply supported opposite sides placed on a Winkler elastic foundation under uniform load. The boundary condition expression of the tube-roof structure, that is, the boundary condition expression of the thin plate is as follows:

[0065] The fixed edge is parallel to the x-axis, so the deflection and slope of both sides of the plate are 0 at y=0 and y=b:

[0066] (w) y＝0 =(w) y＝b =0(5)

[0067]

[0068] The direction of the simply supported edge is parallel to the y-axis, so the deflection and bending moment on both sides of the plate at x = 0 and x = b are both 0:

[0069] (w) x＝0 =(w) x＝a =0(7)

[0070]

[0071] In formula (8), w is the deflection of the thin plate, and μ is the Poisson's ratio of the thin plate.

[0072] Optionally, the simplified thin plate boundary conditions in the solution module are: the opposite side in the x direction is fixed, and the opposite side in the y direction is simply supported; the thin plate boundary is equivalent to an elastic thin plate with four simply supported sides, and at the same time, a bending moment M(x) that changes with the x value and a bending moment M(y) that changes with the y value are applied to y=0 and y=b, x=0 and x=a, respectively. It can be seen from formula (8) that M(y) is 0. According to the differential equation of the bending surface of the thin plate on the Winkler elastic foundation, that is, according to formula (4), the deflection w of the thin plate is solved by a double sine series:

[0073]

[0074] In formula (12), a is the transverse length of the thin plate, b is the longitudinal length of the thin plate, m and n are equal to 1, 2, 3, ...; a mn is a function of x and y. For the entire system of the elastic thin plate and the Winkler elastic foundation, when it is deformed by load, the deformation energy is composed of the deformation energy U of the elastic thin plate itself. 1 and elastic foundation deformation energy U 2 composition;

[0075] The deformation energy of the elastic thin plate itself is U 1 The calculation formula is as follows:

[0076]

[0077] Elastic foundation deformation energy U 2 The calculation formula is as follows:

[0078]

[0079] Total strain energy U:

[0080]

[0081] The slope of the elastic plate at the four sides of y = 0, y = b and x = 0, x = a can be expressed as:

[0082]

[0083] when a mn Increase to a mn +δa mn When , the strain energy increment δU is:

[0084]

[0085] External load q, bending moment M(x), and the work δT done by the bending moment M(y) are:

[0086]

[0087] Where E m and F n These are the coefficients of M(x) and M(y) when they are expanded into Fourier series:

[0088]

[0089] Formula (20) is equal to Formula (21). Combining the virtual displacement principle, we can get:

[0090]

[0091] Substitute the bending stiffness D of the tube-roof structure in step S2 into equation (24) to obtain a mn , the obtained a mn Substituting into formula (12) we can get:

[0092]

[0093] The two sides of the thin plate parallel to the y-axis are simply supported, so M(y) = 0, that is, F n =0; the two sides of the thin plate parallel to the x-axis are fixed constraints, and the rotation angle is 0. From equations (16) and (17), we can get:

[0094]

[0095] Sum the series of equation (26):

[0096]

[0097] Where:

[0098]

[0099] From formula (27), we can get:

[0100]

[0101] Substituting equation (30) into equation (25) we can obtain the deflection formula of an elastic thin plate placed on an elastic foundation and subjected to a uniformly distributed load.

[0102] The present invention provides an electronic device, comprising a processor and a memory.

[0103] The memory is used to store a computer program, and the computer program is run by the processor to execute the above-mentioned pipe curtain structure deformation calculation method considering the soil resistance between the pipe and the culvert.

[0104] The present invention provides a computer storage medium storing a computer program. The computer program is run by a processor to execute the above-mentioned pipe curtain structure deformation calculation method considering the soil resistance between the pipe and the culvert.

[0105] Beneficial effects: Compared with the prior art, the present invention has the following significant advantages: (1) The selection of boundary conditions in the present invention is more in line with reality than the existing theory. The existing deformation theory of the pipe curtain structure of the pipe curtain box culvert method currently sets the boundary as four-sided simple support, and the boundary in the longitudinal direction is inconsistent with the actual situation. During the construction of the pipe curtain box culvert method, after the pipe curtain steel pipe is pushed in above the box culvert jacking area, the soil in the starting and arriving end areas of the box culvert will first be grouted and reinforced to prevent the collapse of the tunnel gate soil at the starting and arriving time of the box culvert, and also play a fixing role on the longitudinal ends of the pipe curtain structure. Therefore, the present invention selects fixed constraints as the pipe curtain structure. The boundary conditions at both ends in the longitudinal direction and the boundary conditions in the lateral direction remain unchanged, which is more in line with the actual situation. At the same time, the existing theory only simplifies the boundary of the pipe curtain structure into four-sided simple supports. During the box culvert jacking process, the pipe curtain structure in the unjacking area has no excavation of the soil below, and the soil inhibits the rotation of the pipe curtain structure in the longitudinal direction, and is more inclined to a fixed boundary. Therefore, the deformation of the pipe curtain structure during the box culvert jacking process cannot be predicted. The boundary condition selection of the present invention fully takes into account the two situations during the box culvert jacking process and after the jacking is completed, and can provide an accurate reference for predicting the deformation of the pipe curtain structure during the box culvert jacking process and after the jacking is completed.

[0106] (2) The present invention introduces the force method into the solution process for the differential equation of pipe curtain structure deformation. Compared with the traditional solution, the strain energy generated by the deformation of the two is introduced to fully consider the coordinated deformation process of the pipe curtain structure and the soil. The traditional solution only expands the deflection and load in a simple series and brings in the boundary conditions for solution, ignoring the coordinated deformation of the soil and the pipe curtain structure, resulting in large errors in the calculation results. The final result of the present invention is a series that converges very quickly. A more accurate result can be obtained by calculating the first three items. Compared with the existing theory, it can effectively reduce the amount of calculation and improve its wide application in engineering. BRIEF DESCRIPTION OF THE DRAWINGS

[0107] Figure 1 This is a diagram of the theoretical calculation model of the elastic thin plate in the present invention;

[0108] Figure 2 It is a simplified schematic diagram of the lateral boundary of the tube-roof structure in the present invention;

[0109] Figure 3 It is a simplified schematic diagram of the longitudinal boundary of the tube-roof structure in the present invention;

[0110] Figure 4 It is a simplified diagram for calculating the pipe curtain structure in the present invention;

[0111] Figure 5 It is a schematic diagram of the "opposite side simply supported, opposite side fixed" coordinate system in the present invention;

[0112] Figure 6 It is a simplified schematic diagram of the pipe curtain structure in the present invention. DETAILED DESCRIPTION

[0113] The technical solution of the present invention is further described below in conjunction with the accompanying drawings.

[0114] Embodiment 1: A method for calculating deformation of a pipe curtain structure taking into account the resistance of soil between pipes and culverts according to the present invention comprises the following steps:

[0115] S1. Simplify the tube-roof structure into an elastic thin plate, determine the corresponding assumptions, and simplify the problem into the deformation problem of an elastic thin plate with fixed opposite sides and simply supported opposite sides under uniform load on a Winkler elastic foundation according to the boundary conditions. The differential equation of the bending surface of the thin plate on the Winkler elastic foundation and the boundary condition expression of the thin plate are obtained.

[0116] The specific steps of step S1 are: according to the provisions of elastic mechanics, verify the feasibility of simplifying the tube curtain structure into an elastic thin plate, and determine the necessary assumptions to ensure the accuracy of the model; at the same time, simplify the problem into the deformation problem of an elastic thin plate with fixed opposite sides and simply supported opposite sides under uniform load on a Winkler elastic foundation according to the boundary conditions;

[0117] According to elastic mechanics, a plate with a ratio of plate thickness to short side length between 1 / 80 and 1 / 5 is called a thin plate. In the pipe-curtain-box culvert construction method, the diameter of the steel pipe is generally 800-1000mm, which is the thickness when simplified as an elastic thin plate. The longitudinal jacking distance of the box culvert is greater than the transverse width of the pipe curtain, which is slightly greater than the cross-sectional width of the box culvert. The transverse distance of the pipe curtain is the short side of the pipe curtain structure, and the transverse width of the pipe curtain is generally 6-9m. Therefore, the pipe curtain structure can be simplified as an elastic thin plate.

[0118] like Figure 1 As shown in the figure, the maximum deflection of the pipe-roof structure caused by the unloading of the soil under the pipe-roof structure by the pipe jacking machine is generally no more than 100 mm; the maximum deflection is much smaller than the thickness of the pipe-roof structure, which belongs to the category of small deflection of thin plate bending. The following assumptions are established:

[0119] (a) Neutral plane assumption: When the elastic thin plate is deformed in the z-axis direction, each point on the neutral plane has displacement only in the z-axis direction, and the displacement in the x-axis and y-axis directions is 0;

[0120] (b) Straight Normal Assumption: The elastic thin plate is assumed to be composed of several line segments of height h perpendicular to the mid-plane. Before the elastic thin plate is deformed, the line segments perpendicular to the mid-plane of the elastic thin plate are still perpendicular to the bent mid-plane after the elastic thin plate is deformed. That is, it is assumed that when the elastic thin plate is deformed in the z-axis direction, there is no shear strain in the mid-plane of the elastic thin plate.

[0121] (c) No compression assumption: When the elastic sheet is deformed, the fibers of each layer of the elastic sheet do not compress each other, that is, the normal stress σ in each cross section parallel to the midplane z Much smaller than the normal stress σ in the x direction in the cross section x , normal stress in y direction σ y and the shear force τ in the xy plane xy , so the normal stress σ z Ignore;

[0122] In actual construction, the soil gap between the pipe and the culvert is generally 10-20cm, and the foundation thickness is much smaller than the thickness of the elastic thin plate. When the plane size of the plate is constant, the deformation calculation results of the elastic thin plate on the Winkler elastic foundation and the dual-parameter elastic foundation are similar, so the Winkler elastic foundation model is selected;

[0123] Winkler elastic foundation assumes that the elastic foundation is composed of a series of closely arranged, unconnected linear springs. When the foundation surface is loaded, the deformation of a point on the foundation is proportional to the pressure on that point. The pressure can be expressed as:

[0124]

[0125] In formula (1): w is the foundation deformation, that is, w is the deflection of the plate, k is the foundation coefficient, and q is the pressure per unit area;

[0126] If an elastic thin plate is located on a continuous Winkler elastic foundation and is bent by a load q(x,y) perpendicular to the plate surface; when the deflection value of the thin plate is much smaller than the thickness of the thin plate, and according to the assumption of the Winkler elastic foundation, the pressure per unit area at any point of the thin plate is proportional to the deflection of the thin plate at that point, as shown in formula (2):

[0127] q=kw(2)

[0128] Therefore, the load acting on each point of the thin plate is the overburden load on the thin plate minus the foundation reaction force generated by the deformation of the thin plate, as shown in formula (3):

[0129] q(x,y)-kw(3)

[0130] Therefore, the differential equation for the bending surface of a thin plate on a Winkler elastic foundation is:

[0131]

[0132] In formula (4), D is the bending stiffness of the thin plate, w is the deflection of the plate, k is the foundation coefficient, and (x, y) is the coordinate of the point on the thin plate on the mid-plane;

[0133] During the actual construction of the pipe-curtain-box culvert method, the jacking of the box culvert causes minimal disturbance to the soil below the steel pipes at both ends; the transversely arranged steel pipes are connected by locks, and the bending resistance is weak; therefore, it is assumed that the two sides of the pipe-curtain structure are simply supported; after the jacking of the pipe-curtain structure is completed, grouting reinforcement is required at the tunnel portal before the jacking of the box culvert to prevent the tunnel portal soil from collapsing when the box culvert arrives; during the jacking of the box culvert, the soil below the pipe-curtain structure in the unjacked area is less disturbed; therefore, it is assumed that the two sides of the pipe-curtain structure are fixed constraints in the longitudinal direction; the longitudinal calculation length is the jacking distance of the box culvert, and the simplified calculation diagram is as follows Figure 2 and Figure 3 As shown;

[0134] So far, the deformation problem of the pipe curtain structure has been simplified to the deformation problem of an elastic thin plate with fixed opposite sides and simply supported opposite sides and placed on a Winkler elastic foundation under uniform load. The x direction is the transverse direction of the pipe curtain, and the y direction is the longitudinal direction of the pipe curtain, that is, the jacking direction of the box culvert. The simplified calculation diagram is as follows: Figure 4 As shown;

[0135] Establish a rectangular coordinate system with the upper left corner of the tube curtain structure as the origin, such as Figure 5 As shown in the figure, the boundary condition expression of the tube curtain structure, that is, the boundary condition expression of the thin plate is as follows:

[0136] The fixed edge is parallel to the x-axis, so the deflection and slope of both sides of the plate are 0 at y=0 and y=b:

[0137] (w) y＝0 =(w) y＝b =0(5)

[0138]

[0139] The direction of the simply supported edge is parallel to the y-axis, so the deflection and bending moment on both sides of the plate at x = 0 and x = b are both 0:

[0140] (w) x＝0 =(w) x＝a =0(7)

[0141]

[0142] In formula (8): w is the deflection of the thin plate, μ is the Poisson's ratio of the thin plate;

[0143] S2. According to the assumptions in step S1, determine the elastic modulus when the tube-roof structure is simplified as an elastic thin plate, and calculate the bending stiffness D of the tube-roof structure;

[0144] In the actual construction of the pipe-curtain box culvert method, the displacement deviation of the steel pipe is limited by welding male and female lock buckles on both sides of the steel pipe, and the pipe-curtain steel pipe is connected as a whole;

[0145] It can be seen from formula (4) that in the differential equation of the bending surface of the thin plate on the Winkler elastic foundation, the bending stiffness D of the thin plate is a core parameter in the deflection calculation. The calculation formula of the bending stiffness D of the thin plate is as follows:

[0146]

[0147] In formula (9): D is the bending stiffness of the thin plate, E eq is the elastic modulus of the thin plate, t eq is the thickness of the thin plate, μ is the Poisson’s ratio of the thin plate;

[0148] When the tube roof structure is simplified into an elastic thin plate, the elastic modulus E of the thin plate eq It can be determined according to the following formula:

[0149]

[0150] In formulas (10) and (11), K 1 and K 2 is the bending stiffness of the steel pipe and slurry, D 1 and D 2 is the compressive stiffness of the steel pipe and grouting body, b is the bearing width of the pipe curtain, and the pipe curtain structure is simplified to a schematic diagram of an elastic thin plate, as shown in Figure 6 As shown;

[0151] S3. Use the mixed solution of trigonometric series and force method to solve the differential equation of the bending surface of the thin plate on the Winkler elastic foundation, and obtain the deflection formula of the elastic thin plate placed on the elastic foundation and subjected to uniform load;

[0152] The simplified boundary conditions of the thin plate are: the opposite side in the x direction is fixed, and the opposite side in the y direction is simply supported; the boundary of the thin plate is equivalent to an elastic thin plate with four simply supported sides, and at the same time, a bending moment M(x) that changes with the x value and a bending moment M(y) that changes with the y value are applied on y = 0 and y = b, x = 0 and x = a respectively. It can be seen from formula (8) that M(y) is 0. According to the differential equation of the bending surface of the thin plate on the Winkler elastic foundation, that is, according to formula (4), the deflection w of the thin plate is solved by a double sine series:

[0153]

[0154] In formula (12), a is the transverse length of the thin plate, b is the longitudinal length of the thin plate, m and n are equal to 1, 2, 3, ...; a mn is a function of x and y. For the entire system of elastic thin plate and elastic foundation, when it is deformed by load, the deformation energy is composed of the deformation energy U of the elastic thin plate itself. 1 and elastic foundation deformation energy U 2 composition;

[0155] The deformation energy of the elastic thin plate itself is U 1 The calculation formula is as follows:

[0156]

[0157] Elastic foundation deformation energy U 2 The calculation formula is as follows:

[0158]

[0159] Total strain energy U:

[0160]

[0161] The slope of the elastic plate at the four sides of y = 0, y = b and x = 0, x = a can be expressed as:

[0162]

[0163] when a mn Increase to a mn +δa mn When , the strain energy increment δU is:

[0164]

[0165] External load q, bending moment M(x), and the work δT done by the bending moment M(y) are:

[0166]

[0167] Where E m and F n These are the coefficients of M(x) and M(y) when they are expanded into Fourier series:

[0168]

[0169] Formula (20) is equal to Formula (21). Combining the virtual displacement principle, we can get:

[0170]

[0171] Substitute the bending stiffness D of the tube-roof structure calculated in step S2 into equation (24) to obtain a mn, the obtained a mn Substituting into formula (12) we can get:

[0172]

[0173] The two sides of the thin plate parallel to the y-axis are simply supported, so M(y) = 0, that is, F n =0; the two sides of the thin plate parallel to the x-axis are fixed constraints, and the rotation angle is 0. From equations (16) and (17), we can get:

[0174]

[0175] Sum the series of equation (26):

[0176]

[0177] Where:

[0178]

[0179] From formula (27), we can get:

[0180]

[0181] Substituting equation (30) into equation (25) we can obtain the deflection formula of an elastic thin plate placed on an elastic foundation and subjected to a uniformly distributed load.

[0182] Embodiment 2: The present invention discloses a pipe-roof structure deformation calculation system taking into account the soil resistance between pipes and culverts, comprising:

[0183] The simplification module is used to simplify the tube-roof structure into an elastic thin plate and determine the corresponding assumptions. At the same time, according to the boundary conditions, the problem is simplified into the deformation problem of an elastic thin plate with fixed opposite sides and simply supported opposite sides under uniform load on a Winkler elastic foundation, and the differential equation of the bending surface of the thin plate on the Winkler elastic foundation and the boundary condition expression of the thin plate are obtained;

[0184] In the simplified module, according to the provisions of elastic mechanics, the feasibility of simplifying the pipe-roof structure into an elastic thin plate is verified, and the necessary assumptions are determined to ensure the accuracy of the model; at the same time, according to the boundary conditions, the problem is simplified to the deformation problem of an elastic thin plate with fixed opposite sides and simply supported opposite sides under uniform load on a Winkler elastic foundation;

[0185] According to elastic mechanics, a plate with a ratio of plate thickness to short side length between 1 / 80 and 1 / 5 is called a thin plate. In the pipe-curtain-box culvert construction method, the diameter of the steel pipe is generally 800-1000mm, which is the thickness when simplified as an elastic thin plate. The longitudinal jacking distance of the box culvert is greater than the transverse width of the pipe curtain, which is slightly greater than the cross-sectional width of the box culvert. The transverse distance of the pipe curtain is the short side of the pipe curtain structure, and the transverse width of the pipe curtain is generally 6-9m. Therefore, the pipe curtain structure can be simplified as an elastic thin plate.

[0186] like Figure 1 As shown in the figure, the maximum deflection of the pipe-roof structure caused by the unloading of the soil under the pipe-roof structure by the pipe jacking machine is generally no more than 100 mm; the maximum deflection is much smaller than the thickness of the pipe-roof structure, which belongs to the category of small deflection of thin plate bending. The following assumptions are established:

[0187] (a) Neutral plane assumption: When the elastic thin plate is deformed in the z-axis direction, each point on the neutral plane has displacement only in the z-axis direction, and the displacement in the x-axis and y-axis directions is 0;

[0188] (b) Straight Normal Assumption: The elastic thin plate is assumed to be composed of several line segments of height h perpendicular to the mid-plane. Before the elastic thin plate is deformed, the line segments perpendicular to the mid-plane of the elastic thin plate are still perpendicular to the bent mid-plane after the elastic thin plate is deformed. That is, it is assumed that when the elastic thin plate is deformed in the z-axis direction, there is no shear strain in the mid-plane of the elastic thin plate.

[0189] (c) No compression assumption: When the elastic sheet is deformed, the fibers of each layer of the elastic sheet do not compress each other, that is, the normal stress σ in each cross section parallel to the midplane z Much smaller than the normal stress σ in the x direction in the cross section x , normal stress in y direction σ y and the shear force τ in the xy plane xy , so the normal stress σ z Ignore;

[0190] In actual construction, the soil gap between the pipe and the culvert is generally 10-20cm, and the foundation thickness is much smaller than the thickness of the elastic thin plate. When the plane size of the plate is constant, the deformation calculation results of the elastic thin plate on the Winkler elastic foundation and the dual-parameter elastic foundation are similar, so the Winkler elastic foundation model is selected;

[0191] Winkler elastic foundation assumes that the elastic foundation is composed of a series of closely arranged, unconnected linear springs. When the foundation surface is loaded, the deformation of a point on the foundation is proportional to the pressure on that point. The pressure can be expressed as:

[0192]

[0193] In formula (1): w is the foundation deformation, that is, w is the deflection of the plate, k is the foundation coefficient, and q is the pressure per unit area;

[0194] If an elastic thin plate is located on a continuous Winkler elastic foundation and is bent by a load q(x,y) perpendicular to the plate surface; when the deflection value of the thin plate is much smaller than the thickness of the thin plate, and according to the assumption of the Winkler elastic foundation, the pressure per unit area at any point of the thin plate is proportional to the deflection of the thin plate at that point, as shown in formula (2):

[0195] q=kw(2)

[0196] Therefore, the load acting on each point of the thin plate is the overburden load on the thin plate minus the foundation reaction force generated by the deformation of the thin plate, as shown in formula (3):

[0197] q(x,y)-kw(3)

[0198] Therefore, the differential equation for the bending surface of a thin plate on a Winkler elastic foundation is:

[0199]

[0200] In formula (4), D is the bending stiffness of the thin plate, w is the deflection of the plate, k is the foundation coefficient, and (x, y) is the coordinate of the point on the thin plate on the mid-plane;

[0201] During the actual construction of the pipe-curtain-box culvert method, the jacking of the box culvert causes minimal disturbance to the soil below the steel pipes at both ends; the transversely arranged steel pipes are connected by locks, and the bending resistance is weak; therefore, it is assumed that the two sides of the pipe-curtain structure are simply supported; after the jacking of the pipe-curtain structure is completed, grouting reinforcement is required at the tunnel portal before the jacking of the box culvert to prevent the tunnel portal soil from collapsing when the box culvert arrives; during the jacking of the box culvert, the soil below the pipe-curtain structure in the unjacked area is less disturbed; therefore, it is assumed that the two sides of the pipe-curtain structure are fixed constraints in the longitudinal direction; the longitudinal calculation length is the jacking distance of the box culvert, and the simplified calculation diagram is as follows Figure 2 and Figure 3 As shown;

[0202] So far, the deformation problem of the pipe curtain structure has been simplified to the deformation problem of an elastic thin plate with fixed opposite sides and simply supported opposite sides and placed on a Winkler elastic foundation under uniform load. The x direction is the transverse direction of the pipe curtain, and the y direction is the longitudinal direction of the pipe curtain, that is, the jacking direction of the box culvert. The simplified calculation diagram is as follows: Figure 4 As shown;

[0203] Establish a rectangular coordinate system with the upper left corner of the tube curtain structure as the origin, such as Figure 5 As shown in the figure, the boundary condition expression of the tube curtain structure, that is, the boundary condition expression of the thin plate is as follows:

[0204] The fixed edge is parallel to the x-axis, so the deflection and slope of both sides of the plate are 0 at y=0 and y=b:

[0205] (w) y＝0 =(w) y＝b =0(5)

[0206]

[0207] The direction of the simply supported edge is parallel to the y-axis, so the deflection and bending moment on both sides of the plate at x = 0 and x = b are both 0:

[0208] (w) x＝0 =(w) x＝a =0(7)

[0209]

[0210] In formula (8): w is the deflection of the thin plate, μ is the Poisson's ratio of the thin plate;

[0211] A calculation module is used to determine the elastic modulus when the tube-roof structure is simplified into an elastic thin plate according to the assumptions in the simplification module, and calculate the bending stiffness D of the tube-roof structure;

[0212] In the actual construction of the pipe-curtain box culvert method, the displacement deviation of the steel pipe is limited by welding male and female lock buckles on both sides of the steel pipe, and the pipe-curtain steel pipe is connected as a whole;

[0213] It can be seen from formula (4) that in the differential equation of the bending surface of the thin plate on the Winkler elastic foundation, the bending stiffness D of the thin plate is a core parameter in the deflection calculation. The calculation formula of the bending stiffness D of the thin plate is as follows:

[0214]

[0215] In formula (9): D is the bending stiffness of the thin plate, E eq is the elastic modulus of the thin plate, t eq is the thickness of the thin plate, μ is the Poisson’s ratio of the thin plate;

[0216] When the tube roof structure is simplified into an elastic thin plate, the elastic modulus E of the thin plate eq It can be determined according to the following formula:

[0217]

[0218] In formulas (10) and (11), K 1 and K 2 is the bending stiffness of the steel pipe and slurry, D 1 and D 2 is the compressive stiffness of the steel pipe and grouting body, b is the bearing width of the pipe curtain, and the pipe curtain structure is simplified to a schematic diagram of an elastic thin plate, as shown in Figure 6 As shown;

[0219] The solution module is used to solve the differential equation of the bending surface of a thin plate on a Winkler elastic foundation by using a hybrid solution of trigonometric series and force method, and obtain the deflection formula of an elastic thin plate placed on an elastic foundation and subjected to a uniformly distributed load.

[0220] The simplified boundary conditions of the thin plate are: the opposite side in the x direction is fixed, and the opposite side in the y direction is simply supported; the boundary of the thin plate is equivalent to an elastic thin plate with four simply supported sides, and at the same time, a bending moment M(x) that changes with the x value and a bending moment M(y) that changes with the y value are applied on y = 0 and y = b, x = 0 and x = a respectively. It can be seen from formula (8) that M(y) is 0. According to the differential equation of the bending surface of the thin plate on the Winkler elastic foundation, that is, according to formula (4), the deflection w of the thin plate is solved by a double sine series:

[0221]

[0222] In formula (12), a is the transverse length of the thin plate, b is the longitudinal length of the thin plate, m and n are equal to 1, 2, 3, ...; a mn is a function of x and y. For the entire system of elastic thin plate and elastic foundation, when it is deformed by load, the deformation energy is composed of the deformation energy U of the elastic thin plate itself. 1 and elastic foundation deformation energy U 2 composition;

[0223] The deformation energy of the elastic thin plate itself is U 1 The calculation formula is as follows:

[0224]

[0225] Elastic foundation deformation energy U 2 The calculation formula is as follows:

[0226]

[0227] Total strain energy U:

[0228]

[0229] The slope of the elastic plate at the four sides of y = 0, y = b and x = 0, x = a can be expressed as:

[0230]

[0231] when a mn Increase to a mn +δa mn When , the strain energy increment δU is:

[0232]

[0233] External load q, bending moment M(x), and the work δT done by the bending moment M(y) are:

[0234]

[0235] Where E m and F n These are the coefficients of M(x) and M(y) when they are expanded into Fourier series:

[0236]

[0237] Formula (20) is equal to Formula (21). Combining the virtual displacement principle, we can get:

[0238]

[0239] Substitute the bending stiffness D of the tube-roof structure calculated in step S2 into equation (24) to obtain a mn , the obtained a mn Substituting into formula (12) we can get:

[0240]

[0241] The two sides of the thin plate parallel to the y-axis are simply supported, so M(y) = 0, that is, F n =0; the two sides of the thin plate parallel to the x-axis are fixed constraints, and the rotation angle is 0. From equations (16) and (17), we can get:

[0242]

[0243] Sum the series of equation (26):

[0244]

[0245] Where:

[0246]

[0247] From formula (27), we can get:

[0248]

[0249] Substituting equation (30) into equation (25) we can obtain the deflection formula of an elastic thin plate placed on an elastic foundation and subjected to a uniformly distributed load.

[0250] Embodiment 3: Corresponding to the method of embodiment 1 of the present invention, embodiment 3 of the present invention further provides an electronic device, in which the electronic device includes: at least one communication bus, at least one processor, at least one memory, at least one network interface, and at least one peripheral interface. The memory contains programs and data.

[0251] The communication bus may be a communication device for transmitting data between components inside an electronic device, such as an internal bus (CPU and memory bus), an external bus (Universal Serial Bus port, Peripheral Component Interconnect Express port, etc.).

[0252] The memory may include a high-speed RAM memory, and may also include a non-volatile memory (non-volatile memory), such as at least one disk memory.

[0253] The processor calls the program and data stored in the memory to execute a pipe curtain structure deformation calculation method considering the soil resistance between the pipe and the culvert provided in Example 1 of the present invention.

[0254] The peripheral interface is used to connect to peripherals, that is, external devices, which may include but are not limited to keyboards, displays, cursor control devices (such as mice, touch pads or touch screens), video input devices, etc.

[0255] The network interface provides wired or wireless communication with an external network (eg, the Internet, an intranet, a local area network, a mobile communication network, etc.).

[0256] Example 4: Corresponding to the method of Example 1 of the present invention, Example 4 of the present invention further provides a computer storage medium for data collection and reception, wherein the computer storage medium stores a computer program, and the computer program is run by a processor to execute a pipe curtain structure deformation calculation method considering the soil resistance between the pipe and the culvert provided in Example 1 of the present invention.

[0257] Each functional unit in each embodiment of the present invention may be integrated into one processing unit, or each unit may exist physically separately, or two or more units may be integrated into one unit. The above-mentioned integrated unit may be implemented in the form of hardware, or in the form of software functional unit, or in the form of a combination of software and hardware.

[0258] If the integrated unit is implemented in the form of a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art, or all or part of the technical solution can be embodied in the form of a software product. The computer software product is stored in a storage medium, including several instructions for a computer device (which can be a personal computer, server or network device, etc.) to perform all or part of the steps of the method described in each embodiment of the present invention. The aforementioned storage medium includes: a mobile hard disk, a USB flash drive, a read-only memory (ROM, Read-Only Memory), a random access memory (RAM, Random Access Memory), a disk or an optical disk, and other media that can store program codes.

[0259] The present invention provides a method, system, device and storage medium for calculating the deformation of a pipe curtain structure taking into account the resistance of the soil between the pipe and the culvert. The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principle of the present invention. These improvements and modifications should also be regarded as the protection scope of the present invention. All components not specified in this embodiment can be implemented by existing technologies.

Claims

1. A method for calculating the deformation of a pipe-roof structure taking into account the resistance of the soil between the pipe and the culvert, characterized in that: The steps include: S1. The tube-roof structure is simplified into an elastic thin plate. At the same time, according to the boundary conditions, the problem is simplified into the deformation problem of an elastic thin plate with fixed opposite sides and simply supported opposite sides under uniform load on a Winkler elastic foundation. The differential equation of the bending surface of the thin plate on the Winkler elastic foundation and the boundary condition expression of the thin plate are obtained. S2. Determine the elastic modulus when the tube-roof structure is simplified as an elastic thin plate, and calculate the bending stiffness D of the tube-roof structure; S3. The differential equation of the bending surface of a thin plate on a Winkler elastic foundation is solved by a hybrid solution of trigonometric series and force method, and the deflection formula of an elastic thin plate placed on an elastic foundation and subjected to a uniformly distributed load is obtained.

2. A method for calculating deformation of a pipe-roof structure taking into account the resistance of soil between pipes and culverts according to claim 1, characterized in that: The differential equation of the bending surface of the thin plate on the Winkler elastic foundation obtained in step S1 is: In formula (4), D is the bending stiffness of the thin plate, w is the deflection of the plate, k is the foundation coefficient, (x, y) is the coordinate of the point on the thin plate on the mid-plane, and q(x, y) is the load perpendicular to the plate surface.

3. The method for calculating the deformation of a pipe-roof structure taking into account the soil resistance between the pipe and the culvert according to claim 2 is characterized in that: The specific steps of obtaining the boundary condition expression of the thin plate in step S1 include: Assuming that the two sides of the tube-roof structure are simply supported, and the two sides of the tube-roof structure are fixed in the longitudinal direction, the deformation problem of the tube-roof structure is simplified to the deformation problem of an elastic thin plate with fixed opposite sides and simply supported opposite sides placed on a Winkler elastic foundation under uniform load. The boundary condition expression of the tube-roof structure, that is, the boundary condition expression of the thin plate is as follows: The fixed edge is parallel to the x-axis, so the deflection and slope of both sides of the plate are 0 at y=0 and y=b: (In) y＝0 =(in) y＝b =0(5) The direction of the simply supported edge is parallel to the y-axis, so the deflection and bending moment on both sides of the plate at x = 0 and x = b are both 0: (In) x＝0 =(in) x＝a =0(7) In formula (8), w is the deflection of the thin plate, and μ is the Poisson's ratio of the thin plate.

4. The method for calculating the deformation of a pipe-roof structure taking into account the soil resistance between the pipe and the culvert according to claim 3 is characterized in that: The specific steps of step S3 include: The simplified boundary conditions of the thin plate are: the opposite side in the x direction is fixed, and the opposite side in the y direction is simply supported; the boundary of the thin plate is equivalent to an elastic thin plate with four simply supported sides, and at the same time, a bending moment M(x) that changes with the x value and a bending moment M(y) that changes with the y value are applied on y = 0 and y = b, x = 0 and x = a respectively. It can be seen from formula (8) that M(y) is 0. According to the differential equation of the bending surface of the thin plate on the Winkler elastic foundation, that is, according to formula (4), the deflection w of the thin plate is solved by a double sine series: In formula (12), a is the transverse length of the thin plate, b is the longitudinal length of the thin plate, m and n are equal to 1, 2, 3, ...; a mn is a function of x and y; for the entire system of the elastic thin plate and the Winkler elastic foundation, when deformed by load, the deformation energy is composed of the deformation energy U1 of the elastic thin plate itself and the deformation energy U2 of the elastic foundation; The calculation formula of the elastic thin plate's own deformation energy U1 is as follows: The calculation formula of elastic foundation deformation energy U2 is as follows: Total strain energy U: The slope of the elastic plate at the four sides of y = 0, y = b and x = 0, x = a can be expressed as: when a mn Increase to a mn +δa mn When , the strain energy increment δU is: External load q, bending moment M(x), and the work δT done by the bending moment M(y) are: Where E m and F n These are the coefficients of M(x) and M(y) when they are expanded into Fourier series: Formula (20) is equal to Formula (21). Combining the virtual displacement principle, we can get: Substitute the bending stiffness D of the tube-roof structure in step S2 into equation (24) to obtain a mn , the obtained a mn Substituting into formula (12) we can get: The two sides of the thin plate parallel to the y-axis are simply supported, so M(y) = 0, that is, F n =0; the two sides of the thin plate parallel to the x-axis are fixed constraints, and the rotation angle is 0. From equations (16) and (17), we can get: Sum the series of equation (26): Where: From formula (27), we can get: Substituting equation (30) into equation (25) we can obtain the deflection formula of an elastic thin plate placed on an elastic foundation and subjected to a uniformly distributed load.

5. A pipe-roof structure deformation calculation system considering the soil resistance between pipes and culverts, characterized in that: include: Simplification module, used to simplify the tube-roof structure into an elastic thin plate, and simplify the problem into the deformation problem of an elastic thin plate with fixed opposite sides and simply supported opposite sides under uniform load on a Winkler elastic foundation according to the boundary conditions, and obtain the differential equation of the bending surface of the thin plate on the Winkler elastic foundation and the boundary condition expression of the thin plate; A calculation module is used to determine the elastic modulus when the tube-roof structure is simplified into an elastic thin plate, and calculate the bending stiffness D of the tube-roof structure; The solution module is used to solve the differential equation of the bending surface of a thin plate on a Winkler elastic foundation by using a hybrid solution of trigonometric series and force method, and obtain the deflection formula of an elastic thin plate placed on an elastic foundation and subjected to a uniformly distributed load.

6. A pipe-roof structure deformation calculation system considering the soil resistance between pipes and culverts according to claim 5, characterized in that: The differential equation of the bending surface of the thin plate on the Winkler elastic foundation obtained in the simplified module is: In formula (4), D is the bending stiffness of the thin plate, w is the deflection of the plate, k is the foundation coefficient, (x, y) is the coordinate of the point on the thin plate on the mid-plane, and q(x, y) is the load perpendicular to the plate surface.

7. A pipe-roof structure deformation calculation system considering the soil resistance between pipes and culverts according to claim 6, characterized in that: The boundary condition expression of the thin plate obtained in the simplified module is: Assuming that the two sides of the tube-roof structure are simply supported, and the two sides of the tube-roof structure are fixed in the longitudinal direction, the deformation problem of the tube-roof structure is simplified to the deformation problem of an elastic thin plate with fixed opposite sides and simply supported opposite sides placed on a Winkler elastic foundation under uniform load. The boundary condition expression of the tube-roof structure, that is, the boundary condition expression of the thin plate is as follows: The fixed edge is parallel to the x-axis, so the deflection and slope of both sides of the plate are 0 at y=0 and y=b: (In) y＝0 =(in) y＝b =0(5) The direction of the simply supported edge is parallel to the y-axis, so the deflection and bending moment on both sides of the plate at x = 0 and x = b are both 0: (In) x＝0 =(in) x＝a =0(7) In formula (8), w is the deflection of the thin plate, and μ is the Poisson's ratio of the thin plate.

8. The pipe-roof structure deformation calculation system considering the soil resistance between pipe and culvert according to claim 7 is characterized by: The simplified thin plate boundary conditions in the solution module are: the opposite side in the x direction is fixed, and the opposite side in the y direction is simply supported; the thin plate boundary is equivalent to an elastic thin plate with four simply supported sides, and at the same time, a bending moment M(x) that changes with the x value and a bending moment M(y) that changes with the y value are applied to y=0 and y=b, x=0 and x=a, respectively. It can be seen from formula (8) that M(y) is 0. According to the differential equation of the bending surface of the thin plate on the Winkler elastic foundation, that is, according to formula (4), the deflection w of the thin plate is solved by a double sine series: In formula (12), a is the transverse length of the thin plate, b is the longitudinal length of the thin plate, m and n are equal to 1, 2, 3, ...; a mn is a function of x and y; for the entire system of the elastic thin plate and the Winkler elastic foundation, when deformed by load, the deformation energy is composed of the deformation energy U1 of the elastic thin plate itself and the deformation energy U2 of the elastic foundation; The calculation formula of the elastic thin plate's own deformation energy U1 is as follows: The calculation formula of elastic foundation deformation energy U2 is as follows: Total strain energy U: The slope of the elastic plate at the four sides of y = 0, y = b and x = 0, x = a can be expressed as: when a mn Increase to a mn +δa mn When , the strain energy increment δU is: External load q, bending moment M(x), and the work δT done by the bending moment M(y) are: Where E m and F n These are the coefficients of M(x) and M(y) when they are expanded into Fourier series: Formula (20) is equal to Formula (21). Combining the virtual displacement principle, we can get: Substitute the bending stiffness D of the tube-roof structure in step S2 into equation (24) to obtain a mn , the obtained a mn Substituting into formula (12) we can get: The two sides of the thin plate parallel to the y-axis are simply supported, so M(y) = 0, that is, F n =0; the two sides of the thin plate parallel to the x-axis are fixed constraints, and the rotation angle is 0. From equations (16) and (17), we can get: Sum the series of equation (26): Where: From formula (27), we can get: Substituting equation (30) into equation (25) we can obtain the deflection formula of an elastic thin plate placed on an elastic foundation and subjected to a uniformly distributed load.

9. An electronic device, characterized in that: including a processor and memory, A memory for storing a computer program, wherein the computer program is executed by a processor to perform the method according to any one of claims 1 to 4.

10. A computer storage medium, characterized in that: The computer storage medium stores a computer program, which is executed by a processor to perform the method according to any one of claims 1 to 4.

Images