Tunnel lining design method and system based on complex variable function method

Abstract

The invention discloses a tunnel lining design method and system based on a complex variable function method, and relates to the field of tunnel construction.The method comprises the steps that the tunnel excavation radius, the tunnel burial depth, the lining elasticity modulus and the lining thickness are selected, and a rock mass area and a lining area of a tunnel are determined; according to the mapping function, the rock mass area and the lining area of the tunnel are mapped into the rock mass area and the lining circular ring area respectively, so that analytic functions of the two areas under different contact conditions are constructed respectively; solving an analytic function according to boundary conditions and continuous conditions of the rock mass area, the lining area and the contact surface of the rock mass area and the lining area; respectively calculating and acquiring the stress and displacement of any point in the lining area and the rock mass area by combining the stress and displacement expressions of the lining and the rock mass; and judging whether the tunnel design meets the design requirements or not, and if not, adjusting the lining elasticity modulus and the lining thickness until the design requirements are met. The method is suitable for lining design parameters of tunnels in different shapes, and the accuracy of lining design parameter calculation can be effectively improved.

Description

Technical Field

[0001] The present invention relates to the technical field of tunnel construction, and in particular to a tunnel lining design method and system based on complex function method. Background Art

[0002] The statements herein merely provide background information related to the present invention and do not necessarily constitute prior art.

[0003] With the rapid development of highways and railways, the demand for tunnels is increasing. In order to ensure the safe construction of tunnels, lining is usually used to support the tunnel rock mass. The supporting effect of the lining is determined by the elastic modulus, thickness and other parameters of the lining. In turn, the lining parameter design affects the safe construction of the tunnel. Studying the lining parameter design suitable for tunnels is one of the main research directions of current tunnel construction.

[0004] At present, the elastic modulus (abbreviated as elastic modulus) and thickness of the lining are generally determined based on a combination of factors such as the service life of the tunnel, geological conditions, and tunnel diameter. However, the thickness and elastic modulus of the tunnel lining determined by this method are less accurate. With the continuous development of mechanization and automation technology, the production and support of linings have become faster and faster. How to accurately calculate and optimize parameters such as the elastic modulus and thickness of the lining has become the key to flexible support. Designing a tunnel lining that is more suitable for tunnel construction has important economic and technical value. Summary of the invention

[0005] In order to solve the shortcomings of the above-mentioned prior art, the present invention provides a tunnel lining design method and system based on the complex function method, which adopts the complex function method to map tunnels of different shapes, and also analyzes the lining design under different tunnel rock and lining contact conditions, optimizes the elastic modulus and thickness of the lining design, and improves the accuracy of the calculation of lining design parameters. The method has wide universality.

[0006] In a first aspect, the present invention provides a tunnel lining design method based on complex function method.

[0007] A tunnel lining design method based on complex function method, comprising:

[0008] Select the tunnel excavation radius, tunnel burial depth, lining elastic modulus and lining thickness to determine the rock mass area and lining area of ​​the tunnel;

[0009] According to the mapping function, the rock mass area and the lining area of ​​the physical plane tunnel are mapped to the image plane area respectively;

[0010] Based on the rock mass annular area and the lining annular area in the mapped image plane, analytical functions of the rock mass area and the lining area under different contact conditions are constructed respectively;

[0011] Solve the analytical function according to the boundary conditions and continuity conditions of the rock mass area, lining area and their contact surface;

[0012] Based on the solved analytical function, combined with the stress expression and displacement expression of the lining and rock mass, the stress and displacement of any point in the lining area and the rock mass area are calculated respectively;

[0013] Based on stress and displacement, it is determined whether the tunnel design based on the selected lining elastic modulus and lining thickness meets the design requirements. If not, the lining elastic modulus and lining thickness are adjusted until the design requirements are met.

[0014] In a second aspect, the present invention provides a tunnel lining design system based on complex function method.

[0015] A tunnel lining design system based on complex function method, comprising:

[0016] The data acquisition module is used to select the tunnel excavation radius, tunnel burial depth, lining elastic modulus and lining thickness, and determine the rock mass area and lining area of ​​the tunnel;

[0017] A mapping module, used for mapping the rock mass area and the lining area of ​​the tunnel to the image plane rock mass ring area and the lining ring area respectively according to the mapping function;

[0018] An analytical function construction module is used to construct analytical functions of the rock mass area and the lining area under different contact conditions respectively based on the rock mass ring area and the lining ring area in the mapped image plane;

[0019] The analytical function solving module is used to solve the analytical function according to the boundary conditions and continuity conditions of the rock mass area, the lining area and their contact surface;

[0020] The stress and displacement calculation module is used to calculate the stress and displacement of any point in the lining area and the rock mass area based on the solved analytical function and the stress and displacement expressions of the lining and the rock mass;

[0021] The lining design adjustment module is used to determine whether the tunnel design based on the selected lining elastic modulus and lining thickness meets the design requirements based on stress and displacement. If not, the lining elastic modulus and lining thickness are adjusted until the design requirements are met.

[0022] In a third aspect, the present invention further provides an electronic device comprising a memory and a processor, and computer instructions stored in the memory and executed on the processor, wherein when the computer instructions are executed by the processor, the steps of the method described in the first aspect are completed.

[0023] In a fourth aspect, the present invention further provides a computer-readable storage medium for storing computer instructions, which, when executed by a processor, complete the steps of the method described in the first aspect.

[0024] One or more of the above technical solutions have the following beneficial effects:

[0025] The present invention provides a tunnel lining design method and system based on a complex function method, which solves the problem of poor accuracy of the existing method for determining the thickness of the tunnel lining by comprehensively considering multiple factors such as the service life of the tunnel, geological conditions, and tunnel diameter. In this embodiment, the stress and displacement solutions of the tunnel rock mass and lining under the action of the lining support are calculated based on the complex function method, and the elastic modulus and thickness of the lining are optimized according to the stress and displacement solutions of the tunnel rock mass and lining. Since the complex function method can map tunnels of various shapes, it can be applicable to all types of tunnel caverns, and the elastic modulus of the lining can be calculated. Combined with the thickness of the lining, it can provide guidance for the model selection of the lining material, provide a basis for flexible support of variable lining thickness, and have important economic and technical value. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] The accompanying drawings in the specification, which constitute a part of the present invention, are used to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute improper limitations on the present invention.

[0027] Figure 1 It is a flow chart of the tunnel lining design method based on the complex function method according to an embodiment of the present invention;

[0028] Figure 2 It is a flow chart for solving stress and displacement of the lining area supporting the circular tunnel rock mass area under different contact conditions in an embodiment of the present invention;

[0029] Figure 3 It is a schematic diagram of a lining area supporting a circular tunnel rock mass area in an embodiment of the present invention;

[0030] Figure 4 Schematic diagram of the rock mass area S1 and the lining area S2 being mapped to the rock mass annular area Ω1 and the lining annular area Ω2 respectively in an embodiment of the present invention. DETAILED DESCRIPTION

[0031] It should be noted that the following detailed descriptions are exemplary only, are intended to describe specific embodiments, are intended to provide further explanation of the present invention, and are not intended to limit exemplary embodiments according to the present invention. Unless otherwise specified, all technical and scientific terms used herein have the same meanings as those of ordinary skill in the art to which the present invention belongs. In addition, it should also be understood that when the terms "comprising" and / or "including" are used in this specification, it indicates the presence of features, steps, operations, devices, components and / or combinations thereof.

[0032] Embodiment 1

[0033] This embodiment provides a tunnel lining design method based on complex function method, such as Figure 1 As shown, including:

[0034] Set the tunnel excavation radius, tunnel burial depth, lining elastic modulus and lining thickness to determine the rock mass area and lining area of ​​the tunnel respectively;

[0035] According to the mapping function, the rock mass area and the lining area of ​​the tunnel in the physical plane are mapped to the rock mass ring area and the lining ring area in the image plane respectively;

[0036] Based on the mapped rock mass ring area and lining ring area, analytical functions of the rock mass area and lining area under different contact conditions are constructed respectively;

[0037] Solve the analytical function according to the boundary conditions and continuity conditions of the rock mass area, lining area and their contact surface;

[0038] Based on the solved analytical function, combined with the stress expression and displacement expression of the lining and rock mass, the stress and displacement of any point in the lining area and the rock mass area are calculated respectively;

[0039] Based on stress and displacement, it is determined whether the tunnel design based on the selected lining elastic modulus and lining thickness meets the design requirements. If not, the lining elastic modulus and lining thickness are adjusted until the design requirements are met.

[0040] The tunnel lining design method based on the complex function method proposed in this embodiment is introduced in more detail through the following content.

[0041] Step S1, select the tunnel excavation radius, tunnel burial depth, lining elastic modulus and lining thickness, determine the rock mass area and lining area of ​​the tunnel, and map the rock mass area and lining area of ​​the tunnel in the physical plane to the rock mass ring area and lining ring area in the image plane according to the mapping function.

[0042] Specifically, firstly, the tunnel excavation radius, tunnel burial depth, lining elastic modulus and lining thickness are selected to determine the rock mass area and lining area of ​​the tunnel, so as to analyze whether the tunnel lining design meets the design requirements. Through a mapping function, a region with complex boundary shape on the physical plane (z plane) is transformed into a region with simple boundary shape on the imaging plane (ζ plane), and then the solution of the problem can be obtained under the simple boundary by using the complex variable function method. According to the two mapping functions, the two regions of the z plane and the z1 plane, namely the rock mass region S1 and the lining region S2, are mapped to the two annular regions of the ζ plane and the ζ1 plane, namely the rock mass annular region Ω1 and the lining annular region Ω2, respectively, as shown in FIG. Figure 4 As shown in the figure, (a) is the mapping of rock mass area S1 to rock mass ring area Ω1, (b) is the mapping of lining area S2 to lining ring area Ω2, in which L1 is the surface boundary of the physical plane, L2 is the interface between physical plane S1 and S2, L3 is the inner boundary of the physical plane lining, L'1 is the surface boundary of the image plane, L'2 is the interface between image plane S1 and S2, and L'3 is the inner boundary of the physical plane lining, where the expressions of the mapping functions are:

[0043]

[0044] Among them, the z plane refers to the plane where the rock mass area S1 is located, the z1 plane refers to the plane where the lining area S2 is located, R0 is the tunnel excavation radius, a = H (1-α 2 ) / (1+α 2 ), H is the tunnel depth.

[0045] Step S2, based on the mapped rock mass annular area and lining annular area, respectively construct analytical functions of the rock mass area and the lining area under different contact conditions, wherein, in the process of constructing the analytical functions, respectively construct analytical functions of the rock mass area without support, the rock mass area under the support of the lining area, and the lining area under the action of the rock mass area, and the different contact conditions include: a full contact condition between the rock mass area and the lining area and a smooth contact condition between the rock mass area and the lining area.

[0046] Specifically, when the tunnel rock mass area is unsupported and only subjected to gravity, the analytical function corresponding to the rock mass area S1 is given by and ψ1(z); Figure 3 As shown in the figure, R1 is the inner radius of the lining, L1 is the surface boundary of the physical plane, L2 is the interface between the physical plane S1 and S2 areas, and L3 is the inner boundary of the physical plane lining. After the lining is constructed, the rock mass and the lining interact with each other. The analytical function corresponding to the rock mass area S1 only under the support of the lining area is given by and ψ2(z) indicates that the rock mass region S1 is mapped to the region Ω1, and the analytical function corresponding to the region Ω1 is given by and ψ2(ζ); after the lining is constructed, the analytical function corresponding to the lining area S2 under the action of the rock mass area is expressed by and ψ3(z1) indicate that the lining area S2 is mapped to the area Ω2, and the analytical function corresponding to the area Ω2 is given by and ψ3(ζ1). The above analytical function can be specifically expressed as:

[0047]

[0048] Among them, F x is the horizontal force, F x =0, F y is the vertical force, κ1 is the coefficient, κ1=3-4μ1, μ1 is the Poisson's ratio of the rock mass, a k 、b k 、c k ,d k are the coefficients of the analytic function to be solved.

[0049] Step S3: Solve the analytical function according to the boundary conditions and continuity conditions of the rock mass area, lining area and their contact surface. Figure 2 As shown, according to the boundary conditions and continuity conditions of the rock mass area, the lining area and their contact surfaces, the analytical functions of the rock mass area and the lining area under full contact conditions and under smooth contact conditions are solved respectively.

[0050] Step S3.1, solving the analytical function of the rock mass area and the lining area under the condition of full contact, including: solving the analytical functions according to the stress boundary conditions of the inner boundary of the lining area, the stress continuity conditions of the excavation boundary and the displacement boundary conditions of the excavation boundary (the conditions are common knowledge in the art), and solving the coefficients of the analytical functions; wherein the excavation boundary refers to the contact surface when the lining area and the rock mass area are in full contact.

[0051] First, since there is no external load on the inner boundary of the lining, the stress boundary condition of the inner boundary of the lining can be expressed as:

[0052]

[0053] Where C1 is an unknown complex constant.

[0054] Secondly, since the contact surface between the lining and the rock mass satisfies the complete contact condition, the stress continuity condition must be satisfied on the contact surface, and its expression is:

[0055]

[0056] Where C2 is an unknown complex constant.

[0057] Finally, the displacement continuity conditions of the contact surface when the lining area and the rock area are in full contact are determined based on the displacement of the rock area without support, the displacement of the rock area under the support of the lining area, and the displacement of the lining area under the action of the rock area.

[0058] Specifically, under the action of gravity alone, the displacement expression of any point in the rock mass of an unsupported shallow circular tunnel is:

[0059]

[0060] Where G1 is the shear modulus of the tunnel, G1 = E1 / [2(1+μ1)], E1 is the elastic modulus of the rock mass, μ1 is the Poisson's ratio, and They are the horizontal and vertical displacement components of the rock mass under the action of gravity.

[0061] The displacement expression of any point in the rock mass of a shallow tunnel under the lining support alone is:

[0062]

[0063] In the formula, and They are the horizontal and vertical displacement components of the rock mass under the action of gravity.

[0064] The displacement expression of any point of the lining under the action of rock mass is:

[0065]

[0066] In the formula, u L and v L They are the horizontal and vertical displacement components of the lining under the action of rock mass, G2 is the shear modulus of the lining, G2=E2 / [2(1+μ2)], E2 and μ2 are the elastic modulus and Poisson's ratio of the lining, κ2=3-4μ2.

[0067] Since the contact surface between the lining and the rock mass satisfies the complete contact condition, the displacement continuity condition is satisfied on the contact surface, and its expression is:

[0068]

[0069] By combining the above analytical functions and solving the linear equations, the coefficients of the analytical functions can be obtained.

[0070] Step S3.2, solving the analytical function of the rock mass area and the lining area under smooth contact conditions, including: solving the analytical functions according to the stress boundary conditions of the inner boundary of the lining area, the stress continuity conditions of the excavation boundary, the shear stress conditions of the excavation boundary and the normal displacement continuity conditions of the excavation boundary, and solving the coefficients of the analytical functions; wherein the excavation boundary refers to the contact surface when the lining area and the rock mass area are in full contact.

[0071] First, since there is no external load on the inner boundary of the lining, the expression of the stress boundary condition is:

[0072]

[0073] In the formula, β k is the coefficient, σ1 is the point on the outer boundary of the lining, c 01 +ic 02 represents a real parameter and κ2 is the parameter of the lining.

[0074] Secondly, since the contact surface between the lining and the rock mass satisfies the complete contact condition, the stress continuity condition must be satisfied on the contact surface, and its expression is:

[0075]

[0076] In the formula, σ is a point on the excavation boundary.

[0077] Then, the shear stress on the excavation boundary is zero, and the formula is:

[0078]

[0079] In the formula, τ ρθ is the shear stress on the rock mass and lining surface.

[0080] Finally, the continuity condition for the normal displacement on the excavation boundary is:

[0081]

[0082] In the formula, is the normal displacement of the excavation boundary of the unlined tunnel under gravity, is the normal displacement of the tunnel excavation boundary under the lining support only, It is the normal displacement of the outer boundary of the lining under the action of the rock mass.

[0083] By combining the above analytical functions and solving the linear equations, the coefficients of the analytical functions can be obtained.

[0084] Step S4: Based on the solved analytical function, combined with the stress expressions and displacement expressions of the lining and the rock mass, the stress and displacement of any point in the lining area and the rock mass area are calculated and obtained respectively.

[0085] Step S4.1, calculate and obtain the stress at any point in the lining area and the rock mass area. The stress component expression at any point in the lining is:

[0086]

[0087] in, They are the normal stress, tangential stress and shear stress in the lining in the orthogonal curvilinear coordinate system; They are respectively the normal stress, tangential stress and shear stress in the lining in the orthogonal curvilinear coordinate system when the original ground stress is not considered. Therefore, the stress components are superimposed as follows:

[0088]

[0089] In the formula, are respectively the normal stress, tangential stress and shear stress at any point in the rock mass under the orthogonal curve. The stress at any point in the lining area and the rock mass area can be calculated by the above formula.

[0090] Step S4.2, calculate and obtain the displacement of any point in the lining area and the rock mass area. The displacement component expression of any point in the lining area is:

[0091]

[0092] In the formula, u L and v L are the horizontal and vertical displacements of any point in the lining, respectively.

[0093] The displacement component expression of any point in the rock mass area is:

[0094]

[0095] In the formula, u R and v R are the horizontal and vertical displacements of any point in the rock mass, respectively.

[0096] Based on the selected lining parameters (lining elastic modulus and lining thickness), the stress and displacement of the lining area and rock mass area of ​​the corresponding tunnel under the lining support condition can be obtained.

[0097] Step S5: Based on stress and displacement, determine whether the tunnel design based on the selected lining elastic modulus and lining thickness meets the design requirements. If not, adjust the lining elastic modulus and lining thickness, recalculate the stress and displacement and determine until the design requirements are met. If yes, optimize the lining elastic modulus and lining thickness to obtain the optimal lining parameter design.

[0098] Specifically, by consulting the tunnel support design specifications, if the stress and displacement of the tunnel under the action of lining support meet the specifications, the tunnel design can be met; if the lining design is too conservative, the elastic modulus and thickness of the lining are reduced until the tunnel stress and displacement reach the minimum value required by the specifications; if the lining design does not meet the design specifications, the elastic modulus and thickness of the lining are increased until the tunnel stress and displacement meet the design specifications.

[0099] The tunnel lining design method based on the complex function method proposed in this embodiment solves the problem of poor accuracy of the existing method for determining the thickness of the tunnel lining by comprehensively considering multiple factors such as the service life of the tunnel, geological conditions, and tunnel diameter. In this embodiment, the stress and displacement solutions of the tunnel rock mass and lining under the action of the lining support are calculated based on the complex function method, and the elastic modulus and thickness of the lining are optimized according to the stress and displacement solutions of the tunnel rock mass and lining. Since the complex function method can map tunnels of various shapes, it can be applicable to all types of tunnel caverns, and the elastic modulus of the lining can be calculated. Combined with the thickness of the lining, it can provide guidance for the model selection of the lining material, provide a basis for flexible support of variable lining thickness, and have important economic and technical value.

[0100] Embodiment 2

[0101] This embodiment provides a tunnel lining design system based on complex function method, including:

[0102] The data acquisition module is used to select the tunnel excavation radius, tunnel burial depth, lining elastic modulus and lining thickness, and determine the rock mass area and lining area of ​​the tunnel;

[0103] A mapping module, used for mapping the rock mass area and the lining area of ​​the tunnel in the physical plane to the rock mass ring area and the lining ring area in the image plane respectively according to the mapping function;

[0104] An analytical function construction module is used to construct analytical functions of the rock mass area and the lining area under different contact conditions respectively based on the mapped rock mass ring area and the lining ring area;

[0105] The analytical function solving module is used to solve the analytical function according to the boundary conditions and continuity conditions of the rock mass area, the lining area and their contact surface;

[0106] The stress and displacement calculation module is used to calculate the stress and displacement of any point in the lining area and the rock mass area based on the solved analytical function and the stress and displacement expressions of the lining and the rock mass;

[0107] The lining design adjustment module is used to determine whether the tunnel design based on the selected lining elastic modulus and lining thickness meets the design requirements based on stress and displacement. If not, the lining elastic modulus and lining thickness are adjusted until the design requirements are met.

[0108] Embodiment 3

[0109] This embodiment provides an electronic device, including a memory and a processor, and computer instructions stored in the memory and running on the processor. When the computer instructions are run by the processor, the steps in the tunnel lining design method based on the complex function method as described above are completed.

[0110] Embodiment 4

[0111] This embodiment also provides a computer-readable storage medium for storing computer instructions. When the computer instructions are executed by a processor, the steps in the tunnel lining design method based on the complex function method as described above are completed.

[0112] The steps involved in the above embodiments 2 to 4 correspond to the method embodiment 1, and the specific implementation methods can refer to the relevant description part of embodiment 1. The term "computer-readable storage medium" should be understood as a single medium or multiple media including one or more instruction sets; it should also be understood to include any medium that can store, encode or carry an instruction set for execution by a processor and enable the processor to execute any method in the present invention.

[0113] Those skilled in the art should understand that the modules or steps of the present invention described above can be implemented by a general-purpose computer device, or alternatively, they can be implemented by a program code executable by a computing device, so that they can be stored in a storage device and executed by the computing device, or they can be made into individual integrated circuit modules, or multiple modules or steps therein can be made into a single integrated circuit module for implementation. The present invention is not limited to any specific combination of hardware and software.

[0114] The above description is only a preferred embodiment of the present invention. Although the specific implementation mode of the present invention is described in conjunction with the accompanying drawings, it is not intended to limit the scope of protection of the present invention. Those skilled in the art should understand that on the basis of the technical solution of the present invention, various modifications or variations that can be made by those skilled in the art without creative work are still within the scope of protection of the present invention.

Claims

1. A tunnel lining design method based on complex function method, characterized in that: include: Select the tunnel excavation radius, tunnel burial depth, lining elastic modulus and lining thickness to determine the rock mass area and lining area of ​​the tunnel; According to the mapping function, the rock mass area and lining area of ​​the tunnel are mapped to the rock mass ring area and the lining ring area respectively; Based on the mapped rock mass ring area and lining ring area, analytical functions of the rock mass area and lining area under different contact conditions are constructed respectively; Solve the analytical function according to the boundary conditions and continuity conditions of the rock mass area, lining area and their contact surface; Based on the solved analytical function, combined with the stress expression and displacement expression of the lining and rock mass, the stress and displacement of any point in the lining area and the rock mass area are calculated respectively; Based on stress and displacement, it is determined whether the tunnel design based on the selected lining elastic modulus and lining thickness meets the design requirements. If not, the lining elastic modulus and lining thickness are adjusted until the design requirements are met.

2. The tunnel lining design method based on complex function method as claimed in claim 1 is characterized in that: The different contact conditions include: a complete contact condition between the rock mass area and the lining area and a smooth contact condition between the rock mass area and the lining area.

3. The tunnel lining design method based on complex function method as claimed in claim 1 is characterized in that: The process of solving an analytical function involves: Based on the mapped rock mass annular area and lining annular area, analytical functions of the rock mass area without support, the rock mass area under the support of the lining area, and the lining area under the rock mass area are constructed respectively; According to the boundary conditions and continuity conditions of the rock mass area, lining area and their contact surface, the analytical functions of the rock mass area and lining area under full contact conditions and smooth contact conditions are solved respectively.

4. The tunnel lining design method based on complex function method as claimed in claim 3 is characterized in that: Solve the analytical functions for the rock mass and lining areas under full contact conditions, including: According to the stress boundary conditions of the inner boundary of the lining area, the stress continuity conditions of the excavation boundary and the displacement boundary conditions of the excavation boundary, the analytical functions are solved simultaneously to obtain the coefficients of the analytical functions; wherein the excavation boundary refers to the contact surface when the lining area and the rock area are in full contact.

5. The tunnel lining design method based on complex function method as claimed in claim 4 is characterized in that: Based on the displacement of the rock area without support, the displacement of the rock area under the support of the lining area, and the displacement of the lining area under the action of the rock area, the displacement continuity conditions of the contact surface when the lining area and the rock area are in full contact are determined.

6. The tunnel lining design method based on complex function method as claimed in claim 3 is characterized in that: Solve the analytical functions for the rock mass and lining areas under smooth contact conditions, including: According to the stress boundary conditions of the inner boundary of the lining area, the stress continuity conditions of the excavation boundary, the shear stress conditions of the excavation boundary and the normal displacement continuity conditions of the excavation boundary, the analytical functions are solved simultaneously to obtain the coefficients of the analytical functions; among which, the excavation boundary refers to the contact surface when the lining area and the rock area are in full contact.

7. The tunnel lining design method based on complex function method as claimed in claim 1 is characterized in that: Based on stress and displacement, it is judged whether the tunnel design based on the selected lining elastic modulus and lining thickness meets the design requirements. If not, the lining elastic modulus and lining thickness are increased, and the stress and displacement are recalculated and judged until the stress and displacement meet the tunnel design requirements; if so, the lining elastic modulus or lining thickness is reduced to obtain the optimal lining parameter design.

8. A tunnel lining design system based on complex function method, characterized in that: include: The data acquisition module is used to select the tunnel excavation radius, tunnel burial depth, lining elastic modulus and lining thickness, and determine the rock mass area and lining area of ​​the tunnel; A mapping module, used for mapping the rock mass area and the lining area of ​​the tunnel to the rock mass ring area and the lining ring area respectively according to the mapping function; An analytical function construction module is used to construct analytical functions of the rock mass area and the lining area under different contact conditions respectively based on the mapped rock mass ring area and the lining ring area; The analytical function solving module is used to solve the analytical function according to the boundary conditions and continuity conditions of the rock mass area, the lining area and their contact surface; The stress and displacement calculation module is used to calculate the stress and displacement of any point in the lining area and the rock mass area based on the solved analytical function and the stress and displacement expressions of the lining and the rock mass; The lining design adjustment module is used to determine whether the tunnel design based on the selected lining elastic modulus and lining thickness meets the design requirements based on stress and displacement. If not, the lining elastic modulus and lining thickness are adjusted until the design requirements are met.

9. An electronic device, characterized in that: The method comprises a memory and a processor and computer instructions stored in the memory and executed on the processor. When the computer instructions are executed by the processor, the steps of a tunnel lining design method based on complex function method as described in any one of claims 1 to 7 are completed.

10. A computer-readable storage medium, characterized in that: Used to store computer instructions, which, when executed by a processor, complete the steps of a tunnel lining design method based on a complex function method as described in any one of claims 1 to 7.

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