A method and system for determining and optimizing anchor rod length based on complex function method

Abstract

The present invention proposes a method and system for determining and optimizing anchor rod length based on a complex function method, relating to the technical field of tunnel construction. The method includes determining the unsupported analytical function of the tunnel under gravity; assuming the force exerted by the surrounding rock on the anchor rod as a pair of equal and opposite concentrated forces, and solving the analytical functions of the shallow tunnel soil under the equal and opposite concentrated forces without gravity; accumulating the unsupported analytical function of the tunnel under gravity and the analytical function of the shallow tunnel soil under the equal and opposite concentrated forces to obtain the analytical function of the tunnel under gravity and anchor rods; based on the analytical function of the tunnel under gravity and anchor rods, calculating the stress and displacement of the surrounding rock and the axial force of the anchor rod under anchor rod support conditions, and obtaining the optimal length of the anchor rod. The present invention uses a complex function method to calculate the adapted length of the anchor rod, calculate the axial force, elongation, and surrounding rock deformation of the anchor rod, and further determine the anchor rod design parameters.

Description

Technical Field

[0001] The present invention belongs to the technical field of tunnel construction, and in particular relates to a method and system for determining and optimizing anchor rod length based on a complex function method. Background Art

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

[0003] To ensure safe tunnel construction, anchor support is often used in existing technologies. The design of anchor length mainly adopts empirical methods or theoretical calculation methods. The empirical method directly determines the anchor length by referring to similar engineering geological conditions, which is relatively inaccurate. The theoretical calculation method is mainly used for system anchors. In the theoretical calculation method, the anchor length is generally composed of three parts: the anchor section length, the free section length, and the exposed section length.

[0004] The length of the anchoring section is determined by the number and length of the drug rolls. Generally speaking, the anchoring length of the resin anchor rod should be 200-250mm, and the anchoring length of the fast-hardening cement anchor rod should be 300-400mm.

[0005] The length of the exposed section is determined by the structure of the tray and nut. After the material and diameter of the anchor rod are selected, it is determined by the thickness of the matching steel strip, tray and nut.

[0006] The length of the free section depends on the range of rock formations that can be effectively supported by the anchor rod. The range of its value varies depending on the different support theories.

[0007] The inventors have found that the above-mentioned method for determining the length of the anchor rod has poor accuracy and is prone to situations where the design is too conservative, resulting in the anchor rod being subjected to too little force and the anchor rod being too long. Summary of the Invention

[0008] In order to overcome the shortcomings of the above-mentioned existing technologies, the present invention provides a method and system for determining and optimizing the anchor rod length based on the complex function method. The method adopts a rigorous theoretical analysis method of the complex function method to calculate the adaptive length of the anchor rod, which is scientific and can calculate the axial force, elongation and surrounding rock deformation of the anchor rod, and then further determine the anchor rod design parameters, providing guidance for the selection of anchor rod models.

[0009] To achieve the above objectives, one or more embodiments of the present invention provide the following technical solutions:

[0010] A first aspect of the present invention provides a method for determining and optimizing anchor rod length based on a complex function method.

[0011] A method for determining and optimizing anchor rod length based on a complex function method comprises the following steps:

[0012] Step 1: Determine the analytical function of the unsupported tunnel under gravity;

[0013] Step 2: Assume that the force exerted by the surrounding rock on the anchor is a pair of equal and opposite concentrated forces, and solve the analytical functions of the shallow tunnel soil under the action of equal and opposite concentrated forces in the absence of gravity.

[0014] Step 3: Accumulate the analytical function of the unsupported tunnel under gravity and the analytical function of the shallow tunnel soil under equal and opposite concentrated forces to obtain the analytical function of the tunnel under gravity and anchors;

[0015] Step 4: Based on the analytical function of the tunnel under the action of gravity and anchors, calculate the stress, displacement of the surrounding rock and the axial force of the anchor under the anchor support conditions, and determine whether the stress, displacement of the surrounding rock and the axial force of the anchor meet the requirements. If not, adjust the anchor length and elastic modulus, and repeat steps 2 to 4 until the requirements are met to obtain the optimal anchor length.

[0016] Optionally, a stress boundary condition of the tunnel excavation boundary is determined, and based on the stress boundary condition of the tunnel excavation boundary, an analytical function of the tunnel without support under the action of gravity is obtained.

[0017] Optionally, assuming that the concentrated forces of equal and opposite directions of the surrounding rock on the anchor rod are P and P' respectively, the analytical function of the rock mass under the action of the concentrated force P without excavation, the analytical function of simulating the rock mass to offset the concentrated force P at the tunnel boundary during tunnel excavation, the analytical function of the rock mass under the action of the concentrated force P' without excavation, and the analytical function of simulating the rock mass to offset the concentrated force P' at the tunnel boundary during tunnel excavation are solved and accumulated to obtain the analytical function of the shallow tunnel soil under the action of equal and opposite concentrated forces.

[0018] Optionally, assume that there is a virtual circular hole with a radius of R and the concentrated force point Z0 as the center in the half-plane, and a uniform surface force parallel to the concentrated force P or P' is applied on the boundary of the virtual circular hole. When the radius R of the virtual circular hole infinitely tends to 0 and the magnitude of the surface force remains unchanged, the analytical function of the rock mass under the action of the concentrated force P without excavation and the analytical function of the rock mass under the action of the concentrated force P' without excavation can be obtained.

[0019] Alternatively, the tunnel excavation process can be viewed as eliminating the forces along the tunnel boundary or applying equal but opposite surface forces on the boundary, and let X n and Y n It represents the surface force component on the boundary of the proposed tunnel, and the surface force component X is applied on the boundary of the circular tunnel. n and Y nThe surface force components of equal magnitude but opposite direction can be used to obtain analytical functions that simulate the rock mass offsetting the concentrated force P at the tunnel boundary during tunnel excavation, and analytical functions that simulate the rock mass offsetting the concentrated force P' at the tunnel boundary during tunnel excavation.

[0020] Optionally, when solving the analytical function of the rock mass under the action of concentrated force P without excavation and the analytical function of the rock mass under the action of concentrated force P' without excavation:

[0021] With the ground surface as the x-axis and the perpendicular line through point z0 as the y-axis, a new coordinate system x'o'y' is established. A mapping function is determined to map the area in the physical plane to a circle in the image plane of the new coordinate system x'o'y'.

[0022] Solve the analytical function in the new coordinate system x'o'y' by using the boundary conditions of the virtual circular hole;

[0023] Based on the analytical function in the new coordinate system x'o'y', determine the analytical function in the physical plane.

[0024] Optionally, the analytical function of the unsupported tunnel under the action of gravity, the analytical function of the rock mass under the action of a concentrated force P without excavation, the analytical function of simulating the rock mass to offset the concentrated force P at the tunnel boundary during tunnel excavation, the analytical function of the rock mass under the action of a concentrated force P' without excavation, and the analytical function of simulating the rock mass to offset the concentrated force P' at the tunnel boundary during tunnel excavation are all solved by the complex function method.

[0025] A second aspect of the present invention provides a system for determining and optimizing anchor rod length based on a complex function method.

[0026] A system for determining and optimizing anchor rod length based on a complex function method, comprising:

[0027] The module for determining an analytical function of a tunnel without support under gravity is configured to: determine an analytical function of a tunnel without support under gravity;

[0028] The module for determining the analytical function of shallow tunnel soil under the action of equal and opposite concentrated forces is configured to: assume the force exerted by the surrounding rock on the anchor bolt as a pair of equal and opposite concentrated forces, and solve the analytical function of the shallow tunnel soil under the action of equal and opposite concentrated forces in the absence of gravity;

[0029] The module for determining the analytical function of the tunnel under the action of gravity and anchors is configured to: accumulate the analytical function of the unsupported tunnel under the action of gravity and the analytical function of the shallow tunnel soil under the action of equal and opposite concentrated forces to obtain the analytical function of the tunnel under the action of gravity and anchors;

[0030] The module for obtaining the optimal anchor length is configured as follows: based on the analytical function of the tunnel under the action of gravity and anchors, the stress, displacement of the surrounding rock and the axial force of the anchor under the anchor support condition are calculated, and whether the stress, displacement of the surrounding rock and the axial force of the anchor meet the requirements are judged. If not, the anchor length and elastic modulus are adjusted, and the analytical function determination module for the shallow tunnel soil under the action of equal and large reverse concentrated forces is cycled to the module for obtaining the optimal anchor length until the requirements are met, thereby obtaining the optimal anchor length.

[0031] A third aspect of the present invention provides a computer-readable storage medium having a program stored thereon, which, when executed by a processor, implements the steps of the anchor rod length determination and optimization method based on the complex function method as described in the first aspect of the present invention.

[0032] The fourth aspect of the present invention provides an electronic device, including a memory, a processor, and a program stored in the memory and runnable on the processor. When the processor executes the program, it implements the steps in the anchor rod length determination and optimization method based on the complex function method as described in the first aspect of the present invention.

[0033] One or more of the above technical solutions have the following beneficial effects:

[0034] 1. The present invention proposes a method and system for determining and optimizing anchor rod length based on the complex function method. Compared with the traditional method for determining and optimizing anchor rod length, the present invention adopts a rigorous theoretical analysis method of the complex function method to calculate the adaptation length of the anchor rod, which is scientific.

[0035] 2. Compared with the traditional anchor rod determination method, the anchor rod length determination and optimization method based on the complex function method proposed in this invention assumes that the interaction between the anchor rod and the surrounding rock is a pair of equal and opposite concentrated forces. The problem of concentrated force support cannot be considered in the innovative theoretical calculation.

[0036] 3. The anchor rod length determination and optimization method based on the complex function method proposed in the present invention can map the advantages of tunnels of different shapes compared to traditional anchor rod length determination and optimization methods. This method can also be used for calculations of tunnels of different shapes, and is universal.

[0037] 4. Compared with the traditional anchor rod determination method, the anchor rod length determination and optimization method based on the complex function method proposed in the present invention can accurately calculate the axial force, elongation and surrounding rock deformation of the anchor rod, and further determine the anchor rod design parameters. It can also provide guidance for the selection of anchor rod models and is instructive.

[0038] 5. The anchor rod length determination and optimization method based on the complex function method proposed in the present invention can be adapted to both shallow buried caverns and deep buried caverns, and has wide applicability.

[0039] Advantages of additional aspects of the present invention will be given in part in the following description and in part will be obvious from the following description, or will be learned through practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] The accompanying drawings, 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.

[0041] Figure 1 This is a flow chart of a method according to an embodiment of the present invention.

[0042] Figure 2 It is a schematic diagram of an end anchoring anchor rod according to an embodiment of the present invention.

[0043] Figure 3 It is a schematic diagram of a tunnel supported by end-anchored anchor rods according to an embodiment of the present invention.

[0044] Figure 4 4 is a mapping diagram of the anchor rod length and the anchor rod axial force in the first embodiment of the present invention. DETAILED DESCRIPTION

[0045] It should be noted that the following detailed descriptions are exemplary and intended to provide further explanation of the present invention. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by those skilled in the art to which the present invention belongs.

[0046] It should be noted that the terms used herein are for describing particular embodiments only and are not intended to limit the exemplary embodiments according to the present invention.

[0047] In the absence of conflict, the embodiments of the present invention and the features thereof may be combined with each other.

[0048] The overall idea proposed by the present invention is:

[0049] Traditional anchor bolt length design relies primarily on empirical methods or simple theoretical calculations, which are relatively inaccurate. With the continuous development of mechanization and automation, anchor bolt production and support are becoming increasingly efficient, making flexible support with variable anchor bolt lengths possible. Therefore, accurately calculating and optimizing the correct anchor bolt length is crucial for flexible support with variable anchor bolt lengths and holds significant economic and technical value.

[0050] The present invention calculates the adaptive length of the anchor rod based on the theoretical analysis method of the complex function method. Since the complex function method can map tunnels of various shapes and is applicable to all types of tunnel chambers, the present invention can calculate the axial force, elongation and surrounding rock deformation of the anchor rod, and further determine and optimize the anchor rod design parameters. It can provide guidance for the selection of anchor rod models and lay the foundation for flexible support of variable anchor rod length, which has important economic and technical value.

[0051] The anchor length determination and optimization method provided by this invention, based on the complex function method, assumes that the interaction between the anchor and the surrounding rock is a pair of equal and opposite concentrated forces, thus solving the problem that the complex function method cannot calculate the support. It includes:

[0052] (1) Determine the analytical function of the unsupported tunnel under gravity;

[0053] (2) Determine the solution for the concentrated forces acting on the tunnel soil;

[0054] (3) Calculate the analytical function of tunnel support anchors;

[0055] (4) Calculation of anchor axial force and anchor elongation;

[0056] (5) Optimization of anchor parameters.

[0057] Example 1

[0058] This embodiment discloses a method for determining and optimizing anchor rod length based on a complex function method.

[0059] like Figure 1 As shown, a method for determining and optimizing anchor rod length based on a complex function method includes the following steps:

[0060] Step 1: Determine the analytical function of the unsupported tunnel under gravity;

[0061] Step 2: Assume that the force exerted by the surrounding rock on the anchor is a pair of equal and opposite concentrated forces, and solve the analytical functions of the shallow tunnel soil under the action of equal and opposite concentrated forces in the absence of gravity.

[0062] Step 3: Accumulate the analytical function of the unsupported tunnel under gravity and the analytical function of the shallow tunnel soil under equal and opposite concentrated forces to obtain the analytical function of the tunnel under gravity and anchors;

[0063] Step 4: Based on the analytical function of the tunnel under the action of gravity and anchors, calculate the stress, displacement of the surrounding rock and the axial force of the anchor under the anchor support conditions, and determine whether the stress, displacement of the surrounding rock and the axial force of the anchor meet the requirements. If not, adjust the anchor length and elastic modulus, and repeat steps 2 to 4 until the requirements are met to obtain the optimal anchor length.

[0064] Specifically, such as Figure 1 As shown, this embodiment is based on the anchor rod length determination and optimization method of the complex function method. First, the analytical function of the unsupported tunnel under the action of gravity is determined. Secondly, a virtual circular hole with an infinitesimal radius is set, and a uniform surface force parallel to the concentrated force P is applied on the boundary of the virtual circular hole to represent the effect of the concentrated force. Then, a surface force equal to Xn and Yn in magnitude but opposite in direction is applied to offset the original stress field to simulate tunnel excavation. Similarly, the superposition of the concentrated force P' is also achieved in the above manner.

[0065] 1. Determine the form of analytical function and stress boundary condition for unsupported tunnel under gravity

[0066] 1-1. Order is the analytical function of the unsupported tunnel under gravity, then its expression is

[0067]

[0068] Where, and Refers to the analytical function, R0 is the excavation diameter, κ is the coefficient, for plane strain problems κ = 3-4μ, μ is Poisson's ratio, γ is the gravity; z represents the point on the boundary of the region, H is the tunnel depth, R0 is the tunnel excavation radius, and z and a are expressed in the form of imaginary numbers.

[0069] 1-2. According to the stress boundary conditions at the tunnel excavation boundary, the following formula can be obtained. The analytical function described in (1-1) can be solved based on the stress boundary conditions.

[0070]

[0071] Where, X n and Y n are the surface force components along the X-axis and Y-axis respectively, C A is a complex constant; A and B represent two points on the boundary, forming the integration path.

[0072] Substituting equation (1-1) into equation (1-2) and comparing the coefficients of terms with the same power can obtain a set of linear equations. By solving the linear equations, the analytical function can be obtained. The coefficient of can be used to determine the analytical function of the tunnel without support under gravity.

[0073] 2. Determine the solution of the tunnel soil under concentrated force

[0074] like Figure 2 As shown, in order to reflect the effect of concentration, the problem is divided into the following two steps.

[0075] Step 1: Ignoring the effect of gravity, apply a concentrated force P on the half-plane. Assume that there is a virtual circular hole with point Z0 (the point of application of the concentrated force) as the center in the half-plane, and the radius of the virtual circular hole is R. Then, apply a uniform surface force parallel to the concentrated force P on the boundary of the virtual circular hole. When the radius R of the virtual circular hole infinitely approaches 0 and the magnitude of the surface force remains unchanged, the analytical function expression of the concentrated force P can be obtained.

[0076] Step 2: Simulate tunnel excavation. The tunnel excavation process can be regarded as eliminating the forces along the tunnel boundary or applying equal but opposite surface forces on the boundary. Let X n and Y n It represents the surface force component on the boundary of the proposed tunnel, and the surface force component X is applied on the boundary of the circular tunnel. n and Y n The equal but opposite components of the surface forces can be used to obtain the analytical function of tunnel excavation.

[0077] The analytical functions of these two steps are superimposed to obtain the solution of the tunnel soil subjected to concentrated forces.

[0078] 2-1. Ignoring the effect of gravity, a concentrated force P is applied on the half plane.

[0079] 2-1-1. Determine the mapping function under the condition of applying concentrated force P

[0080] A new coordinate system is established with the surface as the x-axis and the perpendicular line through point z0 as the y-axis. In the new coordinate system x'o'y', the area in the physical plane is mapped to a ring in the image plane, and the mapping function is determined as

[0081]

[0082] Where z' represents a point in the new coordinate system, ζ' represents the independent variable of the mapping function, ω(ζ') represents the mapping function, and a'=H2(1-α' 2 ) / (1+α' 2 ), α' is the inner radius of the ring, and the expression of α' is

[0083]

[0084] Among them, H2 is the vertical distance from the center of the virtual circular hole to the ground surface, and R' is the radius of the virtual circular hole, which approaches 0 infinitely.

[0085] 2-1-2. Determine the stress conditions and analytical functions at the hole edge boundary

[0086] use represents the analytical function corresponding to the original coordinate (physical plane) xoy, Represents the analytical function in the new coordinate system, and solves the analytical function through the boundary conditions of the virtual circular hole Then, the stress condition of the virtual circular hole boundary can be obtained:

[0087]

[0088] in

[0089]

[0090] c k and d k is the coefficient of the undetermined analytic function; P x represents the component of the concentrated force P in the x direction; P y represents the component of the concentrated force P in the y direction.

[0091] When z' is at the boundary of the hole

[0092]

[0093] Where σ' is a point on the boundary of the circular hole.

[0094] The analytical function is solved as

[0095]

[0096] 2-1-3. Determine the analytical function in the original coordinate system

[0097] The expression is:

[0098]

[0099] Where L is the offset radius.

[0100] Integrate the above formula,

[0101]

[0102] 2-2. Simulate excavation

[0103] Apply X on the boundary of the circular tunnel n and Y n The surface force components of equal magnitude but opposite direction offset the existing stress.

[0104] For analytical functions According to the proposed excavation boundary L h The stress boundary condition can be obtained

[0105]

[0106] use It represents the analytical function corresponding to step 2, and its expression is

[0107]

[0108] Where, e k ,f k are coefficients.

[0109] Solve the equations (1-12) by stress boundary conditions, and according to the proposed excavation boundary L n The stress boundary conditions, The following equation must be satisfied

[0110]

[0111] C2 is a complex constant; z1 is a point different from z;

[0112] Substituting formula (1-13) into formula (1-11) yields:

[0113]

[0114] The solution is

[0115]

[0116] Where α is the inner radius of the ring;

[0117] A1=-U1[κ(T1-α)+(T2+α)]-U2[W1(T1-2α)+W2α];

[0118] A0=-U1[κ(T3-α 2 )+(αT4-α 2 )]-U2[W1-W2(1+α 2 -αT 3 )];

[0119]

[0120] Assume that ζ is The highest positive and negative power in is N, so there are 2N undetermined coefficients (c k , d k , k=1,2,…,N), there are 2N equations in total. Solving the linear equations can obtain the analytical function The undetermined coefficient e k and f k .

[0121] 2-3. Ignoring the effect of gravity, a concentrated force P' is applied on the half plane.

[0122] Obtain the analytical function of the concentrated force P' acting on the tunnel surrounding rock and The calculation process is the same as and Same.

[0123] 3. Calculation of analytical functions for tunnel support anchors

[0124] The analytical function of the tunnel support anchor is:

[0125]

[0126] 4. Determination of anchor axial force and elongation

[0127] The displacement coordination condition means that the displacement of the anchor and the surrounding rock should be equal, which is used to solve the analytical function. The following displacement coordination conditions must be met between the anchor and the soil:

[0128] (1-η)Δμ r1 (j)+Δu r2 =Δu(j) (1-17)

[0129] Where η is the displacement release coefficient, which reflects the displacement of the soil before the anchor is installed. r1 (j) and Δu r2 In (j), j represents the position of the jth anchor rod. In Δu(j), j represents the position of the jth anchor rod. Δu r1 (j) represents the relative radial displacement of the soil between the two ends of the anchor under the action of tunnel excavation only, Δu r2 (j) represents the relative radial displacement of the soil between the fixed points at both ends of the anchor under the action of only one pair of concentrated forces, and Δu(j) represents the axial elongation of the anchor.

[0130]

[0131] Where Nj is the axial force of the jth anchor rod, N j =P j *S1, S1 is the spacing of anchor rods in the tunnel axis, E s is the elastic modulus of the anchor, d s is the diameter of the anchor rod.

[0132] For prestressed anchor rods, the anchor rod elongation is

[0133]

[0134] Where N 0j is the initial load of the prestressed anchor.

[0135] The axial force of the anchor rod is:

[0136]

[0137] Therefore, given a set of anchor elastic modulus and length, the stress, displacement of the surrounding rock and the axial force of the anchor in the corresponding tunnel under the anchor support condition can be calculated.

[0138] 5. Optimization of anchor parameters

[0139] Since the expression of the analytical function contains parameters such as anchor length and elastic modulus, given a set of anchor length L and elastic modulus, the stress, displacement of the surrounding rock and the axial force of the anchor in the corresponding tunnel under the anchor support condition can be calculated.

[0140] By querying the design specifications, if the stress and displacement of the tunnel under the action of the anchor support and the anchor axial force meet the specifications, the tunnel design can be met. If not, the anchor length and elastic modulus are changed until the tunnel stress and displacement and the anchor axial force meet the design specifications.

[0141] pass Figure 4 It can be seen that increasing the anchor rod length within a certain range can increase the anchor rod axial force. Therefore, the method shown in the present invention can be used to optimize the optimal anchor rod length at various angles of the surrounding rock.

[0142] Example 2

[0143] This embodiment discloses a system for determining and optimizing anchor rod length based on a complex function method.

[0144] A system for determining and optimizing anchor rod length based on a complex function method, comprising:

[0145] The module for determining an analytical function of a tunnel without support under gravity is configured to: determine an analytical function of a tunnel without support under gravity;

[0146] The module for determining the analytical function of shallow tunnel soil under the action of equal and opposite concentrated forces is configured to: assume the force exerted by the surrounding rock on the anchor bolt as a pair of equal and opposite concentrated forces, and solve the analytical function of the shallow tunnel soil under the action of equal and opposite concentrated forces in the absence of gravity;

[0147] The module for determining the analytical function of the tunnel under the action of gravity and anchors is configured to: accumulate the analytical function of the unsupported tunnel under the action of gravity and the analytical function of the shallow tunnel soil under the action of equal and opposite concentrated forces to obtain the analytical function of the tunnel under the action of gravity and anchors;

[0148] The module for obtaining the optimal anchor length is configured as follows: based on the analytical function of the tunnel under the action of gravity and anchors, the stress, displacement of the surrounding rock and the axial force of the anchor under the anchor support condition are calculated, and whether the stress, displacement of the surrounding rock and the axial force of the anchor meet the requirements are judged. If not, the anchor length and elastic modulus are adjusted, and the analytical function determination module for the shallow tunnel soil under the action of equal and large reverse concentrated forces is cycled to the module for obtaining the optimal anchor length until the requirements are met, thereby obtaining the optimal anchor length.

[0149] Example 3

[0150] The purpose of this embodiment is to provide a computer-readable storage medium.

[0151] A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps in the method for determining and optimizing the length of an anchor rod based on a complex function method as described in Example 1 of the present disclosure.

[0152] Example 4

[0153] The purpose of this embodiment is to provide an electronic device.

[0154] An electronic device includes a memory, a processor, and a program stored in the memory and executable on the processor. When the processor executes the program, the steps of the anchor rod length determination and optimization method based on the complex function method as described in Example 1 of the present disclosure are implemented.

[0155] The steps involved in the apparatuses of Examples 2, 3, and 4 above correspond to those of Method Example 1. For detailed implementations, please refer to the relevant description of Example 1. The term "computer-readable storage medium" should be understood to mean a single medium or multiple media containing one or more instruction sets; it should also be understood to include any medium capable of storing, encoding, or carrying an instruction set for execution by a processor and causing the processor to perform any method of the present invention.

[0156] Those skilled in the art will appreciate that the modules or steps of the present invention described above can be implemented using a general-purpose computer device. Alternatively, they can be implemented using program code executable by a computing device, which can then be stored in a storage device and executed by the computing device. Alternatively, they can be fabricated into separate integrated circuit modules, or multiple modules or steps can be fabricated into a single integrated circuit module for implementation. The present invention is not limited to any specific combination of hardware and software.

[0157] Although the above describes the specific embodiments of the present invention 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 various modifications or variations that can be made by those skilled in the art on the basis of the technical solution of the present invention without any creative work are still within the scope of protection of the present invention.

Claims

1. A method for determining and optimizing anchor rod length based on complex function method, characterized in that: The following steps are involved: Step 1: Determine the analytical function of the unsupported tunnel under gravity; Step 2: Assume that the force exerted by the surrounding rock on the anchor is a pair of equal and opposite concentrated forces, and solve the analytical functions of the shallow tunnel soil under the action of equal and opposite concentrated forces in the absence of gravity. Step 3: Accumulate the analytical function of the unsupported tunnel under gravity and the analytical function of the shallow tunnel soil under equal and opposite concentrated forces to obtain the analytical function of the tunnel under gravity and anchors; Step 4: Based on the analytical function of the tunnel under the action of gravity and anchor bolts, calculate the stress, displacement of the surrounding rock, and the axial force of the anchor bolt under the anchor bolt support condition. Determine whether the stress, displacement, and axial force of the surrounding rock and anchor bolt meet the requirements. If not, adjust the anchor bolt length and elastic modulus. Repeat steps 2 to 4 until the requirements are met to obtain the optimal anchor bolt length. Assume that the concentrated forces of equal and opposite directions applied to the surrounding rock on the anchor rod are P and P', respectively. Solve and accumulate the analytical functions of the rock mass under the action of the concentrated force P without excavation, the analytical function simulating the rock mass offsetting the concentrated force P at the tunnel boundary during tunnel excavation, the analytical function of the rock mass under the action of the concentrated force P' without excavation, and the analytical function simulating the rock mass offsetting the concentrated force P' at the tunnel boundary during tunnel excavation. The analytical function of the shallow tunnel soil under the action of equal and opposite concentrated forces is obtained. Assume that there is a virtual circular hole with a radius of R and a concentrated force point Z0 as the center in the half-plane. A uniform surface force parallel to the concentrated force P or P' is applied on the boundary of the virtual circular hole. When the radius R of the virtual circular hole approaches 0 infinitely and the magnitude of the surface force remains unchanged, the analytical function of the rock mass under the action of the concentrated force P without excavation and the analytical function of the rock mass under the action of the concentrated force P' without excavation can be obtained. The tunnel excavation process is considered as eliminating the forces along the tunnel boundary or applying equal but opposite surface forces on the boundary. X n and Y n It represents the surface force component on the boundary of the proposed tunnel, which is applied on the boundary of the circular tunnel. X n and Y n The surface force components of equal magnitude but opposite direction can be used to obtain analytical functions that simulate the rock mass offsetting the concentrated force P at the tunnel boundary during tunnel excavation, and analytical functions that simulate the rock mass offsetting the concentrated force P' at the tunnel boundary during tunnel excavation.

2. The anchor rod length determination and optimization method based on the complex function method according to claim 1 is characterized in that: The stress boundary conditions of the tunnel excavation boundary are determined. Based on the stress boundary conditions of the tunnel excavation boundary, the analytical function of the unsupported tunnel under gravity is obtained.

3. The anchor rod length determination and optimization method based on the complex function method according to claim 1, characterized in that: When solving the analytical function of the rock mass under the action of concentrated force P without excavation and the analytical function of the rock mass under the action of concentrated force P' without excavation: Based on the surface x Axis, through z The vertical line at point 0 is the y-axis, and a new coordinate system is established. x'o'y' , determine the mapping function to map the area in the physical plane to the new coordinate system x'o'y' A ring in the image plane; Solve the new coordinate system by using the virtual circular hole edge boundary condition x'o'y' The analytical function in ; Based on the new coordinate system x'o'y' The analytical function in , determines the analytical function in the physical plane.

4. The anchor rod length determination and optimization method based on the complex function method according to claim 1, characterized in that: The analytical function of the unsupported tunnel under the action of gravity, the analytical function of the rock mass under the action of a concentrated force P without excavation, the analytical function of simulating the rock mass to offset the concentrated force P at the tunnel boundary during tunnel excavation, the analytical function of the rock mass under the action of a concentrated force P' without excavation, and the analytical function of simulating the rock mass to offset the concentrated force P' at the tunnel boundary during tunnel excavation are all solved by the complex function method.

5. A system for determining and optimizing anchor rod length based on complex function method, characterized by: include: The module for determining an analytical function of a tunnel without support under gravity is configured to: determine an analytical function of a tunnel without support under gravity; The module for determining the analytical function of shallow tunnel soil under the action of equal and opposite concentrated forces is configured to: assume the force exerted by the surrounding rock on the anchor bolt as a pair of equal and opposite concentrated forces, and solve the analytical function of the shallow tunnel soil under the action of equal and opposite concentrated forces in the absence of gravity; The module for determining the analytical function of the tunnel under the action of gravity and anchors is configured to: accumulate the analytical function of the unsupported tunnel under the action of gravity and the analytical function of the shallow tunnel soil under the action of equal and opposite concentrated forces to obtain the analytical function of the tunnel under the action of gravity and anchors; The anchor rod optimal length acquisition module is configured to: based on the analytical function of the tunnel under the action of gravity and anchor rods, calculate the stress, displacement of the surrounding rock and the axial force of the anchor rod under the anchor rod support condition, determine whether the stress, displacement of the surrounding rock and the axial force of the anchor rod meet the requirements, and if not, adjust the anchor rod length and elastic modulus, and cycle through the analytical function determination module of the shallow tunnel soil under the action of equal and opposite concentrated forces to the anchor rod optimal length acquisition module until the requirements are met, thereby obtaining the optimal anchor rod length; Assume that the concentrated forces of equal and opposite directions applied to the surrounding rock on the anchor rod are P and P', respectively. Solve and accumulate the analytical functions of the rock mass under the action of the concentrated force P without excavation, the analytical function simulating the rock mass offsetting the concentrated force P at the tunnel boundary during tunnel excavation, the analytical function of the rock mass under the action of the concentrated force P' without excavation, and the analytical function simulating the rock mass offsetting the concentrated force P' at the tunnel boundary during tunnel excavation. The analytical function of the shallow tunnel soil under the action of equal and opposite concentrated forces is obtained. Assume that there is a virtual circular hole with a radius of R and a concentrated force point Z0 as the center in the half-plane. A uniform surface force parallel to the concentrated force P or P' is applied on the boundary of the virtual circular hole. When the radius R of the virtual circular hole approaches 0 infinitely and the magnitude of the surface force remains unchanged, the analytical function of the rock mass under the action of the concentrated force P without excavation and the analytical function of the rock mass under the action of the concentrated force P' without excavation can be obtained. The tunnel excavation process is considered as eliminating the forces along the tunnel boundary or applying equal but opposite surface forces on the boundary. X n and Y n It represents the surface force component on the boundary of the proposed tunnel, which is applied on the boundary of the circular tunnel. X n and Y n The surface force components of equal magnitude but opposite direction can be used to obtain analytical functions that simulate the rock mass offsetting the concentrated force P at the tunnel boundary during tunnel excavation, and analytical functions that simulate the rock mass offsetting the concentrated force P' at the tunnel boundary during tunnel excavation.

6. A computer-readable storage medium having a program stored thereon, characterized in that: When the program is executed by a processor, the steps of the method for determining and optimizing anchor rod length based on a complex function method as described in any one of claims 1 to 4 are implemented.

7. An electronic device comprising a memory, a processor, and a program stored in the memory and executable on the processor, wherein: When the processor executes the program, the steps of the anchor rod length determination and optimization method based on the complex function method as described in any one of claims 1 to 4 are implemented.

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