Method for optimizing parameters of deep circular tunnel anchor in non-uniform stress field

Abstract

The application provides a non-uniform stress field deep buried circular tunnel anchor rod parameter optimization method, including the following steps: S1. Obtain engineering data; S2. Build an anchor rod parameter optimization model F(X); S3. Take the minimum value of the anchor rod parameter optimization model as a target to solve the anchor rod parameter, and obtain the optimal anchor rod parameter; the non-uniform stress field deep buried circular tunnel anchor rod parameter can be optimized, the optimal parameter suitable for the non-uniform force field anchor rod is determined, the algorithm process is simpler than that of the prior art, the efficiency is high, the universality is strong, and the engineering quality is guaranteed.

Description

Technical Field

[0001] This invention relates to the field of tunnel engineering, and more particularly to a method for optimizing the parameters of anchor bolts in deeply buried circular tunnels under non-uniform stress fields. Background Technology

[0002] Anchor bolt support is a reinforcement and support method used in surface engineering such as slopes and deep foundation pits, as well as underground chamber construction such as tunnels and mining areas, to provide stability for construction.

[0003] When using anchor bolt support, it is necessary to determine an optimized value for the anchor bolt parameters that can adapt to the construction scenario in order to ensure the quality of the project. In the existing technology, the optimization of anchor bolt parameters includes numerical simulation method and mechanical analysis method.

[0004] Numerical simulation methods use software such as FLAC3D and combine field monitoring or test results to analyze anchor bolt support schemes. It has significant advantages in studying anchor bolt support schemes in complex geological models. However, it can only compare and select from a limited number of schemes to obtain a relatively optimal solution, and its adaptability is poor.

[0005] Most analytical mechanical methods are based on the assumption of a uniform stress field and perform mechanical analysis on a single anchor rod. Theoretically, analytical methods can obtain the absolute optimal solution of the scheme, but the calculation process is relatively complex, and the force field is non-uniform in actual working conditions. Therefore, existing analytical mechanical methods are difficult to apply.

[0006] Therefore, in order to solve the above-mentioned technical problems, it is urgent to propose a new technical approach. Summary of the Invention

[0007] In view of this, the purpose of this invention is to provide a method for optimizing the parameters of anchor bolts in deeply buried circular tunnels under non-uniform stress fields. This method can optimize the parameters of anchor bolts in deeply buried circular tunnels under non-uniform stress fields, determine the optimal parameters of the anchor bolts suitable for non-uniform force fields, and its algorithm is simpler, more efficient, and more versatile than existing technologies, thus ensuring the quality of engineering projects.

[0008] This invention provides a method for optimizing the parameters of anchor bolts in deeply buried circular tunnels under non-uniform stress fields, comprising the following steps:

[0009] S1. Obtain project data;

[0010] S2. Construct the anchor bolt parameter optimization model F(X):

[0011] F(X) = Δσ 前 -△σ 后 Where: △σ 前 Δσ represents the difference between the tangential and radial stresses around a deeply buried circular tunnel without support. 后This represents the difference between the tangential and radial stresses around the tunnel under the combined action of the anchor bolt and the lining.

[0012] Where p represents the vertical ground stress; λ is the horizontal lateral pressure coefficient of the deep-buried tunnel; θ is the circumferential angle of the anchor bolt, θ∈[0,π / 2], θ j This represents the angle of the j-th division after dividing the circumferential angle θ into m equal parts. R0 is the excavation radius of the deep-buried tunnel, and ξ with subscript is an undetermined coefficient;

[0013] The constraints of the anchor bolt parameter optimization model are:

[0014] ζ represents the relative net displacement around the tunnel after anchor bolt support, and ζ is the control value. η represents the relative net displacement around the tunnel before anchor bolt support, and η is the relative net displacement release coefficient around the tunnel.

[0015] S3. Solve for the anchor bolt parameters with the goal of minimizing the anchor bolt parameter optimization model to obtain the optimal anchor bolt parameters.

[0016] Furthermore, in step S3, the relative net displacement around the tunnel after anchor bolt support is determined according to the following method.

[0017]

[0018]

[0019] Where: μ1 is the Poisson's ratio of the rock mass, E1 is the elastic modulus of the rock mass, G1 is the shear modulus of the rock mass, μ2 is the equivalent Poisson's ratio of the anchor bolt, E2 is the equivalent elastic modulus of the anchor bolt, R1 is the outer radius of the support, G2 is the shear modulus of the anchor bolt support reinforcement, and ξ with subscript is an undetermined coefficient.

[0020] Furthermore, in step S3, the relative net displacement around the tunnel before anchor bolt support is determined according to the following method.

[0021] Where: e is the natural constant, i is the imaginary number, and z is the complex plane variable;

[0022] in: Indicates to Take the conjugate after differentiation. This indicates that ψ(z) takes the conjugate form;

[0023] Furthermore, the equivalent Poisson's ratio and equivalent elastic modulus of the anchor bolt are determined according to the following method:

[0024]

[0025] Where: E b For the elastic model of the anchor bolt, μ b Let r be the Poisson's ratio of the anchor bolt. b Let s be the radius of the anchor bolt. l s represents the anchor bolt spacing. ρ s represents the circumferential spacing of the anchor bolts. ρ = (R0 + l / 2)θ, where l is the length of the anchor rod.

[0026] Furthermore, the undetermined coefficients are determined using the following method:

[0027] Construct the equation for solving the undetermined coefficients:

[0028]

[0029] The undetermined coefficients are obtained by solving the equation.

[0030] The beneficial effects of this invention are as follows: This invention enables the optimization of the parameters of anchor bolts for deeply buried circular tunnels in non-uniform stress fields, determining the optimal parameters of anchor bolts suitable for non-uniform force fields. Moreover, its algorithm is simpler and more efficient than existing technologies, and has strong versatility, thus ensuring the quality of engineering projects. Attached Figure Description

[0031] The present invention will be further described below with reference to the accompanying drawings and embodiments:

[0032] Figure 1 This is a flowchart of the present invention.

[0033] Figure 2 This is a mechanical model diagram of the deep-buried circular tunnel of the present invention.

[0034] Figure 3 This is a schematic diagram of a specific example of the present invention. Detailed Implementation

[0035] The present invention will be further described in detail below:

[0036] This invention provides a method for optimizing the parameters of anchor bolts in deeply buried circular tunnels under non-uniform stress fields, comprising the following steps:

[0037] S1. Obtain project data;

[0038] S2. Construct the anchor bolt parameter optimization model F(X):

[0039] F(X) = Δσ 前 -△σ 后 Where: △σ 前Δσ represents the difference between the tangential and radial stresses around a deeply buried circular tunnel without support. 后 This represents the difference between the tangential and radial stresses around the tunnel under the combined action of the anchor bolt and the lining.

[0040] Where p represents the vertical ground stress; λ is the horizontal lateral pressure coefficient of the deep-buried tunnel; θ is the circumferential angle of the anchor bolt, θ∈[0,π / 2], θ j This represents the angle of the j-th division after dividing the circumferential angle θ into m equal parts. R0 is the excavation radius of the deep-buried tunnel, and ξ with subscript is an undetermined coefficient;

[0041] The constraints of the anchor bolt parameter optimization model are:

[0042] ζ represents the relative net displacement around the tunnel after anchor bolt support, and ζ is the control value. η represents the relative net displacement around the tunnel before anchor bolt support, and η is the relative net displacement release coefficient around the tunnel.

[0043] S3. Solve for the anchor bolt parameters with the goal of minimizing the anchor bolt parameter optimization model to obtain the optimal anchor bolt parameters. Through the above method, the parameters of anchor bolts in deeply buried circular tunnels under non-uniform stress fields can be optimized, and the optimal parameters of anchor bolts suitable for non-uniform force fields can be determined. Moreover, its algorithm process is simpler and more efficient than existing technologies, and has strong versatility, thus ensuring the quality of engineering projects. The solution process can be achieved using existing methods, which will not be elaborated here.

[0044] In this embodiment, in step S3, the relative net displacement around the tunnel after anchor bolt support is determined according to the following method.

[0045]

[0046] Where: μ1 is the Poisson's ratio of the rock mass, E1 is the elastic modulus of the rock mass, G1 is the shear modulus of the rock mass, μ2 is the equivalent Poisson's ratio of the anchor bolt, E2 is the equivalent elastic modulus of the anchor bolt, R1 is the outer radius of the support, G2 is the shear modulus of the anchor bolt support reinforcement, and ξ with subscript is an undetermined coefficient.

[0047] In this embodiment, in step S3, the relative net displacement around the tunnel before anchor bolt support is determined according to the following method.

[0048] Where: e is the natural constant, i is the imaginary number, and z is the complex plane variable;

[0049] in: Indicates to Take the conjugate after differentiation. This indicates that ψ(z) takes the conjugate form;

[0050] In this embodiment, the equivalent Poisson's ratio and equivalent elastic modulus of the anchor bolt are determined according to the following method:

[0051] Where: E b For the elastic model of the anchor bolt, μ b Let r be the Poisson's ratio of the anchor bolt. b Let s be the radius of the anchor bolt. l s represents the anchor bolt spacing. ρ s represents the circumferential spacing of the anchor bolts. ρ = (R0 + l / 2)θ, where l is the length of the anchor rod.

[0052] In this embodiment, the undetermined coefficients are determined by the following method:

[0053] Construct the equation for solving the undetermined coefficients:

[0054]

[0055] The undetermined coefficients are obtained by solving the equation for the undetermined coefficients, where p0 is the internal uniformly distributed pressure of the support.

[0056] Taking the optimization of anchor bolt length parameters as an example:

[0057] Given a circular tunnel with vertical ground stress P = 10 MPa, horizontal lateral pressure coefficient of 1.3, tunnel excavation radius R0 = 3.0 m, rock mass elastic modulus E1 = 5.0 GPa, Poisson's ratio u1 = 0.25, anchor bolt length l = 2.5 m, and radius r... b =10mm, elastic modulus E b =210GPa, Poisson's ratio u b =0.3, row spacing s l =1.0m, uniformly distributed pressure p0=3MPa.

[0058] The parameter table for comparing different options is shown in Table 1:

[0059] Table 1. Parameters for Scheme Comparison

[0060]

[0061] In Table 1, under the four different support schemes, Scheme 1 represents the parameters determined by the optimized scheme of this invention, while Schemes 2 to 4 represent the optimization results of existing technologies. The variation of the virtual support force at the tunnel excavation boundary with the angle is as follows: Figure 3 As shown, from Figure 1 It can be seen from the data that Scheme 1 has the minimum virtual support force, thus Scheme 1 is the optimal method.

[0062] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A method for optimizing the parameters of anchor bolts in deeply buried circular tunnels under non-uniform stress fields, characterized in that: Includes the following steps: S1. Obtain project data; S2. Constructing an anchor bolt parameter optimization model : ;in: This represents the difference between the tangential and radial stresses around a deeply buried circular tunnel without support. This represents the difference between the tangential and radial stresses around the tunnel under the combined action of the anchor bolt and the lining. ;in Indicates vertical ground stress; This refers to the horizontal lateral pressure coefficient of a deeply buried tunnel. The circumferential angle of the anchor bolt. , Indicates the circumferential angle The angle between the j-th division after dividing the material into m equal parts. , The excavation radius of the deeply buried tunnel is indicated by a subscript. These are coefficients to be determined; The constraints of the anchor bolt parameter optimization model are: ; ; This represents the relative net displacement around the tunnel after anchor bolt support. For control values, This represents the relative net displacement around the tunnel before anchor bolt support. The relative net displacement release coefficient around the tunnel; S3. Solve for the anchor bolt parameters with the goal of minimizing the anchor bolt parameter optimization model to obtain the optimal anchor bolt parameters; In step S3, the relative net displacement around the tunnel after anchor bolt support is determined according to the following method. : ； in: Poisson's ratio of the rock mass The elastic modulus of the rock mass. The shear modulus of the rock mass. The equivalent Poisson's ratio of the anchor bolt. Let be the equivalent elastic modulus of the anchor bolt. The outer radius of the support, The shear modulus of the anchor bolt support reinforcement, with subscript. These are coefficients to be determined; In step S3, the relative net displacement around the tunnel before anchor bolt support is determined according to the following method. : ,in: It is a natural constant. It is an imaginary number. For complex plane variables; ;in: Indicates to Take the conjugate after differentiation. express Take conjugate; Where: undetermined coefficients with subscripts Determined using the following method: Construct the equation for solving the undetermined coefficients: The undetermined coefficients are obtained by solving the equation.

2. The method for optimizing anchor bolt parameters in a deeply buried circular tunnel under non-uniform stress field according to claim 1, characterized in that: The equivalent Poisson's ratio and equivalent elastic modulus of the anchor bolt are determined using the following method: ； ;in: This is the elastic model of the anchor bolt. The Poisson's ratio of the anchor bolt. Where is the anchor radius. The anchor bolt spacing, The circumferential spacing of the anchor bolts. , This represents the length of the anchor bolt.

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