Design method for pre-applying counter-force to advance hole of multi-arch tunnel without middle guide

Abstract

The invention relates to the technical field of highway engineering, and discloses a middle-guide-free multi-arch tunnel preceding hole counter-force pre-applying design method which is based on a radial reinforcing anchor rod and comprises the steps that a middle-guide-free multi-arch tunnel preceding hole counter-force pre-applying design method is adopted, and the middle-guide-free multi-arch tunnel preceding hole counter-force pre-applying design method is adopted; radial reinforcing anchor rods are arranged at the position, close to the arch shoulder of the rear hole side, of the front hole in a driving mode, unstable surrounding rock of the triangular area is reinforced through the radial reinforcing anchor rods, and radial pre-applied counter force is provided so that the arch shoulder structure of the front hole can be effectively restrained. After the preceding hole is excavated, the counter-force pre-applying design method for the preceding hole of the middle-guiding-free multi-arch tunnel can guide the arch shoulder radial reinforcing anchor rod to be driven at the most economical and effective position, angle and length through calculation, unstable surrounding rock in a triangular area is pre-reinforced before the following hole is excavated, and tension is provided to restrain the deformation of the arch shoulder structure; therefore, possible cracking and even damage of the first hole structure are prevented, the local stability of the hidden middle wall side of the first hole is improved, and tunnel structure safety and construction safety are guaranteed.

Description

Technical Field

[0001] The invention relates to the technical field of highway engineering, and in particular to a method for designing a pre-addition reaction force for a pilot hole of a non-central guide multi-arch tunnel. Background Art

[0002] In the process of highway tunnel construction, non-central guide multi-arch tunnels are widely used in some parts of China due to factors such as fast construction speed, less land use and low cost. In the construction process of non-central guide multi-arch tunnels, the leading tunnel is affected by shallow buried bias, weak surrounding rock and excavation of the trailing tunnel, which may cause engineering accidents or structural diseases. Especially after the excavation of the trailing tunnel, the surrounding rock in the triangular area is disturbed for the second time, the surrounding rock is broken and the stress is concentrated in the area, which makes the lining of the arch shoulder of the leading tunnel prone to large deformation, resulting in structural cracking. In more serious cases, structural damage and collapse may even occur, which brings great risks to the construction of non-central guide multi-arch tunnels. Summary of the invention

[0003] In order to solve the above problems, the present invention provides a method for designing a pre-reaction force for the pilot tunnel of a non-central guide continuous arch tunnel. The method for designing a pre-reaction force for the pilot tunnel of a non-central guide continuous arch tunnel is intended to control the structural deformation of the arch shoulder of the pilot tunnel, prevent structural damage, and ensure the structural safety and construction safety of the non-central guide continuous arch tunnel.

[0004] The technical solution adopted by the present invention is:

[0005] A method for designing a preloaded reaction force for a pilot tunnel of a non-central guide multi-arch tunnel is based on radial reinforcement anchor rods. Radial reinforcement anchor rods are driven at the side shoulders of the pilot tunnel close to the rear tunnel, and the unstable surrounding rock in the triangular area is reinforced by the radial reinforcement anchor rods. A radial preloaded reaction force is provided so that the shoulder structure of the pilot tunnel is effectively constrained.

[0006] Furthermore, before the radial reinforcement anchor rods are driven, two inflection points at the side spandrels and the inverted arch of the hidden middle wall of the tunnel need to be obtained through numerical calculation, and the local structural force calculation is performed at the inflection points to obtain the position, angle and preload reaction force of the spandrel radial reinforcement anchor rods, and the length of the radial reinforcement anchor rods is obtained by reverse calculation based on the preload reaction force.

[0007] Furthermore, the method for designing the pre-addition reaction force of the leading hole of the non-central guide multi-arch tunnel comprises the following steps:

[0008] Step 1, numerical calculation and structural analysis: numerical simulation software is used to obtain the tunnel structure bending moment diagram according to numerical simulation calculation, and the inflection points where the bending moment of the arch shoulder and the inverted arch of the hidden middle wall of the first tunnel is zero are marked, that is, the inflection point A where the bending moment of the arch shoulder of the hidden middle wall of the first tunnel is zero and the inflection point D where the bending moment of the inverted arch is zero;

[0009] Step 2, determine the radial reinforcement anchor rod driving position: select the best driving point below the arch span of the leading hole and above the overlap of the hidden middle wall, and ensure that the driving angle of the radial reinforcement anchor rod is greater than the angle δ formed by the center point O of the leading hole and the tangent point H of the subsequent hole;

[0010] Step 3, structural stress analysis: intercept the known inflection points of the arch shoulder and the inflection points of the inverted arch for structural analysis, and pre-add the reaction force through structural analysis;

[0011] Step 4, calculation of the length and number of radial reinforcement anchor rods: the length L and number N of the radial reinforcement anchor rods are calculated based on the required preload reaction force.

[0012] Furthermore, in step 2, the process of selecting the best placement point below the spandrel of the first tunnel and above the overlap of the hidden middle wall is as follows:

[0013] Based on the tunnel structure bending moment diagram, the intersection point C of the middle wall of the leading tunnel and the rear tunnel is marked in the tunnel structure bending moment diagram, and the center point O of the leading tunnel is marked at the same time. A tangent line is drawn from point O to the rear tunnel to obtain the tangent point H and the intersection point G of the tangent line and the leading tunnel; a point B is randomly selected between the inflection point A and the intersection point G as the driving position of the radial reinforcement anchor.

[0014] Furthermore, in step 3, the structural analysis process of intercepting the known inflection points of the spandrels of the first tunnel and the inflection points of the inverted arch is as follows:

[0015] Firstly, the inflection points A and D are regarded as sliding hinge supports, and the corresponding force conditions are set; among them, the inflection point A generates an axial force FA when subjected to the vertical load of the soil above the tunnel, and the angle between FA and the horizontal plane is α; the radial reinforcement anchor generates a pull-out force FB after being driven at point B, and the angle between FB and the horizontal plane is β, and the value range of β is δ≤β≤90°; the force FC transmitted by the steel arch frame at the overlap of the leading tunnel and the rear tunnel is generated at the intersection point C of the middle wall of the leading tunnel and the rear tunnel, and the angle between FC and the horizontal plane is θ; the inflection point D generates an axial force FD when subjected to the vertical load of the soil above the tunnel; because the inflection points A and D are inflection points with zero bending moment, the local structural moment equilibrium is calculated by setting the inflection point D with zero bending moment of the inverted arch as the moment center of the structure.

[0016] Furthermore, the process of obtaining the moment equilibrium of the local structure includes the following steps:

[0017] Step I: Establishment of mechanical equilibrium equation: The horizontal distance between inflection point A and inflection point D is A. x , vertical distance is A y ; The horizontal distance between point B and inflection point D is B x , vertical distance is B y ; The horizontal distance between the middle wall intersection point C and the inflection point D is C x , vertical distance is Cy ;

[0018] Then the moment equilibrium equation of the local structure is established:

[0019]

[0020] Where F is the external force acting on the structure; F A 、F B 、F C is the external force on the inflection points A, B, and the intersection point C between the middle wall; F _x and F _y Represents the components of external force in the horizontal and vertical directions;

[0021] Step II, geometric constraint equation setting: The center point O of the pilot tunnel is known, the distance between point O and the center line of the initial steel arch frame at the hidden middle wall of the pilot tunnel is r, and the horizontal distance between point O and the inflection point D is O x , the vertical distance is O y ;

[0022] Then use the geometric relationship of the known circle to establish the constraint equation:

[0023] O x +B x =rcosβ Formula 2, B y -O y =rsinβ Formula 3;

[0024] Step III, iterative solution: Combine equation 1, equation 2 and equation 3 to obtain:

[0025]

[0026] Solving for unknown quantities B x , and B y ;

[0027] Set up an iterative process and program it to find F B The radial reinforcement anchor rod driving angle β at the minimum value is used to calculate the radial reinforcement anchor rod length L and number N.

[0028] The beneficial effects of the present invention are:

[0029] After the pilot tunnel is excavated, the pre-reaction design method for the pilot tunnel of the non-central guide continuous arch tunnel can guide the placement of the radial reinforcement anchors of the arch shoulders at the most economical and effective position, angle and length through calculation, and pre-reinforce the unstable surrounding rock in the triangular area and provide tension to restrain the deformation of the arch shoulder structure before the subsequent tunnel is excavated; thereby preventing possible cracking or even damage of the pilot tunnel structure, improving the local stability of the hidden middle wall side of the pilot tunnel, and ensuring the safety of the tunnel structure and construction.

[0030] Improve safety: Through targeted reinforcement design, the risk of instability of the tunnel surrounding rock is reduced, and safety during construction is enhanced. Optimize resource allocation: On the basis of numerical analysis, the number and length of radial reinforcement anchors are reasonably set, which can effectively reduce the consumption of construction resources and improve resource utilization. Reduce construction costs and time: Through effective pre-reaction design, material waste caused by insufficient or excessive reinforcement can be reduced, and the overall construction cost can be reduced. At the same time, the optimized design can shorten the construction period. Enhance construction reliability: This method makes the construction design more reasonable through scientific procedures and detailed structural analysis, thereby improving the overall construction quality and reliability of the tunnel. Strong adaptability: This method can adapt to different geological conditions and tunnel design requirements, has good versatility, and provides new ideas for the design of future tunnel projects.

[0031] In summary, the pre-addition reaction force design method for the pilot tunnel of the non-central guide double-arch tunnel can not only effectively solve the technical problems in tunnel construction, but also has good economic and social benefits. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] Figure 1 It is a flow chart of the method for designing the pre-addition reaction force of the pilot hole of the non-central guide multi-arch tunnel of the present invention;

[0033] Figure 2 The bending moment diagram of the tunnel structure obtained by the present invention according to numerical simulation calculation;

[0034] Figure 3 It is a local force analysis diagram based on the tunnel structure bending moment diagram of the present invention;

[0035] In the figure: 1—preliminary tunnel, 2—post-tunnel, 3—radial reinforcement anchor rods, 4—center line of primary support steel arch. DETAILED DESCRIPTION

[0036] The following will be combined with the accompanying drawings of the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0037] In the construction process of a non-central guide multi-arch tunnel, the leading tunnel is affected by factors such as shallow buried bias, weak surrounding rock and excavation of the following tunnel, which may cause engineering accidents or structural problems. Therefore, this embodiment provides a pre-reaction design method for the leading tunnel of a non-central guide multi-arch tunnel.

[0038] The pre-reaction design method for the leading tunnel of the non-central guide multi-arch tunnel is based on radial reinforcement anchor rods. Radial reinforcement anchor rods are installed at the side shoulders of the leading tunnel close to the rear tunnel, and the unstable surrounding rock in the triangular area is reinforced by the radial reinforcement anchor rods. The radial pre-reaction force is provided to effectively constrain the arch shoulder structure of the leading tunnel, thereby controlling the structural deformation of the arch shoulder of the leading tunnel, preventing structural damage, and ensuring the structural safety and construction safety of the non-central guide multi-arch tunnel.

[0039] Furthermore, before the radial reinforcement anchor rod is driven, two inflection points of the spandrel and the inverted arch of the hidden middle wall of the first hole need to be obtained by numerical calculation, and the local structural force calculation is performed at the inflection points to obtain the position, angle and preload reaction force of the spandrel radial reinforcement anchor rod, and the length of the radial reinforcement anchor rod is obtained by back-calculation based on the preload reaction force. Therefore, this embodiment provides the following method steps to obtain the position, angle and preload reaction force of the spandrel radial reinforcement anchor rod, and the length of the radial reinforcement anchor rod is obtained by back-calculation based on the preload reaction force.

[0040] like Figure 1 As shown in the figure, the pre-addition reaction force design method for the pilot hole of the non-central guide multi-arch tunnel specifically includes the following steps:

[0041] Step 1, numerical calculation and structural analysis:

[0042] The tunnel structure bending moment diagram is obtained by numerical simulation software. Figure 2 As shown in the figure, the bending moment diagram of the tunnel structure is obtained through numerical simulation, and the inflection point can be accurately located. This provides a scientific basis for the design of subsequent radial reinforcement anchors, ensuring the rationality and effectiveness of the design. In the bending moment diagram of the tunnel structure, the inflection points where the bending moment of the side spandrel and the inverted arch of the hidden middle wall of the pilot tunnel 1 is zero are marked, that is, the inflection point A where the bending moment of the side spandrel of the hidden middle wall of the pilot tunnel 1 is zero, and the inflection point D where the bending moment of the inverted arch is zero.

[0043] Step 2: Determine the location of the radial reinforcement anchor bolts:

[0044] Select the best driving point below the spandrel of the first tunnel and above the overlap of the hidden middle wall to ensure that the driving angle of the radial reinforcement anchor 3 is greater than the angle δ formed by the center point O of the first tunnel 1 and the tangent point H of the subsequent tunnel. Select a reasonable driving position for the radial reinforcement anchor 3 to ensure that the action angle of the radial reinforcement anchor 3 is optimal, which helps to improve the reinforcement effect. Avoid the selection of singular points to reduce the potential risk of structural instability.

[0045] The process of selecting the best placement point below the spandrel of the pilot tunnel 1 and above the overlap of the hidden middle wall is as follows:

[0046] like Figure 2As shown, based on the tunnel structure bending moment diagram, the middle wall intersection C of the leading tunnel 1 and the rear tunnel 2 is marked in the tunnel structure bending moment diagram, and the center point O of the leading tunnel 1 is marked, and a tangent line is drawn from point O to the rear tunnel 2 to obtain the tangent point H and the intersection point G of the tangent line and the leading tunnel 1; a point B is randomly selected between the inflection point A and the intersection point G as the driving position of the radial reinforcement anchor 3.

[0047] Step 3, structural stress analysis:

[0048] The known inflection point A of the arch span of the pilot tunnel 1 and the inflection point D of the inverted arch are intercepted for structural analysis, and the size of the preloaded reaction force is determined through structural analysis. Analyzing the stress conditions of the structure helps to accurately predict the required preloaded reaction force; through this step, the reinforcement design can be optimized and material waste can be reduced.

[0049] The structural analysis process of intercepting the known inflection points of the spandrel and the inflection points of the inverted arch of the pilot tunnel 1 is as follows:

[0050] like Figure 2 and Figure 3 As shown in Figure 1, first, the inflection points A and D are regarded as sliding hinge supports, and the corresponding force conditions are set; among them, the inflection point A is under the vertical load q of the soil above the tunnel. l +q z In this case, an axial force FA is generated, and the angle between FA and the horizontal plane is α; after the radial reinforcement anchor rod 3 is driven at point B, a pull-out force FB is generated, and the angle between FB and the horizontal plane is β, and the value range of β is δ≤β≤90°.

[0051] At the same time, the force FC transmitted by the steel arch frame at the overlap of the leading tunnel 1 and the rear tunnel 2 is generated at the intersection C of the middle wall of the leading tunnel 1 and the rear tunnel 2, and the angle between FC and the horizontal plane is θ. In addition, the inflection point D is at the vertical load q of the soil above the tunnel. l +q z In this case, an axial force FD is generated.

[0052] Since the inflection point A and the inflection point D are inflection points with zero bending moment, the moment balance of the local structure can be calculated by setting the inflection point D with zero bending moment of the inverted arch as the moment centroid of the structure.

[0053] Step 4, calculation of radial reinforcement anchor length and quantity:

[0054] The length L and number N of the radial reinforcement anchor rods 3 are calculated based on the required preload reaction force. The length and number of the radial reinforcement anchor rods 3 are reasonably calculated based on the determined preload reaction force, thereby ensuring the effectiveness and economy of the reinforcement measures; this process helps to reduce construction costs and time.

[0055] Specifically, based on the structural analysis of the known inflection points of the spandrel and the inflection points of the inverted arch of the pilot tunnel 1 in step 3, the process of obtaining the bending moment balance of the local structure includes the following steps:

[0056] Step I: Establishment of mechanical equilibrium equation:

[0057] like Figure 3 As shown, the horizontal distance between the inflection point A and the inflection point D is A x , vertical distance is A y ; The horizontal distance between point B and inflection point D is B x , vertical distance is B y ; The horizontal distance between the middle wall intersection point C and the inflection point D is C x , vertical distance is C y .

[0058] Then the moment equilibrium equation of the local structure is established:

[0059]

[0060] Where F is the external force acting on the structure; F A 、F B 、F C is the external force on the inflection points A, B, and the intersection point C between the middle wall; F _x and F _y Represents the components of the external force in the horizontal and vertical directions.

[0061] Step II, geometric constraint equation setting:

[0062] like Figure 2 As shown in the figure, the center point O of the pilot tunnel is known, and the distance between point O and the center line 4 of the initial steel arch frame at the hidden middle wall of the pilot tunnel 1 is r, as shown in the figure. Figure 3 As shown, the horizontal distance between point O and the inflection point D is O x , the vertical distance is O y .

[0063] Then use the geometric relationship of the known circle to establish the constraint equation:

[0064] O x +B x =rcosβFormula 2, B y -O y =rsinβFormula 3.

[0065] Step III, iterative solution:

[0066] Combining equation 1, equation 2 and equation 3, we get:

[0067]

[0068] In formula 4, B x , and B y is an unknown quantity. Since δ≤β≤α, a simple program can be compiled to solve it multiple times to obtain F B The radial reinforcement anchor is set at an angle β when the minimum value is reached, so that according to F B The length L and number N of radial reinforcement anchor rods are calculated.

[0069] In order to verify the pre-reaction design method of the pilot tunnel without central guide double arch tunnel, the following actual verification is carried out:

[0070] Taking a non-central guide multi-arch tunnel in Yunnan as an example, the most unfavorable working condition is taken: the buried depth is about 25m, the height of the triangle area is 5.1m, the surrounding rock is strongly weathered muddy sandstone, and the gravity γ is 23KN / m 3 , the vertical load on the tunnel is q, q = q l +q z =692.3KN / m 2 ;

[0071] Through numerical simulation calculation, the positions of the inflection points A and D on the side of the hidden tunnel wall are obtained; the local structure is intercepted at points A and D for analysis:

[0072] Where α=54°, FA=2420.06KN, A x =0.664, A y =8.963m, θ=21°, FC=4182.09KN, C x =1.807, C y =5.539, in this structure, δ=30°;

[0073] A simple program was established to calculate the β at the minimum FB, β = 45°; the preload reaction force FB = 2089KN, that is, the radial reinforcement anchor rod needs to provide a tensile force of 2089KN on each square meter of the spandrel structure. The surrounding rock in the triangular area of ​​the tunnel was broken and it was difficult to form a hole. Self-propelled anchor rods were used for reinforcement. A total of 4 self-propelled anchor rods with a length of L=6m were installed per square meter on site with a circumferential spacing of 0.5m and a longitudinal spacing of 0.5m. That is, each anchor rod provided a tensile force of about 522KN, which had a good pre-reinforcement effect on the arch shoulders of the pilot tunnel.

[0074] In summary, after the pilot tunnel is excavated, the pre-reaction design method for the pilot tunnel of the non-central guide multi-arch tunnel can guide the placement of the radial reinforcement anchors of the spandrels at the most economical and effective position, angle and length through calculation, and pre-reinforce the unstable surrounding rock in the triangular area and provide tension to constrain the deformation of the spandrel structure before the subsequent tunnel is excavated; thereby preventing the possible cracking or even damage of the pilot tunnel structure, improving the local stability of the hidden middle wall side of the pilot tunnel, and ensuring the safety of the tunnel structure and construction.

[0075] The above shows and describes the basic principles, main features and advantages of the present invention. It should be understood by those skilled in the art that the present invention is not limited to the above embodiments, and the above embodiments and descriptions are only for explaining the principles of the present invention. Without departing from the spirit and scope of the present invention, the present invention may have various changes and improvements, which fall within the scope of the present invention to be protected. The scope of protection of the present invention is defined by the attached claims and their equivalents.

Claims

1. A method for designing pre-reaction force of a pilot tunnel without a central guide double arch tunnel, characterized by: The preload reaction design method for the leading tunnel of the non-central guide multi-arch tunnel is based on radial reinforcement anchor rods. Radial reinforcement anchor rods are driven at the side spans of the leading tunnel close to the rear tunnel, and the unstable surrounding rock in the triangular area is reinforced by radial reinforcement anchor rods. The radial preload reaction force is provided to effectively constrain the spandrel structure of the leading tunnel.

2. The method for designing the pre-reaction force of the pilot hole of a non-central guide double-arch tunnel according to claim 1 is characterized in that: Before the radial reinforcement anchor rods are driven, two inflection points at the side spandrels and the inverted arch of the hidden middle wall of the tunnel need to be obtained through numerical calculation, and the local structural force calculation is performed at the inflection points to obtain the position, angle and preload reaction force of the spandrel radial reinforcement anchor rods, and the length of the radial reinforcement anchor rods is obtained by reverse calculation based on the preload reaction force.

3. The method for designing the pre-reaction force of the pilot hole of a non-central guide multi-arch tunnel according to claim 2 is characterized in that: The method for designing the pre-addition reaction force of the leading hole of the non-central guide multi-arch tunnel comprises the following steps: Step 1, numerical calculation and structural analysis: numerical simulation software is used to obtain the tunnel structure bending moment diagram according to numerical simulation calculation, and the inflection points where the bending moment of the arch shoulder and the inverted arch of the hidden middle wall side of the tunnel is zero are marked, the inflection point A where the bending moment of the arch shoulder of the hidden middle wall side of the tunnel is zero, and the inflection point D where the bending moment of the inverted arch is zero; Step 2, determine the radial reinforcement anchor rod driving position: select the best driving point below the arch span of the leading hole and above the overlap of the hidden middle wall, and ensure that the driving angle of the radial reinforcement anchor rod is greater than the angle δ formed by the center point O of the leading hole and the tangent point H of the subsequent hole; Step 3, structural stress analysis: intercept the known inflection points of the arch shoulder and the inflection points of the inverted arch for structural analysis, and pre-add the reaction force through structural analysis; Step 4, calculation of the length and number of radial reinforcement anchor rods: the length L and number N of the radial reinforcement anchor rods are calculated based on the required preload reaction force.

4. The method for designing the pre-reaction force of the pilot hole of a non-central guide double-arch tunnel according to claim 3 is characterized in that: In step 2, the process of selecting the best placement point below the spandrel of the pilot hole and above the overlap of the hidden middle wall is as follows: Based on the tunnel structure bending moment diagram, the intersection point C of the middle wall of the leading tunnel and the rear tunnel is marked in the tunnel structure bending moment diagram, and the center point O of the leading tunnel is marked at the same time. A tangent line is drawn from point O to the rear tunnel to obtain the tangent point H and the intersection point G of the tangent line and the leading tunnel; a point B is randomly selected between the inflection point A and the intersection point G as the driving position of the radial reinforcement anchor.

5. The method for designing the pre-reaction force of the pilot hole of a non-central guide double-arch tunnel according to claim 4 is characterized in that: In step 3, the structural analysis process of intercepting the known inflection points of the spandrel and the inverted arch is as follows: Firstly, the inflection points A and D are regarded as sliding hinge supports, and the corresponding force conditions are set; among them, the inflection point A generates an axial force FA when subjected to the vertical load of the soil above the tunnel, and the angle between FA and the horizontal plane is α; the radial reinforcement anchor generates a pull-out force FB after being driven at point B, and the angle between FB and the horizontal plane is β, and the value range of β is δ≤β≤90°; the force FC transmitted by the steel arch frame at the overlap of the leading tunnel and the rear tunnel is generated at the intersection point C of the middle wall of the leading tunnel and the rear tunnel, and the angle between FC and the horizontal plane is θ; the inflection point D generates an axial force FD when subjected to the vertical load of the soil above the tunnel; because the inflection points A and D are inflection points with zero bending moment, the local structural moment equilibrium is calculated by setting the inflection point D with zero bending moment of the inverted arch as the moment center of the structure.

6. The method for designing the pre-reaction force of the pilot hole of a non-central guide double-arch tunnel according to claim 5 is characterized in that: The process of obtaining the moment equilibrium of the local structure includes the following steps: Step I: Establishment of mechanical equilibrium equation: The horizontal distance between inflection point A and inflection point D is A. x , vertical distance is A y ; The horizontal distance between point B and inflection point D is B x , vertical distance is B y ; The horizontal distance between the middle wall intersection point C and the inflection point D is C x , vertical distance is C y ; Then the moment equilibrium equation of the local structure is established: Where F is the external force acting on the structure; F A 、F B 、F C is the external force on the inflection points A, B, and the intersection point C between the middle wall; F _x and F _y Represents the components of external force in the horizontal and vertical directions; Step II, geometric constraint equation setting: The center point O of the pilot tunnel is known, the distance between point O and the center line of the initial steel arch frame at the hidden middle wall of the pilot tunnel is r, and the horizontal distance between point O and the inflection point D is O x , the vertical distance is O y ; Then use the geometric relationship of the known circle to establish the constraint equation: O x +B x =rcosβ Formula 2, B y -O y =rsinβ Formula 3; Step III, iterative solution: Combine equation 1, equation 2 and equation 3 to obtain: Solving for unknown quantities B x , and B y ; Set up an iterative process and program it to find F B The radial reinforcement anchor rod driving angle β at the minimum value is used to calculate the radial reinforcement anchor rod length L and number N.

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