Method for determining bearing arch loose load of long-span tunnel based on plastic zone parameters
The method for determining the loosening load of the bearing arch of a mega-span tunnel using plastic zone parameters has solved the problem of load parameter transformation in underground rock engineering, realized the scientificity and reliability of load calculation, and improved the safety and economy of the design.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- CHINA RAILWAY LIUYUAN GRP CO LTD
- Filing Date
- 2026-04-21
- Publication Date
- 2026-07-31
AI Technical Summary
Existing technologies cannot accurately convert the plastic zone state parameters in numerical simulations into design load parameters, leading to a disconnect in the design of support structures in underground rock engineering, and posing risks of material waste or surrounding rock instability.
A standardized load determination process is formed by using a method for determining the loosening load of the bearing arch of a mega-span tunnel based on plastic zone parameters, including calculating the equivalent loosening load height, vertical and horizontal loosening pressure, and combining non-uniform pressure distribution and load-displacement verification cycle.
It achieves scientific and repeatable load calculations, improves the reliability of structural internal force analysis and the robustness of design schemes, avoids human experience errors, and ensures the safety and economy of the project.
Smart Images
Figure CN122088205B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of geotechnical engineering and underground engineering support design technology, specifically to a method for determining the loosening load of the bearing arch of a mega-span tunnel based on plastic zone parameters. Background Technology
[0002] In underground rock engineering, especially in the design of long-span tunnels, accurately determining the loosening loads acting on the support structure is a fundamental challenge throughout the entire process of safety and economic decision-making. This challenge stems from the complexity of the interaction between the surrounding rock and the support: the load is not pre-existing but gradually forms and changes during the dynamic process of tunnel excavation, stress redistribution, surrounding rock damage, and support intervention. Overestimating the load will result in an excessively large support structure, material waste, and prolonged construction time, leading to significant economic losses; underestimating it may cause surrounding rock instability, support failure, or even catastrophic engineering accidents, threatening lives.
[0003] Traditional design methods often resort to simplistic or empirical approaches when faced with this complex problem. Classical methods such as Protodyakonov's theory, based on the assumption of a loose medium, neglect the structural strength of the rock mass itself and the actual failure mechanism. Their calculation results are often conservative under high ground stress or intact hard rock conditions. While modern numerical simulation technology can precisely reveal key quantitative information such as the extent of the plastic zone and stress field distribution of the surrounding rock, these valuable quantitative results are usually only used for qualitative evaluation of the surrounding rock stability and have not yet been systematically and reliably converted into design loads that can be directly used for structural dimensional design and safety verification. This has led to a disconnect between analysis and design in current engineering practice, the key issue being the lack of a standardized method for converting plastic zone state parameters into design load parameters.
[0004] Therefore, there is an urgent need for a method to determine loosening loads that can directly bridge numerical analysis results with engineering design inputs, has a clear physical mechanism, and possesses self-verification capabilities. Summary of the Invention
[0005] The technical problem to be solved by the present invention is to address the shortcomings of the prior art by providing a method for determining the loosening load of the bearing arch of a giant-span tunnel based on plastic zone parameters.
[0006] To achieve the above objectives, the technical solution adopted by the present invention is as follows: The method for determining the loosening load of the bearing arch of a mega-span tunnel based on plastic zone parameters includes the following steps: Step S1: Input the geometric parameters of the target tunnel, the physical and mechanical parameters of the surrounding rock, and the preset support structure parameters, and obtain the height of the plastic zone of the tunnel arch through numerical simulation analysis; Step S2: Based on the system anchor parameters in the support structure parameters, calculate the equivalent thickness of the bearing arch formed after the system anchors reinforce the surrounding rock of the tunnel; Step S3: Compare the height of the plastic zone with the equivalent thickness of the bearing arch, and determine the equivalent loose load height used to calculate the loose load according to the preset rules; Step S4: Based on the equivalent loosening load height and the unit weight of the surrounding rock, calculate the vertical loosening pressure acting on the bearing arch; Step S5: Determine the lateral pressure coefficient used to calculate the loosening pressure based on the macroscopic strength index of the surrounding rock; Step S6: Based on the vertical loosening pressure and the lateral pressure coefficient, calculate the horizontal loosening pressure acting on the bearing arch; Step S7: Perform a verification loop for the loosening load of the bearing arch and output the final verified loosening load of the bearing arch; The loosening load of the bearing arch includes vertical loosening pressure and horizontal loosening pressure acting on the bearing arch.
[0007] Further, in step S2, the calculation process of the equivalent thickness of the bearing arch includes: obtaining the length of the free section of the anchor bolt and the average angle between the anchor bolt direction and the normal direction of the tunnel wall; multiplying the length of the free section of the anchor bolt by the cosine of the average angle to obtain the foundation thickness; adding an additional equivalent thickness to the foundation thickness, the additional equivalent thickness being obtained by comprehensively considering the contributions of the prestressed anchor cable, the shotcrete layer and the bearing capacity of the surrounding rock itself to the thickness of the reinforced arch.
[0008] Furthermore, the method for determining the average angle between the anchor bolt direction and the tunnel wall normal direction specifically includes: simplifying the reinforcement range of a single anchor bolt into a cone whose axis coincides with the anchor bolt direction, and the average angle is the statistical average value of the angle between the generatrix and the normal when the cone is projected onto the tunnel wall normal direction.
[0009] Furthermore, in step S3, the specific rules for determining the equivalent loosening load height include: taking the maximum value among the plastic zone height, the equivalent thickness of the bearing arch, and the preset minimum calculation height; the preset minimum calculation height is set based on engineering experience to ensure that the load calculation can still take into account the self-weight of the bearing arch structure and the weight of the unstable rock mass above, even if the plastic zone height is not detected by numerical simulation.
[0010] Furthermore, in step S4, the method for calculating the vertical loosening pressure includes: multiplying the unit weight of the surrounding rock by the equivalent loosening load height, and applying the calculation result as a uniformly distributed load to the bearing arch ring.
[0011] Furthermore, in step S5, the method for determining the lateral pressure coefficient specifically includes: constructing an empirical function, wherein the empirical function uses the geological strength index of the surrounding rock and the initial geostress field lateral pressure coefficient as variables, and introduces a correction coefficient determined through regional engineering experience and numerical inversion analysis for adjustment, wherein the empirical function is used to ensure that the calculated lateral pressure coefficient is always not greater than the initial geostress field lateral pressure coefficient.
[0012] Furthermore, in step S6, the distribution of the horizontal loosening pressure along the bearing arch ring is non-uniform. The non-uniform distribution pattern is determined by a function including the calculated section position angle, lateral pressure coefficient, vertical loosening pressure intensity, and distribution morphology coefficient. The distribution morphology coefficient is calibrated by comparing the proportional relationship between the horizontal and vertical expansion depths of the plastic zone in the numerical simulation.
[0013] Furthermore, step S7 specifically includes the following steps: Vertical and horizontal loosening pressures were applied to the mechanical model of the load-bearing arch structure, and the first displacement response was calculated. Obtain the tunnel surrounding rock displacement results output by the numerical simulation in step S1 under the same preset support structure parameters, and obtain the tunnel surrounding rock displacement results output by the numerical simulation based on the input parameters in step S1 as the second displacement response. Compare the displacement values of the first displacement response and the second displacement response at the arch crown and arch foot; if the relative error between the two exceeds the preset threshold, adjust the lateral pressure coefficient and distribution morphology coefficient and recalculate until the error does not exceed the preset threshold, and output the final verified bearing arch loosening load.
[0014] A storage medium storing instructions that, when read by a computer, cause the computer to execute any method for determining the loosening load of a giant-span tunnel bearing arch based on plastic zone parameters.
[0015] An electronic device includes a processor and a storage medium, the processor executing instructions in the storage medium.
[0016] Compared with the prior art, the beneficial effects of the present invention are as follows: 1. This invention changes the traditional model that relies on fixed empirical coefficients by directly using the height of the plastic zone, a key parameter characterizing the failure state of the surrounding rock, as the calculation input. Combined with the proposed equivalent thickness model of the bearing arch and the non-uniform horizontal pressure distribution function, it forms a standardized load determination process with clear parameter meanings and calculation steps, which improves the scientific nature and repeatability of the design and realizes the mechanisticization of the load source and the standardization of the calculation process.
[0017] 2. This invention proposes a non-uniform distribution model defined by coefficients calibrated by the morphology of the plastic zone, which makes the calculation of horizontal loosening pressure, especially the loads of key parts such as arch feet and arch shoulders, more reflective of the actual stress state of the loosened surrounding rock, thereby significantly improving the reliability of structural internal force analysis and safety evaluation.
[0018] 3. The load-displacement verification loop constructed in this invention constitutes the self-verification core of the method. By comparing the mechanical model response with the numerical simulation benchmark, the key parameters are automatically adjusted until convergence, which effectively avoids human experience errors and ensures that the final output load simultaneously satisfies mechanical equilibrium and deformation coordination, thus guaranteeing the robustness and economic rationality of the design scheme. Attached Figure Description
[0019] Other features, objects, and advantages of the invention will become more apparent from the following detailed description of non-limiting embodiments with reference to the accompanying drawings: Figure 1 This is a flowchart illustrating an embodiment of the present invention; Figure 2 This is a schematic diagram illustrating the calculation of the equivalent thickness of the load-bearing arch according to an embodiment of the present invention; Figure 3 This is a schematic diagram of the load cycle verification logic in an embodiment of the present invention. Detailed Implementation
[0020] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be described in detail below with reference to the accompanying drawings and specific embodiments.
[0021] like Figure 1 As shown, the method for determining the loosening load of the bearing arch of a mega-span tunnel based on plastic zone parameters includes the following steps: Step S1: Input the geometric parameters of the target tunnel, the physical and mechanical parameters of the surrounding rock, and the preset support structure parameters, and obtain the height of the plastic zone of the tunnel arch through numerical simulation analysis; Step S2: Based on the system anchor parameters in the support structure parameters, calculate the equivalent thickness of the bearing arch formed after the system anchors reinforce the surrounding rock of the tunnel; Step S3: Compare the height of the plastic zone with the equivalent thickness of the bearing arch, and determine the equivalent loose load height used to calculate the loose load according to the preset rules; Step S4: Based on the equivalent loosening load height and the unit weight of the surrounding rock, calculate the vertical loosening pressure acting on the bearing arch; Step S5: Determine the lateral pressure coefficient used to calculate the loosening pressure based on the macroscopic strength index of the surrounding rock; Step S6: Based on the vertical loosening pressure and the lateral pressure coefficient, calculate the horizontal loosening pressure acting on the bearing arch; Step S7: Perform a verification loop for the loosening load of the bearing arch and output the final verified loosening load of the bearing arch; The loosening load of the bearing arch includes vertical loosening pressure and horizontal loosening pressure acting on the bearing arch.
[0022] The geometric parameters of the target tunnel include: span, sag, and sidewall height.
[0023] The physical and mechanical parameters of the surrounding rock include: unit weight, geological strength index, Hawke-Brown criterion parameters, and elastic modulus.
[0024] The preset support structure parameters include: system anchor length, free section length, circumferential longitudinal spacing, prestress; prestressed anchor cable parameters; and shotcrete thickness.
[0025] A numerical model containing the above input parameters was established using finite element / finite difference software such as FLAC3D to simulate the entire process of tunnel excavation and support. After the simulation was completed, the maximum development height of the plastic zone above the arch in the vertical direction was extracted, which is the height of the plastic zone of the tunnel, in meters.
[0026] like Figure 2 As shown, in step S2, the calculation process of the equivalent thickness of the bearing arch includes: obtaining the length of the free section of the anchor rod and the average angle between the anchor rod direction and the normal direction of the tunnel wall; multiplying the length of the free section of the anchor rod by the cosine of the average angle to obtain the foundation thickness; adding an additional equivalent thickness to the foundation thickness, the additional equivalent thickness being obtained by comprehensively considering the contributions of the prestressed anchor cable, the shotcrete layer and the bearing capacity of the surrounding rock itself to the thickness of the reinforced arch.
[0027] The formula for calculating the equivalent thickness of the load-bearing arch is: in, Indicates the equivalent thickness of the load-bearing arch. Indicates the length of the free section of the anchor bolt. This represents the average angle between the direction of the anchor bolt and the direction of the normal to the tunnel wall. The additional equivalent thickness is represented by the following formula: in, This indicates the thickness contributed by the anchor cable, specifically 0.3 times the difference between the anchor cable length and the anchor bolt length. This represents the anchor cable contribution coefficient, typically ranging from 0.5 to 1.2. Indicates the thickness of the shotcrete layer. This represents the equivalent coefficient of the sprayed layer, which is an empirical coefficient and typically ranges from 1.0 to 3.0. Indicates geological strength index, This represents the contribution coefficient of the surrounding rock, which is an empirical coefficient, typically taken as 0.5 to 1.5. This represents the proportionality coefficient, typically ranging from 0.1 to 0.3. This indicates the initial anchor reinforcement thickness, i.e. The above formula transforms the additional equivalent thickness, which is difficult to measure directly, into a function associated with measurable and designable support parameters and assessable rock mass parameters, and is calibrated by a series of regional or rock type empirical coefficients.
[0028] The value is mainly proportional to the anchor cable tension and inversely proportional to the anchor cable spacing. In a specific embodiment, for anchor cables with a prestress of 1500kN and a spacing of 3m, it is taken as 0.8; when the prestress increases to 2000kN, it can be increased to 1.0. A higher value, such as 2.0 to 3.0, is taken when the surrounding rock is fractured and jointed to reflect the key protective role of the spray layer on the surface rock mass; a lower value, such as 1.0 to 1.5, is taken when the surrounding rock is relatively intact. and Inversion calibration can be performed by comparing the calculation results of the simplified model and the refined discrete element model, for thick limestone (Class II surrounding rock). The initial empirical value can be taken as 0.15. Version 1.0 is acceptable.
[0029] The method for determining the average angle between the anchor bolt direction and the tunnel wall normal direction specifically includes: simplifying the reinforcement range of a single anchor bolt into a cone whose axis coincides with the anchor bolt direction, and the average angle is the statistical average value of the angle between the generatrix and the normal when the cone is projected onto the tunnel wall normal direction.
[0030] In step S3, the specific rules for determining the equivalent loosening load height include: taking the maximum value among the plastic zone height, the equivalent thickness of the bearing arch, and the preset minimum calculation height; the preset minimum calculation height is set based on engineering experience to ensure that the load calculation can still take into account the self-weight of the bearing arch structure and the weight of the unstable rock mass above, even if the plastic zone height is not detected by numerical simulation. The specific formula is as follows: in, Indicates the equivalent loosening load height. Indicates the height of the plastic zone. This represents the preset minimum calculation height, set based on engineering experience. For example, it can be 0.5 to 1.0 times the equivalent thickness of the bearing arch. The purpose is to ensure that the load calculation can still cover the self-weight of the bearing arch and the weight of the most basic loose rock mass above it when the height of the plastic zone is too small or the plastic zone is not displayed in the simulation, thus ensuring the lower limit of design safety. For projects with high requirements for support reliability or where the rock mass has rheological properties, a higher value should be used, such as 1 times the equivalent thickness of the bearing arch. For temporary projects or cases with extremely good rock mass quality, a lower value should be used, such as 0.5 times the equivalent thickness of the bearing arch.
[0031] In step S4, the calculation method for the vertical loosening pressure includes: multiplying the unit weight of the surrounding rock by the equivalent loosening load height, and applying the calculation result as a uniformly distributed load to the bearing arch ring. The specific formula is as follows: in, Indicates vertical loosening pressure. This indicates the density of the surrounding rock.
[0032] In step S5, the method for determining the lateral pressure coefficient specifically includes: constructing an empirical function, which uses the surrounding rock geological strength index and the initial geostress field lateral pressure coefficient as variables, and introduces a correction coefficient determined through regional engineering experience and numerical inversion analysis for adjustment. The empirical function is used to ensure that the calculated lateral pressure coefficient is always no greater than the initial geostress field lateral pressure coefficient. The specific formula is as follows: in, Indicates the lateral pressure coefficient. , , This represents a regional empirical correction coefficient, dimensionless, determined based on local engineering cases through numerical inversion and fitting of measured data. This represents a geological strength index, dimensionless. It represents the lateral pressure coefficient of the initial geostress field at the site, is dimensionless, and is obtained through geostress testing or inversion.
[0033] Methods for determining regional empirical correction coefficients include: Collect GSI data from 3-5 similar existing projects in the region. Measured values, and measured values of surrounding rock loosening pressure obtained through inverse analysis; for each engineering case, a numerical model is established and adjusted. , , The formula calculates After substituting the loads into the calculations, the model displacement best fits the actual monitored displacement; the best result obtained by inverting all cases is... , , Combined statistical analysis is performed to provide suggested value ranges. For example, for the limestone surrounding rock of a hydropower station project in Southwest China, inversion analysis of five tunnels... Use a value of 0.85~1.05. Take a value of 0.5~0.7. Take a value of 0.2 to 0.4.
[0034] In step S6, the horizontal loosening pressure is distributed non-uniformly along the bearing arch ring. This non-uniform distribution is determined by a function that includes the calculated section position angle, lateral pressure coefficient, vertical loosening pressure intensity, and distribution morphology coefficient. The distribution morphology coefficient is calibrated by comparing the proportional relationship between the horizontal and vertical expansion depths of the plastic zone in the numerical simulation. The specific formula is as follows: in, Indicates horizontal loosening pressure. , This represents the horizontal pressure distribution shape coefficient, which is dimensionless. This indicates the angle between the calculated section position and the vertical direction. It represents the angle between the cross section of the arch foot of the supporting arch and the vertical direction.
[0035] Distribution shape coefficient Calibrate according to the following steps: From the numerical simulation results of step S1, measure the horizontal distance from the plastic zone boundary to the tunnel wall at four characteristic locations: the arch crown, the quarter arch, the arch shoulder, and the arch foot. Calculate the ratio R(θ) of the horizontal distance to the vertical plastic zone depth at each location; Assuming the horizontal pressure distribution coefficient is proportional to the plastic zone morphology coefficient, and using R(0)=1 at the arch crown as a benchmark, the curve is fitted using the least squares method to solve for... and The specific value; For the lateral pressure coefficient The surrounding rock is approximately equal to grade II or III with a strength of 1.0. It is usually between 0.3 and 0.8. Between 1.5 and 2.5.
[0036] like Figure 3 As shown, step S7 specifically includes the following steps: Vertical and horizontal loosening pressures were applied to the mechanical model of the load-bearing arch structure, and the first displacement response was calculated. Obtain the tunnel surrounding rock displacement results output by the numerical simulation in step S1 under the same preset support structure parameters, and obtain the tunnel surrounding rock displacement results output by the numerical simulation based on the input parameters in step S1 as the second displacement response. Compare the displacement values of the first displacement response and the second displacement response at the arch crown and arch foot; if the relative error between the two exceeds the preset threshold, adjust the lateral pressure coefficient and distribution morphology coefficient and recalculate until the error does not exceed the preset threshold, and output the final verified bearing arch loosening load.
[0037] Vertical and horizontal loosening pressures are applied to a simplified load-bearing arch structural mechanical model. The displacement of the model under load is calculated, and the settlement of the arch crown and the horizontal displacement of the arch foot are extracted to form the first displacement response set. From the numerical simulation results of step S1, the displacement values of the same monitoring points are extracted to form the second displacement response set; Calculate the relative error between the first displacement response set and the second displacement response set, with a preset threshold of 10%; If the relative error is greater than 10%, the parameters are automatically adjusted. Usually, the regional empirical correction coefficient in the lateral pressure coefficient and the horizontal pressure distribution morphology coefficient in the horizontal loosening pressure are finely adjusted first. Then, the process returns to step S5 / S6 to recalculate the load and repeats this verification step until the relative error is less than or equal to 10%. When the error meets the requirements, the currently verified vertical loosening pressure and horizontal loosening pressure are output as the final design load.
[0038] A storage medium storing instructions that, when read by a computer, cause the computer to execute any method for determining the loosening load of a giant-span tunnel bearing arch based on plastic zone parameters.
[0039] An electronic device includes a processor and a storage medium, the processor executing instructions in the storage medium.
[0040] Any combination of one or more computer-readable media may be used. A computer-readable medium can be a computer-readable signal medium or a computer-readable storage medium. A computer-readable storage medium can be, for example, but not limited to, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination thereof. More specific examples (a non-exhaustive list) of computer-readable storage media include: an electrical connection having one or more wires, a portable computer disk, a hard disk, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fiber, portable compact disk read-only memory (CD-ROM), optical storage device, magnetic storage device, or any suitable combination thereof. In this document, a computer-readable storage medium can be any tangible medium that contains or stores a program that can be used by or in connection with an instruction execution system, apparatus, or device.
[0041] The examples described herein are merely preferred embodiments of the invention and are not intended to limit the concept and scope of the invention. Any modifications and improvements made by those skilled in the art to the technical solutions of the invention without departing from the design concept of the invention should fall within the protection scope of the invention.
Claims
1. A method for determining the loosening load of the bearing arch of a mega-span tunnel based on plastic zone parameters, characterized in that, Includes the following steps: Step S1: Input the geometric parameters, surrounding rock physical and mechanical parameters, and preset support structure parameters of the target tunnel, and obtain the height of the plastic zone of the tunnel arch through numerical simulation analysis. Specifically, this includes: establishing a model containing geometric parameters, surrounding rock physical and mechanical parameters, and preset support structure parameters using FLAC3D numerical simulation software, simulating the entire process of tunnel excavation and support, and extracting the maximum development height of the plastic zone in the vertical direction as the height of the plastic zone. Step S2: Based on the system anchor parameters in the support structure parameters, calculate the equivalent thickness of the bearing arch formed after the system anchors reinforce the tunnel surrounding rock. The calculation process of the equivalent thickness of the bearing arch includes: obtaining the length of the free section of the anchor and the average angle between the anchor direction and the tunnel wall normal direction; multiplying the length of the free section of the anchor by the cosine of the average angle to obtain the foundation thickness; adding an additional equivalent thickness to the foundation thickness. The additional equivalent thickness is obtained by comprehensively considering the contributions of the prestressed anchor cable, the shotcrete layer, and the bearing capacity of the surrounding rock itself to the thickness of the reinforced arch. The specific formula is as follows: in, Indicates the equivalent thickness of the load-bearing arch. Indicates the length of the free section of the anchor bolt. This represents the average angle between the direction of the anchor bolt and the direction of the normal to the tunnel wall. Indicates the additional equivalent thickness; Step S3: Compare the height of the plastic zone with the equivalent thickness of the bearing arch, and determine the equivalent loosening load height for calculating the loosening load according to preset rules. Specifically, this includes taking the maximum value among the height of the plastic zone, the equivalent thickness of the bearing arch, and the preset minimum calculation height. The preset minimum calculation height is set based on engineering experience to ensure that the load calculation can still take into account the self-weight of the bearing arch structure and the weight of the unstable rock mass above it, even if the height of the plastic zone is not detected by numerical simulation. The specific formula is as follows: in, Indicates the equivalent loosening load height. Indicates the height of the plastic zone. Indicates the preset minimum calculation height; Step S4: Based on the equivalent loosening load height and the unit weight of the surrounding rock, calculate the vertical loosening pressure acting on the bearing arch; Step S5: Based on the macroscopic strength index of the surrounding rock, determine the lateral pressure coefficient used to calculate the loosening pressure. The method for determining the lateral pressure coefficient specifically includes: constructing an empirical function, which uses the geological strength index of the surrounding rock and the initial geostress field lateral pressure coefficient as variables, and introduces a correction coefficient determined through regional engineering experience and numerical inversion analysis for adjustment. The empirical function is used to ensure that the calculated lateral pressure coefficient is always no greater than the initial geostress field lateral pressure coefficient. The specific formula is as follows: in, Indicates the lateral pressure coefficient. , , This represents the regional empirical correction coefficient. Indicates geological strength index, Indicates the lateral pressure coefficient of the initial geostress field at the site; Step S6: Based on the vertical loosening pressure and the lateral pressure coefficient, calculate the horizontal loosening pressure acting on the bearing arch; Step S7: Perform a verification loop for the loosening load of the bearing arch and output the final verified loosening load of the bearing arch; The loosening load of the bearing arch includes vertical loosening pressure and horizontal loosening pressure acting on the bearing arch.
2. The method according to claim 1, characterized in that, The method for determining the average angle between the anchor bolt direction and the tunnel wall normal direction specifically includes: simplifying the reinforcement range of a single anchor bolt into a cone whose axis coincides with the anchor bolt direction, and the average angle is the statistical average value of the angle between the generatrix and the normal when the cone is projected onto the tunnel wall normal direction.
3. The method according to claim 1, characterized in that, In step S4, the method for calculating the vertical loosening pressure includes: multiplying the unit weight of the surrounding rock by the equivalent loosening load height, and applying the calculation result as a uniformly distributed load to the bearing arch ring.
4. The method according to claim 1, characterized in that, In step S6, the distribution of the horizontal loosening pressure along the bearing arch ring is non-uniform. The non-uniform distribution pattern is determined by a function that includes the calculated section position angle, lateral pressure coefficient, vertical loosening pressure intensity, and distribution morphology coefficient. The distribution morphology coefficient is calibrated by comparing the proportional relationship between the horizontal and vertical expansion depths of the plastic zone in the numerical simulation.
5. The method according to claim 1, characterized in that, Step S7 specifically includes the following steps: Vertical and horizontal loosening pressures were applied to the mechanical model of the load-bearing arch structure, and the first displacement response was calculated. Obtain the tunnel surrounding rock displacement results output by the numerical simulation in step S1 under the same preset support structure parameters, and obtain the tunnel surrounding rock displacement results output by the numerical simulation based on the input parameters in step S1 as the second displacement response. Compare the displacement values of the first displacement response and the second displacement response at the arch crown and arch foot; if the relative error between the two exceeds the preset threshold, adjust the lateral pressure coefficient and distribution morphology coefficient and recalculate until the error does not exceed the preset threshold, and output the final verified bearing arch loosening load.
6. A storage medium, characterized in that, The storage medium stores instructions that, when read by a computer, cause the computer to execute the method for determining the loosening load of the bearing arch of a mega-span tunnel based on plastic zone parameters, as described in any one of claims 1-5.
7. An electronic device, characterized in that, It includes a processor and the storage medium of claim 6, wherein the processor executes instructions in the storage medium.