Method, medium and device for analyzing stability of tunnel bearing arch based on loose pressure

Abstract

The application discloses a tunnel bearing arch stability analysis method based on loose pressure, a medium and equipment, relates to the technical field of engineering data analysis, and comprises the following steps: delimiting the height of the arch top loose area based on construction numerical simulation results; simplifying the reinforced loose surrounding rock into a hingeless bearing arch structure elastically fixed with side walls; determining a load system comprising vertical pressure, horizontal pressure and support counterforce, wherein the side pressure coefficient of the horizontal pressure is determined through iterative optimization; establishing a bearing arch-elastic foundation side wall collaborative mechanical model and calculating internal forces; calculating the comprehensive strength of the bearing arch composite rock mass based on the Hoek-Brown criterion and considering the equivalent confining pressure provided by the anchor rod; and calculating the compression and tension safety factors to realize quantitative evaluation of stability. The application optimizes the horizontal loose pressure load, accurately simulates the collaborative action of the bearing arch and the surrounding rock, and provides a scientific and economic safety evaluation means for support design of super-large-span tunnels.

Description

Technical Field

[0001] This invention relates to the field of engineering data analysis technology, specifically to a method, medium, and equipment for analyzing the stability of tunnel bearing arches based on loosening pressure. Background Technology

[0002] In tunnel engineering projects with ultra-large spans (30m and above) and small rise-to-span ratios, traditional support design theories face severe challenges. Currently, the common approach is to generalize the anchor-sprayed reinforced zone as a load-bearing arch for analysis. However, existing methods have significant shortcomings: for the critical load of horizontal loosening pressure, a fixed lateral pressure coefficient is usually given based on empirical formulas in the specifications, failing to consider its dynamic relationship with the tunnel span, shape, and specific support structure; the value is arbitrary and often conservative. Calculation models often simplify the load-bearing arch to a three-hinged arch or one that bears all the ground stress, ignoring its characteristic of being a hingeless arch co-stressed with the surrounding rock, and the active reinforcement effect provided by the support prestress, leading to distorted internal force analysis. Existing methods lack refined calculation methods for key parameters such as the strength of the composite rock mass formed by anchor bolt reinforcement and the nonlinear resistance of the surrounding rock. These deficiencies make it difficult for traditional analysis methods to accurately reflect the complex real stress state of ultra-large span tunnels, easily leading to design waste or safety hazards.

[0003] Therefore, there is a need for a stability analysis method for large-span tunnel bearing arches that can scientifically determine horizontal loosening pressure, accurately simulate the collaborative stress mechanism between the bearing arch and the surrounding rock, and quantitatively calculate the support reinforcement effect, so as to guide safe, economical and reliable support design. Summary of the Invention

[0004] The technical problem to be solved by the present invention is to address the shortcomings of the prior art by providing a method, medium and equipment for analyzing the stability of tunnel bearing arches based on loosening pressure.

[0005] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0006] The stability analysis method for tunnel bearing arches based on loosening pressure includes the following steps:

[0007] Step S1: Based on the numerical simulation results of the tunnel construction process, identify the inner boundary of the pressure arch that is naturally formed above the tunnel arch, and delineate the height of the loose zone below the pressure arch that needs to be borne by the support structure.

[0008] Step S2: The surrounding rock in the loosened area, after being reinforced by the system anchor bolts, anchor cables and grouting, is simplified into a single circular arc curve-shaped load-bearing arch structure; wherein the load-bearing arch is a hingeless arch, and the arch foot is elastically fixedly connected to the tunnel sidewall;

[0009] Step S3: Determine the loads acting on the bearing arch, including the vertical loosening pressure caused by the self-weight of the loosened surrounding rock, the corresponding horizontal loosening pressure, and the support reaction force acting on the inner boundary of the bearing arch by the prestress of the anchor bolts and anchor cables.

[0010] Step S4: Establish a mechanical model for the coordinated stress analysis of the load-bearing arch and the side wall. The load-bearing arch ring is calculated as a hingeless arch elastically fixed to the top of the side wall, and the side wall is calculated as a beam vertically placed on an elastic foundation.

[0011] Step S5: Based on the collaborative force analysis mechanical model, calculate the distribution of internal forces in the cross section of the bearing arch under load, and then identify the control section with the most unfavorable internal forces.

[0012] Step S6: Based on the strength criterion and considering the equivalent confining pressure effect provided by the support, calculate the comprehensive compressive strength and comprehensive tensile strength of the bearing arch composite rock mass formed after reinforcement.

[0013] Step S7: Based on the most unfavorable control section and the corresponding internal forces of the section, and combined with the comprehensive compressive strength and comprehensive tensile strength, calculate the compressive safety factor and tensile safety factor of the bearing arch respectively, so as to achieve a quantitative evaluation of the stability of the bearing arch.

[0014] Furthermore, in step S2, when simplifying to a load-bearing arch structure, it is necessary to determine the equivalent calculated thickness of the load-bearing arch. The equivalent calculated thickness is determined by the system anchor length, the compression angle of the anchorage zone, and the group anchor effect coefficient.

[0015] Furthermore, in step S2, when simplifying to a load-bearing arch structure, it is necessary to determine the equivalent elastic modulus of the load-bearing arch. The equivalent elastic modulus of the load-bearing arch is calculated using a modified hybrid law model that considers the bond slip effect at the interface between the anchor bolt and the surrounding rock.

[0016] Furthermore, in step S3, the horizontal loosening pressure is distributed in a trapezoidal shape along the arch and sidewalls, and the distribution intensity is determined by multiplying the vertical loosening pressure by the lateral pressure coefficient. The value of the lateral pressure coefficient is optimized through iterative calculation.

[0017] Furthermore, in step S3, the support reaction force acting on the inner boundary of the bearing arch by the prestress of the anchor rods and anchor cables is calculated based on the prestress design value of the anchor rods, the circumferential spacing, and the longitudinal spacing.

[0018] Furthermore, in step S4, when establishing the collaborative stress analysis mechanical model, the constraint effect of the surrounding rock on the deformation of the bearing arch is taken into account, i.e., the surrounding rock resistance. The application of the surrounding rock resistance follows the following judgment conditions: the radial stress at the calculation point of the bearing arch is a non-tensile stress, and the point generates a radial displacement toward the surrounding rock; the relationship between the surrounding rock resistance and the radial displacement is described by a piecewise nonlinear function to simulate the elastoplastic constraint behavior of the surrounding rock.

[0019] Furthermore, in step S6, the comprehensive compressive strength is calculated according to the Hawke-Brown strength criterion. The minimum principal stress value used in the comprehensive compressive strength is the equivalent confining pressure, which is calculated by the anchor prestress and the grouting pressure. The comprehensive tensile strength is directly calculated using the expression for the tensile strength of rock mass in the Hawke-Brown strength criterion.

[0020] Further, in step S7, the compressive safety factor is the ratio of the comprehensive compressive strength to the maximum calculated compressive stress on the most unfavorable control section; the tensile safety factor is the ratio of the comprehensive tensile strength to the maximum calculated tensile stress on the most unfavorable control section;

[0021] Among them, the maximum calculated tensile stress on the most unfavorable control section is positive. When the maximum calculated tensile stress on the most unfavorable control section is zero or negative, the section is determined to meet the tensile safety requirements.

[0022] A storage medium, characterized in that the storage medium stores instructions that, when a computer reads the instructions, cause the computer to execute any one of the methods for analyzing the stability of a tunnel bearing arch based on loosening pressure.

[0023] An electronic device, characterized in that it includes a processor and a storage medium, wherein the processor executes instructions in the storage medium.

[0024] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0025] 1. This invention uses the horizontal loosening pressure lateral pressure coefficient as an optimization variable, so that its value is dynamically adapted to the actual mechanical response of the bearing arch, avoiding the blindness of empirical values, making the load calculation more in line with engineering practice, and improving the accuracy of analysis and the safety of the structure.

[0026] 2. This invention adopts a hingeless arch-elastic foundation sidewall collaborative mechanical model and introduces nonlinear surrounding rock resistance considering elastoplastic softening, which can more realistically simulate the combined action of the bearing arch and the surrounding rock, and solves the problem of internal force distortion in traditional simplified models.

[0027] 3. By optimizing the load and quantitatively considering the confining pressure effect of the support, this invention can fully tap the self-supporting potential of the surrounding rock and the effectiveness of the support materials. Under the premise of ensuring safety, it can provide clear guidance for optimizing the anchor bolt parameters, which helps to achieve the refined and economical design of the support scheme.

[0028] 4. This invention provides calculation formulas for key parameters such as the equivalent thickness and equivalent elastic modulus of the bearing arch, which include microscopic mechanisms such as the group anchor effect and interface bond slip. The physical meaning of the parameters is clear and there are corresponding engineering determination methods. The whole set of methods is complete and convenient for engineers to apply and implement in design and analysis. Attached Figure Description

[0029] 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:

[0030] Figure 1 This is a flowchart illustrating an embodiment of the present invention;

[0031] Figure 2 This is a schematic diagram of the load-bearing arch model and load analysis in an embodiment of the present invention. Detailed Implementation

[0032] 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.

[0033] like Figure 1 As shown, the stability analysis method for tunnel bearing arch based on loosening pressure includes the following steps:

[0034] Step S1: Based on the numerical simulation results of the tunnel construction process, identify the inner boundary of the pressure arch that is naturally formed above the tunnel arch, and delineate the height of the loose zone below the pressure arch that needs to be borne by the support structure.

[0035] Step S2: The surrounding rock in the loosened area, after being reinforced by the system anchor bolts, anchor cables and grouting, is simplified into a single circular arc curve-shaped load-bearing arch structure; wherein the load-bearing arch is a hingeless arch, and the arch foot is elastically fixedly connected to the tunnel sidewall;

[0036] Step S3: Determine the loads acting on the bearing arch, including the vertical loosening pressure caused by the self-weight of the loosened surrounding rock, the corresponding horizontal loosening pressure, and the support reaction force acting on the inner boundary of the bearing arch by the prestress of the anchor bolts and anchor cables.

[0037] Step S4: Establish a mechanical model for the coordinated stress analysis of the load-bearing arch and the side wall. The load-bearing arch ring is calculated as a hingeless arch elastically fixed to the top of the side wall, and the side wall is calculated as a beam vertically placed on an elastic foundation.

[0038] Step S5: Based on the collaborative force analysis mechanical model, calculate the distribution of internal forces in the cross section of the bearing arch under load, and then identify the control section with the most unfavorable internal forces.

[0039] Step S6: Based on the strength criterion and considering the equivalent confining pressure effect provided by the support, calculate the comprehensive compressive strength and comprehensive tensile strength of the bearing arch composite rock mass formed after reinforcement.

[0040] Step S7: Based on the most unfavorable control section and the corresponding internal forces of the section, and combined with the comprehensive compressive strength and comprehensive tensile strength, calculate the compressive safety factor and tensile safety factor of the bearing arch respectively, so as to achieve a quantitative evaluation of the stability of the bearing arch.

[0041] In step S2, when simplifying to a load-bearing arch structure, it is necessary to determine the equivalent calculated thickness of the load-bearing arch. The equivalent calculated thickness is determined by the system anchor length, the compression angle of the anchorage zone, and the group anchor effect coefficient.

[0042] In step S2, when simplifying to a load-bearing arch structure, it is necessary to determine the equivalent elastic modulus of the load-bearing arch. The equivalent elastic modulus of the load-bearing arch is calculated using a modified hybrid law model that considers the bond slip effect at the interface between the anchor bolt and the surrounding rock.

[0043] In step S3, the horizontal loosening pressure is distributed in a trapezoidal shape along the arch and sidewalls. The distribution intensity is determined by multiplying the vertical loosening pressure by the lateral pressure coefficient. The value of the lateral pressure coefficient is optimized through iterative calculation.

[0044] In step S3, the support reaction force acting on the inner boundary of the bearing arch by the prestress of the anchor rod and anchor cable is calculated based on the prestress design value of the anchor rod, the circumferential spacing and the longitudinal spacing.

[0045] Based on a refined three-dimensional numerical simulation of the tunnel excavation process, the lower boundary of the naturally formed pressure arch above the tunnel crown was identified by analyzing the plastic zone, displacement field, and stress redistribution characteristics of the surrounding rock. The rock mass from this boundary to the tunnel crown is the loosened zone, and its height is denoted as [height not specified]. The vertical loosening pressure originates from the self-weight of this part of the rock mass.

[0046] The loosened rock mass within the system's anchor reinforcement range is generalized as a load-bearing arch. The equivalent thickness of the load-bearing arch is not simply the anchor length, but rather a comprehensive result considering the group anchor effect and stress diffusion. The calculation formula is as follows:

[0047]

[0048] in, Indicates the equivalent thickness of the load-bearing arch. Indicates the design length of the system anchor bolts. This represents the compression angle of the anchorage zone, reflecting the diffusion range of the anchor bolt tension in the surrounding rock. It is initially estimated based on the internal friction angle φ of the surrounding rock, using the empirical relationship θ = 45° - φ / 2, and then corrected by combining the rock mass integrity coefficient or determined through field tests. The group anchoring effect coefficient is represented by the following formula:

[0049]

[0050] in, This represents an empirical coefficient, typically ranging from 1.0 to 1.5, obtained through indoor model tests or numerical simulation back analysis of existing projects. and These represent the circumferential spacing and longitudinal spacing of the anchor bolts, respectively.

[0051] The load-bearing arch is a composite material consisting of rock mass, anchor bolts, and a bonding interface. Its equivalent elastic modulus is calculated using a modified model considering interface slip, with the specific formula as follows:

[0052]

[0053] in, This represents the equivalent elastic modulus of the load-bearing arch. This represents the elastic modulus of the surrounding rock before reinforcement. This indicates the elastic modulus of the anchor bolt steel. This represents the cross-sectional area of ​​a single anchor bolt. This indicates the average area of ​​surrounding rock supported by a single anchor bolt. Indicates the diameter of the anchor bolt. The interfacial bonding efficiency coefficient reflects the grouting fullness and bonding strength, and is determined through experiments. The length-to-diameter ratio influence coefficient of the anchor bolt is a dimensionless empirical parameter that reflects the influence of the anchor bolt's slenderness ratio on its ability to deform in tandem with the surrounding rock; among which... It can be obtained by inverting the load-displacement curve from the anchor pull-out test. The determination can be made through composite compression tests of anchors with different length-to-diameter ratios.

[0054] The vertical loosening pressure is generated by the self-weight of the rock mass in the loosened area and is considered to be uniformly distributed along the arch axis. The specific formula is as follows:

[0055]

[0056] in, Indicates vertical loosening pressure. Indicates the density of the surrounding rock. Indicates the height of the loosened area.

[0057] The horizontal loosening pressure is distributed in a trapezoidal shape along the depth, and its intensity is calculated by the following formula:

[0058]

[0059] in, Indicates horizontal loosening pressure. Indicates depth, Indicates the height of the straight wall section of the tunnel. This represents the lateral pressure coefficient.

[0060] The lateral pressure coefficient of horizontal loosening pressure is determined through an optimization process aimed at the mechanical response of the bearing arch structure itself, specifically including:

[0061] The optimization objective is to minimize the absolute value of the tensile stress inside the cross section of the arch crown. The aim is to actively improve the stress state of this key part of the arch crown by adjusting the lateral compression coefficient of the horizontal load, so that it is under compression or without tensile stress as much as possible, thereby improving the structural stability from the source of load design.

[0062] The lower limit of the objective function search interval is determined based on the recommended value for the corresponding surrounding rock level in the relevant tunnel design specifications, serving as an engineering experience benchmark. The upper limit of the interval is determined by calculation, and its value is the critical lateral pressure coefficient that makes the circumferential tensile stress of the arch crown section just change from tension to compression.

[0063] The specific optimization solution is completed through iterative calculation. Within the interval, the value of the lateral pressure coefficient is gradually adjusted with a preset step size. For each trial value of the lateral pressure coefficient, a complete internal force analysis of the bearing arch is performed to obtain the corresponding tensile stress at the top of the arch. Finally, all trial results are compared, and the lateral pressure coefficient that minimizes the tensile stress is selected as the optimal lateral pressure coefficient.

[0064] The support reaction force is provided by prestressed anchor bolts / cables, acting uniformly on the inner surface of the bearing arch. The specific formula is as follows:

[0065]

[0066] in, Indicates the support reaction force. This indicates the number of anchor bolts / cables on the calculated cross-section. This represents the effective prestress design value for a single anchor bolt / cable.

[0067] In step S4, when establishing the collaborative stress analysis mechanical model, the constraint effect of the surrounding rock on the deformation of the bearing arch is taken into account, i.e., the surrounding rock resistance. The application of the surrounding rock resistance follows the following judgment conditions: the radial stress at the calculation point of the bearing arch is non-tensile stress, and the point generates a radial displacement toward the surrounding rock; the relationship between the surrounding rock resistance and the radial displacement is described by a piecewise nonlinear function to simulate the elastoplastic constraint behavior of the surrounding rock.

[0068] The load-bearing arch-sidewall co-mechanical model treats the load-bearing arch as an elastically fixed, hingeless arch at the top of the sidewalls, and the sidewalls as vertical beams on a Winkler elastic foundation. Both satisfy displacement compatibility and moment equilibrium conditions at the arch foot, forming a statically indeterminate system, which is solved simultaneously using structural mechanics methods. The model incorporates surrounding rock resistance to more realistically simulate rock constraints; its relationship with the radial displacement of the load-bearing arch is a piecewise function, specifically:

[0069]

[0070] in, Indicates the resistance of the surrounding rock. This represents the initial elastic resistance coefficient of the surrounding rock. Indicates the radial displacement of the bearing arch. It represents the critical displacement at which the surrounding rock transitions from elastic to plastic deformation. Indicates the ultimate resistance strength of the surrounding rock. It represents the plastic softening coefficient, used to control the rate of resistance decay.

[0071] This model is applied only in regions where the radial compressive stress is less than or equal to 0 and the radial displacement of the bearing arch is greater than 0. Solving this model can yield the bending moment and axial force of each section of the bearing arch, thereby identifying the control section with the most unfavorable internal forces, which is usually the arch crown, arch foot, etc.

[0072] The sections with the largest bending moment and the smallest axial force, as well as the sections with the largest axial force and tensile stress, are designated as the most unfavorable control sections.

[0073] In step S6, the comprehensive compressive strength is calculated according to the Hawke-Brown strength criterion. The minimum principal stress value used in the comprehensive compressive strength is the equivalent confining pressure, which is calculated by the anchor prestress and the grouting pressure. The comprehensive tensile strength is directly calculated using the expression for the tensile strength of rock mass in the Hawke-Brown strength criterion.

[0074] One of the core functions of anchor bolts and grouting is to increase the confining pressure of the rock mass, thereby enhancing its peak strength. The equivalent confining pressure is calculated using the Hawke-Brown criterion, and the formula is as follows:

[0075]

[0076] in, Indicates equivalent confining pressure. and Let represent the effective prestress of the i-th anchor rod and the angle between its direction and the direction of the minimum principal stress, respectively. Indicates the grouting pressure. Indicates the total number of anchor bolts;

[0077] The formula for calculating the overall compressive strength is:

[0078]

[0079] in, Indicates overall compressive strength. This represents the uniaxial compressive strength of a complete rock block; , , Hawke-Brown empirical parameters for describing rock mass quality;

[0080] The formula for calculating the overall tensile strength is:

[0081]

[0082] In step S7, the compressive safety factor is the ratio of the comprehensive compressive strength to the maximum calculated compressive stress on the most unfavorable control section; the tensile safety factor is the ratio of the comprehensive tensile strength to the maximum calculated tensile stress on the most unfavorable control section.

[0083] Among them, the maximum calculated tensile stress on the most unfavorable control section is positive. When the maximum calculated tensile stress on the most unfavorable control section is zero or negative, the section is determined to meet the tensile safety requirements.

[0084] The formula for calculating the compressive strength safety factor is:

[0085]

[0086] in, Indicates the compressive safety factor. This represents the maximum calculated compressive stress on the most unfavorable control section;

[0087] The formula for calculating the tensile safety factor is:

[0088]

[0089] in, Indicates the tensile safety factor. This represents the maximum calculated tensile stress on the most unfavorable control section.

[0090] A storage medium storing instructions that, when read by a computer, cause the computer to execute any of the methods described above for analyzing the stability of tunnel bearing arches based on loosening pressure.

[0091] An electronic device includes a processor and a storage medium, the processor executing instructions in the storage medium.

[0092] like Figure 2As shown, a mechanical model of the hingeless bearing arch and the elastic foundation sidewalls working together is first constructed. A load system including vertical loosening pressure, optimizable horizontal loosening pressure, and active support reaction force is established. Simultaneously, based on the Hawke-Brown criterion and considering the equivalent confining pressure provided by the anchor bolts, the strength of the composite rock mass of the bearing arch is calculated. The model, load, and strength parameters are analyzed collaboratively to obtain the internal force distribution of the bearing arch. Finally, the compressive and tensile safety factors are calculated based on the internal forces and strength, completing the quantitative evaluation of stability. Iterative optimization of the horizontal loosening pressure lateral pressure coefficient, aiming to minimize the tensile stress at the arch crown, dynamically adjusts the load, achieving an integrated design of load-structure response.

[0093] 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.

[0094] 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 analyzing the stability of a tunnel bearing arch based on loosening pressure, characterized in that, Includes the following steps: Step S1: Based on the numerical simulation results of the tunnel construction process, identify the inner boundary of the pressure arch that is naturally formed above the tunnel arch, and delineate the height of the loose zone below the pressure arch that needs to be borne by the support structure. Step S2: The surrounding rock in the loosened area, after being reinforced by the system anchor bolts, anchor cables and grouting, is simplified into a single circular arc curve-shaped load-bearing arch structure; wherein the load-bearing arch is a hingeless arch, and the arch foot is elastically fixedly connected to the tunnel sidewall; Step S3: Determine the loads acting on the bearing arch, including the vertical loosening pressure caused by the self-weight of the loosened surrounding rock, the corresponding horizontal loosening pressure, and the support reaction force acting on the inner boundary of the bearing arch by the prestress of the anchor bolts and anchor cables. Step S4: Establish a mechanical model for the coordinated stress analysis of the load-bearing arch and the side wall. The load-bearing arch ring is calculated as a hingeless arch elastically fixed to the top of the side wall, and the side wall is calculated as a beam vertically placed on an elastic foundation. Step S5: Based on the collaborative force analysis mechanical model, calculate the distribution of internal forces in the cross section of the bearing arch under load, and then identify the control section with the most unfavorable internal forces. Step S6: Based on the strength criterion and considering the equivalent confining pressure effect provided by the support, calculate the comprehensive compressive strength and comprehensive tensile strength of the bearing arch composite rock mass formed after reinforcement. Step S7: Based on the most unfavorable control section and the corresponding internal forces of the section, and combined with the comprehensive compressive strength and comprehensive tensile strength, calculate the compressive safety factor and tensile safety factor of the bearing arch respectively, so as to achieve a quantitative evaluation of the stability of the bearing arch; In step S4, when establishing the collaborative stress analysis mechanical model, the constraint effect of the surrounding rock on the deformation of the bearing arch is taken into account, i.e., the surrounding rock resistance. The application of the surrounding rock resistance follows the following judgment conditions: the radial stress at the calculation point of the bearing arch is non-tensile stress, and the point generates a radial displacement toward the surrounding rock; the relationship between the surrounding rock resistance and the radial displacement is described by a piecewise nonlinear function to simulate the elastoplastic constraint behavior of the surrounding rock. In step S6, the comprehensive compressive strength is calculated according to the Hawke-Brown strength criterion. The minimum principal stress value used in the comprehensive compressive strength is the equivalent confining pressure, which is calculated by the anchor prestress and the grouting pressure. The comprehensive tensile strength is directly calculated using the expression for the tensile strength of rock mass in the Hawke-Brown strength criterion. In step S7, the compressive safety factor is the ratio of the comprehensive compressive strength to the maximum calculated compressive stress on the most unfavorable control section; the tensile safety factor is the ratio of the comprehensive tensile strength to the maximum calculated tensile stress on the most unfavorable control section. Among them, the maximum calculated tensile stress on the most unfavorable control section is positive. When the maximum calculated tensile stress on the most unfavorable control section is zero or negative, the section is determined to meet the tensile safety requirements.

2. The method according to claim 1, characterized in that, In step S2, when simplifying to a load-bearing arch structure, it is necessary to determine the equivalent calculated thickness of the load-bearing arch. The equivalent calculated thickness is determined by the system anchor length, the compression angle of the anchorage zone, and the group anchor effect coefficient.

3. The method according to claim 2, characterized in that, In step S2, when simplifying to a load-bearing arch structure, it is necessary to determine the equivalent elastic modulus of the load-bearing arch. The equivalent elastic modulus of the load-bearing arch is calculated using a modified hybrid law model that considers the bond slip effect at the interface between the anchor bolt and the surrounding rock.

4. The method according to claim 3, characterized in that, In step S3, the horizontal loosening pressure is distributed in a trapezoidal shape along the arch and sidewalls. The distribution intensity is determined by multiplying the vertical loosening pressure by the lateral pressure coefficient. The value of the lateral pressure coefficient is optimized through iterative calculation.

5. The method according to claim 4, characterized in that, In step S3, the support reaction force acting on the inner boundary of the bearing arch by the prestress of the anchor rod and anchor cable is calculated based on the prestress design value of the anchor rod, the circumferential spacing and the longitudinal spacing.

6. A storage medium, characterized in that, The storage medium stores instructions that, when read by a computer, cause the computer to execute the stability analysis method for tunnel bearing arch based on loosening pressure 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.

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