A method for determining a tunnel surrounding rock pressure arch boundary and a determination terminal

Abstract

The present application relates to the technical field of tunnel and underground engineering construction and safety monitoring, and particularly relates to a method and a terminal for determining the boundary of a tunnel surrounding rock pressure arch, comprising: theoretical prediction, field measurement and comparative verification; the present application constructs a comprehensive determination system of the boundary of the tunnel surrounding rock pressure arch by fusing theoretical calculation and field measurement, at the theoretical level, the theoretical boundary of the pressure arch is defined by quantifying the specific proportional position of the radius of the plastic zone and the peak value of the tangential stress of the elastic zone; at the measurement level, the propagation characteristics of the transient Rayleigh surface wave in the non-uniform medium are used to identify the surface of property mutation of the rock mass by capturing the inflection point of the wave velocity changing with depth in the dispersion curve; finally, the theoretical prediction result is compared with the field measurement result for checking, so as to determine the final boundary of the pressure arch.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of tunnel and underground engineering construction and safety monitoring, in particular to a method for determining the boundary of a pressure arch in surrounding rock of a tunnel and a determination terminal, and more particularly to a method for predicting and non-destructively measuring the range and shape of a pressure arch formed in surrounding rock after tunnel excavation. BACKGROUND

[0002] In tunnel engineering, excavation unloading will cause stress redistribution in surrounding rock when passing through soft and broken rock mass, leading to the expansion of plastic zone and the formation of surrounding rock loose zone, which seriously threatens the safety during construction and operation. In this process, the "pressure arch" formed in the surrounding rock, as a key bearing structure to bear the overburden load and maintain the stability of the cavern, its shape and distribution characteristics directly affect the design optimization of the supporting structure and the long-term safety of the tunnel. Therefore, accurately identifying and quantitatively analyzing the range and mechanical properties of the pressure arch has important theoretical significance and engineering value for the stability control of tunnel engineering.

[0003] Currently, the research on pressure arch mainly focuses on theoretical analysis and numerical simulation. Based on elastoplasticity, scholars have proposed various criteria for identifying the boundary of pressure arch from the perspective of stress redistribution, such as using the shear stress rise area or the position where the tangential stress is equal before and after tunnel excavation as the boundary. However, these methods are not unified and rely heavily on theoretical assumptions, lacking effective validation of field measurement data. Since the pressure arch is deep inside the rock mass, its boundary cannot be obtained by direct observation, and traditional methods such as borehole stress testing have limitations such as high cost, large disturbance, and limited detection range, which poses great challenges to the field identification and quantitative analysis of pressure arch. SUMMARY

[0004] To solve the above technical problems, the present application provides a method for determining the boundary of a pressure arch in surrounding rock of a tunnel and a determination terminal, which realizes accurate, efficient, and non-destructive identification of the boundary of the pressure arch.

[0005] The present application is achieved by the following technical solutions:

[0006] A method for determining the boundary of a pressure arch in surrounding rock of a tunnel, comprising: theoretical prediction, field measurement, and comparative verification;

[0007] The theoretical prediction step comprises:

[0008] Establishing a tunnel surrounding rock mechanics model under non-hydrostatic pressure conditions based on the Mohr-Coulomb elastoplasticity theory;

[0009] Calculating the radius of the plastic zone in surrounding rock to determine the inner boundary of the pressure arch;

[0010] Determining the outer boundary of the pressure arch according to the radial position of the maximum tangential stress in the elastic zone of the surrounding rock;

[0011] The on-site measurement steps include:

[0012] The transient Rayleigh surface wave method is used for non-destructive testing in tunnels. Vibration signals generated by the excitation source are collected by a detector array, and the Rayleigh surface wave dispersion curve is obtained by processing the signals.

[0013] Based on the inflection point in the relationship between wave velocity and depth in the dispersion curve, the inner and outer boundaries of the pressure arch are identified.

[0014] The comparison and verification steps include:

[0015] The pressure arch boundary obtained by the theoretical prediction step is compared and analyzed with the pressure arch boundary obtained by the field measurement step, and the error between the two is calculated.

[0016] Based on the fact that the error is within the allowable range, the pressure arch boundary identified in the on-site measurement steps is determined to be valid and is identified as the pressure arch boundary of the tunnel surrounding rock.

[0017] Optionally, in the theoretical prediction step:

[0018] The inner boundary of the pressure arch The radius of the plastic zone of the surrounding rock With tunnel radius difference, ;

[0019] The outer boundary of the pressure arch The maximum tangential stress in the elastic zone of the surrounding rock. of Radial position corresponding to times With tunnel radius difference, ,in, This is the default value.

[0020] Optionally, the radius of the plastic zone of the surrounding rock is calculated as follows: ,in, For vertical stress, The lateral pressure coefficient, For the cohesion of the surrounding rock, The internal friction angle of the surrounding rock. The equivalent support resistance provided by the steel frame and shotcrete combination, as well as anchor bolts or cables, is calculated using the load-structure method and displacement equivalence principle. From an analytical perspective;

[0021] The maximum tangential stress in the elastic zone of the surrounding rock The formula for calculation is: ;

[0022] radial position The formula for calculation is: ,in, , and For intermediate parameters, .

[0023] Optionally, in the theoretical prediction step, if the tunnel is non-circular, the tunnel radius... Equivalent radius calculated using the equal area method : ,in, This represents the actual excavated cross-sectional area of ​​the tunnel.

[0024] Optionally, in the field measurement step, the array of detectors is arranged to meet the following conditions:

[0025] Multiple low-frequency detectors are arranged linearly along the measurement line and used to receive vibration signals;

[0026] The excitation source is located at a preset offset distance from the detector array, ensuring that a complete Rayleigh surface wave signal is received.

[0027] Optionally, in the on-site measurement step, the method for generating the excitation source is as follows:

[0028] Rubber sheets were laid at the activation points on the tunnel walls;

[0029] The rubber sheet is struck with a hammer to induce transient seismic waves.

[0030] Optionally, in the field measurement step, the method for obtaining the Rayleigh surface wave dispersion curve specifically includes:

[0031] The collected vibration signals are processed to generate the FK domain spectrum of Rayleigh surface waves;

[0032] The fundamental Rayleigh surface wave is extracted from the FK domain spectrum and converted to obtain the VR-H domain dispersion curve.

[0033] Optionally, in the field measurement step, the method for identifying the inner and outer boundaries of the pressure arch specifically includes:

[0034] Analyze the trend of wave velocity variation with depth in the dispersion curve;

[0035] Identify inflection points in a trend that exhibit a zigzag pattern;

[0036] The depth position corresponding to the inflection point of the zigzag feature is determined as the abrupt change surface of the rock mass properties, that is, the inner or outer boundary of the pressure arch.

[0037] Optionally, the detector is a low-frequency moving-coil electromagnetic detector with a frequency of 4Hz; multiple detectors are arranged linearly along the measurement line, and the channel spacing between adjacent detectors is 0.5 meters or 1 meter; the offset distance between the excitation source and the nearest detector is 6 meters or 8 meters.

[0038] A terminal for determining the boundary of a tunnel surrounding rock pressure arch includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the method for determining the boundary of a tunnel surrounding rock pressure arch as described above.

[0039] Compared with the prior art, the present invention has the following features and beneficial effects:

[0040] This invention constructs a comprehensive system for determining the boundary of the tunnel surrounding rock pressure arch by integrating theoretical calculations and field measurements. At the theoretical level, the theoretical boundary of the pressure arch is defined by quantifying the radius of the plastic zone and the specific proportional position of the peak value of the tangential stress in the elastic zone. At the experimental level, the propagation characteristics of transient Rayleigh surface waves in non-uniform media are utilized to identify the abrupt change surface of rock mass properties by capturing the inflection point of wave velocity change with depth in the dispersion curve. Finally, the final boundary of the pressure arch is determined by comparing and verifying the theoretical prediction results with the field measurement results.

[0041] This invention combines theoretical prediction based on mechanical models with field non-destructive testing based on Rayleigh surface waves, and introduces a comparison and verification step. This invention effectively overcomes the limitations of single theoretical calculation or single field measurement, realizes the complementary advantages and mutual verification of the two methods, and greatly reduces the misjudgment rate of boundary determination. Attached Figure Description

[0042] The accompanying drawings illustrate exemplary embodiments of the present invention and, together with the description thereof, serve to explain the principles of the invention. These drawings are included to provide a further understanding of the invention and are incorporated in and constitute a part of this specification, but do not constitute a limitation on the embodiments of the present invention.

[0043] Figure 1 This is a flowchart illustrating a method for determining the boundary of a tunnel surrounding rock pressure arch according to the present invention.

[0044] Figure 2 This is a schematic diagram of the inner boundary, outer boundary, and thickness of the pressure arch according to the present invention.

[0045] Figure 3 This is a schematic diagram of the setup for on-site data acquisition of transient Rayleigh surface waves according to the present invention.

[0046] Figure 4 This is a photograph of the actual field detector setup according to the present invention.

[0047] Figure 5 It is the FK domain map of the test results according to the present invention.

[0048] Figure 6 It is the VR-H domain map of the test results according to the present invention. Detailed Implementation

[0049] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are for illustrative purposes only and are not intended to limit the scope of the invention.

[0050] It should also be noted that, for ease of description, only the parts relevant to the present invention are shown in the accompanying drawings.

[0051] Where there is no conflict, the embodiments and features described in the present invention can be combined with each other. The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0052] Example 1

[0053] like Figure 1 As shown, this embodiment provides a method for determining the boundary of the pressure arch of the tunnel surrounding rock, including: theoretical prediction, field measurement and comparative verification; by constructing a dual determination mechanism that combines "theoretical model prediction" and "field physical detection", the limitations of a single method are eliminated by using the mutual verification of the results of the two, thereby achieving accurate identification of the boundary of the tunnel pressure arch.

[0054] The theoretical prediction steps include:

[0055] A mechanical model of tunnel surrounding rock under non-hydrostatic pressure conditions is established based on the Mohr-Coulomb elastoplastic theory. The Mohr-Coulomb theory is a classic strength theory in geotechnical engineering, used to describe the failure characteristics of soil and rock materials under shear stress. Based on the Mohr-Coulomb yield criterion and elastoplastic theory, the stress state of the surrounding rock after tunnel excavation is analyzed. The true pressure arch forms in the portion of the elastic zone near the plastic zone, where the tangential stress increases significantly, forming an effective load-bearing ring (such as...). Figure 2 (As shown). Furthermore, considering that vertical stress and horizontal stress are often unequal in actual geological formations, this model is analyzed under non-hydrostatic pressure conditions to better reflect engineering realities.

[0056] The radius of the plastic zone of the surrounding rock is calculated to determine the inner boundary of the pressure arch. The plastic zone refers to the area where the stress exceeds the rock mass strength after excavation, causing yielding or failure. The edge of this area is determined as the inner boundary of the pressure arch.

[0057] The outer boundary of the pressure arch is determined by the radial location of the maximum tangential stress in the elastic zone of the surrounding rock. Within the elastic zone, the rock mass is intact and bears the main load. The location where the tangential stress reaches its peak marks the area with the strongest bearing capacity of the surrounding rock, and this location is determined as the outer boundary of the pressure arch.

[0058] The on-site measurement steps include:

[0059] Rayleigh surface waves are elastic waves that propagate along the surface of a medium. Their energy is mainly concentrated near the surface and they have dispersion characteristics, meaning that waves of different frequencies have different propagation speeds and different detection depths. They are often used to detect shallow geological structures.

[0060] The transient Rayleigh surface wave method is used for non-destructive testing in tunnels. Vibration signals generated by excitation sources (such as hammering) are collected by a detector array, and the signals are processed (such as spectrum analysis) to obtain the Rayleigh surface wave dispersion curve.

[0061] Based on the inflection points in the wave velocity versus depth relationship in the dispersion curve, the inner and outer boundaries of the pressure arch can be identified. When Rayleigh waves propagate from the loose plastic zone to the dense pressure arch zone, the change in the medium properties leads to a significant change in wave velocity. By identifying the inflection points in the wave velocity versus depth relationship in the curve, the actual locations of the inner and outer boundaries of the pressure arch can be determined.

[0062] The comparison and verification steps include:

[0063] The pressure arch boundary obtained by the theoretical prediction step is compared and analyzed with the pressure arch boundary obtained by the field measurement step, and the error between the two is calculated.

[0064] Based on the fact that the error is within the allowable range (e.g., 5% or 10%), the pressure arch boundary identified in the field measurement steps is determined to be valid and identified as the pressure arch boundary of the tunnel surrounding rock.

[0065] In addition, after determining that the identification is valid, the final tunnel surrounding rock pressure arch boundary is determined according to the actual engineering needs. This can be achieved using any of the following methods:

[0066] Method 1 (Prioritizing on-site measurement): Considering that the on-site measurement data directly reflects the true physical state of the rock mass, the boundary value obtained from the on-site measurement steps is directly determined as the final boundary of the tunnel surrounding rock pressure arch.

[0067] Method 2 (Comprehensive Average): In order to comprehensively consider the guiding significance of the theoretical model and smooth out the random errors that may exist in the field measurement, the arithmetic mean of the theoretical prediction value and the field measured value can also be calculated, and this average value is determined as the final tunnel surrounding rock pressure arch boundary.

[0068] Method 3 (Weighted Processing): Based on the complexity of the on-site geological conditions, different weighting coefficients are assigned to the theoretical prediction values ​​and the measured values ​​on-site, and the weighted average value is calculated as the final boundary.

[0069] Example 2

[0070] This embodiment, based on Embodiment 1, further details the specific parameter definitions and calculation logic in the "theoretical prediction step." By establishing quantitative mechanical calculation formulas, it provides accurate theoretical numerical support for determining the boundary of the pressure arch.

[0071] The inner boundary of the pressure arch The radius of the plastic zone of the surrounding rock With tunnel radius difference, This reflects the thickness of the plastic loosening zone extending from the tunnel wall into the depths.

[0072] The outer boundary of the pressure arch The maximum tangential stress in the elastic zone of the surrounding rock. of Radial position corresponding to times With tunnel radius difference, ,in, This is a preset value (e.g., 0.95) used to define the effective range of the high-stress bearing zone; it reflects the radial depth of the outer edge of the pressure arch from the tunnel wall.

[0073] Based on the Mohr-Coulomb elastoplastic theory and non-hydrostatic pressure conditions, the calculation methods for each key parameter are as follows:

[0074] The radius of the plastic zone of the surrounding rock ,in, This is the vertical stress (which can be calculated based on the burial depth). The lateral pressure coefficient, For the cohesion of the surrounding rock, The internal friction angle of the surrounding rock. The equivalent support resistance provided by the steel frame and shotcrete combination, as well as anchor bolts or cables, is calculated using the load-structure method and displacement equivalence principle. From an analytical perspective;

[0075] The maximum tangential stress in the elastic zone of the surrounding rock ;

[0076] radial position Satisfy the following quartic equation: ,in, , and For intermediate parameters, By solving the equation, the stress threshold can be obtained. Radial location of peak stress (multiple times the peak stress) .

[0077] Considering that tunnel cross-sections in actual engineering are mostly horseshoe-shaped or other non-circular structures, this embodiment uses the "equal area method" for equivalent treatment.

[0078] The tunnel radius Equivalent radius calculated using the equal area method : ,in, This represents the actual excavated cross-sectional area of ​​the tunnel.

[0079] Example 3

[0080] This embodiment, based on Embodiment 1, further details the specific steps in the "on-site measurement steps".

[0081] In order to effectively receive seismic wave signals, the detector array must be deployed to meet the following conditions:

[0082] Multiple low-frequency detectors are arranged linearly along the measurement line and used to receive vibration signals. Low-frequency detectors are chosen because they have longer wavelengths and greater penetration depth, enabling them to detect deep pressure arch structures.

[0083] The excitation source is located at a preset offset distance from the detector array, ensuring the reception of a complete Rayleigh surface wave signal. This offset is set to prevent near-field interference and to ensure the detector can receive a fully developed Rayleigh surface wave signal, facilitating subsequent separation of the surface wave from the volume wave.

[0084] To improve detection depth and optimize signal quality, the excitation source is generated in the following manner:

[0085] A rubber sheet is laid at the excitation point on the tunnel wall; the rubber sheet is then struck using a hammer to excite transient seismic waves. The rubber sheet acts as a buffer medium, effectively filtering out high-frequency interference and reducing the excitation frequency. Since the detection depth of Rayleigh waves is inversely proportional to their frequency, reducing the excitation frequency can significantly increase the detection depth, thereby reaching the deeply buried pressure arch region.

[0086] After acquiring the raw vibration signal, it is necessary to extract the dispersion curve that reflects the formation information:

[0087] The collected vibration signals are processed to generate the FK domain spectrum (frequency-wavenumber domain spectrum) of Rayleigh surface waves; the FK transform can effectively separate Rayleigh surface waves from other types of seismic waves (such as body waves and sound waves) in the energy spectrum.

[0088] The fundamental Rayleigh surface wave is extracted from the FK domain spectrum. Based on the dispersion characteristics of Rayleigh waves (wave velocity varies with frequency), the VR-H domain dispersion curve (wave velocity-depth curve) is obtained, which reflects the distribution of surrounding rock wave velocity at different depths.

[0089] The specific methods for identifying the inner and outer boundaries of a pressure arch include:

[0090] Analyze the trend of wave velocity variation with depth in the dispersion curve;

[0091] Identify inflection points in changing trends that exhibit a zigzag pattern; the zigzag pattern is usually manifested as a sudden decrease or increase in wave velocity at a certain depth, followed by a reversal or stabilization.

[0092] The depth position corresponding to the inflection point of the zigzag feature is determined as the abrupt change surface of rock mass properties (e.g., from the loose zone to the dense bearing zone), that is, the inner or outer boundary of the pressure arch.

[0093] Based on the zigzag inflection points that appear in the wave velocity versus depth relationship in the dispersion curve, the depth at which the inflection points appear is identified as the inner boundary of the pressure arch, and the depth at which the inflection points disappear is identified as the outer boundary of the pressure arch.

[0094] To achieve the best test results, this embodiment also provides a set of verified preferred parameter combinations:

[0095] Twelve low-frequency geophones, employing a 4Hz low-frequency moving-coil electromagnetic geophone, are deployed at the tunnel test location. Multiple geophones are arranged linearly along the test line, with a spacing of 0.5 meters between adjacent geophones. The offset between the excitation source and its nearest geophone is 6 meters (e.g., ...). Figure 3 (As shown).

[0096] Example 4

[0097] This embodiment provides an example of its application in a newly constructed railway tunnel.

[0098] I. Theoretical Prediction Methods

[0099] 1. Obtaining Engineering Parameters:

[0100] The tunnel is a single-track railway tunnel with an excavation area of ​​[missing information]. Calculate the equivalent radius .

[0101] The tunnel is 246m deep, and the unit weight of the surrounding rock is... The vertical stress was calculated. .

[0102] Lateral pressure coefficient Cohesion of surrounding rock internal friction angle .

[0103] Based on the initial support parameters, C25 shotcrete (25cm thickness) + HW150 steel frame (spacing) / frame) + anchor bolts (length 3.5m, diameter 25mm, spacing) (Ring × Longitudinal)), the equivalent support resistance is calculated. .

[0104] 2. Theoretical calculations:

[0105] Substitute the above parameters into the formula for calculating the inner boundary of the pressure arch to calculate the position of the sidewall ( Pressure arch inner boundary .

[0106] Calculate the outer boundary of the pressure arch based on the formula for the maximum tangential stress in the elastic zone and the outer boundary criterion. and thickness .

[0107] The prediction results are summarized in the table below:

[0108] Position Inner boundary Outer boundary Thickness Side wall 4.82m 5.29m 0.47m

[0109] II. On-site measurement methods

[0110] 1. Test setup:

[0111] Twelve 4Hz low-frequency detectors were installed on the tunnel test sidewalls, with a channel spacing of 0.5m (e.g., Figure 4 (As shown).

[0112] The excitation point offset distance was set to 6m, and a sledgehammer was used to strike the rubber sheet laid on the excitation point on the tunnel wall to induce vibration.

[0113] 2. Data Analysis:

[0114] The collected data is processed to obtain the FK domain spectrum and VR-H domain dispersion curve (e.g., Figure 5 and Figure 6 (As shown).

[0115] Analysis of the dispersion curve revealed a distinct zigzag inflection point at a depth of approximately 4.7m from the tunnel sidewall, indicating that this point is the inner boundary of the pressure arch.

[0116] Based on the wave velocity variation trend, the outer boundary of the pressure arch is further determined to be approximately 5.2m.

[0117] The calculated thickness of the pressure arch is approximately 0.5m.

[0118] 3. Comparative verification:

[0119] The measured results are compared with the theoretical predictions, as shown in the table below:

[0120] Pressure arch parameters Theoretical prediction In-situ measurement Error Inner boundary 4.82m 4.7m 2.55% Outer boundary 5.29m 5.2m 1.73% Thickness 0.47m 0.5m 6.00%

[0121] The results show that the theoretical predictions are in high agreement with the field measurement results, and the average error of all parameters is 3.44%, which fully verifies the rationality and reliability of the method described in this invention.

[0122] Example 4

[0123] A terminal for determining the boundary of a tunnel surrounding rock pressure arch includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the method for determining the boundary of a tunnel surrounding rock pressure arch as described above.

[0124] Memory is used to store software programs and modules. The processor executes various terminal functions and data processing by running the software programs and modules stored in memory. Memory can mainly consist of a program storage area and a data storage area. The program storage area can store the operating system, at least one executable program required for a given function, etc.

[0125] The storage data area can store data created based on the use of the terminal. Furthermore, the memory can include high-speed random access memory, and may also include non-volatile memory, such as at least one disk storage device, flash memory, or other volatile solid-state storage devices.

[0126] In the description of this specification, the references to terms such as "one embodiment / mode," "some embodiments / modes," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment / mode or example is included in at least one embodiment / mode or example of this application. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment / mode or example. Moreover, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments / modes or examples. Furthermore, without contradiction, those skilled in the art can combine and integrate the different embodiments / modes or examples described in this specification, as well as the features of different embodiments / modes or examples.

[0127] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one of that feature. In the description of this application, "multiple" means at least two, such as two, three, etc., unless otherwise explicitly specified.

[0128] Those skilled in the art should understand that the above embodiments are merely for illustrating the present invention and are not intended to limit the scope of the invention. Those skilled in the art can make other changes or modifications based on the above invention, and these changes or modifications still fall within the scope of the present invention.

Claims

1. A method for determining the boundary of a pressure arch in tunnel surrounding rock, characterized in that, include: Theoretical prediction, field measurement, and comparative verification; The theoretical prediction steps include: A mechanical model of tunnel surrounding rock under non-hydrostatic pressure conditions was established based on the Mohr-Coulomb elastoplastic theory. Calculate the radius of the plastic zone of the surrounding rock to determine the inner boundary of the pressure arch; The outer boundary of the pressure arch is determined by the radial location of the maximum tangential stress in the elastic zone of the surrounding rock; The on-site measurement steps include: The transient Rayleigh surface wave method is used for non-destructive testing in tunnels. Vibration signals generated by the excitation source are collected by a detector array, and the Rayleigh surface wave dispersion curve is obtained by processing the signals. Based on the inflection point in the relationship between wave velocity and depth in the dispersion curve, the depth where the inflection point appears is determined as the inner boundary of the pressure arch, and the depth where the inflection point disappears is determined as the outer boundary of the pressure arch. The comparison and verification steps include: The pressure arch boundary obtained by the theoretical prediction step is compared and analyzed with the pressure arch boundary obtained by the field measurement step, and the error between the two is calculated. Based on the fact that the error is within the allowable range, the pressure arch boundary identified in the on-site measurement steps is determined to be valid and is identified as the pressure arch boundary of the tunnel surrounding rock. In the theoretical prediction step: The inner boundary of the pressure arch The radius of the plastic zone of the surrounding rock With tunnel radius difference, ; The outer boundary of the pressure arch The maximum tangential stress in the elastic zone of the surrounding rock. of The radial position corresponding to the multiple With tunnel radius difference, ,in, This is the default value.

2. The method for determining the boundary of the pressure arch in tunnel surrounding rock according to claim 1, characterized in that, The formula for calculating the radius of the plastic zone of the surrounding rock is: ,in, For vertical stress, The lateral pressure coefficient, For the cohesion of the surrounding rock, The internal friction angle of the surrounding rock. The equivalent support resistance provided by the steel frame and shotcrete combination, as well as anchor bolts or cables, is calculated using the load-structure method and displacement equivalence principle. From an analytical perspective; The maximum tangential stress in the elastic zone of the surrounding rock The formula for calculation is: ; radial position The formula for calculation is: ,in, , and For intermediate parameters, .

3. The method for determining the boundary of the pressure arch in tunnel surrounding rock according to claim 1, characterized in that, In the theoretical prediction step, if the tunnel is non-circular, the tunnel radius... Equivalent radius calculated using the equal area method : ,in, This represents the actual excavated cross-sectional area of ​​the tunnel.

4. The method for determining the boundary of the pressure arch in tunnel surrounding rock according to claim 1, characterized in that, In the field measurement steps, the array of detectors is arranged to meet the following conditions: Multiple low-frequency detectors are arranged linearly along the measurement line and used to receive vibration signals; The excitation source is located at a preset distance from the detector array, and ensures that a complete Rayleigh surface wave signal is received.

5. The method for determining the boundary of the pressure arch in tunnel surrounding rock according to claim 1, characterized in that, In the on-site measurement steps, the method of generating the excitation source is as follows: Rubber sheets were laid at the activation points on the tunnel walls; The rubber sheet is struck with a hammer to induce transient seismic waves.

6. The method for determining the boundary of the pressure arch in tunnel surrounding rock according to claim 1, characterized in that, The method for obtaining the Rayleigh surface wave dispersion curve in the field measurement steps specifically includes: The collected vibration signals are processed to generate the FK domain spectrum of Rayleigh surface waves; The fundamental Rayleigh surface wave is extracted from the FK domain spectrum and converted to obtain the VR-H domain dispersion curve.

7. The method for determining the boundary of the pressure arch in tunnel surrounding rock according to claim 1, characterized in that, In the aforementioned field measurement steps, the method for identifying the inner and outer boundaries of the pressure arch specifically includes: Analyze the trend of wave velocity variation with depth in the dispersion curve; Identify inflection points in a trend of change that exhibit a zigzag pattern; The depth at which the inflection point of the zigzag feature appears is determined as the inner boundary of the pressure arch, and the depth at which the inflection point disappears is determined as the outer boundary of the pressure arch.

8. The method for determining the boundary of the pressure arch in tunnel surrounding rock according to claim 4, characterized in that, The detector is a low-frequency moving-coil electromagnetic detector with a frequency of 4Hz; multiple detectors are arranged linearly along the measurement line, and the channel spacing between adjacent detectors is 0.5 meters or 1 meter; the offset distance between the excitation source and the nearest detector is 6 meters or 8 meters.

9. A terminal for determining the boundary of a tunnel surrounding rock pressure arch, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements a method for determining the boundary of the pressure arch of the surrounding rock of a tunnel as described in any one of claims 1-8.

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