Dynamic Calculation Method for Crack Resistance Safety Factor of Railway Tunnel Lining under Multiple Defect Coupling

Abstract

This invention discloses a dynamic calculation method for the crack resistance safety factor of railway tunnel lining under multi-defect coupling, belonging to the technical field of railway tunnel structure service safety assessment. The method establishes a defect-free lining baseline mechanical model, collects detection data on arch voids, insufficient lining thickness, and insufficient concrete strength, converts the three types of hidden defects into mechanical damage equivalents, and calculates the corresponding deterioration reduction coefficients. Then, combining the comprehensive coupling correction coefficients of high ground stress, train dynamic load, environmental effects, and construction quality dispersion, it substitutes these into the multi-defect coupling master equation to obtain the dynamic crack resistance safety factor. Based on the maximum principal tensile stress and the rate of change of the safety factor, it outputs the cracking risk state, deterioration level, and maintenance information. This method can be executed by a computing terminal, realizing a quantitative and dynamic evaluation of the crack resistance safety state of the lining under multi-defect coexistence conditions.

Description

Technical Field

[0001] This invention belongs to the technical field of railway tunnel structure service safety assessment. Specifically, it relates to a method for calculating the crack resistance safety factor of railway tunnel lining based on non-destructive testing data of lining hidden defects, structural mechanical damage equivalence model and multi-field environmental correction model. It is particularly applicable to the dynamic calculation of the crack resistance safety factor of railway tunnel lining under multiple defect coupling conditions such as arch voids, insufficient lining thickness and insufficient concrete strength, crack risk assessment and deterioration level evaluation, and can be executed by a computing terminal to output maintenance and treatment information. Background Technology

[0002] During long-term service, railway tunnel linings are susceptible to various defects such as arch voids, insufficient lining thickness, insufficient concrete strength, cracks, and water leakage due to factors including adjustments in surrounding rock stress, train dynamic load disturbances, temperature and humidity changes, water seepage erosion, and variations in construction quality. Among these, arch voids, insufficient lining thickness, and insufficient concrete strength are often hidden defects, typically requiring detection methods such as ground-penetrating radar, core drilling, rebound hammer tests, and ultrasonic testing. These defects not only reduce the local bearing capacity of the lining but may also alter the stress transfer relationship between the lining and the surrounding rock, leading to redistribution of internal forces within the lining section, localized tensile stress concentration, and a reduction in crack resistance safety reserves. Therefore, accurately calculating the crack resistance safety factor of the lining based on field testing data is a crucial technical issue in railway tunnel service safety assessment and maintenance decision-making.

[0003] In existing technologies, some patent documents have attempted to correlate tunnel lining defect detection results with structural safety evaluation results. For example, patent document CN110514518B discloses a method for detecting the service performance of tunnel lining structures based on tunnel lining defect characteristics. This method establishes a correspondence between lining defect characteristics and the remaining bearing capacity range through similar model tests, and determines the remaining bearing capacity range of the prototype tunnel lining structure through on-site detection of defect characteristics. This type of method can quickly determine the lining service performance using defect characteristics, but its evaluation results mainly reflect the remaining bearing capacity range, and it places more emphasis on the mapping relationship between defect characteristics and bearing capacity range. When railway tunnel linings simultaneously have multiple hidden defects such as arch voids, insufficient lining thickness, and insufficient concrete strength, this type of method struggles to further distinguish the mechanical mechanisms of different defects and cannot directly output a dynamic crack resistance safety factor corresponding to the lining cracking risk.

[0004] For example, patent document CN113868735A discloses a method and device for rapid safety evaluation of tunnels based on parametric modeling. This method achieves rapid calculation of tunnel unit safety factors and display of safety factor cloud maps through steps such as discretization, determining tunnel cross-sectional parameters, establishing a tunnel model, applying constraints and loads, and extracting calculation results. While this type of method is beneficial for improving the modeling efficiency and result display capabilities of tunnel structural safety evaluation, its technical focus lies in parametric modeling and the rapid output of the safety factor field. It does not address the three common hidden defects in railway tunnel linings—arch voids, insufficient lining thickness, and insufficient concrete strength—by establishing corresponding relationships between defect detection parameters, mechanical damage equivalents, and nonlinear degradation reduction coefficients. Therefore, when facing actual detection scenarios with multiple coexisting defects, this type of method still requires additional working condition modeling, empirical reduction, or manual judgment.

[0005] For example, patent document CN115047142A discloses a method and system for analyzing tunnel lining quality. It collects internal and external inspection data of the lining, analyzes the causes and determines the deterioration level of internal and external defects, and performs correlation analysis on combinations of internal and external defects to construct a tunnel lining quality diagnostic model. This type of method can improve the comprehensive diagnostic capability of lining quality and is suitable for defect identification, defect cause analysis, and quality deterioration level judgment. However, its evaluation object is mainly the lining quality state and defect combination relationship; it does not convert different hidden defects into crack resistance safety factor reductions with clear mechanical meaning, nor does it establish a multi-defect coupled master control calculation equation based on a defect-free baseline crack resistance safety factor. Therefore, this type of method is difficult to directly reflect the true crack resistance safety reserve of the lining.

[0006] Furthermore, patent document CN116070322A discloses a method for evaluating the safety of karst tunnel lining structures under heavy rainfall. This method establishes a load-structure model of the tunnel lining structure and surrounding rock, calculates the safety factor under different water pressure ranges, and thus evaluates the safety of karst tunnel lining structures under heavy rainfall conditions. While this type of method can analyze the safety status of linings under specific environmental loads, it primarily addresses structural safety evaluation under specific external load conditions such as heavy rainfall and water pressure. It does not address the coexistence of multiple hidden defects in long-term service inspections of railway tunnels, nor does it establish differentiated defect deterioration sub-functions for arch voids, insufficient lining thickness, and insufficient concrete strength.

[0007] Another patent document, CN117993073A, discloses a method, device, system, and storage medium for evaluating the stress safety of subway shield tunnel structures based on a support vector machine surrogate model. It constructs a sample library of internal force-displacement responses under multiple working conditions using a finite element model and trains a support vector machine surrogate model to derive safety status ratings from convergent measurement results, thus meeting the need for rapid judgment in daily inspections. While this type of method can improve the rapid identification of the stress safety status of shield tunnel structures, its evaluation object is mainly subway shield tunnel structures. Its input features focus on deformation indicators such as cross-sectional convergence. The evaluation process relies on sample library training and surrogate model classification. It does not establish a direct analytical calculation model for the crack resistance safety factor based on the detection data of hidden defects in railway tunnel linings, nor does it develop a dynamic calculation method applicable to the coupled working conditions of multiple defects such as arch voids, insufficient lining thickness, and insufficient concrete strength in railway tunnels.

[0008] In summary, while existing technologies can achieve tunnel lining defect detection, quality diagnosis, safety factor calculation, and service status evaluation to a certain extent, they still have the following shortcomings: First, some methods mainly evaluate single defects or specific disease characteristics. When faced with multiple hidden defects such as arch voids, insufficient lining thickness, and insufficient concrete strength, they are unable to accurately reflect the stress amplification and crack resistance safety reserve reduction caused by the coupling of multiple defects. Second, some methods focus on defect level, remaining bearing capacity range, or quality status classification, without further converting defect detection parameters into damage equivalents with clear mechanical meaning. This leads to insufficient quantitative correlation between evaluation results and the risk of lining cracking; third, some methods rely on parametric modeling, finite element calculation, surrogate model training, or desktop computing software, which presents problems such as large modeling workload, high parameter calibration requirements, long calculation chains, and inconvenience in data import and result output when applied in the field, making it difficult to meet the operation and maintenance needs of rapid detection, rapid assessment, and rapid handling during railway tunnel maintenance windows; fourth, existing technologies usually do not integrate the service conditions of railway tunnels, such as high ground stress, train dynamic load, environmental effects, and construction quality dispersion, with the deterioration effects of various hidden defects into the same crack resistance safety factor calculation framework.

[0009] Therefore, the field of railway tunnel structure service safety assessment still needs a method that can convert arch voids, insufficient lining thickness, and insufficient concrete strength into mechanical damage equivalents based on field inspection data, and dynamically calculate the crack resistance safety factor of railway tunnel lining by combining the defect-free benchmark crack resistance safety factor, the defect nonlinear degradation reduction factor, and the multi-field environmental comprehensive coupling correction factor. This method should also be adaptable to the requirements of importing field inspection data, rapid calculation, and result output to improve the accuracy of lining cracking risk assessment and degradation level evaluation under multi-defect coupled conditions, as well as the efficiency of engineering applications. Summary of the Invention

[0010] Existing methods for assessing the safety of railway tunnel linings often focus on single-defect calculations, damage level determinations, or remaining bearing capacity range evaluations. These methods struggle to simultaneously address the coexistence of multiple hidden defects, such as lining arch voids, insufficient lining thickness, and inadequate concrete strength. Furthermore, they fail to convert the detection parameters of different defects into damage equivalents with clear mechanical meanings, making it difficult to accurately quantify the stress amplification effect and the reduction in crack resistance safety reserves caused by multi-defect coupling. Simultaneously, existing methods do not adequately consider the service conditions of railway tunnels, such as high ground stress, train dynamic loads, environmental effects, and the variability of construction quality, thus failing to meet the requirements for railway tunnel safety assessment. To address the needs for rapid detection, assessment, and maintenance decisions during tunnel maintenance windows, this invention provides a dynamic calculation method for the crack resistance safety factor of railway tunnel lining under multi-defect coupling. Based on the benchmark crack resistance safety factor for defect-free lining, this method quantifies arch voids, insufficient lining thickness, and insufficient concrete strength into corresponding mechanical damage equivalents. It also constructs nonlinear degradation reduction coefficients for these three types of defects and, combined with a comprehensive coupling correction coefficient, dynamically calculates the crack resistance safety factor of railway tunnel lining under multi-defect coupling conditions. This provides a quantitative basis for lining crack risk assessment, degradation level evaluation, and maintenance treatment plan formulation.

[0011] The technical solution adopted in this invention is as follows: A dynamic calculation method for the crack resistance safety factor of railway tunnel lining under multi-defect coupling includes the following steps: S1. Establish a defect-free baseline mechanical model of the railway tunnel lining to be evaluated, obtain the lining geometric parameters, material parameters, surrounding rock load parameters, and operational load parameters, and calculate the defect-free lining baseline crack resistance safety factor. ; S2. Collect hidden defect detection data for the section or segment to be evaluated, forming a data set including the length of continuous voids in the arch. Radial clearance height Measured effective lining thickness and measured equivalent compressive strength of concrete The set of defect parameters; S3, based on the continuous void length of the arch. and radial clearance height The arch void defect is converted into the comprehensive mechanical reduction equivalent of the arch void. And calculate the reduction factor for arch void deterioration. ; S4. Based on the measured effective lining thickness With design lining thickness The relationship between the two factors transforms the insufficient lining thickness defect into an equivalent of insufficient thickness damage. And calculate the degradation reduction factor for insufficient thickness. ; S5. Based on the measured equivalent compressive strength of concrete With design concrete strength The relationship between the two transforms the concrete strength deficiency defect into a strength degradation damage equivalent. And calculate the reduction factor for insufficient concrete strength and deterioration. ; S6. Calculate the comprehensive coupling correction coefficient based on the high ground stress, train dynamic load, environmental effects, and construction quality dispersion parameters of the railway tunnel to be evaluated. ; S7, the benchmark crack resistance safety factor for defect-free lining Arch deterioration reduction coefficient Insufficient thickness reduces degradation factor Concrete strength insufficient degradation reduction factor and integrated coupling correction coefficient Substituting into the multi-defect coupling master equation, the dynamic crack resistance safety factor is calculated. ; S8. Based on the dynamic crack resistance safety factor and the maximum principal tensile stress at the most unfavorable section of the lining. To determine whether the section or segment to be evaluated has reached the critical state of lining cracking; S9. Based on the dynamic crack resistance safety factor Safety factor change rate Based on the results of the cracking critical state judgment, the lining deterioration classification threshold is matched and the deterioration level and maintenance treatment information are output.

[0012] Furthermore, in step S1, the benchmark crack resistance safety factor for defect-free lining... Calculate using the following formula: ; ; ; In the formula, for Ultimate crack-resistant bending moment of defect-free lining section; for Maximum bending moment of the lining section under constant service load; for Standard value of axial tensile strength of concrete at any given time; for The section modulus of crack resistance of a defect-free lining section at all times; for Bending moment under constant surrounding rock pressure; for The bending moment caused by the self-weight of the lining at all times; for The bending moment caused by the train's operating load at any given time.

[0013] Furthermore, in step S3, the equivalent mechanical reduction of the arch void is... and arch deterioration reduction factor Calculate using the following formula: ; ; In the formula, This is the upper limit of the comprehensive mechanical reduction equivalent value for the arch void; This is a correction factor for the surrounding rock grade. for The length of continuous void in the arch at any given moment; The reference length for the detachment; The index is influenced by the length of the void. for Radial clearance height at any moment; The reference clearance height; To remove the influence of space gaps; The fitting coefficients for stress relief in the arch section are used. Represented by natural constant An exponential function with base 0; This indicates taking the minimum value among the candidate values ​​within the parentheses.

[0014] Furthermore, the fitting coefficient for the stress relief of the suspended arch portion. The stress release data was obtained through in-situ stress release tests in the arch void area or calibration using existing railway tunnel measurement databases. Furthermore, in the absence of in-situ stress release tests, the corresponding values ​​for Class III surrounding rock were determined. Take 0.95, corresponding to Class IV surrounding rock. Take 1.20, corresponding to Class V surrounding rock. Take 1.45.

[0015] Furthermore, in step S4, the thickness is insufficient to compensate for the damage equivalent. and thickness insufficient degradation reduction factor Calculate using the following formula: ; ; In the formula, for The effective lining thickness is measured at all times. To design the lining thickness; for The thickness at any given moment is insufficient to compensate for the damage equivalent. For thickness degradation calibration coefficient, and ; for The degradation reduction factor is applied to insufficient thickness at any given time. This indicates taking the maximum value among the candidate values ​​within the parentheses; when hour, The thickness degradation calibration coefficient Obtained through insufficient thickness test conditions or finite element inversion calibration.

[0016] Furthermore, in step S5, the strength degradation damage equivalent and concrete strength insufficient degradation reduction factor Calculate using the following formula: ; ; In the formula, for The equivalent compressive strength of concrete was measured at all times. To design concrete strength; This is the synergistic attenuation index for converting compressive strength to tensile strength, and ; for Damage equivalent due to intensity degradation over time; For the tensile strength synergistic attenuation calibration coefficient, and ; for The reduction factor for insufficient concrete strength at any given time; This indicates taking the maximum value among the candidate values ​​within the parentheses; when hour, The coordinated decay index Co-attenuation calibration coefficient of tensile strength The strength is obtained through standard test block testing, core drilling testing, or calibration using existing railway tunnel lining strength databases.

[0017] Furthermore, in step S6, the comprehensive coupling correction coefficient Calculate using the following formula: ; ; ; ; ; In the formula, for Correction factor for high ground stress at any time; for Train dynamic load correction factor at any time; for Time-based environmental effect correction factor; for Correction factor for construction quality dispersion over time; , , , These are the lower limits of the corresponding correction coefficients; when any of the influencing factors among high ground stress, train dynamic load, environmental effects, or construction quality dispersion is absent or negligible, the corresponding correction coefficient is taken as 1. for Coefficient of lateral pressure of surrounding rock at any given time; The reference side pressure coefficient; It is the high ground stress sensitivity coefficient; for The dynamic load disturbance index of the train at any given time is determined by the ratio of the measured dynamic stress amplitude to the static stress value of the lining. This is the dynamic load sensitivity coefficient; for The environmental impact index is obtained by normalizing the indicators of temperature and humidity alternation, water leakage, corrosive media, or freeze-thaw cycle. Environmental sensitivity coefficient; for The construction quality dispersion index at any time is determined by the coefficient of variation of the measured values ​​of lining thickness, concrete strength or density within the same assessment section. The sensitivity coefficient for construction dispersion; This indicates taking the maximum value among the candidate values ​​within the parentheses.

[0018] Furthermore, in step S7, the multi-defect coupling master equation is: ; In the formula, for Dynamic crack resistance safety factor after multi-defect coupling at any time; for The benchmark crack resistance safety factor for defect-free lining at all times; for The reduction factor for the deterioration of the arched section due to voiding at any given moment; for The degradation reduction factor is applied to insufficient thickness at any given time. for The reduction factor for insufficient concrete strength at any given time; for Moment-time integrated coupling correction coefficient.

[0019] Furthermore, in step S8, the critical state of lining cracking is determined according to the following conditions: when and When the section or segment to be evaluated reaches the critical state of lining cracking; In the formula, This is the critical threshold for the crack resistance safety factor; for The maximum principal tensile stress at the most unfavorable section of the lining at any given moment; for Standard value of axial tensile strength of concrete at any given time; In step S9, at the continuous evaluation time and Between, the rate of change of safety factor Calculate using the following formula: ; In the formula, This is the current assessment moment; This refers to the previous assessment point; This represents the dynamic crack resistance safety factor at the current assessment moment. The dynamic crack resistance safety factor at the previous assessment time; The rate of change of the safety factor at the current assessment time; when Below the degradation grading threshold or If the value is negative for at least two consecutive evaluation periods and its absolute value exceeds the preset rate of change threshold, the deterioration level of the section or segment to be evaluated will be increased.

[0020] Furthermore, the method is executed by a railway tunnel lining crack resistance safety factor calculation terminal, which includes a memory, a processor electrically connected to the memory, a data interface module, a communication module, and a display module; The data interface module is used to receive one or more of the following: ground-penetrating radar detection data, rebound detection data, core drilling detection data, stress monitoring data, environmental monitoring data, and operational load data. The memory is used to store computer-executable programs and a database of operating condition parameters. The computer-executable programs include: a global operating condition parameter collection module, a multi-defect non-destructive measurement module, a defect-free benchmark crack resistance safety factor calculation module, a three-type defect degradation reduction calculation module, a multi-field environment coupling correction module, a multi-defect coupling master control equation calculation module, and a cracking critical determination and degradation grading output module. When the processor executes the computer-executable program, it is used to: call the global working condition parameter collection module to obtain the tunnel structure geometric parameters, material parameters, surrounding rock load parameters, and operating load parameters; call the multi-defect non-destructive measurement and quantification module to quantify the arch void length, radial void height, effective lining thickness, and equivalent compressive strength of concrete, and generate the corresponding defect parameter set; and call the defect-free benchmark crack resistance safety factor calculation module to calculate the defect-free lining benchmark crack resistance safety factor. Call the three types of defect degradation reduction calculation module to calculate the arch void degradation reduction coefficient respectively. Insufficient thickness reduces degradation factor and the reduction factor for insufficient concrete strength and deterioration Call the multi-field environment coupling correction module to calculate the comprehensive coupling correction coefficient. ; Call the multi-defect coupling master equation calculation module, based on:

[0021] Calculate the dynamic crack resistance safety factor Call the cracking criticality judgment and deterioration grading output module, based on the dynamic crack resistance safety factor. Safety factor change rate and the maximum principal tensile stress at the most unfavorable section of the lining Output information on the risk status, deterioration level, and maintenance treatment of lining cracking; The communication module is used to synchronize the lining cracking risk status, deterioration level, and maintenance information to the operation and maintenance platform, and the display module is used to display the dynamic crack resistance safety factor. Information on cracking risk status, deterioration level, and maintenance treatment.

[0022] Compared with the prior art, the present invention has the following beneficial effects: 1. Achieving mechanical decoupling and quantitative characterization of multiple types of hidden defects, improving the physical consistency of evaluation. This invention addresses three typical hidden defects in railway tunnel linings: arch voids, insufficient lining thickness, and insufficient concrete strength. It establishes damage equivalent models based on geometric parameters, stiffness degradation laws, and material strength attenuation laws, respectively. This transforms defect detection results, which were previously difficult to describe uniformly, into dimensionless damage indices with clear mechanical meaning, thus avoiding the insufficient physical interpretability caused by traditional methods relying on empirical grading or single defect descriptions.

[0023] 2. A multi-defect nonlinear coupled crack resistance safety factor model is constructed to improve the accuracy of safety factor calculation results. This invention multiplicatively couples the degradation reduction coefficients of three types of defects with the defect-free baseline crack resistance safety factor and introduces an exponential nonlinear decay function. This makes the influence of different defects on the crack resistance performance of the structure exhibit a nonlinear coupling effect, thereby reflecting the stress redistribution and crack resistance safety reserve decay law under the condition of coexistence of defects. Compared with traditional linear reduction or single-factor evaluation methods, this invention improves the mechanical consistency and engineering applicability of the safety factor calculation results.

[0024] 3. A multi-field environmental comprehensive correction mechanism is introduced to improve the adaptability to railway service conditions. This invention further considers multiple influencing factors such as high ground stress, train dynamic load, environmental effects, and the dispersion of construction quality, and constructs a comprehensive coupled correction coefficient. This unifies the mapping of complex service conditions into the safety factor calculation framework, enabling the calculation results to reflect the structural degradation characteristics of railway tunnels under the combined effects of multiple factors during long-term operation, and improving the model's adaptability to real service environments.

[0025] 4. A standardized calculation chain based on "detection data - damage equivalent - reduction coefficient - coupled equation - result output" is established to improve engineering feasibility and on-site calculation efficiency. This invention maps on-site data such as ground-penetrating radar, core drilling, rebound testing, stress monitoring, environmental monitoring, and operational loads into model input parameters, and achieves dynamic crack resistance safety factor solution through the main control calculation equation of a fixed structure, avoiding the extensive preprocessing work required by traditional finite element modeling, parametric modeling, and surrogate model training. Simultaneously, this method can be executed by a computing terminal, facilitating the import of on-site detection data, rapid calculation, risk status display, and maintenance information output, thereby reducing the complexity of engineering applications and improving the efficiency of rapid assessment and decision-making during railway tunnel maintenance windows.

[0026] 5. Achieve dynamic evolution assessment of crack resistance safety status and improve risk early warning capabilities. This invention introduces the time series and rate of change index of safety factor, and combines it with the critical judgment condition of maximum principal tensile stress to achieve dynamic tracking and trend analysis of the crack resistance safety status of the lining. It can identify the trend of safety reserve decay, realize the transformation from static evaluation to dynamic risk early warning, and improve the early identification and early warning capabilities of railway tunnel structural defects.

[0027] 6. Improve the objectivity and consistency of lining deterioration level assessment. This invention maps the crack resistance safety factor and the rate of change index to the deterioration grading system in a unified manner, so that the deterioration level is determined by calculable mechanical indicators, reducing the subjective differences caused by relying on human experience judgment, and improving the consistency and comparability of evaluation results between different sections and different lines. Attached Figure Description

[0028] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments recorded in this invention. For those skilled in the art, other drawings can be obtained based on these drawings.

[0029] Figure 1 A flowchart of the overall process logic for dynamically calculating the crack resistance safety factor of railway tunnel lining under multiple defect coupling; Figure 2 A schematic diagram showing the relationship between hidden defects in railway tunnel lining and elastic support of surrounding rock. Figure 3 A schematic diagram of the plane strain mechanical model and polar coordinate calculation of the lining; In the diagram: 1 - Arch void defect; 2 - Insufficient lining thickness defect; 3 - Insufficient concrete strength defect; 4 - Elastic resistance of surrounding rock. - Length of continuous void in the arch section; - Radial clearance height; -Design lining thickness; -Measured effective lining thickness; -Inner radius of the lining; -Outer radius of the lining; - The equivalent uniform radial pressure exerted by the surrounding rock on the outer edge of the lining; -Radial stress of the lining's annular cross section; - Circumferential stress in the annular section of the lining; -Origin of polar coordinates; - Calculate the polar coordinates of the point; - Calculate the radius of the point; -Polar angle. Detailed Implementation

[0030] The following description, in conjunction with the technical solution of this invention, further illustrates the dynamic calculation method for the crack resistance safety factor of railway tunnel lining under multi-defect coupling. It should be understood that the following embodiments are for illustrative purposes only and are not intended to limit the scope of protection of this invention. Equivalent substitutions made by those skilled in the art regarding parameter values, detection methods, threshold libraries, data interfaces, and computing terminal forms without departing from the concept of this invention should all fall within the scope of protection of this invention.

[0031] Example 1:

[0032] This embodiment provides a dynamic calculation method for the crack resistance safety factor of railway tunnel lining under multi-defect coupling. This method is used when multiple hidden defects coexist in railway tunnel linings during long-term service, such as arch voids, insufficient lining thickness, and insufficient concrete strength. Instead of simply scoring the defect levels, this method converts different types of defects into damage equivalents with clear mechanical meanings. Then, through a nonlinear degradation reduction function, a multi-field environmental comprehensive coupling correction mechanism, and a multi-defect coupling master equation, the dynamic crack resistance safety factor of the section or segment to be evaluated at the current evaluation time is calculated.

[0033] In this embodiment, the main control calculation relationship for the dynamic crack resistance safety factor is as follows:

[0034] In the formula, for Dynamic crack resistance safety factor of lining after multi-defect coupling at any time; for The benchmark crack resistance safety factor for defect-free lining at all times; for The reduction factor for the deterioration of the arched section due to voiding at any given moment; for The degradation reduction factor is applied to insufficient thickness at any given time. for The reduction factor for insufficient concrete strength at any given time; for Moment-time integrated coupling correction coefficient.

[0035] The above calculation parameters can be updated according to the detection cycle, monitoring time window, or maintenance assessment cycle. In other words, when new ground-penetrating radar detection data, core drilling data, rebound detection data, stress monitoring data, environmental monitoring data, or operational load data are imported, the system recalculates. This allows for dynamic updating of the lining crack resistance safety factor.

[0036] like Figure 1 As shown in the figure, the dynamic calculation method for the crack resistance safety factor of railway tunnel lining under multi-defect coupling provided in this embodiment is executed according to the following logical flow: "Collection of full-domain working condition parameters - Non-destructive measurement of multiple defects - Calculation or retrieval of crack resistance safety factor of defect-free benchmark - Calculation of deterioration reduction coefficient of three types of defects - Calculation of multi-field environmental comprehensive coupling correction coefficient - Calculation of multi-defect coupling master equation - Crack critical state determination - Output of deterioration level and maintenance treatment information", specifically including the following steps: Establish a defect-free benchmark mechanical model for the railway tunnel lining to be evaluated: Step S1: Establish a defect-free baseline mechanical model of the railway tunnel lining to be evaluated, obtain the lining geometric parameters, material parameters, surrounding rock load parameters, and operational load parameters, and calculate the defect-free lining baseline crack resistance safety factor. .

[0037] The function of this step is to provide a unified benchmark value for subsequent defect reduction calculations. The defect-free benchmark mechanical model represents the theoretical crack resistance safety reserve of the lining section to be evaluated under the same surrounding rock grade, the same operating load, and the same environmental conditions, without considering arch voids, insufficient thickness, or insufficient concrete strength.

[0038] like Figure 3 As shown, in this embodiment, the cross-section of the railway tunnel lining to be evaluated is simplified to a ring-shaped elastic member under plane strain conditions, and the origin of the polar coordinate system is used as the reference point. Establish a polar coordinate calculation system. Figure 3 In Let represent the polar coordinates of any calculated point on the annular cross section of the lining; where, The distance from the calculation point to the origin of the polar coordinates. The radius of the calculation point, The polar angle of the calculation point relative to the reference axis. The inner radius of the lining. For the outer radius of the lining, This represents the equivalent uniformly distributed radial pressure exerted by the surrounding rock on the outer edge of the lining. For the radial stress of the lining annular section, This represents the circumferential stress of the lining's annular cross-section. This defect-free baseline mechanical model is used to describe the baseline stress state of the lining under the action of surrounding rock pressure, lining self-weight, and train operating loads, before considering the deterioration reduction caused by defects such as arch voids, insufficient lining thickness, and insufficient concrete strength.

[0039] The following basic assumptions can be adopted during modeling: the surrounding rock is equivalent to a continuous medium near the evaluation section; the lining and the surrounding rock maintain contact and deform together under the non-void reference state; the lining is an annular section with equal thickness or treated according to the equivalent thickness; the concrete conforms to the small deformation linear elasticity assumption before cracking, and the critical cracking state is determined by the subsequent maximum principal tensile stress and the standard value of the axial tensile strength; for the identified defects such as voids, insufficient thickness, and insufficient concrete strength, the geometric boundary of the defect-free reference model is not directly changed, but its influence is introduced in subsequent steps through the corresponding damage equivalent and deterioration reduction coefficient.

[0040] Combination Figure 3 The diagram shows the plane strain mechanical model and polar coordinate calculation of the lining. In the polar coordinate system, the annular section of the lining is subjected to radial stress. Circumferential stress radial strain Circumferential strain and radial displacement Description. For an axisymmetric plane strain reference model, its radial equilibrium differential equation is: ; The geometric equation is: ; ; The physical equation is: ; ; In the formula, The radial stress of the annular cross section of the lining; The circumferential stress of the lining annular cross section; To calculate the radius of the point; Radial strain; For circumferential strain; Radial displacement; The elastic modulus of the lining concrete; The Poisson's ratio for the lining concrete.

[0041] For a defect-free baseline condition, the inner and outer boundaries of the lining can be treated as follows: Lining inner boundary Location: ; Lining outer boundary Location: ; In the formula, The inner radius of the lining. For the outer radius of the lining, Design the lining thickness to represent the equivalent uniformly distributed radial pressure exerted by the surrounding rock on the outer edge of the lining. Substituting the above boundary conditions into the radial equilibrium equation, geometric equation, and physical equation, the radial stress distribution and circumferential stress distribution of the lining annular section under defect-free conditions can be obtained.

[0042] Under the sign convention of tensile stress being positive and compressive stress being negative, the control value of the circumferential stress at the inner edge of the lining corresponding to uniformly distributed external pressure on the surrounding rock can be expressed as: ; In the formula, This represents the absolute value of the circumferential stress at the inner edge of the lining under a defect-free baseline condition. This value characterizes the baseline circumferential stress level at the inner edge of the lining under uniformly distributed surrounding rock pressure. If the engineering notation for positive compressive stress is adopted, the above result can be directly used as the compressive stress control value. For subsequent determination of the critical state of lining cracking, this embodiment does not solely rely on the circumferential stress under uniformly distributed external pressure as the basis for cracking. Instead, it combines eccentric pressure, train load, bending moment effect, and the stress state after defect reduction to calculate the maximum principal tensile stress at the most unfavorable section of the lining. and the standard value of axial tensile strength of concrete Compare them.

[0043] While establishing a defect-free baseline mechanical model, three types of basic input parameters are collected to lock the solution boundary of the formula. The first type is structural geometric mechanical parameters, including the inner radius of the lining. Lining outer radius Design lining thickness Moment of inertia of cross section Section modulus of crack resistance of defect-free section , elastic modulus of concrete Poisson's ratio and the standard value of axial tensile strength of concrete The second category is the surrounding rock stress parameters, including the equivalent radial pressure of the surrounding rock. lateral pressure coefficient of surrounding rock The self-weight stress component in the initial geostress and the elastic resistance coefficient of the surrounding rock The third category consists of line operation dynamic parameters, including the conversion factor for single-track or double-track tunnel sections, train operating load, design speed, and train dynamic disturbance index. And the corresponding power amplification parameters.

[0044] Using the aforementioned defect-free baseline mechanical model, the circumferential stress distribution, the reference value of the maximum principal tensile stress, and the maximum service bending moment of the section to be evaluated under defect-free conditions can be obtained. and the benchmark crack resistance safety factor for defect-free lining During project implementation, if a baseline safety factor database for the tunnel under the same cross-section, surrounding rock grade, and operating load conditions has been established, it can be directly accessed through parameter matching. However, its calculation basis should still satisfy the mechanical boundary conditions of the above-mentioned plane strain ring elastic member model.

[0045] In this embodiment, the benchmark crack resistance safety factor for defect-free lining Calculate using the following formula: ; ; ; In the formula, for Ultimate crack-resistant bending moment of defect-free lining section; for Maximum bending moment of the lining section under constant service load; for Standard value of axial tensile strength of concrete at any given time; for The section modulus of crack resistance of a defect-free lining section at all times; for Bending moment under constant surrounding rock pressure; for The bending moment caused by the self-weight of the lining at all times; for The bending moment caused by the train's operating load at any given time.

[0046] in, It can be calculated based on the geometric parameters of the lining ring section, or it can be called from a preset section parameter library; It can be calculated based on the surrounding rock pressure, lateral pressure coefficient, and lining cross-sectional dimensions; It can be calculated based on the density, cross-sectional area, and gravitational acceleration of the lining material; It can be calculated based on the line type, train axle load, operating speed, and power amplification factor. Through the above calculations, the benchmark value of the crack resistance safety factor corresponding to the defect-free lining at the current evaluation time can be obtained. .

[0047] Collect hidden defect detection data and form a defect parameter set: like Figure 2 As shown, the hidden defects in railway tunnel lining mainly include arch void defect 1, insufficient lining thickness defect 2, and insufficient concrete strength defect 3. The surrounding rock elastic resistance 4 is used to illustrate the supporting effect of the surrounding rock on the outer edge of the lining. Step S2 is used to collect hidden defect detection data for the section or segment to be evaluated, forming a data set including the continuous void length of the arch. Radial clearance height Measured effective lining thickness and measured equivalent compressive strength of concrete The defect parameter set. Among them, Figure 2 In For illustration Continuous detachment length of the arch , For illustration Radial clearance height at any moment , For illustration Real-time measured effective lining thickness , Used to illustrate the design lining thickness.

[0048] The function of this step is to convert the on-site inspection data into a unified input required for subsequent calculations. Hidden defects in railway tunnel linings often cannot be accurately identified solely through visual inspection. Therefore, this embodiment preferably uses ground-penetrating radar, ultrasonic testing, core drilling, rebound testing, infrared detection, or a combination of multiple detection methods to obtain defect data.

[0049] In this embodiment, the defect parameter set can be represented as: ; In the formula, for The set of defect parameters for the section or segment to be evaluated at any given time; for The length of continuous void in the arch at any given moment; for The radial clearance height of the arch at any given moment; for The effective lining thickness is measured at all times. for The equivalent compressive strength of concrete is measured at all times.

[0050] in, and It can be obtained from images detected by ground-penetrating radar through waveform recognition, reflection interface localization, and spatial conversion; It can be determined by combining the results of ground-penetrating radar detection with the results of borehole verification; It can be obtained from rebound testing, core drilling compressive strength testing, or a combination of both. When there are multiple test points in the same evaluation section, the most unfavorable test value, the statistical representative value, or the section weighted average value can be selected as the calculation input; for different locations such as the arch crown, arch waist, and sidewalls, parameter sets can also be established separately and the safety factor can be calculated separately.

[0051] The purpose of this step is to avoid evaluation based solely on disease severity or human experience, so that subsequent calculations are directly based on measurable and traceable test data.

[0052] Convert the arch voiding into the comprehensive mechanical reduction equivalent of arch voiding: Step S3: Based on the continuous void length of the arch and radial clearance height , will be Figure 2 The arch void defect 1 shown is converted into the comprehensive mechanical reduction equivalent of arch void. And calculate the reduction factor for arch void deterioration. .

[0053] The function of this step is to characterize the impact of arch void defect 1 on the lining's crack resistance safety reserve. Arch void defect 1 causes the lining to lose the support of the surrounding rock elastic resistance 4 locally, forming a local suspended stress zone, resulting in amplified bending moment and concentrated circumferential tensile stress near the void boundary. The larger the void length and the larger the radial void clearance, the closer the lining stress is to a local cantilever or local open span state, and the more significant the reduction in its crack resistance safety reserve.

[0054] In this embodiment, the continuous length of the arch is removed. and radial clearance height Converted to dimensionless arch void comprehensive mechanical reduction equivalent The calculation formula is: ; In the formula, for Equivalent mechanical reduction of the momentary arch detachment; The upper limit of the comprehensive mechanical reduction equivalent of the arch void is used to limit the abnormal amplification caused by extreme detection values; This is a correction factor for the surrounding rock grade, determined based on the value of the surrounding rock grade or calibrated from an engineering database. for The length of continuous void in the arch at any given moment; The reference length for the detachment; The index is influenced by the length of the void. for Radial clearance height at any moment; The reference clearance height; To remove the influence of space gaps; This indicates taking the minimum value among the candidate values ​​within the parentheses.

[0055] in, and The benchmark can be set based on railway tunnel inspection regulations, historical inspection databases, or engineering experience. and It can be calibrated through in-situ tests, finite element inversion, model tests, or existing railway tunnel measured databases; This is used to reflect the differences in the confinement capacity of surrounding rock under different rock grades. For example, in weak and fractured surrounding rock, the weakening effect of voids on the lining support conditions is more significant. A relatively large value can be taken.

[0056] In obtaining Subsequently, the reduction factor for arch deterioration due to voiding. Calculated according to the exponential decay form: ; In the formula, for The reduction factor for the deterioration of the arched section due to voiding at any given moment; The fitting coefficients for stress relief in the arch section are used. Represented by natural constant An exponential function with base 0. It is a dimensionless value, usually not greater than 1; The larger, The smaller the value, the more significant the reduction in the safety factor against cracking due to the arch void.

[0057] In this embodiment, the fitting coefficient for stress relief in the arched section is... This can be obtained through in-situ stress release tests in the arch void area or calibration using existing railway tunnel measurement databases. Specifically, stress monitoring points can be arranged in test sections with different void lengths and void clearances to record the circumferential stress changes at the void boundary and adjacent lining sections, and then the stress can be inverted based on the degree of stress amplification. Value. In the absence of in-situ stress relief tests, recommended values ​​can be taken according to the surrounding rock grade, for example, the value corresponding to Grade III surrounding rock. Take 0.95, corresponding to Class IV surrounding rock. Take 1.20, corresponding to Class V surrounding rock. Take 1.45.

[0058] Converting insufficient lining thickness into the equivalent of insufficient thickness damage: Step S4: Based on the measured effective lining thickness With design lining thickness The relationship between them will be as follows Figure 2 The lining thickness deficiency defect 2 shown is converted into insufficient thickness damage equivalent. And calculate the degradation reduction factor for insufficient thickness. .

[0059] The function of this step is to characterize the impact of insufficient lining thickness defect 2 on the flexural stiffness and crack resistance of the cross section. For the lining cross section, a reduction in effective thickness leads to a nonlinear decrease in the moment of inertia and flexural stiffness. Since the flexural stiffness of the cross section is approximately cubically related to the thickness, a simple linear reduction method is not suitable for evaluating insufficient thickness.

[0060] In this embodiment, the thickness is insufficient to cause damage equivalent. Calculate using the following formula: ; In the formula, for The thickness at any given moment is insufficient to compensate for the damage equivalent. for The effective lining thickness is measured at all times. To design the lining thickness. This indicates that the maximum value among the candidate values ​​within the parentheses is selected. The function is used to avoid negative damage values ​​when the measured thickness is not less than the design thickness. hour, ;when hour, Follow It decreases and then increases.

[0061] In obtaining Subsequently, the thickness deficiency degradation reduction factor Calculate using the following formula: ; In the formula, for The degradation reduction factor is applied to insufficient thickness at any given time. For thickness degradation calibration coefficient, and . This can be obtained through insufficient thickness test conditions, finite element inversion, or calibration using existing engineering databases. In this embodiment, The larger the value, the stronger the sensitivity of insufficient lining thickness to crack safety reserve.

[0062] Through the above calculations, the detection phenomenon of "the measured thickness is too small" can be converted into a mechanical damage index related to the degradation of cross-sectional stiffness, and further a nonlinear reduction of the crack resistance safety factor can be formed.

[0063] Converting insufficient concrete strength into strength degradation damage equivalent: Step S5: Based on the measured equivalent compressive strength of concrete With design concrete strength The relationship between them will be as follows Figure 2 The concrete strength deficiency defect 3 shown is converted into strength deterioration damage equivalent. And calculate the reduction factor for insufficient concrete strength and deterioration. .

[0064] The function of this step is to characterize the impact of insufficient concrete strength defect 3 on crack resistance. Insufficient concrete strength defect 3 reduces the compressive strength, axial tensile strength, elastic modulus, and crack initiation threshold of the lining concrete, and the risk of lining cracking is directly related to the tensile strength of the concrete. Therefore, this embodiment converts the difference between the measured equivalent compressive strength of the concrete and the design concrete strength into the strength degradation damage equivalent in the sense of tensile capacity reduction.

[0065] In this embodiment, the strength degradation damage equivalent Calculate using the following formula: ; In the formula, for Damage equivalent due to intensity degradation over time; for The equivalent compressive strength of concrete was measured at all times. To design concrete strength; This is the synergistic attenuation index for converting compressive strength to tensile strength, and . This indicates that the maximum value among the candidate values ​​within the parentheses is selected. The function is used to avoid negative damage values ​​when the measured strength is not lower than the design strength. hour, ;when hour, Follow It decreases and then increases.

[0066] In obtaining Subsequently, the reduction factor for insufficient concrete strength deterioration. Calculate using the following formula: ; In the formula, for The reduction factor for insufficient concrete strength at any given time; For the tensile strength synergistic attenuation calibration coefficient, and . and It can be obtained through standard test block testing, core drilling testing, or calibration using existing railway tunnel lining strength databases.

[0067] The purpose of this step is to transform the insufficient concrete strength from a simple material indicator into a crack resistance safety factor reduction indicator, so that material degradation can participate in subsequent multi-defect coupling calculations.

[0068] Constructing a multi-field environment integrated coupling correction coefficient: Step S6: Calculate the comprehensive coupling correction coefficient based on the high ground stress, train dynamic load, environmental effects, and construction quality dispersion parameters of the railway tunnel to be evaluated. .

[0069] This step incorporates the actual service conditions of railway tunnels into the safety factor calculation process. Railway tunnel linings are subjected to a complex environment involving multiple factors, including surrounding rock pressure, tectonic stress, train dynamic loads, water leakage, fluctuating temperature and humidity, and inconsistent construction quality. Even with the same defect type and severity, the lining's crack resistance safety reserve may differ under different service environments. Therefore, this embodiment constructs a comprehensive coupling correction coefficient. Among them, such as Figure 2 As shown, the elastic resistance 4 of the surrounding rock is used to illustrate the supporting effect of the surrounding rock on the outer edge of the lining. Under high ground stress, surrounding rock creep, or construction disturbance, the constraint state of the elastic resistance 4 of the surrounding rock will affect the stress distribution of the lining. Therefore, this embodiment uses a high ground stress correction factor. Construction quality dispersion correction factor An equivalent correction should be made for this type of impact.

[0070] Calculate using the following formula: ; In the formula, for Timing-based integrated coupling correction coefficient; for Correction factor for high ground stress at any time; for Train dynamic load correction factor at any time; for Time-based environmental effect correction factor; for Correction coefficients for the dispersion of construction quality at any given time. All correction coefficients are dimensionless values. When the corresponding influencing factor is non-existent or negligible, the corresponding correction coefficient is set to 1.

[0071] In this embodiment, the high ground stress correction factor Calculate using the following formula: ; In the formula, This represents the lower limit of the high ground stress correction factor. for Coefficient of lateral pressure of surrounding rock at any given time; The reference side pressure coefficient; It is the high ground stress sensitivity coefficient; This indicates taking the maximum value among the candidate values ​​within the parentheses. The formula represents when... No more than At that time, the impact of high ground stress is relatively small; when Exceed At that time, as the lateral pressure coefficient increases, A decrease indicates that the safety reserve against cracking has been reduced.

[0072] Train dynamic load correction factor Calculate using the following formula: ; In the formula, This is the lower limit of the train dynamic load correction factor; This is the dynamic load sensitivity coefficient; for Train dynamic load disturbance index at any time; This indicates taking the maximum value among the candidate values ​​within the parentheses. It can be determined by the ratio of the measured dynamic stress amplitude to the static stress value of the lining, that is: ,in This represents the amplitude of dynamic stress in the lining when a train passes. This corresponds to the static stress value.

[0073] Environmental impact correction factor Calculate using the following formula: ; In the formula, This is the lower limit of the environmental impact correction factor; Environmental sensitivity coefficient; for The influence of the environment at any given time; This indicates taking the maximum value among the candidate values ​​within the parentheses. It can be obtained by weighting normalized environmental indicators such as temperature and humidity changes, water leakage, corrosive media, and freeze-thaw cycles. For example: ; In the formula, The normalized index for temperature and humidity alternation; The normalized index of leakage water; The normalized index for corrosive media; The freeze-thaw cycle normalization index; , , , These represent the weights of each environmental factor, and For tunnels where there is no freeze-thaw cycle or corrosive medium, the corresponding indices and weights can be set to 0 or normalized according to the actual situation.

[0074] Construction quality dispersion correction factor Calculate using the following formula: ; In the formula, This is the lower limit of the correction factor for the dispersion of construction quality; The sensitivity coefficient for construction dispersion; for Construction quality dispersion index at any given time; This indicates taking the maximum value among the candidate values ​​within the parentheses. It can be determined by the coefficient of variation of the measured values ​​of lining thickness, concrete strength, or density within the same assessment section, for example: ; In the formula, The standard deviation of quality testing indicators within the same assessment segment; This represents the average value of quality inspection indicators within the same assessment section. Quality inspection indicators can include lining thickness, concrete strength, density, or a combination thereof.

[0075] This step allows for the unified integration of high ground stress, train dynamic load, environmental effects, and construction quality dispersion into the crack resistance safety factor calculation framework, making the calculation results closer to the actual service state of railway tunnels.

[0076] Substituting into the multi-defect coupling master equation to calculate the dynamic crack resistance safety factor: Step S7: Set the benchmark crack resistance safety factor for defect-free lining. Arch deterioration reduction coefficient Insufficient thickness reduces degradation factor Concrete strength insufficient degradation reduction factor and integrated coupling correction coefficient Substituting into the multi-defect coupling master equation, the dynamic crack resistance safety factor is calculated. .

[0077] The function of this step is to unify the defect-free baseline safety reserve, the degradation effects of three types of hidden defects, and the influence of multiple environmental fields into a single safety factor calculation model. Unlike simple addition or linear scoring, this embodiment adopts a multiplicative coupling method, so that the reduction effect of various defects on the crack resistance safety reserve is jointly reflected in the same master equation.

[0078] The master equation for multi-defect coupling is: ; In the formula, for Dynamic crack resistance safety factor after multi-defect coupling at any time; for The benchmark crack resistance safety factor for defect-free lining at all times; for The reduction factor for the deterioration of the arched section due to voiding at any given moment; for The degradation reduction factor is applied to insufficient thickness at any given time. for The reduction factor for insufficient concrete strength at any given time; for Moment-time integrated coupling correction coefficient.

[0079] When a certain type of defect is absent in the lining, the damage equivalent corresponding to that defect is 0, and the corresponding degradation reduction factor is 1. When the influence of a certain type of service environment is absent or negligible, the corresponding correction factor is 1. Therefore, this master equation is applicable to operating conditions where three types of defects coexist, as well as operating conditions with a single defect or a combination of two types of defects.

[0080] Establish criteria for determining the critical state of lining cracking: Step S8: Based on the dynamic crack resistance safety factor and the maximum principal tensile stress at the most unfavorable section of the lining. To determine whether the section or segment to be evaluated has reached the critical state of lining cracking.

[0081] The purpose of this step is to avoid making a judgment based solely on the size of the safety factor, and instead consider both the structural crack resistance safety reserve and the actual tensile stress state of the lining. For concrete linings, cracking is usually controlled by tensile stress; therefore, this embodiment introduces the maximum principal tensile stress. Standard value of axial tensile strength of concrete Comparison between them. Combination. Figure 3 The radial stress shown and circumferential stress In the plane strain mechanical model of the lining, the maximum principal tensile stress at each calculation point of the lining section can be further calculated, and the maximum value at the most unfavorable location is taken as the maximum value. .

[0082] In this embodiment, the maximum principal tensile stress at any point on the lining section is... It can be calculated using the following formula: ; In the formula, for The maximum principal tensile stress at the calculation point at any given moment; for The circumferential stress at the calculation point at any given time; for Calculate the radial stress at the point of time; for The shear stress at each calculation point within the cross-section to be evaluated. Take the maximum value, that is, Under approximate conditions where the influence of shear stress is relatively small, the maximum circumferential tensile stress at the most unfavorable section can also be used to approximate the effect. .

[0083] The critical state of lining cracking is determined according to the following conditions: when and When the section or segment to be evaluated reaches the critical state of lining cracking; In the formula, This is the critical threshold for the crack resistance safety factor; for The maximum principal tensile stress at the most unfavorable section of the lining at any given moment; for Standard value of axial tensile strength of concrete at any given time.

[0084] if but near If the condition is determined to be in a state of insufficient crack resistance safety reserve, information on retesting, intensified monitoring, or preventive maintenance treatment will be output.

[0085] Output degradation level and maintenance information: Step S9: Based on the dynamic crack resistance safety factor Safety factor change rate Based on the results of the cracking critical state judgment, the lining deterioration classification threshold is matched and the deterioration level and maintenance treatment information are output.

[0086] The function of this step is to convert the calculated safety factor results into an evaluation conclusion usable in engineering. Dynamic crack resistance safety factor. The safety reserve reflects the current moment, while the rate of change of the safety factor... It reflects the changing trend of safety reserves.

[0087] In this embodiment, during continuous evaluation time and Between, the rate of change of safety factor Calculate using the following formula: ; In the formula, This is the current assessment moment; This refers to the previous assessment point; This represents the dynamic crack resistance safety factor at the current assessment moment. The dynamic crack resistance safety factor at the previous assessment time; This represents the rate of change of the safety factor at the current assessment moment.

[0088] when Below the corresponding degradation level threshold, or If the value is negative for at least two consecutive assessment periods and its absolute value is greater than a preset rate of change threshold, the deterioration level corresponding to the higher risk state will be output. The deterioration grading threshold can be set according to railway tunnel maintenance assessment standards, the company's internal threshold library, or historical project database.

[0089] As an optional implementation method, the lining deterioration level can be divided into four grades: A, B, C, D, and E. Grade A indicates sufficient crack resistance safety reserve; Grade B indicates slight deterioration; Grade C indicates moderate deterioration requiring monitoring; Grade D indicates significantly insufficient crack resistance safety reserve requiring timely intervention; and Grade E indicates reaching or approaching the critical cracking state and requiring special remediation. Specific thresholds can be adjusted according to different line grades, surrounding rock grades, design specifications, and operational safety requirements.

[0090] The output results should include at least: the section or segment number to be evaluated, the evaluation time, , , , , , , , Information on cracking risk status, deterioration level, and maintenance treatment. Maintenance treatment information may include types such as continued monitoring, increased retesting, targeted grouting, local reinforcement, crack treatment, speed-limited operation, or special rectification.

[0091] In summary, this embodiment establishes a defect-free baseline mechanical model through step S1, and uses a defect-free lining baseline crack resistance safety factor. As a unified calculation benchmark, it solves the problems of existing methods lacking a unified crack resistance safety reserve benchmark and difficulty in comparing evaluation results under different working conditions; the continuous void length of the arch is collected through step S2. Radial clearance height Measured effective lining thickness and measured equivalent compressive strength of concrete This allows the lining safety assessment to be based directly on measurable data from the field, avoiding reliance solely on human experience or disease severity assessment.

[0092] Furthermore, in this embodiment, steps S3 to S5 respectively convert the arch void, insufficient lining thickness, and insufficient concrete strength into the comprehensive mechanical reduction equivalent of the arch void. Insufficient thickness and damage equivalent and strength degradation damage equivalent And calculate the corresponding degradation reduction factor respectively. , and This allows three types of hidden defects to participate in the calculation according to their respective mechanical action mechanisms. Specifically, arch voids correspond to the loss of surrounding rock support and amplification of local bending moments, insufficient lining thickness corresponds to a nonlinear reduction in the flexural stiffness of the cross section, and insufficient concrete strength corresponds to a decrease in the tensile strength of the material. This solves the problem that existing technologies cannot distinguish the mechanical action mechanisms of different defects and that relying solely on empirical linear reduction or single-disease evaluation leads to inaccurate calculation results.

[0093] Meanwhile, this embodiment introduces a high ground stress correction factor through step S6. Train dynamic load correction factor Environmental impact correction factor Construction quality dispersion correction factor And form a comprehensive coupling correction coefficient. This allows the high ground stress, train dynamic load, environmental effects, and construction quality dispersion during the long-term service of railway tunnels to be uniformly incorporated into the crack resistance safety factor calculation framework, solving the problem that existing technologies do not adequately consider the actual service conditions of railway tunnels.

[0094] Based on this, this embodiment establishes the multi-defect coupling master equation in step S7, unifying the defect-free baseline safety reserve, the nonlinear degradation effect of three types of hidden defects, and the multi-field environmental correction effect into a directly calculable dynamic crack resistance safety factor. This solves the problem of the difficulty in uniformly and quantitatively calculating the crack resistance safety factor under multi-defect coexistence conditions. Steps S8 and S9 further combine the maximum principal tensile stress... Safety factor change rate The method establishes a lining deterioration grading threshold, determines the critical cracking state and deterioration level of the section or segment to be evaluated, and outputs information on maintenance and treatment. This solves the problem that existing methods cannot establish a quantitative correspondence between defect detection results, structural crack resistance safety reserves, and maintenance and treatment information.

[0095] Therefore, this embodiment forms a complete calculation chain of "establishment of a defect-free benchmark model - acquisition of hidden defect detection data - mechanical damage equivalent conversion - nonlinear degradation reduction calculation - multi-field environmental correction - dynamic crack resistance safety factor solution - cracking critical state determination - degradation level and maintenance treatment information output". It can realize the quantitative, dynamic and engineering evaluation of the crack resistance safety status of railway tunnel lining under multi-defect coupled working conditions, and improve the accuracy, consistency and field applicability of railway tunnel structure service safety assessment.

[0096] It should be noted that, Figure 2 The arch void defect 1, insufficient lining thickness defect 2 and insufficient concrete strength defect 3 correspond to the mechanical damage equivalent calculation objects of the three types of hidden defects in steps S3, S4 and S5, respectively. Figure 2 The elastic resistance of the surrounding rock 4 corresponds to the supporting and corrective effect of the surrounding rock on the outer edge of the lining in steps S1 and S6. Figure 3 In , and These correspond to the origin of the polar coordinates, the radius of the calculation point, and the polar angle, respectively, and are used to explain the calculation coordinate system of the plane strain mechanical model of the lining in step S1.

[0097] Example 2:

[0098] Based on the dynamic calculation method for the crack resistance safety factor of railway tunnel lining under multi-defect coupling provided in Example 1, this example further provides a railway tunnel lining crack resistance safety factor calculation terminal for executing the method. This calculation terminal receives railway tunnel lining inspection data, structural design parameters, surrounding rock stress parameters, operational load parameters, and environmental monitoring parameters, and outputs the dynamic crack resistance safety factor, crack risk status, deterioration level, and maintenance information according to the calculation process described in Example 1.

[0099] In this embodiment, the computing terminal can be an industrial-grade handheld inspection terminal, a desktop workstation, an edge computing device, or a cloud-based operation and maintenance platform. For on-site inspection scenarios, the computing terminal can be an industrial-grade handheld inspection terminal or a portable workstation; for centralized operation and maintenance management scenarios, the computing terminal can be deployed in a railway tunnel service performance evaluation platform, an edge server, or a cloud server. All of the above-mentioned computing terminals of different forms can execute the dynamic calculation method for the crack resistance safety factor of railway tunnel lining under multi-defect coupling described in Embodiment 1.

[0100] The computing terminal includes a memory, a processor, a data interface module, a communication module, and a display module. The memory is electrically connected to the processor, and the data interface module, communication module, and display module are each communicatively connected to the processor. The data interface module is used to receive one or more of the following: ground-penetrating radar detection data, rebound detection data, core drilling detection data, stress monitoring data, environmental monitoring data, and operational load data; the communication module is used to interact with external detection equipment, railway tunnel operation and maintenance platforms, or cloud databases; the display module is used to display dynamic crack resistance safety factors, crack risk status, deterioration level, and maintenance and treatment information.

[0101] As an implementation method for on-site inspection, the data interface module includes one or more of the following: a ground-penetrating radar data interface, a vibrating wire sensor acquisition interface, a USB data interface, an Ethernet interface, or a wireless communication interface. The ground-penetrating radar data interface is used to receive detection data on the arch void length, radial void height, and effective lining thickness; the vibrating wire sensor acquisition interface is used to receive lining stress monitoring data; the USB data interface, Ethernet interface, or wireless communication interface is used to receive core drilling data, rebound detection data, environmental monitoring data, operational load data, and manually verified data. The communication module can employ 4G, 5G, wireless LAN, or wired communication methods and is used to synchronize calculation results, evaluation reports, and maintenance information to a railway tunnel operation and maintenance platform or cloud database. The display module can be a touch display module, used to display the dynamic crack resistance safety factor, crack risk status, deterioration level, and maintenance information.

[0102] The memory stores computer-executable programs, tunnel foundation parameter libraries, surrounding rock grade parameter libraries, defect detection databases, deterioration grading threshold libraries, and historical assessment result databases. The computer-executable programs include a global operating condition parameter collection module, a multi-defect non-destructive measurement and quantification module, a defect-free benchmark crack resistance safety factor calculation module, a three-type defect deterioration reduction calculation module, a multi-field environmental coupling correction module, a multi-defect coupling master control equation calculation module, a cracking critical determination and deterioration grading output module, and an assessment report generation module.

[0103] The comprehensive operating condition parameter collection module is used to receive and organize the structural geometric parameters, material parameters, surrounding rock load parameters, and operational load parameters of the railway tunnel to be evaluated. Structural geometric parameters include the inner radius of the lining. Lining outer radius Design lining thickness Moment of inertia of cross section and the section modulus of crack resistance of defect-free sections Material parameters include the elastic modulus of concrete. Poisson's ratio Standard value of axial tensile strength of concrete and design concrete strength The surrounding rock load parameters include the equivalent radial pressure of the surrounding rock. lateral pressure coefficient of surrounding rock The self-weight stress component in the initial geostress and the elastic resistance coefficient of the surrounding rock Operational load parameters include track type, single-track or double-track conversion factor, train operating load, design speed, and train dynamic load disturbance index. .

[0104] The multi-defect non-destructive measurement module is used to receive on-site inspection data and generate a set of defect parameters. The on-site inspection data includes the length of continuous void in the arch as detected by ground-penetrating radar. Radial clearance height and measured effective lining thickness And the measured equivalent compressive strength of concrete obtained by rebound testing, core drilling testing, or a combination of both. The defect parameter set Represented as: ; In the formula, for The set of defect parameters for the section or segment to be evaluated at any given time; for The length of continuous void in the arch at any given moment; for The radial clearance height of the arch at any given moment; for The effective lining thickness is measured at all times. for The equivalent compressive strength of concrete is measured at all times.

[0105] The defect-free baseline crack resistance safety factor calculation module is used to calculate the defect-free lining baseline crack resistance safety factor based on the lining geometric parameters, material parameters, surrounding rock load parameters, and operational load parameters provided by the global operating condition parameter aggregation module. In one implementation, the defect-free baseline crack resistance safety factor calculation module calculates it according to the following formula: ; ; ; In the formula, for Ultimate crack-resistant bending moment of defect-free lining section; for Maximum bending moment of the lining section under constant service load; for Standard value of axial tensile strength of concrete at any given time; for The section modulus of crack resistance of a defect-free lining section at all times; for Bending moment under constant surrounding rock pressure; for The bending moment caused by the self-weight of the lining at all times; for The bending moment caused by the train's operating load at any given time.

[0106] In another implementation, the defect-free benchmark crack resistance safety factor calculation module can also call upon a pre-established benchmark safety factor library based on the tunnel cross-section type, surrounding rock grade, design lining thickness, material strength, and operating load conditions. The call result is then matched and verified against the on-site parameters.

[0107] The three-category defect degradation reduction calculation module is used to calculate the defect parameter set generated by the multi-defect non-destructive measurement and quantification module. Calculate the reduction factor for arch void deterioration respectively. Insufficient thickness reduces degradation factor and concrete strength insufficient degradation reduction factor .

[0108] Specifically, the three types of defect degradation reduction calculation module first calculates based on... and Calculate the comprehensive mechanical reduction equivalent of arch void And further calculation : ; ; In the formula, This is the upper limit of the comprehensive mechanical reduction equivalent value for the arch void; This is a correction factor for the surrounding rock grade. The reference length for the detachment; The index is influenced by the length of the void. The reference clearance height; To remove the influence of space gaps; The fitting coefficients for stress relief in the arch section are used. This indicates taking the minimum value among the candidate values ​​within the parentheses.

[0109] Then, the three types of defect degradation reduction calculation module calculates according to and Calculate the damage equivalent of insufficient thickness And further calculation : ; ; In the formula, for The thickness at any given moment is insufficient to compensate for the damage equivalent. For thickness degradation calibration coefficient, and ; This indicates taking the maximum value among the candidate values ​​within the parentheses.

[0110] Then, the three types of defect degradation reduction calculation module calculates based on and Calculate the strength degradation damage equivalent And further calculation : ; ; In the formula, This is the synergistic attenuation index for converting compressive strength to tensile strength, and ; for Damage equivalent due to intensity degradation over time; For the tensile strength synergistic attenuation calibration coefficient, and ; This indicates taking the maximum value among the candidate values ​​within the parentheses.

[0111] The multi-field environmental coupling correction module is used to calculate the comprehensive coupling correction coefficient based on high ground stress, train dynamic load, environmental effects, and construction quality dispersion parameters. The comprehensive coupling correction coefficient Calculate using the following formula: ; ; ; ; ; In the formula, for Correction factor for high ground stress at any time; for Train dynamic load correction factor at any time; for Time-based environmental effect correction factor; for Correction factor for construction quality dispersion over time; , , , These are the lower limits of the corresponding correction coefficients; for Coefficient of lateral pressure of surrounding rock at any given time; The reference side pressure coefficient; It is the high ground stress sensitivity coefficient; for Train dynamic load disturbance index at any time; This is the dynamic load sensitivity coefficient; for The influence of the environment at any given time; Environmental sensitivity coefficient; for Construction quality dispersion index at any given time; The sensitivity coefficient for construction dispersion; This indicates taking the maximum value among the candidate values ​​within the parentheses.

[0112] The multi-defect coupled master control equation calculation module is used to receive... , , , and The dynamic crack resistance safety factor was calculated according to the multi-defect coupling master control equation. : ; In the formula, for The dynamic crack resistance safety factor after multi-defect coupling at different times. The multi-defect coupling master equation calculation module is also used to calculate the dynamic crack resistance safety factor of the same assessment section or segment at different assessment times. Store the data to form a time series with a safety factor.

[0113] The crack criticality determination and deterioration grading output module is used to determine the dynamic crack resistance safety factor. Safety factor change rate and the maximum principal tensile stress at the most unfavorable section of the lining This determines the cracking risk status and deterioration level of the section or segment to be evaluated. The rate of change of the safety factor at the current evaluation moment. Calculate using the following formula: ; In the formula, This is the current assessment moment; This refers to the previous assessment point; This represents the dynamic crack resistance safety factor at the current assessment moment. This is the dynamic crack resistance safety factor at the previous assessment time.

[0114] when and When the critical cracking determination and deterioration grading output module determines that the section or segment to be evaluated has reached the critical state of lining cracking; when Below the corresponding degradation level threshold, or When the value is negative for at least two consecutive assessment periods and its absolute value is greater than the preset rate of change threshold, the degradation level corresponding to the higher risk state is output.

[0115] The assessment report generation module is used to generate standardized assessment reports. These standardized assessment reports must include at least: tunnel name, route section, assessment section or segment number, assessment time, and input test data. , , , , , , , , , , The data source identifier includes the crack risk status, deterioration level, maintenance and treatment information, and data source identification. The data source identifier is used to record which source each input parameter comes from: ground-penetrating radar detection, core drilling detection, rebound detection, stress monitoring, environmental monitoring, manual input, or historical database retrieval.

[0116] In this embodiment, when the processor executes a computer-executable program stored in the memory, it performs the following processes in sequence: First, the full-domain working condition parameter collection module is invoked to obtain the structural geometric parameters, material parameters, surrounding rock load parameters, and operational load parameters of the tunnel to be evaluated, and the integrity of the parameters is verified. Secondly, the multi-defect non-destructive measurement and formatting module is invoked to read and format the results of ground-penetrating radar, rebound, core drilling, or ultrasonic testing, generating a set of defect parameters. ; Next, the defect-free baseline crack resistance safety factor calculation module is invoked to calculate or call the defect-free lining baseline crack resistance safety factor. ; Then, the three types of defect degradation reduction calculation module is called to calculate the arch void degradation reduction coefficient respectively. Insufficient thickness reduces degradation factor and the reduction factor for insufficient concrete strength and deterioration ; Subsequently, the multi-field environment coupling correction module was invoked to calculate the comprehensive coupling correction coefficient. ; Furthermore, the multi-defect coupling master equation calculation module is invoked, based on: Calculate the dynamic crack resistance safety factor and will The change rate of the safety factor was obtained by comparing it with historical assessment results. ; Finally, the cracking criticality determination and degradation grading output module is called, combined with... , , , The system outputs information on the lining cracking risk status, deterioration level, and maintenance treatment, along with the deterioration grading threshold. A standardized assessment report is then generated by the assessment report generation module.

[0117] As an optional implementation, the computing terminal further includes a data preprocessing module. The data preprocessing module is used to perform outlier removal, unit standardization, missing value indication, and mileage coordinate matching on the input detection data. For ground-penetrating radar detection data, the data preprocessing module converts the detection mileage, detection location, void boundary, void length, void height, and lining thickness identification results into a unified data format; for rebound and core drilling detection data, the data preprocessing module converts the concrete strength results at different detection points into the measured equivalent compressive strength of concrete at the same evaluation section or segment. .

[0118] As an alternative implementation, the computing terminal further includes a parameter calibration module. The parameter calibration module is used to calibrate parameters based on in-situ stress relief tests, insufficient thickness condition tests, standard block tests, core drilling tests, or existing railway tunnel databases. , , , , , , , The calibration parameters are updated as needed. The parameter calibration module can group and manage parameters according to line, surrounding rock grade, design speed, lining type, or climate environment, so that the calculation parameters under different engineering conditions can be configured independently.

[0119] As another optional implementation, the computing terminal further includes a threshold library management module. This module stores the Fcr, deterioration classification thresholds, and rate of change thresholds corresponding to different line grades, surrounding rock grades, operating speeds, lining types, and maintenance standards. When the computing terminal completes... and After calculation, the cracking critical determination and deterioration grading output module calls the threshold data in the threshold library management module to determine the corresponding deterioration level.

[0120] As an alternative implementation, the computing terminal further includes a communication synchronization module. This module synchronizes on-site assessment data, calculation results, and standardized assessment reports to the railway tunnel operation and maintenance platform or cloud database, and receives updated parameter libraries, threshold libraries, and historical assessment data from the cloud. The communication synchronization module can employ 4G, 5G, Ethernet, wireless LAN, or wired data transmission methods.

[0121] In one specific configuration, the computing terminal uses an embedded processor and a local working condition parameter database, and is equipped with a ground radar data USB interface, a vibrating wire sensor acquisition interface, a 5G wireless transmission module, and a touch display module. After importing the detection data of a single evaluation section, the computing terminal completes the defect quantification, sub-item reduction coefficient calculation, comprehensive coupling correction coefficient calculation, dynamic crack resistance safety factor calculation, and deterioration level output in a total time of no more than 10 seconds.

[0122] The railway tunnel lining crack resistance safety factor calculation terminal provided in this embodiment can be used to engineer and deploy the multi-defect coupled crack resistance safety factor dynamic calculation method in Embodiment 1 in on-site inspection or centralized operation and maintenance scenarios. This calculation terminal can automate the processes of importing detection data, collecting parameters, quantifying defects, calculating the baseline safety factor, reducing three types of defects, correcting for multiple environmental conditions, solving for the dynamic crack resistance safety factor, determining the critical cracking state, outputting the deterioration level, and generating an assessment report. This improves the calculation efficiency, result consistency, and on-site applicability of the multi-defect coupled safety assessment of railway tunnel linings.

[0123] Furthermore, to verify the dynamic calculation method for the crack resistance safety factor of railway tunnel lining under multi-defect coupling provided in Example 1, this application example uses an evaluation section of an operating tunnel on a double-track railway of the Yunnan-Guizhou High-Speed ​​Railway as an example. This tunnel is located in a Class IV surrounding rock zone, belonging to a typical high-stress operating tunnel condition. The lining design thickness of this evaluation section is... =40cm, design concrete strength =35MPa, standard value of axial tensile strength of concrete =2.2MPa, inner radius of lining =5.8m, outer radius of lining =6.2m, the line is designed for a speed of 350km / h.

[0124] During on-site testing, ground-penetrating radar was used to scan the assessment section and its adjacent sections before and after it to identify the length of continuous void in the arch. =2.8m, and the radial clearance height was determined by combining radar reflection waveform characteristics and on-site verification results. .Will and After substituting into the calculation model for the comprehensive mechanical reduction equivalent of arch void, the comprehensive mechanical reduction equivalent of arch void is obtained. =0.32. The measured effective lining thickness of this section was obtained through ground-penetrating radar thickness identification and borehole verification. =29cm. The measured equivalent compressive strength of the concrete was obtained through rebound testing and core drilling compression tests. =25.2MPa.

[0125] First, based on the inner radius of the lining of this section. Lining outer radius Design lining thickness Standard value of axial tensile strength of concrete Considering the surrounding rock pressure, lining self-weight, and train operating load, calculate or retrieve the benchmark crack resistance safety factor for defect-free linings under the same working conditions. In this application example, the benchmark safety factor library for defect-free linings under the same cross-section, surrounding rock grade, and operating load conditions is retrieved, yielding: =5.31.

[0126] Secondly, the fitting coefficient for the stress release of the arch section is determined based on the surrounding rock grade of the assessment section. Since the surrounding rock at this section is Class IV, and no separate in-situ stress release test was conducted on site, the recommended values ​​in Example 1 were used. =1.20. The reduction factor for arch void deterioration is calculated according to the following formula: ; Substitution =0.32、 =1.20, resulting in: .

[0127] The results indicate that the arch void caused the lining to lose local support from the surrounding rock, resulting in a significant reduction in the crack resistance safety reserve of the assessed section.

[0128] Secondly, based on the measured effective lining thickness =29cm and design lining thickness =40cm, calculated thickness insufficient for damage equivalent The damage equivalent for insufficient thickness is calculated using the following formula: ; Substitution =29cm =40cm, therefore: .

[0129] In this application example, the thickness degradation calibration coefficient Based on the existing insufficient thickness test and finite element inversion results, =0.55, the degradation reduction factor for insufficient thickness is calculated according to the following formula: ; Substitution =0.55、 =0.619, therefore: .

[0130] The results show that when the measured effective thickness of the lining is reduced from the design thickness of 40cm to 29cm, the flexural stiffness and crack resistance of the cross section both decrease nonlinearly.

[0131] Then, based on the measured equivalent compressive strength of concrete =25.2MPa and design concrete strength =35MPa, calculate the equivalent strength degradation damage. The strength degradation damage equivalent is calculated according to the following formula: ; In this application example, the synergistic attenuation index for converting compressive strength to tensile strength is used. Take 0.85 and substitute it into the equation. =25.2MPa =35MPa, therefore: .

[0132] In this application example, the tensile strength synergistic attenuation calibration coefficient The reduction factor for insufficient concrete strength is taken as 1.12, and is calculated according to the following formula: ; Substitution =1.12、 =0.244, therefore: .

[0133] The results indicate that when the measured strength of concrete is lower than the design strength, the tensile strength and cracking threshold of the lining material decrease, thereby reducing the safety reserve against cracking.

[0134] Subsequently, based on the lateral pressure coefficient of the surrounding rock, the train dynamic load disturbance index, the environmental effect index, and the construction quality dispersion index of this section, the high ground stress correction coefficient was calculated respectively. Train dynamic load correction factor Environmental impact correction factor Construction quality dispersion correction factor In this application example, based on on-site in-situ stress data, train operation dynamic stress monitoring data, temperature, humidity and leakage records, and statistical results of the dispersion of lining quality in the same section, the following conclusions are drawn: .

[0135] Finally, , , , and Substituting into the multi-defect coupling master equation: ; get: .

[0136] Therefore, it can be seen that under the combined effects of arch void, insufficient lining thickness, insufficient concrete strength, and multiple service environments, the dynamic crack resistance safety factor of the assessed section decreased from 5.31 in the defect-free baseline state to 1.80, indicating that the crack resistance safety reserve of this section has significantly decreased.

[0137] Furthermore, by combining stress monitoring data and the mechanical model in step S1, the maximum principal tensile stress at the current evaluation moment of the cross-section is calculated. =1.76MPa. Assume a critical threshold for the crack resistance safety factor. =1.0, because: ; and: ; Therefore, it was determined that the assessed section had not yet reached the critical state of lining cracking.

[0138] To demonstrate the effectiveness of dynamic calculations, the results of this assessment of the cross-section are compared with those of the previous monitoring cycle. Previous assessment time Corresponding dynamic crack resistance safety factor =1.92, current evaluation time Corresponding dynamic crack resistance safety factor =1.80, and the interval between two consecutive assessments is 30 days, then the change rate of the safety factor is: ; .

[0139] The results indicate that the crack resistance safety factor of this cross-section is decreasing, but the rate of decrease does not exceed the preset change rate threshold for this project. Combined with the cross-section's... , The system establishes a critical cracking state and a lining deterioration grading threshold library, outputting that the assessed section corresponds to a C-level moderate deterioration state, and outputs maintenance and treatment information as follows: maintain operation status, strengthen follow-up monitoring, implement targeted verification testing of the arch void area, prioritize local grouting filling based on the verification results, and conduct intensified radar re-testing and borehole verification for sections with insufficient thickness.

[0140] To further illustrate the multi-defect coupling evaluation effect of this method, the cross-section was compared and calculated based on the effects of a single defect. When only the arch void defect is considered and the comprehensive coupling correction coefficient is retained, the safety factor is approximately: ; When only the thickness deficiency defect is considered and the comprehensive coupling correction factor is retained, the safety factor is approximately: ; When only considering the defect of insufficient concrete strength and retaining the comprehensive coupling correction factor, the safety factor is approximately: ; In the formula, , and These are the crack resistance safety factors when only considering the arch void defect, the lining thickness deficiency defect, and the concrete strength deficiency defect, respectively. It means approximately equal to.

[0141] The above comparison shows that if only a single defect calculation method is used, the safety factor of this section is significantly higher than that calculated by multi-defect coupling, which easily underestimates the degree of reduction in crack resistance safety reserve under the condition of multiple defects coexisting. This invention converts arch voids, insufficient lining thickness, and insufficient concrete strength into mechanical damage equivalents respectively, and performs unified calculations through the multi-defect coupling master equation, which can more accurately reflect the crack resistance safety level of the lining under actual service conditions.

[0142] Application results show that this dynamic calculation method for the crack resistance safety factor of railway tunnel lining under multi-defect coupling can directly complete the entire technical closed loop based on field detection data, from defect identification, damage equivalent conversion, nonlinear reduction calculation, multi-field correction, dynamic safety factor calculation to degradation level output. Compared with traditional single-defect accounting or manual experience-based grading methods, this method can more fully reflect the coupled degradation effect caused by the coexistence of multiple defects, reduce the reliance on repeated finite element modeling and subjective human judgment, and help improve the accuracy, traceability, and field implementation efficiency of railway tunnel lining service safety assessment.

[0143] Furthermore, to further verify the accuracy of the dynamic calculation method for the crack resistance safety factor of railway tunnel lining under multi-defect coupling, this verification embodiment selects several typical cross-sections of railway operating tunnels as verification samples. The verification samples cover Class III, IV, and V surrounding rock conditions, and include typical working conditions such as single defect, double defect coupling, and triple defect coupling.

[0144] I. Verification Benchmark and Comparison Methods: This verification embodiment uses the crack resistance safety factor calculated from on-site measurements as the baseline true value. Specifically, vibrating wire strain gauges or stress gauges are installed at the tension control position of the lining or the most unfavorable tension section to continuously monitor the actual tensile stress of the lining under stable operating conditions; simultaneously, core samples are drilled at the corresponding sections, and the measured value of the axial tensile strength of concrete is determined through indoor tests or converted from the results of compressive strength tests. The true crack resistance safety factor calculated from on-site measurements is calculated according to the following formula: ; In the formula, The actual crack resistance safety factor is calculated from on-site measurements. The measured or converted value of the axial tensile strength of the concrete at the corresponding cross section; This represents the measured maximum principal tensile stress at the tension-controlled location of the lining. When the tensile stress at the tension-controlled location of the lining is primarily circumferential tensile stress, The circumferential tensile stress can be measured from the inner edge of the lining. This is an approximate representation based on actual measurements. The true crack resistance safety factor reflects the actual crack resistance safety reserve of the corresponding cross-section and serves as a benchmark value for error comparison.

[0145] This verification example selects the traditional linear reduction evaluation method as a control method. This traditional linear reduction evaluation method uses the defect-free baseline crack resistance safety factor as the base, and reduces insufficient lining thickness and insufficient concrete strength according to linear proportions. Arch voids are reduced using an empirical correction factor. It does not further quantify the local bending moment amplification effect caused by arch voids, nor does it consider the nonlinear coupling degradation effect under conditions of multiple defects coexisting. The traditional linear reduction evaluation method can be expressed as: ; In the formula, The crack resistance safety factor is calculated using the traditional linear reduction evaluation method. The standard crack resistance safety factor is the one for defects-free benchmarks. For the thickness linear reduction term, we can take... ; This is a linear reduction term for material strength, which can be taken as... ; This is an empirical correction factor for arch voids. It is taken as an empirical value. Use 1.0 for no vacancy, 0.98 for slight vacancy, 0.95 for moderate vacancy, and 0.92 for severe vacancy.

[0146] Following the steps described in Example 1, calculate the equivalent mechanical reduction of the arch void. Insufficient thickness and damage equivalent Strength deterioration damage equivalent Type III Defect Degradation Reduction Factor , , and the comprehensive coupling correction coefficient The dynamic crack resistance safety factor was calculated by substituting it into the multi-defect coupling master equation. .

[0147] The relative error is calculated using the following formula: ; In the formula, The crack resistance safety factor is calculated using the traditional linear reduction evaluation method or this method. This indicates taking the absolute value.

[0148] II. Selection of Validation Samples: The verification samples in this embodiment cover three operating tunnels: the Fenghuangshan Tunnel on the Shanghai-Kunming High-Speed ​​Railway, the Hongdoushan Tunnel on the Dali-Lincang Railway, and the Yulongxueshan Tunnel on the Lijiang-Xianggelila Railway, totaling six verification sections. Each verification section covers Class III, IV, and V surrounding rock conditions and includes single-defect, double-defect coupled, and triple-defect coupled working conditions. It can reflect the crack resistance and safety status of railway tunnel lining under different surrounding rock conditions and different combinations of hidden defects, and has engineering representativeness.

[0149] III. Comparison data of typical cross-sectional errors: The error comparison results of the six verification sections are shown in Table 1.

[0150] Table 1. Comparison of Calculation Errors for Crack Resistance Safety Factors of Typical Cross-Sections:

[0151] IV. Overall Error Statistical Conclusions: Statistical analysis of the errors of the six verification sections in Table 1 shows that the relative error range of the traditional linear reduction evaluation method is 27.5% to 47.8%, with an average relative error of 36.5%, and the error of each verification section exceeds 25%. This result indicates that the traditional linear reduction evaluation method tends to overestimate the lining's crack resistance safety reserve under conditions of multiple defects, especially when arch voids, insufficient lining thickness, and insufficient concrete strength coexist. It struggles to accurately reflect the coupled deterioration effect between defects, posing a risk of overlooking high-risk hazards.

[0152] The relative error range of this method is 2.7% to 4.7%, with an average relative error of 3.6%, and the errors of each verification section are all below 5%. These results indicate that the method of this invention, by converting arch voids, insufficient lining thickness, and insufficient concrete strength into mechanical damage equivalents and superimposing a comprehensive coupling correction coefficient, can more accurately reflect the actual attenuation degree of the lining's crack resistance safety reserve under multi-defect coupling conditions. The calculated results show a high degree of agreement with the back-calculated results from field measurements.

[0153] The above verification results show that the method of the present invention can maintain good computational stability and engineering applicability under single defect, double defect coupling and triple defect coupling conditions, and can meet the needs of rapid, quantitative and traceable evaluation in the service safety assessment of railway tunnel lining.

[0154] The above are merely preferred embodiments of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and inventive concept of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A dynamic calculation method for the crack resistance safety factor of railway tunnel lining under multi-defect coupling, characterized in that, Includes the following steps: S1. Establish a defect-free baseline mechanical model of the railway tunnel lining to be evaluated, obtain the lining geometric parameters, material parameters, surrounding rock load parameters, and operational load parameters, and calculate the defect-free lining baseline crack resistance safety factor. ; S2. Collect hidden defect detection data for the section or segment to be evaluated, forming a data set including the length of continuous voids in the arch. Radial clearance height Measured effective lining thickness and measured equivalent compressive strength of concrete The set of defect parameters; S3, based on the continuous void length of the arch. and radial clearance height The arch void defect is converted into the comprehensive mechanical reduction equivalent of the arch void. And calculate the reduction factor for arch void deterioration. ; S4. Based on the measured effective lining thickness With design lining thickness The relationship between the two factors transforms the insufficient lining thickness defect into an equivalent of insufficient thickness damage. And calculate the degradation reduction factor for insufficient thickness. ; S5. Based on the measured equivalent compressive strength of concrete With design concrete strength The relationship between the two transforms the concrete strength deficiency defect into a strength degradation damage equivalent. And calculate the reduction factor for insufficient concrete strength and deterioration. ; S6. Calculate the comprehensive coupling correction coefficient based on the high ground stress, train dynamic load, environmental effects, and construction quality dispersion parameters of the railway tunnel to be evaluated. ; S7, the benchmark crack resistance safety factor for defect-free lining Arch deterioration reduction coefficient Insufficient thickness reduces degradation factor Concrete strength insufficient degradation reduction factor and integrated coupling correction coefficient Substituting into the multi-defect coupling master equation, the dynamic crack resistance safety factor is calculated. ; S8. Based on the dynamic crack resistance safety factor and the maximum principal tensile stress at the most unfavorable section of the lining. To determine whether the section or segment to be evaluated has reached the critical state of lining cracking; S9. Based on the dynamic crack resistance safety factor Safety factor change rate Based on the results of the cracking critical state judgment, the lining deterioration classification threshold is matched and the deterioration level and maintenance treatment information are output.

2. The method for dynamically calculating the safety factor of railway tunnel lining crack resistance under multi-defect coupling as described in claim 1, characterized in that: In step S1, the benchmark crack resistance safety factor for defect-free lining Calculate using the following formula: ； ； ； In the formula, for Ultimate crack-resistant bending moment of defect-free lining section; for Maximum bending moment of the lining section under constant service load; for Standard value of axial tensile strength of concrete at any given time; for The section modulus of crack resistance of a defect-free lining section at all times; for Bending moment under constant surrounding rock pressure; for The bending moment caused by the self-weight of the lining at all times; for The bending moment caused by the train's operating load at any given time.

3. The method for dynamically calculating the crack resistance safety factor of railway tunnel lining under multi-defect coupling as described in claim 1, characterized in that: In step S3, the equivalent mechanical reduction of the arch void is... and arch deterioration reduction factor Calculate using the following formula: ； ； In the formula, This is the upper limit of the comprehensive mechanical reduction equivalent value for the arch void; This is a correction factor for the surrounding rock grade. for The length of continuous void in the arch at any given moment; The reference length for the detachment; The index is influenced by the length of the void. for Radial clearance height at any moment; The reference clearance height; To remove the influence of space gaps; The fitting coefficients for stress relief in the arch section are used. Represented by natural constant An exponential function with base 0; This indicates taking the minimum value among the candidate values ​​within the parentheses.

4. The method for dynamically calculating the crack resistance safety factor of railway tunnel lining under multi-defect coupling as described in claim 3, characterized in that: The fitting coefficient for stress relief in the suspended arch section The stress release data was obtained through in-situ stress release tests in the arch void area or calibration using existing railway tunnel measurement databases. Furthermore, in the absence of in-situ stress release tests, the corresponding values ​​for Class III surrounding rock were determined. Take 0.95, corresponding to Class IV surrounding rock. Take 1.20, corresponding to Class V surrounding rock. Take 1.

45.

5. The method for dynamically calculating the safety factor of railway tunnel lining crack resistance under multi-defect coupling as described in claim 1, characterized in that: In step S4, the thickness is insufficient to cause damage equivalent. and thickness insufficient degradation reduction factor Calculate using the following formula: ； ； In the formula, for The effective lining thickness is measured at all times. To design the lining thickness; for The thickness at any given moment is insufficient to compensate for the damage equivalent. For thickness degradation calibration coefficient, and ; for The degradation reduction factor is applied to insufficient thickness at any given time. This indicates taking the maximum value among the candidate values ​​within the parentheses; when hour, The thickness degradation calibration coefficient Obtained through insufficient thickness test conditions or finite element inversion calibration.

6. The method for dynamically calculating the safety factor of railway tunnel lining crack resistance under multi-defect coupling as described in claim 1, characterized in that: In step S5, the strength degradation damage equivalent and concrete strength insufficient degradation reduction factor Calculate using the following formula: ； ； In the formula, for The equivalent compressive strength of concrete was measured at all times. To design concrete strength; This is the synergistic attenuation index for converting compressive strength to tensile strength, and ; for Damage equivalent due to intensity degradation over time; For the tensile strength synergistic attenuation calibration coefficient, and ; for The reduction factor for insufficient concrete strength at any given time; This indicates taking the maximum value among the candidate values ​​within the parentheses; when hour, The coordinated decay index Co-attenuation calibration coefficient of tensile strength The strength is obtained through standard test block testing, core drilling testing, or calibration using existing railway tunnel lining strength databases.

7. The method for dynamically calculating the safety factor of railway tunnel lining crack resistance under multi-defect coupling as described in claim 1, characterized in that: In step S6, the integrated coupling correction coefficient Calculate using the following formula: ； ； ； ； ； In the formula, for Correction factor for high ground stress at any time; for Train dynamic load correction factor at any time; for Time-based environmental effect correction factor; for Correction factor for construction quality dispersion over time; , , , These are the lower limits of the corresponding correction coefficients; when any of the influencing factors among high ground stress, train dynamic load, environmental effects, or construction quality dispersion is absent or negligible, the corresponding correction coefficient is taken as 1. for Coefficient of lateral pressure of surrounding rock at any given time; The reference side pressure coefficient; It is the high ground stress sensitivity coefficient; for The dynamic load disturbance index of the train at any given time is determined by the ratio of the measured dynamic stress amplitude to the static stress value of the lining. This is the dynamic load sensitivity coefficient; for The environmental impact index is obtained by normalizing the indicators of temperature and humidity alternation, water leakage, corrosive media, or freeze-thaw cycle. Environmental sensitivity coefficient; for The construction quality dispersion index at any time is determined by the coefficient of variation of the measured values ​​of lining thickness, concrete strength or density within the same assessment section. The sensitivity coefficient for construction dispersion; This indicates taking the maximum value among the candidate values ​​within the parentheses.

8. The method for dynamically calculating the crack resistance safety factor of railway tunnel lining under multi-defect coupling as described in claim 1, characterized in that: In step S7, the multi-defect coupling master equation is: ； In the formula, for Dynamic crack resistance safety factor after multi-defect coupling at any time; for The benchmark crack resistance safety factor for defect-free lining at all times; for The reduction factor for the deterioration of the arched section due to voiding at any given moment; for The degradation reduction factor is applied to insufficient thickness at any given time. for The reduction factor for insufficient concrete strength at any given time; for Moment-time integrated coupling correction coefficient.

9. The method for dynamically calculating the safety factor of railway tunnel lining crack resistance under multi-defect coupling as described in claim 1, characterized in that: In step S8, the critical state of lining cracking is determined according to the following conditions: when and When the section or segment to be evaluated reaches the critical state of lining cracking; In the formula, This is the critical threshold for the crack resistance safety factor; for The maximum principal tensile stress at the most unfavorable section of the lining at any given moment; for Standard value of axial tensile strength of concrete at any given time; In step S9, at the continuous evaluation time and Between, the rate of change of safety factor Calculate using the following formula: ； In the formula, This is the current assessment moment; This refers to the previous assessment point; This represents the dynamic crack resistance safety factor at the current assessment moment. The dynamic crack resistance safety factor at the previous assessment time; The rate of change of the safety factor at the current assessment time; when Below the degradation grading threshold or If the value is negative for at least two consecutive evaluation periods and its absolute value exceeds the preset rate of change threshold, the deterioration level of the section or segment to be evaluated will be increased.

10. The method for dynamically calculating the safety factor of railway tunnel lining crack resistance under multi-defect coupling as described in claim 1, characterized in that: The method is executed by a railway tunnel lining crack resistance safety factor calculation terminal, which includes a memory, a processor electrically connected to the memory, a data interface module, a communication module, and a display module. The data interface module is used to receive one or more of the following: ground-penetrating radar detection data, rebound detection data, core drilling detection data, stress monitoring data, environmental monitoring data, and operational load data. The memory is used to store computer-executable programs and a database of operating condition parameters. The computer-executable programs include: a global operating condition parameter collection module, a multi-defect non-destructive measurement module, a defect-free benchmark crack resistance safety factor calculation module, a three-type defect degradation reduction calculation module, a multi-field environment coupling correction module, a multi-defect coupling master control equation calculation module, and a cracking critical determination and degradation grading output module. When the processor executes the computer-executable program, it is used to: call the global working condition parameter collection module to obtain the tunnel structure geometric parameters, material parameters, surrounding rock load parameters, and operating load parameters; call the multi-defect non-destructive measurement and quantification module to quantify the arch void length, radial void height, effective lining thickness, and equivalent compressive strength of concrete, and generate the corresponding defect parameter set; and call the defect-free benchmark crack resistance safety factor calculation module to calculate the defect-free lining benchmark crack resistance safety factor. Call the three types of defect degradation reduction calculation module to calculate the arch void degradation reduction coefficient respectively. Insufficient thickness reduces degradation factor and the reduction factor for insufficient concrete strength and deterioration Call the multi-field environment coupling correction module to calculate the comprehensive coupling correction coefficient. ; Call the multi-defect coupling master equation calculation module, based on: Calculate the dynamic crack resistance safety factor Call the cracking criticality judgment and deterioration grading output module, based on the dynamic crack resistance safety factor. Safety factor change rate and the maximum principal tensile stress at the most unfavorable section of the lining Output information on the risk status, deterioration level, and maintenance treatment of lining cracking; The communication module is used to synchronize the lining cracking risk status, deterioration level, and maintenance information to the operation and maintenance platform, and the display module is used to display the dynamic crack resistance safety factor. Information on cracking risk status, deterioration level, and maintenance treatment.

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