Train dynamic load-surrounding rock loose coupling tunnel lining service life prediction method

Abstract

This invention relates to the field of railway tunnel structure service performance evaluation technology, and discloses a method for predicting the service life of tunnel linings under train dynamic load-surrounding rock loosening coupling. This method addresses the problems of accurately determining the current damage state of existing tunnel linings, the disconnect between static load analysis of surrounding rock loosening and train dynamic load analysis, and the difficulty in continuously feeding back long-term fatigue damage and stiffness degradation. The method inverts the current effective bending stiffness through field vibration tests and measured responses, and distinguishes non-fatigue defects to determine current fatigue damage. It combines the surrounding rock loosening state and train passing response to form the total stress time history of the lining and the total axial force-bending moment vector of the lining section, performing material strength assessment and sub-mode fatigue damage calculation. At the end of the prediction period, the effective bending stiffness is updated based on the cumulative fatigue damage, and a safety factor is calculated to maintain the continuity of the fatigue state across cycles, thus determining the remaining service life or lower limit of the remaining service life of the tunnel lining.

Description

Technical Field

[0001] This invention relates to the field of railway tunnel structure service performance evaluation technology, and in particular to a method for predicting the service life of tunnel lining under train dynamic load-surrounding rock loosening coupling. Background Technology

[0002] After a railway tunnel is put into operation, in addition to bearing static loads such as the pressure of the surrounding rock and the weight of the structure, the lining will also be repeatedly subjected to vibration loads generated by train operation. As the service time increases, the surrounding rock may loosen or its mechanical properties may decline, and the lining may also develop defects such as cracks, spalling, material deterioration, steel corrosion, and voids behind it. These changes will affect the stress state, structural stiffness, and load-bearing capacity of the lining.

[0003] Current methods for predicting the lifespan of tunnel linings typically rely on design parameters, inspection results, and structural calculations. Some methods still use fixed material parameters and structural stiffness in subsequent predictions, or directly calculate fatigue damage based on the degree of reduction in current stiffness relative to the initial stiffness. Since the reduction in lining stiffness can be caused by train cyclic loading or by non-fatigue defects such as cracks and spalling, failing to differentiate between these factors can easily lead to overestimation of fatigue damage.

[0004] The static effects of surrounding rock loosening and the dynamic effects of train operation are often calculated separately in existing analyses. Train dynamic loads are generally determined based on parameters such as train speed, axle load, and track condition, and the on-site lining response is rarely used to verify the dynamic model and load inputs. Therefore, there may be discrepancies between the calculation results and the actual service condition of the tunnel.

[0005] Furthermore, existing fatigue analyses typically count cycles and accumulate damage based on stress time histories, but they do not adequately consider different stress modes and the order of loads. When calculations are performed only for established closed cycles, situations where static stress is excessive or instantaneous stress peaks exceed limits may be missed. After fatigue damage accumulates, the lining stiffness changes, further affecting subsequent dynamic response and cross-sectional bearing capacity. If a fixed stiffness is always used for life extrapolation, or if cycle statistics are performed separately for different prediction periods, cross-period cycles may be truncated or residual stress changes may be missed.

[0006] Therefore, existing methods still need further improvement in terms of identifying current damage to linings, the interaction of static and dynamic forces, and continuous prediction of long-term damage. Summary of the Invention

[0007] The purpose of this invention is to provide a method for predicting the service life of tunnel lining under the coupling of train dynamic load and surrounding rock loosening, so as to solve the problems existing in the prior art.

[0008] To achieve the above objectives, the present invention adopts the following technical solution: a method for predicting the service life of tunnel lining under train dynamic load-surrounding rock loosening coupling, comprising the following steps: S1. Divide the tunnel to be predicted into mileage sections, determine the calculation cross section, lining control location and control stress component in each mileage section, determine the current monitoring update time point and obtain surrounding rock data, lining data, train passing event data and field vibration test data. S2. Establish static and dynamic calculation models for calculating the static and dynamic responses of the surrounding rock-lining, respectively. Use the field vibration test data to calibrate the dynamic calculation model and invert the current effective bending stiffness. After distinguishing the stiffness reduction caused by non-fatigue defects, determine the current fatigue damage. S3. Determine the lining reference stress based on the surrounding rock data and calculate the static axial force-bending moment vector using the static calculation model. Invert the equivalent train dynamic load vector based on the train passing event data and calculate the dynamic stress increment time history and dynamic axial force-bending moment vector using the dynamic calculation model. Form the total stress time history of the lining and the total axial force-bending moment vector of the lining section by static and dynamic superposition. S4. Directly determine the material strength failure point based on the total stress time history of the lining, and count rainflow during the period when material strength failure has not occurred. Calculate the fatigue damage of the foundation for each fatigue cycle, and perform time-series correction and accumulation according to fatigue cycle blocks. S5. Divide the service time after the current monitoring update point into a finite number of prediction cycles, and update the cumulative fatigue damage, effective bending stiffness and safety factor according to the prediction cycle. Continuously process fatigue cycles across prediction cycles, and determine the remaining service life or the lower limit of the remaining service life based on material strength failure, fatigue damage failure, safety factor failure and the preset maximum prediction time.

[0009] Compared with the prior art, the present invention has the following beneficial effects: This invention utilizes in-situ vibration and measured response to invert the current effective bending stiffness of the lining, and distinguishes stiffness reduction caused by non-fatigue defects, thus avoiding the repeated inclusion of disease effects and making the determination of current fatigue damage more consistent with the actual state. This invention calculates the static and dynamic effects of surrounding rock loosening and train dynamic effects in corresponding models, and inverts the equivalent train dynamic load based on the measured response, improving the accuracy of lining stress time history and cross-sectional internal force calculations. This invention performs material strength assessment before rainflow counting and accumulates damage according to different fatigue modes and loading sequences, taking into account both instantaneous strength exceeding limits and fatigue damage caused by variable amplitude loads. This invention updates fatigue damage, effective bending stiffness, and safety factor according to the prediction cycle, and continuously processes cross-cycle cycles and residual half-cycles at the prediction endpoint, reducing cycle cutoff and damage omissions, and reasonably determining the remaining service life of the lining or its lower limit. Attached Figure Description

[0010] Figure 1 This is a flowchart illustrating the overall process of predicting the service life of tunnel lining under the coupling of train dynamic load and surrounding rock loosening, as described in this invention.

[0011] Figure 2 This is a cross-sectional schematic diagram of the boundary of the loosened rock zone, the lining control area, and the control stress component of the present invention.

[0012] Figure 3 This is a schematic diagram illustrating the relationship between static and dynamic superposition in this invention. Figure 3 (a) is a schematic diagram showing the relationship between the time histories of the original static stress of the lining, the additional static stress due to loosening of the surrounding rock, and the time histories of the dynamic stress increment, forming the time histories of the total stress of the lining. Figure 3 (b) is a schematic diagram showing the relationship between the total axial force and bending moment vector of the lining section under the original static load condition of the lining, the static load condition after the surrounding rock loosens, and the train dynamic condition.

[0013] Figure 4 This is a flowchart illustrating the process of material strength assessment, fatigue damage calculation, stiffness feedback, safety factor calculation, and life determination across prediction cycles in this invention. Figure 4 (a) is a flowchart of the process for directly determining material strength, rainflow counting, fatigue cycle segmentation, damage updating, stiffness updating, and safety factor calculation within a single prediction cycle. Figure 4 (b) is a flowchart of the process of state retention across prediction cycles, failure check before settlement at the maximum prediction endpoint, residual half-cycle settlement, and output of remaining service life or lower bound of remaining service life. Detailed Implementation

[0014] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be noted that the following embodiments are used to illustrate the technical principles and implementation process of the present invention, and are not intended to limit the present invention to a certain tunnel cross-section, a certain sensor, a certain numerical calculation software, or a certain set of fixed parameters. All accompanying drawings are schematic diagrams and do not represent the actual dimensions, scale, or quantity of components. Unless otherwise specified, all stresses adopt the sign rule of positive for compression and negative for tension; time, length, stress, internal force, and stiffness adopt a consistent dimensional system in the same calculation process.

[0015] Example

[0016] like Figure 1 As shown, the method for predicting the service life of tunnel lining under train dynamic load-surrounding rock loosening coupling provided in this embodiment includes the following steps: Step S1: Divide the tunnel to be predicted into mileage sections, determine the calculation cross section, lining control location and control stress components in each mileage section, determine the current monitoring update time point and obtain surrounding rock data, lining data, train passing event data and field vibration test data; First, candidate boundary points are set along the longitudinal direction of the tunnel based on the surrounding rock grade, burial depth, lining cross-section, lining thickness, reinforcement type, construction joint location, loosening zone of the surrounding rock, and distribution of defects. If any of the above parameters changes significantly in adjacent sections, the candidate boundary point is preferably retained; if the structural and surrounding rock parameters of adjacent sections are within the preset allowable range and there are no new significant defects, they can be merged into the same mileage section.

[0017] For example, allowable relative difference thresholds can be set for burial depth, lining thickness, loosened zone thickness, and crack density. Let a positive parameter between two adjacent candidate intervals be... and The relative difference can be calculated as follows: ; When all controlled parameters When all values ​​are not greater than the corresponding threshold, and the surrounding rock grade, cross-sectional shape, and main disease type are the same or compatible, adjacent intervals can be merged. This relative difference rule is only used for auxiliary division. The actual division should also comply with the construction segmentation, changes in lining type, and significant disease boundaries to avoid forcibly merging intervals with significantly different mechanical properties.

[0018] For each mileage section, the following cross-sections are determined based on the defect detection results, existing static calculation results, and peak train response: the cross-section containing the most severe defect, the cross-section containing the most unfavorable static calculation result, and the cross-section containing the maximum dynamic train response. If two or three cross-sections overlap, they are merged; otherwise, all are retained as calculation cross-sections.

[0019] Within the same mileage section, first determine the pre-selected lining space locations on each calculation cross section, then treat the inner and outer edges of each pre-selected lining space location as independent lining control points; all lining control points determined jointly by the calculation cross section, the pre-selected lining space locations, and the inner or outer edges are uniformly and consecutively numbered as follows: , so that each group ( , Each location uniquely corresponds to a pre-selected lining spatial position and its inner or outer edge on a calculation cross section. Inner and outer edge lining control sections belonging to the same pre-selected lining spatial position share the stiffness and model parameters of the corresponding section, but retain their respective stress time history and life determination results. For example... Figure 2 As shown, corresponding lining control points are determined within the arch crown, left arch waist, right arch waist, left side wall, right side wall, and invert arch area of ​​each calculated cross section; the radial distance of the excavation outline in the figure is shown. Radial distance from the outer boundary of the loosened zone of surrounding rock And the thickness of the loosened zone formed by the difference between the two. This term is used to uniformly represent the extent of loosening of the surrounding rock in the radial direction where the lining control area is located. The degree of damage can be evaluated by comprehensively considering crack width, crack depth, spalling area, thickness of the material deterioration layer, cross-sectional loss of steel reinforcement corrosion, and the extent of voids behind the lining; the degree of static adverseness can be evaluated by the degree to which the axial force-bending moment combination approaches the boundary of the bearing capacity domain under static load conditions; the degree of dynamic adverseness can be evaluated by the strain peak-to-peak value, displacement peak-to-peak value, or dynamic stress range calculated by the model when a train passes.

[0020] For each pre-selected lining space location, calculate or pre-test the range of circumferential normal stress at the inner and outer edges of the lining: ; ; The circumferential normal stresses at the inner and outer edges of the lining are used as two candidate control stress components, and are respectively incorporated into material strength assessment, fatigue calculation, and life summarization. The aforementioned stress ranges are only used to prioritize monitoring and verification, and are not used to pre-exclude either side; the most unfavorable life is ultimately determined by the combined prediction results of all control components of the inner and outer linings.

[0021] Response measurement points should be set up at each lining control point and its adjacent locations. Fixed strain or displacement measurement points should be used first if they are available; if no fixed measurement points are available, one or more of the following should be temporarily deployed: strain sensors, fiber optic grating sensors, displacement gauges, or laser ranging devices. The measurement points should cover the inner edge, outer edge, or adjacent section locations that are sensitive to bending stiffness, and the coordinates, direction, sensor range, sampling frequency, and calibration coefficients of the measurement points should be recorded.

[0022] Field vibration tests can be conducted using a hammer, a controllable electromagnetic vibrator, or a hydraulic vibrator to apply a known load time history that will not cause additional damage to the lining. The known excitation load and the lining response must be acquired using the same clock, or time-scale alignment must be achieved through a trigger pulse. The excitation location, direction, and area of ​​action should be input into the dynamic calculation model to ensure that the calculated values ​​correspond to the measured values.

[0023] The surrounding rock data should include at least the in-situ in-situ stress, radial distance of the excavation profile, radial distance of the outer boundary of the loosened zone, elastic modulus, Poisson's ratio, cohesion, and internal friction angle of the unloosened surrounding rock and the loosened zone. The in-situ stress tensor can be obtained from hydraulic fracturing, stress relief, borehole deformation, or in-situ verified in-situ stress inversion results.

[0024] Lining data should include at least the original static stress of the lining, lining section parameters, material properties, and defect detection data. Lining section parameters include cross-sectional dimensions and reinforcement configuration; material properties include concrete and reinforcement material properties; and defect detection data includes reinforcement corrosion section loss, crack location and depth, void extent behind the lining, spalling depth, and material degradation layer thickness. For cracks, spalling, and material degradation, construction records, defect evolution records, and detection characteristics should be used to determine whether they belong to clearly defined non-fatigue defects. If it is not reliably possible to determine whether a defect belongs to a non-fatigue defect, supplementary detection, material testing, or defect evolution data should be used for attribution. Before the distinction is completed, definitive current fatigue damage and remaining service life prediction results should not be output to avoid arbitrarily classifying unconfirmed stiffness reductions as non-fatigue defects.

[0025] Train passage event data must include at least the train passage time and at least one of the synchronously acquired dynamic strain time history and dynamic displacement time history of the lining. Data preprocessing may include outlier removal, sensor zero drift correction, power frequency interference suppression, bandwidth uniformity, and clock skew correction. The filtering bandwidth should cover the main response frequency band of the train action, and structurally significant response peaks should not be filtered out in order to obtain a smooth curve.

[0026] For observations with different dimensions, their physical dimensions are preserved, and dimensionlessness is achieved by normalizing reference values ​​in the objective function. Each processed observation corresponds to a sampled value of "one measurement point - one response type - one sampling time", avoiding the confusion of complete time history, peak value, and root mean square value as the same observation.

[0027] The purpose of step S1 is to discretize the continuous spatial object of the entire tunnel into several mileage sections with relatively consistent structure and environmental conditions, and to select a calculation object that can reflect defects, unfavorable static load conditions, and unfavorable train dynamic conditions within each mileage section. This step is also used to establish a unified time scale and unified symbol rules, providing a traceable data foundation for subsequent stiffness inversion, static and dynamic calculations, and fatigue cycle sequencing.

[0028] Step S2: Establish static and dynamic calculation models for calculating the static and dynamic responses of the surrounding rock-lining, respectively. Use field vibration test data to calibrate the dynamic calculation model and invert the current effective bending stiffness. After distinguishing stiffness reduction caused by non-fatigue defects, determine the current fatigue damage. To enable static and dynamic calculation models to be directly established by those skilled in the art, a modeling method is presented below. Taking the longitudinal direction of the tunnel... The width is calculated, and a two-dimensional plane strain model of the cross-section is established. The surrounding rock is modeled using four-node or eight-node plane strain continuum elements, while the lining is modeled using Timoshenko beam elements capable of simultaneously outputting axial force, bending moment, and edge stress. The track slab, track bed, or invert arch filling layer is modeled using beam elements or plane strain elements according to its actual structure. A zero-thickness contact interface element is set between the surrounding rock and the lining, with a compressive-only contact relationship in the normal direction. The normal stiffness is expressed in the closed state, and the tangential stiffness is expressed using a spring-slip relationship. This indicates the initial tangential stiffness; for the detected void section behind the lining, no normal bearing contact is set, or the corresponding normal and tangential stiffness are set to the preset reduction ratio of the intact contact area.

[0029] The minimum distance from the left and right boundaries and the bottom boundary of the surrounding rock calculation domain to the excavation profile is preferably not less than [amount missing]. When the thickness of the overlying strata is less than When the upper boundary is set to the actual ground surface, otherwise the distance from the upper boundary to the excavation outline shall not be less than [the actual ground surface]. In static calculations, the left and right boundaries constrain the normal displacement, the bottom boundary constrains both horizontal and vertical displacement, and the upper boundary is set as a free boundary when it is the actual ground surface. In-situ stress is applied through an initial stress field or equivalent boundary load, and stress equilibrium is first performed to ensure that the ratio of unbalanced force to characteristic external load before excavation is no greater than [value missing]. During dynamic calculations, viscous absorbing boundaries are added to the left, right, and bottom boundaries to reduce artificial boundary reflections; the equivalent train dynamic load vector is applied to the track-ballast force transmission area and distributed to adjacent nodes according to the actual sleeper or track slab width.

[0030] The static constitutive model of the surrounding rock preferably adopts the Mohr-Coulomb elastoplastic model, which can utilize the elastic modulus, Poisson's ratio, cohesion, and internal friction angle obtained in step S1. The lining adopts a linear elastic model in the service response inversion stage, and its bending stiffness is determined by the parameters to be inverted. Control. Dynamic damping employs Rayleigh damping: ; Two angular frequencies covering the main frequency band of the measured response were selected. and And according to the corresponding damping ratio and Solution: ; In the formula, , and These are the damping matrix, mass matrix, and current stiffness matrix, respectively. and These are the mass proportional damping coefficient and the stiffness proportional damping coefficient, respectively. The dynamic integral optimization uses the Newmark average acceleration method, taking... , ; Calculate the time step Not greater than the measured sampling interval, and satisfying: ; In the formula, The highest effective frequency to be included in the inversion and fatigue analysis. The preferred frequency for the lining perimeter and contact area is no greater than [value missing]. The element characteristic size is gradually enlarged for the far-field surrounding rock, but the size ratio of adjacent elements is no greater than 1.5. The mesh is checked by halving the mesh size around the lining; the mesh is considered satisfactory when the changes in stress amplitude, displacement amplitude, and peak axial force-bending moment at the lining control points are all no greater than 2%. The relative residual force at each time step is no greater than [missing value]. And the relative change of displacement increment between two consecutive iterations is no greater than When the time step is considered converged, the above values ​​constitute only one preferred setting that can be directly implemented; when using other elements and integration methods, the same response error, mesh convergence, and time step convergence tests should be performed.

[0031] When the same calculation model contains multiple lining control points, stiffness parameter zones are divided along the lining circumferential direction according to the influence range of each pre-selected spatial location, and each currently effective bending stiffness parameter is assigned to the corresponding beam element range; the inner and outer edges of the same pre-selected spatial location share a single stiffness parameter. Beam elements not covered by control points use stiffness obtained from detected values, prior values, or interpolation from adjacent parameter zones. When there is significant response coupling between multiple stiffness parameters, they are combined into a stiffness parameter vector for joint inversion; the following formula, with a single bending stiffness as the independent variable, represents one component of the vector.

[0032] The parameter vector to be calibrated for the dynamic calculation model is set as follows: ; In the formula, The dynamic elastic modulus of the surrounding rock; The damping ratio corresponding to the first target circular frequency ω1; The damping ratio corresponding to the second target circular frequency ω2; Normal stiffness of the rock-lining contact interface; Tangential stiffness of the rock-lining interface; superscript This indicates the matrix transpose.

[0033] The known load time histories from the in-situ vibration test are input into the dynamic calculation model. For the first... Establish the response error term based on each response observation: ; In the formula, The effective bending stiffness variable to be inverted; In response to the total number of observations; This is the measured response; Calculate the response for the model; This is a normalized reference value with the same dimensions as the observation; The dimensionless observation weights.

[0034] In one feasible setup, the same response type The maximum value among the peak absolute value of the time history, the root mean square value, and the lower limit of the instrument's effective resolution can be taken for this experiment. It can be set and normalized according to the reciprocal of the measurement noise variance, so that... This approach prevents small-dimensional observations from losing their effect in the objective function and reduces the dominance of high-noise measurement points on the inversion results.

[0035] To suppress ill-conditioned complementarity between stiffness and contact parameters, separate stiffness prior regularization terms and parameter prior regularization terms are set: ; ; In the formula, This is the stiffness regularization coefficient; For the prior effective bending stiffness, the value obtained from calculations using intact lining can be used during the initial inversion. As a priori value; For the parameter prior vector; Let be a positive semi-definite weight matrix. In one specific setting, it can be set as follows: For a diagonal matrix, the first... Take the diagonal elements This makes the deviations of parameters with different dimensions comparable.

[0036] Solve within the upper and lower limits determined by design data, material testing, and field testing: ; The solution can be obtained using a quasi-Newton algorithm with boundaries, a trust region algorithm, a sequential quadratic programming algorithm, or a combination of global and local search algorithms. To check the identifiability, the solution can be started from multiple initial points, and the curvature of the objective function or the correlation of parameters near the optimal solution can be checked. When different initial points converge to similar results, it indicates that the current excitation test has a good ability to identify parameters; when the parameters are highly correlated, the excitation location, frequency band, or response type should be added, rather than relying solely on a single numerical value provided by the optimizer.

[0037] When multiple optimal solutions exist, the following rules are used sequentially to determine the unique result: first select... The smallest solution; if there are still multiple solutions, choose the one that best fits the context. The solution with the smallest normalized Euclidean distance is selected when multiple solutions still exist. If multiple solutions still exist, the solution with the smallest normalized Euclidean distance between the parameter vector and the prior vector is chosen. The normalized Euclidean distance is: ; if If they are still the same, then follow , , , and The parameters are compared sequentially, and the solution with the smaller parameter value is selected at the first distinct parameter component. This rule ensures that the equivalent train dynamic load vector inversion is used in subsequent operations. It possesses uniqueness and recalculation properties.

[0038] After the joint inversion is completed, independent verification is performed using verification measurement points or verification periods that did not participate in the inversion. For the first... For a given response, the normalized root mean square error, correlation coefficient, and peak relative error are defined as follows: ; ; ; In the formula, To verify the number of sampling points in the response; and These are the mean values ​​of the measured response and the calculated response, respectively. A preferred acceptance criterion is that both the strain and displacement responses satisfy... , and If any critical response fails to meet the conditions, lifetime prediction is not initiated. Instead, measurement points are added, parameter boundaries are adjusted, contact and boundary conditions are rechecked, and recalibration is performed. The aforementioned thresholds can be tightened based on instrument accuracy and engineering acceptance requirements, but cannot be arbitrarily relaxed after the inversion results are observed.

[0039] Based on the confirmed non-fatigue defects, a non-fatigue effective section is established. The non-fatigue reference material's elastic modulus, excluding the train cyclic fatigue modulus reduction, is used to calculate the non-fatigue reduced flexural stiffness without considering fatigue damage. To avoid mistakenly taking the neutral axis of the reinforced concrete composite section as the geometric centroid of the remaining concrete area, the neutral axis of the composite section is first determined by weighting the elastic modulus. ; Redefining: ; Therefore, we can conclude that: ; In the formula, and These are the non-fatigue reference elastic moduli for concrete and steel reinforcement, respectively. The non-fatigue reference elastic moduli are obtained through material tests in the reference area under the same environment and age, and not under the main control of train cyclic fatigue, or by correcting the material parameters before service combined with a non-fatigue time-varying model that only characterizes age, environment and chemical degradation. The measured elastic moduli of the control parts that may already contain cyclic fatigue modulus reduction are not directly used. The effective area of ​​concrete after deducting non-fatigue spalling, material deterioration layer, and areas confirmed by testing not to participate in the stress; For the first root or first The effective area of ​​the reinforcing steel layer after deducting corrosion losses; Its cross-sectional coordinates; The moment of inertia of the reinforcing bar relative to its centroid can be ignored when the diameter of the reinforcing bar is much smaller than the thickness of the lining. and All are weighted by the same elastic modulus neutral axis Based on.

[0040] For non-fatigue cracks that have been confirmed to have opened by testing, in order to determine At that time, the tensile contribution of the concrete in the cracked zone is neglected; by iterating the position of the neutral axis, the compression zone, the uncracked zone, and the effective reinforcement are made to jointly satisfy the axial force equilibrium of the section. If other cracked section stiffness models are used, it should be ensured that the stiffness reduction caused by cracks only enters the section. Once, it must not be mapped to fatigue damage again in subsequent instances.

[0041] The voids behind the lining are included in the model based on the actual contact range and contact stiffness of the contact interface, and are no longer repeatedly deducted from the lining section thickness.

[0042] The current fatigue damage is determined based on the difference between the inverted stiffness and the stiffness after non-fatigue reduction. ; In the formula, The stiffness-fatigue damage coupling coefficient is calibrated through representative amplitude fatigue stiffness attenuation tests under full compression, full tension, and tension-compression conditions, with the same or similar concrete mix proportions, strength grades, ages, and environmental conditions as the lining to be predicted. Represents the natural logarithm function. Outer layer and Used to limit negative damage caused by measurement error or values ​​exceeding 1 to... Inside.

[0043] No earlier than any point in time The relationship between stiffness and fatigue damage is as follows: ; The principle behind this treatment is that it first addresses the impact of cracks, spalling, material deterioration, steel corrosion, and voids that can be directly identified from the inspection results. Alternatively, the contact model can only map the remaining reduction of the current measured stiffness relative to the non-fatigue reduced bending stiffness as equivalent fatigue damage, thereby reducing the risk of the same defect being counted repeatedly.

[0044] Instead of using empirically specified values, the results are fitted through variable amplitude fatigue stiffness attenuation tests. For the first... The calibration specimen was in the first Each detection node is based on the corresponding fatigue mode. Calculate reference cumulative damage: ; In the formula, For the g-th calibration specimen up to the th A set of fatigue cycle numbers that have occurred at each detection node; measure the secant stiffness of that node. And based on the stiffness at the start of the test Normalization was performed using weighted least squares fitting: ; When the upper and lower bound constraints are not triggered, its closed-form estimate is: ; In the formula, The weights are determined based on the variance of stiffness measurements. Data from all three types of tests—total compression, total tension, and tension-compression—should be included in the fitted set, and the singleness of the data should be confirmed through residual tests of each mode. It can characterize three modes within a preset error range. If the residual of a certain mode continuously exceeds the acceptance limit, a single mode will be used. The implementation method described above is not applicable to this mode. The applicable fatigue modes of this method should be narrowed down, or a unified relationship should be re-established after supplementary testing. Another set of mode-specific coefficients cannot be arbitrarily used without modifying the technical solution. If calibration data covering the actual mode is not obtained, data from other modes must not be used as a substitute; instead, corresponding data quality indicators should be output.

[0045] Step S2 updates the design state calculation model to one that reflects the current rock-lining contact state and the current lining stiffness. This implementation establishes a static calculation model and a dynamic calculation model, both using the same calculation cross-sectional geometry, lining section, rock zoning, and rock-lining contact interface. The static calculation model uses static material parameters and outputs the lining static stress and static axial force-bending moment vector; the dynamic calculation model adds mass, damping, and dynamic contact parameters, and outputs the lining dynamic strain time history, lining dynamic displacement time history, dynamic stress increment time history, and dynamic axial force-bending moment vector.

[0046] Step S3: Determine the reference stress of the lining based on the surrounding rock data and calculate the static axial force-bending moment vector using the static calculation model. Invert the equivalent train dynamic load vector based on the train passing event data and calculate the dynamic stress increment time history and dynamic axial force-bending moment vector using the dynamic calculation model. Form the total stress time history of the lining and the total axial force-bending moment vector of the lining section by superimposing static and dynamic data. Using the design geometric center of the cross-section as the radial distance reference point, along the path passing through the first... The radial direction of each lining control point determines the radial distance of the excavation profile. radial distance from the outer boundary of the loosened zone of the surrounding rock And calculate: ; ; ; In the formula, The thickness of the loosened zone of the surrounding rock; This represents the compressive stress component of the in-situ stress tensor along the radial direction. This is a dimensionless coefficient for the loosening effect of surrounding rock; Add static stress to loosen the surrounding rock; The original static stress of the lining before taking into account the effect of loosening of the surrounding rock; This represents the initial lining reference stress at the current monitoring update point.

[0047] The calibration can be performed by combining the batch calculation results from the Fenner elastoplastic model with the field measurement results. For the first... Group calibration sample definition: ; When the regression intercept is constrained to zero, the least squares estimate is: ; The calibration samples should cover the surrounding rock grade, geostress range, relative thickness of the loosened zone, and lining type actually used in this application. If a sample to be predicted exceeds the calibration range, corresponding numerical calculations or field samples should be added and recalibrated; unconstrained extrapolation is not advisable.

[0048] when season , ,at this time .

[0049] In order to obtain the axial force and bending moment of the cross section that cannot be uniquely inferred from a single local stress, two complete static load cases are established in the static calculation model.

[0050] In the original static load condition of the lining, the elastic modulus, Poisson's ratio, cohesion, and internal friction angle of the surrounding rock are used in the calculation domain. In-situ stress and other dead loads are input, and time points are used. Corresponding effective flexural stiffness of the lining Output for this operating condition: ; In static load conditions after the surrounding rock has loosened, to The loosened zone of the surrounding rock is assigned the elastic modulus, Poisson's ratio, cohesion, and internal friction angle, while the surrounding rock outside the loosened zone is assigned the parameters of the unloosened surrounding rock, maintaining in-situ stress, lining section, contact relationship, and other boundary conditions unchanged. Output for this condition: ; The static axial force-bending moment vector resulting from the loosening of surrounding rock and the static axial force-bending moment vector incorporating the effects of loosening of surrounding rock are respectively: ; ; In the formula, The static axial force-bending moment vector is added to the loosening of the surrounding rock. This is the static axial force-bending moment vector that takes into account the effect of surrounding rock loosening. When there is no loosening zone in the surrounding rock, let... , It is a two-dimensional zero vector consisting of zero axial force and zero bending moment.

[0051] Lining reference stress Used for material strength assessment and fatigue cycle calculation; the static axial force-bending moment vector is used for axial force-bending moment bearing capacity verification. Both are obtained according to the aforementioned stress calculation relationship and static calculation model, respectively, and are confirmed to correspond to the same static load state through the following benchmark stress consistency check. A single local stress cannot replace the internal force vector of the complete cross section.

[0052] To prevent empirically applied static stress and the static axial force-bending moment vector output by the static calculation model from representing two inconsistent static load states, in A baseline stress consistency check should also be performed. Based on the axial force and bending moment output under static load after loosening, calculate the static stress of the model at the control edge: ; In the formula, and These are the converted areas of the combined section and the converted section modulus of the corresponding inner or outer edge, obtained by using the non-fatigue reference elastic modulus of concrete as the conversion benchmark, converting according to the ratio of the elastic modulus of steel reinforcement to concrete, and using the same elastic modulus weighted neutral axis. For sections with open cracks, the tensile contribution of the concrete in the crack opening zone is ignored during conversion, and the neutral axis is determined iteratively to ensure that the converted area, converted section modulus, and non-fatigue reduced flexural stiffness use the same effective section and material parameters. The positive and negative signs are determined according to the selected control edge and bending moment direction. Consistency error is defined as follows: ; In the formula, For the first Within the first mileage section The representative value of the concrete compressive strength of each lining control section is determined by test method as shown in step S4.

[0053] A preferred approach is to require If this limit is exceeded, check. The calibration range, the source of the original static stress of the lining, the contact state of the surrounding rock, and the effective section parameters should be determined and recalibrated or recalculated. Two sets of inconsistent static load results should not be used for fatigue judgment and bearing capacity verification respectively.

[0054] The lining reference stress obtained in step S3 is the initial value at the current monitoring update time. After entering the prediction cycle, the static state is recalculated with the initial effective bending stiffness in each prediction cycle, and the lining reference stress for that cycle is obtained using the stress recovery relationship of the combined section consistent with the bending stiffness after non-fatigue reduction. This reference stress remains unchanged within the current prediction cycle and is recalculated with the initial stiffness at the beginning of the next prediction cycle; therefore, it is not fixed for all prediction cycles. When new surrounding rock data, lining data, or field vibration test data are obtained, the time point when the data collection is completed is determined as the new current monitoring update time point, and steps S1 to S5 are repeated.

[0055] For the first For each train passing event, the equivalent train dynamic load vector to be identified, composed of the load values ​​at each load sampling time, is denoted as: ; In the formula, For the first Equivalent train dynamic load sampling values ​​at each load sampling time. This represents the number of load sampling points during the train's passage event. The load sampling interval is the same as or an integer multiple of the dynamic calculation time step.

[0056] The equivalent train dynamic load vector does not necessarily have to be equivalent to the contact force of a single wheel, but rather it can reproduce the equivalent input of the measured lining response in the calibrated dynamic calculation model. A feasible set is established based on the load application location, direction, event duration, sampling frequency, and measured response frequency band. For example, the load can be limited to be non-zero only during the train's occupancy time window, the load direction can conform to the direction of force transmission from the track to the structure, and unreasonable high-frequency oscillations can be restricted.

[0057] The equivalent train dynamic load vector inversion formula is: ; In the formula, For events within the corresponding mileage segment The corresponding set of all valid response observation numbers, each response observation records its corresponding calculation cross section and lining control location, in the formula Indicates the first The sequence number of the lining control part corresponding to each response observation; For observation weights; and These are the measured values ​​and the model values, respectively. This is a normalized reference value; Identify regularization coefficients for loads; It is a first-order difference matrix; It is a 2-norm.

[0058] The first requirement is to invert the load to reproduce the measured response, and the second requirement restricts the occurrence of drastic jumps in adjacent load sample values ​​without any physical basis. It can be determined by using L-curves, generalized cross-validation, or by leaving some measurement points for verification. If the load is too small, the inverted load will easily fit the noise; if it is too large, it will over-smooth the true impact peak value.

[0059] When multiple optimal solutions exist, choose the one that best fits the given conditions. Choose the smallest solution. The smallest solution is selected; if multiple solutions still exist, they are compared sequentially according to the sampling time, and the solution corresponding to the smaller value at the first different sampling value is selected. For the same train passing event within the same mileage section, only one equivalent train dynamic load vector is obtained, shared among all lining control points. The lining control point number is only used to identify the response output position and is not included in the load vector subscript. This results in a unique... .

[0060] Each equivalent train dynamic load vector should be verified by setting up measurement points. Re-enter the dynamic calculation model and calculate the strain or displacement measurement points that were not involved in the inversion. , And peak relative error; preferably using the same acceptance limit as the model joint calibration. Events that fail validation must not be directly copied to the baseline loading sequence. They can be re-identified after ruling out sensor anomalies; if they still fail, they should be marked as anomalous events and modeled separately. The saved event log should include at least: , The objective function value, verification error, event start and end times, and load sampling interval are used to enable subsequent predictions to recalculate the dynamic input of the event.

[0061] The function of this inversion method is that it does not require the speed, axle load, wheelbase and track irregularity parameters of each train to be directly obtained on site. Instead, it uses the lining response that is actually available to identify the equivalent dynamic input that matches the current structural and track force transmission state.

[0062] Will Input the calibrated dynamic calculation model at time point use Calculate the time within the event Corresponding dynamic stress increment time history: ; And the dynamic axial force-bending moment vector of the lining section: ; The static load reference and the dynamic increment are superimposed to form the total stress time history of the lining that controls the stress components: ; The axial force-bending moment vectors of the original static load condition of the lining, the additional static axial force-bending moment vectors due to loosening of the surrounding rock, and the dynamic axial force-bending moment vectors are superimposed according to the same cross section and the same sign rule to form the total axial force-bending moment vector of the lining cross section: ; ; In the formula, and The first The train passes through the event at the time of the event. Prediction timing The corresponding total axial force and total bending moment of the lining section. The total stress of the lining is used for material strength assessment and fatigue damage calculation, while the total axial force-bending moment vector of the lining section is used for axial force-bending moment bearing capacity domain verification. The two types of outputs have different functions and a single local stress cannot replace the internal force vector of the section.

[0063] This formula retains the static compressive or tensile stress baseline, enabling subsequent strength assessments to identify situations where "the reference static stress has exceeded the limit but fatigue cycles have not yet formed," and also ensuring that the maximum and minimum stresses of the rainflow cycle reflect the true average stress level.

[0064] Step S3 is used to establish the static load baseline caused by the loosening of the surrounding rock and the dynamic increment caused by the passing of the train in the corresponding static calculation model and dynamic calculation model, and output the local control stress and the axial force-bending moment vector of the lining section respectively. Figure 3 The diagram illustrates the correspondence between three operating conditions and two types of outputs: Figure 3 In section (a), the original static stress of the lining is superimposed with the additional static stress caused by the loosening of the surrounding rock to form the reference stress of the lining; Figure 3 In section (b), the axial force-bending moment vectors of the original static load condition of the lining and the static load condition after the surrounding rock loosening are calculated using a static calculation model. The difference between the two is used to determine the additional static axial force-bending moment vector after the surrounding rock loosening. The axial force-bending moment vector of the original static load condition of the lining and the additional static axial force-bending moment vector after the surrounding rock loosening are superimposed to form the static axial force-bending moment vector. The dynamic stress increment time history and the dynamic axial force-bending moment vector are calculated using a dynamic calculation model and superimposed to form the total stress time history of the lining and the total axial force-bending moment vector of the lining section.

[0065] Step S4: Determine the material strength failure point directly based on the total stress time history of the lining, and count rainflow during the period when material strength failure has not occurred. Calculate the fatigue damage of the foundation for each fatigue cycle, and perform time-series correction and accumulation according to fatigue cycle blocks. According to the order in which the train passes, the time within the event is... Converted to global continuous time Let the first... The start time of each event is Then the consecutive times of the sampling points within the event can be expressed as: ; Each event Connect events in chronological order; time periods without train power load between adjacent events are considered. The stresses at the start and end points of the continuous time history are also set to... This leads to: ; Introducing a reference stress at the start and end points clarifies the boundary conditions of the rainflow counting interval, but does not render the reference stress itself a closed loop. Linear interpolation is used between adjacent sampling points to determine the consecutive moments when the first intensity exceeds the limit.

[0066] The representative value of concrete compressive strength is determined based on the test results of core samples taken on-site or samples with the same mix proportion and age. and representative value of tensile strength The set of time points when material strength exceeds the limit is as follows: ; If the set is not empty, then: ; To improve time-point accuracy, when adjacent sampled values ​​cross a certain intensity threshold... When this happens, the intersection points can be found using linear interpolation. Let... and The corresponding stress is and ,but: ; When compressive stress exceeds the limit, When tensile stress exceeds the limit, Set of time points when material strength exceeds limits Records only from the current monitoring update point. The point in the continuous total stress time history where the material strength failure condition is actually met; when the continuous total stress time history is in When the reference stress of the lining at the location satisfies the material strength failure condition, Included The initial set of candidate failure times at the current monitoring update time. according to The reference stress, initial cumulative fatigue damage, and initial safety factor of the lining at the location are determined; the dynamic stress exceedances generated by the reference loading sequence are included in the actual exceedance time points within the corresponding prediction period. The current monitoring update time point is not traced back. .

[0067] The "material strength failure" referred to in this embodiment is a material-level limit state set for the selected concrete control stress components, rather than a claim that the entire reinforced concrete lining has collapsed without cross-sectional analysis. The compressive stress reaches... This indicates that the concrete at the lining control section has reached the representative value of the adopted compressive strength; the tensile stress has reached... This indicates that the uncracking concrete has reached its first tensile cracking strength. This method uses both as conservative life-end conditions, its purpose being to promptly identify situations where local material strength can no longer be satisfied. This represents the ultimate limit state of the axial force-bending moment bearing capacity of the overall section after considering reinforcement, cracks, and effective cross-section. The two criteria correspond to local material and overall section respectively, and are not interchangeable.

[0068] for Existing and confirmed cracks, the effects of which first penetrate the area. And bearing capacity domain, the same historical cracking point can no longer be used as The new material subsequently failed due to strength limitations. Subsequent strength searches only determine... The time history of the total stress of the lining afterward should be checked to determine whether the effective strength limit of the corresponding control material has been reached. If the control point is located at an existing through crack that no longer transmits concrete tensile force, the nominal concrete tensile stress at that crack and the stress of the uncracked concrete should not be used. Instead of repeating the assessment, a new adjacent, uncracked location capable of transmitting concrete tensile force should be selected as the control point for the lining on the same side. Material strength assessment and concrete fatigue cycle identification should be performed, and the axial force-bending moment bearing capacity domain check of the original crack section should continue. This treatment does not replace the overall bearing capacity evaluation of the original crack section with an adjacent uncracked location.

[0069] like If the value is empty, it only means that no material strength failure has occurred within the current continuous total stress time history coverage area, and does not mean that there is no fatigue damage.

[0070] for For the previous continuous total stress time history, or for all continuous total stress time histories without material strength failure, first delete intermediate sampling points that do not change the stress direction, retain local maxima, local minima, and interval endpoints as stress inflection point sequences, and then perform rainflow counting.

[0071] In computer implementation, a stack of inflection points can be used to push inflection points one by one. Each time a new inflection point is pushed, the stress range adjacent to the top of the stack is compared; if the closure condition is met, the corresponding inflection point is popped and the closed loop is recorded; otherwise, the process continues. Regardless of whether the four-point method or the equivalent stack algorithm is used, the same set of rainflow closure criteria is used for the calculation of each prediction cycle and the maximum prediction endpoint for the same project; the current monitoring update time point... Previous historical periods were only used to construct the baseline loading sequence, and their residual inflection points are not included in the self-loading sequence. Initial rain flow count.

[0072] The moment of the last turning point constituting each closed fatigue cycle is defined as the occurrence moment of that cycle, and the cycles are numbered sequentially according to their occurrence moments. And record: ; in, The count weight of the closed loop is 1. This occurrence time definition is only used to preserve the time sequence of the closed loop and does not replace the first time point when the material strength exceeds the limit obtained along the total stress history of the lining in step S4.

[0073] Fatigue modes are classified according to the maximum and minimum cyclic stress: ; ; ; in, , and These represent the full compression, full tension, and tension-compression fatigue modes, respectively. To normalize the compressive and tensile stresses according to their respective material strengths, the following definitions are used: ; ; and These are the dimensionless maximum and minimum stress coordinates, respectively. Through this normalization, the same interpolation frame can represent the relative stress levels of concrete of different strength grades under full compression, full tension, and tension-compression modes.

[0074] Only when the following formula is satisfied will the cycle proceed to fatigue life calculation: ; For the The fatigue failure cycle number is: ; This is a fatigue life function established based on constant-amplitude fatigue test data of the corresponding fatigue mode. For the first The number of fatigue failure cycles per fatigue cycle.

[0075] Fatigue life function Piecewise linear interpolation was used to establish the data based on full compression, full tension, and tension-compression constant amplitude fatigue test data, respectively. Triples were recorded for each test sample: ; Take first ,exist The test points are triangulated within the plane. Points to be calculated. When located within a triangle formed by three test points, calculate the coordinates of the centroid. , and ,satisfy: ; ; but: ; ; One-dimensional linear interpolation of adjacent points is used on the boundary of the test grid. The points to be calculated must fall within the calibration domain of the corresponding fatigue mode; if they exceed the calibration domain, supplementary tests should be conducted or the state should be marked as unreliable for calculation, and unconstrained extrapolation values ​​should not be used. The concrete mix proportion, strength grade, age, temperature, and moisture content of the specimens should be the same as or similar to those of the lining to be predicted.

[0076] To make the three categories The test should be repeatable, and a servo fatigue testing machine is preferred for axial constant-amplitude testing. For full-compression testing, a prism or cylinder capable of stably transmitting pressure is used; for full-tension and tension-compression testing, a specimen with the same mix ratio and curing regime as the full-compression specimen, and whose bidirectional axial force is transmitted through bonded end plates or mechanical clamps at both ends, is used. Each The stress combination should consist of no fewer than three parallel specimens. The loading waveform should be a sine wave or a triangular wave, maintaining consistency for the same calibration item. The preferred loading frequency is 1–10 Hz, and surface temperature rise monitoring should ensure the specimen temperature rise does not exceed 2°C; if it does, the frequency should be reduced. Every preset number of cycles, pause or use low-amplitude probes to measure the secant stiffness until the specimen can no longer reach the predetermined upper or lower load limits or the main crack penetrates, causing a continuous decrease in load-bearing capacity. The cycle number corresponding to this moment is recorded as [number missing]. The end-bonded areas should also be checked during full-tension and tension-compression tests; specimens with clamp or bonded end failure should not be included in the calibration.

[0077] The test points for each mode should cover the convex hull of the region to be calculated. For the full compression mode, it is preferable to set at least three maximum compressive stress coordinate levels and three minimum compressive stress coordinate levels under each maximum coordinate; the same principle applies to the full tension and tension-compression modes. For the same stress combination... First, take the commonly used logarithm, then use the median or the mean after removing outliers confirmed by statistical testing as the grid point. Record the mix proportion, age, moisture content, temperature, loading frequency, waveform, stress coordinates, failure cycle number, and failure mode for each specimen.

[0078] The numerical examples in the instruction manual can only use clearly identified exemplary data to illustrate the interpolation method. When making engineering predictions, if there is a lack of three types of fatigue test data that match the lining to be predicted, or if a certain calculation point is located outside the calibration domain, the program must output "Insufficient fatigue life interpolation data" and must not use exemplary data or data from another fatigue mode to replace it and output a determined life.

[0079] Based on the order in which the loops occur, the first loop that has not yet been grouped is taken as the first... The reference cycle for each fatigue cycle block, its sequence number is The following loop Only when the fatigue patterns are the same and simultaneously satisfy the following conditions: ; ; Only then is it included in the current fatigue cycle block, where The tolerance is for dimensionless stress grouping. When any condition is not met, the current fatigue cycle block ends, and the cycle to be judged is used as the reference cycle for the next fatigue cycle block.

[0080] Let the first The set of cycle numbers of each fatigue cycle block is: Its basic fatigue damage is as follows: ; This formula uses its respective iterations in succession. Instead of averaging the stress within the block first and then calculating only one fatigue life, it is able to retain the larger damage contribution of a small number of high-stress cycles within the block.

[0081] No. The representative fatigue severity of a fatigue cycle block is defined as follows: ; The more severe the baseline cycle, The smaller, The larger.

[0082] Fatigue cycle blocks formed after the current monitoring update time are numbered sequentially according to their occurrence order, and the fatigue cycle block numbers are not renumbered due to prediction cycle switching; the first fatigue cycle block formed after the current monitoring update time is denoted as... And order: If a previous fatigue cycle exists and both have the same fatigue mode, let: ; When a previous fatigue cycle exists but the fatigue modes of the two are different, let: ; In the formula, and The time-series influence coefficients are jointly calibrated through low-high and high-low stress sequence tests under the same fatigue mode. Both coefficients and the reciprocal of the representative fatigue severity use the same cycle number unit, thus keeping the time-series correction coefficients dimensionless. These are the upper and lower limits of the amplitude. Indicates when Time to take ,when Time to take In other cases, take .

[0083] In the same mode, when the severity of the current fatigue cycle block is higher than that of the previous block, ,therefore This is used to represent the amplification effect of low stress history on subsequent high stress damage; when the current fatigue cycle severity is low, This is used to represent the relative mitigating effect of high-low sequences. When crossing fatigue modes, since same-mode sequence experiments cannot provide reliable parameter data for mode switching, this implementation conservatively does not perform time-series amplification or reduction, allowing... .

[0084] and After conducting low-high and high-low two-stage sequence tests in full-compression, full-tension, and tension-compression modes respectively, the results were jointly calibrated. For the first... For specimens in the same mode sequence, first, based on the measured stiffness after the previous stage of load and the calibrated... Determine the pre-existing damage Then, the measured new damage is determined based on the stiffness change during the subsequent load stage. The basic additional damage, without considering the order effect, is: Define the measured damage ratio: Solving regression problems with non-negativity constraints within the same fatigue mode: ; In the formula, and These represent the representative severity of the preceding and following load levels, respectively. For experimental weights. The three models should be checked and standardized separately. The residuals of the regression; if any model cannot meet the preset fitting error, then the implementation method using uniform coefficients does not cover the model, and cannot forcibly extrapolate with a set of coefficients. and The effective sequence can be obtained separately. The 5th and 95th percentiles, and further restricted to When the calibrated sample is insufficient to stably estimate the quantiles, it is preferable not to make order corrections and let .

[0085] The damage after fatigue cycle block action is as follows: ; Before the first fatigue cycle block takes effect after the current monitoring update point, let .when The fatigue damage failure condition is met at that time. (Additionally...) This is the threshold for transitioning between fatigue damage stages, calibrated through fatigue testing; to reach The system outputs an accelerated degradation warning, but this threshold is not considered equivalent to the fatigue failure threshold.

[0086] This can be determined through piecewise regression of the stiffness-damage curve. For candidate inflection points... Fitting respectively and Two segments A straight line, and select the two segments with the smallest weighted sum of squared residuals and the latter segment with a significantly larger absolute value of slope. This serves as a threshold for stage transition. If the experimental curve does not have a stable inflection point, no numerical warning threshold is set; only the threshold is retained. The fatigue failure conditions cannot be directly determined by empirical values ​​such as 0.4 used in other mix proportions or under other environmental conditions.

[0087] Step S4 first directly searches for material strength exceeding limits based on the total stress time history of the lining, without considering whether a closed fatigue cycle has formed. Only during periods when material strength failure has not yet occurred will fatigue cycle identification and fatigue damage calculation continue. This sequence avoids missing situations such as static baseline exceeding limits, stress peak exceeding limits before the closed cycle, and actual exceeding limits occurring earlier than the final turning point of the cycle.

[0088] Step S5: Divide the service time after the current monitoring update point into a finite number of prediction cycles, update the cumulative fatigue damage, effective bending stiffness and safety factor according to the prediction cycle, continuously process fatigue cycles across prediction cycles, and determine the remaining service life or the lower bound of the remaining service life based on material strength failure, fatigue damage failure, safety factor failure and preset maximum prediction time. Record the current monitoring update time as The subsequent service time is divided into There are several equal-duration prediction periods, each period lasting [duration value]. : ; ; Maximum prediction duration is . The timeframe can be determined based on the complete cycle of train passage data, the frequency of detection updates, and computational efficiency; for example, a month, a quarter, or a year. The maximum forecast period is determined based on the required output.

[0089] from Previously, a duration of Furthermore, the most recent historical period with complete lining response data is used to form a baseline loading sequence, which consists of the equivalent train dynamic load vectors obtained in the order of occurrence within that period and their relative occurrence times. The baseline loading sequence preserves the order of events, event intervals, and load time histories within events to reproduce the load sequence under the most recent operational state in each prediction period. The most recent historical period is only used to provide the equivalent train dynamic load vectors, relative occurrence times of events, and event order used in each prediction period. It does not inherit the rainflow residual inflection points or fatigue cycle block states formed in that historical period, nor does it re-include fatigue damage within that historical period.

[0090] The applicable condition for reusing the baseline loading sequence is that the operating schedule, train type composition, and train passing response statistics remain basically stable during the forecast period. The number of events, peak response distribution, and main frequency bands of the most recent two or three historical periods of equal length can be compared. When the relative difference in the number of events is no greater than 10%, the relative difference in the median of the peak response is no greater than 10%, and no new significant peaks appear in the main frequency bands, the most recent historical period can be used as the baseline loading sequence. If there are clear changes in train services, speed increases, vehicle replacements, or track conditions, corresponding baseline loading sequences should be established for each operating scenario, or online rolling updates should be triggered in advance after new data is obtained. Unless future operational assumptions are specified, the lifetime output only represents the prediction result under the "repeated baseline loading sequence scenario" and is not extrapolated to an unconditional lifetime under any future operational conditions.

[0091] make: ; use and benchmark loading sequence calculation Let the safety factor be determined, and let: ; Before entering the first prediction period, the initial set of candidate failure times for the current monitoring update time is constructed according to the following formula: ; In the formula, This is only used to record failure states that already exist at the current monitoring update point; the dynamic stress peak generated by the benchmark loading sequence within the first prediction period is used to determine material strength based on its actual occurrence time, and the failure time point corresponding to the dynamic stress peak is not predetermined. .

[0092] Before counting rainflow in the first prediction cycle, the rainflow residual inflection point stack and fatigue cycle block state are initialized to empty, based on the current monitoring update time. As the starting point for rainflow counting, and The reference stress of the lining at the specified location is used as the initial stress in the continuous total stress time history and is not inherited. Previous residual inflection points and fatigue cycle blocks that have not yet ended; current fatigue damage As The first fatigue cycle block will then process the accumulated fatigue damage from previous cycles.

[0093] For the Each prediction cycle will execute the following process sequentially.

[0094] First, The lining stiffness parameters are fixed for both the static and dynamic calculation models for the predicted cycle. First, the initial static state of the cycle is calculated. The reference stress of the lining for that cycle is obtained according to the aforementioned stress recovery relationship of the combined sections. Then, the reference loading sequence is input to calculate the train's dynamic response. The reference stress of the lining is superimposed with the time history of the dynamic stress increment to form the total stress time history of the lining, and the dynamic axial force-bending moment vector is calculated. Even if fatigue damage increases block by block within the cycle, the dynamic response that has already occurred in the current cycle is not recalculated.

[0095] Second, material strength failure is directly retrieved along the total stress time history of the lining during the predicted period. The obtained over-limit time points are then incorporated into... If material strength failure occurs, the first time point exceeding the limit within the continuous time history is recorded, and the end of the cycle is not used to replace the actual time point exceeding the limit. At the same time, the life search for subsequent prediction cycles of the lining control part is immediately terminated, and rainflow counting is no longer performed on the stress time history after the failure time point, nor is the residual half-cycle settlement of the maximum prediction endpoint executed. Fatigue cycles that have been closed and included before the failure time point are only recorded as pre-failure states and are not used to postpone the determined strength failure time point.

[0096] Third, during the period before material strength failure occurs, when At that time, for the current monitoring update point Rainflow counting was performed on the time history of the total stress of the lining formed; when At that time, the residual turning point retained in the previous prediction cycle is connected with the time history of the total stress of the lining in the current prediction cycle and the rainflow counting is continued; the fatigue failure cycle number and the fatigue damage of the foundation are calculated for each fatigue cycle, and the time-corrected fatigue damage is calculated according to the state of the fatigue cycle block.

[0097] Fourth, assuming no material strength failure occurs during the predicted cycle, complete the additional fatigue cycle treatment. For The cumulative fatigue damage obtained after processing all new fatigue cycles is determined as the cumulative fatigue damage at the end of the period. This includes the damage increment corresponding to the new cycles added to blocks that have not yet completed their fatigue cycles within this prediction period; for After completing all closed-loop fatigue cycle processing within the maximum prediction time, the accumulated fatigue damage is first recorded as the accumulated fatigue damage before final settlement. The effective bending stiffness before final settlement is determined according to the aforementioned stiffness update relationship. The safety factor before final settlement is determined using static calculation models, dynamic calculation models, and the axial force-bending moment bearing capacity domain. ;when or At that time, Add to the failure candidate time point set and terminate the terminal settlement of the lining control section; only when , Furthermore, if no material strength failure has occurred prior to this, the final residual half-cycle will be processed according to the following maximum predicted endpoint residual half-cycle terminal settlement rules, and the cumulative fatigue damage after settlement will be determined as... .when And if no new fatigue cycles are generated during the prediction period: ; Fifth, update the stiffness based on the final damage after all accrued fatigue damage for this cycle has been completed: ; The inner and outer edges of the same pre-selected lining spatial location accumulate fatigue damage separately, but they correspond to the same physical section. At the end of each prediction cycle, the larger value of the accumulated fatigue damage of the inner and outer edges is substituted into the stiffness update relationship, and the same effective bending stiffness obtained from the update is assigned to both, so as to avoid the same physical section having two different bending stiffnesses at the same prediction point.

[0098] Sixth, with Recalculate The static axial force-bending moment vector and the dynamic axial force-bending moment vector at the point are calculated, and the final safety factor is determined based on the axial force-bending moment bearing capacity domain. .like or Then Add to the failure candidate time point set and terminate the lifetime search for the subsequent prediction cycle of the lining control part; only when all three failure conditions are not met and Only then is the final stiffness considered as the first... The initial stiffness of each prediction cycle is calculated, and residual inflection points and fatigue cycle block states are retained for the next cycle. Thus, material strength failure is determined by the actual first time point exceeding the limit within the continuous time history, while fatigue damage and safety factor failure are determined by the end of the prediction cycle when the corresponding conditions are first met.

[0099] The above-mentioned "fixed within the cycle, feedback at the end of the cycle" process ensures that there is only one determined dynamic stiffness input for each prediction cycle, eliminating the uncertainty of fatigue cycle block-level stiffness updates without specifying whether the dynamic response of the current cycle is recalculated.

[0100] at any point in time The total axial force-bending moment vector of the lining section is: ; ; Both axial force and bending moment retain their signs and are first vectorized, without converting them into scalars that lack a unified basis before adding them directly.

[0101] Establishment time The corresponding effective cross section. The effective area of ​​the reinforcing steel is equal to the area of ​​the original reinforcing steel minus the loss of the corroded section; the effective thickness of the lining is equal to the design thickness minus the spalling depth and the thickness of the material deterioration layer; crack weakening is taken into account through the effective cross section area, the effective cross section modulus, or the local non-tension zone; the void behind continues to be taken into account through the contact range and contact stiffness in the rock-lining contact relationship of the static calculation model and the dynamic calculation model.

[0102] In one implementation of cross-section analysis, it is assumed that the plane section remains planar, and for a given axial strain... and curvature Cross-sectional coordinates The strain at the point is: ; In a straightforward and conservative calculation method, tensile stress in concrete is neglected, compressive stress is assessed using a parabolic-plateau constitutive model, and reinforcing steel is assessed using an ideal elastoplastic constitutive model. When compressive stress is kept positive: ; ; In the formula, For time point The representative value of concrete compressive strength; This refers to the compressive strain of concrete when it reaches its peak compressive stress. This represents the ultimate compressive strain of the concrete. For the first The current yield strength of the reinforcement. The strain of the reinforcement should also meet the following requirements. , The ultimate strain of the reinforcing steel is given by material testing or design standards. For projects without open cracks and using section models that account for the tensile contribution of concrete, it can be... Take within range The tensile stress in the concrete should be reduced to zero after the initial cracking strain is exceeded; the tensile model should not be arbitrarily switched between different prediction periods for the same project.

[0103] The effective concrete section is discretized along its thickness into at least 200 fiber layers, with the fiber layer width being the actual section width; the reinforcing steel is treated as discrete reinforcement layers. Based on the above constitutive model, the following is obtained: and And by integrating, the resistance points of the cross section are obtained: ; ; Taking positive and negative curvature directions respectively, traversing the neutral axis position, and ensuring that the outermost compressive concrete reaches... At the same time, any steel bar with strain exceeding To achieve the state of concrete compressibility control. Limit boundary points; simultaneously, each reinforcement layer reaches its tensile limit strain. Or the ultimate strain under compression To control the conditions, the compressive strain of the concrete should not exceed And the absolute value of the strain of the remaining steel bars does not exceed their respective values. Under the condition of obtaining the reinforcement control boundary point; for the pure axial compression direction, set the curvature to zero and make the concrete compressive strain reach For the pure axial tension direction, set the curvature to zero and gradually increase the uniform axial tensile strain until any reinforcement layer reaches its tensile limit strain. Merge the above boundary points and sort them according to their polar angles to form a closed axial force-bending moment bearing capacity domain. After doubling the number of fiber layers, the boundary points... and When the relative changes are all no greater than 1%, the cross-section is considered to have discrete convergence. The bearing capacity domain should simultaneously include pure axial compression, positive bending, negative bending, and the tension boundary controlled by reinforcement; it cannot be replaced by a few rectangular envelope points.

[0104] For each lining section, calculate the capacity amplification factor along the current axial force-bending moment ratio direction for the total axial force-bending moment vector: ; In the formula, The variable representing the non-negative proportional amplification of the total axial force-bending moment vector of the lining section. This is the capacitance amplification factor. This indicates taking the maximum value; Actual calculations can be performed on A binary search is employed: the initial lower bound is set to 0, and the upper bound is progressively increased until the corresponding internal force point is located outside the bearing capacity domain, then the interval is iteratively narrowed; when the difference between the upper and lower bounds is not greater than 0. Or the relative error is not greater than The process terminates at a certain time. The safety factor is taken as the minimum capacity amplification factor for static load, all train events, and all time intervals within all events: ; Among them, event number 0 represents the static load condition without train dynamic load, which means... .when When this occurs, it indicates that the total axial force-bending moment vector of the current lining section has reached or exceeded the boundary of the bearing capacity domain, thus satisfying the safety factor failure condition.

[0105] Before obtaining new material and defect detection data, each prediction cycle can be fixed and adopted. The bearing capacity domain is established based on the determined concrete strength, steel reinforcement strength, effective steel reinforcement area, effective lining thickness, and crack weakening parameters; the bearing capacity domain is re-established through rolling updates as new test data arrives.

[0106] when At the end of the current cycle, residual inflection points that have not yet formed a closed loop are retained and connected to the time history of the total lining stress for the next predicted cycle. Closed loops that have been identified and included in the damage are removed from the residual inflection point stack to avoid double counting in the next cycle.

[0107] If a fatigue cycle block has not ended by the end of the cycle because the new cycle does not meet the grouping conditions, then retain: the reference cycle number. Fatigue mode Timing correction coefficient The set of cycle numbers already included in the damage calculation, the cumulative value of the baseline damage, and the representative severity of the baseline cycle. The new cycle arriving in the next cycle will still be judged according to the original baseline cycle to determine whether to enter the block; only newly added cycles... Multiply by the already determined The time series will not be re-adjusted due to crossing the forecast period.

[0108] At the same time, retain the most recent fatigue cycle block that has ended since the current monitoring update point. and The timing correction factor is used to calculate the next new fatigue cycle block; fatigue cycle block number. The prediction period increases continuously between each prediction period, without restarting from 1 at the period boundary. In this way, the prediction period only serves as a stiffness feedback boundary and does not change the continuity of the actual stress cycle and fatigue cycle block.

[0109] when No material strength failure has occurred by the maximum predicted endpoint, and the cumulative fatigue damage is before final settlement. Security factor before terminal settlement At that time, after all closed fatigue cycle damage updates and failure checks are completed before terminal settlement, a terminal settlement is performed on the final residual inflection point. The specific process is as follows.

[0110] First, they are arranged in chronological order of occurrence from the current monitoring update time. The final residual inflection point, which accumulates from the beginning and has not yet formed a closed fatigue cycle by the maximum predicted endpoint, is considered as a residual half-cycle for the stress change between two adjacent final residual inflection points; only the time corresponding to the latter final residual inflection point is later than... The remaining half-cycle is used for terminal counting. Because this round of rainflow counting... Starting from the point of origin, the final residual turning point does not include... A turning point in the remnants of the past.

[0111] The final residual turning points are numbered sequentially according to their occurrence time, and their sequence number is denoted as h; from the first The h+1th and h+1th final residual inflection points form a residual half-cycle, and the terminal settlement order is determined according to the time of the next inflection point. Each residual half-cycle continues to be numbered c after the already counted closed cycles; if there are no closed cycles, the numbering starts from 1. For the c-th residual half-cycle, let: ; In the formula, and This is to form the stress at the adjacent final residual inflection point of this half-cycle. The fatigue mode is then determined according to the same rules as in step S4. , , And basic damage, and connect to fatigue cycle blocks that have not yet ended or form new fatigue cycle blocks according to the terminal settlement order.

[0112] The moment of the next inflection point is only used for filtering and sorting, and is not considered as the actual point in which the damage of that half-cycle is counted; the damage of all terminal residual half-cycles is unified at... Include it and set a "Terminal Settlement Completed" flag to ensure that it is only included once per half-cycle. End-of-cycle damage includes closed-loop damage and the aforementioned terminal residual half-cycle damage.

[0113] When the When the period has neither a closed loop nor a residual half-loop that meets the terminal counting condition: ; After taking into account the residual half-cycle damage at the terminal, the calculation is then performed. and This ensures that the lower bound of the remaining service life is based on the assumption that all accrued fatigue damage within the maximum predicted duration has been accounted for.

[0114] Construct the first Within the first mileage section Set of candidate failure time points for each lining control component: ; ; ; In the formula, This is the initial set of candidate failure time points. This is the set of candidate time points for safety factor failure. This is the set of candidate time points for fatigue damage failure.

[0115] The material strength time points in this set are the actual time points when the continuous total stress time history first exceeds the limit; fatigue damage and safety factors are based on the corresponding cycle-end feedback granularity of this implementation method, using the corresponding cycle-end time points. If it is necessary to further improve the resolution of fatigue or safety factor failure time points, the time point within the first satisfactory prediction cycle can be shortened. Recalculate, but do not directly present the end-of-period inspection results as the actual point in time within the uncalculated period.

[0116] when hour: ; ; when At that time, output the lower bound of the remaining service life: ; In the formula, The earliest time point in the set of candidate failure time points. The remaining service life is defined as follows: Material strength failure is defined as the first time point exceeding the limit within the continuous total stress history; fatigue damage failure and safety factor failure are defined as the end of the prediction period when the corresponding conditions are first met. The aforementioned life formula is no longer multiplied by an independent environmental time correction factor. Temperature, water content, and corrosive environment are taken into account through experimental calibration or parameter updates of the fatigue life function, stiffness-fatigue damage coupling coefficient, material strength, and axial force-bending moment bearing capacity domain to avoid repeated corrections for the same environmental effects.

[0117] For each lining control point, the remaining service life or the lower limit of the remaining service life is recorded as the service life comparison value, and its type is also recorded.

[0118] Within the same mileage segment, the minimum service life comparison value is taken. If at least one finite value is equal to the minimum value, then the minimum value is taken as the remaining service life of the mileage segment; otherwise, it is taken as the lower bound of the remaining service life of the mileage segment. The same rule is then applied to all mileage segments to obtain the remaining service life or the lower bound of the remaining service life of the tunnel to be predicted.

[0119] For example, if the results for three lining control points in a certain section are "remaining service life of 8 years", "lower limit of remaining service life of 10 years", and "lower limit of remaining service life of 12 years", then the section result is a remaining service life of 8 years; if they are "lower limit of remaining service life of 8 years", "lower limit of remaining service life of 10 years", and "lower limit of remaining service life of 12 years", then the section result is a lower limit of remaining service life of 8 years; if one point has a remaining service life of 10 years and another point has a lower limit of remaining service life of 8 years, then it cannot be claimed that the section will fail in 10 years. Instead, the lower limit of remaining service life should be conservatively output as 8 years, and the limited failure time should be determined after expanding the prediction period or updating the monitoring.

[0120] After obtaining new data on surrounding rock, lining, train passage events, or on-site vibration tests, the point in time when the data collection is completed will be considered the new data. Then, S1 through S5 are re-executed. During the rolling update, the current stiffness is re-inverted, non-fatigue defects and fatigue damage are re-distinguished, the loosening state of the surrounding rock and the bearing capacity domain are updated, and a benchmark loading sequence is established based on the new actual operational response. The old prediction results are retained as historical records, but do not directly replace the new round of inversion states.

[0121] To further illustrate the feasibility of this method, the prediction of individual lining control points can be performed in a computer program in the following order.

[0122] Read , , And the parameters of the dynamic calculation model, initialize the rainflow residual inflection point stack and fatigue cycle block state to empty, and then... Set as the initial value for subsequent cumulative fatigue damage; Based on the current lining reference stress Initial cumulative fatigue damage and initial safety factor Build When any initial failure condition is met, Set by The set of single elements is formed and the subsequent lifetime search of the lining control part is ended; otherwise, it is set to an empty set and the prediction cycle loop is entered. right to Loop, fixed Calculate the response for this period; Search for material strength exceeding limits along the continuous total stress time history of this cycle; once the first exceeding point is obtained, add it to the candidate set and exit the cycle loop; Rainflow counting is performed only when there is no intensity failure, outputting a closed loop and updating the residual inflection point stack; Fatigue mode obtained in cycle , , and And update the damage according to the fatigue cycle block status; when Update based on cumulative fatigue damage at the end of the period. Calculate the total axial force-bending moment vector, capacity magnification factor, and... ;like or ,Record Exit the prediction cycle loop; otherwise, save the state of the remaining inflection points, fatigue cycle blocks that have not yet ended, and fatigue cycle blocks that have recently ended. when Furthermore, if no material strength failure has occurred previously, the cumulative fatigue damage should be determined based on the total fatigue damage after all closed fatigue cycles. , and ;like or ,Record And exit the prediction cycle loop; otherwise, perform terminal settlement for the final residual half-cycle that meets the conditions, and only apply the corresponding fatigue damage to the remaining half-cycle. Counted as one; In the After taking into account the terminal residual half-cycle fatigue damage of the predicted cycle, the determination is redetermined. , and And check again or ; Summarize the candidate time points corresponding to initial failure candidates, material strength exceeding limits, fatigue damage, and safety factors; output the remaining service life when the set is not empty, and output the lower bound of the remaining service life that has been settled by the terminal only when the set is empty.

[0123] In the program data structure, different status identifiers should be set for "closed loop", "residual turning point", "fatigue loop block in progress" and "terminated half loop", and a unique number should be saved for each loop to prevent duplicate counting from the data level.

[0124] The purpose of step S5 is to establish a closed-loop recursive model of fatigue damage, effective bending stiffness, dynamic response, and structural bearing capacity, while setting a clear maximum prediction boundary to avoid endless iterative calculations when failure has not yet occurred. Figure 4 As shown, Figure 4 (a) shows the order of fixing the initial stiffness within the period, directly judging the material strength along the total stress time history of the lining, performing rainflow counting and fatigue damage updating for periods where strength failure has not occurred, and updating the stiffness and calculating the safety factor at the end of the period, with the predicted period as the stiffness feedback boundary. Figure 4 Figure (b) shows the cross-cycle retention of residual inflection points and fatigue cycle blocks that have not yet ended, the failure check before terminal settlement based on the results of closed fatigue cycle processing for the maximum predicted endpoint, the residual half-cycle terminal settlement with a weight of 0.5 only when there is no failure, the redetering of the end-of-period stiffness and safety factor after settlement, and the order of outputting the remaining service life or the lower bound of the remaining service life from the set of failure candidate time points.

[0125] The following is a set of exemplary numerical data to illustrate the calculation process. This data, generated from the aforementioned formulas and the established numerical model, is used only to demonstrate data transfer, calculation methods, and verification logic between steps. It does not represent actual measured conclusions from a specific engineering project, nor is it intended to prove material parameters that have not been experimentally verified. Formal predictions must utilize measured data from the tunnel to be predicted, along with data calibrated according to the aforementioned experimental procedures. , , and .

[0126] (a) Project objects and input data A section of an operating railway tunnel in Yunnan was selected as the first... Section 1. Based on defect detection, preliminary static calculations, and train response comparison, the same cross-section of the right arch waist is simultaneously a section with severe defects and a large dynamic response; therefore, its inner edge is designated as the first... The first lining control section, with the outer edge serving as the first... =2 lining control points; ( , ) = (1, 1) corresponds to the inner edge of the right arch waist, ( , (1, 2) corresponds to the outer edge of the right arch waist. Both share the stiffness and model parameters of the corresponding sections and retain their respective stress time histories. The following discussion uses the inner edge of the right arch waist ( , The calculation process is fully demonstrated using the example of (1, 1). The outer edge of the right arch waist and other lining control parts are calculated using the same steps and are compared together in the final life summary. In this numerical demonstration, the cumulative fatigue damage of the inner edge of the right arch waist in each prediction cycle is not less than that of the outer edge. Therefore, the cumulative fatigue damage of the inner edge is used to update the cross-sectional stiffness shared by the two. If the cumulative fatigue damage of the outer edge is larger, the cumulative fatigue damage of the outer edge is used to update.

[0127] This example takes the sample along the longitudinal direction of the tunnel. Calculate the width. The lining design thickness is... ,deduct The effective thickness of the material after the degradation layer is The effective area of ​​both inner and outer reinforcing bars is The distance from the centroid of the reinforcing bar to the corresponding effective edge is... The design elastic modulus of the concrete in its intact state is taken as... Through material tests in a reference area under the same environment and age, and without the main control effect of train cyclic fatigue, and combined with correction using a non-fatigue time-varying model, the non-fatigue reference elastic modulus of the remaining concrete was obtained as 28.0 GPa, and the elastic modulus of the steel reinforcement was taken as... The yield strength of the steel reinforcement is taken as .

[0128] Other key inputs include: radial distance of the excavation profile. Radial distance from the outer boundary of the loosened zone of the surrounding rock Radial in-situ compressive stress ; Coefficient of surrounding rock loosening effect Original static stress of lining The representative values ​​of concrete compressive and tensile strengths are respectively and .

[0129] The distances from the left, right, top, and bottom artificial boundaries of the model to the excavation outline are all taken as... The characteristic dimensions of the grid around the lining are taken as follows: When the mesh was halved for verification, the stress amplitude change at the lining control location was 1.3% and the displacement amplitude change was 1.0%, satisfying the 2% convergence condition. The upper limit of the measured effective frequency was taken as... Calculate the time step. ,satisfy The power credit adopts , The Newmark average acceleration method.

[0130] In the field vibration test, a known load time history was used, and temporary strain and displacement measurement points were sampled simultaneously. In the demonstrative joint inversion, The prior value is The upper and lower limits are respectively and ;Pick Select the first target frequency. =5Hz and second target frequency =40Hz, corresponding to angular frequencies of 10Hz and 40Hz respectively. =2π and =2π The prior values, upper and lower limits, and inversion results of the dynamic calculation model parameters are as follows: dynamic elastic modulus of the surrounding rock. , ~ , First target circular frequency The corresponding damping ratios are 0.050, 0.020–0.100, and 0.048; the second target circular frequency. The corresponding damping ratios are 0.030, 0.010–0.080, and 0.034; the interface normal stiffness... , ~ , ; Interface tangential stiffness , ~ , The joint inversion yields: ; Based on calculations of the current effective cross-section: the cross-section and reinforcement are symmetrical about the mid-thickness plane; the weighted neutral axis of the elastic modulus is located at the mid-plane of the cross-section; the moment of inertia of the concrete cross-section... =1×0.70 3 / 12=0.028583 m 4 The moment of inertia of the two layers of reinforcing bars relative to the neutral axis =2×0.005×0.30 2 =9.00×10 -4 m 4 ; Neglecting the moment of inertia of the reinforcing steel bars themselves, =28.0×10 9 ×0.028583+200×10 9 ×9.00×10 -4 =9.803×10 8 N·m 2 / m, take three significant figures: ; Strain response with time allotted for verification The values ​​are 0.078, 0.94, and 0.091 for peak relative error; the corresponding displacement response values ​​are 0.083, 0.93, and 0.104, all meeting the acceptance limits. These error values ​​are merely numerical examples used to illustrate acceptance criteria and do not replace actual engineering verification records.

[0131] The stiffness-fatigue damage coupling coefficient uses the exemplary value obtained according to the aforementioned fitting process. The prediction period is taken as follows: The maximum number of prediction cycles is taken in years. In this example, the fatigue life function, stiffness-fatigue damage coupling coefficient, material strength, and bearing capacity domain are all determined according to the corresponding environmental conditions, and the life results are no longer scaled independently according to environmental time.

[0132] (II) Current fatigue damage calculation Current fatigue damage is: ; This value is located at Within this range, no further correction by the limiting function is needed. This means that after deducting identifiable non-fatigue defects, the remaining reduction in current effective stiffness relative to the non-fatigue reduced bending stiffness is equivalent to fatigue damage of 0.1269.

[0133] (III) Effects of loosening and static loads on surrounding rock The thickness of the loosened zone of the surrounding rock is: ; The additional static stress due to loosening of the surrounding rock is: ; The reference stress for the lining is: ; The static calculation model yields the axial force-bending moment vectors for the original static load condition of the lining and the static load condition after the surrounding rock loosens, respectively: ; ; therefore: ; Using the non-fatigue benchmark elastic modulus of concrete as the conversion standard, the ratio of the elastic modulus of steel reinforcement to that of concrete is 200 / 28 = 7.1429; the converted effective area is 0.700 + 7.1429 × (2 × 0.005) = 0.77143 m². 2 The converted moment of inertia is 0.028583 + 7.1429 × 9.00 × 10⁻⁶. -4 =0.035012m 4 The equivalent section modulus of the selected inner edge is 0.035012 / 0.35 = 0.10003m. 3 The static stress of the selected inner edge model is: ; therefore: ; The empirical reference stress and the static calculation model output meet the consistency requirements and can be used to calculate the total stress time history of the lining and the bearing capacity of the section, respectively.

[0134] (iv) Train dynamic load inversion and strength assessment Train passing events during a complete historical period of a year are used as the baseline loading sequence.

[0135] use Calculate the initial safety factor at the current monitoring update point using the benchmark loading sequence. In this example: ; ; ;and ,therefore .

[0136] For each event, inversion was performed using measured strain and displacement. The total stress of the lining is then calculated using a dynamic calculation model. To enable recalculation of representative events, this numerical demonstration will use a continuous event obtained through inversion. The equivalent train dynamic load vector is expressed by the following formula, and according to... Interval sampling formation Individual load sample values: ; The load inversion regularization coefficient for this demonstration event was selected by leaving measurement points for verification; the strain time history was verified. , The peak relative error is 0.087, which meets the acceptance criteria. Inputting the equivalent train dynamic load vector into the calibrated dynamic calculation model, the maximum and minimum values ​​of the total stress at the control points are obtained as follows: ; ; because: ; No material strength failure occurred during this cycle and the corresponding time period. Its fatigue mode was total pressure mode. The dimensionless coordinates are: ; ; If the instantaneous peak of another train event that has not yet formed a closed loop reaches Therefore, Material strength failure should be determined directly at the first point of exceeding the limit as determined by linear interpolation, without waiting for the stress peak to form a closed loop with subsequent inflection points. This reflects the principle that strength failure judgment and rainflow counting are independent of each other.

[0137] (v) Fatigue damage and stiffness update over a prediction cycle To explain In the actual interpolation process, this example selects three exemplary vertices within the full-pressure mode calibration domain: , and Three vertices Located on the following plane: ; This plane is merely an explicit representation of piecewise linear interpolation within the triangle in this demonstration unit and is not considered a true fatigue test result. The aforementioned representative cycle... Substituting, we get: ; Suppose two main total-pressure fatigue cycle blocks are identified in the first prediction cycle. The first fatigue cycle block consists of 30,000 complete cycles with identical parameters, and its representative coordinates are as follows: The second fatigue cycle block includes 12,000 complete cycles with identical parameters, and its representative coordinates are... Obtained from the exemplary interpolation unit Approximately The actual program still performs summation loop by loop; this example only allows it to be written in multiplicative form because the loop parameters within the block are the same. For engineering applications, the above exemplary vertices must be replaced with actual fatigue test meshes.

[0138] The basic damage of the first fatigue cycle block is: ; Since this fatigue cycle block is the first fatigue cycle block after the current monitoring update point, let After the first piece takes effect: ; The representative severity levels of the first and second fatigue cycle blocks are as follows: ; ; Assuming the test calibration yields , , , Since both blocks are in full-voltage mode, the timing correction factor for the second block is: ; This value is within the limiting range. The basic damage of the second fatigue cycle block is: ; The estimated damage at the end of the first prediction period is: The updated effective bending stiffness is: ; This stiffness is used only as the initial stiffness for the second prediction cycle and is not used to recalculate the dynamic response already completed in the first prediction cycle. When entering the second prediction cycle, the static state is also recalculated and a new lining reference stress is restored using this initial stiffness; the reference stress is updated at the cycle boundary in the same way for each subsequent cycle, instead of using the reference stress at the current monitoring update point for ten prediction cycles.

[0139] (vi) Safety factor calculation After recalculating the static state using the effective bending stiffness updated at the end of the first prediction period, the dynamic axial force-bending moment vector at time t1, for a most unfavorable event, is: ; The total axial force-bending moment vector of the lining section is: ; ; Establish using the current effective cross section This example takes... , Reinforcing steel is used , The ideal elastic-plastic constitutive model is assumed, and the tensile contribution of concrete is negligible. The thick concrete section was discretized into 400 fiber layers; compared with the result of 200 layers, the boundary changes of axial force and bending moment in the target loading direction were 0.6% and 0.8%, respectively, satisfying the 1% convergence condition.

[0140] along Based on the proportional loading direction and fiber cross-section analysis, the intersection point of the bearing capacity domain boundary is approximately: ; The corresponding capacity ratio is cross-checked using the axial force component and the bending moment component: ; Take the common proportional ratio after the binary search converges Of all the demonstration events and static load conditions, this event is the most unfavorable. The failure condition due to the safety factor is not met at the end of the first prediction period. The above boundary points are directly calculated from the given cross-sectional dimensions, constitutive model, and fiber discretization, and the calculation process of the bearing capacity domain is no longer replaced by "assumed" values.

[0141] (vii) Residual half-cycle of the maximum predicted endpoint Subsequent prediction cycles repeat the two full-pressure fatigue cycle blocks in the same order, retaining the severity of the previous fatigue cycle block across cycles. This process is repeated block by block until the 10th prediction cycle. The fatigue damage after completing the closed-loop treatment is as follows: ; The final residual inflection point sequence contains three accrual residual half-cycles, which They are respectively , and With a counting weight of 0.5 for each terminal, the total basic damage is: ; All three semi-cycles were in full-pressure mode and connected to the fatigue cycle block according to the terminal settlement sequence. Based on the grouping conditions of dimensionless maximum and minimum stress coordinates, none of the three residual semi-cycles met the condition of being grouped into the same fatigue cycle block as the preceding or adjacent residual semi-cycles. Therefore, they formed three sequentially occurring fatigue cycle blocks, and the corresponding timing correction coefficients were calculated for each. The timing correction coefficients calculated based on the severity difference between each block and the preceding fatigue cycle block were 0.8847, 1.0673, and 0.9071, respectively. The corrected terminal damage is: ; This injury only Counted once. All three residual semi-cycles originate from the current monitoring update point. The final residual inflection point is formed from the accumulation, excluding Previous historical remnant turning points; after completing the final settlement, a "finalized settlement" flag is set for the three residual half-cycles, and they are no longer retained as unsettled cross-prediction cycle states. The end-of-period damage and stiffness after final settlement are: ; ; Recalculated using the final stiffness, the total axial force-bending moment vector of the most unfavorable lining section is: The algorithm for the same fiber cross section yields the following intersection point of the bearing capacity domain boundary in this loading direction: approximately... ,therefore: ; In this example, the initial set of candidate failure times is empty, and there are no times when the material strength exceeds the limit within the maximum prediction time. , ,so Output: ; This result indicates that no failure was detected within the specific baseline loading sequence repetition scenario and the 10-year maximum prediction boundary, therefore the lower bound of the remaining service life is 10 years; it does not mean that the actual remaining service life is exactly 10 years, nor does it prove that it is still safe after the 10th year.

[0142] The above embodiments are only used to illustrate the present invention and are not intended to limit the scope of protection of the present invention; any modifications, substitutions or improvements made by those skilled in the art within the spirit and principles of the present invention should fall within the scope of protection of the present invention.

Claims

1. A method for predicting the service life of tunnel lining under train dynamic load-surrounding rock loosening coupling, characterized in that, Includes the following steps: S1. Divide the tunnel to be predicted into mileage sections, determine the calculation cross section, lining control location and control stress component in each mileage section, determine the current monitoring update time point and obtain surrounding rock data, lining data, train passing event data and field vibration test data. S2. Establish static and dynamic calculation models for calculating the static and dynamic responses of the surrounding rock-lining, respectively. Use the field vibration test data to calibrate the dynamic calculation model and invert the current effective bending stiffness. After distinguishing the stiffness reduction caused by non-fatigue defects, determine the current fatigue damage. S3. Determine the lining reference stress based on the surrounding rock data and calculate the static axial force-bending moment vector using the static calculation model. Invert the equivalent train dynamic load vector based on the train passing event data and calculate the dynamic stress increment time history and dynamic axial force-bending moment vector using the dynamic calculation model. Form the total stress time history of the lining and the total axial force-bending moment vector of the lining section by static and dynamic superposition. S4. Directly determine the material strength failure point based on the total stress time history of the lining, and count rainflow during the period when material strength failure has not occurred. Calculate the fatigue damage of the foundation for each fatigue cycle, and perform time-series correction and accumulation according to fatigue cycle blocks. S5. Divide the service time after the current monitoring update point into a finite number of prediction cycles, and update the cumulative fatigue damage, effective bending stiffness and safety factor according to the prediction cycle. Continuously process fatigue cycles across prediction cycles, and determine the remaining service life or the lower limit of the remaining service life based on material strength failure, fatigue damage failure, safety factor failure and the preset maximum prediction time.

2. The method for predicting the service life of tunnel lining under train dynamic load-surrounding rock loosening coupling according to claim 1, characterized in that, In step S1, the surrounding rock data includes in-situ ground stress, radial distance of the excavation profile, radial distance of the outer boundary of the loosened zone of the surrounding rock, and elastic modulus, Poisson's ratio, cohesion and internal friction angle of the unloosened surrounding rock and the loosened zone. The lining data includes the original static stress of the lining, lining section parameters, material properties and defect detection data. The train passing event data includes the train passing time and at least one of the synchronously acquired dynamic strain time history and dynamic displacement time history of the lining. The field vibration test data includes the known vibration load time history and at least one of the synchronously acquired strain response time history and displacement response time history of the lining. For each pre-selected lining space location, the circumferential normal stress at the inner edge of the lining and the circumferential normal stress at the outer edge of the lining are determined as two candidate control stress components, and the two are treated as independent lining control parts to perform steps S2 to S5, without pre-excluding one side based on the pre-detected stress range. The mileage section number is denoted as When one or more calculation cross sections are retained within the same mileage section, all lining control parts determined jointly by the calculation cross section, the pre-selected lining spatial location, and the inner or outer edge side are uniformly and consecutively numbered, and the serial number of the lining control part is recorded as follows: , so that each group ( , Each pre-selected lining spatial location corresponds uniquely to a pre-selected lining spatial location and its inner or outer edge on a calculation cross section; the inner and outer edge lining control parts belonging to the same pre-selected lining spatial location use the same cross-sectional stiffness and model parameters.

3. The method for predicting the service life of tunnel lining under train dynamic load-surrounding rock loosening coupling according to claim 2, characterized in that, In step S2, based on the lining section parameters, the non-fatigue defect parameters confirmed by testing, and the elastic modulus of the non-fatigue reference material obtained through independent reference tests or non-fatigue time-varying models, the non-fatigue reduced bending stiffness, which takes into account the influence of non-fatigue defects but not fatigue damage, is determined. The elastic modulus of the non-fatigue reference material does not include the modulus reduction caused by train cyclic fatigue. The inner and outer edge lining control parts belonging to the same pre-selected lining spatial location share the same non-fatigue reduced bending stiffness and the current effective bending stiffness. With the objective of minimizing the sum of the response error term, stiffness prior regularization term, and model parameter prior regularization term between the measured response in the field vibration test data and the calculated response in the dynamic calculation model, the current effective bending stiffness is inverted while calibrating the dynamic calculation model. The current fatigue damage is determined according to the following formula: ； In the formula, For current fatigue damage, , , This is the stiffness-fatigue damage coupling coefficient. This represents the natural logarithm function.

4. The method for predicting the service life of tunnel lining under train dynamic load-surrounding rock loosening coupling according to claim 3, characterized in that, In step S3, based on the radial distance of the excavation profile and the radial distance of the outer boundary of the loosened rock zone, the thickness of the loosened rock zone, the additional static stress due to loosening of the surrounding rock, and the lining reference stress at the current monitoring update point are determined according to the following formula: ； ； ； In the formula, The radial distance of the excavation profile. The radial distance from the outer boundary of the loosened zone of the surrounding rock is given. The thickness of the loosened zone of the surrounding rock. This represents the compressive stress component of the in-situ ground stress along the radial direction of the lining control area. The coefficient for the loosening effect of surrounding rock. Add static stress to loosen the surrounding rock. To compensate for the original static stress of the lining, The reference stress for the lining at the current monitoring update point; In the static calculation model, the original static load condition of the lining and the static load condition after the surrounding rock loosens are established respectively. The original static load condition of the lining adopts the elastic modulus, Poisson's ratio, cohesion, and internal friction angle of the unloose surrounding rock. The static load condition after the surrounding rock loosens will... to The region between these regions is assigned the elastic modulus, Poisson's ratio, cohesion, and internal friction angle of the loosened zone, while the surrounding rock outside this region is assigned the elastic modulus, Poisson's ratio, cohesion, and internal friction angle of the unloosened surrounding rock. The axial force-bending moment vectors for the two static load conditions are obtained using the static calculation model, and the additional static axial force-bending moment vector for loosened surrounding rock and the static axial force-bending moment vector are determined according to the following formula: ； ； In the formula, and The original static load condition of the lining and the static load condition after the surrounding rock loosening are respectively at the predicted time points. The resulting axial force-bending moment vector, The static axial force-bending moment vector is added to the loosening of the surrounding rock. This is the static axial force-bending moment vector that takes into account the effect of surrounding rock loosening.

5. The method for predicting the service life of tunnel lining under train dynamic load-surrounding rock loosening coupling according to claim 4, characterized in that, In step S3, for the first For each train passing event, the effective measured responses of each calculated cross section and each lining control part within the corresponding mileage section are collected. The objective is to minimize the sum of the weighted error between the effective measured responses and the calculated responses of the dynamic calculation model, and the load time history smoothing regularization term, within the feasible load set. Internal inversion equivalent train dynamic load vector The equivalent train dynamic load vector is input into the dynamic calculation model to obtain the dynamic stress increment time history. and dynamic axial force-bending moment vector The total stress of the lining and the total axial force-bending moment vector of the lining section are calculated time-by-time according to the following formula, and the total stress of the lining at each time point within each event is arranged in chronological order to form the time history of the total stress of the lining: ； ； In the formula, This is the set of feasible loads determined based on the load's location, direction, duration of the train passage event, and response frequency band. For the corresponding mileage segment, the first The equivalent train dynamic load vector shared by each train passing through the various lining control points. For the first The train passes through the event at the time of the event. The corresponding dynamic stress increment time history, For the first The train passes through the event at the time of the event. The corresponding dynamic axial force-bending moment vector, For the first The train passes through the event at the time of the event. The corresponding total stress of the lining, which varies with time within the event. The sequence of changes constitutes the time history of the total stress of the lining. For the first The train passes through the event at the time of the event. The corresponding total axial force-bending moment vector of the lining section, For the predicted time point.

6. The method for predicting the service life of tunnel lining under train dynamic load-surrounding rock loosening coupling according to claim 5, characterized in that, In step S4, a stress sign rule of positive for compression and negative for tension is adopted. The total stress time histories of the lining corresponding to each train passing event are connected according to the order of occurrence of the train passing events. The stress between adjacent train passing events is set as the lining reference stress to obtain the continuous total stress time histories. The set of time points when the material strength exceeds the limit is determined according to the following formula: ； In the formula, For continuous time intervals, and These are the representative values ​​of concrete compressive strength and concrete tensile strength, respectively. For through cracks that existed before the current monitoring update point, were confirmed to be open and no longer transmit concrete tensile force, the circumferential normal stress at the location adjacent to the through crack, which is not cracked and can transmit concrete tensile force is used as the control stress component on the corresponding side, and the influence of the through crack is retained in the calculation of bending stiffness and section bearing capacity after non-fatigue reduction. When the set of time points when the material strength exceeds the limit is not empty, the earliest time point is determined as the material strength failure time point, and rainflow count is performed on the continuous total stress time history before the material strength failure time point. When the set of time points when the material strength exceeds the limit is empty, rainflow count is performed on the entire continuous total stress time history. The closed fatigue cycles obtained from rainflow counting are numbered sequentially according to the time corresponding to their last stress inflection point. And record the first Maximum stress in one fatigue cycle Minimum stress and cycle count weight ,in, Cycle count weight of closed fatigue cycle .

7. The method for predicting the service life of tunnel lining under train dynamic load-surrounding rock loosening coupling according to claim 6, characterized in that, For the period during which material strength failure has not yet occurred, the rainflow count obtained is the first... A fatigue cycle, which satisfies: ； when At that time, switch to fatigue mode. Determined to be full pressure mode ,when At that time, switch to fatigue mode. Determined to be full pull mode ,when At that time, switch to fatigue mode. Determined as tension-compression mode The dimensionless maximum stress coordinates, dimensionless minimum stress coordinates, and fatigue failure cycle number are determined according to the following formula: ； ； ； In the formula, and The first Dimensionless maximum stress coordinates and dimensionless minimum stress coordinates for each fatigue cycle. Indicates taking and The larger value in This is a fatigue life function established based on constant-amplitude fatigue test data of the corresponding fatigue mode. For the first The number of fatigue failure cycles per fatigue cycle.

8. The method for predicting the service life of tunnel lining under train dynamic load-surrounding rock loosening coupling according to claim 7, characterized in that, According to the order in which fatigue cycles occur, the first fatigue cycle that has not yet been assigned to a fatigue cycle block is taken as the base cycle of the current fatigue cycle block, and the second fatigue cycle is assigned as the base cycle. The reference cycle number of each fatigue cycle block is denoted as: For the fatigue cycle to be determined immediately following the current fatigue cycle block ,when And if the following formula is satisfied, the fatigue cycle to be determined is included in the current fatigue cycle block: ； When the fatigue cycle to be determined does not meet the aforementioned conditions, the current fatigue cycle block ends, and the fatigue cycle to be determined is used as the reference cycle for the next fatigue cycle block; the first... The set of fatigue cycle numbers contained in a fatigue cycle block is denoted as The basic fatigue damage, representative fatigue severity, and fatigue mode are determined according to the following formula: ； ； ； According to the order of occurrence of fatigue cycle blocks Number them consecutively and determine the timing correction factor according to the following formula: ； Update the cumulative fatigue damage according to the following formula: ； In the formula, The sequence number of the fatigue cycle block. For dimensionless stress grouping tolerance, satisfy , For the first The basic fatigue damage of a fatigue cycle block without timing correction. For the first The representative fatigue severity of each fatigue cycle block. For the first Fatigue patterns of a fatigue cycle block For the first Timing correction coefficients for each fatigue cycle block and The first The cumulative fatigue damage before and after each fatigue cycle block treatment. and The time-series influence coefficients are calibrated based on low-high stress sequence tests and high-low stress sequence tests under the same fatigue mode. This is the lower limit of the timing correction factor. The upper limit of the timing correction coefficient, and the two satisfy the following: , Indicates will Restricted to closed intervals Inside; Current fatigue damage As the first fatigue cycle block after the current monitoring update time, it processes the accumulated fatigue damage before that point. The fatigue damage failure condition is met at that time.

9. The method for predicting the service life of tunnel lining under train dynamic load-surrounding rock loosening coupling according to claim 8, characterized in that, In step S5, the current monitoring update time point is recorded as... ,Will The subsequent service time is divided into Each duration is The prediction period, in which, The maximum number of prediction periods is a positive integer. The duration of a single forecast period. The preset maximum prediction duration, The maximum predicted endpoint; And order: ； ； ； ； In the formula, y is the prediction period number. , For the first The end point of each forecast period, This is the beginning of the first forecast period. and These are the initial cumulative fatigue damage and initial effective bending stiffness at the current monitoring update point, respectively. from Previously, a duration of Furthermore, the most recent historical period with complete train passing event data is used to form a benchmark loading sequence by assembling the equivalent train dynamic load vectors obtained in the order of occurrence within that historical period and their relative occurrence times. During the period before the material strength failure point occurs, in the first Within the forecast period, The lining stiffness parameters are fixed as those of the static calculation model and the dynamic calculation model. The static state at the beginning of the prediction period is recalculated using the static calculation model. The lining reference stress is determined according to the stress recovery relationship of the combined section consistent with the non-fatigue reduced bending stiffness. The dynamic stress increment time history is calculated according to the reference loading sequence. The lining reference stress and the dynamic stress increment time history are superimposed to form the lining total stress time history of the prediction period. Material strength failure is judged along the lining total stress time history. The obtained material strength exceeding time points are merged into the material strength exceeding time point set. The cumulative fatigue damage is updated according to the aforementioned rainflow counting, fatigue life calculation, fatigue cycle segmentation and time sequence correction methods. Will process the first The cumulative fatigue damage obtained after adding all new fatigue cycles in each prediction cycle is denoted as . When no new fatigue cycles are generated during the prediction period, let: ； Update the following formula: Effective bending stiffness at the end of each prediction period: ； In the formula, and The first The cumulative fatigue damage and effective bending stiffness at the end of each prediction period. Represents the natural exponential function; For the inner and outer edge lining control parts that belong to the same pre-selected lining space location, at the end of each prediction cycle, the larger value of the cumulative fatigue damage of the two is first taken and substituted into the aforementioned stiffness update formula, and the resulting effective bending stiffness is simultaneously assigned to both. for ,use Recalculate the time points using the static calculation model. The corresponding static axial force-bending moment vector The dynamic axial force-bending moment vector is recalculated using the dynamic calculation model according to the aforementioned benchmark loading sequence. The total axial force-bending moment vector of the lining section is determined according to the aforementioned superposition relationship. The capacity amplification factor and safety factor are determined according to the following formula: ； ； In the formula, Based on time point The axial force-bending moment bearing capacity domain, established based on the corresponding material properties, lining section parameters, and defect detection data, is used in each prediction cycle to establish the axial force-bending moment bearing capacity domain based on the material properties, lining section parameters, and defect detection data at the current monitoring update point, before new lining data is obtained. The variable representing the non-negative proportional amplification of the total axial force-bending moment vector of the lining section. This is the capacitance amplification factor. This indicates taking the maximum value. The set of train passing event numbers to be included in the safety factor calculation; Serial number 0 indicates a static load condition without train dynamic load, and makes... , The static load condition is a two-dimensional zero vector consisting of zero axial force and zero bending moment. The capacity amplification factor is related to the time within the event. Irrelevant For time point The safety factor, This is the failure condition for the safety factor.

10. The method for predicting the service life of tunnel lining under train dynamic load-surrounding rock loosening coupling according to claim 9, characterized in that, In step S5, the initial set of candidate failure time points for the current monitoring update time point is constructed according to the following formula: ； Before rainflow counting is performed in the first forecast period, at the current monitoring update time... As the starting point for rainflow counting, it does not inherit residual turning points before the current monitoring update time. Between adjacent prediction periods, the residual turning points that have not yet formed a closed fatigue cycle, the baseline cycle number of the fatigue cycle block that has not yet ended, the fatigue mode, the timing correction coefficient and the cumulative value of basic fatigue damage, as well as the fatigue mode and representative fatigue severity of the most recently ended fatigue cycle block are retained. When entering the next prediction period, only the basic fatigue damage corresponding to the newly added fatigue cycle is included in the fatigue cycle block that has not yet ended, and the accumulated basic fatigue damage is not counted again. If no material strength failure occurs by the maximum prediction endpoint, and neither the fatigue damage failure condition nor the safety factor failure condition is met at the current monitoring update time or the end of each prediction cycle, after completing the damage update for all closed fatigue cycles within the maximum prediction duration, the final residual inflection points that have not yet formed a closed fatigue cycle are arranged in chronological order of occurrence. The stress change between every two adjacent final residual inflection points is considered as a residual half-cycle. Only the time corresponding to the latter final residual inflection point is later than... The remaining half-cycles are counted at the end. Each remaining half-cycle is numbered c after the closed fatigue cycle according to the terminal settlement order. If there is no closed fatigue cycle, the numbering starts from 1, and its cycle count weight is assigned. The corresponding fatigue damage is determined according to the aforementioned fatigue mode determination, fatigue life calculation, fatigue cycle segmentation and timing correction method; According to the order of the times corresponding to the next final residual inflection point, each residual half-cycle is sequentially connected to the fatigue cycle block that has not yet ended or forms a new fatigue cycle block. The time corresponding to the next final residual inflection point is only used to filter and determine the terminal settlement order, and is not used as the actual time point for fatigue damage to be counted. The fatigue damage corresponding to each residual half-cycle is only counted at the maximum predicted endpoint. Counted once, and re-determined after counting. , and ; Construct the first according to the following formula Within the first mileage section Set of candidate failure time points for each lining control component: ； when When not in use, the earliest failure point and remaining service life are determined according to the following formula: ； ； when When empty, output the lower bound of the remaining service life according to the following formula: ； In the formula, This is the initial set of candidate failure times for the current monitoring update time. Represents the empty set. For the set of candidate failure time points, The earliest time point in the set of candidate failure time points. For the remaining service life; Within each mileage segment and across all mileage segments, the smallest remaining service life or the lower bound of the remaining service life is selected as the prediction result for the corresponding mileage segment and the tunnel to be predicted. When the smallest value corresponds to both the remaining service life and the lower bound of the remaining service life, the remaining service life is used as the prediction result.

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