Method and system for evaluating dynamic mechanical properties of subway tunnel lining coupled with interlayer and strain rate

Abstract

The present application relates to the field of urban rail transit engineering and structural dynamics, and provides a sandwich and strain rate coupled subway tunnel lining dynamic mechanical property evaluation method and system, the method comprising the following steps: step 1, preparing a cement-based cylindrical sample containing a sandwich; step 2, applying a strain rate loading and collecting original data; step 3, reconstructing the stress-strain response and performing stress balance and constant strain rate criteria; step 4, obtaining energy absorption rate, dynamic compressive strength and yield inflection point strain, and recording the failure mode type; step 5, establishing a statistical damage model and inverting the model parameters; step 6, extracting the initial damage coefficient and damage rate, and establishing an empirical regression formula; step 7, constructing an evaluation index set, performing a grading evaluation, and outputting material optimization and process recommendations. The present scheme significantly improves the design, checking and rapid evaluation capability of subway tunnel lining under high strain rate conditions such as impact or explosion.

Description

Technical Field

[0001] This invention relates to the field of urban rail transit engineering and structural dynamics technology, specifically to a method and system for evaluating the dynamic mechanical performance of subway tunnel linings coupled with interlayer and strain rate. Background Technology

[0002] Throughout their entire lifespan, urban subway tunnels, in addition to bearing static loads such as their own weight, surrounding rock pressure, and temperature and humidity changes, are frequently subjected to short-duration, high-amplitude, high-rate, and energy-concentrated dynamic loads, such as near-field explosions, falling impacts, seismic stress waves, and rapid stress changes caused by local repairs. These loads significantly exacerbate crack initiation and propagation, easily leading to brittle failures such as material spalling and bursting, especially in areas of structural discontinuity.

[0003] Actual lining structures are not ideal homogeneous bodies, and generally contain construction joints, cold joints, repair layers, and various interlayers between the surrounding rock and the lining. Different interlayer materials (such as ordinary mortar, high-strength mortar, or polymer-modified mortar) differ in modulus, strength, and fracture energy, leading to impedance mismatch and stress wave redistribution, forming local tensile stress zones. Under high loading rates, the differences in material rate sensitivity can amplify damage evolution, easily forming "damage-locked" or "rapid degradation" regions near the interlayers, causing local deterioration to expand into overall failure.

[0004] Currently, research on material properties under high strain rates largely employs split Hopkinson bars (SHPBs), focusing on the dynamic strength gain factor (DIF) and failure modes. However, the research subjects are mostly homogeneous concrete or mortar specimens. Systematic experiments on specimens with sandwich structures remain insufficient, and the coupled effects of different sandwich types and thickness ratios on strain rate-strength-deformation-failure modes lack systematic research. Furthermore, although energy analysis methods are used to explain the energy absorption mechanisms of materials, inconsistent calculation standards and inconsistencies in index definitions mean that energy and strength indices are often used separately, making it difficult to form a comprehensive criterion for material selection and process evaluation.

[0005] In constructing constitutive models, existing models are mostly based on the homogeneous body assumption, which makes it difficult to reflect the multi-peak distribution characteristics of modulus and strength brought about by sandwich structures. Parameter identification often relies on overall curve fitting, lacking independent characterization of the "initial damage" stage and inversion strategies under energy constraints, resulting in unclear physical meaning of parameters and insufficient robustness. In terms of engineering evaluation, existing systems mostly focus on DIF or nominal strength, lacking practical indicators such as "damage rate" that can directly relate to early degradation and service life. At the same time, SHPB testing of specimens containing sandwich structures faces challenges such as stress balance and end effects: sudden changes in wave impedance can enhance interface reflection and disrupt stress uniformity; the stiffness difference between thin sandwich structures and the matrix can easily lead to local strain concentration, affecting the effectiveness of the constant strain rate assumption; traditional loading methods can amplify end effects, making early damage identification unstable.

[0006] Therefore, it is urgent to establish standardized specimen and SHPB testing procedures for sandwich structures, unify energy analysis methods and indicators, and construct a comprehensive evaluation system that integrates strength, energy, and interpretable damage indicators to provide directly applicable technical support for tunnel blast-resistant and impact-resistant design and material selection. Summary of the Invention

[0007] To address the problems existing in the background technology, this invention proposes a method and system for evaluating the dynamic mechanical properties of subway tunnel linings that couples interlayer and strain rate. This fills the technical gap in the integrated evaluation of "interlayer type-strain rate-energy-damage" and significantly improves the design, verification and rapid evaluation capabilities of subway tunnel linings under high strain rate conditions such as impact or explosion.

[0008] To achieve the above objectives, the present invention adopts the following solution:

[0009] A method for evaluating the dynamic mechanical properties of subway tunnel lining coupled with interlayer and strain rate includes the following steps:

[0010] Step 1: Prepare a cement-based cylindrical sample with interlayer;

[0011] Step 2: Apply multi-level strain rate loading to the sample using a split Hopkinson bar (SHPB) and collect raw data of incident wave, reflected wave and transmitted wave.

[0012] Step 3: Based on the original data, the stress-strain response of the specimen is reconstructed using the three-wave method, and unqualified data is eliminated by the criteria of approximate stress balance and constant strain rate to obtain the reconstructed data;

[0013] Step 4: Based on the reconstructed data, obtain the energy absorption rate. or E Dynamic compressive strength f cd and yield inflection point strain e y Output the energy time history and energy percentage diagram, and record the failure mode type of the sample;

[0014] Step 5: Based on the data obtained in Step 4, establish a statistical damage model of rate effect-sandwich coupling, and invert the model parameters through optimization algorithm;

[0015] Step 6, extract the initial damage coefficient D 0 and damage rate β Based on the aforementioned indicators and interlayer and strain rate parameters, an empirical regression formula is established.

[0016] Step 7, construct including or E , fcd , D 0 and β The evaluation index set includes a classification evaluation of the combination of sandwich type and thickness, and outputs material optimization and process recommendations.

[0017] Optionally, in step 1, the interlayer of the sample includes a single-layer interlayer or multiple interlayers arranged axially, wherein the thickness of the single-layer interlayer accounts for 5% to 30% of the sample height and is located in the middle of the sample; the interlayer spacing of the multiple interlayers is not less than 3 mm; the interlayer material includes at least one of the following: ordinary cement mortar. H.M. High-strength mortar HS Polymer-modified mortar PM Quick Repair Mortar RM The sample matrix material is a cement-based material with a strength grade of C35~C50; and a representative mechanical comparison factor to represent the interlayer and the matrix is ​​introduced. x Its expression is x=E i / E m or x=f ci / f cm In the formula, E i The elastic modulus of the sandwich material; E m The elastic modulus of the matrix material; f ci The axial compressive strength of the sandwich material; f cm It represents the axial compressive strength of the matrix material.

[0018] Optionally, in step 1, the end face of the sample is ground to a flatness ≤0.02 mm and a roughness of Ra The thickness is ≤0.8μm, and the surface is roughened or an interface agent is applied at the interface between the interlayer and the substrate.

[0019] Optionally, in step 2, the strain rate setting is between 10 and 800 s. -1 At least four strain rate ranges are selected within the range, and each strain rate condition is repeated at least three times, with a randomized test sequence. Resistance strain gauges made of copper, paper, or rubber are used to achieve approximately constant strain rate loading on the specimen, and the sampling frequency is not less than 5 MHz.

[0020] Optionally, in step 3, the following method is used to determine the criteria for approximate stress equilibrium and constant strain rate:

[0021] When satisfied If the current data is determined to meet the approximate stress balance requirement, and the absolute value of the relative deviation does not meet the above requirement, the current data is discarded, or the sample is reloaded by changing the material, thickness or diameter of the resistance strain gauge and adjusting the impact air pressure.

[0022] Regarding the constant strain rate verification, first obtain the stress-strain curve, calculate the variance of the plateau segment of the curve, and when the variance is less than or equal to a preset threshold, it is determined that the approximate constant strain rate requirement is met.

[0023] Optionally, in step 4, the energy absorption rate or E The calculation formula is:

[0024] ,

[0025] in, W in For input energy; E b Let be the elastic modulus of the incident wave; A b Let be the area of ​​the incident wave; C b The constant coefficient of the incident wave; e i ( t () represents the reconstructed incident wave; e r ( t The reconstructed reflected wave is shown below. e t ( t () represents the reconstructed transmitted wave; W re To reconstruct energy; W tr For transmitted energy; W ab The energy absorbed by the sample; W in The total energy input to the sample;

[0026] The failure modes are those observed by high-speed camera or post-test fracture surface as splitting, shearing, or delamination.

[0027] Optionally, step 5 specifically includes:

[0028] Step 5.1: The Weibull statistical damage model is used to describe the dynamic damage evolution of the material, with damage variables... D Represented as:

[0029] ,

[0030] In the formula, For damage variables; e In response to the situation; In order to adapt to strain e Scale factors related to environmental conditions χ; In order to adapt to strain e An index parameter related to environmental conditions χ;

[0031] Step 5.2, based on the damage variables, establish the stress response under the damage state:

[0032] ,

[0033] In the formula, Stress under damaged conditions; E 0 represents the initial elastic modulus;

[0034] Step 5.3, couple the strain rate and interlayer into the Weibull statistical damage model. The coupling expression is as follows:

[0035]

[0036] In the formula, The reference strain rate; α 0, m 0, m 1, m 2, n , s These are the parameters of the undetermined model.

[0037] Step 5.4, based on the information obtained in step 4 W ab The objective function is defined as:

[0038] ,

[0039] In the formula, W ab,model,i It is the energy absorption rate given by the model. W ab,exp,i It refers to the energy absorption rate in the experimental data;

[0040] The parameters of the undetermined model are obtained through inversion using a hybrid algorithm of global optimization and local least squares, and the goodness-of-fit is output. R 2. Residual distribution, and introduce energy-side constraints, i.e., model internal energy and... W ab Consistency constraints are used to improve parameter robustness.

[0041] Optionally, in step 6, the empirical regression formula is:

[0042] , ;

[0043] In the formula, the coefficients k 0, k 1, k 2, b 0, p , q Calibrated from experimental data.

[0044] Optionally, in step 7, based on the evaluation index set, a multi-index comprehensive evaluation is performed using the range normalization and weight allocation method, and the results are divided into three levels: A, B, and C.

[0045] A dynamic mechanical performance evaluation system for subway tunnel lining coupled with interlayer and strain rate includes a sample preparation module, an SHPB loading and acquisition module, a data processing and analysis module, and a model inversion and evaluation module.

[0046] The sample preparation module is used to control the sample geometry, sandwich structure and interface treatment; the SHPB loading and acquisition module is used to implement the impact test and acquire waveform data; the data processing and analysis module is used to reconstruct the stress-strain relationship, check the stress balance and constant strain rate, and calculate the energy absorption rate and damage index; the model inversion and evaluation module is used to fit the statistical damage model parameters and output the material classification conclusion.

[0047] The beneficial effects of this invention are as follows: First, this solution establishes a dynamic mechanical performance evaluation method and system that takes into account the repeatability of experiments, the interpretability of indicators, and the engineering application of results. It effectively solves the problems of fragmentation, one-sidedness, and disconnect from engineering in existing technologies in this field, fills the technical gap in integrated evaluation of "interlayer type-strain rate-energy-damage," and significantly improves the design, verification, and rapid evaluation capabilities of tunnel linings under high strain rate conditions such as impact or explosion, thus possessing broad engineering application prospects. Specifically, as follows:

[0048] (1) A standardized test framework was constructed: a standardized specimen design and SHPB multi-strain rate loading process for short cylindrical axially compressed cylinders with interlayer were proposed, and the end face treatment, interlayer thickness ratio and stress balance criteria were clarified, so as to realize comparable and reproducible tests between different laboratories.

[0049] (2) Unified energy analysis and strength evaluation: Established a standardized calculation of incident / reflected / transmitted / absorbed energy and an energy absorption rate index system, and linked it with dynamic compressive strength and yield inflection point strain to form an integrated strength-energy evaluation framework.

[0050] (3) An interpretable damage criterion is proposed: strain rate and interlayer type factor are explicitly introduced into the statistical damage model, and two core indicators, the initial damage coefficient and the damage rate, are defined and calibrated to quantify the speed of early damage occurrence and evolution, and improve the discrimination accuracy of resistance to initial damage and toughness degradation.

[0051] (4) Achieved interlayer-strain rate coupling calibration: The law and calibration method of the effect of interlayer and matrix mechanical comparison (modulus / strength ratio) on damage parameters and energy distribution are given, which solves the problem of the absence of interlayer influence in the existing assessment.

[0052] (5) Engineering classification and selection criteria have been established: a comprehensive classification and recommendation rule based on energy absorption rate, dynamic compressive strength, initial damage coefficient and damage rate has been established, and conclusions that can be directly used for the verification of explosion resistance or impact resistance of subway lining, material selection and repair process optimization have been generated. Attached Figure Description

[0053] Figure 1 This is a flowchart of the evaluation method of the present invention;

[0054] Figure 2 This is a schematic diagram of the sample geometry and interlayer arrangement in an embodiment of the present invention;

[0055] Figure 3 This is a schematic diagram of the SHPB device in an embodiment of the present invention;

[0056] Figure 4 This is a schematic diagram of typical waveforms and stress balance verification in an embodiment of the present invention;

[0057] Figure 5 The figures show stress-strain curves at different strain rates in embodiments of the present invention.

[0058] Figure 6 This is a schematic diagram illustrating the evolution of incident / reflected / transmitted / absorbed energy over time in an embodiment of the present invention;

[0059] Figure 7 The diagram shows the stress-strain curve fitting effect and residual distribution based on the Weibull statistical damage model in this embodiment of the invention, where (a) is a schematic diagram of the stress-strain curve fitting effect; and (b) is a schematic diagram of the residual distribution. Detailed Implementation

[0060] To make the present invention clearer and more understandable, the present invention will be described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the given embodiments are only one implementation method and do not represent all embodiments.

[0061] Example 1

[0062] Combination Figure 1This embodiment provides a method for evaluating the dynamic mechanical properties of subway tunnel linings coupled with interlayer and strain rate, including the following steps:

[0063] Step 1: Prepare cement-based cylindrical specimens with interlayers, construct a standardized test framework, and produce matrix-interlayer composite specimens that conform to the characteristics of tunnel lining materials. Ensure the consistency and comparability of specimens, provide a qualified research carrier for subsequent impact tests, and avoid test results distortion due to specimen differences.

[0064] Specifically, such as Figure 2 The specimen is a short cylindrical specimen with a diameter of 40-74 mm, preferably 50 mm, and a height of 20-30 mm, preferably 25 mm. The specimen's interlayer comprises a single-layer or multiple-layer interlayers arranged axially, wherein the thickness of the single-layer interlayer accounts for 5%-30% of the specimen height, preferably 8%-15%, and is located in the middle of the specimen; the interlayer spacing of the multiple-layer interlayers is not less than 3 mm. The interlayer material includes at least one of the following: ordinary cement mortar. H.M. High-strength mortar HS Polymer-modified mortar PM Quick Repair Mortar RM The sample matrix material is a cement-based material (mortar or micro-concrete) with a strength grade equivalent to that of the subway lining; preferably a cement-based material with a strength grade of C35~C50.

[0065] Furthermore, the samples were cured under a standard curing regime: curing temperature controlled at 20±2℃, relative humidity (RH) ≥95%, and curing period of 28 days; to verify long-term mechanical stability, a 56-day curing check group was added if necessary. The end faces of the samples were ground to a flatness ≤0.02 mm and a roughness of Ra The thickness should be ≤0.8μm, and the surface roughening or interface agent treatment should be performed at the interface between the interlayer and the substrate. To control the end effect, a thin layer of paper or silicone rubber film (0.1-0.3 mm thick) can be attached to the end face of the sample for pulse shaping and friction reduction.

[0066] In addition, this embodiment introduces a representative mechanical comparison factor χ to represent the interlayer and the matrix, comprehensively characterizing the relative relationship between the interlayer and the matrix in terms of stiffness and strength. This is used to quantify the degree of "soft-hard matching" between the two, facilitating the rapid assessment of the mechanical compatibility of different interlayer-matrix combinations before and after testing using a single index, and providing quantifiable structural parameter inputs for subsequent statistical damage models or empirical regression formulas. Specifically, when χ≈1, the interlayer and the matrix are relatively matched in modulus and strength, with small differences in interface wave impedance, which is conducive to uniform stress transmission; when χ>1, the interlayer is significantly harder than the matrix, classified as a "hard interlayer," which may cause local stress concentration; when χ<1, the interlayer is a "soft interlayer," with relatively weakened overall stiffness and load-bearing capacity but beneficial for energy dissipation.

[0067] Its expression is x=E i / E m or x=f ci / f cm In the formula, E i The elastic modulus of the sandwich material; E m The elastic modulus of the matrix material; f ci The axial compressive strength of the sandwich material; f cm It represents the axial compressive strength of the matrix material.

[0068] Step 2: An impact loading test is conducted on the specimen using a split Hopkinson bar (SHPB). The specific configuration is as follows: it includes an impact device, impact projectile, incident bar, transmission bar, specimen, centering support, and strain testing and data acquisition system. Compressed air within the impact device drives the impact projectile along the barrel and impacts the left end of the incident bar at a set velocity. A resistance strain gauge is attached between the incident bar and the transmission bar. The incident wave, reflected wave, and transmitted wave signals are obtained through a strain amplifier and data acquisition system, providing raw data for subsequent three-wave reconstruction of the stress-strain curve. Figure 3 Specifically, the diameters of the incident rod and the transmission rod should be consistent and compatible with the sample; the preferred materials are high-strength steel or high-strength aluminum alloy; the wave velocity needs to be determined before the test. C b Elastic modulus E b , Column cross-sectional area A b Calibration. To achieve approximately constant strain rate loading, copper, paper, or rubber sheets can be selected as resistance strain gauges depending on the actual loading scenario. The loading pulse waveform can be optimized by adjusting the material, thickness, or diameter of the resistance strain gauge.

[0069] Furthermore, the loading regime of this device is set as follows: within 10~800 s -1 Within the strain rate range, at least four typical strain rates are selected (example values ​​are 50, 100, 200, and 400 s). -1 The test covers the strain rate range of impact loads that tunnel lining may encounter. For each strain rate condition, at least three parallel tests are repeated to ensure the statistical validity of the data. Tests for all conditions are conducted in a randomized order to avoid the accumulation of systematic errors caused by continuous testing of the same strain rate and to improve the objectivity of the test results.

[0070] Regarding sensor setup and data sampling: the resistance strain gauges are connected using a Wheatstone bridge, with either a full-bridge or half-bridge connection selected based on testing accuracy requirements to improve signal response sensitivity. Specifically, the sampling frequency is set to no less than 5MHz to ensure the capture of high-frequency signals during the impact loading process.

[0071] Step 3: Based on the original data, the stress-strain response of the specimen is reconstructed using the Three-Wave Method. Unacceptable data is eliminated using the criteria of approximate stress equilibrium and constant strain rate, selecting valid mechanical reconstruction data that meets the accuracy requirements. Distorted data is removed, providing reliable core mechanical foundation data for subsequent energy analysis and parameter extraction. The standard formula for reconstructing the stress-strain relationship of the specimen using the Three-Wave Method is:

[0072]

[0073] In the formula, denoted as axial strain rate of the specimen; The height of the sample; e i ( t () represents the original incident wave; e r ( t The original reflected wave is represented by the wave. e t ( t A represents the original transmitted wave; s The cross-sectional area of ​​the sample; This represents the axial stress of the specimen.

[0074] Furthermore, the approximate stress equilibrium is checked using the following method:

[0075] When satisfied The current data is determined to meet the approximate stress equilibrium requirement, such as... Figure 4 The “typical waveform” in the figure refers to the incident wave collected in the SHPB experiment. e i (t), reflected wave e r (t), transmitted wave e t (t) and the stress-time curves at both ends calculated therefrom are used to verify the approximate stress equilibrium. In this embodiment, a comparison σ is used. i +σ r With σ T The stress equilibrium criterion is considered satisfied when the two time histories essentially overlap during the main loading phase. If the absolute value of the relative deviation does not meet the above requirements, the current data is discarded, or the specimen is reloaded by changing the material, thickness, or diameter of the resistance strain gauge and adjusting the impact gas pressure.

[0076] Regarding the verification of constant strain rate, first obtain the stress-strain curve, calculate the variance of the plateau segment of the curve, and when the variance is less than or equal to a preset threshold (strain rate plateau variation coefficient ≤ 10%), it is determined that the requirement of approximately constant strain rate is met.

[0077] Step 4: Based on the reconstructed data, obtain the energy absorption rate. or E Dynamic compressive strength f cd and yield inflection point strain e y It outputs parallel energy time history and energy percentage pie / bar charts to visually compare the differences in different interlayers and strain rates, clearly demonstrating the differences in energy absorption capacity under different interlayers and strain rates. Figure 5 This study characterizes the effect of strain rate on peak strength, stiffness, and yield inflection point strain, providing a basis for extracting dynamic compressive strength and yield inflection point strain.

[0078] In addition, by combining high-speed camera or post-test fracture observation to record the failure morphology of the specimen, such as splitting, shearing, and delamination, key mechanical inputs are provided for the construction of subsequent statistical damage models.

[0079] This step standardizes energy analysis and intensity assessment by establishing standardized calculations for incident / reflected / transmitted / absorbed energy and energy absorption rates. or E Indicator system, and dynamic compressive strength f cd The linkage with the yield inflection point strain forms an integrated strength-energy evaluation framework. For example... Figure 6 This demonstrates the calculation process for energy distribution and energy absorption rate, and compares the differences in energy absorption under different interlayer and strain rate conditions. Specifically, the energy absorption rate... or E The calculation formula is:

[0080] ,

[0081] In the formula, W in For input energy; E b Let be the elastic modulus of the incident wave; A b Let be the area of ​​the incident wave; C b The constant coefficient of the incident wave; e i ( t () represents the reconstructed incident wave; e r (t The reconstructed reflected wave is shown below. e t ( t () represents the reconstructed transmitted wave; W re To reconstruct energy; W tr For transmitted energy; W ab The energy absorbed by the sample; W in The total energy input to the sample. Specifically, the dynamic compressive strength. f cd Pick s s ( e s Peak value; the yield inflection point strain e y Automatic identification using piecewise linear / spline fitting and tangent stiffness abrupt change criteria (such as K) t / K0≤0.6 corresponding point).

[0082] Step 5: Based on the data obtained in Step 4, establish a statistical damage model of rate effect-interlayer coupling. In the statistical damage model, explicitly introduce strain rate and interlayer type factors to realize interlayer-strain rate coupling calibration, solve the problem of missing interlayer influence in the existing assessment, and invert the model parameters through optimization algorithm.

[0083] The specific methods for this step include:

[0084] Step 5.1: The Weibull statistical damage model is used to describe the dynamic damage evolution of the material, with damage variables... D Represented as:

[0085] ,

[0086] In the formula, For damage variables; e In response to the situation; In order to adapt to strain e Scale factors related to environmental conditions χ; In order to adapt to strain e The exponential parameter χ related to environmental conditions; the representative mechanical contrast factor φ between the interlayer and the matrix is ​​used in this step to characterize the relative strength or stiffness influence of different interlayer configurations in the overall mechanical environment of the structure, and to quantify damage parameters. and Dependency on configuration conditions.

[0087] Step 5.2, based on the damage variables, establish the stress response under the damage state:

[0088] ,

[0089] In the formula, Stress under damaged conditions; E 0 represents the initial elastic modulus.

[0090] Step 5.3, couple the strain rate and interlayer into the Weibull statistical damage model. The coupling expression is as follows:

[0091]

[0092] In the formula, The reference strain rate; α 0, m 0, m 1, m 2, n , s These are the parameters for the undetermined model.

[0093] Step 5.4, based on the information obtained in step 4 W ab The objective function is defined as:

[0094] ,

[0095] In the formula, W ab,model,i It is the energy absorption rate given by the model. W ab,exp,i It refers to the energy absorption rate in the experimental data;

[0096] Furthermore, the parameters of the undetermined model are obtained through inversion using a hybrid algorithm of global optimization and local least squares, and the goodness-of-fit is output. R 2. Residual distribution, such as Figure 7 And introduce energy-side constraints, namely the model's internal energy and W ab Consistency constraints are used to improve parameter robustness.

[0097] Step 6: Through regression fitting of the damage variable-strain curve, two core indicators, the initial damage coefficient *f0* and the damage rate *ft*, are extracted to characterize the material's initial damage resistance and subsequent damage evolution trend. Subsequently, based on these two indicators and the interlayer / strain rate parameters... Establishing multiple regression relationships enables rapid prediction and classification assessment of material damage evolution under different working conditions.

[0098] Specifically, initial damage coefficient D 0 is used to quantify the initial damage accumulation level of a material in its early stages, and its core calculation formula is: , DThe smaller the value of 0, the less damage accumulates in the early stages, and the stronger the material's resistance to initial damage. Damage rate β This formula describes the rate at which damage increases with strain during the damage development stage of a material, reflecting the material's ability to resist accelerated damage propagation after the initial damage occurs. Its core formula is:

[0099] ,

[0100] in, Select Alternatively, after the inflection point, a fixed strain value (which can be determined by sensitivity analysis) can be used to determine the damage rate. β The smaller the value, the slower the damage increases with strain, the better the material's toughness, and the smoother the crack propagation.

[0101] Specifically, the empirical regression formula can be expressed as:

[0102] , ;

[0103] In the formula, the coefficients k 0, k 1, k 2, b 0, p , q Calibrated from experimental data.

[0104] Step 7, construct including or E , f cd , D 0 and β The evaluation index set includes a range normalization and weight allocation method to classify and evaluate the combination of sandwich type and thickness, and divide the results into three levels: A, B and C, and output material optimization and process recommendations.

[0105] Among them, Grade A: f cd ≥ f th,A , or E ≥ or th,A , D 0≤ D th,A , β ≤ β th,A ,in f th,A , or th,A , D th,A ,β th,A The A-level performance threshold was obtained through extensive experiments and statistics.

[0106] Grade B: , , , This means that the performance of each indicator is at a medium level, between Grade A and Grade C.

[0107] Grade C: or or or If one or more indicators are below the B-level threshold, the product is classified as a poor C-level product.

[0108] This step constructs a comprehensive evaluation index set encompassing strength, energy, and damage, which can fully reflect the impact resistance, energy absorption efficiency, initial damage resistance, and damage evolution toughness of materials and structures, overcoming the one-sidedness of traditional methods that rely solely on strength or the dynamic gain coefficient DIF.

[0109] In summary, the method of this embodiment forms a complete standardized system from sample design, experimental testing, data processing to performance evaluation. It effectively solves the problems of fragmentation, one-sidedness and disconnect from engineering in the existing technology in this field, fills the technical gap of integrated evaluation of "interlayer type-strain rate-energy-damage", and significantly improves the design, verification and rapid evaluation capabilities of tunnel lining under high strain rate conditions such as impact / explosion, and has broad engineering application prospects.

[0110] Example 2

[0111] This embodiment provides a dynamic mechanical performance evaluation system for subway tunnel lining coupled with interlayer and strain rate, used to implement the evaluation method of Embodiment 1. The evaluation system includes a sample preparation module, an SHPB loading and acquisition module, a data processing and analysis module, and a model inversion and evaluation module.

[0112] The sample preparation module is the foundation of the system, responsible for preparing test samples to ensure the comparability and reliability of subsequent experimental data. Specifically, it is responsible for preparing cement-based cylindrical samples with specific interlayers (such as ordinary mortar, polymer mortar, etc.) according to standard specifications, and ensuring the representativeness of the samples and the reproducibility of the experiments through geometric control, material proportioning, and interface treatment.

[0113] The SHPB loading and acquisition module uses a split Hopkinson bar device to perform dynamic impact tests on the sample at different strain rates, and simultaneously acquires incident wave, reflected wave and transmitted waveform data to provide reliable raw data for subsequent analysis.

[0114] The data processing and analysis module is used to receive raw waveform data, reconstruct stress-strain curves using the three-wave method, and perform approximate stress balance and constant strain rate verification; at the same time, it calculates key mechanical indicators such as dynamic compressive strength and energy absorption rate, completing the extraction of feature information from the raw signal.

[0115] The model inversion and evaluation module, based on experimental data, inverts to obtain a statistical damage model that considers strain rate and interlayer coupling effect; thereby quantifying the initial damage coefficient and damage rate, and finally combining strength, energy and damage indicators to comprehensively evaluate the interlayer performance, outputting conclusions that can be directly used for engineering material selection and design.

[0116] Furthermore, the system's workflow is as follows: Based on the evaluation objectives, standard specimens of a specific sandwich type are prepared using the specimen preparation module. Subsequently, the SHPB loading and acquisition module performs impact tests on the specimens and acquires waveform data. The raw data is transmitted to the data processing and analysis module for stress-strain curve reconstruction, energy calculation, and characteristic parameter extraction. Finally, the model inversion and evaluation module uses the processed data to invert the damage model parameters, calculate damage indices (initial damage coefficient and damage rate), and outputs the final grading evaluation and engineering recommendations. This establishes a dynamic mechanical performance evaluation system that balances test repeatability, index interpretability, and the engineering applicability of results.

[0117] Simulation Example:

[0118] The present invention will be further illustrated below with a typical engineering example, but the scope of protection of the present invention is not limited thereto.

[0119] Project Background: A section of the third phase of the Guangzhou Metro project is located in a bustling area of ​​the old city. It is shallowly buried and features a typical uniform-thickness annular reinforced concrete lining with an inner radius of 3.3m and a lining thickness of 0.35m. Due to the high population density and the presence of sensitive facilities in the surrounding area, an blast resistance assessment of the metro structure is required, simulating an impact condition equivalent to an 8-15kg TNT explosion in the near field. Given the insufficient capability of existing blast resistance calculation methods to assess interlayers (such as grout-repaired crack repair zones and fiber-reinforced linings), this project employs the assessment method and supporting system proposed in this invention for systematic research.

[0120] Regarding the experimental procedure: Based on the method of this invention, the project team used a split Hopkinson bar (SHPB) device and a multi-channel strain acquisition system to prepare Φ50mm×25mm reinforced concrete axially compressed cylindrical specimens. A 3mm thick interlayer was set in the middle of the specimen, and three interlayer materials were used: ordinary cement mortar (Group A), high-strength mortar (Group B), and elastomer-reinforced mortar (Group C). A baseline group without interlayer (Group D) was also set up for comparison.

[0121] At 50, 100, 200 and 400 seconds -1 Impact compression tests were conducted under strain rate, and the system collected multi-dimensional parameters such as damage, energy, and strength. The accompanying software system performed dynamic stress balance verification, incident / reflected / transmitted wave decomposition and energy calculation, and dynamic stress-strain curve plotting. Based on the Weibull damage model, parameter inversion was performed, ultimately outputting a blast resistance classification report and material selection recommendations.

[0122] The test results show that the high-strength mortar interlayer group performs outstandingly in terms of dynamic performance, achieving a result within 400 seconds. -1 Under strain rate, its peak compressive strength increased by 32.5% compared to the baseline group without interlayer, and its initial stiffness increased by 19%. Regarding energy absorption characteristics, the energy absorption rate of the elastomer-reinforced mortar interlayer group was approximately 41% higher than that of the ordinary cement mortar group, and the reflected wave amplitude was significantly reduced, demonstrating excellent stress regulation and failure delay capabilities. In terms of damage parameters, the initial damage coefficient of the ordinary cement mortar interlayer group was lower. D 0≈0, while the high-strength mortar group decreased to D 0≈0.08 indicates that its ability to inhibit early damage is significantly enhanced.

[0123] Based on the above test results, it is recommended to prioritize the use of high-strength mortar interlayers or elastomer-reinforced mortar interlayers in the direction of potential impact loads, and to incorporate numerical simulation results into the lining design and local reinforcement schemes. This embodiment verifies the effectiveness and practicality of the method of the present invention in engineering blast resistance assessment, and provides an important reference for blast resistance design and safety assessment of similar subway projects.

[0124] The specific embodiments of the present invention have been described in detail above with reference to the figures, but the present invention is not limited to the described embodiments. For those skilled in the art, various changes, modifications, substitutions, and variations can be made to these embodiments without departing from the principles and spirit of the present invention, and these variations still fall within the protection scope of the present invention.

Claims

1. A method for evaluating the dynamic mechanical properties of a subway tunnel lining coupled with the interlayer and strain rate, characterized in that, The evaluation method comprises the following steps: Step 1, preparing a cement-based cylindrical sample containing interlayer, the interlayer of the sample including single-layer interlayer or multi-layer interlayer arranged along the axial direction, the thickness ratio of the single-layer interlayer being 5%~30% of the height of the sample, and the single-layer interlayer being located in the middle of the sample; the spacing between the layers of the multi-layer interlayer being not less than 3mm; the interlayer material including at least one of the following: ordinary cement mortar HM , high-strength mortar HS , polymer modified mortar PM , rapid repair mortar RM ; the base material of the sample being cement-based material with strength grade C35~C50; introducing a representative mechanical contrast factor between the interlayer and the matrix χ whose expression is χ=E i / E m or χ=f ci / f cm in which, E i Ei is the modulus of elasticity of the interlayer material; E m Em is the modulus of elasticity of the matrix material; f ci σci is the axial compressive strength of the interlayer material; f cm σm is the axial compressive strength of the matrix material; Step 2, a split Hopkinson pressure bar (SHPB) is used to apply multi-gear strain rate loading to the sample, and original data of incident waves, reflected waves and transmitted waves are collected; Step 3, the stress-strain response of the sample is reconstructed based on the original data through a three-wave method, and unqualified data is removed through the criterion of approximate stress balance and constant strain rate to obtain reconstructed data; Step 4, based on the reconstruction data, obtain energy absorption rate η E , dynamic compressive strength f cd and yield inflection point strain ε y , output energy time history and energy proportion diagram, and record the failure mode type of the sample; Step 5, a statistical damage model of rate effect-laminate coupling is established according to the data obtained in step 4, and model parameters are inverted through an optimization algorithm, specifically including: Step 5.1, the dynamic damage evolution of the material is described using the Weibull statistical damage model, the damage variable D is represented as: ， wherein is a damage variable; ε is a strain; is a scale factor related to the strain rate and environmental conditions χ; is an exponential parameter related to the strain rate and environmental conditions χ; Step 5.2, a stress response under a damage state is established based on the damage variable: ， wherein is the stress in the damaged state; E 0 is the initial elastic modulus; Step 5.3, strain rate and laminate coupling are coupled into a Weibull statistical damage model, and the expression of the coupling is: ， ； wherein is the reference strain rate; α 0, m 0, m 1, m 2, n , s is a model parameter to be determined; Step 5.4, based on the acquisition in step 4 W ab The objective function is defined as: ， wherein W ab,model,i is the energy absorption rate given by the model, W ab,exp,i is the energy absorption rate in the experimental data; The undetermined model parameters are obtained by inversion through a global optimization and local least square hybrid algorithm, and a fitting goodness is output R 2, residual distribution, and introduce energy side constraints, that is, the consistency constraint of model internal energy and W ab The consistency constraint is used to improve the robustness of parameters. Step 6, extracting initial damage coefficient D 0 and damage rate β an index, based on which an empirical regression formula is established with the interlayer and strain rate parameters; Step 7, construction includes η E , f cd , D 0 and β The evaluation index set including the interlayer type and thickness combination is graded and evaluated, and the material optimization and process suggestion are output.

2. The sandwich and strain rate coupling dynamic mechanical property evaluation method of a subway tunnel lining according to claim 1, characterized in that: In step 1, the end face of the sample is ground to a flatness of ≤ 0.02 mm and a roughness of ≤ 0.8 μm, and the interface between the interlayer and the base is roughened or treated with an interface agent. Ra In step 1, the end face of the sample is ground to a flatness of ≤ 0.02 mm and a roughness of ≤ 0.8 μm, and the interface between the interlayer and the base is roughened or treated with an interface agent.

3. The method for evaluating the dynamic mechanical properties of the sandwich and strain rate coupled metro tunnel lining according to claim 1, characterized in that: In step 2, the strain rate range is selected from 10 to 800 s -1 at least four levels, each strain rate condition is repeated for not less than 3 times, and a random test sequence is adopted; a copper sheet, a paper sheet or a rubber sheet is used as a resistance strain gauge to achieve approximately constant strain rate loading of the sample, and the sampling frequency is not less than 5 MHz.

4. The method for evaluating the dynamic mechanical properties of a sandwich and strain rate coupled metro tunnel lining according to claim 1, characterized in that: In step 3, the criterion of approximate stress balance and constant strain rate is performed by the following method: When the condition is met , it is determined that the current data meets the approximate stress balance requirement. If the relative deviation absolute value does not meet the above requirement, the current data is rejected, or the sample is reloaded by changing the material, thickness or diameter of the resistance strain gauge and adjusting the impact air pressure. For constant strain rate checking, the stress-strain curve is first obtained, the variance of the platform segment of the curve is calculated, and when the variance is less than or equal to a preset threshold, it is determined that the requirement of approximate constant strain rate is met.

5. The method for evaluating the dynamic mechanical properties of a sandwich and strain rate coupled metro tunnel lining according to claim 1, characterized in that: In step 4, the energy absorption rate η E The calculation formula is: ， wherein, W in is the input energy; E b is the modulus of elasticity of the incident wave; A b is the area of the incident wave; C b is the constant factor of the incident wave; ε i t is the reconstructed incident wave; ε r t is the reconstructed reflected wave; ε t t is the reconstructed transmitted wave; W re is the reconstructed energy; W tr is the transmitted energy; W ab is the energy absorbed by the sample; W in is the total energy input by the sample.​​​ 6. The method for evaluating the dynamic mechanical properties of a sandwich and strain rate coupled metro tunnel lining according to claim 1, characterized in that: In step 6, the empirical regression formula is: ， ； where the coefficients k 0, k 1, k 2, b 0, p , q are calibrated from experimental data.

7. The method for evaluating the dynamic mechanical properties of a sandwich and strain rate coupled metro tunnel lining according to claim 1, characterized in that: In step 7, based on the evaluation index set, a range normalization and weight distribution method is used for multi-index comprehensive evaluation, and the results are divided into three levels of A, B and C.

8. A system for evaluating the dynamic mechanical properties of a subway tunnel lining coupled with interlayer and strain rate, characterized in that, The method for evaluating the dynamic mechanical properties of the subway tunnel lining according to any one of claims 1-7, wherein: the method comprises a sample preparation module, an SHPB loading and collecting module, a data processing and analysis module, and a model inversion and evaluation module; The sample preparation module is used to control the sample geometry, laminate structure and interface treatment; the SHPB loading and collecting module is used to implement impact testing and collect waveform data; the data processing and analysis module is used to reconstruct the stress-strain relationship, check the stress balance and constant strain rate, calculate the energy absorption rate and damage index; and the model inversion and evaluation module is used to fit the statistical damage model parameters and output the material classification conclusion.

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