Concrete frost resistance durability evaluation and improvement method for bridges and tunnels in seasonal frozen region

Abstract

The application discloses a kind of season freezing area existing bridge and tunnel concrete anti-freezing durability evaluation and promotion method, its method is: first step, service period anti-freezing durability damage information acquisition and the establishment of characterization model;Second step, the variable model of comprehensive anti-freezing durability damage is constructed;Third step, the establishment of damage evolution and decision analysis model;Fourth step, the establishment of durability promotion strategy recommendation model in stages.There are beneficial effects: realize the quantitative characterization of existing bridge and tunnel concrete internal hidden, gradual freeze-thaw damage, overcome the problem of large dispersion of single index evaluation result.Make durability promotion measure from experience judgment to quantitative analysis based on comprehensive freeze-thaw damage variable, improve the scientificity and economy of existing bridge and tunnel anti-freezing maintenance decision.The scientificity of long-term freeze-thaw durability evaluation and decision is improved.Effectively delay freeze-thaw deterioration process, improve the anti-freezing service reliability and engineering economy of existing bridge and tunnel structure, with good engineering popularization value.

Description

Technical Field

[0001] This invention relates to a method for evaluating and improving the freeze-thaw durability of concrete, and particularly to a method for evaluating and improving the freeze-thaw durability of existing bridge and tunnel concrete in seasonally frozen areas. Background Technology

[0002] Currently, in the environment of seasonally frozen zones, pore water inside concrete undergoes a phase change when the temperature drops below freezing, forming ice crystals and causing volume expansion. When the expansion pressure of the ice crystals exceeds the tensile strength of the concrete matrix or the limit that the pore structure can withstand, microcracks are easily induced at the interface between the cement paste and aggregates. With the increase of freeze-thaw cycles, these microcracks continuously expand and connect, leading to a gradual loosening of the overall concrete structure and a continuous decline in its mechanical and durability properties. After entering the thawing stage, external moisture can more easily seep into the concrete through existing cracks and pores, providing sufficient water for the next round of freezing, thus forming a vicious cycle of freezing, thawing, water absorption, and refreezing.

[0003] Bridges and tunnels in seasonally frozen regions often operate under frequent traffic loads and complex environmental conditions. In winter, de-icing agents are widely used to ensure road safety, resulting in prolonged exposure of concrete structures to chloride-containing environments. Chloride solutions not only lower the freezing point of pore water, exacerbating the salt-freezing damage effect, but also accelerate surface erosion, steel corrosion, and structural performance degradation under the synergistic effect of freeze-thaw cycles. Studies have shown that the coupling effect of freeze-thaw cycles and salt-freezing has become one of the main environmental factors contributing to the degradation of concrete durability in seasonally frozen regions.

[0004] For existing bridge and tunnel structures, their concrete has often undergone long-term service and multiple freeze-thaw cycles, resulting in internal damage that is both hidden and cumulative. Increased cracking, porosity, and material property degradation make the structures more sensitive to subsequent freeze-thaw cycles and chloride erosion, leading to an accelerated decline in durability. Therefore, the unique climatic conditions and service environment of seasonally frozen regions determine the complexity and severity of the freeze-thaw durability problem for existing bridge and tunnel concrete, and also place higher demands on the scientific rigor of freeze-thaw durability evaluation methods and the targeted nature of improvement technologies.

[0005] Although a great deal of research has been conducted both domestically and internationally on the mechanism of freeze-thaw damage to concrete in seasonally frozen regions and its impact on structural durability, existing technical solutions still have certain limitations in practical engineering applications, mainly in the following aspects.

[0006] Existing research largely focuses on the analysis of freeze-thaw damage or chloride erosion mechanisms under single environmental conditions. Experimental conditions are typically conducted in ideal laboratory environments, making it difficult to comprehensively reflect the real service environment of bridge and tunnel engineering in seasonally frozen zones, influenced by freeze-thaw cycles and salt freezing. The conclusions obtained still lack applicability and accuracy at the engineering scale, and are insufficient for effectively describing the durability degradation process of existing structures.

[0007] Existing methods for evaluating freeze-thaw durability mainly rely on macroscopic mechanical property degradation indicators or mass loss indicators, such as relative dynamic elastic modulus and compressive strength retention rate. Although these methods can reflect freeze-thaw damage to a certain extent, they have limited ability to characterize the evolution of the internal pore structure of concrete, the propagation of microcracks, and the process of damage accumulation. They are difficult to identify early or hidden damage to the structure in a timely manner, and the evaluation results are often lagging.

[0008] For existing bridge and tunnel concrete structures, current testing and evaluation methods mostly rely on core sampling tests or localized damage detection methods. These methods not only cause significant construction interference but also make it difficult to achieve continuous and systematic assessment of the durability status of a large area of ​​the structure. At the same time, traditional methods are still insufficient in considering differences in service life, the cumulative effect of historical freeze-thaw damage, and the influence of salt-freezing environments, making it difficult to accurately reflect the actual durability level of the structure.

[0009] In terms of freeze-thaw durability improvement technology, existing measures are mostly focused on optimizing material mix ratios or surface protection treatments. They have limited adaptability to existing concrete structures that have already suffered internal damage and lack differentiated and refined technical solutions that address damage evolution characteristics and service environment conditions, making it difficult to effectively slow down the process of durability deterioration. Summary of the Invention

[0010] The main purpose of this invention is to solve the many problems existing in the evaluation methods of the freeze-thaw damage mechanism of concrete in seasonally frozen areas and its impact on structural durability, and to provide a method for evaluating and improving the freeze-thaw durability of existing bridge and tunnel concrete in seasonally frozen areas.

[0011] The present invention provides a method for evaluating and improving the freeze-thaw durability of existing bridge and tunnel concrete in seasonally frozen areas, the method comprising the following steps:

[0012] Step 1: Information Acquisition and Characterization Model of Freeze-Thaw Durability Damage During Service: The characterization model of freeze-thaw durability damage during service is based on multi-source non-destructive testing methods to obtain freeze-thaw deterioration information of existing bridge and tunnel concrete, including parameters such as dynamic elastic modulus, ultrasonic wave velocity and energy attenuation. Different physical quantities are uniformly mapped into quantifiable freeze-thaw damage characterization indicators to provide basic data for subsequent analysis.

[0013] The second step is to construct a comprehensive freeze-thaw durability damage variable model. Based on the freeze-thaw damage characterization in the first step, the influencing factors of service life and standard freeze-thaw resistance level are introduced to construct a weighted coupling model of several parameters, forming a comprehensive freeze-thaw damage variable that can reflect the overall freeze-thaw deterioration level of the structure, which is used to characterize the freeze-thaw damage state at different stages.

[0014] The third step is to establish a damage evolution and decision analysis model: The damage evolution and decision analysis model regards the change process of comprehensive freeze-thaw damage variables as a time-series evolution process. By establishing a mapping relationship between damage state and engineering intervention measures, the development trend of freeze-thaw damage is analyzed, providing a basis for durability improvement decisions.

[0015] The fourth step is to establish a phased durability improvement strategy recommendation model: Based on the range of the comprehensive freeze-thaw damage variables, three types of durability improvement measures are identified: surface protection, local repair, and structural reinforcement. The effects of different intervention methods are quantitatively evaluated through mathematical models to achieve matching recommendations between freeze-thaw damage status and engineering measures.

[0016] The specific steps for obtaining information on service-life freeze-thaw durability damage and establishing a characterization model in the first step are as follows:

[0017] Step 1: Using dynamic elastic modulus and ultrasonic wave velocity nondestructive testing parameters as core state variables, and combining continuous damage mechanics and probabilistic evolution theory, establish the mapping relationship between parameter degradation, damage variables, and reliability to form a freeze-thaw damage evaluation process applicable to existing bridge and tunnel concrete, as follows:

[0018] Scalar damage variable The formula is as follows:

[0019] ;

[0020] in: It is the damage variable of the existing bridge and tunnel service life of q years, 0≤ ≤1;

[0021] N is an equivalent variable for the service life of existing bridges and tunnels;

[0022] It is the area of ​​internal concrete damage after freeze-thaw cycles in bridges and tunnels in seasonally frozen areas.

[0023] A is the initial effective load-bearing area of ​​the material. When D=0, it means that the material is intact and in an undamaged state. When D→1, it means that the effective load-bearing capacity inside the material is basically lost and the material is close to failure.

[0024] Step 2: Establishment of the dynamic elastic modulus degradation model: One of the most direct macroscopic characteristics of freeze-thaw damage is the degradation of concrete stiffness. Based on the equivalent continuous medium assumption, freeze-thaw damage can be equivalent to the continuous decay of the material's elastic modulus, and the relationship is expressed as follows:

[0025] ;

[0026] in: It is the dynamic elastic modulus of existing bridges and tunnels after 1 year of freeze-thaw cycles, and the unit is MPa;

[0027] It is the initial dynamic elastic modulus of concrete, i.e., the state without freeze-thaw damage;

[0028] This is the effective stiffness retention factor;

[0029] Equation (2) yields the freeze-thaw damage variable defined based on the dynamic elastic modulus. The formula is as follows:

[0030] ;

[0031] in: It is a freeze-thaw damage variable index based on dynamic modulus definition;

[0032] It can be obtained through the resonance frequency method or the ultrasonic method, so formula (3) is one of the most operational expressions in the evaluation of freeze-thaw damage of existing bridge and tunnel concrete;

[0033] Step 3: Establishment of a freeze-thaw damage characterization model based on ultrasonic parameters: Freeze-thaw cycles increase the number of microcracks and enhance pore connectivity within concrete, thereby lengthening the ultrasonic wave propagation path and reducing its propagation speed. This model is suitable for rapid on-site detection. Let the longitudinal wave velocity after *n* freeze-thaw cycles be V(N), and the initial wave velocity be... The wave velocity type freeze-thaw damage variable is defined as follows:

[0034] ;

[0035] in: The ultrasonic longitudinal wave velocity after 1 year of freeze-thaw cycles of existing bridges and tunnels is expressed in m / s.

[0036] The ultrasonic longitudinal wave velocity in the initial state of concrete is expressed in m / s.

[0037] For freeze-thaw damage variables based on ultrasonic wave velocity;

[0038] Step 4: Establishment of the ultrasonic energy attenuation model: Considering the scattering, reflection, and energy dissipation effects of ultrasonic waves in freeze-thaw damaged concrete, an ultrasonic energy attenuation coefficient is introduced. The formula is as follows:

[0039] ;

[0040] in: It is the ultrasonic energy attenuation coefficient after existing bridges and tunnels have been in service for 1 year and have undergone freeze-thaw cycles, with the unit being 1 / m;

[0041] L is the propagation path length of the ultrasonic wave in concrete, measured in meters (m).

[0042] It is the amplitude of the received signal in the initial state;

[0043] A(N) is the received signal amplitude after 𝑁 freeze-thaw cycles;

[0044] ln is the logarithm to the base 10;

[0045] To facilitate a unified evaluation, an energy-based freeze-thaw damage variable is introduced. The formula is as follows:

[0046] ;

[0047] in: It is the energy attenuation coefficient of concrete in its initial state;

[0048] It is the energy decay coefficient corresponding to the state of freeze-thaw failure of concrete;

[0049] It is an index of freeze-thaw damage variables based on energy decay;

[0050] Step 5: Establishment of a comprehensive freeze-thaw damage model with coupling of three non-destructive parameters: Based on the above three types of damage variables, the first type of damage variable is the dynamic elastic modulus degradation model. The damage variable based on the definition of dynamic elastic modulus degradation is denoted by the following symbols: The second type of damage variable is the freeze-thaw damage characterization model based on ultrasonic parameters. The damage variable symbol is defined based on the change in ultrasonic longitudinal wave velocity. The third type of damage variable is the ultrasonic energy attenuation model, which defines damage variables based on the characteristics of ultrasonic energy attenuation, and is symbolically represented as follows: ;

[0051] The three types of damage variables are uniformly denoted as N represents the service life, 𝑖 represents the non-destructive testing parameter type identifier, i=E represents the dynamic elastic modulus, i=V represents the ultrasonic wave velocity, and i=α represents the ultrasonic energy attenuation.

[0052] The specific steps for constructing a variable model of comprehensive freeze-thaw durability damage in the second step are as follows:

[0053] Step 1: Weighted coupling model of comprehensive service-life damage variables, defining three types of non-destructive parameter coupling comprehensive freeze-thaw damage variables as follows:

[0054] ;

[0055] The weights must satisfy the normalization constraint:

[0056] ;

[0057] in: Integrating freeze-thaw damage variables;

[0058] These are the weighting coefficients corresponding to the three types of nondestructive testing parameters E, V, and α, where i=E: dynamic elastic modulus, i=V: ultrasonic wave velocity, and i=α: ultrasonic energy attenuation.

[0059] Using historical and existing detection data, the optimal weight vector is determined. ;

[0060] The data that can be obtained includes: historical inspection data, i.e., early service stage; current inspection data, i.e., current status; and corresponding macroscopic degradation characteristics, including strength reduction, damage level, and maintenance records.

[0061] Weight To reflect the contribution of each nondestructive testing parameter to the actual freeze-thaw damage, a learning calibration method based on historical data combined with current testing data is adopted, as follows:

[0062] ;

[0063] Where: m is the detection time step;

[0064] D(m) is the damage predicted by the model. D(m) = Dc(Nm) as shown in formula (7), which represents the comprehensive coupled damage value at the time of the m-th detection, corresponding to the number of freeze-thaw cycles Nm.

[0065] This is a reference damage value;

[0066] Reference damage value The definition is as follows:

[0067] Indicates the first At each detection moment, a standardized reference damage level determined based on the specification level, service life, and equivalent freeze-thaw cycle count is used to reinforce the environmental feedback signal in the learning process.

[0068] ;

[0069] The above formula This indicates the percentage of durability that has been consumed, i.e., the percentage of remaining durability.

[0070] in: Indicates the current service life;

[0071] This indicates the number of design freeze-thaw cycles corresponding to the specification level;

[0072] Step 2: Model the freeze-thaw damage assessment and performance improvement problem as a Markov decision process, and use a deep Q-network to jointly learn the weights of multi-source nondestructive testing parameters and intervention strategies;

[0073] Markov decision processes are represented as quintuples, as follows:

[0074] ;

[0075] The meaning of each element in the evaluation and performance improvement of freeze-thaw damage in existing bridge and tunnel concrete is as follows:

[0076] Where: M represents the Markov decision process;

[0077] S represents the state space, a complete representation of the current freeze-thaw damage state of the structure;

[0078] A represents the action space—the set of engineering decisions and weight adjustments;

[0079] R represents the reward function—a quantitative indicator of evaluation accuracy and engineering rationality;

[0080] 𝛾 represents the discount factor—the level of concern regarding long-term durability;

[0081] state space — A complete characterization of the current freeze-thaw damage state of the structure;

[0082] Define the state space S, with the following formula:

[0083] ;

[0084] in: It is the system state vector at the nth detection or decision time;

[0085] Freeze-thaw damage variables defined based on dynamic elastic modulus degradation;

[0086] Freeze-thaw damage variables defined based on changes in ultrasonic longitudinal wave velocity;

[0087] Freeze-thaw damage variables defined based on ultrasonic energy attenuation characteristics;

[0088] Normalized service life of existing bridge and tunnel structures;

[0089] P represents the porosity growth rate, which measures the rate of microstructure degradation.

[0090] This indicates that the object is transposed.

[0091] The state space 𝑆 is used to describe the current health state of concrete under freeze-thaw action. This state vector integrates mechanical degradation information, namely stiffness loss, acoustic degradation information, namely crack and pore evolution, and time / environment cumulative effects.

[0092] Satisfying the Markov property assumption: Given the current state Under these conditions, the future damage evolution of the structure is independent of its historical path;

[0093] Step 3: Define the action space A, with the following formula:

[0094] ;

[0095] Among them: a0 No intervention is taken, i.e., the baseline state; a1 Adaptive weight calibration, adjusting the weight vector of non-destructive testing parameters; a2 Maintain the current state, only continue monitoring; a3 Take surface protection measures, including hydrophobic coatings; a4 Crack grouting or local repair; a5 Structural durability reinforcement;

[0096] The state transition probability P—the uncertainty in the evolution of freeze-thaw damage—is given by the following formula:

[0097] ;

[0098] in: Indicates the current state. Indicates the action currently being taken; Indicates the state at the next moment;

[0099] Implicit state transition relationships are learned through an interactive learning process involving historical monitoring data, environmental exposure data, and DQN.

[0100] The reward function R is a quantitative indicator for evaluating accuracy and engineering rationality. The specific formula is as follows:

[0101] ;

[0102] ;

[0103] Where: 𝑟𝑘: the immediate reward obtained after taking action 𝑎𝑘 in state 𝑠𝑘, D(k)=Dc(Nk) see formula (7), representing the comprehensive coupled damage value at the k-th detection time corresponding to the number of freeze-thaw cycles Nk, Dref(k): the reference damage value from the specification level, C(ak): the engineering cost or intervention cost corresponding to action 𝑎𝑘, and 𝜆: cost penalty coefficient;

[0104] Discount factor 𝛾—the level of concern for long-term durability, the specific formula is as follows:

[0105] ;

[0106] Where: ☐→0: focuses more on current testing accuracy; ☐→1: focuses more on long-term freeze-thaw durability and service life. In the durability evaluation of existing bridges and tunnels, ☐→1 is taken as ☐→0. ;

[0107] Step 4, DQN algorithm input: Non-destructive testing data: 𝐸d, 𝑉, 𝛼, Service information: Nserv, Specification parameters: Ngrade;

[0108] Output: Total freeze-thaw damage: D(k), Optimal weight vector: 𝑤∗, Optimal decision strategy: 𝜋∗

[0109] The Q-function and optimal policy definition, the state-action value function, the Q-function is defined as follows:

[0110] ;

[0111] in: It is a state-action value function, representing the expected cumulative reward that the system can obtain from the moment it takes action ak when it is in state sk under policy 𝜋; 𝜋 is the policy. Let represent the probability rule for choosing action a in state s; sk represent the state at time k; ak represent the action taken at time k; rk+t represent the immediate reward obtained at time k+t; γ∈(0,1) is a discount factor, representing the degree of importance controlling future rewards and the degree of long-term durability attention. Take the expected value of the random variable; Let π represent the expected value of all possible future paths under policy π and environment probability transition, and φ be the immediate reward obtained after taking action φ in state π.

[0112] The optimal Q function is as follows:

[0113] ;

[0114] in: It is the optimal state-action value function, which represents the Q-value that maximizes the reward among all policies;

[0115] Finding the maximum value among all policies is equivalent to finding the optimal policy, which is: ,in ;

[0116] Step 5: Deep Q-Network Approximation Model. The neural network approximation uses a deep neural network with parameter K to approximate the Q function, as follows:

[0117] ;

[0118] Where: the Q-function is approximated by the neural network, the input is the state s, the output is the Q-value corresponding to all actions, and the parameter θ is the neural network parameter, including: the weight matrix and the bias term, in the following form:

[0119] DQN neural network structure, neural network parameter set :

[0120] ;

[0121] Network layer structure: 5→512→512→256→6;

[0122] The calculation formula for each layer is as follows:

[0123] First layer:

[0124] ;

[0125] ;

[0126] in: In this context, M is the set of real numbers; s is a 5-dimensional real vector, i.e., a column vector. It is a 512-row × 5-column matrix; representing 512 neurons, each neuron has 5 weights, and each weight is a real number; This indicates that there are 512 bias values, each bias being a real number, and every element in the matrix is ​​a real number. The specific formula is as follows:

[0127] ;

[0128] Where: Wij∈M, each element is a regular floating-point number;

[0129] By mapping five original physical damage variables to a 512-dimensional latent damage feature space, it learns the combination relationship of each index, nonlinear degradation mode, and potential damage interaction effect.

[0130] The number of parameters is 512×5=2560. With the bias, the number is 2560+512=3072. The first layer has a total of 3072 parameters.

[0131] Second layer:

[0132] ;

[0133] ;

[0134] Parameter Dimensions ;

[0135] The number of parameters is 512 × 512 = 262144. Adding the bias value: 262144 + 512 = 262656.

[0136] The second layer of function: it performs deep nonlinear combination in a high-dimensional feature space, which captures the accelerated stage of freeze-thaw damage, the nonlinear feedback of repair effects, and the long-term evolution path dependence.

[0137] Third layer:

[0138] ;

[0139] ;

[0140] Parameter Dimensions

[0141] The number of parameters is 256 × 512 = 131072, and the bias value is 131072 + 256 = 131328.

[0142] The third layer is the decision feature compression layer, which compresses the high-dimensional damage pattern into 256-dimensional decision features to prepare for action value calculation.

[0143] Output layer:

[0144] ;

[0145] Right now

[0146] ;

[0147] The target Q-value is calculated using the target network parameter φ, and the target value is defined as:

[0148] ;

[0149] Where: yk is the target Q-value, representing the ideal Q-value after performing the action in the current state, and rk is the immediate reward. γ is a discount factor, taken as γ=0.95, focusing more on long-term lifetime. It is the state in the next moment. All possible actions in the next state, This represents the Q-value corresponding to the optimal action in the next state, which means the maximum benefit brought by the optimal decision in the future; These are stable network parameters that are updated with a delay to avoid training oscillations. Their values ​​are determined by copying the current θ to θ' after every 20 learning updates.

[0150] loss function

[0151] ;

[0152] in: It is the mean squared error, representing the difference between the current network's predicted Q-value and the target Q-value. Here, yk is the mathematical expectation, and yk is the target Q value, representing the ideal Q value after performing the action in the current state. It's the squared error; the larger the error, the more the network needs adjustment.

[0153] The parameter update formula is as follows:

[0154] ;

[0155] in: These are the neural network parameters during the k-th training iteration. The neural network parameters at the (k+1)th training iteration; It is the learning rate, taken as... ; It is the gradient of the loss function with respect to the parameters, indicating how much each parameter should be adjusted.

[0156] The specific steps for establishing the damage evolution and decision analysis model in the third step are as follows:

[0157] For existing bridge and tunnel concrete structures in seasonally frozen areas, without core sampling or structural damage, a freeze-thaw durability evaluation process is established based on multi-source non-destructive testing parameters, taking into account the current state of freeze-thaw damage, historical evolution trends, and standard durability requirements. This process includes "detection - damage quantification - comprehensive evaluation - durability determination".

[0158] The evaluation results are presented in the form of a comprehensive assessment of freeze-thaw damage variables, durability level, and remaining durability capacity. They can be directly used for the technical condition assessment and maintenance decisions of existing bridge and tunnel structures. The specific steps are as follows:

[0159] Step 1: Collect non-destructive testing data 𝐸d, 𝑉, 𝐴;

[0160] Step 2: Calculate the three types of freeze-thaw damage variables 𝐷𝐸, 𝐷𝑉, 𝐷𝛼;

[0161] Step 3: Calculate the overall damage 𝐷 by calibrating the weights using DQN;

[0162] Step 4: Determine the 𝐷ref based on the specification level;

[0163] Step 5: Compare D with 𝐷ref to determine the level of freeze resistance durability;

[0164] Step 6: Output durability rating and engineering recommendations;

[0165] The engineering implications of the combined freeze-thaw damage variables are as follows:

[0166] D(k) ≈ 0 indicates that the microcracks inside the concrete have not yet developed significantly, the dynamic stiffness and acoustic parameters are close to the initial state, and the structure is in a good frost-resistant state.

[0167] D(k) ∈ (0.2, 0.4) indicates that microcracks and pores induced by freeze-thaw cycles have begun to appear inside the concrete, and the stiffness and acoustic parameters show identifiable degradation, which belongs to the stage of mild freeze-thaw damage.

[0168] D(k) ∈ (0.4, 0.6) indicates that freeze-thaw damage has entered an accelerated development stage, microcracks gradually connect, local effective bearing capacity decreases, and freeze-thaw resistance is significantly weakened.

[0169] D(k) > 0.6 indicates that the internal damage of the concrete has reached the level of macroscopic deterioration. Freeze-thaw damage has a significant impact on the service performance of the structure, and the freeze-thaw durability is insufficient, so engineering intervention measures need to be taken.

[0170] The specific steps for establishing the phased durability improvement strategy recommendation model in step four are as follows:

[0171] For the three types of durability improvement methods—surface protection, local repair, and structural reinforcement—corresponding mathematical models are constructed to be uniformly incorporated into the aforementioned comprehensive freeze-thaw damage evolution and decision-making framework.

[0172] Step 1: Establishment of a freeze-thaw inhibition model for surface protection enhancement measures: Surface protection measures weaken the driving force of freeze-thaw phase change at the source by reducing the pore water content of concrete and blocking the intrusion path of external moisture. Its mechanism of action is demonstrated through a moisture content regulation model, as follows:

[0173] ;

[0174] in: Equivalent pore water content after implementing surface protection measures;

[0175] This represents the initial moisture content of the concrete pores without any protective measures.

[0176] The hydrophobic efficiency coefficient of surface protection measures. It reflects the ability of coatings and penetrating materials to inhibit moisture intrusion;

[0177] Based on this, the damage driving force caused by freeze-thaw phase transition is expressed as: ,in Equivalent damage driving force induced by freeze-thaw phase change The freeze-thaw sensitivity coefficient reflects the degree to which a material responds to changes in moisture content. The coefficient of volume expansion caused by pore water freezing;

[0178] The above model shows that surface protection reduces This can significantly weaken the source driving mechanism of freeze-thaw damage;

[0179] Step 2: Establishment of a damage blocking model for local repair and crack intervention: For situations where the comprehensive freeze-thaw damage variables are at a medium to high level and damage evolution is accelerated, the core role of local crack repair is to restore the effective local bearing area and block the crack propagation channel, as follows:

[0180] ;

[0181] in: The equivalent freeze-thaw damage variable for the repaired local area;

[0182] For the freeze-thaw damage variables in the local area before repair;

[0183] This refers to the effective bearing area of ​​the concrete section before repair.

[0184] This refers to the effective load-bearing area after repair.

[0185] The above model quantitatively reflects the reversal effect of grouting and crack sealing measures on local freeze-thaw damage;

[0186] Step 3: Establishment of an overall improvement model for structural durability strengthening: When the comprehensive freeze-thaw damage variable exceeds the critical threshold, it is necessary to improve the structure's freeze resistance at the overall level. The essence of structural strengthening lies in increasing the structure's "tolerance threshold" for freeze-thaw damage. The critical damage level after strengthening is defined as follows:

[0187] ;

[0188] in: The freeze-thaw damage failure threshold for unreinforced structures;

[0189] This is the equivalent failure threshold after reinforcement;

[0190] The structural reinforcement gain coefficient reflects the effect of external cladding and reinforcement measures on improving durability margin;

[0191] The overall structural freeze-resistance reliability function is further defined as follows:

[0192] ;

[0193] in: This serves as a reliability indicator for the structure's freeze-thaw resistance and durability.

[0194] This represents the current overall freeze-thaw damage variable;

[0195] The above model shows that structural reinforcement, by increasing the upper limit of damage tolerance, enables the structure to maintain acceptable freeze-thaw reliability even at higher damage levels.

[0196] For different stages of freeze-thaw damage, durability improvement models for surface protection, local repair, and structural reinforcement are established respectively. Engineering intervention measures are transformed into quantifiable mathematical expressions. With comprehensive freeze-thaw damage variables as the core, hierarchical control of freeze-thaw damage inhibition, propagation blocking, and allowable threshold improvement is achieved. This shifts durability improvement decisions from experience-based judgment to quantitative analysis, effectively delaying the freeze-thaw deterioration process of existing bridge and tunnel concrete in seasonally frozen areas and improving the structural freeze-thaw resistance reliability and engineering economy.

[0197] The beneficial effects of this invention are:

[0198] This invention provides a method for evaluating and improving the freeze-thaw durability of existing bridge and tunnel concrete in seasonally frozen areas. It proposes a unified characterization method for freeze-thaw damage from multiple sources using non-destructive testing (NDT). Unlike traditional freeze-thaw evaluation methods based on mass loss or apparent damage, this invention, for the first time, integrates three types of NDT parameters—dynamic elastic modulus, ultrasonic longitudinal wave velocity, and ultrasonic energy attenuation—into a unified freeze-thaw damage modeling framework. Based on the theory of continuous damage mechanics, corresponding freeze-thaw damage variables are constructed, enabling quantitative characterization of hidden and progressive freeze-thaw damage within existing bridge and tunnel concrete. This method is applicable to non-destructive testing conditions for in-service structures.

[0199] This invention establishes a multi-parameter weighted coupled freeze-thaw damage model that considers service life and specification requirements. By introducing weight normalization constraints and a learning calibration method based on historical-current test data, this invention constructs a weighted coupled model of multi-source nondestructive testing parameters. It organically integrates service life, number of freeze-thaw cycles, and specification freeze resistance level to form a comprehensive freeze-thaw damage variable. This enables a quantitative comparison between the degree of freeze-thaw damage and the specification reference level, overcoming the problem of large dispersion in evaluation results from a single indicator.

[0200] This invention unifies the evaluation of freeze-thaw damage and the problem of durability improvement into a Markov decision process (MDP), and introduces a deep Q-network for joint learning. Addressing the long-term, irreversible, and incomplete information characteristics of freeze-thaw damage evolution in existing bridge and tunnel concrete, this invention integrates the freeze-thaw damage state, engineering intervention actions, and damage evolution process into a unified MDP framework. It utilizes a deep Q-network to adaptively learn the weights of non-destructive testing parameters and durability improvement strategies, achieving dynamic coupling between freeze-thaw damage evaluation and engineering decision-making, thus overcoming the limitations of traditional static evaluation methods.

[0201] This invention constructs a phased and categorized mathematical model for improving freeze-thaw durability, enabling quantitative decision-making for engineering intervention measures. For different stages of freeze-thaw damage, this invention establishes durability improvement models for surface protection, local repair, and structural reinforcement. It transforms engineering mechanisms such as pore water content control, restoration of local effective bearing area, and improvement of the allowable threshold for structural damage into calculable mathematical expressions. This shifts durability improvement measures from empirical judgment to quantitative analysis based on comprehensive freeze-thaw damage variables, improving the scientific rigor and economic efficiency of freeze-thaw maintenance decisions for existing bridges and tunnels.

[0202] This invention addresses the challenges of concealed, complex, and difficult-to-quantify freeze-thaw damage in existing bridges and tunnels in seasonally frozen regions. It constructs a comprehensive method for evaluating freeze-thaw damage and improving durability based on multi-source non-destructive testing parameters. By introducing readily obtainable field-obtainable non-destructive testing parameters such as dynamic elastic modulus, ultrasonic longitudinal wave velocity, and ultrasonic energy attenuation, and combining them with continuous damage mechanics and probabilistic evolution theory, the invention achieves quantitative characterization of the degree of freeze-thaw damage in existing bridge and tunnel concrete, avoiding the limitations of traditional methods that rely on core sampling or damage detection.

[0203] This invention further establishes a multi-parameter weighted coupling model that considers service life and standard freeze-thaw resistance requirements. Through learning and calibration using historical and existing test data, it effectively reduces the uncertainty of single-index evaluation, making the comprehensive freeze-thaw damage results more consistent with the actual degradation level in engineering projects. Based on this, freeze-thaw damage evaluation and durability improvement decisions are unified into a Markov decision process, and a deep Q-network is introduced to achieve adaptive optimization of weights and intervention strategies, thereby improving the scientific rigor of long-term freeze-thaw durability assessment and decision-making.

[0204] Meanwhile, this invention establishes mathematical models for durability improvement at different stages of freeze-thaw damage, including surface protection, local repair, and structural reinforcement. This enables quantitative determination and effectiveness evaluation of engineering intervention measures, transforming durability improvement from experience-based judgment to graded decision-making based on damage status. This method can effectively slow down the freeze-thaw degradation process without affecting the normal service of the structure, improving the freeze-thaw resistance reliability and engineering economy of existing bridge and tunnel structures, and has significant value for engineering application. Attached Figure Description

[0205] Figure 1 This is a schematic diagram illustrating the evolution of dynamic and capacitive damage variables of existing bridge concrete over service time, as described in this invention.

[0206] Figure 2 This is a schematic diagram illustrating the mapping between the non-destructive testing parameters and concrete freeze-thaw damage variables described in this invention.

[0207] Figure 3 This is a schematic diagram illustrating the relationship between ultrasonic amplitude attenuation and energy damage variables as described in this invention.

[0208] Figure 4 This is a schematic diagram comparing the rating model and standards described in this invention.

[0209] Figure 5 This is a schematic diagram of the convergence curve of the reinforcement learning described in this invention.

[0210] Figure 6 This is a schematic diagram illustrating the convergence of the neural network loss described in this invention.

[0211] Figure 7 This is a schematic diagram illustrating the evolution of the multi-source nondestructive testing indexes described in this invention.

[0212] Figure 8 This is a schematic diagram of the DQN weight calibration described in this invention.

[0213] Figure 9 This is a schematic diagram illustrating the blocking effect of the local repair measures described in this invention on the damage evolution pathway. Detailed Implementation

[0214] Please see Figures 1 to 9 As shown:

[0215] The present invention provides a method for evaluating and improving the freeze-thaw durability of existing bridge and tunnel concrete in seasonally frozen areas, the method comprising the following steps:

[0216] Step 1: Information Acquisition and Characterization Model of Freeze-Thaw Durability Damage During Service: The characterization model of freeze-thaw durability damage during service is based on multi-source non-destructive testing methods to obtain freeze-thaw deterioration information of existing bridge and tunnel concrete, including parameters such as dynamic elastic modulus, ultrasonic wave velocity and energy attenuation. Different physical quantities are uniformly mapped into quantifiable freeze-thaw damage characterization indicators to provide basic data for subsequent analysis.

[0217] The second step is to construct a comprehensive freeze-thaw durability damage variable model. Based on the freeze-thaw damage characterization in the first step, the influencing factors of service life and standard freeze-thaw resistance level are introduced to construct a weighted coupling model of several parameters, forming a comprehensive freeze-thaw damage variable that can reflect the overall freeze-thaw deterioration level of the structure, which is used to characterize the freeze-thaw damage state at different stages.

[0218] The third step is to establish a damage evolution and decision analysis model: The damage evolution and decision analysis model regards the change process of comprehensive freeze-thaw damage variables as a time-series evolution process. By establishing a mapping relationship between damage state and engineering intervention measures, the development trend of freeze-thaw damage is analyzed, providing a basis for durability improvement decisions.

[0219] The fourth step is to establish a phased durability improvement strategy recommendation model: Based on the range of the comprehensive freeze-thaw damage variables, three types of durability improvement measures are identified: surface protection, local repair, and structural reinforcement. The effects of different intervention methods are quantitatively evaluated through mathematical models to achieve matching recommendations between freeze-thaw damage status and engineering measures.

[0220] The specific steps for obtaining information on service-life freeze-thaw durability damage and establishing a characterization model in the first step are as follows:

[0221] Step 1: Using dynamic elastic modulus and ultrasonic wave velocity nondestructive testing parameters as core state variables, and combining continuous damage mechanics and probabilistic evolution theory, establish the mapping relationship between parameter degradation, damage variables, and reliability to form a freeze-thaw damage evaluation process applicable to existing bridge and tunnel concrete, as follows:

[0222] Scalar damage variable The formula is as follows:

[0223] ;

[0224] in: It is the damage variable of the existing bridge and tunnel service life of q years, 0≤ ≤1;

[0225] N is an equivalent variable for the service life of existing bridges and tunnels;

[0226] It is the area of ​​internal concrete damage after freeze-thaw cycles in bridges and tunnels in seasonally frozen areas.

[0227] A is the initial effective load-bearing area of ​​the material. When D=0, it means that the material is intact and in an undamaged state. When D→1, it means that the effective load-bearing capacity inside the material is basically lost and the material is close to failure.

[0228] Step 2: Establishment of the dynamic elastic modulus degradation model: One of the most direct macroscopic characteristics of freeze-thaw damage is the degradation of concrete stiffness. Based on the equivalent continuous medium assumption, freeze-thaw damage can be equivalent to the continuous decay of the material's elastic modulus, and the relationship is expressed as follows:

[0229] ;

[0230] in: It is the dynamic elastic modulus of existing bridges and tunnels after 1 year of freeze-thaw cycles, and the unit is MPa;

[0231] It is the initial dynamic elastic modulus of concrete, i.e., the state without freeze-thaw damage;

[0232] This is the effective stiffness retention factor;

[0233] Equation (2) yields the freeze-thaw damage variable defined based on the dynamic elastic modulus. The formula is as follows:

[0234] ;

[0235] in: It is a freeze-thaw damage variable index based on dynamic modulus definition;

[0236] It can be obtained through the resonance frequency method or the ultrasonic method, so formula (3) is one of the most operational expressions in the evaluation of freeze-thaw damage of existing bridge and tunnel concrete;

[0237] Step 3: Establishment of a freeze-thaw damage characterization model based on ultrasonic parameters: Freeze-thaw cycles increase the number of microcracks and enhance pore connectivity within concrete, thereby lengthening the ultrasonic wave propagation path and reducing its propagation speed. This model is suitable for rapid on-site detection. Let the longitudinal wave velocity after *n* freeze-thaw cycles be V(N), and the initial wave velocity be... The wave velocity type freeze-thaw damage variable is defined as follows:

[0238] ;

[0239] in: The ultrasonic longitudinal wave velocity after 1 year of freeze-thaw cycles of existing bridges and tunnels is expressed in m / s.

[0240] The ultrasonic longitudinal wave velocity in the initial state of concrete is expressed in m / s.

[0241] For freeze-thaw damage variables based on ultrasonic wave velocity;

[0242] Step 4: Establishment of the ultrasonic energy attenuation model: Considering the scattering, reflection, and energy dissipation effects of ultrasonic waves in freeze-thaw damaged concrete, an ultrasonic energy attenuation coefficient is introduced. The formula is as follows:

[0243] ;

[0244] in: It is the ultrasonic energy attenuation coefficient after existing bridges and tunnels have been in service for 1 year and have undergone freeze-thaw cycles, with the unit being 1 / m;

[0245] L is the propagation path length of the ultrasonic wave in concrete, measured in meters (m).

[0246] It is the amplitude of the received signal in the initial state;

[0247] A(N) is the received signal amplitude after 𝑁 freeze-thaw cycles;

[0248] ln is the logarithm to the base 10;

[0249] To facilitate a unified evaluation, an energy-based freeze-thaw damage variable is introduced. The formula is as follows:

[0250] ;

[0251] in: It is the energy attenuation coefficient of concrete in its initial state;

[0252] It is the energy decay coefficient corresponding to the state of freeze-thaw failure of concrete;

[0253] It is an index of freeze-thaw damage variables based on energy decay;

[0254] Step 5: Establishment of a comprehensive freeze-thaw damage model with coupling of three non-destructive parameters: Based on the above three types of damage variables, the first type of damage variable is the dynamic elastic modulus degradation model. The damage variable based on the definition of dynamic elastic modulus degradation is denoted by the following symbols: The second type of damage variable is the freeze-thaw damage characterization model based on ultrasonic parameters. The damage variable symbol is defined based on the change in ultrasonic longitudinal wave velocity. The third type of damage variable is the ultrasonic energy attenuation model, which defines damage variables based on the characteristics of ultrasonic energy attenuation, and is symbolically represented as follows: ;

[0255] The three types of damage variables are uniformly denoted as N represents the service life, 𝑖 represents the non-destructive testing parameter type identifier, i=E represents the dynamic elastic modulus, i=V represents the ultrasonic wave velocity, and i=α represents the ultrasonic energy attenuation.

[0256] The specific steps for constructing a variable model of comprehensive freeze-thaw durability damage in the second step are as follows:

[0257] Step 1: Weighted coupling model of comprehensive service-life damage variables, defining three types of non-destructive parameter coupling comprehensive freeze-thaw damage variables as follows:

[0258] ;

[0259] The weights must satisfy the normalization constraint:

[0260] ;

[0261] in: Integrating freeze-thaw damage variables;

[0262] These are the weighting coefficients corresponding to the three types of nondestructive testing parameters E, V, and α, where i=E: dynamic elastic modulus, i=V: ultrasonic wave velocity, and i=α: ultrasonic energy attenuation.

[0263] Using historical and existing detection data, the optimal weight vector is determined. ;

[0264] The data that can be obtained includes: historical inspection data, i.e., early service stage; current inspection data, i.e., current status; and corresponding macroscopic degradation characteristics, including strength reduction, damage level, and maintenance records.

[0265] Weight To reflect the contribution of each nondestructive testing parameter to the actual freeze-thaw damage, a learning calibration method based on historical data combined with current testing data is adopted, as follows:

[0266] ;

[0267] Where: m is the detection time step;

[0268] D(m) is the damage predicted by the model. D(m) = Dc(Nm) as shown in formula (7), which represents the comprehensive coupled damage value at the time of the m-th detection, corresponding to the number of freeze-thaw cycles Nm.

[0269] This is a reference damage value;

[0270] Reference damage value The definition is as follows:

[0271] Indicates the first At each detection moment, a standardized reference damage level determined based on the specification level, service life, and equivalent freeze-thaw cycle count is used to reinforce the environmental feedback signal in the learning process.

[0272] Based on the definition of frost resistance grade Fn and reference damage value in the People's Republic of China industry standard for concrete durability testing and evaluation JGJ / T 193-2009 ;

[0273] Current Standard Classification Table of Concrete Freeze-Thaw Resistance

[0274]

[0275] The durability of concrete is classified into grades based on the "permissible number of freeze-thaw cycles".

[0276] For example:

[0277] Freeze resistance rating Corresponding design freeze-thaw cycles F50 50 times F100 100 times F150 150 times F200 200 times F250 250 times F300 300 times F350 350 times F400 400 times

[0278]

[0279] The above formula This indicates the percentage of durability that has been consumed, i.e., the percentage of remaining durability.

[0280] in: Indicates the current service life; Indicates the number of design freeze-thaw cycles corresponding to the specification level (e.g., F200 → 200).

[0281] One example: If the engineering design level is F200 → Ngrade = 200, and if it is F300 → Ngrade = 300, This represents the current service life, the cumulative number of freeze-thaw cycles experienced by the current service life up to the m-th inspection. If there are 5 freeze-thaw cycles per year and the service life is 20 years, then: Nserv = 5 × 20 = 100.

[0282] Assumptions: Design grade: F200, Ngrade = 200, currently has undergone 100 freeze-thaw cycles. Then:

[0283] 𝐷𝑟𝑒𝑓(m)=1−100 / 200=0.5, indicating that 50% of the antifreeze capacity has been consumed, and 50% of the lifespan remains.

[0284] when If Dref=0, it means that the gauge limit has been reached.

[0285] The freeze-thaw damage evolution of existing bridge and tunnel concrete is a long-term, irreversible, and dynamic process with incomplete information. Non-destructive testing can only obtain partial state information at discrete time points, while the actual damage level needs to be comprehensively judged by combining specifications, historical data, and model inferences.

[0286] Step 2: Model the freeze-thaw damage assessment and performance improvement problem as a Markov decision process, and use a deep Q-network to jointly learn the weights of multi-source nondestructive testing parameters and intervention strategies;

[0287] Markov decision processes are represented as quintuples, as follows:

[0288] ;

[0289] The meaning of each element in the evaluation and performance improvement of freeze-thaw damage in existing bridge and tunnel concrete is as follows:

[0290] Where: M represents the Markov decision process;

[0291] S represents the state space, a complete representation of the current freeze-thaw damage state of the structure;

[0292] A represents the action space—the set of engineering decisions and weight adjustments;

[0293] R represents the reward function—a quantitative indicator of evaluation accuracy and engineering rationality;

[0294] 𝛾 represents the discount factor—the level of concern regarding long-term durability;

[0295] state space — A complete characterization of the current freeze-thaw damage state of the structure;

[0296] Define the state space S, with the following formula:

[0297] ;

[0298] in: It is the system state vector at the nth detection or decision time;

[0299] Freeze-thaw damage variables defined based on dynamic elastic modulus degradation;

[0300] Freeze-thaw damage variables defined based on changes in ultrasonic longitudinal wave velocity;

[0301] Freeze-thaw damage variables defined based on ultrasonic energy attenuation characteristics;

[0302] Normalized service life of existing bridge and tunnel structures;

[0303] P represents the porosity growth rate, which measures the rate of microstructure degradation.

[0304] This indicates that the object is transposed.

[0305] The state space 𝑆 is used to describe the current health state of concrete under freeze-thaw action. This state vector integrates mechanical degradation information, namely stiffness loss, acoustic degradation information, namely crack and pore evolution, and time / environment cumulative effects.

[0306] Satisfying the Markov property assumption: Given the current state Under these conditions, the future damage evolution of the structure is independent of its historical path;

[0307] Step 3: Define the action space A, with the following formula:

[0308] ;

[0309] Among them: a0 No intervention is taken, i.e., the baseline state; a1 Adaptive weight calibration, adjusting the weight vector of non-destructive testing parameters; a2 Maintain the current state, only continue monitoring; a3 Take surface protection measures, including hydrophobic coatings; a4 Crack grouting or local repair; a5 Structural durability reinforcement;

[0310] The state transition probability P—the uncertainty in the evolution of freeze-thaw damage—is given by the following formula:

[0311] ;

[0312] in: Indicates the current state. Indicates the action currently being taken; Indicates the state at the next moment;

[0313] Implicit state transition relationships are learned through an interactive learning process involving historical monitoring data, environmental exposure data, and DQN.

[0314] The reward function R is a quantitative indicator for evaluating accuracy and engineering rationality. The specific formula is as follows:

[0315] ;

[0316] ;

[0317] Where: 𝑟𝑘: the immediate reward obtained after taking action 𝑎𝑘 in state 𝑠𝑘, D(k)=Dc(Nk) see formula (7), representing the comprehensive coupled damage value at the k-th detection time corresponding to the number of freeze-thaw cycles Nk, Dref(k): the reference damage value from the specification level, C(ak): the engineering cost or intervention cost corresponding to action 𝑎𝑘, and 𝜆: cost penalty coefficient;

[0318] Discount factor 𝛾—the level of concern for long-term durability, the specific formula is as follows:

[0319] ;

[0320] Where: ☐→0: focuses more on current testing accuracy; ☐→1: focuses more on long-term freeze-thaw durability and service life. In the durability evaluation of existing bridges and tunnels, ☐→1 is taken as ☐→0. ;

[0321] Step 4, DQN algorithm input: Non-destructive testing data: 𝐸d, 𝑉, 𝛼, Service information: Nserv, Specification parameters: Ngrade;

[0322] Output: Total freeze-thaw damage: D(k), Optimal weight vector: 𝑤∗, Optimal decision strategy: 𝜋∗

[0323] The Q-function and optimal policy definition, the state-action value function, the Q-function is defined as follows:

[0324] ;

[0325] in: It is a state-action value function, representing the expected cumulative reward that the system can obtain from the moment it takes action ak when it is in state sk under policy 𝜋; 𝜋 is the policy. Let represent the probability rule for choosing action a in state s; sk represent the state at time k; ak represent the action taken at time k; rk+t represent the immediate reward obtained at time k+t; γ∈(0,1) is a discount factor, representing the degree of importance controlling future rewards and the degree of long-term durability attention. Take the expected value of the random variable; Let π represent the expected value of all possible future paths under policy π and environment probability transition, and φ be the immediate reward obtained after taking action φ in state π.

[0326] The optimal Q function is as follows:

[0327] ;

[0328] in: It is the optimal state-action value function, which represents the Q-value that maximizes the reward among all policies;

[0329] Finding the maximum value among all policies is equivalent to finding the optimal policy, which is: ,in ;

[0330] Step 5: Deep Q-Network Approximation Model. The neural network approximation uses a deep neural network with parameter K to approximate the Q function, as follows:

[0331] ;

[0332] Where: the Q-function is approximated by the neural network, the input is the state s, the output is the Q-value corresponding to all actions, and the parameter θ is the neural network parameter, including: the weight matrix and the bias term, in the following form:

[0333] DQN neural network structure, neural network parameter set :

[0334] ;

[0335] Network layer structure: 5→512→512→256→6;

[0336] The calculation formula for each layer is as follows:

[0337] First layer:

[0338] ;

[0339] ;

[0340] in: In this context, M is the set of real numbers; s is a 5-dimensional real vector, i.e., a column vector. It is a 512-row × 5-column matrix; representing 512 neurons, each neuron has 5 weights, and each weight is a real number; This indicates that there are 512 bias values, each bias being a real number, and every element in the matrix is ​​a real number. The specific formula is as follows:

[0341] ;

[0342] Where: Wij∈M, each element is a regular floating-point number;

[0343] By mapping five original physical damage variables to a 512-dimensional latent damage feature space, it learns the combination relationship of each index, nonlinear degradation mode, and potential damage interaction effect.

[0344] The number of parameters is 512×5=2560. With the bias, the number is 2560+512=3072. The first layer has a total of 3072 parameters.

[0345] Second layer:

[0346] ;

[0347] ;

[0348] Parameter Dimensions ;

[0349] The number of parameters is 512 × 512 = 262144. Adding the bias value: 262144 + 512 = 262656.

[0350] The second layer of function: it performs deep nonlinear combination in a high-dimensional feature space, which captures the accelerated stage of freeze-thaw damage, the nonlinear feedback of repair effects, and the long-term evolution path dependence.

[0351] Third layer:

[0352] ;

[0353] ;

[0354] Parameter Dimensions

[0355] The number of parameters is 256 × 512 = 131072, and the bias value is 131072 + 256 = 131328.

[0356] The third layer is the decision feature compression layer, which compresses the high-dimensional damage pattern into 256-dimensional decision features to prepare for action value calculation.

[0357] Output layer:

[0358] ;

[0359] Right now

[0360] ;

[0361] The target Q-value is calculated using the target network parameter φ, and the target value is defined as:

[0362] ;

[0363] Where: yk is the target Q-value, representing the ideal Q-value after performing the action in the current state, and rk is the immediate reward. γ is a discount factor, taken as γ=0.95, focusing more on long-term lifetime. It is the state in the next moment. All possible actions in the next state, This represents the Q-value corresponding to the optimal action in the next state, which means the maximum benefit brought by the optimal decision in the future; These are stable network parameters that are updated with a delay to avoid training oscillations. Their values ​​are determined by copying the current θ to θ' after every 20 learning updates.

[0364] loss function

[0365] ;

[0366] in: It is the mean squared error, representing the difference between the current network's predicted Q-value and the target Q-value. Here, yk is the mathematical expectation, and yk is the target Q value, representing the ideal Q value after performing the action in the current state. It's the squared error; the larger the error, the more the network needs adjustment.

[0367] The parameter update formula is as follows:

[0368] ;

[0369] in: These are the neural network parameters during the k-th training iteration. The neural network parameters at the (k+1)th training iteration; It is the learning rate, taken as... ; It is the gradient of the loss function with respect to the parameters, indicating how much each parameter should be adjusted.

[0370] The specific steps for establishing the damage evolution and decision analysis model in the third step are as follows:

[0371] For existing bridge and tunnel concrete structures in seasonally frozen areas, without core sampling or structural damage, a freeze-thaw durability evaluation process is established based on multi-source non-destructive testing parameters, taking into account the current state of freeze-thaw damage, historical evolution trends, and standard durability requirements. This process includes "detection - damage quantification - comprehensive evaluation - durability determination".

[0372] The evaluation results are presented in the form of a comprehensive assessment of freeze-thaw damage variables, durability level, and remaining durability capacity. They can be directly used for the technical condition assessment and maintenance decisions of existing bridge and tunnel structures. The specific steps are as follows:

[0373] Step 1: Collect non-destructive testing data 𝐸d, 𝑉, 𝐴;

[0374] Step 2: Calculate the three types of freeze-thaw damage variables 𝐷𝐸, 𝐷𝑉, 𝐷𝛼;

[0375] Step 3: Calculate the overall damage 𝐷 by calibrating the weights using DQN;

[0376] Step 4: Determine the 𝐷ref based on the specification level;

[0377] Step 5: Compare D with 𝐷ref to determine the level of freeze resistance durability;

[0378] Step 6: Output durability rating and engineering recommendations;

[0379] The engineering implications of the combined freeze-thaw damage variables are as follows:

[0380] D(k) ≈ 0 indicates that the microcracks inside the concrete have not yet developed significantly, the dynamic stiffness and acoustic parameters are close to the initial state, and the structure is in a good frost-resistant state.

[0381] D(k) ∈ (0.2, 0.4) indicates that microcracks and pores induced by freeze-thaw cycles have begun to appear inside the concrete, and the stiffness and acoustic parameters show identifiable degradation, which belongs to the stage of mild freeze-thaw damage.

[0382] D(k) ∈ (0.4, 0.6) indicates that freeze-thaw damage has entered an accelerated development stage, microcracks gradually connect, local effective bearing capacity decreases, and freeze-thaw resistance is significantly weakened.

[0383] D(k) > 0.6 indicates that the internal damage of the concrete has reached the level of macroscopic deterioration. Freeze-thaw damage has a significant impact on the service performance of the structure, and the freeze-thaw durability is insufficient, so engineering intervention measures need to be taken.

[0384] Frost resistance and durability classification standards

[0385] Durability rating Damage variable range D(k) Performance Evaluation Structural treatment recommendations Level I 0 ≤ D(k) < 0.2 Good freeze resistance and durability Normal maintenance Level II 0.2 ≤ D(k) < 0.4 The freeze resistance and durability are basically satisfactory. Regular observation Level III 0.4 ≤ D(k) < 0.6 Decreased freeze resistance Local repair Level IV 0.6 ≤ D(k) < 1.0 Insufficient freeze resistance Structural reinforcement

[0386] In the above model, the value of the multi-source coupling damage D(k) is restricted to between 0 and 1, and it grows exponentially and nonlinearly.

[0387] The reward function imposes a heavy penalty on cases where 𝐷(k) > 0.6 and no reinforcement measures are taken; 0.6 is considered a significant degradation threshold.

[0388] Similarly, the table shows Level III (0.4–0.6 is the declining stage) and Level IV (>0.6 is the insufficient stage).

[0389] The intervals of 0.2, 0.4, and 0.6 form a segmented progression, representing the evolution of freeze-thaw damage from "initial slow-moderate to medium-speed to accelerated" and facilitating reinforcement learning to trigger different maintenance actions.

[0390] The specific steps for establishing the phased durability improvement strategy recommendation model in step four are as follows:

[0391] For the three types of durability improvement methods—surface protection, local repair, and structural reinforcement—corresponding mathematical models are constructed to be uniformly incorporated into the aforementioned comprehensive freeze-thaw damage evolution and decision-making framework.

[0392] Step 1: Establishment of a freeze-thaw inhibition model for surface protection enhancement measures: Surface protection measures weaken the driving force of freeze-thaw phase change at the source by reducing the pore water content of concrete and blocking the intrusion path of external moisture. Its mechanism of action is demonstrated through a moisture content regulation model, as follows:

[0393] ;

[0394] in: Equivalent pore water content after implementing surface protection measures;

[0395] This represents the initial moisture content of the concrete pores without any protective measures.

[0396] The hydrophobic efficiency coefficient of surface protection measures. It reflects the ability of coatings and penetrating materials to inhibit moisture intrusion;

[0397] Based on this, the damage driving force caused by freeze-thaw phase transition is expressed as: ,in Equivalent damage driving force induced by freeze-thaw phase change The freeze-thaw sensitivity coefficient reflects the degree to which a material responds to changes in moisture content. The coefficient of volume expansion caused by pore water freezing;

[0398] The above model shows that surface protection reduces This can significantly weaken the source driving mechanism of freeze-thaw damage;

[0399] Step 2: Establishment of a damage blocking model for local repair and crack intervention: For situations where the comprehensive freeze-thaw damage variables are at a medium to high level and damage evolution is accelerated, the core role of local crack repair is to restore the effective local bearing area and block the crack propagation channel, as follows:

[0400] ;

[0401] in: The equivalent freeze-thaw damage variable for the repaired local area;

[0402] For the freeze-thaw damage variables in the local area before repair;

[0403] This refers to the effective bearing area of ​​the concrete section before repair.

[0404] This refers to the effective load-bearing area after repair.

[0405] The above model quantitatively reflects the reversal effect of grouting and crack sealing measures on local freeze-thaw damage;

[0406] Step 3: Establishment of an overall improvement model for structural durability strengthening: When the comprehensive freeze-thaw damage variable exceeds the critical threshold, it is necessary to improve the structure's freeze resistance at the overall level. The essence of structural strengthening lies in increasing the structure's "tolerance threshold" for freeze-thaw damage. The critical damage level after strengthening is defined as follows:

[0407] ;

[0408] in: The freeze-thaw damage failure threshold for unreinforced structures;

[0409] This is the equivalent failure threshold after reinforcement;

[0410] The structural reinforcement gain coefficient reflects the effect of external cladding and reinforcement measures on improving durability margin;

[0411] The overall structural freeze-resistance reliability function is further defined as follows:

[0412] ;

[0413] in: This serves as a reliability indicator for the structure's freeze-thaw resistance and durability.

[0414] This represents the current overall freeze-thaw damage variable;

[0415] The above model shows that structural reinforcement, by increasing the upper limit of damage tolerance, enables the structure to maintain acceptable freeze-thaw reliability even at higher damage levels.

[0416] For different stages of freeze-thaw damage, durability improvement models for surface protection, local repair, and structural reinforcement are established respectively. Engineering intervention measures are transformed into quantifiable mathematical expressions. With comprehensive freeze-thaw damage variables as the core, hierarchical control of freeze-thaw damage inhibition, propagation blocking, and allowable threshold improvement is achieved. This shifts durability improvement decisions from experience-based judgment to quantitative analysis, effectively delaying the freeze-thaw deterioration process of existing bridge and tunnel concrete in seasonally frozen areas and improving the structural freeze-thaw resistance reliability and engineering economy.

Claims

1. A method for evaluating and improving the freeze-thaw durability of existing bridge and tunnel concrete in seasonally frozen areas, characterized in that: The method includes the following steps: Step 1: Information Acquisition and Characterization Model of Freeze-Thaw Durability Damage During Service: The characterization model of freeze-thaw durability damage during service is based on multi-source non-destructive testing methods to obtain freeze-thaw deterioration information of existing bridge and tunnel concrete, including parameters such as dynamic elastic modulus, ultrasonic wave velocity and energy attenuation. Different physical quantities are uniformly mapped into quantifiable freeze-thaw damage characterization indicators to provide basic data for subsequent analysis. The second step is to construct a comprehensive freeze-thaw durability damage variable model. Based on the freeze-thaw damage characterization in the first step, the influencing factors of service life and standard freeze-thaw resistance level are introduced to construct a weighted coupling model of several parameters, forming a comprehensive freeze-thaw damage variable that can reflect the overall freeze-thaw deterioration level of the structure, which is used to characterize the freeze-thaw damage state at different stages. The third step is to establish a damage evolution and decision analysis model: The damage evolution and decision analysis model regards the change process of comprehensive freeze-thaw damage variables as a time-series evolution process. By establishing a mapping relationship between damage state and engineering intervention measures, the development trend of freeze-thaw damage is analyzed, providing a basis for durability improvement decisions. The fourth step is to establish a phased durability improvement strategy recommendation model: Based on the range of the comprehensive freeze-thaw damage variables, three types of durability improvement measures are identified: surface protection, local repair, and structural reinforcement. The effects of different intervention methods are quantitatively evaluated through mathematical models to achieve matching recommendations between freeze-thaw damage status and engineering measures.

2. The method for evaluating and improving the freeze-thaw durability of existing bridge and tunnel concrete in seasonally frozen areas according to claim 1, characterized in that... The specific steps for acquiring and characterizing the service-life freeze-thaw durability damage information and establishing the model in the first step are as follows: Step 1: Using dynamic elastic modulus and ultrasonic wave velocity nondestructive testing parameters as core state variables, and combining continuous damage mechanics and probabilistic evolution theory, establish the mapping relationship between parameter degradation, damage variables, and reliability to form a freeze-thaw damage evaluation process applicable to existing bridge and tunnel concrete, as follows: Scalar damage variable The formula is as follows: ； in: It is the damage variable of the existing bridge and tunnel service life of q years, 0≤ ≤1; N is an equivalent variable for the service life of existing bridges and tunnels; It is the area of ​​internal concrete damage after freeze-thaw cycles in bridges and tunnels in seasonally frozen areas. A is the initial effective load-bearing area of ​​the material. When D=0, it means that the material is intact and in an undamaged state. When D→1, it means that the effective load-bearing capacity inside the material is basically lost and the material is close to failure. Step 2: Establishment of the dynamic elastic modulus degradation model: One of the most direct macroscopic characteristics of freeze-thaw damage is the degradation of concrete stiffness. Based on the equivalent continuous medium assumption, freeze-thaw damage can be equivalent to the continuous decay of the material's elastic modulus, and the relationship is expressed as follows: ； in: It is the dynamic elastic modulus of existing bridges and tunnels after 1 year of freeze-thaw cycles, and the unit is MPa; It is the initial dynamic elastic modulus of concrete, i.e., the state without freeze-thaw damage; This is the effective stiffness retention factor; Equation (2) yields the freeze-thaw damage variable defined based on the dynamic elastic modulus. The formula is as follows: ； in: It is a freeze-thaw damage variable index based on dynamic modulus definition; It can be obtained through the resonance frequency method or the ultrasonic method, so formula (3) is one of the most operational expressions in the evaluation of freeze-thaw damage of existing bridge and tunnel concrete; Step 3: Establishment of a freeze-thaw damage characterization model based on ultrasonic parameters: Freeze-thaw cycles increase the number of microcracks and enhance pore connectivity within concrete, thereby lengthening the ultrasonic wave propagation path and reducing its propagation speed. This model is suitable for rapid on-site detection. Let the longitudinal wave velocity after *n* freeze-thaw cycles be V(N), and the initial wave velocity be... The wave velocity type freeze-thaw damage variable is defined as follows: ； in: The ultrasonic longitudinal wave velocity after 1 year of freeze-thaw cycles of existing bridges and tunnels is expressed in m / s. The ultrasonic longitudinal wave velocity in the initial state of concrete is expressed in m / s. For freeze-thaw damage variables based on ultrasonic wave velocity; Step 4: Establishment of the ultrasonic energy attenuation model: Considering the scattering, reflection, and energy dissipation effects of ultrasonic waves in freeze-thaw damaged concrete, an ultrasonic energy attenuation coefficient is introduced. The formula is as follows: ； in: It is the ultrasonic energy attenuation coefficient after existing bridges and tunnels have been in service for 1 year and have undergone freeze-thaw cycles, with the unit being 1 / m; L is the propagation path length of the ultrasonic wave in concrete, measured in meters (m). It is the amplitude of the received signal in the initial state; A(N) is the received signal amplitude after 𝑁 freeze-thaw cycles; ln is the logarithm to the base 10; To facilitate a unified evaluation, an energy-based freeze-thaw damage variable is introduced. The formula is as follows: ； in: It is the energy attenuation coefficient of concrete in its initial state; It is the energy decay coefficient corresponding to the state of freeze-thaw failure of concrete; It is an index of freeze-thaw damage variables based on energy decay; Step 5: Establishment of a comprehensive freeze-thaw damage model with coupling of three non-destructive parameters: Based on the above three types of damage variables, the first type of damage variable is the dynamic elastic modulus degradation model. The damage variable based on the definition of dynamic elastic modulus degradation is denoted by the following symbols: The second type of damage variable is the freeze-thaw damage characterization model based on ultrasonic parameters. The damage variable symbol is defined based on the change in ultrasonic longitudinal wave velocity. The third type of damage variable is the ultrasonic energy attenuation model, which defines damage variables based on the characteristics of ultrasonic energy attenuation, and is symbolically represented as follows: ; The three types of damage variables are uniformly denoted as N represents the service life, 𝑖 represents the non-destructive testing parameter type identifier, i=E represents the dynamic elastic modulus, i=V represents the ultrasonic wave velocity, and i=α represents the ultrasonic energy attenuation.

3. The method for evaluating and improving the freeze-thaw durability of existing bridge and tunnel concrete in seasonally frozen areas according to claim 1, characterized in that... The specific steps for constructing the variable model of comprehensive freeze-thaw durability damage in the second step are as follows: Step 1: Weighted coupling model of comprehensive service-life damage variables, defining three types of non-destructive parameter coupling comprehensive freeze-thaw damage variables as follows: ； The weights must satisfy the normalization constraint: ； in: Integrating freeze-thaw damage variables; These are the weighting coefficients corresponding to the three types of nondestructive testing parameters E, V, and α, where i=E: dynamic elastic modulus, i=V: ultrasonic wave velocity, and i=α: ultrasonic energy attenuation. Using historical and existing detection data, the optimal weight vector is determined. ; The data that can be obtained includes: historical inspection data, i.e., early service stage; current inspection data, i.e., current status; and corresponding macroscopic degradation characteristics, including strength reduction, damage level, and maintenance records. Weight To reflect the contribution of each nondestructive testing parameter to the actual freeze-thaw damage, a learning calibration method based on historical data combined with current testing data is adopted, as follows: ； Where: m is the detection time step; D(m) is the damage predicted by the model. D(m) = Dc(Nm) as shown in formula (7), which represents the comprehensive coupled damage value at the time of the m-th detection, corresponding to the number of freeze-thaw cycles Nm. This is a reference damage value; Reference damage value The definition is as follows: Indicates the first At each detection moment, a standardized reference damage level determined based on the specification level, service life, and equivalent freeze-thaw cycle count is used to reinforce the environmental feedback signal in the learning process. ； The above formula This indicates the percentage of durability that has been consumed, i.e., the percentage of remaining durability. in: Indicates the current service life; This indicates the number of design freeze-thaw cycles corresponding to the specification level; Step 2: Model the freeze-thaw damage assessment and performance improvement problem as a Markov decision process, and use a deep Q-network to jointly learn the weights of multi-source nondestructive testing parameters and intervention strategies; Markov decision processes are represented as quintuples, as follows: ； The meaning of each element in the evaluation and performance improvement of freeze-thaw damage in existing bridge and tunnel concrete is as follows: Where: M represents the Markov decision process; S represents the state space, a complete representation of the current freeze-thaw damage state of the structure; A represents the action space—the set of engineering decisions and weight adjustments; R represents the reward function—a quantitative indicator of evaluation accuracy and engineering rationality; 𝛾 represents the discount factor—the level of concern regarding long-term durability; state space — A complete characterization of the current freeze-thaw damage state of the structure; Define the state space S, with the following formula: ； in: It is the system state vector at the nth detection or decision time; Freeze-thaw damage variables defined based on dynamic elastic modulus degradation; Freeze-thaw damage variables defined based on changes in ultrasonic longitudinal wave velocity; Freeze-thaw damage variables defined based on ultrasonic energy attenuation characteristics; Normalized service life of existing bridge and tunnel structures; P represents the porosity growth rate, which measures the rate of microstructure degradation. This indicates that the object is transposed. The state space 𝑆 is used to describe the current health state of concrete under freeze-thaw action. This state vector integrates mechanical degradation information, namely stiffness loss, acoustic degradation information, namely crack and pore evolution, and time / environment cumulative effects. Satisfying the Markov property assumption: Given the current state Under these conditions, the future damage evolution of the structure is independent of its historical path; Step 3: Define the action space A, with the following formula: ； Among them: a0 No intervention is taken, i.e., the baseline state; a1 Adaptive weight calibration, adjusting the weight vector of non-destructive testing parameters; a2 Maintain the current state, only continue monitoring; a3 Take surface protection measures, including hydrophobic coatings; a4 Crack grouting or local repair; a5 Structural durability reinforcement; The state transition probability P—the uncertainty in the evolution of freeze-thaw damage—is given by the following formula: ； in: Indicates the current state. Indicates the action currently being taken; Indicates the state at the next moment; Implicit state transition relationships are learned through an interactive learning process combining historical monitoring data, environmental exposure data, and DQN. The reward function R is a quantitative indicator for evaluating accuracy and engineering rationality. The specific formula is as follows: ； ； Where: 𝑟𝑘: the immediate reward obtained after taking action 𝑎𝑘 in state 𝑠𝑘, D(k)=Dc(Nk) see formula (7), representing the comprehensive coupled damage value at the k-th detection time corresponding to the number of freeze-thaw cycles Nk, Dref(k): the reference damage value from the specification level, C(ak): the engineering cost or intervention cost corresponding to action 𝑎𝑘, and 𝜆: cost penalty coefficient; Discount factor 𝛾—the level of concern for long-term durability, the specific formula is as follows: ； Where: ☐→0: focuses more on current testing accuracy; ☐→1: focuses more on long-term freeze-thaw durability and service life. In the durability evaluation of existing bridges and tunnels, ☐→1 is taken as ☐→0. ; Step 4, DQN algorithm input: Non-destructive testing data: 𝐸d, 𝑉, 𝛼, Service information: Nserv, Specification parameters: Ngrade; Output: Total freeze-thaw damage: D(k), Optimal weight vector: 𝑤∗, Optimal decision strategy: 𝜋∗ The Q-function and optimal policy definition, the state-action value function, the Q-function is defined as follows: ； in: It is a state-action value function, representing the expected cumulative reward that the system can obtain from the moment it takes action ak when it is in state sk under policy 𝜋; 𝜋 is the policy. Let represent the probability rule for choosing action a in state s; sk represent the state at time k; ak represent the action taken at time k; rk+t represent the immediate reward obtained at time k+t; γ∈(0,1) is a discount factor, representing the degree of importance controlling future rewards and the degree of long-term durability attention. Take the expected value of the random variable; Let π represent the expected value of all possible future paths under policy π and environment probability transition, and φ be the immediate reward obtained after taking action φ in state π. The optimal Q function is as follows: ； in: It is the optimal state-action value function, which represents the Q-value that maximizes the reward among all policies; Finding the maximum value among all policies is equivalent to finding the optimal policy, which is: ,in ; Step 5: Deep Q-Network Approximation Model. The neural network approximation uses a deep neural network with parameter K to approximate the Q function, as follows: ； Where: the Q-function is approximated by the neural network, the input is the state s, the output is the Q-value corresponding to all actions, and the parameter θ is the neural network parameter, including: the weight matrix and the bias term, in the following form: DQN neural network structure, neural network parameter set : ； Network layer structure: 5→512→512→256→6; The calculation formula for each layer is as follows: First layer: ; ； in: In this context, M is the set of real numbers; s is a 5-dimensional real vector, i.e., a column vector. It is a 512-row × 5-column matrix; representing 512 neurons, each neuron has 5 weights, and each weight is a real number; This indicates that there are 512 bias values, each bias being a real number, and every element in the matrix is ​​a real number. The specific formula is as follows: ； Where: Wij∈M, each element is a regular floating-point number; By mapping five original physical damage variables to a 512-dimensional latent damage feature space, it learns the combination relationship of each index, nonlinear degradation mode, and potential damage interaction effect. The number of parameters is 512×5=2560. With the bias, the number is 2560+512=3072. The first layer has a total of 3072 parameters. Second layer: ; ； Parameter Dimensions ; The number of parameters is 512 × 512 = 262144. Adding the bias value: 262144 + 512 = 262656. The second layer of function: it performs deep nonlinear combination in a high-dimensional feature space, which captures the accelerated stage of freeze-thaw damage, the nonlinear feedback of repair effects, and the long-term evolution path dependence. Third layer: ; ； Parameter Dimensions ; The number of parameters is 256 × 512 = 131072, and the bias value is 131072 + 256 = 131328. The third layer is the decision feature compression layer, which compresses the high-dimensional damage pattern into 256-dimensional decision features to prepare for action value calculation. Output layer: ; Right now ； The target Q-value is calculated using the target network parameter φ, and the target value is defined as: ； Where: yk is the target Q-value, representing the ideal Q-value after performing the action in the current state, and rk is the immediate reward. γ is a discount factor, taken as γ=0.95, focusing more on long-term lifetime. It is the state in the next moment. All possible actions in the next state, This represents the Q-value corresponding to the optimal action in the next state, which means the maximum benefit brought by the optimal decision in the future; These are stable network parameters that are updated with a delay to avoid training oscillations. Their values ​​are determined by copying the current θ to θ' after every 20 learning updates. loss function ； in: It is the mean squared error, representing the difference between the current network's predicted Q-value and the target Q-value. Here, yk is the mathematical expectation, and yk is the target Q value, representing the ideal Q value after performing the action in the current state. It's the squared error; the larger the error, the more the network needs adjustment. The parameter update formula is as follows: ； in: These are the neural network parameters during the k-th training iteration. The neural network parameters at the (k+1)th training iteration; It is the learning rate, taken as... ; It is the gradient of the loss function with respect to the parameters, indicating how much each parameter should be adjusted.

4. The method for evaluating and improving the freeze-thaw durability of existing bridge and tunnel concrete in seasonally frozen areas according to claim 1, characterized in that... The specific steps for establishing the damage evolution and decision analysis model in the third step are as follows: For existing bridge and tunnel concrete structures in seasonally frozen areas, without core sampling or structural damage, a freeze-thaw durability evaluation process is established based on multi-source non-destructive testing parameters, taking into account the current state of freeze-thaw damage, historical evolution trends, and standard durability requirements. This process includes "detection—damage quantification—comprehensive evaluation—durability determination". The evaluation results are presented in the form of a comprehensive assessment of freeze-thaw damage variables, durability level, and remaining durability capacity. They can be directly used for the technical condition assessment and maintenance decisions of existing bridge and tunnel structures. The specific steps are as follows: Step 1: Collect non-destructive testing data 𝐸d, 𝑉, 𝐴; Step 2: Calculate the three types of freeze-thaw damage variables 𝐷𝐸, 𝐷𝑉, 𝐷𝛼; Step 3: Calculate the overall damage 𝐷 by calibrating the weights using DQN; Step 4: Determine the 𝐷ref based on the specification level; Step 5: Compare D with 𝐷ref to determine the level of freeze resistance durability; Step 6: Output durability rating and engineering recommendations; The engineering implications of the combined freeze-thaw damage variables are as follows: D(k) ≈ 0 indicates that the microcracks inside the concrete have not yet developed significantly, the dynamic stiffness and acoustic parameters are close to the initial state, and the structure is in a good frost-resistant state. D(k) ∈ (0.2, 0.4) indicates that microcracks and pores induced by freeze-thaw cycles have begun to appear inside the concrete, and the stiffness and acoustic parameters show identifiable degradation, which belongs to the stage of mild freeze-thaw damage. D(k) ∈ (0.4, 0.6) indicates that freeze-thaw damage has entered an accelerated development stage, microcracks gradually connect, local effective bearing capacity decreases, and freeze-thaw resistance is significantly weakened. D(k) > 0.6 indicates that the internal damage of the concrete has reached the level of macroscopic deterioration. Freeze-thaw damage has a significant impact on the service performance of the structure, and the freeze-thaw durability is insufficient, so engineering intervention measures need to be taken.

5. The method for evaluating and improving the freeze-thaw durability of existing bridge and tunnel concrete in seasonally frozen areas according to claim 1, characterized in that... The specific steps for establishing the phased durability improvement strategy recommendation model in the fourth step are as follows: For the three types of durability improvement methods—surface protection, local repair, and structural reinforcement—corresponding mathematical models are constructed to be uniformly incorporated into the aforementioned comprehensive freeze-thaw damage evolution and decision-making framework. Step 1: Establishment of a freeze-thaw inhibition model for surface protection enhancement measures: Surface protection measures weaken the driving force of freeze-thaw phase change at the source by reducing the pore water content of concrete and blocking the intrusion path of external moisture. Its mechanism of action is demonstrated through a moisture content regulation model, as follows: ； in: Equivalent pore water content after implementing surface protection measures; This represents the initial moisture content of the concrete pores without any protective measures. The hydrophobic efficiency coefficient of surface protection measures. It reflects the ability of coatings and penetrating materials to inhibit moisture intrusion; Based on this, the damage driving force caused by freeze-thaw phase transition is expressed as: ,in Equivalent damage driving force induced by freeze-thaw phase change The freeze-thaw sensitivity coefficient reflects the degree to which a material responds to changes in moisture content. The coefficient of volume expansion caused by pore water freezing; The above model shows that surface protection reduces This can significantly weaken the source driving mechanism of freeze-thaw damage; Step 2: Establishment of a damage blocking model for local repair and crack intervention: For situations where the comprehensive freeze-thaw damage variables are at a medium to high level and damage evolution is accelerated, the core role of local crack repair is to restore the effective local bearing area and block the crack propagation channel, as follows: ； in: The equivalent freeze-thaw damage variable for the repaired local area; For the freeze-thaw damage variables in the local area before repair; This refers to the effective bearing area of ​​the concrete section before repair. This refers to the effective load-bearing area after repair. The above model quantitatively reflects the reversal effect of grouting and crack sealing measures on local freeze-thaw damage; Step 3: Establishment of an overall improvement model for structural durability strengthening: When the comprehensive freeze-thaw damage variable exceeds the critical threshold, it is necessary to improve the structure's freeze resistance at the overall level. The essence of structural strengthening lies in increasing the structure's "tolerance threshold" for freeze-thaw damage. The critical damage level after strengthening is defined as follows: ； in: The freeze-thaw damage failure threshold for unreinforced structures; This is the equivalent failure threshold after reinforcement; The structural reinforcement gain coefficient reflects the effect of external cladding and reinforcement measures on improving durability margin; The overall structural freeze-resistance reliability function is further defined as follows: ； in: This serves as a reliability indicator for the structure's freeze-thaw resistance and durability. This represents the current overall freeze-thaw damage variable; The above model shows that structural reinforcement, by increasing the upper limit of damage tolerance, enables the structure to maintain acceptable freeze-thaw reliability even at higher damage levels. For different stages of freeze-thaw damage, durability improvement models for surface protection, local repair, and structural reinforcement are established respectively. Engineering intervention measures are transformed into quantifiable mathematical expressions. With comprehensive freeze-thaw damage variables as the core, hierarchical control of freeze-thaw damage inhibition, propagation blocking, and allowable threshold improvement is achieved. This shifts durability improvement decisions from experience-based judgment to quantitative analysis, effectively delaying the freeze-thaw deterioration process of existing bridge and tunnel concrete in seasonally frozen areas and improving the structural freeze-thaw resistance reliability and engineering economy.

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