Method for modeling the reliability of the bond strength of geopolymer coatings to steel

Abstract

The application provides a geopolymer coating and steel material bonding strength reliability modeling method, relates to the technical field of steel material bonding strength reliability analysis, and through full-process data driving and probability modeling, the application collects multiple-source influence factor data and constructs a joint probability distribution, introduces a mapping relationship between a constitutive parameter and an influence factor into a constitutive model, realizes multi-factor self-adaptation and space coupling of structure performance, dynamically describes a time sequence degradation process of the steel material bonding strength in a service period in combination with a Markov degradation model, further introduces a Bayesian inversion method to realize dynamic updating of a parameter distribution, and quantifies a probability that a structure satisfies a safety standard by reliability integration. The overall scheme can not only truly reflect durability and safety of the structure under complex actual working conditions, effectively improve the scientificity and coverage of reliability evaluation under a long-term service environment, but also provide quantifiable tracking decision basis for engineering design, acceptance and operation and maintenance management.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of steel bonding strength reliability analysis, in particular to a geopolymer coating and steel bonding strength reliability modeling method. BACKGROUND

[0002] In the field of infrastructure engineering, building structure and bridge durability assessment, geopolymer coating steel is widely used in concrete structures in harsh environments to improve the interfacial bonding strength of steel and concrete due to its excellent protective performance. However, in the process of practical engineering application, the coating thickness, steel surface state, concrete quality, environmental temperature and humidity, corrosion medium concentration and service time and other multi-source influencing factors have significant influence on the bonding performance. These factors show high uncertainty and complex volatility in field construction, long-term service and environmental changes. The existing technology usually relies on empirical analysis or static parameter setting of a single working condition, which cannot fully reflect the multi-factor coupling and parameter time-varying degradation process of the actual engineering, and it is also difficult to scientifically quantify the reliability and risk of the structure in the whole life cycle, resulting in limitations in structure design and durability management.

[0003] In the prior art, the modeling method and prediction method for the reliability of the bonding strength between steel and concrete at high temperature with publication number CN109885964A are disclosed. The method uses the Fréchet distribution function to describe the distribution law of the measured value of the bonding strength between steel and concrete, and proposes a modeling method and prediction method for the reliability of the bonding strength between steel and concrete at high temperature, which provides technical support for damage assessment and prediction of the bonding interface between steel and concrete under high temperature. Although this scheme can predict the reliability of the bonding strength between steel and concrete at high temperature, it is only based on temperature single factor for static parameter fitting, without considering the joint action of multi-source influencing factors and the dynamic time sequence degradation of parameters, lacking full probability analysis and dynamic updating of the bonding strength reliability under actual complex working conditions, and the applicability and scientificity are limited.

[0004] The above information disclosed in the background section is only used to enhance the understanding of the background of the present disclosure, and therefore it can include information that does not constitute prior art known to those of ordinary skill in the art. SUMMARY

[0005] The purpose of the present application is to provide a geopolymer coating and steel bonding strength reliability modeling method to solve the problems raised in the background.

[0006] To achieve the above-mentioned purpose, the present application provides the following technical scheme:

[0007] The geopolymer coating and steel bonding strength reliability modeling method comprises the following specific steps:

[0008] S1: Collecting the multi-source influence factor data related to the bonding strength between the geopolymer coating and the steel material, fitting the probability distribution of each multi-source influence factor, and generating the joint probability distribution of the multi-source influence factors for random modeling;

[0009] S2: Performing the bonding-slip test under different combinations of multi-source influence factors, extracting the constitutive parameters of the bonding-slip based on the test data analysis, and establishing the mapping relationship between the constitutive parameters and the multi-source influence factors;

[0010] S3: Introducing the multi-source influence factors into the constitutive model of the bonding-slip, and realizing the coupling between the constitutive model and the multi-source influence factors based on the mapping relationship between the constitutive parameters and the multi-source influence factors;

[0011] S4: Describing the time-series degradation of the bonding strength based on the Markov degradation model, and modeling the change of the bonding strength of the steel material with the geopolymer coating during the service process;

[0012] S5: Setting the prior probability distribution of different constitutive parameters based on engineering experience, and then using the Bayesian inversion method based on the test data to perform posterior inference, obtaining the probability distribution of different constitutive parameters under the time-series degradation, and calculating the reliability of the steel material with the geopolymer coating during the service process to meet the preset bonding strength standard.

[0013] Preferably, the multi-source influence factors include but are not limited to the coating thickness, the steel material surface roughness, the concrete compressive strength, the environmental temperature and humidity, and the corrosion medium concentration.

[0014] The logic for generating the joint probability distribution of the multi-source influence factors is as follows:

[0015] Collecting several groups of multi-source influence factor data, fitting the probability distribution of each multi-source influence factor, and obtaining the probability density function of each multi-source influence factor;

[0016] Combining all the multi-source influence factors to obtain the influence factor vector and its joint probability distribution;

[0017] Where the influence factor vector is represented as:

[0018] ;

[0019] The joint probability distribution is represented as:

[0020] ;

[0021] In the formula, represents the influence factor vector, represents the th multi-source influence factor, and the subscript Index representing multi-source impact factors, This represents the total number of multi-source influence factors. This represents the joint probability distribution of the influencing factor vector. Indicates the first The probability density function of multiple influencing factors.

[0022] Preferably, step S2 includes the following sub-steps:

[0023] S201: Develop different impact factor vectors The bond-slip test under the combined conditions was used to obtain data pairs of slip and bond stress under the influence of the influencing factor vector. The bond stress was used to reflect the bond strength between steel with geopolymer coating and concrete.

[0024] S202: Extract constitutive parameters for each data pair, including but not limited to maximum bond stress and characteristic slip.

[0025] S203: Using the multiple regression method, the mapping relationship between constitutive parameters and multi-source influencing factors is established. The mapping function expression is as follows:

[0026] ;

[0027] ;

[0028] In the formula Indicates the maximum bond stress. Indicates the first Each characteristic slip amount, Index representing the characteristic slip amount, , , , All represent regression coefficients. , This represents random error.

[0029] Preferably, the constitutive model for the bond-slip relationship adopts the simplified CEB-FIB constitutive model, and the model expression is as follows:

[0030] ;

[0031] In the formula This indicates that the slip is Bond stress at that time ~ Both represent characteristic slip;

[0032] Introducing multi-source influencing factors into the above constitutive model, the coupled constitutive model expression is:

[0033] ;

[0034] wherein represents the bond stress when the slip is under the influence of the influence factor vector, ~ all represent the characteristic slip under the influence of the influence factor vector.

[0035] Preferably, the S4 comprises the following sub-steps:

[0036] S401: Collect the maximum bond stress of the steel material with the geopolymer coating under the influence of the influence factor vector at different service ages;

[0037] S402: Use the Markov degradation model to describe the change relationship between the maximum bond stress and the service age, and the expression is as follows:

[0038] ;

[0039] wherein represents the maximum bond stress at the service age under the influence of the influence factor vector, represents the strength retention coefficient at the service age under the influence of the influence factor vector, which is calculated from the data collected in step S401, represents the index of the service age;

[0040] S403: Recursion is performed according to the expression of the change relationship between the maximum bond stress and the service age to obtain the probability distribution of the maximum bond stress at different service ages.

[0041] Preferably, the S5 comprises the following sub-steps:

[0042] S501: Divide the constitutive parameters, the slip, the bond stress and the corresponding influence factor vector under the joint action of the influence factor vector and the service age into observation data, and divide the regression coefficients and the random error in the mapping function and the strength retention coefficient in the Markov degradation model into model parameters;

[0043] S502: Set the prior distribution of the model parameters, establish the likelihood function between the model parameters and the data to be predicted, perform posterior inference based on the Bayes formula, generate the probability density function of the bond stress at the service age under the influence of the influence factor vector and constantly update it;

[0044] S503: Set the minimum bonding stress and the maximum service life required based on engineering requirements, calculate the probability that the bonding stress of the steel material with the geopolymer coating is greater than the minimum bonding stress at the maximum service life, and output it as the reliability that meets the preset bonding strength standard.

[0045] Preferably, the reliability is represented as:

[0046] ;

[0047] The calculation method of the probability that the bonding stress of the steel material with the geopolymer coating is greater than the minimum bonding stress at the maximum service life is:

[0048] ;

[0049] In the formula, represents the reliability, represents the probability that the bonding stress is greater than the minimum bonding stress, represents the bonding stress when the slip amount under the action of the influence factor vector is at the maximum service life, represents the maximum service life, represents the minimum bonding stress, represents the probability density function of the bonding stress.

[0050] Preferably, when the reliability meets , it is considered that the steel material meets the engineering requirements, otherwise it does not meet the engineering requirements.

[0051] Compared with the prior art, the beneficial effects of the present application are:

[0052] The present application realizes multi-factor self-adaptation and spatial coupling of structural performance by full-process data driving and probability modeling, systematically collects multi-source influence factor data and constructs joint probability distribution, introduces the mapping relationship between constitutive parameters and influence factors into the constitutive model, realizes multi-factor self-adaptation and spatial coupling of structural performance; combined with the Markov degradation model, the time sequence degradation process of the bonding strength of the steel material during the service period is dynamically described, the Bayesian inversion method is further introduced to realize dynamic updating of the parameter distribution, and the reliability integral is used to quantify the probability that the structure meets the safety standard. The overall scheme not only can truly reflect the durability and safety of the structure under complex actual working conditions, effectively improve the scientificity and coverage of reliability evaluation under long-term service environment, but also can provide quantifiable tracking decision basis for engineering design, acceptance and operation management. BRIEF DESCRIPTION OF DRAWINGS

[0053] Fig. 1 is the flowchart of the overall method of the present application;

[0054] Fig. 2 is the flowchart of step S2 in the present application;

[0055] Fig. 3 A flowchart for step S4 in the present application;

[0056] Fig. 4 A flowchart for step S5 in the present application. DETAILED DESCRIPTION

[0057] For the purposes of the present application, the technical solutions and advantages are more clearly and specifically described below in further detail with reference to specific embodiments.

[0058] It should be noted that, unless otherwise defined, the technical terms or scientific terms used in the present application should be understood as the usual meanings understood by those skilled in the art to which the present application belongs. The terms "first", "second", and similar terms used in the present application do not represent any order, quantity, or importance, but are only used to distinguish different components. The terms "include" or "contain" and similar terms mean that the elements or objects listed before the terms cover the elements or objects listed after the terms and their equivalents, and do not exclude other elements or objects. The terms "connect" or "connected" and similar terms are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. The terms "up", "down", "left", "right", and the like are only used to represent relative positional relationships, and when the absolute positions of the described objects change, the relative positional relationships may also change accordingly.

[0059] EMBODIMENT

[0060] Please refer to Figs. 1-4 The present application provides a technical solution:

[0061] A method for modeling the reliability of the bonding strength between a geopolymer coating and steel, including the following specific steps:

[0062] S1: Collecting multi-source influence factor data related to the bonding strength between the geopolymer coating and the steel, fitting the probability distribution of each multi-source influence factor, and generating a joint probability distribution of the multi-source influence factors for random modeling.

[0063] Geopolymer, short for geopolymer, has not only fire resistance and excellent adhesion and corrosion resistance, but also is more environmentally friendly than traditional metal coatings, compound coatings, etc. Therefore, it is currently commonly used as a steel coating to protect steel reinforced concrete structures from corrosion and durability problems.

[0064] The multi-source influence factors include, but are not limited to, coating thickness, steel surface roughness, concrete compressive strength, environmental temperature and humidity, and corrosion medium concentration.

[0065] The logic of generating the joint probability distribution of multi-source influence factors is as follows:

[0066] Collect several sets of multi-source influence factor data, and respectively fit the probability distribution of each multi-source influence factor to obtain the probability density function of each multi-source influence factor. When collecting data, it can be obtained by field measurement (such as multi-batch coating thickness, environmental temperature, etc.), historical engineering database or laboratory system test.

[0067] After a large amount of sample data is collected, descriptive statistics is performed, such as calculating the mean, standard deviation, extreme value, skewness, kurtosis, or drawing a histogram, box plot, etc., to observe the data distribution form. According to the distribution form of the data and engineering experience, the possible probability distribution type is preliminarily selected. In engineering design, the common distribution types of multi-source influence factors include normal distribution (commonly used for various errors), lognormal distribution (typical for non-negative skewed data such as coating thickness, concrete compressive strength, etc.), Weibull distribution, etc. After selecting the distribution model, the distribution parameters are estimated using sample data, and the degree of agreement between the selected distribution and the actual sample data is tested, such as goodness of fit. If the fitting is not ideal, the distribution type or distribution parameter should be changed until a reasonable fitting result is obtained. Finally, the probability distribution of each multi-source influence factor is expressed in the form of probability density function. Specifically, the estimation methods include maximum likelihood estimation, moment estimation, least squares method, etc., and the test methods include KS test, AD test, chi-square test, etc., which can be determined according to expert experience.

[0068] All multi-source influence factors are combined to obtain an influence factor vector and its joint probability distribution;

[0069] Where the influence factor vector is represented as:

[0070] ;

[0071] The joint probability distribution is represented as:

[0072] ;

[0073] Where represents the influence factor vector, represents the th multi-source influence factor, and the subscript represents the index of the multi-source influence factor, represents the total number of multi-source influence factors, represents the joint probability distribution of the influence factor vector, represents the probability density function of the th multi-source influence factor.

[0074] It can be understood that in real engineering, each multi-source influencing factor itself has volatility and uncertainty. In this step, the probability distribution of each multi-source influencing factor is determined and the joint probability distribution is constructed through data collection and statistical analysis. Thus, all subsequent model inputs are no longer single deterministic values, but a "distribution" with statistical characteristics, laying a foundation for subsequent random analysis (i.e. reliability evaluation). That is, if the joint probability distribution is not constructed, the model can only be corrected for a single scenario, and the reliability analysis cannot reflect the overall engineering scenario. On the contrary, through the joint probability distribution, different influencing factor vectors can be generated in batches to simulate thousands of "possible scenarios", which are then substituted into the constitutive model to obtain the distribution of other parameters, so as to statistically obtain the probability of "safe" or "unsafe" events, and obtain the global engineering reliability or risk level.

[0075] Unlike the single working condition used in traditional technology, in this step, the randomness and volatility of each influencing factor are reflected through a large amount of actual data collection, statistical fitting and probability distribution construction, so that the model can consider the coupling effect of multiple factors at the same time, truly reflect the actual results of the joint action of multiple variables under complex engineering scenarios, and better fit the actual engineering conditions, so as to cover all possible real scenarios, predict more reliable results, and have a wider range of applications.

[0076] S2: Perform bond-slip tests under different combinations of multi-source influencing factors, extract the bond-slip constitutive parameters based on the test data analysis, and establish the mapping relationship between the constitutive parameters and the multi-source influencing factors.

[0077] S2 includes the following sub-steps:

[0078] S201: Perform bond-slip tests under different combinations of influencing factor vectors, and obtain data pairs of slip and bond stress under the action of the influencing factor vectors;

[0079] S202: Extract the constitutive parameters for each data pair, including but not limited to the maximum bond stress and the characteristic slip;

[0080] S203: Use multivariate regression method to establish the mapping relationship between the constitutive parameters and the multi-source influencing factors, and the mapping function expression is as follows:

[0081] ;

[0082] ;

[0083] In the formula, represents the maximum bond stress, represents the characteristic slip, ​​an index representing a characteristic slip amount, , , , all represent regression coefficients, , represent random errors.

[0084] It can be understood that the bond stress refers to the actual shearing force on the unit area interface between the steel bar and the concrete during the force process, and thus can be used to reflect the bond strength. Various data involved in the scheme can be obtained by testing the construction test piece. The test adopts the center pull-out test, and the test piece is made according to the provisions in the relevant engineering standards. In this embodiment, the test piece is designed to be 150mmx150mmx150mm, a customized detachable steel mold is used, the free end of the test piece is 20mm beyond the surface of the concrete to facilitate the lead-out of the strain gauge lead wire and the placement of the displacement meter, considering the space limitation of the loading frame and the minimum requirement of the specification, 150mm of the steel bar at the loading end is reserved, the steel bar in the non-bonding section is spaced apart from the concrete by a PVC sleeve, when pouring the test piece, the steel bar is at the center position of the test mold, at the same time, the strain gauges are evenly and alternately arranged within the bonding length, the lead wire is led out from the free end, and the epoxy resin is coated on the steel bar groove and the cut surface, the two half steel bars are closed, and the binding wire is cut after the epoxy resin is solidified, and finally the test piece is poured into a mold by using a steel mold. Finally, when performing the test, the test piece is placed on the reaction frame, the reaction frame can be connected to the upper clamp of the testing machine through the upper holding screw, the upper clamp can keep the reaction frame vertically suspended after clamping the screw, and the test piece is placed on the steel plate below the reaction frame, and the steel bar is clamped by the lower clamp of the testing machine, so that the test loading can be performed. A large number of data samples can be obtained by modifying the parameters of various multi-source influencing factors.

[0085] In this step, a large number of samples are collected by large sample tests, the constitutive parameters under different combinations of influencing factors are collected, the constitutive parameters are converted from a single constant to a multi-factor function, so as to better reflect the actual change rule of the material performance. Moreover, the parameter distribution and the factor functionization make the subsequent output also be distributed, so that the whole modeling process supports reliability and probability analysis, rather than only giving a single result. That is to say, without this step, the subsequent input can only use fixed parameters, and the automatic adjustment and prediction of the structure performance under different working conditions cannot be realized.

[0086] S3: Introducing multi-source influencing factors into the bond-slip constitutive model, and realizing the coupling of the constitutive model and the multi-source influencing factors based on the mapping relationship between the constitutive parameters and the multi-source influencing factors.

[0087] The bond-slip constitutive model adopts a simplified CEB-FIB constitutive model, and the model expression is as follows:

[0088] ;

[0089] where is the bond stress at the slip amount of , ~ Each of them represents a characteristic slip amount. Characteristic slip amounts are several key slip amounts in the bond-slip curve, which have physical meanings. Each of them usually corresponds to a turning point of the mechanical behavior of a stage. Take the CEB-FIP model as an example, three characteristic slip amounts are commonly used, is the initial yield amount, which represents the slip amount of , is the plateau amount, which represents the slip amount of ~ , is the failure amount, which represents the slip amount of

[0090] From the simplified CEB-FIB model, in order to reduce the calculation amount, the exponent of is set to 1, and the bond stress at the slip amount of is set to 0. This is because in actual tests, the initial bond stress is mainly determined by the mechanical interlocking effect and the interface friction, and it can often be described by an approximate linear relationship. Especially when the interface of the test specimen itself is consistent and the data noise is not significant, the linear assumption can meet the engineering accuracy requirements. Therefore, in scenarios such as large-scale data processing or Monte Carlo simulation, which require repeated invocation of the constitutive model, the power function will significantly increase the calculation amount. By setting the exponent to 1, it becomes a linear relationship. At the slip amount of ,it can be ensured that when the slip amount exceeds the limit, the model will not produce unreasonable residual bond stress, ensuring the engineering safety and conservation of the predicted value. This simplification meets the actual engineering requirements and is allowed by the CEB-FIB constitutive model, which helps parameter regression and multi-source factor coupling, greatly simplifying subsequent calculations and parameter regression, thereby improving the engineering efficiency of the model.

[0091] By introducing multi-source influencing factors into the above constitutive model, the expression of the coupled constitutive model is:

[0092] ;

[0093] where is the bond stress at the slip amount of , Both represent the characteristic slip amount under the action of the influence factor vector.

[0094] In this step, the multi-source influence factor is introduced into the constitutive model for coupling, so that the parameters in the constitutive model are no longer fixed values, but are self-adapted as functions of the multi-source influence factor through a mapping relationship. Each combination of different multi-source influence factors can obtain a corresponding influence factor vector, thereby deriving a unique set of constitutive parameters, accurately simulating the structural response in any scenario, not just the result of a typical scenario, enabling the model to automatically adapt to the performance under different environmental, material and working condition combinations, greatly enhancing the flexibility and practical engineering applicability of the model. That is, this step is equivalent to a "bridge" connecting the input and output, ensuring that the input uncertainty can be completely transmitted and reflected in the subsequent distributions. Moreover, since the constitutive parameters can be directly "automatically given" by the influence factor, one-to-one efficient simulation and analysis can be achieved, without the need for repeated parameter regression or manual adjustment, greatly improving the calculation efficiency.

[0095] S4: The time sequence degradation of the bond strength is described based on the Markov degradation model, and the change of the bond strength of the steel material with the geopolymer coating during the service process is modeled. The Markov recursive formula is used to model the change of the bond strength as "annual recursion", which can reflect the dynamic process of degradation over time and facilitate tracking of the performance change every year, providing a scientific basis for structure life prediction.

[0096] S4 includes the following sub-steps:

[0097] S401: Collect the maximum bond stress of the steel material with the geopolymer coating under the action of the influence factor vector at different service life;

[0098] S402: The Markov degradation model is used to describe the change relationship between the maximum bond stress and the service life, and the expression is as follows:

[0099]

[0100] In the formula, F (t) represents the maximum bond stress at the t-th service year under the action of the influence factor vector, F (t) represents the strength retention coefficient at the t-th service year under the action of the influence factor vector, which is calculated from the data collected in step S401, F (t) represents the strength retention coefficient at the t-th service year under the action of the influence factor vector, which is calculated from the data collected in step S401, F (t) represents the strength retention coefficient at the t-th service year under the action of the influence factor vector, which is calculated from the data collected in step S401, F (t) represents the strength retention coefficient at the t-th service year under the action of the influence factor vector, which is calculated from the data collected in step S401, F (t) represents the strength retention coefficient at the t-th service year under the action of the influence factor vector, which is calculated from the data collected in step S401,

[0101] The strength retention coefficient calculation formula is derived from the change relationship between the maximum bond stress and the service life:

[0102] ​​ ;

[0103] Wherein each parameter on the right side can be obtained by step S401.

[0104] Here the strength retention coefficient is also modeled as a probability distribution (usually normal distribution) rather than a fixed value, fully reflecting the uncertainty and volatility of degradation under the influence of environment, material, coating state, etc., making the model results more realistic.

[0105] S403: Recursion according to the expression of the change relationship between the maximum bond stress and the service life to obtain the probability distribution of the maximum bond stress under different service lives.

[0106] In this step, by considering the time sequence effect of service life, a Markov degradation model is introduced, so as to not only reflect the spatial (influence factor) difference, but also accurately depict the degradation process on the time axis, realize the space-time global modeling of structure performance, and enable the subsequent reliability analysis to be aimed at different states, realize the safety and risk analysis of "whole life cycle".

[0107] S5: Based on engineering experience, set the prior probability distribution of different constitutive parameters, and then based on the test data, use the Bayesian inversion method for posterior inference to obtain the probability distribution of different constitutive parameters under the time sequence degradation effect, and calculate the reliability of steel with geopolymer coating in the service process to meet the preset bond strength standard.

[0108] S5 includes the following sub-steps:

[0109] S501: Divide the constitutive parameters, slip, bond stress and corresponding influence factor vectors under the joint action of influence factor vectors and service life into observation data, and divide the regression coefficients and random errors in the mapping function and the strength retention coefficients in the Markov degradation model into model parameters.

[0110] It can be understood that in Bayesian analysis, it is necessary to distinguish between which are observation data (real measurement or test, used for fitting and correction of model) and which are model parameters (describe the system law, need to be determined by data inference), Regression coefficients, strength retention coefficients and other parameters cannot be directly measured, but can only be inversely calculated or estimated depending on observation data, so clear division is the premise of subsequent inference.

[0111] S502: Set the prior distribution of the model parameters, establish the likelihood function between the model parameters and the data to be predicted, and based on the Bayesian formula, carry out posterior inference to generate the probability density function of the bond stress under the action of the influence factor vector at the service of the year and continuously update it.

[0112] Bayesian analysis is the mainstream method for engineering uncertainty modeling and parameter identification, which can combine subjective experience (prior) and objective test data (likelihood) to form a dynamic and updateable posterior inference. The prior distribution reflects the engineering experience and historical knowledge, and the likelihood function reflects the probability relationship between the parameter change and the actual observation value. Moreover, the posterior inference can be continuously corrected with the accumulation of new data. When setting the prior distribution, sample data under various working conditions are collected in advance, so a reasonable probability distribution (such as normal, uniform, lognormal, etc.) can be set for each model parameter (such as regression coefficient, strength retention coefficient) based on these data, reflecting the preliminary confidence and uncertainty of the parameter. Then the probability relationship between the model parameters and the observation data (i.e. the likelihood function) is constructed, which is usually assumed to follow a normal distribution. Finally, Bayesian theorem is applied to combine the prior distribution and the likelihood function to obtain the posterior inference, thereby generating the probability density function of the bond stress of steel under a specific influencing factor and service life, which can be continuously updated with new data.

[0113] S503: Based on the engineering requirements, set the minimum bond stress and the maximum service life required, calculate the probability that the bond stress of the steel with geopolymer coating is greater than the minimum bond stress at the maximum service life, and output it as the reliability of meeting the preset bond strength standard.

[0114] The reliability is represented as:

[0115] ;

[0116] The calculation method of the probability that the bond stress of the steel with geopolymer coating is greater than the minimum bond stress at the maximum service life is:

[0117] ;

[0118] In the formula, represents the reliability, represents the probability that the bond stress is greater than the minimum bond stress, represents the bond stress when the slip amount under the influence of the influencing factor vector is at the maximum service life, represents the maximum service life, represents the minimum bond stress, represents the probability density function of the bond stress.

[0119] From this integral formula, it can be seen that the actual meaning it reflects is in all possible maximum bond strength value intervals (i.e. to ), and the probability density in the interval is counted, so as to obtain the probability of the event that the bonding strength is greater than the safety standard (i.e. the minimum bonding stress), which is used to measure the probability that the bonding strength of the steel material with the geopolymer coating reaches the safety standard during the service period, so as to reflect the durability and safety, and serve as a judgment index of reliability.

[0120] When the reliability meets , it is considered that the steel material meets the engineering requirements, otherwise it does not meet the engineering requirements.

[0121] In this step, by introducing the Bayesian inversion method for analysis, the traditional static and empirical structure performance evaluation method can be upgraded to dynamic, distributed and probabilistic intelligent reliability analysis, supporting dynamic evaluation and risk control in the whole life cycle, so as to provide quantitative indexes and scientific basis for engineering management, structure design and maintenance decision.

[0122] The above formulas are dimensionless numerical calculations, the formulas are obtained by collecting a large amount of data to simulate the latest real situation, and the preset parameters in the formulas are set by the person skilled in the art according to the actual situation.

[0123] The above embodiments can be realized wholly or partially by software, hardware, firmware or any combination thereof. When realized by software, the above embodiments can be realized wholly or partially in the form of a computer program product. Those skilled in the art can realize that the units and algorithm steps of the examples described in connection with the embodiments disclosed herein can be realized by electronic hardware or a combination of computer software and electronic hardware. Whether the functions are realized by hardware or software methods depends on the specific application and design constraints of the technical solutions.

[0124] The units described as separate components can or can not be physically separated, and the components shown as units can or can not be physical units, which can be located in one place or distributed on multiple network units. Part or all of the units can be selected according to actual needs to achieve the purpose of the embodiments.

[0125] The above is only a specific embodiment of the present application, but the protection scope of the present application is not limited thereto, and any person skilled in the art can easily think of changes or replacements within the technical scope disclosed in the present application, which should be covered within the protection scope of the present application.

Claims

1. A method for modeling the reliability of the bond strength between geopolymer coatings and steel, characterized in that, The specific steps include: S1: Collect multi-source influencing factor data related to the bonding strength between the geopolymer coating and the steel, fit the probability distribution of each multi-source influencing factor to generate the joint probability distribution of the multi-source influencing factors, and randomly generate different combinations of multi-source influencing factors based on the joint probability distribution as inputs for subsequent models. S2: Conduct bond-slip experiments under different combinations of multi-source influencing factors, extract constitutive parameters of bond-slip based on experimental data analysis, and establish the mapping relationship between constitutive parameters and multi-source influencing factors; S3: Introduce multi-source influence factors into the bond-slip constitutive model, and realize the coupling of constitutive model and multi-source influence factors based on the mapping relationship between constitutive parameters and multi-source influence factors; S4: Based on the Markov degradation model, the temporal degradation of bond strength is described, and the change of bond strength of steel with geopolymer coating during service is modeled. S5: Based on the prior probability distribution of different constitutive parameters, and then using the Bayesian inversion method to perform posterior inference based on the experimental data, the probability distribution of different constitutive parameters under the action of time degradation is obtained, and the reliability of steel with geopolymer coating in meeting the preset bond strength standard during service is calculated accordingly.

2. The method for modeling the reliability of the bond strength between the geopolymer coating and steel according to claim 1, characterized in that: The multi-source influencing factors include, but are not limited to, coating thickness, steel surface roughness, concrete compressive strength, ambient temperature and humidity, and concentration of corrosive media; The logic for generating the joint probability distribution of multi-source influence factors is as follows: Collect several sets of multi-source impact factor data, and fit the probability distribution of each multi-source impact factor to obtain the probability density function of each multi-source impact factor. All multi-source impact factors are combined to obtain an impact factor vector, and their joint probability distribution is obtained. The influence factor vector is represented as follows: The joint probability distribution is expressed as: In the formula Represents the vector of influence factors. Indicates the first Multiple source influencing factors, subscript An index representing multi-source impact factors. This represents the total number of types of multi-source influencing factors. This represents the joint probability distribution of the influencing factor vector. Indicates the first The probability density function of multiple influencing factors.

3. The method for modeling the reliability of the bond strength between the geopolymer coating and steel according to claim 2, characterized in that: S2 includes the following sub-steps: S201: Develop different impact factor vectors The bond-slip test under the combined conditions was used to obtain data pairs of slip and bond stress under the influence of the influencing factor vector. The bond stress was used to reflect the bond strength between steel with geopolymer coating and concrete. S202: Extract constitutive parameters for each data pair, including but not limited to maximum bond stress and characteristic slip. S203: Using the multiple regression method, the mapping relationship between constitutive parameters and multi-source influencing factors is established. The mapping function expression is as follows: In the formula Indicates the maximum bond stress. Indicates the first Each characteristic slip amount, Index representing the characteristic slip amount, , , , All represent regression coefficients. , This represents random error.

4. The method for modeling the reliability of the bond strength between the geopolymer coating and steel according to claim 3, characterized in that: The constitutive model for the bond-slip relationship adopts a simplified CEB-FIB constitutive model, and the model expression is as follows: In the formula This indicates that the slip is Bond stress at that time ~ Both represent characteristic slip; Introducing multi-source influencing factors into the above constitutive model, the coupled constitutive model expression is: In the formula This indicates that, under the influence of the influence factor vector, the slip is... Bond stress at that time ~ Both represent the feature slippage under the influence of the factor vector.

5. The method for modeling the reliability of the bond strength between the geopolymer coating and steel according to claim 4, characterized in that: S4 includes the following sub-steps: S401: Collect the maximum bond stress of steel with geopolymer coating at different service years under the influence factor vector; S402: The relationship between maximum bond stress and service life is described using a Markov degradation model, as shown in the following expression: In the formula This indicates that under the influence of the influence factor vector, the service term... Maximum bond stress at year , This indicates that under the influence of the influence factor vector, the service term... The strength retention coefficient over the years is calculated from the data collected in step S401. An index indicating years of service; S403: Based on the expression for the relationship between maximum bond stress and service life, the probability distribution of maximum bond stress under different service years is obtained by recursion.

6. The method for modeling the reliability of the bond strength between the geopolymer coating and steel according to claim 5, characterized in that: S5 includes the following sub-steps: S501: Constitutive parameters, slip, bond stress and corresponding influence factor vectors under the combined effect of influence factor vector and service life will be divided into observation data, and regression coefficients and random errors in the mapping function and strength retention coefficients in the Markov degradation model will be divided into model parameters. S502: Define the prior distribution of model parameters, establish the likelihood function between model parameters and the data to be predicted, perform posterior inference based on Bayes' theorem, and generate the service-ready data under the influence of the influence factor vector. The probability density function of the bond stress over a year is obtained and continuously updated. S503: Based on engineering requirements, set the minimum bond stress and maximum service life, calculate the probability that the bond stress of the steel with the geopolymer coating is greater than the minimum bond stress at the maximum service life, and output it as the reliability of meeting the preset bond strength standard.

7. The method for modeling the reliability of the bond strength between geopolymer coatings and steel according to claim 6, characterized in that: The reliability is expressed as: The probability that the bond stress of steel with a geopolymer coating is greater than the minimum bond stress at the maximum service life is calculated as follows: In the formula Indicates reliability. This represents the probability that the bond stress is greater than the minimum bond stress. This represents the slip at the maximum service life under the influence of the factor vector. The bond stress, Indicates the maximum service life. Indicates the minimum bond stress. The probability density function represents the bond stress.

8. The method for modeling the reliability of the bond strength between the geopolymer coating and steel according to claim 7, characterized in that: When reliability satisfies If the steel meets the project requirements, it is considered to meet the requirements; otherwise, it does not.

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