Method for evaluating durability life of reinforced concrete structure in chlorine salt environment

Abstract

Aiming at the problem of evaluating the durability life of the reinforced concrete structure in the chlorine salt environment, the invention provides the method for evaluating the durability life of the reinforced concrete structure in the chlorine salt environment, and according to the durability degradation process of the reinforced concrete structure, a steel bar initial rust, concrete protective layer cracking and critical crack width limit state expression is established. Based on the basic principle of a design value method, a probability durability design expression of the durability degradation three stages of the reinforced concrete structure is established. Reliability analysis is carried out according to the established probability durability expression, and the result shows that compared with an existing method, the probability durability design method established through the design value method has higher reliability control precision; the relative errors between the target reliability indexes based on the steel bar initial rust life criterion, the concrete protective layer cracking life criterion and the critical crack width life criterion and the actual reliability indexes are 5%, 7% and 7.8% respectively, and the method can be used for evaluating the durability life of the reinforced concrete structure.

Description

Technical Field

[0001] The present invention relates to the field of civil engineering, and particularly to a method for evaluating the durability life of a reinforced concrete structure in a chloride environment. Background Art

[0002] In a chloride environment, the degradation of the performance of a concrete structure due to the corrosion of steel bars caused by chloride ion erosion is a key factor in the durability problem of the concrete structure. Affected by many uncertain factors, chloride ion erosion is a random process. Therefore, the durability of a concrete structure in a chloride environment is a probabilistic problem. Studying the durability of a concrete structure using a probabilistic method is a major trend in the development of the durability of a concrete structure. In recent years, a large number of studies have been conducted on the probabilistic model of the entire life cycle of a concrete structure. Currently, the probabilistic model of the entire life of a concrete structure is divided into three stages, namely, the initial rust stage of the steel bar, the stage from the initial rust of the steel bar to the cracking of the concrete, and the stage when the concrete crack reaches the maximum value or affects the normal use.

[0003] Currently, the probabilistic design method for concrete durability is mainly the partial factor method based on probability, which is an internationally recognized structural reliability design method and an important basis for the current structural design code system in China. There have been many studies on concrete durability in the prior art. Deby et al. selected the cover thickness of the concrete as the durability design parameter and carried out a probabilistic analysis of the durability of a concrete structure in a marine environment; Schiess et al. calculated the reliability index that meets the service life requirements starting from the analytical expression of the cover thickness; Liu Hai et al. used the Monte Carlo method to simulate the randomness of the cover thickness of the concrete and the cube compressive strength of the concrete, and the values of the durability design parameters can be obtained at a certain reliability level; Zhong et al. based on the three stages of the structural durability research, introduced the resistance partial factor and the load partial factor according to the characteristics of the structural performance degradation in a chloride erosion environment, and established a durability design expression for the three stages of durability degradation in a chloride erosion environment through a probabilistic method. In the above methods, the value of the partial factor is the key parameter for controlling the reliability, but its calculation is cumbersome, and the value-taking method lacks flexibility, and it cannot directly reflect the relationship between the probability characteristics of random variables, the target reliability index, and the design service life, and the reliability control accuracy needs to be improved. Summary of the Invention

[0004] The purpose of the present invention is to provide a method for evaluating the durability life of a reinforced concrete structure in a chloride environment to solve the technical problems raised in the above background art.

[0005] To solve the above problems, the present invention adopts the following technical solutions to solve:

[0006] In the first aspect, the present invention provides a method for evaluating the durability life of a reinforced concrete structure in a chloride environment, which includes:

[0007] The durability degradation process of reinforced concrete structures in a chloride environment is divided into a first stage, a second stage, and a third stage;

[0008] In the first stage, from the time the structure is put into service until the initial rusting of the steel bars, it is assumed that the initial rusting time t1 of the steel bars is not less than the first design service life T1; taking the reference chloride ion diffusion coefficient D0, the surface chloride ion concentration C s , and the concrete cover thickness c as random variables, the design values of each random variable are obtained based on the design value method, and the structural durability design expression of the initial rusting life criterion of the steel bars is obtained;

[0009] In the second stage, from the initial rusting of the steel bars until the surface of the concrete cracks, it is assumed that the time t2 when cracks occur in the concrete structure is not less than the second design service life T2. Taking the concrete cover thickness c and the concrete cube compressive strength f c as random variables, the design values of each random variable are obtained based on the design value method, and the structural durability design expression of the concrete cover cracking life criterion is obtained;

[0010] In the third stage, from the surface cracking of the concrete until the cracks reach the limit value, it is assumed that the time t3 when the cracks in the concrete structure develop to critical cracks is not less than the third design service life T3. Taking the concrete cover thickness c and the concrete cube compressive strength f c as random variables, the design values of each random variable are obtained based on the design value method, and the structural durability design expression of the critical crack width life criterion is obtained;

[0011] The structural durability design expressions of the three life criteria are used for reliability analysis to obtain the reliability analysis results.

[0012] As a preferred embodiment, the target reliability index β within the first design service life T1, the second design service life T2, and the third design service life T3 is determined by the JC method.

[0013] As a preferred embodiment, the initial rusting time t1 of the steel bars is calculated using a pre-corrected chloride ion diffusion model and is not less than the first design service life T1. The formula is expressed as:

[0014]

[0015] η1 = C(x,t) - C cr = 0

[0016]

[0017] Where: C(x,t) is the chloride ion concentration at the depth of x at time t; is the error function; q T is the temperature coefficient, qRH is the relative humidity coefficient, q t is the time-varying coefficient of concrete age; C S is the chloride ion concentration on the surface of the diffusion medium, C0 is the initial chloride ion concentration inside the diffusion medium, and D0 is the chloride ion diffusion coefficient under standard temperature and humidity curing of concrete;

[0018] H c is the relative humidity of the concrete curing environment; H is the relative humidity in the service environment; t0 is the initial age of the concrete structure; m is the age attenuation coefficient; T0 is the curing temperature of the concrete; U is the energy coefficient; R is the gas parameter, η1 represents the ultimate state of the initial rust of the steel bar, C cr represents the critical value of the chloride ion concentration.

[0019] As a preferred embodiment, the structural durability design expression of the initial rust life criterion of the steel bar is:

[0020]

[0021] In the formula, t 1d represents the service life of the first stage, c d , D 0d , C sd respectively represent the design values of the concrete cover thickness c, the reference chloride ion diffusion coefficient D0, and the surface chloride ion concentration C s of.

[0022] As a preferred embodiment, the structural durability design expression of the concrete cover cracking life criterion is:

[0023]

[0024] In the formula, t 1d represents the service life of the first stage, W / C represents the water-cement ratio; c represents the concrete cover thickness, n1, n2, n3 are the coefficient values corresponding to different steel bar types, d is the steel bar diameter, c d and f cd respectively represent the design values of the concrete cover thickness c and the concrete cube compressive strength f c of.

[0025] As a preferred embodiment, the structural durability design expression of the critical crack width life criterion is:

[0026]

[0027] In the formula, t 1d represents the design value of the initial rust time of the steel bar, Δt 2dIt represents the design value of the time experienced from the initial rusting of the steel bars to the cracking of the concrete protective layer, w cr is the critical value of the maximum crack width for concrete cracking; k is the condition coefficient after steel bar corrosion; c is the thickness of the concrete protective layer; f c is the cube compressive strength of the concrete, and m1, m2, and m3 are the coefficient values corresponding to different steel bar types, c d and f cd respectively represent the design values of the concrete protective layer thickness c and the cube compressive strength f of the concrete c of the design value.

[0028] As a preferred embodiment, the method further includes: substituting the design values of the random variables in the first stage into the calculation formula of the initial rusting time t1 of the steel bars to obtain the design value t1d of the initial rusting time t1 of the steel bars as the service life of the first stage, substituting the design values of the random variables in the second stage into the calculation formula of the time t2 when cracks occur in the concrete structure to obtain the design value t2d of the time t2 when cracks occur in the concrete structure as the service life of the second stage, substituting the design values of the random variables in the third stage into the calculation formula of the time t3 when the cracks in the concrete structure develop to the critical cracks to obtain the design value t3d of the time t3 when cracks occur in the concrete structure as the service life of the third stage, and cumulatively summing the service lives of the first stage, the second stage, and the third stage to obtain the total service life; comparing the total service life with the design life to evaluate whether the reinforced concrete structure meets the design requirements.

[0029] Compared with the prior art, the present invention has the following beneficial effects:

[0030] 1. According to the durability degradation process of reinforced concrete structures in a chloride environment, the present invention establishes degradation models and limit states for each stage. Based on the basic principle of the design value method, the present invention establishes a durability probability design expression for the performance degradation of reinforced concrete structures in a chloride erosion environment in three stages. Using this expression for reliability analysis, the results show that the relative error between the reliability index of each stage and the actual reliability index is controlled within 8%, and it can be used for the durability design of reinforced concrete structures. And the newly established expression solves the defects of the general applicability, flexibility, etc. of the reliability analysis by the partial factor method, which is convenient for the owner to select different target reliability indexes and use new statistical data.

[0031] 2. The corrected chloride ion diffusion model in the present invention can more accurately simulate the actual diffusion process of chloride ions. Using this method to numerically simulate the case and comparing it with the measured values, the results show that the fitting degree between the measured values and the simulated values is relatively high, proving the applicability of the diffusion model. At the same time, based on the Poisson correlation test, the means of the fitting data and the measured data are compared and analyzed, and the Pearson correlation coefficient is 0.931829, further verifying the applicability of the chloride ion diffusion model under the action of multiple factors to the actual engineering structure.

[0032] 3. According to the basic principle of the design value method, the present invention can directly calculate the design values of the random variables affecting the structure without introducing the reference sensitivity coefficient α0 and the reference target reliability index β0 to calculate the reference design values and partial coefficients of the variables, making the design more convenient. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 is a physical picture of the chloride salt erosion disease;

[0034] Figure 2 is a composition diagram of the service life of the chloride salt eroded concrete structure;

[0035] Figure 3 is a comparison diagram of the measured data of chloride ion concentration and the model fitting data. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0036] The present invention will be further described below with reference to the drawings. The following embodiments are only used to more clearly illustrate the technical solutions of the present invention and cannot be used to limit the protection scope of the present invention.

[0037] This embodiment provides a method for evaluating the durability life of a reinforced concrete structure in a chloride salt environment, and the specific content is as follows:

[0038] 1. Basic principle of the design value method

[0039] Among the prior arts known to the inventors of the present application, for the basic principle of the design value method, the international standard "General Principles of Structural Reliability" (ISO 2394: 1998) proposed a method for determining partial coefficients - the design value method. This method establishes the relationship between the probability characteristics, sensitivity coefficients, target reliability index of variables and the design values of variables, and defines the checking point of variables in reliability analysis as the design value. The basic expression is:

[0040] F X (x d ) = Φ(-αx) (1)

[0041] In the formula: F X (x d ) is the probability distribution function of the basic variable X; x dDesign value of the basic variable X; Φ(·) is the standard normal distribution function; α is the sensitivity coefficient, and β is the target reliability index. According to Equation (1), x d can be expressed as:

[0042] x d = F -1 [Φ(−αβ)] (2)

[0043] When the variable follows a normal distribution, it is obtained by the design value method:

[0044]

[0045] x d = μ x −αβσ x (4)

[0046] The partial factor can be expressed as the ratio of the design value to the standard value:

[0047]

[0048] The design value method can directly consider the probability characteristics of the basic variables and the influence of the target reliability index on the design results, fundamentally overcoming the flexibility and generality of the partial factor method. However, the current design value method lacks necessary practicality, that is, designers must understand the probability characteristics of each basic variable, the probability combination method of the involved actions, and the probability distribution of the actions at different time periods, resulting in difficulties in application. Therefore, the literature proposed the reference design value x d , and expressed the partial factor as the ratio of the design value to the reference design value.

[0049]

[0050] Among them, the reference design value α0, β0 are the reference values of the sensitivity coefficient and the target reliability index.

[0051] After determining the probability characteristics and reliability index of the random variable, the partial factor in the design expression is a univariate function of the sensitivity coefficient, and the reliability control accuracy of the design expression is determined by the sensitivity coefficient. At present, the value-taking methods of the sensitivity coefficient are not unified, mainly including the empirical value-taking method, the enumeration optimization method, the analytical optimization method, etc. The literature made a detailed comparison of the value-taking of the sensitivity coefficient. The analytical optimization method can obtain the optimal value of the sensitivity coefficient. Take the sensitivity coefficient of the main control parameter as ±0.85, the non-main control parameter as ±0.35, and take the positive value if the parameter is beneficial to the structure and the negative value if it is unfavorable, which is called the standard sensitivity coefficient.

[0052] 2. Durability degradation process of reinforced concrete structures under chloride erosion environment

[0053] Regarding the durability degradation process of reinforced concrete structures in a chloride salt erosion environment, the durability of concrete structures in a chloride salt erosion environment can be expressed as "the ability of a concrete structure to maintain its structural performance at an acceptable level under the combined action of chloride salt erosion and its own factors within a predetermined service life". There are various factors affecting the durability of concrete structures in a chloride salt erosion environment. Chloride ions enter the interior of the concrete, causing corrosion of the steel bars. As the steel bars continue to corrode, they eventually break, posing a safety hazard to the structure. Figure 1 Damage to reinforced concrete structures due to chloride ion erosion is presented.

[0054] For reinforced concrete structures in coastal areas, due to the large amount of chloride ions in the ocean, their service life is significantly reduced compared to other areas.

[20] . The durability degradation of reinforced concrete structures in a chloride salt environment is an irreversible and slow process, which can be divided into three stages: the stage from the structure's service to the initial rusting of the steel bars, the stage from the initial rusting of the steel bars to the cracking of the concrete surface, and the stage from the cracking of the concrete surface to the stage where the cracks reach the limit. The service life composition is as Figure 2 shown.

[0055] As Figure 2 can be seen, the time period t1 is the stage from the start of the structure's service to the initial rusting of the steel bars, that is, the chloride ion diffusion stage. In this stage, chloride ions enter the interior of the concrete and reach the surface of the steel bars through various ways such as

[0056] penetration or diffusion. When the chloride ion concentration on the surface of the steel bars reaches a certain value, the steel bars start to rust. Denote the limit state at this time as η1, and η1 is the durability limit state of the structure according to the initial rust life criterion of the steel bars. The time period t2 is the stage from the initial rusting of the steel bars to the cracking of the concrete, that is, the steel bar corrosion stage. In this stage, the steel bars in the concrete structure are gradually chemically corroded by chloride ions, continuously generating rust products. The rust products cause circumferential tensile stress around the steel bars in the concrete protective layer covering the steel bars. When the tensile stress is greater than the ultimate tensile bearing capacity of the concrete, the concrete surface cracks

[21] , and denote the limit state when the first crack appears on the concrete surface as η2, and η2 is the durability limit state according to the cracking life criterion of the concrete protective layer. The time period t3 is the stage from the cracking of the concrete surface until the cracks reach the limit. In this stage, due to the generation of cracks, it accelerates the entry of chloride ions, water, oxygen and other compounds in the environment into the interior of the structure, accelerates the corrosion of the steel bars, resulting in a decrease in the tensile capacity of the steel bars, and the cracks on the concrete surface become larger and larger. When the cracks on the concrete surface reach the maximum, the structure cannot meet the normal use conditions. Denote the limit state when the crack width of the concrete protective layer reaches the critical value as η3, and η3 is the durability limit state according to the critical crack width life criterion. The present invention will select the target reliability index according to the durability requirements of the limit state in each stage.

[0057] 3. Durability calculation model of reinforced concrete structures in a chloride salt erosion environment

[0058] 3.1 Chloride salt erosion environment concrete structure steel bar initial rust stage calculation model and numerical verification

[0059] Diffusion is the main transmission mode for chloride ions to enter the interior of the concrete structure, and diffusion is divided into two main forms: steady-state diffusion and non-steady-state diffusion. At present, the most commonly used chloride ion diffusion equation is the Fick's second law diffusion equation proposed by Callepari, but this diffusion equation is only applicable to the steady-state diffusion form where the diffusion coefficient D is a constant. In the actual chloride salt erosion environment during the service process of concrete, due to the influence of factors such as temperature, relative humidity and the age of concrete on the diffusion coefficient, the chloride ions in the concrete are in non-steady-state diffusion. Therefore, in this embodiment, the analytical solution of the Fick's second law chloride ion diffusion equation under one-dimensional diffusion is corrected to obtain a chloride ion diffusion model based on the action of multiple factors: the corrected chloride ion diffusion model can more accurately simulate the actual diffusion process of chloride ions. Using this method to numerically simulate the case and compare it with the measured value, the results show that the degree of fitting between the measured value and the simulated value is relatively high, which proves the applicability of the diffusion model. At the same time, based on the Poisson correlation test, the means of the fitting data and the measured data are compared and analyzed, and the Pearson correlation coefficient is 0.931829, further verifying the applicability of the chloride ion diffusion model under the action of multiple factors to the actual engineering structure.

[0060]

[0061] In the formula: C(x,t) is the chloride ion concentration at the depth of x at time t; is the error function; q T is the temperature coefficient, q RH is the relative humidity coefficient, q t is the time-varying coefficient of concrete age; C S is the chloride ion concentration on the surface of the diffusion medium, C0 is the initial chloride ion concentration inside the diffusion medium, and D0 is the chloride ion diffusion coefficient under the standard temperature and humidity curing of concrete, that is, the reference chloride ion diffusion coefficient. is the relative humidity of the concrete curing environment, generally taken as 0.75; H is the relative humidity in the service environment. t0 is the initial age of the concrete structure; m is the age attenuation coefficient, and for ordinary concrete, the value mostly concentrates on 0.3. T0 is the curing temperature of the concrete (generally taken as 293K); U = 35000 J / mol is the energy coefficient; R is the gas parameter, generally taken as 8.314 J / (mol·K).

[0062] To verify the applicability of the corrected chloride ion diffusion model, the measured value of the chloride ion concentration of the actual wharf structure is compared with the predicted value fitted by the corrected chloride ion diffusion model, and the results are as Figure 3As shown. The basic parameters of the structure and the measured data of chloride ions are shown in Table 1. N1, N2, and N3 are the measured values of chloride ion concentrations at different depths in the same direction for three groups.

[0063] Table 1 Basic parameters of wharf structure

[0064] Table 1 Basic parameters of wharf structure

[0065]

[0066] It can be seen from Figure 3 that the curve of the simulated chloride ion concentration values fitted by the modified chloride ion diffusion model has a high degree of fitting with the curve of the measured chloride ion concentration values in the project, which proves the rationality and applicability of the diffusion model. At the same time, the Pearson correlation coefficient based on the Poisson correlation test is used to verify the correlation between the simulated values and the measured values. The calculated Pearson correlation coefficient is 0.931829, indicating a strong data correlation, further verifying the applicability of the modified chloride ion diffusion model under the action of multiple factors to the actual engineering structure.

[0067] 3.2 Chloride salt erosion concrete structure rust depth calculation model and crack width calculation model

[0068] During the process of steel bar corrosion, the rust depth of the steel bar is used as a variable in the corrosion process before the concrete cover cracks. At present, there are many studies on the rust depth prediction model at home and abroad. The rust depth prediction model adopted in this embodiment is:

[0069]

[0070] In the formula: δ t is the rust depth of the steel bar at any time after the initial rust of the steel bar; t is the time elapsed from the start of the initial rust of the steel bar to the cracking of the concrete; λ(t) is the rust rate at time t after the initial rust of the steel bar, and the calculation formula is:

[0071]

[0072] In the formula, W / C represents the water-cement ratio; c represents the thickness of the concrete cover.

[0073] Based on the experimental and actual engineering test results in China's code, an expression for the critical rust depth δ cr of concrete cracking is established based on different steel bar types at the corners of the structure.

[0074]

[0075] In the formula, n1, n2, and n3 are the coefficient values corresponding to different steel bar types, as shown in Table 2.

[0076] Table 2 The value of the coefficient in the expression of the critical corrosion depth of steel bar

[0077] Table2 The value of the coefficient in the expression of the criticalcorrosion depth of steel bar

[0078]

[0079] At present, there are many studies on the calculation model of crack width at any time. The calculation expression of the maximum crack width on the concrete surface at any time after the concrete structure cracks in the chloride erosion environment adopted in this embodiment is:

[0080]

[0081] In the formula: w t is the maximum crack width at any time after the concrete cracks; k is the condition coefficient after the steel bar corrodes; c is the concrete cover thickness; f c is the cube compressive strength of the concrete; R w is the crack resistance coefficient of the concrete.

[0082] Condition coefficient after the steel bar corrodes:

[0083] k = 46k cr k ce e 0.04T (RH - 0.45) 2 / 3 (12)

[0084] In the formula: k cr is the steel bar position correction coefficient (1.6 for the corner and 1.0 for the middle); k ce is the local environment correction coefficient (4.0 for the outdoor environment in humid areas, 3.5 for the indoor environment in humid areas, 3.0 for the outdoor environment in dry areas, and 1.0 for the indoor environment in dry areas)

[0085] R w is related to the steel bar type, the cover thickness of the structure and the compressive strength of the concrete, and the expression is:

[0086] R w = m1 + m2f c + m3c (13)

[0087] In the formula, m1, m2, and m3 are the values of the coefficients corresponding to different steel bar types, as shown in Table 3.

[0088] Table 3 The value of the coefficient in the expression of the crack resistance coefficient of the concrete

[0089] Table 3 The value of the coefficient in the expression of concrete crack resistance coefficient

[0090]

[0091] 4. Durability expression of concrete structure under chloride erosion based on design value method

[0092] 4.1 Probability distribution of random variables

[0093] According to the probability model in Section 3, the design variables that need to consider randomness are determined. In the first stage, the reference chloride ion diffusion coefficient D0, the surface chloride ion concentration C s , and the concrete cover thickness c are regarded as random variables. In the second and third stages, the concrete cover thickness c and the concrete cube compressive strength f c are regarded as random variables. A large number of studies show that the reference chloride ion diffusion coefficient follows a normal distribution or a lognormal distribution. In this embodiment, D0 is regarded as a normal distribution, c is a normal distribution, f c is a normal distribution, and C s is a normal distribution. The probability distribution of random variables is shown in Table 4

[0094] Table 4 Probability distribution of random variables

[0095] Table 4 Probability distribution of random variables

[0096]

[0097] As can be seen from Section 1, the design value method follows a normal distribution. The design value and the reference design value of the variable are x d = μ x (1 - α x β T δ x ). Since the difference between the reference design value and the design value is only the different values of the target reliability index and the sensitivity coefficient, and the partial coefficient is the ratio of the design value to the reference design value, and the design value is the product of the partial coefficient and the reference design value, therefore, in this embodiment, the design value of the variable is directly calculated according to the design value method without repeating the calculation of the reference design value and the partial coefficient

[0098] 4.2 Durability expression of concrete based on the criterion of initial corrosion life of steel bars

[0099] 4.2.1 Establishment of durability expression

[0100] According to Section 2, the steel bars start to corrode when the chloride ion concentration on the surface of the steel bars reaches the critical value. Therefore, the critical value of the chloride ion concentration on the surface of the steel bars is taken as the ultimate state η1 of the initial corrosion of the steel bars, and it is obtained from Equation (7):

[0101] η1 = C(x, t) - C cr = 0 (14)

[0102] In the formula, x takes the concrete cover thickness, and the initial corrosion time t1 of the steel bars is solved by combining with (7). It is assumed that the structure meets the durability requirements, that is

[0103]

[0104] In the formula, T1 is the design service life of the structure, t1 is the initial corrosion time of the steel bars, and the formula is a function of the random variables c, D0, C s function.

[0105] It is assumed that the reliability index within T1 is determined by the JC method (single-variable normalization method) as β. At the design check point, there is

[0106]

[0107] Based on the probability-based design value method, from the coordinates of the design check points of each random variable sensitivity coefficient and the reliability index β, it is obtained that

[0108]

[0109] In the formula: F X (X * ) is the probability distribution function of each random variable; Φ() is the standard normal distribution function. If β is the target reliability index, then the coordinates at the design check point are the design values of the random variables:

[0110]

[0111] In summary, the durability design expression of the initial corrosion structure of steel bars based on the design values of random variables is obtained as:

[0112]

[0113] 4.2.2 Selection of Main Control Quantities and Reliability Analysis

[0114] Now, a reliability analysis is carried out on the reinforced concrete columns in the splash zone of the chloride salt erosion environment. The average annual temperature of the area where the components are located is 19°C, and the average relative humidity is 75%. The coefficient of variation is taken according to Table 1.

[0115] Based on the design value method, the design values of each random variable are obtained. Assuming that the design value of the initial rusting time of the steel bar is the design service life of the structure, the first-order second-moment method is adopted, and the actual reliability index is calculated through Equation (22) and compared with the target reliability index to calculate the relative error. The calculation results are shown in Table 5.

[0116] Table 5 Reliability analysis results

[0117] Table 5 Reliability analysis results

[0118]

[0119] As can be seen from Table 5, for the structure located in the tidal zone and the splash zone, when c is selected as the main control quantity, the error of the reliability index is small; from the reliability analysis results, for the expression obtained by the design value method, the relative error between the calculated reliability index and the actual reliability index is controlled within 5%, which can be used for the durability design of concrete structures in the newly built chloride erosion environment based on the initial rusting life criterion of steel bars.

[0120] 4.3 Based on the cracking life criterion of concrete cover

[0121] 4.3.1 Establishment of durability expression

[0122] When the steel bar starts to rust, when the rusting depth of the steel bar reaches the critical rusting depth δ cr the concrete cracks, and the corresponding concrete structure that does not allow cracking reaches the durability limit state η2. The limit state equation of η2 is expressed as:

[0123] η2 = δ t -δ cr = 0 (24)

[0124] In the formula: δ t is the rusting depth of the steel bar at any time; δ cr is the critical rusting depth, and its value is calculated according to Equation (10).

[0125] As can be seen from Section 2, the calculation model of the rusting depth of the steel bar at any time is:

[0126]

[0127] Denote Δt2 as the time elapsed from the initial rusting of the steel bar to the cracking of the concrete cover, and solve for Δt2:

[0128]

[0129] Since the component has experienced the initial rusting stage of the steel bars and the stage where corrosion causes concrete cracking, the design is carried out separately. Assuming that the structure meets the durability requirements, the time \(t_2\) for the concrete structure to crack should be not less than the second design service life \(T_2\) of the structure, that is:

[0130] \(t_2 - T_2=t_1+\Delta t_2 - T_2\geq0\) (27)

[0131] Therefore, the durability design expression for the structure in the concrete cover cracking stage is:

[0132] \(t\) 2d \(=t\) 1d \(+\Delta t\) 2d \(\geq T_2\) (28)

[0133] The design value \(t\) of the initial rusting time of the steel bars 1d is designed according to Equation (23): Assuming that the reliability index within \(T_2\) is determined by the JC method as \(\beta\), at the design check point:

[0134]

[0135] where \(x\) * is the coordinate of the design check point of the random variable \(X\), is the sensitivity coefficient.

[0136] The coordinates of the design check points of each random variable The corresponding sensitivity coefficients and the reliability index \(\beta\) have the following relationship:

[0137]

[0138] If \(\beta\) is the target reliability index, then the coordinates at the design check point are the design values of the random variables:

[0139]

[0140] In summary, the durability design expression of the structure based on the design values of the random variables of the critical crack width can be obtained as:

[0141]

[0142] 4.3.2 Selection of Main Control Quantities and Reliability Analysis

[0143] Assume various target reliability indices \(\beta\). For different main control quantities, reliability analysis is carried out based on the design expression of the concrete cover cracking life criterion. The steel bar diameter is selected as 20 mm, round steel bars at the corners, the water-cement ratio is taken as 0.4, and the random variables are selected according to Table 4. The reliability analysis results are shown in Table 6.

[0144] Table 6 Reliability analysis results

[0145]

[0146] As can be seen from Table 6, when c is selected as the main control variable, the reliability control accuracy of the structural durability design expression is higher, and the relative error of the reliability index is less than 7%. It can be used for the durability design of concrete structures in a newly built chloride erosion environment based on the cracking life criterion of the concrete cover.

[0147] 4.4 Based on the critical crack width life criterion

[0148] 4.4.1 Establishment of the durability expression

[0149] During the service process of the structure, the diffusion of chloride ions causes the steel bars in the concrete to corrode, and then cracks appear on the concrete surface. The maximum crack on the concrete surface gradually reaches its corresponding critical crack width w cr , indicating that the concrete structure reaches its durability limit state η3, and the limit state equation is:

[0150] η3 = w t - w cr = 0 (35)

[0151] As can be seen from Section 2, the expression of the crack width w t at any time of the structure is:

[0152]

[0153] In the formula: W / C is the water-cement ratio; c is the concrete cover thickness; f c is the cube compressive strength of concrete; d is the diameter of the steel bar; t2 is the time experienced by the concrete surface cracking.

[0154] Denote Δt3 as the time experienced from the concrete surface cracking to the maximum crack reaching the critical crack width. According to Eqs. (35) and (36), solve for Δt3:

[0155]

[0156] Assume that the structure meets the durability requirements. Then, the time t3 for the cracks in the concrete structure to develop to the critical crack should not be less than the design service life T3 of the structure, that is:

[0157] t3 - T3 = t 1d + Δt2 + Δt3 - T3 ≥ 0 (38)

[0158] Therefore, the durability design expression for the concrete cover cracking stage of the structure should be:

[0159] t 3d =t 1d +Δt 2d +Δt 3d -T3≥0 (39)

[0160] Design value of initial rusting time t 1d and rust expansion cracking time Δt 2d shall be calculated respectively according to the design expressions in Formulas (53) and (34). Assume that the reliability index within T3 determined by the JC method is β. At the design check point, there are:

[0161]

[0162] In the formula, x * is the coordinate of the design check point of the random variable X, is the corresponding sensitivity coefficient.

[0163] Coordinates of the design check point of each random variable Corresponding sensitivity coefficient and the reliability index β have the following relationship:

[0164]

[0165] If β is the target reliability index, then the coordinates at the design check point are the design values of the random variables, and there are:

[0166]

[0167] In summary, the structural durability design expression based on the design values of random variables is obtained as:

[0168]

[0169] 4.4.2 Selection of main control quantities and reliability analysis

[0170] According to Section 2.3, take c = 60mm, f c = 51.28 Mpa, the diameter d of circular steel bars is 20mm. Each variable is selected according to Table 4. For the outdoor environment in humid areas, the critical crack width value is taken as 1mm. Assume each target reliability index β. For different main control quantities, reliability analysis is carried out based on the design expression of the critical crack width life criterion, and the results are shown in Table 7.

[0171] Table 7 Reliability analysis results

[0172]

[0173] As can be seen from Table 7, select f cis the main control quantity, and the reliability control accuracy of the structural durability design expression is higher, with the relative error of the reliability index less than 7.8%. It can be used for the durability design of newly built concrete structures in chloride salt erosion environments based on the life of the critical crack width of concrete.

[0174] 5. Case Study

[0175] Design a reinforced concrete column in the splash zone in a chloride salt erosion environment. The water-cement ratio (W / C = 0.4), considering one-dimensional chloride ion diffusion, the average annual temperature in the area where the component is located is 19 °C, the average relative humidity is 75%, the age attenuation coefficient m = 0.3, the initial concrete age t0 = 28d, the initial chloride ion concentration C0 = 0, the critical chloride ion concentration C cr = 0.4%, the reference chloride ion diffusion coefficient is 25 mm 2 / a, the concrete cover is taken as 60 mm, the steel bar diameter is 20 mm, the steel bars are selected in two types: round and deformed, and the maximum crack allowed for the component is w cr = 1.0 mm, and the reliability indices for the three stages of concrete degradation are β = 1.28 (P f = 10%), β = 1.64 (P f = 5%) and β = 2.32 (P f = 1%). If the design life of the component is 45 years, the durability design method of the concrete structure in this embodiment is used to design the concrete column.

[0176] 5.1. Round Steel Bars:

[0177] (1) First, according to the known conditions in the case study, calculate the relative humidity influence coefficient q RH 、temperature influence coefficient q T values:

[0178]

[0179] (2) Calculate the design values of the first-stage random variables according to the known conditions

[0180] Design value of the concrete cover thickness:

[0181] c d = 60×(1 - 0.85×1.28×0.17) = 48.90 mm

[0182] Design value of the chloride ion diffusion coefficient:

[0183]

[0184] Design value of the surface chloride ion concentration:

[0185]

[0186] Service life of the first stage:

[0187]

[0188] (3) Calculate the design values of each random variable in the second stage according to the known conditions

[0189] c d = 60×(1 - 0.85×1.64×0.17) = 45.78 mm

[0190]

[0191] Service life of the second stage:

[0192]

[0193] (4) Calculate the design values and actual service life of the random variables in the third stage according to the known conditions

[0194] Concrete cover thickness:

[0195] c d = 60×(1 - 0.35×2.32×0.17) = 51.72 mm

[0196]

[0197] Service life of the third stage:

[0198]

[0199] (5) Total service life: 34.5 + 5.3 + 3.16 = 43 a ≤ 45 a, not meeting the design requirements. After calculation, the cover thickness is adjusted to 65 mm, and the design life of the component reaches 52.8 a, meeting the design requirements.

[0200] 5.2 Deformed steel bars:

[0201] Since only the type of steel bars is changed, according to Sections 3 and 4, only the design expressions in the second and third stages are different. Therefore, it is only necessary to calculate the service life of the deformed steel bars in the second and third stages.

[0202] (1) As known from 1, the actual service life in the first stage is 34.5 a.

[0203] (2) Service life of the second stage:

[0204]

[0205] (3) Service life of the third stage:

[0206]

[0207] (4) Service life in total: 34.5 + 3.5 + 9.55 = 47.55 a ≥ 45 a, meeting the design requirements.

[0208] Analysis of the example results shows that the influence of the steel bar type on the durability of concrete structures cannot be ignored. It is preliminarily determined that in the design of reinforced concrete structures, in the second stage, the durability of the circular steel bar structure is better, with a design life of 5.3 a, while that of the deformed steel bar is 3.5 a; in the third stage, the durability of the deformed steel bar structure is better, with a design life of 9.55 a, while that of the circular steel bar is 3.16 a. According to the above results, the better steel bars are selected, and the total design life is 49.35 a, which is greatly improved compared with the design life of a single type of steel bar.

[0209] The above are only the preferred embodiments of the present invention. It should be noted that for those of ordinary skill in the art, without departing from the technical principle of the present invention, several improvements and deformations can be made, and these improvements and deformations should also be regarded as the protection scope of the present invention.

Claims

1. A durability life assessment method for reinforced concrete structures in a chloride salt environment, characterized in that Including: The durability degradation process of reinforced concrete structures in a chloride salt environment is divided into a first stage, a second stage, and a third stage; The first stage is from the structure's service to the initial rusting of the steel bars. Let the initial rusting time t1 of the steel bars be not less than the first design service life T1; taking the reference chloride ion diffusion coefficient D0, the surface chloride ion concentration C s , and the concrete cover thickness c as random variables, obtaining the design values of each random variable based on the design value method, and getting the structural durability design expression of the initial rusting life criterion of the steel bars; The second stage is the stage from the initial rusting of steel bars to the cracking of the concrete surface. Assume that the time t2 for the concrete structure to crack is not less than the second design service life T2. Take the concrete cover thickness c and the concrete cube compressive strength f c as random variables, and based on the design value method, obtain the design values of each random variable and get the structural durability design expression of the concrete cover cracking life criterion; The second stage is from the appearance of cracks on the concrete surface to the stage where the cracks reach the limit value. Assume that the time t3 for the cracks in the concrete structure to develop to the critical cracks is not less than the third design service life T3. Take the concrete cover thickness c and the concrete cube compressive strength f c as random variables, and obtain the design values of each random variable based on the design value method and get the structural durability design expression of the critical crack width life criterion; Reliability analysis is carried out using the structural durability design expressions of three service life criteria to obtain the reliability analysis results.

2. The durability life assessment method of a reinforced concrete structure in a chloride salt environment according to claim 1, characterized in that, The target reliability indices β within the first design service life T1, the second design service life T2, and the third design service life T3 are all determined by the JC method.

3. The durability life evaluation method of a reinforced concrete structure in a chloride salt environment according to claim 1, wherein The initial rusting time t1 of the reinforcement is calculated using a pre-corrected chloride ion diffusion model and is not less than the first design service life T1, and the formula is expressed as: η1 = C(x, t) - C cr = 0 Where: C(x,t) is the chloride ion concentration at depth x at time t; is the error function; q T is the temperature coefficient, q RH is the relative humidity coefficient, q t is the time-varying coefficient of concrete age; C S is the chloride ion concentration on the surface of the diffusion medium, C0 is the initial chloride ion concentration inside the diffusion medium, and D0 is the chloride ion diffusion coefficient under standard temperature and humidity curing of concrete; H c is the relative humidity of the concrete curing environment; H is the relative humidity in the service environment; t0 is the initial age of the concrete structure; m is the age attenuation coefficient; T0 is the curing temperature of concrete; U is the energy coefficient; r is the gas parameter, η1 represents the ultimate state of initial rust of steel bars, and C cr represents the critical value of chloride ion concentration.

4. The durability life assessment method of reinforced concrete structures in a chloride salt environment according to claim 3, characterized in that, The structural durability design expression for the initial rusting life criterion of the reinforcement is: where t 1d represents the service life of the first stage, and c d , D 0d , C sd represent the design values of the concrete cover thickness c, the reference chloride ion diffusion coefficient D0, and the surface chloride ion concentration C s respectively.

5. The durability life assessment method of reinforced concrete structures in chloride environments according to claim 4, characterized in that The structural durability design expression for the concrete cover cracking life criterion is: where t 1d represents the design value of the initial rusting time of the steel bar, W / C represents the water-cement ratio; c represents the concrete cover thickness, n1, n2, n3 are the coefficient values corresponding to different steel bar types, d is the steel bar diameter, c d and f cd represent the design values of the concrete cover thickness c and the concrete cube compressive strength f c respectively.

6. The durability life assessment method of reinforced concrete structures in a chloride salt environment according to claim 5, wherein, The structural durability design expression for the critical crack width life criterion is: where t 3d design value of the time when the concrete structure crack develops to the critical crack; t 1d Denotes the design value of the initial rusting time of the steel bar, Δt 2d Denotes the design value of the time elapsed from the initial rusting of the steel bar to the cracking of the concrete cover, w cr Is the critical value of the maximum crack width for concrete cracking; Δt 3d Is the design value of the time elapsed from the surface cracking of the concrete to the maximum crack reaching the critical crack width; k is the conditional coefficient after steel bar corrosion; c is the concrete cover thickness; f c Is the cube compressive strength of the concrete, m1, m2, m3 are the coefficient values corresponding to different steel bar types, c d And f cd Respectively represent the design values of the concrete cover thickness c and the cube compressive strength f of the concrete c of the concrete 7. The durability life evaluation method of reinforced concrete structures in chloride environments according to claim 1, characterized in that The method further includes: substituting the design value of the random variable in the first stage into the calculation formula of the initial rusting time t1 of the steel bar to obtain the design value t of the initial rusting time t1 of the steel bar 1d to be used as the service life in the first stage, substituting the design value of the random variable in the second stage into the calculation formula of the time t2 when cracks occur in the concrete structure to obtain the design value t of the time t2 when cracks occur in the concrete structure 2d to be used as the service life in the second stage, substituting the design value of the random variable in the third stage into the calculation formula of the time t3 when the cracks in the concrete structure develop to critical cracks to obtain the design value t of the time t3 when cracks occur in the concrete structure 3d to be used as the service life in the third stage, cumulatively summing up the service lives in the first stage, the second stage and the third stage to obtain the total service life; comparing the total service life with the design life to evaluate whether the reinforced concrete structure meets the design requirements.

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