Construction method of probability model for predicting chloride ion concentration based on spatio-temporal variability characteristics of concrete

Abstract

The present invention discloses a method for constructing a probabilistic model for predicting chloride ion concentration based on the characteristics of spatio-temporal variability of concrete. The method uses core samples of retired concrete bridges in cold regions as experimental materials, measures the layered chloride ion concentration of the concrete, statistically analyzes the concentration distribution characteristics, and establishes a concentration probability model; based on the high-precision apparent three-dimensional topography scanning technology, a phase volume probability model of the interfacial transition zone is established, thereby respectively establishing a probabilistic model for the chloride ion diffusion coefficient of concrete mortar and a probabilistic model for the chloride ion diffusion coefficient of the interfacial transition zone; then a three-dimensional three-phase mesoscopic random structure model of the mortar phase, the interfacial transition zone phase, and the aggregate phase is constructed, and combined with the finite element simulation method, the random diffusion behavior of chloride ions in the random mesoscopic structure of concrete is simulated. The present invention can accurately simulate the random diffusion behavior of chloride ions inside the concrete structure under the real natural service environment, and can accurately predict the spatio-temporal probability distribution of chloride ion concentration in the bridge structure.

Description

Technical Field

[0001] The present invention belongs to the field of durability performance of cement-based composites for bridge engineering, and relates to a method for constructing a prediction probability model of chloride ion concentration, specifically to a method for constructing a prediction probability model of chloride ion concentration based on the spatio-temporal variability characteristics of concrete. Background Art

[0002] A large number of engineering practices and theoretical analyses have confirmed that chloride ion erosion is one of the important reasons for steel bar corrosion, continuous cracking of concrete, and degradation of structural performance. In winter in cold regions, inorganic snow melting agents mainly composed of chlorides are mostly used for road surface deicing. Therefore, chloride ions in the snow melting agents will cause relatively serious erosion to the in-service concrete bridges, resulting in a significant reduction in the durability of urban bridge structures in cold regions and a substantial shortening of the service life, which will pose a threat to the service safety of bridge structures. Therefore, studying the diffusion law of chloride ions in concrete structures has high practical value for the safety assessment and grade evaluation of concrete bridges in cold regions.

[0003] At present, many scholars at home and abroad have carried out a large number of studies on the diffusion law of chloride ions in concrete, and the research content covers from the micro scale to the macro scale, and from the single-phase model to the composite multi-phase model. However, there are still some shortcomings and problems in the research considering the spatio-temporal variability characteristics of concrete: First, some studies ignore the characteristics of randomness and time-variability of external environmental factors such as wind, rain, and snow. Therefore, the established model of chloride ion concentration on the concrete surface ignores the random distribution characteristics of chloride ion concentration on the bridge deck surface and cannot well reflect the spatio-temporal variability of surface chloride ion concentration. Second, the random diffusion of chloride ions caused by the complex meso-structure characteristics of concrete is ignored; concrete can be regarded as a composite material composed of mortar phase, aggregate phase, and interfacial transition zone phase, and contains coarse aggregate, fine aggregate, cement hydration products, unhydrated cement particles, etc. inside, showing typical porous, multi-phase, and multi-scale characteristics. Therefore, the diffusion path and rate of chloride ions inside the concrete also have spatio-temporal variability. However, the parameters of traditional chloride ion concentration prediction models are too simplified and are usually fixed values, which cannot effectively characterize the randomness of the chloride ion diffusion process. Third, when most studies on the meso-structure of concrete consider the influence of the interfacial transition zone, the thickness of the interfacial transition zone and its chloride ion diffusion coefficient are taken as fixed values, and the value range is too wide, with a maximum difference of about 10 times. Since the interfacial transition zone has higher chloride ion transport characteristics, rough values will cause large errors and cannot truly reflect the influence of the interfacial transition zone on the chloride ion diffusion process. Therefore, it is urgent to establish a model that can truly and accurately reflect the spatio-temporal variability characteristics of concrete to explore the random diffusion process of chloride ions, so as to accurately predict the probability distribution law of chloride ion concentration inside the concrete. Summary of the Invention

[0004] To solve the problem that the existing chloride ion concentration prediction model cannot well simulate the random distribution of chloride ion concentration in concrete bridge structures under real service environments, the present invention provides a method for constructing a probability model for predicting chloride ion concentration based on the spatio-temporal variability characteristics of concrete. This method accurately statistically analyzes the distribution characteristics of chloride ion concentration, the volume of the interfacial transition zone, and the chloride ion diffusion coefficients of the mortar phase and the interfacial transition zone phase in concrete, establishes corresponding probability models, and conducts simulations through numerical simulation methods. The present invention can accurately simulate the random diffusion behavior of chloride ions inside concrete structures under real natural service environments and can accurately predict the spatio-temporal probability distribution of chloride ion concentration in bridge structures.

[0005] The object of the present invention is achieved through the following technical solutions:

[0006] A method for constructing a probability model for predicting chloride ion concentration based on the spatio-temporal variability characteristics of concrete, comprising the following steps:

[0007] Step 1: Drill core samples from retired concrete bridge components in cold regions, use a grinding instrument to successively grind mortar powder from the concrete core samples along the depth direction, and avoid the coarse aggregate area; measure the chloride ion concentration in the powder through a professional chloride ion concentration testing instrument, obtain the statistical distribution characteristics of the test data, and conduct Monte Carlo simulation based on the probability characteristics of the test data to establish a random probability model for the chloride ion concentration on the concrete surface.

[0008] Step 2: Based on the premise that the total integral of the chloride ion concentration on the concrete surface remains unchanged during the service period, decompose the process of the surface chloride ion concentration accumulating over time into a time series. Based on the distribution characteristics of the time factor α in the random probability model of the chloride ion concentration on the concrete surface in Step 1, calculate the segmentation node t i , and statistically analyze its distribution characteristics; then combine the random probability model of the chloride ion concentration on the concrete surface with Fick's second law to obtain the theoretical formulas for the spatio-temporal concentration prediction probability model of chloride ions inside the concrete and the concrete apparent chloride ion diffusion coefficient model; based on the statistical distribution characteristics of the chloride ion concentration data at different depths inside the concrete, conduct Monte Carlo simulation, fit to obtain the analytical value of the coefficient to be solved in the model theoretical formula, i.e., the initial apparent diffusion coefficient, analyze the statistical distribution characteristics of the initial apparent chloride ion diffusion coefficient, substitute it into the concrete apparent chloride ion diffusion coefficient model, analyze the statistical distribution characteristics of the apparent chloride ion diffusion coefficient, and establish a probability model for the concrete apparent chloride ion diffusion coefficient.

[0009] Step 3: Measure the volume distributions of the aggregate and mortar in the concrete core samples through X-ray CT tomography; measure the thickness of the interfacial transition zone through an apparent three-dimensional topography scanner, analyze the statistical distribution characteristics of the interfacial transition zone thickness, and establish a probability model for the volume of the interfacial transition zone.

[0010] Step 4: Based on the probability model of the apparent chloride diffusion coefficient of concrete established in Step 2 and the aggregate-mortar volume distribution and the probability model of the interfacial transition zone volume measured in Step 3, integrating the three-phase sphere model and the step-by-step homogeneous sphere model, calculate the chloride diffusion coefficients of the concrete mortar and the interfacial transition zone through Monte Carlo simulation, and establish the probability models of the chloride diffusion coefficients of the mortar and the interfacial transition zone based on the statistical distribution characteristics of the chloride diffusion coefficients of the mortar and the interfacial transition zone respectively;

[0011] Step 5: Based on the three-dimensional digital scanning data of the aggregate and mortar of the on-site concrete core sample and the apparent morphology scanning data of the interfacial transition zone, randomly generate three-dimensional polyhedral aggregates, interfacial transition zones and mortars that conform to the actual concrete core sample, and construct a three-dimensional three-phase random model of concrete;

[0012] Step 6: Based on the random probability model of the chloride concentration on the concrete surface, the probability model of the chloride diffusion coefficient of the mortar, the probability model of the chloride diffusion coefficient of the interfacial transition zone, and the three-dimensional random model of concrete, construct a finite element probability model to predict the spatio-temporal probability distribution of the chloride concentration inside the concrete.

[0013] Compared with the prior art, the present invention has the following advantages:

[0014] Based on the surface and internal chloride concentration data of the concrete bridge core samples under the real service environment, the present invention obtains the statistical distribution characteristics of the chloride concentration; based on the mesoscopic structure information of the concrete bridge core samples under the real service environment, the present invention obtains the statistical distribution characteristics of the mesoscopic structure information, establishes the probability model of the interfacial transition zone volume, and thus establishes the probability model of the chloride diffusion coefficient of the mortar phase, the probability model of the chloride diffusion coefficient of the interfacial transition zone phase, and the prediction probability model of the chloride concentration distribution. The present invention can more accurately simulate the random diffusion process of chloride ions during the service life of a concrete bridge, predict the spatio-temporal probability distribution of chloride concentration, and provide strong data support for the safety assessment and grade evaluation of service bridges; at the same time, it can optimize the maintenance decision-making in the whole life cycle, improve the effectiveness of maintenance investment, so as to achieve cost minimization and performance benefit maximization. Description of the Drawings

[0015] Figure 1 For the statistical histogram and distribution fitting of the time factor α;

[0016] Figure 2 For the time segmentation point t i The statistical histogram and distribution fitting of,(a)t 1 ,(b)t 10 ;

[0017] Figure 3 For the statistical histogram and distribution fitting of D(t), (a) t = 1a, (b) t = 24a;

[0018] Figure 4 For V itz Statistical histogram and distribution fitting of;

[0019] Figure 5 For the statistical histogram and distribution fitting of the chloride ion diffusion coefficient of the mesostructure at t = 1a, (a) mortar phase D m , (b) interfacial transition zone phase D itz ;

[0020] Figure 6 Is a three-dimensional three-phase random model of concrete;

[0021] Figure 7 Is a comparison chart of the calculation results of the finite element model and the measured values;

[0022] Figure 8 For the statistical histogram and distribution fitting of the chloride ion concentration on the same depth plane, (a) x = 1.5 cm, (b) x = 2.5 cm. Specific implementation manner

[0023] The technical solution of the present invention will be further described below in conjunction with the accompanying drawings, but it is not limited thereto. Any modification or equivalent replacement of the technical solution of the present invention without departing from the spirit and scope of the technical solution of the present invention shall be covered by the protection scope of the present invention.

[0024] The present invention provides a method for constructing a probabilistic model for predicting chloride ion concentration based on the spatio-temporal variability characteristics of concrete. Taking the core samples of retired concrete bridges in cold regions as experimental materials, measuring the stratified chloride ion concentration of concrete, statistically analyzing the concentration distribution characteristics, and establishing a concentration probability model; based on the high-precision apparent three-dimensional morphology scanning technology, establishing a volume probability model of the interfacial transition zone phase, so as to establish a probabilistic model of the chloride ion diffusion coefficient of the concrete mortar and a probabilistic model of the chloride ion diffusion coefficient of the interfacial transition zone respectively; then constructing a three-dimensional three-phase mesoscopic random structure model of the mortar phase, the interfacial transition zone phase and the aggregate phase, and combining with the finite element simulation method, simulating the random diffusion behavior of chloride ions in the random mesoscopic structure of concrete. As Figure 1 Shown, specifically including the following steps:

[0025] Step 1: Drill core samples from the components of retired concrete bridges in cold regions, use a grinding instrument to grind the concrete core samples into mortar powder along the depth direction in turn, and avoid the coarse aggregate area; measure the chloride ion concentration in the powder through a professional chloride ion concentration testing instrument, obtain the statistical distribution characteristics of the test data, and perform Monte Carlo simulation based on the probability characteristics of the test data to establish a random probability model of the chloride ion concentration on the concrete surface. The specific steps are as follows:

[0026] Step 1: According to the "Technical Standard for In-situ Testing of Concrete Structures" (GB / T 50784-2013), core samples are taken from the in-service concrete bridges on site; according to the "Technical Specification for Testing Chloride Ion Content in Concrete" (JGJ / T 322-2013), the chloride ion concentration in the concrete core samples is measured, and the distribution probability characteristics of the chloride ion concentration in different depth planes are studied; among them, the chloride ion concentration in each depth plane follows a normal distribution.

[0027] Step 1.2: Considering that the chloride ions have not completely eroded the concrete bridge, the value with less fluctuation in the chloride ion concentration at a deeper part inside the structure is taken as the initial concentration value of the concrete, and its statistical distribution characteristics are analyzed. The initial concentration value follows a normal distribution, and a random probability model of the chloride ion concentration on the concrete surface is established:

[0028]

[0029] In the formula: C s (t) is the chloride ion concentration on the concrete surface at time t, C 0 is the initial chloride ion concentration on the concrete surface, C a = C s - C 0 C s is the chloride ion concentration on the concrete surface at the current measurement time, α is the time factor, t 0 is the time when the concrete is first exposed to the chloride ion environment, N(μ, σ 2 ) is the normal distribution, μ 0 , σ 0 are the mean and standard deviation of the initial chloride ion concentration C 0 , μ s , σ s are the mean and standard deviation of C s , μ α , σ α are the mean and standard deviation of α.

[0030] Step 2: Based on the premise that the total integral of the chloride ion concentration on the concrete surface remains unchanged during the service life cycle, the process of the cumulative chloride ion concentration on the surface over time is decomposed into a time series. Based on the distribution characteristics of the time factor α in the random probability model of the chloride ion concentration on the concrete surface in Step 1, the segmentation node t i of the time series is calculated, and its distribution characteristics are statistically analyzed. t iIt follows a lognormal distribution; combined with the stochastic probability model of chloride ion concentration on the concrete surface and Fick's second law, the theoretical formulas for the prediction probability model of the spatio-temporal concentration of chloride ions in concrete and the model of the apparent chloride diffusion coefficient of concrete are obtained; based on the statistical distribution characteristics of chloride ion concentration data at different depths inside the concrete, Monte Carlo simulation is carried out, and the analytical value of the coefficient to be solved in the model theoretical formula, that is, the initial apparent diffusion rate, is obtained by fitting. Analyze the statistical distribution characteristics of the initial apparent chloride diffusion coefficient, which follows a lognormal distribution; substitute it into the model of the apparent chloride diffusion coefficient of concrete, analyze the statistical distribution characteristics of the apparent chloride diffusion coefficient, which follows a lognormal distribution, and establish a probability model for the apparent chloride diffusion coefficient of concrete. The specific steps are as follows:

[0031] Step 2-1: Divide the service life of the concrete bridge into N segments, and at the same time ensure that the total integral of the surface chloride ion concentration in the time dimension remains unchanged, which can be expressed as:

[0032]

[0033] where: t i is the i-th segmented time, τ i is the i-th segmented time corresponding to t i N is the number of time segments, LogN(μ, σ) is the lognormal distribution, μ t , σ t are the location parameter and scale parameter when t i follows a lognormal distribution, μ 1 , σ 1 are the mean and standard deviation statistically obtained for t i .

[0034] Step 2-2: The continuous development of cement hydration will induce the formation of Friedel's salt, resulting in the blockage of the pore structure and a decrease in the total porosity. Therefore, the apparent chloride diffusion coefficient gradually decreases with time. Its dependence on time can be defined by a power function, and an apparent chloride diffusion coefficient model is established;

[0035] Step 2-3: Substitute the stochastic probability model of chloride ion concentration on the concrete surface, the apparent chloride diffusion coefficient model, and the decomposed time series into Fick's second law in sequence, and based on the statistical distribution characteristics of the measured chloride ion concentration data at different depths inside the concrete, Monte Carlo simulation is carried out, and the prediction probability model of the spatio-temporal concentration of chloride ions in concrete and the probability model of the apparent chloride diffusion coefficient of concrete are obtained by fitting, which can be expressed as:

[0036]

[0037] where: D(t) is the apparent chloride diffusion coefficient of concrete at time t, D 0 is the initial apparent chloride diffusion coefficient, t0 is the time when concrete is first exposed to chloride ion environment, m is the time factor of diffusion coefficient, W / C is the water-cement ratio of concrete, FA is the percentage of fly ash in cementitious materials, SL is the percentage of slag in cementitious materials, C(x,t) is the chloride ion concentration at the depth of x cm in concrete at time t, erf is the error function, μ 0 , σ 0 D 0 Location and scale parameters for the lognormal distribution.

[0038] Step 3: Measure the volume distribution of aggregate and mortar in the concrete core sample by X-ray CT tomography technology; measure the thickness of the interface transition zone by an apparent three-dimensional topography scanner, analyze the statistical distribution characteristics of the thickness of the interface transition zone, and establish a volume probability model of the interface transition zone. The specific steps are as follows:

[0039] Step 31. Based on X-ray CT tomography technology, obtain the sample CT grayscale image; use AutoCAD software to depict the aggregate contour in the CT cross-sectional image, measure the area and perimeter information of the aggregate, depict multiple cross-sectional images until the obtained aggregate area ratio and the total perimeter of the aggregate tend to a constant value, and equate the aggregate area ratio to the volume ratio of the aggregate in the three-dimensional core sample.

[0040] Step 3.2: After grinding concrete samples at different depths with 240, 320, 400, 600 and 800 grit sandpaper respectively, use a surface three-dimensional morphology scanner to measure and obtain the sample surface morphology 3D point cloud data to obtain the thickness information of the interface transition zone, where the thickness of the interface transition zone obeys the Gamma distribution; multiply the total circumference of the cross-sectional aggregate measured in step 3.1 by the thickness of the interface transition zone to obtain the area ratio of the interface transition zone, and equate the area ratio of the interface transition zone to the volume ratio of the interface transition zone in the three-dimensional core sample, and establish the volume probability model of the interface transition zone, which can be expressed as:

[0041]

[0042] Where: f(x) is the probability density function of the thickness x (μm) of the interface transition zone, α is the shape parameter, β is the size parameter, Γ() is the gamma function, V itz is the volume fraction of the interface transition zone, μ itz , σ itz V itz Location and scale parameters for the lognormal distribution.

[0043] Step 4: Based on the probability model of the apparent chloride diffusion coefficient of concrete established in Step 2 and the aggregate-mortar volume distribution and the probability model of the interfacial transition zone volume measured in Step 3, integrating the three-phase sphere model and the progressive homogeneous sphere model, calculate the chloride diffusion coefficients of the concrete mortar and the interfacial transition zone through Monte Carlo simulation. Based on the statistical distribution characteristics of the chloride diffusion coefficients of the mortar and the interfacial transition zone, establish the probability models of the chloride diffusion coefficients of the mortar and the interfacial transition zone. The statistical distribution characteristics of the chloride diffusion coefficients of the mortar and the interfacial transition zone and the probability models of the chloride diffusion coefficients of the mortar and the interfacial transition zone are expressed as follows:

[0044]

[0045] In the formula: D is the apparent chloride diffusion coefficient, D m is the chloride diffusion coefficient of the mortar, D itz is the chloride diffusion coefficient of the interfacial transition zone, D ea is the equivalent aggregate chloride diffusion coefficient, V agg is the volume fraction of coarse aggregate, V itz is the volume fraction of coarse aggregate, D itz = kD m , μ k , σ k are the location parameter and scale parameter when k follows a lognormal distribution, μ m , σ m are the location parameter and scale parameter when D m follows a lognormal distribution.

[0046] Step 5: Based on the three-dimensional digital scanning data of the aggregate and mortar of the on-site concrete core sample and the apparent morphology scanning data of the interfacial transition zone, randomly generate three-dimensional polyhedral aggregates, interfacial transition zones, and mortars that conform to the actual concrete core sample, and construct a three-dimensional three-phase random model of concrete. The specific steps are as follows:

[0047] Step 5-1: Based on the CT scanning data of the concrete core sample and the apparent morphology scanning data of the interfacial transition zone, obtain the aggregate volume and the thickness information of the interfacial transition zone. Use the Range function to randomly generate random spherical aggregates that meet the requirements and ensure that there is no interference between the spheres. Then save the coordinate information of the spherical aggregates. The formula for determining whether there is interference between the spheres is as follows:

[0048]

[0049] In the formula: x j , y j , z j are the center coordinates of the circumscribed circle of the polyhedron that has been generated respectively, x i , y i , z iThey are the center coordinates of the circumscribed spheres of the newly generated polyhedra respectively, and r i and r j are the radii of the circumscribed spheres of the newly generated and already generated polyhedra respectively, and δ i and δ j are the thicknesses of the interface transition zones of the newly generated and already generated polyhedra respectively, and η is the influence coefficient of the aggregate interference range.

[0050] Step Five Two: Based on the already generated spherical aggregates, use the Range function to randomly select any number of points on the spherical surface as the vertices of the polyhedral aggregates, and then use the convex hull function to construct random three-dimensional polyhedral aggregates.

[0051] Step Five Three: Based on the spherical aggregates in Step Five One, generate a concentric sphere. The radius of this concentric sphere is the radius of the original sphere plus the thickness of the interface transition zone that follows the gamma distribution. At the same time, extend the original polyhedron vertices to the new spherical surface and use the convex hull function to construct the interface transition zone.

[0052] Step Five Four: Use the Triangulation function to save the coordinate information of the random three-dimensional polyhedral aggregates and the interface transition zone and output it as an stl file.

[0053] Step Six: Based on the random probability model of the chloride ion concentration on the concrete surface, the probability model of the chloride ion diffusion coefficient in the mortar, the probability model of the chloride ion diffusion coefficient in the interface transition zone, and the three-dimensional random model of the concrete, construct a finite element probability model to predict the spatio-temporal probability distribution of the chloride ion concentration inside the concrete. The specific steps are as follows:

[0054] Step Six One: Input the stl files of the random three-dimensional polyhedral aggregates and the interface transition zone in Step Five into the COMSOL Multiphysics finite element software to construct a three-dimensional polyhedral aggregate and an interface transition zone solid model. Then, through Boolean operations, generate a mortar solid model. Select the dilute mass transfer module in the three-dimensional space dimension of the finite element software to conduct a transient simulation analysis of chloride ion diffusion.

[0055] Step Six Two: Define the mortar phase, the aggregate phase, and the interface transition zone phase respectively. Then, conduct mesh generation for each phase and endow each phase with the chloride ion diffusion probability characteristics in the form of an analytical formula, that is, input the probability model of the chloride ion diffusion coefficient in the mortar and the probability model of the chloride ion diffusion coefficient in the interface transition zone. Define the boundary conditions and the initial conditions. One side of the cube is the chloride ion erosion surface, and input the random probability model of the chloride ion concentration on the concrete surface. The other sides are set to have no flux, and then output the initial concentration to calculate and obtain the spatio-temporal concentration probability distribution of the chloride ions after random diffusion in the concrete.

[0056] Example:

[0057] This embodiment is described by combining the chloride ion concentration detection test of a reinforced concrete bridge in actual service and the results of COMSOL Multiphysics finite element numerical simulation analysis.

[0058] The test object is a simply supported slab beam of reinforced concrete retired in a cold region. The calculated span of the slab beam is 9.60 m, the height is 0.60 m, and the width is 1.01 m. The slab beam uses C30 two-graded concrete. The medium-sized aggregate has a particle size of 20 mm to 31.5 mm, the small-sized aggregate has a particle size of 5 mm to 20 mm, and the cement is ordinary Portland cement. The actual service life of the bridge is 24 years. According to the "Technical Standard for In-situ Testing of Concrete Structures" (GB / T 50784-2013), core samples are taken from the concrete at different positions on the top slab within the full length of the reinforced concrete slab beam.

[0059] Step 1: Drill core samples from the components of the retired concrete bridge in the cold region. Use a grinding instrument to grind the mortar powder from the concrete core samples along the depth direction in turn, avoiding the coarse aggregate area. Measure the chloride ion concentration in the powder through a professional chloride ion concentration testing instrument, and obtain the chloride ion concentration C on the concrete surface. s obeys a normal distribution, with a mean of 0.32 and a standard deviation of 0.021; the initial chloride ion concentration C of the concrete 0 obeys a normal distribution, with a mean of 0.03 and a standard deviation of 0.001; C a = C s - C 0 , obeys a normal distribution, with a mean of 0.29 and a standard deviation of 0.022; the time factor α obeys a normal distribution, with a mean of 0.095 and a standard deviation of 0.006, as Figure 1 shown.

[0060] Step 2: Based on the premise that the total integral of the chloride ion concentration on the concrete surface remains unchanged during the service period, decompose the process of the surface chloride ion concentration accumulating over time into a time series. Based on the distribution characteristics of α in Step 1, calculate the segmentation node t of the time series i , and statistically analyze its distribution characteristics. Then, combine the random probability model of the concrete surface chloride ion concentration and Fick's second law to obtain the theoretical formulas of the concrete chloride ion spatio-temporal concentration prediction probability model and the concrete apparent chloride ion diffusion coefficient model; the time t when the concrete is first exposed to the chloride ion environment 0 = 28 days, the time factor m of the diffusion coefficient is 0.2, t i obeys a lognormal distribution, as Figure 2 shown, where the statistical mean mean_t of t i i= [0.5640, 1.6038, 2.7576, 4.0535, 5.5316, 7.2518, 9.3097, 11.8719, 15.2721, 20.3624], t i The statistical standard deviation std_t of i = [0.0126, 0.0387, 0.0663, 0.0956, 0.1263, 0.1579, 0.1887, 0.2141, 0.2189, 0.1349], the initial apparent chloride diffusion coefficient D 0 obeys a lognormal distribution, the statistical mean mean_D 0 = 0.631 cm 2 / a, the statistical standard deviation std_D 0 = 0.159, the location parameter and scale parameter are -0.491 and 0.248 respectively; within 24 years of service life, the apparent chloride diffusion coefficient D(t) changes with the service time, and at any time t, D(t) obeys a lognormal distribution. For example: when t = 1 a, the statistical mean mean_D = 0.377 cm 2 / a, the statistical standard deviation std_D 0 = 0.168, the location parameter and scale parameter are -1.066 and 0.426 respectively; when t = 24 a, the statistical mean mean_D = 0.201 cm 2 / a, the statistical standard deviation std_D 0 = 0.166, the location parameter and scale parameter are -1.871 and 0.724 respectively; as Figure 3 shown.

[0061] Step 3: Measure the volume distributions of the aggregate and mortar in the concrete core sample by X-ray CT tomography; measure the thickness of the interfacial transition zone by an apparent three-dimensional topography scanner, analyze the statistical distribution characteristics of the interfacial transition zone thickness, and establish a probability model for the volume of the interfacial transition zone. The aggregate volume ratio is 50.9%, the average thickness of the interfacial transition zone obeys a gamma distribution, where the shape parameter α = 4.385 and the size parameter β = 11.113 of the probability distribution function; the volume ratio V of the interfacial transition zone itz obeys a lognormal distribution, the statistical mean mean_V itz = 0.731%, the statistical standard deviation std_V itz = 0.517, the location parameter and scale parameter are -0.516 and 0.637 respectively, as Figure 4 shown.

[0062] Step 4: Using a three-dimensional three-phase sphere model, calculate the chloride diffusion coefficient D of concrete mortar during the service life by using the probability model of the apparent chloride diffusion coefficient of concrete measured in Step 2 and the three-phase volume distribution measured in Step 3 m , and the chloride diffusion coefficient D itz of the interfacial transition zone, where D itz = kD m ; among them, at any time t during the service life, D m and D itz both follow a lognormal distribution. For example, when t = 1a, the statistical mean mean_D m = 1.528 cm 2 / a, the statistical standard deviation std_D m = 0.167, and the location parameter and scale parameter are 0.418 and 0.109 respectively; the statistical mean mean_D itz = 15.281 cm 2 / a, the statistical standard deviation std_D itz = 0.472, and the location parameter and scale parameter are 2.726 and 0.031 respectively, as shown in Figure 5 ; k follows a lognormal distribution, the statistical mean mean_k = 10.210, the statistical standard deviation std_k = 0.508, and the location parameter and scale parameter are 2.322 and 0.049 respectively.

[0063] Step 5: Based on the three-dimensional digital scanning data of the aggregate and mortar of the on-site concrete core sample and the apparent morphology scanning data of the interfacial transition zone, randomly generate three-dimensional polyhedron aggregates, interfacial transition zones and mortars that conform to the actual concrete core sample, and construct a three-dimensional three-phase random model of concrete, as shown in Figure 6 .

[0064] Step 6: Input the random probability model of the concrete surface chloride concentration, the probability model of the mortar chloride diffusion coefficient, the probability model of the interfacial transition zone chloride diffusion coefficient, and the three-dimensional random model of concrete into the finite element software to construct a finite element model, calculate the chloride concentration inside the concrete and compare it with the measured value. The results are shown in Figure 7 . It can be seen that the numerical simulation results are in good agreement with the measured values, verifying the accuracy and rationality of the chloride concentration prediction probability model based on the spatio-temporal variability characteristics of concrete proposed in the present invention. At the same time, by extracting the chloride concentration data of some cross-sections of the model, Figure 8 it can be clearly observed that the chloride concentration at the same erosion depth follows a normal distribution, which is consistent with the measured concentration distribution, indicating that the inhomogeneity and randomness of concrete caused by the mesoscopic structure have a significant impact on the chloride diffusion behavior, verifying that the chloride concentration prediction probability model based on the spatio-temporal variability characteristics of concrete established in the present invention has a good prediction effect.

Claims

1. A method for constructing a chloride ion concentration prediction probability model based on the spatiotemporal variability characteristics of concrete, characterized in that The method comprises the following steps: Step 1: Drill core samples of retired concrete bridge components in cold regions, use a grinding instrument to grind the concrete core samples in the depth direction to obtain mortar powder, and avoid the coarse aggregate area; measure the chloride ion concentration in the powder using a professional chloride ion concentration test instrument to obtain the statistical distribution characteristics of the test data, perform Monte Carlo simulation based on the probability characteristics of the test data, and establish a random probability model of chloride ion concentration on the concrete surface; Step 2: Based on the premise that the total amount of chloride ion concentration on the concrete surface remains unchanged during the service life, the accumulation process of chloride ion concentration on the surface over time is decomposed into a time series. Based on the distribution characteristics of the time factor α in the random probability model of chloride ion concentration on the concrete surface in step 1, the node t of the time series is calculated. i , count its distribution characteristics; Combining the random probability model of chloride ion concentration on the concrete surface with Fick's second law, the theoretical formulas of the spatiotemporal chloride ion concentration prediction probability model inside concrete and the apparent chloride ion diffusion coefficient model of concrete are obtained; based on the statistical distribution characteristics of chloride ion concentration data at different depths inside concrete, Monte Carlo simulation is performed to fit the coefficient to be solved in the theoretical formula of the model, i.e., the analytical value of the initial apparent chloride ion diffusion coefficient, and the statistical distribution characteristics of the initial apparent chloride ion diffusion coefficient are analyzed. The coefficient is substituted into the apparent chloride ion diffusion coefficient model of concrete, and the statistical distribution characteristics of the apparent chloride ion diffusion coefficient are analyzed to establish the probability model of the apparent chloride ion diffusion coefficient of concrete. The specific steps are as follows: Step 21: Divide the service life of the concrete bridge into N segments, while ensuring that the total integral of the surface chloride ion concentration in the time dimension remains unchanged, expressed as: Where: t i is the i-th segment time, τ i Corresponding to t i The i-th segment time, N is the number of time segments, LogN(μ,σ) is the log-normal distribution, μ t , σ t t i The location parameter and scale parameter when it obeys the lognormal distribution, μ1, σ1 are t i The mean and standard deviation obtained by statistics; Step 22: define the time dependence of the apparent chloride ion diffusion coefficient using a power function and establish an apparent chloride ion diffusion coefficient model; Step 2 and 3: The random probability model of chloride ion concentration on the concrete surface, the apparent chloride ion diffusion coefficient model and the decomposed time series are sequentially superimposed and substituted into Fick's second law. Monte Carlo simulation is performed based on the statistical distribution characteristics of the chloride ion concentration data at different depths inside the concrete. The spatiotemporal concentration prediction probability model of chloride ions in concrete and the probability model of the apparent chloride ion diffusion coefficient of concrete are fitted, which are expressed as: Where: D(t) is the apparent diffusion coefficient of chloride ions in concrete at time t, D0 is the initial apparent diffusion coefficient of chloride ions, t0 is the time when concrete is first exposed to the chloride ion environment, m is the time factor of the diffusion coefficient, W / C is the water-cement ratio of concrete, FA is the percentage of fly ash in cementitious materials, SL is the percentage of slag in cementitious materials, C(x,t) is the chloride ion concentration at depth x in concrete at time t, erf is the error function, μ0 and σ0 are the location parameters and scale parameters when D0 obeys the lognormal distribution; Step 3: Measure the volume distribution of aggregate and mortar in the concrete core sample by X-ray CT tomography technology; measure the thickness of the interface transition zone by an apparent three-dimensional topography scanner, analyze the statistical distribution characteristics of the thickness of the interface transition zone, and establish a volume probability model of the interface transition zone; Step 4: Based on the probability model of apparent chloride ion diffusion coefficient of concrete established in step 2 and the probability model of aggregate mortar volume distribution and interface transition zone volume measured in step 3, the three-phase sphere model and the stepwise homogenous sphere model are integrated to calculate the chloride ion diffusion coefficient of concrete mortar and interface transition zone through Monte Carlo simulation, and the probability models of chloride ion diffusion coefficient of mortar and interface transition zone are established respectively based on the statistical distribution characteristics of chloride ion diffusion coefficient of mortar and interface transition zone; Step 5: Based on the three-dimensional digital scanning data of the on-site concrete core sample aggregate and mortar and the surface morphology scanning data of the interface transition zone, three-dimensional polyhedral aggregates, interface transition zones and mortar that conform to the actual concrete core sample are randomly generated to construct a three-dimensional three-phase random model of concrete; Step 6. Construct a finite element probability model based on the random probability model of chloride ion concentration on the concrete surface, the probability model of chloride ion diffusion coefficient in mortar, the probability model of chloride ion diffusion coefficient in the interface transition zone, and the three-dimensional three-phase random model of concrete to predict the spatiotemporal probability distribution of chloride ion concentration inside the concrete.

2. The method for constructing a chloride ion concentration prediction probability model based on the spatiotemporal variability characteristics of concrete according to claim 1 is characterized in that The specific steps of step one are as follows: Step 1. According to the Technical Standard for On-site Inspection of Concrete Structures, core samples are taken from the decommissioned concrete bridges on site; according to the Technical Regulations for the Detection of Chloride Ion Content in Concrete, the chloride ion concentration in the concrete core samples is measured, and the distribution probability characteristics of the chloride ion concentration in planes at different depths are studied; Step 1 and 2: Considering that chloride ions have not completely corroded concrete bridges, the value with the smallest fluctuation of chloride ion concentration deep inside the structure is taken as the initial concentration value of concrete, and its statistical distribution characteristics are analyzed to establish a random probability model of chloride ion concentration on the concrete surface.

3. The method for constructing a chloride ion concentration prediction probability model based on the spatiotemporal variability characteristics of concrete according to claim 1 or 2, characterized in that The random probability model of chloride ion concentration on the concrete surface is: Where: C s (t) is the chloride ion concentration on the concrete surface at time t, C0 is the initial chloride ion concentration on the concrete surface, C a =C s -C0,C s is the chloride ion concentration on the concrete surface at the current measurement time, α is the time factor, t0 is the time when the concrete is first exposed to the chloride ion environment, N(μ, σ 2 ) is a normal distribution, μ1 and σ1 are the mean and standard deviation of the initial surface chloride ion concentration C0, μ s , σ s C s The mean and standard deviation, μ α , σ α is the mean and standard deviation of α.

4. The method for constructing a chloride ion concentration prediction probability model based on the spatiotemporal variability characteristics of concrete according to claim 1, characterized in that The specific steps of step three are as follows: Step 31. Based on X-ray CT tomography technology, obtain the sample CT grayscale image; use AutoCAD software to depict the aggregate contour in the CT cross-sectional image, measure the area and perimeter information of the aggregate, depict multiple cross-sectional images until the obtained aggregate area ratio and the total perimeter of the aggregate tend to a constant value, and the aggregate area ratio is equivalent to the volume ratio of the aggregate in the three-dimensional core sample; Step 3.2: After grinding concrete samples at different depths with 240, 320, 400, 600 and 800 grit sandpaper respectively, use a surface 3D topography scanner to measure and obtain the 3D point cloud data of the sample surface topography, so as to obtain the thickness information of the interface transition zone, where the thickness of the interface transition zone obeys the Gamma distribution; multiply the total perimeter of the cross-sectional aggregate measured in step 3.1 by the thickness of the interface transition zone to obtain the area ratio of the interface transition zone, and equate the area ratio of the interface transition zone to the volume ratio of the interface transition zone in the three-dimensional core sample, and establish the volume probability model of the interface transition zone, which is expressed as: Where: f(x) is the probability density function of the thickness x of the interface transition zone, λ is the shape parameter, β is the size parameter, Γ() is the gamma function, V itz is the volume fraction of the interface transition zone, μ itz , σ itz V itz Location and scale parameters for the lognormal distribution.

5. The method for constructing a chloride ion concentration prediction probability model based on the spatiotemporal variability characteristics of concrete according to claim 1, characterized in that In the step 4, the statistical distribution characteristics of the chloride ion diffusion coefficient in the mortar and interface transition zone and the probability model of the chloride ion diffusion coefficient in the mortar and interface transition zone are expressed as: Where: D is the apparent diffusion coefficient of chloride ions, D m is the chloride ion diffusion coefficient of mortar, D itz is the chloride ion diffusion coefficient in the interface transition zone, D ea is the equivalent aggregate chloride ion diffusion coefficient, V agg is the volume fraction of coarse aggregate, V itz is the volume fraction of the interface transition zone, D itz =kD m , μ k , σ k are the location parameter and scale parameter when k follows a lognormal distribution, μ m , σ m D m Location and scale parameters for the lognormal distribution.

6. The method for constructing a chloride ion concentration prediction probability model based on the spatiotemporal variability characteristics of concrete according to claim 1, characterized in that The specific steps of step five are as follows: Step 51: Based on the CT scanning data of the concrete core sample and the surface morphology scanning data of the interface transition zone, the aggregate volume and the thickness information of the interface transition zone are obtained, and the random spherical aggregates that meet the requirements are randomly generated using the Range function, and it is ensured that there is no interference between the spheres, and then the coordinate information of the spherical aggregates is saved; Step 52: Based on the generated spherical aggregate, use the Range function to randomly select any number of points on the spherical surface as the vertices of the polyhedron aggregate, and then use the convex hull function to construct a random three-dimensional polyhedron aggregate; Step 53: Based on the spherical aggregate in step 51, generate concentric spheres, the radius of which is the radius of the original sphere plus the thickness of the interface transition zone that obeys the gamma distribution. At the same time, extend the original polyhedron vertices to the new spherical surface, and use the convexhull convex hull function to construct the interface transition zone. Step 54: Use the Triangulation function to save the coordinate information of the random three-dimensional polyhedron aggregate and the interface transition zone and output it as an stl file.

7. The method for constructing a chloride ion concentration prediction probability model based on the spatiotemporal variability characteristics of concrete according to claim 6, characterized in that In step 51, the formula for determining whether interference occurs between the spheres is as follows: Where: x j ,y j 、z j are the coordinates of the center of the generated polyhedron circumscribed circle, x i ,y i 、z i are the coordinates of the center of the newly generated polyhedron circumscribed circle, r i 、r j are the radii of the newly generated and generated polyhedron circumscribed spheres, δ i , δ j are the thickness of the transition zone between the newly generated and the generated polyhedron interface, and η is the influence coefficient of the aggregate interference range.

8. The method for constructing a chloride ion concentration prediction probability model based on the spatiotemporal variability characteristics of concrete according to claim 6, characterized in that The specific steps of step six are as follows: Step 6: Input the random three-dimensional polyhedral aggregate and interface transition zone stl file in step 5 into COMSOL Mutiphysics finite element software, construct a three-dimensional polyhedral aggregate and interface transition zone solid model, and then generate a mortar solid model through Boolean operation, select the rare species transfer module in the three-dimensional space dimension of the finite element software, and perform transient simulation analysis of chloride ion diffusion; Step 6.2: Define the mortar phase, aggregate phase and interface transition zone phase respectively, and then divide the grids respectively and assign the chloride ion diffusion probability characteristics of each phase in the form of analytical expressions, that is, input the probability model of the chloride ion diffusion coefficient of the mortar and the probability model of the chloride ion diffusion coefficient of the interface transition zone; define the boundary conditions and initial conditions, one side of the cube is the chloride ion erosion surface, and the random probability model of the chloride ion concentration on the concrete surface is input, and the other sides are set to no flux, and then the initial concentration is output to calculate the spatiotemporal concentration probability distribution of chloride ions in concrete after random diffusion.

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