Prestress long-term loss prediction error quantitative evaluation method

Abstract

The invention discloses a pre-stress long-term loss prediction error quantitative evaluation method, and relates to the technical field of pre-stressed concrete structures, and the method comprises the steps: firstly determining a plurality of random variables affecting concrete shrinkage and creep; generating a plurality of sample combinations by adopting a Latin hypercube sampling technology; performing prestress long-term loss calculation on each sample by using the containment structure three-dimensional finite element model to obtain a series of predicted values; and finally, carrying out statistical analysis on the predicted values, calculating an average value and a standard deviation of the predicted values, and determining a confidence interval of the prestress loss according to a preset confidence level. According to the method, through an efficient sampling strategy and probability statistical analysis, accurate quantification of the prediction uncertainty of the long-term loss of the prestress is realized, and a prediction result with high confidence can be provided with relatively low calculation cost; and the safety and reliability judgment precision of major engineering structures such as the nuclear power plant containment vessel in long-term service and life extension evaluation is remarkably improved.

Description

Technical Field

[0001] This invention relates to the field of prestressed concrete structure technology, and more specifically to a method for quantitatively evaluating the prediction error of long-term prestress loss. Background Technology

[0002] The nuclear power plant containment vessel is one of the most important protective structures in a nuclear power plant. Its prestressed concrete structure is subject to factors such as concrete shrinkage, creep, and prestressing tendon relaxation during long-term service, leading to a gradual loss of prestress. This prestress loss directly affects the structural integrity and safety of the containment vessel; therefore, accurately predicting the long-term trend of prestress changes is crucial, especially in life extension assessments.

[0003] Currently, the prediction of prestress loss in containment structures, both domestically and internationally, mainly relies on empirical models (such as ACI 209 and CEB-FIP) and standard formulas. However, these models do not fully consider the coupling effect between concrete shrinkage and creep and prestressing tendon relaxation, nor do they systematically consider the randomness of factors such as materials, construction, and environment. Furthermore, existing methods mostly employ deterministic analysis, which cannot quantify the uncertainty of the prediction results, making it difficult to assess the reliability and confidence level of the predicted values ​​in practical engineering.

[0004] While some studies have attempted to correct model parameters using monitoring data, a systematic, probabilistic, and statistically based method for quantifying the uncertainty of prestress loss remains lacking. Traditional Monte Carlo methods are computationally expensive and unsuitable for predicting the long-term performance of large, complex structures such as containment structures.

[0005] Therefore, there is an urgent need for a quantitative evaluation method for predicting long-term prestressing loss that can comprehensively consider uncertainties from multiple sources such as materials, construction, and environment, and is based on a combination of efficient sampling and finite element analysis, so as to improve prediction accuracy and engineering applicability. Summary of the Invention

[0006] In view of this, the present invention provides a method for quantitatively evaluating the prediction error of long-term prestressing loss, aiming to solve the above-mentioned technical problems.

[0007] To achieve the above objectives, the present invention adopts the following technical solution:

[0008] A method for quantitatively evaluating the prediction error of long-term prestressing loss includes the following steps:

[0009] Identify multiple random variables that affect concrete shrinkage and creep;

[0010] The random variable is sampled using the Latin hypercube sampling method to generate multiple sample combinations;

[0011] Using a three-dimensional finite element model of the containment structure, long-term prestress loss was calculated for each sample combination, resulting in multiple time-related predicted values ​​of prestress loss.

[0012] Statistical analysis was performed on the predicted prestress loss values ​​to calculate their mean and standard deviation;

[0013] Based on a preset confidence level, a confidence interval for the prestress loss value is determined to quantify the uncertainty of the prediction.

[0014] Through the above technical solution, this invention combines Latin hypercube sampling with finite element analysis to quantify the multi-source uncertainties affecting long-term prestress loss, such as materials, construction, and environment, into random variables and perform efficient sampling. Then, it calculates the confidence interval of prestress loss at a specific confidence level using probabilistic statistical methods, thereby achieving a quantitative assessment of the uncertainty of the prediction results. This method significantly improves prediction accuracy while ensuring high reliability, and provides a scientific and reliable decision-making basis for the long-term safety and life extension assessment of important engineering structures at a computational cost far lower than that of the traditional Monte Carlo method.

[0015] Preferably, in the above-mentioned method for quantitatively evaluating the prediction error of long-term prestressing loss, the random variables include θ1, θ2, θ3, θ4, θ5 and θ6, wherein θ1 to θ5 are product factors multiplied with the coefficients q1 to q5 in the creep compliance function of the B3 model, and θ6 is a product factor multiplied with the shrinkage calculation expression of the B3 model.

[0016] Preferably, in the above-mentioned method for quantitatively evaluating the prediction error of long-term prestressing loss, the random variables θ1 to θ6 all follow a normal distribution with a mean of 1, and their coefficients of variation are set as follows: the coefficients of variation for θ1 and θ5 are 0.10, and the coefficients of variation for θ2, θ3, θ4, and θ6 are 0.15.

[0017] Preferably, in the above-mentioned method for quantifying and evaluating the prediction error of long-term prestressing loss, the specific steps of the Latin hypercube sampling include:

[0018] Divide the cumulative probability distribution interval of each random variable into n equal sub-intervals;

[0019] For the j-th sub-interval, according to the formula Determine the probability value corresponding to the sample value, where λ is a random number in the interval [0,1].

[0020] The sample values ​​of each variable are obtained by using the inverse probability distribution function, and the sample values ​​of each variable are randomly combined to form an m×n Latin square matrix, where each row is a random sample sequence.

[0021] Preferably, in the above-mentioned method for quantitatively evaluating the prediction error of long-term prestressing loss, the number of layers in the Latin hypercube sampling is 8.

[0022] Preferably, in the above-mentioned method for quantifying and evaluating the prediction error of long-term prestressing loss, the confidence level is 95%, and the confidence interval is determined by the formula:

[0023]

[0024] Calculation, where S is the average value of the predicted prestress loss. Y Its standard deviation.

[0025] Preferably, in the above-mentioned method for quantitatively evaluating the prediction error of long-term prestress loss, the method is used to quantitatively analyze the prestress loss of circumferential steel strands, vertical steel strands, and dome steel strands in the containment structure of a nuclear power plant.

[0026] Preferably, in the above-mentioned method for quantitatively evaluating the prediction error of long-term prestressing, the safety of the structure at the end of its service life and the end of its extended service life is assessed by comparing the lower limit of the confidence interval with the minimum required value of the containment prestress.

[0027] Preferably, in the above-mentioned method for quantitatively evaluating the prediction error of long-term prestressing loss, before using the B3 model for prediction, the model parameters are identified and corrected using measured data to reduce the uncertainty of the model.

[0028] Preferably, in the above-mentioned method for quantitatively evaluating the prediction error of prestressed long-term loss, the verification of the statistical analysis results includes: at a 95% confidence level, the percentage difference between the lower limit of the confidence interval and the average value does not exceed 2% throughout the entire service life of the structure.

[0029] As can be seen from the above technical solution, compared with the prior art, this invention discloses a method for quantitatively evaluating the prediction error of long-term prestress loss. By systematically constructing a random variable system based on the B3 model and employing efficient Latin hypercube sampling technology to replace the traditional Monte Carlo method, it successfully incorporates the complex uncertainties affecting long-term prestress loss (such as material properties, construction technology, and environmental conditions) into a probabilistic analysis framework. Its core beneficial effect lies in achieving high-precision quantification of the prediction uncertainty of long-term prestress loss in important structures such as nuclear containment structures with significantly reduced computational costs. Specifically, by combining finite element numerical simulation with statistical analysis, it can output a confidence interval for prestress values ​​with a clear confidence level (e.g., 95%), thus providing a reliable quantitative basis for engineering decisions; it ensures that the lower limit of the confidence interval is higher than the safety threshold throughout the entire life cycle of the structure, effectively supporting the safety assessment of the containment structure during its service life and extended service life; the entire method combines theoretical rigor, computational efficiency, and engineering practicality, providing an innovative solution for the long-term performance prediction and safe operation and maintenance of major civil engineering structures. Attached Figure Description

[0030] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0031] Figure 1 The attached diagram illustrates the quantification of the uncertainty of prestressing force values.

[0032] Figure 2 The attached figure shows the process of quantitative analysis of prestress loss uncertainty;

[0033] Figure 3 The attached diagram illustrates Latin hypercube sampling – the cumulative probability distribution function interval is equally divided.

[0034] Figure 4 The attached diagram illustrates Latin hypercube sampling – Latin square.

[0035] Figure 5 The attached figure shows the confidence interval analysis of the prestress values ​​of the containment structure - the confidence interval of the circumferential steel strand prestress values;

[0036] Figure 6 The attached figure shows the confidence interval analysis of the prestress values ​​of the containment structure - the confidence interval of the prestress values ​​of the vertical steel strands;

[0037] Figure 7 The attached figure shows the confidence interval analysis of the prestress values ​​of the containment structure - the confidence interval of the prestress values ​​of the dome steel strands. Detailed Implementation

[0038] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0039] Because of uncertainties in concrete materials, curing conditions, and service environment, the predicted prestressing force value of the containment structure also has uncertainties. In engineering applications, it is necessary to quantify the uncertainty of the predicted prestressing force value during the design life and at the end of the extended service life of the containment structure, i.e., to determine the probability distribution interval of the prestressing force value of the containment structure at each moment, such as... Figure 1 As shown.

[0040] The randomness of various factors, reflected in the B3 model, affects the values ​​of relevant parameters. Although material and environmental parameters are uncertain, they fall under the category of random variables and follow a certain probability distribution, allowing for statistical analysis. First, let's examine the random variable X related to the shrinkage and creep of the concrete in the containment structure. (1) ,X (2) ,X (3) …X (n) By sampling, we can obtain m samples (x1) of a random variable. (1) ,x1 (2) ,x1 (3) …x1 (n) (x2) (1) x2 (2) x2 (3) …x2 (n) ), ..., (x m (1) ,x m (2) ,x m (3) …x m (n) Based on m samples, the time-dependent prestress variation value Y can be calculated m times using the finite element analysis method. j (X (i) ,t).

[0041]

[0042] For a series of prestress values ​​Y obtained from the calculation j (X (i) By performing statistical analysis on t, we can obtain estimates of the average prestress and the variance.

[0043]

[0044] In the formula, S is the average value. Y denoted as standard deviation, and m as the number of samples.

[0045] For the containment structure of nuclear power plants, due to the high importance of the structure, the prediction must have high reliability. The confidence level of the prestress loss prediction must not be lower than 95%. Based on the confidence level, the confidence interval of the predicted prestress value can be determined.

[0046] The technical route of the above process is as follows: Figure 2 As shown.

[0047] The main factors affecting concrete shrinkage and creep include: concrete modulus of elasticity, cement, water-cement ratio, aggregate content, concrete strength, ambient humidity, and structural shape. The B3 model comprehensively describes concrete shrinkage and creep, with creep characterized by a flexibility function. This flexibility function incorporates all the aforementioned influencing factors. The flexibility function includes instantaneous strain, basic creep, and drying creep, resulting in five monomials in the creep flexibility function, each with a product coefficient (q1–q5). Although many factors influence concrete shrinkage and creep, and all are random, the B3 model condenses this into six random variables that represent these various random factors. Of these six random variables, five (θ1–θ5) are multiplied by coefficients q1–q5 respectively, comprehensively reflecting the random factors affecting concrete creep; the remaining random variable (θ6) is multiplied by the shrinkage calculation expression to reflect the random factors affecting concrete shrinkage. These six random variables comprehensively reflect the influence of uncertainties such as concrete material parameters, construction process, and environmental parameters on concrete shrinkage and creep. θ2 to θ4 are the single-term coefficients of parameters including cement weight, water-cement ratio, and aggregate-cement ratio. Considering the significant dispersion of these parameters during construction, their coefficients of variation are set to 0.15. Furthermore, considering the significant influence of environmental factors and structural shape on shrinkage, the coefficient of variation of parameter θ6, which is multiplied by the shrinkage term, is also set to 0.15. The other parameters, mainly collected under laboratory conditions, have relatively accurate and reliable data, and their coefficients of variation are set to 0.1. The probability distribution and statistical characteristics of the introduced random variables are shown in Table 1.

[0048] Table 1. Probability distribution and statistical properties of random variables

[0049]

[0050] Latin hypercube sampling is a type of Monte Carlo method. Compared to traditional Monte Carlo methods, Latin hypercube sampling improves upon traditional methods by employing non-repeating sampling techniques. It can reflect the characteristics of the population with a smaller sample size, thus achieving higher computational accuracy under small-scale sampling conditions, reducing the number of sample calculations and computation time, and significantly improving sampling precision. Latin hypercube sampling is a stratified sampling method that ensures complete coverage of the range of each variable during sampling by maximizing the stratification of each marginal distribution. The specific implementation steps are as follows:

[0051] (1) Each random variable X i The cumulative probability distribution interval [0,1] is divided into n equal subintervals, such as Figure 3 As shown in the figure Represents random variable X i The probability distribution function of the random variable, for the j-th subinterval, gives the following probability values ​​corresponding to a sample value of the random variable:

[0052]

[0053] In the formula, Let λ be the value of the probability distribution function corresponding to the sample value of random variable x in the j-th subinterval; λ is a random number in the interval [0,1].

[0054] (2) Sample values ​​for each random variable were generated according to equation (4). These sample values ​​were randomly combined, with only one sample value for each random variable appearing in each sample arrangement, forming an m×n Latin square matrix. Each row of the m×n Latin square matrix was used as a random sample sequence as the input parameter for each finite element calculation. The m predicted values ​​of prestress loss of the containment structure P1, P2, ... P3 were obtained by calculating m times using the three-dimensional finite element model of the containment structure. m Then, the average value of the prestress loss of the containment structure is estimated according to Equation (2), and the standard deviation of the prestress loss of the containment structure is estimated according to Equation (3).

[0055] Figure 4 A schematic diagram of Latin hypersquare sampling for two random variables divided into four sub-intervals.

[0056] In this embodiment, good computational accuracy can be obtained by using 8-level sampling. In this embodiment, Latin hypercube sampling is performed on 6 random variables, and the sampling results are shown in Table 2.

[0057] Table 2. Latin hypercube sampling results for random variables.

[0058]

[0059] Based on the Latin hypercube sampling results, the long-term prestress loss values ​​under eight different parameters were calculated using a three-dimensional finite element model of the containment system. Statistical analysis was then performed on the calculated data. The predicted long-term prestress loss values ​​follow a standard normal distribution. The confidence interval for the predicted prestress values, ensuring a 95% confidence level on both sides, was calculated using the following formula.

[0060]

[0061] The confidence intervals of the prestress of the circumferential steel strands, vertical steel strands, and dome steel strands of the containment structure over time were calculated based on the above formula (5), as follows: Figures 5-7 As shown, the specific calculated values ​​are detailed in Appendix Table 3-5.

[0062] Table 3. Calculation of Circumferential Steel Strand Prestress Values ​​under Different Sampling Combinations (Unit: MPa)

[0063]

[0064]

[0065] Table 4. Calculation of Vertical Steel Strand Prestress Values ​​under Different Sampling Combinations (Unit: MPa)

[0066]

[0067]

[0068] Table 5. Calculation of prestress values ​​for dome steel strands under different sampling combinations (unit: MPa)

[0069]

[0070]

[0071] As can be seen from the figure, the confidence intervals for various steel strand force values ​​gradually expand over time, and the specific changing patterns are as follows:

[0072] (1) Evolution of circumferential steel strands: By the end of the service life (40 years), the lower confidence limit of the circumferential steel strands was 1281.46 MPa, and the percentage difference from the average value was -1.17%; by the end of the extended service life (60 years), the lower confidence limit of the circumferential steel strands was 1268.21 MPa, and the percentage difference from the average value was -1.35%. The lower confidence limit of the force value of the circumferential prestressed steel strands was higher than the minimum requirement value of the containment prestress throughout the entire service process.

[0073] (2) Evolution of vertical steel strands: By the end of the service life (40 years), the lower confidence limit of the vertical steel strands was 1310.82 MPa, and the percentage difference from the average value was -1.12%; by the end of the extended service life (60 years), the lower confidence limit of the vertical steel strands was 1299.71 MPa, and the percentage difference from the average value was -1.30%. The lower confidence limit of the vertical prestressed steel strand force was higher than the minimum requirement value of the containment prestress throughout the entire service life.

[0074] (3) Evolution of dome steel strands: By the end of the service life (40 years), the confidence lower limit of the dome steel strands was 1296.81 MPa, and the percentage difference from the average value was -1.14%; by the end of the extended service life (60 years), the confidence lower limit of the dome steel strands was 1284.70 MPa, and the percentage difference from the average value was -1.31%. The confidence lower limit of the dome prestressed steel strand force was higher than the minimum requirement value of the containment prestress throughout the entire service process.

[0075] (4) Statistical analysis of the prestressing force values ​​of the containment structure after 60 years of service shows that, under a 95% confidence level on both sides, the lower confidence limit of the prestressing force values ​​of the containment structure does not exceed 2% of the average value, and the confidence interval remains very small, indicating high prediction accuracy. This is mainly because the B3 concrete shrinkage and creep prediction model used in this paper has undergone parameter identification and correction based on measured data. The corrected model reduces uncertainty and significantly improves prediction accuracy.

[0076] To address the uncertainties arising from the randomness of factors such as concrete materials, construction process, and environmental parameters in predicting prestressing time-limit loss in containment structures, and the high computational cost of traditional Monte Carlo sampling, this embodiment employs a probabilistic statistical analysis method, combining Latin hypercube sampling with finite element analysis, to quantify the uncertainty in predicting prestressing loss in containment structures. The main conclusions are as follows:

[0077] (1) In this embodiment, through the analysis of the composition of the B3 model, six main random variables were determined by constructing product factors. These variables include material, construction technology and environmental parameters when predicting prestress loss of prestressed concrete containment structures, which comprehensively reflect the random characteristics of concrete shrinkage and creep. Based on the Latin hypercube sampling method, efficient sampling of random variables was achieved.

[0078] (2) Statistical analysis of the prestress force values ​​at the end of the service life (40 years) and the end of the extended service life (60 years) of the containment structure shows that, under the condition of a 95% confidence level on both sides, the lower limit of the confidence interval of the prestress force value of the containment structure does not exceed 2% of the average value. The lower limits of the confidence intervals of the circumferential steel strands, vertical steel strands and dome steel strands are all higher than the minimum requirement value of the containment prestress.

[0079] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the apparatus disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple; relevant parts can be referred to the method section.

[0080] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for quantitatively evaluating the prediction error of long-term prestressing loss, characterized in that, Includes the following steps: Identify multiple random variables that affect concrete shrinkage and creep; The random variable is sampled using the Latin hypercube sampling method to generate multiple sample combinations; Using a three-dimensional finite element model of the containment structure, long-term prestress loss was calculated for each sample combination, resulting in multiple time-related predicted values ​​of prestress loss. Statistical analysis was performed on the predicted prestress loss values ​​to calculate their mean and standard deviation; Based on a preset confidence level, a confidence interval for the prestress loss value is determined to quantify the uncertainty of the prediction.

2. The method for quantitatively evaluating the prediction error of long-term prestressing loss according to claim 1, characterized in that, The random variables include θ1, θ2, θ3, θ4, θ5 and θ6, where θ1 to θ5 are product factors multiplied with the coefficients q1 to q5 in the creep compliance function of the B3 model, and θ6 is a product factor multiplied with the contraction calculation expression of the B3 model.

3. The method for quantitatively evaluating the prediction error of long-term prestressing loss according to claim 2, characterized in that, The random variables θ1 to θ6 all follow a normal distribution with a mean of 1. Their coefficients of variation are set as follows: θ1 and θ5 have a coefficient of variation of 0.10, and θ2, θ3, θ4, and θ6 have a coefficient of variation of 0.

15.

4. The method for quantitatively evaluating the prediction error of long-term prestressing loss according to claim 1, characterized in that, The specific steps of the Latin hypercube sampling include: Divide the cumulative probability distribution interval of each random variable into n equal sub-intervals; For the j-th sub-interval, according to the formula Determine the probability value corresponding to the sample value, where λ is a random number in the interval [0,1]. The sample values ​​of each variable are obtained by using the inverse probability distribution function, and the sample values ​​of each variable are randomly combined to form an m×n Latin square matrix, where each row is a random sample sequence.

5. The method for quantitatively evaluating the prediction error of long-term prestressing loss according to claim 4, characterized in that, The Latin hypercube sampling method has 8 layers.

6. The method for quantitatively evaluating the prediction error of long-term prestressing loss according to claim 1, characterized in that, The confidence level is 95%, and the confidence interval is determined by the formula: Calculate, where Y is the average value of the predicted prestress loss, and S Y Its standard deviation.

7. The method for quantitatively evaluating the prediction error of long-term prestressing loss according to claim 1, characterized in that, The method is used to quantitatively analyze the prestress loss of circumferential steel strands, vertical steel strands, and dome steel strands in the containment structure of a nuclear power plant.

8. The method for quantitatively evaluating the prediction error of long-term prestressing loss according to claim 1, characterized in that, The safety of the structure at the end of its service life and at the end of its extended service life is assessed by comparing the lower limit of the confidence interval with the minimum required prestress of the containment.

9. The method for quantitatively evaluating the prediction error of long-term prestressing loss according to claim 1, characterized in that, Before using the B3 model for prediction, the model parameters are identified and corrected using measured data to reduce the uncertainty of the model.

10. The method for quantitatively evaluating the prediction error of long-term prestressing loss according to claim 1, characterized in that, Validation of the statistical analysis results includes ensuring that, at a 95% confidence level, the percentage difference between the lower limit of the confidence interval and the mean does not exceed 2% throughout the entire service life of the structure.

Images