Segmented model-based concrete adiabatic temperature rise parameter iterative fitting method

Abstract

The invention provides a concrete adiabatic temperature rise parameter iterative fitting method based on a segmentation model. The method comprises the steps of constructing a concrete adiabatic temperature rise segmentation fitting formula, determining an initial parameter value range, performing first parameter fitting calculation and performing convergence judgment. According to the method, an existing single curve fitting mode is abandoned, a straight line + double-index curve segmentation model is constructed based on cement hydration five-stage characteristics, a straight line is matched with an initial hydrolysis stage and an induction stage, a double-index curve is matched with subsequent three stages, and it is ensured that a fitting result is consistent with an actual heating process on the aspect of architecture; the problem that a traditional method is large in fitting deviation is effectively solved, the concrete adiabatic temperature rise fitting precision and calculation efficiency are remarkably improved, and the high-precision requirement of large projects for concrete temperature control design is met.

Description

Technical Field

[0001] This invention belongs to the field of temperature control and crack prevention technology for large-volume concrete in water conservancy and hydropower projects, and specifically relates to an iterative fitting method for concrete adiabatic temperature rise parameters based on a segmented model. Background Technology

[0002] Temperature cracking is a common quality hazard in concrete dam engineering, seriously affecting the safety and durability of the dam structure. Currently, the engineering field generally uses the finite element method to calculate the temperature field of concrete, then analyzes the stress field and formulates temperature control and crack prevention measures. The core premise of this process is to fit an adiabatic temperature rise curve based on experimental data and then substitute it into a simulation program to complete the analysis.

[0003] The commonly used expressions for existing concrete adiabatic temperature rise curves mainly fall into the following three categories:

[0004] (1)

[0005] (2)

[0006] (3)

[0007] Taking equation (1) as an example, its derivative yields the adiabatic temperature rise rate development curve:

[0008] (4)

[0009] Clearly, equation (4) exhibits a function characteristic that decreases with time, meaning that the adiabatic temperature rise rate described by the equation continuously decreases with time. Similarly, the adiabatic temperature rise rates expressed by equations (2) and (3) both follow this decreasing law, which is essentially due to the fact that they do not fully match the complete reaction process of cement hydration.

[0010] Cement hydration is its main component ( , , and The chemical reaction between cement and water has a reaction rate closely related to temperature: the hydration rate accelerates with increasing temperature and slows down significantly at low temperatures. The complete cement hydration process can be divided into five stages: initial hydrolysis, induction, acceleration, decline, and stabilization. Figure 1 (as shown), but the existing adiabatic temperature rise curve expression does not specifically adapt to the heating characteristics of these five stages.

[0011] In early engineering projects, ordinary Portland cement was mostly used for concrete, which had a relatively short initial hydrolysis and induction period. Therefore, the assumption of a "decreasing rate" in the existing adiabatic temperature rise curve had some applicability. However, with the development of engineering materials and construction technology, the initial hydrolysis and induction periods of concrete are now generally longer. In some projects (such as the JX project shown in Table 1), the induction period even exceeds one day, which is significantly different from the hydration characteristics of early concrete.

[0012] Table 1 Test values ​​of thermal rise of dam concrete

[0013]

[0014] Water cooling is a key technique for reducing the internal temperature of concrete. However, when the concrete heats up rapidly, the internal heat cannot be dissipated in time, easily leading to excessive internal temperatures in large-volume concrete and subsequent temperature cracks. Existing adiabatic temperature rise curves do not accurately reflect the actual heat generation patterns during the initial hydrolysis and induction periods of concrete, making it impossible to precisely fit experimental data. This results in deviations in temperature field calculations based on these curves, directly affecting the effectiveness and specificity of subsequent temperature control and crack prevention measures, and failing to meet the high-precision requirements of current large-scale engineering projects for concrete temperature control design. Summary of the Invention

[0015] The purpose of this invention is to address the problem that existing expressions for concrete adiabatic temperature rise curves do not adequately reflect the heating characteristics of the five stages of cement hydration and are difficult to adapt to the current situation where the initial hydrolysis period and induction period of concrete are generally prolonged, resulting in insufficient fitting accuracy and deviations in temperature field calculation results, which in turn affect the effectiveness of temperature control and crack prevention measures. This invention provides a concrete adiabatic temperature rise fitting formula that takes into account the heating patterns of each hydration stage, along with a fast and efficient parameter inversion fitting method, to improve the accuracy and calculation efficiency of concrete adiabatic temperature rise fitting and meet the high-precision requirements of concrete temperature control design in large-scale projects.

[0016] The objective of this invention is achieved as follows:

[0017] This invention provides an iterative fitting method for concrete adiabatic temperature rise parameters based on a piecewise model, comprising the following steps:

[0018] Step 1: Construct a piecewise fitting formula for the temperature rise of concrete adiabatic heat.

[0019] The piecewise fitting formula is based on the heat generation characteristics of cement hydration during the initial hydrolysis period, induction period, acceleration period, decline period, and steady-state period, and is divided into two parts:

[0020] When the concrete age τ≤c, a linear expression is used to describe the adiabatic temperature rise development during the initial hydrolysis period and the induction period;

[0021] When the concrete age τ≥c, the adiabatic temperature rise development during the acceleration, decline, and stabilization phases is described using a biexponential curve expression. The piecewise fitting formula is as follows:

[0022]

[0023] In the formula, This is the final value of the adiabatic temperature rise. The age at the end of the induction period. This refers to the adiabatic temperature rise of the concrete at the end of the induction period. , b It is a constant.

[0024] Step 2: Determine the initial range of parameter values.

[0025] The parameters include , , b The initial value range of each parameter is as follows:

[0026]

[0027] in, The adiabatic temperature rise of concrete over 28 days. The value is 3~5℃. , , , The value ranges from 0.1 to 1; , , , The value ranges from 1 to 5.

[0028] Step 3, Initial parameter fitting calculation

[0029] Divide the initial value range of each parameter into equal parts, where The range of values ​​is divided into M equal parts. The range of values ​​is divided into N equal parts. The range of values ​​for is divided into O equal parts, and the range of values ​​for b is divided into P equal parts. The range of values ​​is divided into Q equal parts;

[0030] Take the starting values ​​between each partition to form multiple sets of parameter combinations, and substitute each set of parameter combinations into the piecewise fitting formula described in step 1 to calculate the corresponding measured age. Calculated adiabatic temperature rise at time t The error between the calculated and measured values ​​for each parameter combination is calculated using the following formula. :

[0031]

[0032] In the formula, R represents the number of measured values. Age The corresponding measured value of adiabatic temperature rise;

[0033] Select the combination of parameters with the smallest error. The corresponding parameter values ​​are used as the initial fitting results.

[0034] Step 4, Iterative parameter fitting calculation

[0035] The minimum error obtained from the i-th fitting And the corresponding parameter values, determine the range of parameter values ​​for the (i+1)th iteration, and the range of values ​​for each parameter is as follows:

[0036]

[0037] In the formula, k takes values ​​from 3 to 6; , , , and These are the corresponding parameter values ​​obtained from the i-th fitting; the range of each parameter value from the (i+1)-th fitting is divided equally according to the method in step 3, and the starting values ​​of each interval are used to form parameter combinations. These combinations are then substituted into the piecewise fitting formula to calculate the error of each parameter combination. Select the one with the smallest error The corresponding parameter values ​​are used as the fitting result for the (i+1)th time.

[0038] Step 5, Convergence check:

[0039] Calculate the minimum error difference between the (i+1)th and ith fitting iterations:

[0040]

[0041] like If u is a constant between 0.01 and 0.2, then the iteration converges, and the corresponding parameter combination is the final fitted parameter. If it does not converge, repeat step 4 to continue iterating until the convergence condition is met.

[0042] Furthermore, in step 3, The specific calculation method is as follows:

[0043]

[0044] In the formula, Let r be the age corresponding to the r-th measurement. for Measured values ​​of adiabatic temperature rise over age.

[0045] Furthermore, in step 4, during the (i+1)th fitting... The specific calculation method is as follows:

[0046]

[0047] In the formula, For the (i+1)th time The starting value of the m-th part after the range of values ​​is divided equally. For the (i+1)th time The starting value of the nth part after the range of values ​​is divided equally. Let be the starting value of the o-th part after the range of values ​​of 'a' is divided equally in the (i+1)th time. Let be the starting value of the p-th part after the range of values ​​for b is divided equally in the (i+1)-th time. Let c be the starting value of the qth part after the range of c is divided equally for the (i+1)th time.

[0048] Compared with existing concrete adiabatic temperature rise fitting techniques, the concrete adiabatic temperature rise parameter iterative fitting method based on a piecewise model provided by this invention has the following advantages:

[0049] 1. High fitting accuracy, adaptable to all stages of hydration. This invention abandons the existing single curve fitting mode and constructs a "straight line + double exponential curve" piecewise model based on the characteristics of the five stages of cement hydration. The straight line is adapted to the initial hydrolysis period and the induction period, and the double exponential curve is adapted to the subsequent three stages. The structure ensures that the fitting results are consistent with the actual heating process, effectively solving the problem of large fitting deviation in traditional methods. The fitting accuracy is significantly better than the existing technology.

[0050] 2. Wide adaptability, meeting current material development needs. Addressing the current trend of prolonged induction period in concrete, this invention utilizes a parametric design of the end age (c) of the induction period. Without adjusting the model architecture, it can accurately adapt to various types of concrete through parameter iteration alone, covering multiple engineering fields such as water conservancy and hydropower, and large-scale construction, thus solving the problem of insufficient adaptability of traditional methods.

[0051] 3. High fitting efficiency and fast iterative convergence. The "initial equal division fitting + gradual range reduction iteration" strategy is adopted. The parameter range decays exponentially with the number of iterations. Combined with the error convergence judgment mechanism, the number of parameter combinations is greatly reduced, and invalid calculations are avoided. The optimal parameters can be determined quickly, which can meet the rapid design needs of large-scale projects and solve the problems of long time consumption and low efficiency of traditional methods.

[0052] 4. Supports temperature control design and ensures engineering safety. High-precision fitting results can be accurately substituted into temperature field calculations, improving the accuracy of temperature and stress field analysis. This provides a reliable basis for formulating temperature control and crack prevention measures, reduces the risk of cracks, and enhances the safety and durability of engineering structures, demonstrating significant engineering application value. Attached Figure Description

[0053] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0054] Figure 1 This illustrates the hydration process of cement.

[0055] Figure 2 A comparison graph showing the fitting results of different formulas and the measured values. Detailed Implementation

[0056] To make the objectives, technical solutions, and advantages of the present invention clearer, the embodiments disclosed herein will be described in further detail below with reference to the accompanying drawings. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.

[0057] Example:

[0058] This embodiment provides an iterative fitting method for concrete adiabatic temperature rise parameters based on a piecewise model, including the following steps:

[0059] Step 1: Construct a piecewise fitting formula for the temperature rise of concrete adiabatic heat.

[0060] The piecewise fitting formula is based on the initial hydrolysis period, induction period, acceleration period, decline period, and stabilization period of cement hydration (e.g., ...). Figure 1 The heating characteristics (as shown) can be divided into two parts:

[0061] When the concrete age τ≤c, the adiabatic temperature rise during the initial hydrolysis and induction periods is described by a linear expression; the adiabatic temperature rise of the concrete at the end of the induction period can be expressed as:

[0062] (1)

[0063] In the formula, This is the final value of the adiabatic temperature rise. The age at the end of the induction period. This refers to the adiabatic temperature rise of the concrete at the end of the induction period. b It is a constant.

[0064] When the concrete age τ≥c, the adiabatic temperature rise development during the acceleration, decline, and stabilization phases is described using a biexponential curve expression; the adiabatic temperature rise development during the initial hydrolysis and induction phases of concrete is expressed as:

[0065] (2)

[0066] The adiabatic temperature rise development during the accelerated, declining, and stable phases of concrete is represented as follows:

[0067] (3)

[0068] According to equations (2) and (3), the adiabatic temperature rise parameters of concrete include: This is the total adiabatic temperature rise. The age at the end of the induction period. This refers to the adiabatic temperature rise of the concrete at the end of the induction period. b It is a constant. Considering and The relationship can be expressed by equation (1), therefore, the parameters to be inverted include... , b, c Five constants.

[0069] Combining equations (2) and (3) yields the expression for the adiabatic temperature rise, and the piecewise fitting formula is:

[0070] (4)

[0071] In equation (4), This is the final value of the adiabatic temperature rise. The age at the end of the induction period. This refers to the adiabatic temperature rise of the concrete at the end of the induction period. , b It is a constant.

[0072] Step 2: Determine the initial range of parameter values.

[0073] The parameters include , , b The initial value range of each parameter is as follows:

[0074] (5)

[0075] in, The adiabatic temperature rise of concrete over 28 days. The value is 3~5℃. , , , The value ranges from 0.1 to 1; , , , The value ranges from 1 to 5.

[0076] Step 3, Initial parameter fitting calculation

[0077] Divide the initial value range of each parameter into equal parts, where the interval is... Divide the m-th part into M equal parts, where the starting value of the m-th part is... ; the interval Divide into N equal parts, where the starting value of the nth part is... ; the interval Divide the sample into O equal parts, where the starting value of the O-th part is... ; Divide the sample into P equal parts, where the starting value of the p-th part is... ; Divide into Q equal parts, where the starting value of the Qth part is... Based on the current computing power of computers, the values ​​of M, N, O, P, and Q are generally taken as 20-30.

[0078] As shown in Table 1, the adiabatic temperature rise of the experiment consists of a set of ages and a set of measurement data.

[0079] parameter , , , , Substitute into equation (4) and solve. adiabatic temperature rise over time:

[0080] (6)

[0081] In the formula, Let r be the age corresponding to the r-th measurement. for Measured values ​​of adiabatic temperature rise over age.

[0082] This allows us to obtain the error between the calculated and measured values:

[0083] , , , , (7)

[0084] Where R represents the number of measured values.

[0085] This yields M*N*O*P*Q sets of calculation results, and the minimum value among them is selected as the target value for the first calculation:

[0086] , , , ,

[0087] in, This represents the minimum error among the calculation results of the M*N*O*P*Q group at the end of the first calculation. , , , , The parameter values ​​that yield the minimum error.

[0088] Step 4, Iterative parameter fitting calculation

[0089] The minimum error obtained from the i-th fitting And the corresponding parameter values, determine the range of parameter values ​​for the (i+1)th iteration, and the range of values ​​for each parameter is as follows:

[0090]

[0091] In the formula, k takes values ​​from 3 to 6; , , , and These are the corresponding parameter values ​​obtained from the i-th fitting; the range of each parameter value from the (i+1)-th fitting is divided equally according to the method in step 3, and the starting values ​​of each interval are used to form parameter combinations. These combinations are then substituted into the piecewise fitting formula to calculate the error of each parameter combination. Select the one with the smallest error The corresponding parameter values ​​are used as the fitting result for the (i+1)th time.

[0092] Specifically:

[0093] interval Divide the m-th part into M equal parts, where the starting value of the m-th part is... .

[0094] interval Divide into N equal parts, where the starting value of the nth part is... .

[0095] interval Divide the sample into O equal parts, where the starting value of the O-th part is...

[0096] Divide the sample into P equal parts, where the starting value of the p-th part is... .

[0097] Divide into Q equal parts, where the starting value of the Qth part is... .

[0098] parameter , , , , Substitute into equation (4) and solve. adiabatic temperature rise over time:

[0099] (9)

[0100] in, Let r be the age corresponding to the r-th measurement. for Measured values ​​of adiabatic temperature rise over age.

[0101] This allows us to obtain the error between the calculated and measured values:

[0102] , , , , (10)

[0103] Where R represents the number of measured values.

[0104] This yields M*N*O*P*Q sets of calculation results, and the minimum value among them is selected as the target value for the (i+1)th calculation:

[0105] , , , ,

[0106] in, This represents the minimum error among the M*N*O*P*Q sets of calculation results at the end of the i-th calculation. , , , , The parameter values ​​that yield the minimum error.

[0107] Step 5, Convergence check:

[0108] Since equations (8) to (10) provide the method for calculating the i+1th time using the parameters obtained in the i-th calculation, and equations (5) to (7) provide the method for calculating the initial value, the parameters can be iteratively optimized and the accurate parameters can be obtained by following equations (5) to (10).

[0109] Calculate the minimum error difference between the (i+1)th and ith fitting iterations:

[0110]

[0111] like If u is a constant between 0.01 and 0.2, then the iteration converges, and the corresponding parameter combination is the final fitted parameter. If it does not converge, repeat step 4 to continue iterating until the convergence condition is met.

[0112] Comparison of calculation accuracy:

[0113] According to the adiabatic temperature rise formula proposed in this patent, the adiabatic temperature rise of the secondary compaction (JXR2-F-HX) in Table 1 is obtained by parameter fitting according to formulas (5) to (10):

[0114] (12)

[0115] The adiabatic temperature rise of the secondary compaction (JXR2-F-HX) in Table 1 is fitted using formula (3) (i.e., fitted using a double exponential curve), resulting in the following adiabatic temperature rise formula:

[0116] (13)

[0117] The maximum fitting error using the hyperbolic formula was 1.24℃, while the maximum fitting error using the adiabatic temperature rise formula of this invention was 0.19℃. The fitting results show that the adiabatic temperature rise formula proposed in this invention can significantly improve the fitting accuracy of the early-stage concrete adiabatic temperature rise.

[0118] like Figure 2 As shown, the early fitting accuracy of the adiabatic temperature rise formula of this invention is significantly better than that of the hyperbolic formula fitting result.

[0119] Finally, it should be noted that the above is only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention (such as the application of various formulas, the order of steps, etc.) without departing from the spirit and scope of the technical solutions of the present invention.

Claims

1. An iterative fitting method for concrete adiabatic temperature rise parameters based on a piecewise model, characterized in that, The method includes the following steps: Step 1: Construct a piecewise fitting formula for the temperature rise of concrete adiabatic heat. The piecewise fitting formula is based on the heat generation characteristics of cement hydration during the initial hydrolysis period, induction period, acceleration period, decline period, and steady-state period, and is divided into two parts: When the concrete age τ≤c, a linear expression is used to describe the adiabatic temperature rise development during the initial hydrolysis period and the induction period; When the concrete age τ≥c, the adiabatic temperature rise development during the acceleration, decline, and stabilization phases is described using a biexponential curve expression. The piecewise fitting formula is as follows: ; In the formula, This is the final value of the adiabatic temperature rise. The age at the end of the induction period. This refers to the adiabatic temperature rise of the concrete at the end of the induction period. , b It is a constant; Step 2: Determine the initial range of parameter values. The parameters include , , b The initial value range of each parameter is as follows: ; in, The adiabatic temperature rise of concrete over 28 days. The value is 3~5℃. , , , The value ranges from 0.1 to 1; , , , The value can be between 1 and 5; Step 3, Initial parameter fitting calculation Divide the initial value range of each parameter into equal parts, where The range of values ​​is divided into M equal parts. The range of values ​​is divided into N equal parts. The range of values ​​for is divided into O equal parts, and the range of values ​​for b is divided into P equal parts. The range of values ​​is divided into Q equal parts; Take the starting values ​​between each partition to form multiple sets of parameter combinations, and substitute each set of parameter combinations into the piecewise fitting formula described in step 1 to calculate the corresponding measured age. Calculated adiabatic temperature rise at time t The error between the calculated and measured values ​​for each parameter combination is calculated using the following formula. : ; In the formula, R represents the number of measured values. Age The corresponding measured value of adiabatic temperature rise; Select the combination of parameters with the smallest error. The corresponding parameter values ​​are used as the initial fitting results; Step 4, Iterative parameter fitting calculation The minimum error obtained from the i-th fitting And the corresponding parameter values, determine the range of parameter values ​​for the (i+1)th iteration, and the range of values ​​for each parameter is as follows: ; In the formula, k takes values ​​from 3 to 6; , , , and These are the corresponding parameter values ​​obtained from the i-th fitting; the range of each parameter value from the (i+1)-th fitting is divided equally according to the method in step 3, and the starting values ​​of each interval are used to form parameter combinations. These combinations are then substituted into the piecewise fitting formula to calculate the error of each parameter combination. Select the one with the smallest error The corresponding parameter values ​​are used as the fitting result for the (i+1)th time. Step 5, Convergence check: Calculate the minimum error difference between the (i+1)th and ith fitting iterations: ; like If u is a constant between 0.01 and 0.2, then the iteration converges, and the corresponding parameter combination is the final fitted parameter. If it does not converge, repeat step 4 to continue iterating until the convergence condition is met.

2. The fitting method according to claim 1, characterized in that, In step 3, The specific calculation method is as follows: ; In the formula, Let r be the age corresponding to the r-th measurement. for Measured values ​​of adiabatic temperature rise over age.

3. The fitting method according to claim 1, characterized in that, In step 4, during the (i+1)th fitting... The specific calculation method is as follows: ; In the formula, For the (i+1)th time The starting value of the m-th part after the range of values ​​is divided equally. For the (i+1)th time The starting value of the nth part after the range of values ​​is divided equally. Let be the starting value of the o-th part after the range of values ​​of 'a' is divided equally in the (i+1)th time. Let be the starting value of the p-th part after the range of values ​​for b is divided equally in the (i+1)-th time. Let c be the starting value of the qth part after the range of c is divided equally for the (i+1)th time.

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