Asphalt main curve model parameter initial value determination method based on EXCEL macro control

Abstract

The invention relates to an EXCEL macro control-based asphalt main curve model parameter initial value determination method, and belongs to the technical field of numerical analysis preprocessing, and the specific scheme comprises the following steps: 1, obtaining a data curve through a test; 2, performing formula setting on parameters in a time-temperature equivalent WLF formula by using a macro control of EXCEL; 3, horizontally shifting the obtained data curve by setting a macro control to obtain a main curve; 4, selecting a fitting model corresponding to the test data; 5, performing formula setting on parameters of the selected model by using a macro control of EXCEL; 6, taking a model output value as a predicted value, and taking an error between the predicted value and an actual value as an evaluation criterion of parameter adjustment; 7, adjusting the main curve through a macro control set by model parameters; and 8, adjusting parameters of the WLF formula and all model parameters, namely, taking the parameter value at the moment as an initial value for main curve optimization adjustment and constitutive model fitting.

Description

Technical Field

[0001] The invention belongs to the technical field of numerical analysis preprocessing, and in particular relates to a method for determining initial values ​​of asphalt master curve model parameters based on an EXCEL macro control. Background Art

[0002] With the development and progress of asphalt constitutive models and computer technology, data processing modules such as planning solvers can directly perform regression calculations on complex constitutive models from the adjustment of model parameter values ​​to obtain the best fitting model parameter values. Although these numerical software provide a quick calculation channel, the regression calculation is greatly affected by the initial values ​​of the parameters in the numerical regression process, and the calculation results are also greatly affected by the initial values ​​of the parameters, especially the initial value of the shift factor of the asphalt combination master curve that determines the model parameter value. At present, there are two methods to obtain the initial value. First, through the experience of predecessors, and reading literature or materials to find relevant data, to determine the appropriate initial value of the parameter, but its applicability is still relatively poor; second, based on the meaning of the parameter, it is obtained through experimental means. On the one hand, the experimental conditions are harsh and difficult to meet, and on the other hand, the model with unknown parameter meaning also accounts for a considerable proportion of all models. At present, there is a regression fitting software 1stOp that does not require the initial value of the parameter, but the software is not ideal for the data fitting effect in the logarithmic coordinate system. Therefore, determining the initial value is of great significance for the study of asphalt constitutive model fitting. Summary of the invention

[0003] In order to solve the problems existing in the above-mentioned existing fitting technology, the present invention provides a method for determining the initial values ​​of the asphalt master curve model parameters based on EXCEL macro controls. The method can be applied to the viscoelastic parameter master curves of DSR (frequency sweep test) in the medium and high temperature stages and BBR (bending beam creep stiffness test) in the low temperature stage of different types of matrices, modified or aged asphalts.

[0004] In order to achieve the above object, the present invention adopts the following technical solutions:

[0005] A method for determining initial values ​​of asphalt master curve model parameters based on EXCEL macro controls comprises the following steps:

[0006] Step 1: Use a linear range load to perform a frequency sweep test on the asphalt at at least three equally spaced temperatures within the range of 10°C to 80°C, and obtain the viscoelastic parameter curve test results of the complex modulus and phase angle in logarithmic coordinates under medium and high temperature conditions; at the same time, use a standard test load to perform a bending beam creep stiffness test on the asphalt at three low temperature temperatures of -6°C, -12°C, and -18°C, or at three low temperature temperatures of -12°C, -18°C, and -24°C, and take the logarithms of the creep time and creep stiffness, respectively, to obtain the logarithmic creep time-creep stiffness curve test results under low temperature conditions;

[0007] Step 2: Combined with the shift factors C1 and C2 in the WLF formula of the asphalt time-temperature equivalence principle, design the C1 and C2 control formulas: C1 = X control value * control accuracy + fluctuation level c1 value, C2 = Y control value * control accuracy + fluctuation level c2 value;

[0008] Step 3: According to the constraint condition of the WLF formula of asphalt, C1×C2=B / (2.303α f ), B is a constant close to 1, approximately 1, α f The thermal expansion coefficient of the free volume is set based on the conventional data of asphalt. The fluctuation level c1 value, the fluctuation level c2 value and the C1×C2 absolute value are controlled within a reasonable range. The conditional display mode is set based on EXCEL. When it is outside the reasonable range, it is displayed in red. It is necessary to readjust the X control value and the Y control value to achieve the purpose of adjusting the C1 value and the C2 value.

[0009] Step 4: Import the number of EXCEL macro controls required by the WLF formula parameters, set the macro control link X control value and Y control value respectively, and set the macro control step size, maximum value, and minimum value according to the basic conditions of the control control format and accuracy;

[0010] Step 5: Based on the WLF formula of the time-temperature equivalence principle, the shift factor is adjusted in combination with the C1 and C2 control formulas, that is, taking a certain temperature as a reference, the viscoelastic parameter curves at other temperatures are horizontally shifted to obtain the viscoelastic parameter master curve;

[0011] Step 6: Based on the different viscoelastic mechanical behaviors of asphalt, that is, different test methods of asphalt at different temperatures, select the corresponding fitting model;

[0012] Step 7: Design the control formula of model parameters, model parameters = X n Control value*Control accuracy+Control accuracy / (2^Y n Control value), where n = 1, 2, 3, ...; X n Control value * control accuracy is the range of the increase in the value of the control model parameter value, control accuracy / (2^control value Y n ) is the range of the reduced value of the control model parameter value;

[0013] Step 8: Import the number of EXCEL macro controls required for the model parameters and set the macro control link X respectively. n Control value, Y n Control value: set the step size, maximum value and minimum value of the macro control according to the basic conditions of the control format and accuracy;

[0014] Step 9: Click the model parameter macro control adjustment button to modify X n Control value, Yn The control value is adjusted by fitting the creep stiffness master curve, complex modulus master curve, and phase angle master curve after the model is moved. The value output by the model is used as the predicted value. The error between the measured value and the predicted value is used as the judgment standard. The principle of minimizing the average normalized error or relative error or R 2 Based on the principle of being closest to 1, the model parameters and WLF formula parameter values ​​at this time are selected as the initial values ​​for optimizing the main curve and fitting the constitutive model.

[0015] Furthermore, in step six, the CAM model is used in the frequency sweep test DSR, and the Burgers model is used in the bending beam creep stiffness test BBR, which are used to describe the deformation behavior of asphalt under different temperature, frequency and stress conditions, and to predict its performance in practical applications.

[0016] Furthermore, the creep stiffness test of bending beam uses the Burgers model to fit the creep stiffness main curve. The Burgers model is: S(t)-creep stiffness; t-time, where η1-viscous flow parameter; η2-delayed viscosity parameter; E1-instantaneous elastic parameter; E2-delayed elastic parameter, where η1, η2, E1, E2 are all model parameters of the creep stiffness of the Burgers model.

[0017] Furthermore, the frequency sweep test uses the CAM model to fit the master curve of complex modulus and phase angle. CAM model: Complex modulus calculation formula: f′-converted frequency (Hz); - equilibrium complex modulus when f→0, for asphalt - equilibrium complex modulus when f→∞ (Pa); f-test frequency; f c -Elastic limit threshold (Hz); k, m e - shape parameter; where f c 、m e , k These are all model parameters of the complex modulus of the CAM model; the phase angle calculation formula is: δ m - Maximum value of asphalt phase angle (°); f t - is the frequency corresponding to the highest phase angle (Hz); R d , m d - shape parameter; I- adjustment parameter, when f′>f t , I=0, when f′≤f t When , I=1; where f t ,δ m , R d 、m d These are all model parameters of the phase angle of the CAM model.

[0018] Preferably, in step one, a frequency sweep test is performed on the asphalt at 10°C, 20°C, 30°C, 40°C, 50°C, and 60°C using a linear range load.

[0019] Furthermore, in step 1, the linear range load means that there is a linear relationship between the load applied to the material and the deformation of the material, and any value is taken within this load range.

[0020] Specifically explained as follows: The linear range refers to the range within which there is a linear relationship between the stress or strain applied to the material and the deformation of the material. In other words, the stress of the material is proportional to the strain, which conforms to Hooke's law. Within this linear range, the shear modulus of the material is a constant and does not change with changes in stress or strain.

[0021] The linear range load means that there is a linear relationship between the stress or strain value and the deformation of the material, and the value taken is any value within this linear range. The definition condition of the linear range is whether there is a linear relationship between the stress or strain applied to the material and the deformation of the material.

[0022] The linear range load of each type of asphalt (different modified asphalt, asphalt with different modifier dosage, asphalt with different aging degrees) is different.

[0023] Compared with the prior art, the present invention has the following beneficial effects:

[0024] As a method for determining the initial values ​​of asphalt master curve model parameters based on EXCEL macro controls, the initial values ​​of model parameters determined in the present invention are of great significance to model optimization and fitting. Many existing fitting models and fitting optimization software rely on the setting of initial values. Inappropriate initial value settings often lead to abnormal fitting optimization, which in turn leads to poor master curve connection and fitting failure. The present invention can determine the initial values ​​of model parameters and the initial values ​​of shift factors to more accurately connect the master curve, which helps to improve the connection accuracy of the master curve and the accuracy and efficiency of model fitting, and is of great significance for the application of asphalt constitutive models. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] Figure 1 is the complex modulus curve;

[0026] Figure 2 is the phase angle curve;

[0027] Figure 3 is the creep stiffness curve;

[0028] Figure 4 This is a schematic diagram of the BBRWLF formula parameter macro control;

[0029] Figure 5 This is a schematic diagram of the DSRWLF formula parameter macro control;

[0030] Figure 6 This is a schematic diagram of the BBRBugers model parameter macro control;

[0031] Figure 7 It is a schematic diagram of the complex modulus parameter macro control of the DSRCAM model;

[0032] Figure 8 This is a schematic diagram of the phase angle parameter macro control of the DSRCAM model;

[0033] Fig. 9 It is the DSR complex modulus wide frequency master curve;

[0034] Fig.10 It is the DSR phase angle wide frequency main curve;

[0035] Fig.11 It is the wide frequency master curve of BBR creep stiffness;

[0036] Fig.12 It is the main curve of DSR complex modulus wide frequency fitting;

[0037] Fig.13 It is the main curve diagram of DSR phase angle wide frequency fitting;

[0038] Fig.14 It is the main curve of BBR creep stiffness wide frequency fitting. DETAILED DESCRIPTION

[0039] The technical solution of the present invention will be clearly and completely described below in conjunction with the drawings and embodiments. Obviously, the described embodiments are only part of the embodiments of the invention, rather than all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0040] Embodiment 1:

[0041] A method for determining initial values ​​of asphalt master curve model parameters based on EXCEL macro controls comprises the following steps:

[0042] Step 1: Using a DSR dynamic shear rheometer, under the action of a linear range load of 200Pa, frequency sweep tests were performed on the asphalt at 10℃, 20℃, 30℃ based on an 8mm parallel plate and at 40℃, 50℃, 60℃ based on a 25mm parallel plate, and the test results of complex modulus and phase angle viscoelastic parameter curves under logarithmic coordinates of multiple temperature conditions under medium and high temperature conditions were obtained, such as Figure 1 , 2As shown; standard test load is used for 70 # The asphalt was subjected to three bending beam creep stiffness tests at low temperatures of -12°C, -18°C, and -24°C, i.e., a creep test load of 980mN±50mN and a creep test time of 240s. The creep time and creep stiffness were taken logarithmically to obtain the creep time and creep stiffness curves corresponding to the three low temperature temperatures. Figure 3 As shown;

[0043] Step 2: Combined with the shift factors C1 and C2 in the WLF formula of the asphalt time-temperature equivalence principle, design the C1 and C2 control formulas: C1 = X control value * control accuracy + fluctuation level c1, C2 = Y control value * control accuracy + fluctuation level c2;

[0044] Step 3: According to the constraint condition of the WLF formula of asphalt, C1×C2=B / (2.303α f ), B is a constant close to 1, approximately 1, α f The thermal expansion coefficient of the free volume is set based on the conventional data of asphalt. The fluctuation level c1 value, the fluctuation level c2 value and the absolute value of C1×C2 are set to control the reasonable range. The conditional display mode is set based on EXCEL. When it is outside the reasonable range, it is displayed in red. Repeat the adjustment of the X adjustment value and the Y adjustment value to achieve the purpose of adjusting the C1 value and the C2 value. For example, 70 # Matrix asphalt C1 = X*0.1-18, C2 = Y*1+90, the absolute value of C1×C2 is controlled within a reasonable range of 900 to 3000;

[0045] Step 4: Set the formulas of WLF formula parameters C1 and C2 in EXCEL. Insert the WLF formula parameter C1 and C2 macro controls, and set the step size, maximum value, and minimum value of the macro controls according to the basic conditions of the control adjustment format and precision. 10; Maximum value: 1000; Step length: 10. The X control value cell link is A1, the c1 fluctuation level cell B1 is adjusted to -18, the X control precision is 0.1, that is, 10 / 100, and the C1 calculation value C1 cell enters the formula = B1 + A1 / 100. The Y control value cell link is A2, the c2 fluctuation level cell B2 is adjusted to 90, the Y control precision is 1, that is, 10 / 10, and the C2 calculation value C2 cell enters the formula = B2 + A2 / 10. Figure 4 , 5 As shown;

[0046] Step 5: Use the time-temperature equivalence principle WLF formula Where α T(T)-temperature shift factor; T-test temperature (℃), T0-reference temperature (℃), C1, C2-constants; adjust the shift factor in combination with the C1 and C2 control formulas; that is, take a certain temperature as a reference, horizontally shift the viscoelastic parameter curves at other temperatures to obtain the viscoelastic parameter master curve;

[0047] Step 6: Repeatedly click the macro control adjustment button to control the absolute value of C1×C2 within a reasonable range, modify the X control value and the Y control value, and obtain the initial 1.0 version of the master curve of creep stiffness, complex modulus and phase angle after horizontal movement, such as Fig. 9 , 10 , as shown in 11;

[0048] Step 7: Use the same macro control method to determine the master curve model parameters of the initial 1.0 version.

[0049] For example, the test results of the complex modulus and phase angle viscoelastic parameter curves in logarithmic coordinates of the frequency sweep test (DSR) under medium and high temperature conditions are horizontally moved to obtain the master curve of the initial 1.0 version of the complex modulus and phase angle viscoelastic parameters with 20°C as the reference temperature. The CAM model is used for fitting, and the complex modulus calculation formula is: f′-conversion frequency Hz; - equilibrium complex modulus when f→0, for asphalt - equilibrium complex modulus when f→∞ (Pa); f-test frequency; f c -Elastic limit threshold (Hz); k, m e -Shape parameters; Phase angle calculation formula: δ m - Maximum value of asphalt phase angle (°); f t - is the frequency corresponding to the highest phase angle (Hz); R d , m d - shape parameter; I- adjustment parameter, when f′>f t , I=0, when f′≤f t , then I=1.

[0050] The creep stiffness viscoelastic parameter curve test results of the bending beam creep stiffness test (BBR) under low temperature conditions were horizontally moved to obtain the initial 1.0 version of the master curve of the stiffness modulus viscoelastic parameter with a reference temperature of -18°C. The Burgers model was used to fit the creep stiffness master curve S(t)-creep stiffness; t-time, where η1-viscous flow parameter; η2-delayed viscosity parameter; E1-instantaneous elastic parameter; E2-delayed elastic parameter, where η1, η2, E1, and E2 are all model parameters of the creep stiffness of the Burgers model;

[0051] Step 8: Design the model parameter control formula, model parameter value = control value X n *Control accuracy + Control accuracy / (2^Control value Y n ), n = 1, 2, 3, ..., Note: X n Control value * control accuracy is the range of the increase in the value of the control model parameter value, control accuracy / (2^control value Y n ) is the range of the reduced value of the control model parameter value;

[0052] Step 9: Set the low-temperature Burgers model parameter E1. The value displayed in cell E1 is the value of E1. Then select two adjustable cells E2 and E3. 0; Minimum value: 0; Maximum value: 1000; Step length: 1, select E3 as the cell link, and E3 corresponds to Y in the formula of step 8 n . 0; Minimum value: 0; Maximum value: 1000; Step length: 1, select E2 as the cell link, and E2 corresponds to X in the formula of step 8 n . To control the precision X n =Y n =10000, increase step size = 10000, and decrease amplitude by 1 / 2 of each value. For example, enter the formula = E2*10000+10000 / (2^E3) in cell E1. When you need to adjust the parameter upward, first adjust the decrease value to 10000, that is, when E3 = 0, then adjust X separately. n To achieve the purpose of upward adjustment; when the parameters need to be adjusted downward, first adjust the rising value to zero, that is, when E2=0, then adjust Y n In order to achieve the purpose of upward adjustment; the low temperature Burgers model parameters E2, η1, η2 are set in the same way, such as Figure 6 The medium and high temperature model parameter macro control is as shown. Figure 7 , 8 shown.

[0053] Step 10: Repeatedly click the macro control adjustment button to modify the control values ​​of X2, Y2, X3, Y3, X4, and Y4 to obtain the creep stiffness master curve, complex modulus and phase angle master curve fitting master curve version 2.0. The value output by the model is used as the predicted value, and the error between the measured value and the predicted value is used as the judgment standard. The principle of selecting the control is to minimize the average normalized error or the relative error or R 2 Closest to 1. Mean Normalized Error (MNE) formula: Among them, |G * | 实测 - represents the actual value of the i-th observation; |G* | 预测 - represents the predicted value of the i-th observation; n is the total number of observation points; R 2 formula: where y i - represents the actual value of the i-th observation point; - represents the predicted value of the i-th observation point; - represents the average value of the actual values ​​of n observation points; relative error formula: Where |G * | 实测 - represents the actual value of the i-th observation; |G * | 预测 - represents the predicted value of the i-th observation, when the fitted average normalized error value or relative error value is the smallest, or R 2 When it is closest to 1, select the parameter value at this time. After all parameters are adjusted, the parameter values ​​of the asphalt master curve model and the WLF formula parameter values ​​at this time are determined as the initial values ​​for the master curve optimization adjustment and constitutive model fitting. Fig.12 , 13 , as shown in 14.

[0054] In addition, it should be understood that although the present specification is described according to implementation modes, not every implementation mode contains only one independent technical solution. This description of the specification is only for the sake of clarity. Those skilled in the art should regard the specification as a whole. The technical solutions in each embodiment may also be appropriately combined to form other implementation modes that can be understood by those skilled in the art.

Claims

1. A method for determining the initial values ​​of asphalt master curve model parameters based on EXCEL macro controls, characterized in that: The following steps are involved: Step 1: Use a linear range load to perform a frequency sweep test on the asphalt at at least three equally spaced temperatures within the range of 10°C to 80°C, and obtain the viscoelastic parameter curve test results of the complex modulus and phase angle in logarithmic coordinates under medium and high temperature conditions; at the same time, use a standard test load to perform a bending beam creep stiffness test on the asphalt at three low temperature temperatures of -6°C, -12°C, and -18°C, or at three low temperature temperatures of -12°C, -18°C, and -24°C, and take the logarithms of the creep time and creep stiffness, respectively, to obtain the logarithmic creep time-creep stiffness curve test results under low temperature conditions; Step 2: Combined with the shift factors C1 and C2 in the WLF formula of the asphalt time-temperature equivalence principle, design the C1 and C2 control formulas: C1 = X control value * control accuracy + fluctuation level c1 value, C2 = Y control value * control accuracy + fluctuation level c2 value; Step 3: According to the constraint condition of the WLF formula of asphalt, C1×C2=B / (2.303α f ), B is a constant close to 1, approximately 1, α f The thermal expansion coefficient of the free volume is set based on the conventional data of asphalt. The fluctuation level c1 value, the fluctuation level c2 value and the C1×C2 absolute value are controlled within a reasonable range. The conditional display mode is set based on EXCEL. When it is outside the reasonable range, it is displayed in red. It is necessary to readjust the X control value and the Y control value to achieve the purpose of adjusting the C1 value and the C2 value. Step 4: Import the number of EXCEL macro controls required by the WLF formula parameters, set the macro control link X control value and Y control value respectively, and set the macro control step size, maximum value, and minimum value according to the basic conditions of the control control format and accuracy; Step 5: Based on the WLF formula of the time-temperature equivalence principle, the shift factor is adjusted in combination with the C1 and C2 control formulas, that is, taking a certain temperature as a reference, the viscoelastic parameter curves at other temperatures are horizontally shifted to obtain the viscoelastic parameter master curve; Step 6: Based on the different viscoelastic mechanical behaviors of asphalt, that is, different test methods of asphalt at different temperatures, select the corresponding fitting model; Step 7: Design the control formula of model parameters, model parameters = X n Control value*Control accuracy+Control accuracy / (2^Y n Control value), where n = 1, 2, 3, ...; X n Control value * control accuracy is the range of the increase in the value of the control model parameter value, control accuracy / (2^control value Y n ) is the range of the reduced value of the control model parameter value; Step 8: Import the number of EXCEL macro controls required for the model parameters and set the macro control link X respectively. n Control value, Y n Control value: set the step size, maximum value and minimum value of the macro control according to the basic conditions of the control format and accuracy; Step 9: Click the model parameter macro control adjustment button to modify X n Control value, Y n The control value is adjusted by fitting the creep stiffness master curve, complex modulus master curve, and phase angle master curve after the model is moved. The value output by the model is used as the predicted value. The error between the measured value and the predicted value is used as the judgment standard. The principle of minimizing the average normalized error or relative error or R 2 Based on the principle of being closest to 1, the model parameters and WLF formula parameter values ​​at this time are selected as the initial values ​​for optimizing the main curve and fitting the constitutive model.

2. The method for determining the initial values ​​of the asphalt master curve model parameters based on the EXCEL macro control according to claim 1 is characterized in that: In step six, the CAM model is used in the frequency sweep test DSR, and the Burgers model is used in the bending beam creep stiffness test BBR to describe the deformation behavior of asphalt under different temperature, frequency and stress conditions, and to predict its performance in practical applications.

3. The method for determining the initial values ​​of the asphalt master curve model parameters based on the EXCEL macro control according to claim 2 is characterized in that: The creep stiffness test of bending beam uses the Burgers model to fit the creep stiffness main curve. The Burgers model is: S(t)-creep stiffness; t-time, where η1-viscous flow parameter; η2-delayed viscosity parameter; E1-instantaneous elastic parameter; E2-delayed elastic parameter, where η1, η2, E1, E2 are all model parameters of the creep stiffness of the Burgers model.

4. The method for determining the initial values ​​of the asphalt master curve model parameters based on the EXCEL macro control according to claim 2 is characterized in that: The frequency sweep test uses the CAM model to fit the master curve of complex modulus and phase angle. CAM model: Complex modulus calculation formula: f′-converted frequency (Hz); - equilibrium complex modulus when f→0, for asphalt - equilibrium complex modulus when f→∞ (Pa); f-test frequency; f c -Elastic limit threshold (Hz); k, m e - shape parameter; where f c 、m e , k, These are all model parameters of the complex modulus of the CAM model; the phase angle calculation formula is: δ m - Maximum value of asphalt phase angle (°); f t - is the frequency corresponding to the highest phase angle (Hz); R d , m d - shape parameter; I- adjustment parameter, when f′>f t , I=0, when f′≤f t When I = 1, f t ,δ m , R d 、m d These are all model parameters of the phase angle of the CAM model.

5. The method for determining the initial values ​​of the asphalt master curve model parameters based on the EXCEL macro control according to claim 1 is characterized in that: In step one, a frequency sweep test is performed on the asphalt at 10°C, 20°C, 30°C, 40°C, 50°C, and 60°C using a linear range load.

6. The method for determining the initial values ​​of the asphalt master curve model parameters based on the EXCEL macro control according to claim 1 is characterized in that: In step 1, the linear range load means that there is a linear relationship between the load applied to the material and the deformation of the material, and any value is taken within this load range.

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