CN111781077B - Method for improving calculation accuracy of rheological times of asphalt mixture - Google Patents
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- G—PHYSICS
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- G01N3/00—Investigating strength properties of solid materials by application of mechanical stress
- G01N3/32—Investigating strength properties of solid materials by application of mechanical stress by applying repeated or pulsating forces
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
- G01N2203/00—Investigating strength properties of solid materials by application of mechanical stress
- G01N2203/0001—Type of application of the stress
- G01N2203/0005—Repeated or cyclic
- G01N2203/0007—Low frequencies up to 100 Hz
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
- G01N2203/00—Investigating strength properties of solid materials by application of mechanical stress
- G01N2203/0014—Type of force applied
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- G01N2203/0019—Compressive
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
- G01N2203/00—Investigating strength properties of solid materials by application of mechanical stress
- G01N2203/0058—Kind of property studied
- G01N2203/0069—Fatigue, creep, strain-stress relations or elastic constants
- G01N2203/0075—Strain-stress relations or elastic constants
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
- G01N2203/00—Investigating strength properties of solid materials by application of mechanical stress
- G01N2203/02—Details not specific for a particular testing method
- G01N2203/0202—Control of the test
- G01N2203/0212—Theories, calculations
- G01N2203/0218—Calculations based on experimental data
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
- G01N2203/00—Investigating strength properties of solid materials by application of mechanical stress
- G01N2203/02—Details not specific for a particular testing method
- G01N2203/06—Indicating or recording means; Sensing means
- G01N2203/067—Parameter measured for estimating the property
- G01N2203/0682—Spatial dimension, e.g. length, area, angle
Abstract
A method for improving the calculation accuracy of the rheological times of an asphalt mixture relates to a method for calculating the rheological times of the asphalt mixture. The invention aims to solve the technical problem of large error of the existing method for calculating the rheological times of the asphalt mixture. The invention directly adopts the strain rate curve to calculate, and can avoid the error caused by indirect algorithm; according to the method, a local fitting method is adopted, and data in a local area near the lowest point of a strain rate curve are adopted for calculation, so that the fitting effect of the area near the lowest point can be improved, and a more accurate calculation result can be obtained; the invention provides a method for determining a local fitting range by adopting an initial minimum strain rate multiple, and the method can accurately obtain data in different ranges near the lowest point of the strain rate and improve the calculation efficiency. The method for determining the optimal K value based on the relative error is definitely provided, randomness of qualitative evaluation is avoided, and the optimal K value can be determined quantitatively. The method is applied to calculating the rheological times of the asphalt mixture.
Description
Technical Field
The invention relates to a method for calculating the rheological times of an asphalt mixture.
Background
The asphalt mixture is the first choice material for the construction of high-grade highways, and the proportion of asphalt pavements in the high-grade highways is about 80% in the world. Asphalt mixture is a typical temperature sensitive material, and is easy to generate unrecoverable permanent deformation when bearing vehicle load under high temperature condition, thereby generating rutting diseases. The road ruts can form water accumulation in rainy days, which can cause the drift phenomenon of running vehicles and seriously threaten the driving safety. A large number of researches show that the global climate change with warming as the main characteristic occurs, and the earth surface heating rate of China is higher than the global mean value; in addition, in road traffic of China, heavy load and overload conditions generally exist, and the phenomena further aggravate the track diseases of the asphalt pavement. The selection of the proper asphalt mixture can effectively reduce the track diseases, and the reasonable evaluation of the track resistance of the asphalt mixture is the basis for selecting the proper asphalt mixture.
The rheological frequency test is a simple performance test for internationally and generally evaluating the rutting resistance of the asphalt mixture. The rheological frequency experiment is widely applied by researchers due to the fact that experimental equipment is simple and good in correspondence with actual ruts. The permanent deformation process of the asphalt mixture under a rheological frequency experiment (a repeated load permanent deformation experiment) is generally divided into three stages: in the first stage, the void ratio of the asphalt mixture is rapidly reduced, and plastic compaction deformation occurs; in the second stage, the permanent deformation is stably increased, and the deformation rate is basically kept unchanged, which is called a stable stage; in the third stage, the permanent deformation is accelerated and increased, and the destruction stage is entered. The load times when the asphalt mixture enters the failure stage from the stabilization stage are called rheological times, can represent the rutting resistance of the asphalt mixture, are the most important parameters of the experiment, and are important basis for selecting the type of the asphalt mixture.
Generally, the rheological times are load times corresponding to the lowest point of the strain rate, and the calculation method can be divided into an experimental value method and a function fitting method. The experimental value method is to obtain the strain under each load according to the accumulated strain, and then directly search the minimum value or determine the minimum value after simple processing. The function fitting method adopts a function model to fit an experimental curve, and can avoid the influence caused by accidental errors. The function fitting method can be classified into a strain method and a strain rate method. The strain method is that firstly, an actually measured strain curve is fitted, then the second derivative of the fitting function is made to be zero, and the inflection point of the strain fitting curve is obtained; the strain rate method is to fit an actually measured strain rate curve first, then make the first derivative of a fitting function be zero, and obtain the lowest point of the strain rate fitting curve. However, the current calculation result of the rheological number depends heavily on the selected calculation method and mathematical model, and the rheological number obtained by different methods and models has larger difference. Studies suggest that this is due to two problems: firstly, the method comprises the following steps: the rheological times are the load times corresponding to the lowest point of the strain rate curve, so the calculation result of the rheological times is only influenced by a local area near the lowest point, but the whole strain rate curve is generally selected when a function fitting method is applied at present, and the fitting effect of the area near the lowest point cannot be ensured by the method; secondly, the method comprises the following steps: the current calculation method generally adopts a strain curve, and the definition of the flow variable is based on the strain rate, so that the strain rate method is an indirect algorithm and can cause large errors.
Disclosure of Invention
The invention provides a method for improving the calculation accuracy of the rheological times of an asphalt mixture, aiming at solving the technical problem of large error of the conventional calculation method of the rheological times of the asphalt mixture.
The method for improving the calculation accuracy of the rheological times of the asphalt mixture is carried out according to the following steps:
1. determining a strain rate curve: acquiring accumulated strain F (x) after the load is carried for x times by using a repeated load permanent deformation experiment; the strain rate E (x) corresponding to the x-th load is represented by the formula E (x) = F (x) -F (x-1);
2. determining an initial minimum strain rate: according to the strain rate data in the step one, a strain rate model is adopted to fit a strain rate curve, the fitted strain rate curve is derived, a derivative function is made to be zero, and the abscissa of a point with the derivative function being zero is the initial current variable FN 0 ，FN 0 The ordinate corresponding to the fitted strain rate curve is the initial minimum strain rate, and is marked as E 0 ；
3. Determining a local fitting interval: let E K ＝K×E 0 Straight line y = E K Two intersection points of the strain rate curve fitted with the second step are respectively N on the abscissa KL And N KH ，N KL Of which the smaller value, N KH The greater of the two; [ N ] KL ，N KH ]A local fitting interval corresponding to the K value is set; selecting different K values, and calculating corresponding local fitting intervals; the K is 2.42.2, 2, 1.8, 1.6, 1.4 or 1.2;
4. calculating the rheological times: according to the strain rate data in the step one, fitting the abscissa in the step three by using a strain rate model KL ，N KH ]In the range of the strain rate curve, derivative is carried out on the fitted strain rate curve and the derivative function is made to be zero, and the abscissa of the point with the derivative function being zero is the rheological frequency FN corresponding to the K value K ；
5. Determining an optimal K value: FN corresponding to different K values is calculated according to the sequence of the K values from large to small K ；K 1 、K 2 、K 3 、K 4 、K 5 、K 6 And K 7 The corresponding K values are 2.4, 2.2, 2, 1.8, 1.6, 1.4 and 1.2 in sequence;
when | FN K(N) -FN K(N+1) |/[0.5×(FN K(N) +FN K(N+1) )]Stopping calculation when the content is less than or equal to 0.5%, wherein K (N) is the optimal K value, and the rheological times FN corresponding to the optimal K value K As the final number of rheologies FN; FN (FN) K(N) FN corresponding to K having different values K And N is a positive integer from 1 to 7.
Compared with the prior art, the invention has the beneficial effects that:
1. the definition of the rheological times is based on the strain rate, but the traditional method of firstly adopting a strain fitting curve and then obtaining a strain rate curve through derivation is an indirect algorithm, which may cause larger errors; according to the invention, the strain rate curve is directly adopted for calculation, so that errors caused by an indirect algorithm can be avoided;
2. the rheological times are the load times corresponding to the lowest point of the strain rate curve, and in order to avoid the influence of accidental errors (data fluctuation), a strain rate model is generally adopted for fitting, and then the lowest point of the fitting curve is calculated. However, in the prior art, an entire strain rate curve (integral fitting method) is generally selected, fitting parameters are obtained according to an integral optimal principle, and the method cannot ensure the fitting effect of the region near the lowest point, so that the rheological times cannot be accurately calculated. According to the method, a local fitting method is adopted, and data in a local area near the lowest point of a strain rate curve are adopted for calculation, so that the fitting effect of the area near the lowest point can be obviously improved, and a more accurate calculation result can be obtained;
3. according to the method, a common strain rate fitting model is adopted to obtain an initial minimum strain rate by adopting a traditional method, and then a corresponding local fitting interval is obtained according to a multiple of the initial minimum strain rate, so that data in different ranges near the lowest point of the strain rate can be accurately obtained by the method, and the calculation efficiency can be improved;
4. the method for determining the optimal K value based on the relative error is definitely provided, randomness of qualitative evaluation is avoided, and the optimal K value can be determined quantitatively.
When a Francken strain rate model is adopted, the method can improve the calculation precision by 3% -17%, and the average value is 9%; when a Hoerl strain rate model is adopted, the method can improve the calculation precision by 6-19 percent, and the average value is 13 percent.
Drawings
FIG. 1 is a graph showing a fitted curve of experiment one.
Detailed Description
The first embodiment is as follows: the embodiment is a method for improving the rheological time calculation accuracy of an asphalt mixture, which is specifically carried out according to the following steps:
1. determining a strain rate curve: acquiring accumulated strain F (x) after x times of loading by using a repeated load permanent deformation experiment; the strain rate E (x) corresponding to the x-th load is represented by the formula E (x) = F (x) -F (x-1);
2. determining an initial minimum strain rate: according to the strain rate data in the step one, a strain rate model is adopted to fit a strain rate curve, the fitted strain rate curve is derived, a derivative function is made to be zero, and the abscissa of a point with the derivative function being zero is the initial current variable FN 0 ，FN 0 The ordinate corresponding to the fitted strain rate curve is the initial minimum strain rate and is marked as E 0 ；
3. Determining a local fitting interval: let E K ＝K×E 0 Straight line y = E K Two intersection points of the strain rate curve fitted with the step two are respectively provided with the abscissa of N KL And N KH ，N KL Is the smaller of the twoValue, N KH The greater of the two; [ N ] KL ，N KH ]A local fitting interval corresponding to the K value is set; selecting different K values, and calculating corresponding local fitting intervals; k is 2.4, 2.2, 2, 1.8, 1.6, 1.4 or 1.2;
4. calculating the rheological times: according to the strain rate data in the step one, fitting the abscissa in the step three by using a strain rate model KL ，N KH ]In the range of the strain rate curve, derivative is carried out on the fitted strain rate curve and the derivative function is made to be zero, and the abscissa of the point with the derivative function being zero is the rheological frequency FN corresponding to the K value K ；
5. Determining an optimal K value: FN corresponding to different K values is calculated according to the sequence of the K values from large to small K ；K 1 、K 2 、K 3 、K 4 、K 5 、K 6 And K 7 The corresponding K values are 2.4, 2.2, 2, 1.8, 1.6, 1.4 and 1.2 in sequence;
when | FN K(N) -FN K(N+1) |/[0.5×(FN K(N) +FN K(N+1) )]Stopping calculation when the content is less than or equal to 0.5%, wherein K (N) is the optimal K value, and the rheological frequency FN corresponding to the optimal K value K As the final number of rheologies FN; FN (FN) K(N) FN corresponding to K having different values K And N is a positive integer from 1 to 7.
The second embodiment is as follows: the first difference between the present embodiment and the specific embodiment is: and (4) loading the repeated load permanent deformation experiment in the step one indoors by using a material testing machine UTM or MTS. The rest is the same as the first embodiment.
The third concrete implementation mode: the present embodiment is different from the second embodiment in that: and D, a test piece used in the repeated load permanent deformation experiment in the step I is a cylindrical asphalt mixed test piece with the diameter of 10cm and the height of 15 cm. The rest is the same as the second embodiment.
The fourth concrete implementation mode is as follows: the third difference between the present embodiment and the specific embodiment is that: the loading waveform of the repeated load permanent deformation experiment in the step one is a half sine wave, the loading frequency is 1Hz, the loading time is 0.1s, and the intermittent time is 0.9s. The rest is the same as the third embodiment.
The fifth concrete implementation mode is as follows: the difference between this embodiment and one of the first to fourth embodiments is: and step two, adopting a Hoerl strain rate model to fit a strain rate curve. The rest is the same as the first to fourth embodiments.
The sixth specific implementation mode: the difference between this embodiment and one of the first to fifth embodiments is: and in the second step, a Francken strain rate model is adopted to fit a strain rate curve. The rest is the same as one of the first to fifth embodiments.
The seventh embodiment: the sixth embodiment is different from the specific embodiment in that: the Francken strain rate model in the second step is as follows:
E(x)＝ABx B-1 +CDe Dx ，
in the formula, A, B, C and D are fitting parameters. The rest is the same as the sixth embodiment.
The specific implementation mode is eight: the fifth embodiment is different from the fifth embodiment in that: the Hoerl strain rate model in the step two is as follows: e (x) = AB x X C In the formula, A, B and C are fitting parameters. The rest is the same as the fifth embodiment.
The specific implementation method nine: the present embodiment differs from the first to eighth embodiments in that: step four, fitting the abscissa in step three by using a Hoerl strain rate model [ N [ ] KL ，N KH ]Strain rate curve within the range. The others are the same as in the first to eighth embodiments.
The detailed implementation mode is ten: the difference between this embodiment and one of the first to ninth embodiments is that: step four using Francken strain rate model to fit [ N ] of abscissa in step three KL ，N KH ]Strain rate curve within the range. The rest is the same as one of the first to ninth embodiments.
The invention was verified with the following tests:
test one: the test is a method for improving the calculation accuracy of the rheological times of the asphalt mixture, and is specifically carried out according to the following steps:
1. determining a strain rate curve: acquiring accumulated strain F (x) after x times of loading by using a repeated load permanent deformation experiment; the strain rate E (x) corresponding to the x-th load is represented by the formula E (x) = F (x) -F (x-1);
2. determining an initial minimum strain rate: according to the strain rate data in the step one, a Francken strain rate model is adopted to fit a strain rate curve, the fitted strain rate curve is derived, a derivative function is made to be zero, and the abscissa of a point with the derivative function being zero is the initial flow variable FN 0 (803)，FN 0 The ordinate corresponding to the fitted strain rate curve is the initial minimum strain rate, and is marked as E 0 (7.265)；
3. Determining a local fitting interval: let E K ＝K×E 0 Straight line y = E K Two intersection points of the strain rate curve fitted with the second step are respectively N on the abscissa KL And N KH ，N KL For the smaller of the two, N KH The greater of the two; [ N ] KL ，N KH ]Is a local fitting interval corresponding to the value of K; selecting different K values, and calculating corresponding local fitting intervals; k is 2.4, 2.2, 2, 1.8, 1.6, 1.4 or 1.2;
4. calculating the rheological times: according to the strain rate data in the step one, a Francken strain rate model is used for fitting [ N ] of the abscissa in the step three KL ，N KH ]In the range of the strain rate curve, derivative is carried out on the fitted strain rate curve and the derivative function is made to be zero, and the abscissa of the point with the derivative function being zero is the rheological frequency FN corresponding to the K value K ；
5. Determining an optimal K value: FN corresponding to different K values is calculated according to the sequence of the K values from large to small K ；K 1 、K 2 、K 3 、K 4 、K 5 、K 6 And K 7 The corresponding K values are 2.4, 2.2, 2, 1.8, 1.6, 1.4 and 1.2 in sequence;
when | FN K(N) -FN K(N+1) |/[0.5×(FN K(N) +FN K(N+1) )]Stopping calculation when the content is less than or equal to 0.5%, wherein K (N) is the optimal K value, and the rheological frequency FN corresponding to the optimal K value K As the final rheological number FN; FN (FN) device K(N) FN corresponding to K taking different values K And N is a positive integer from 1 to 7.
In the repeated load permanent deformation experiment in the step one, a material testing machine MTS is used for loading indoors, the used test piece is a cylindrical asphalt mixed test piece with the diameter of 10cm and the height of 15cm, the loading waveform is a half sine wave, the loading frequency is 1Hz, the loading time is 0.1s, and the intermittent time is 0.9s.
FIG. 1 is a graph of a fitted curve of experiment one, where curve 1 is y = E K Curve with medium K equal to 2.4, curve 2 being y = E K Curve with medium K equal to 2.2, curve 3 y = E K And (5) a curve when the middle K is equal to 1.4, wherein the curve 4 is a curve obtained by adopting a Francken strain rate model to fit the strain rate in the step two.
The data obtained from the tests are shown in the following table, wherein the relative error is | FN in step five K(N) -FN K(N+1) |/[0.5×(FN K(N) +FN K(N+1) )]Value of (a), finally K 5 And K 6 Is less than 0.5%, FN 5 Overall fitting method for final rheological index FN (875) 0 =803, local fitting (k 5= 1.6), FN =875, the difference being considerable, indicating that the global fitting method cannot calculate FN accurately, resulting in large errors.
Claims (10)
1. A method for improving the calculation accuracy of the rheological times of an asphalt mixture is characterized in that the method for improving the calculation accuracy of the rheological times of the asphalt mixture is carried out according to the following steps:
1. determining a strain rate curve: acquiring accumulated strain F (x) after the load is carried for x times by using a repeated load permanent deformation experiment; the strain rate E (x) corresponding to the x-th load is represented by the formula E (x) = F (x) -F (x-1);
2. determining an initial minimum strain rate: according to the strain rate data in the step one, a strain rate model is adopted to fit a strain rate curve, the fitted strain rate curve is derived, a derivative function is made to be zero, and the abscissa of a point with the derivative function being zero is the initial flow variable FN 0 ，FN 0 In the fittingThe ordinate corresponding to the strain rate curve is the initial minimum strain rate, and is marked as E 0 ；
3. Determining a local fitting interval: let E K ＝K×E 0 Straight line y = E K Two intersection points of the strain rate curve fitted with the second step are respectively N on the abscissa KL And N KH ，N KL Of which the smaller value, N KH The greater of the two; [ N ] KL ，N KH ]A local fitting interval corresponding to the K value is set; selecting different K values, and calculating corresponding local fitting intervals; the K is 2.4, 2.2, 2, 1.8, 1.6, 1.4 or 1.2;
4. calculating the rheological times: according to the strain rate data in the step one, fitting the abscissa in the step three by using a strain rate model KL ，N KH ]In the range of the strain rate curve, derivative is carried out on the fitted strain rate curve and the derivative function is made to be zero, and the abscissa of the point with the derivative function being zero is the rheological frequency FN corresponding to the K value K ；
5. Determining an optimal K value: FN corresponding to different K values is calculated according to the sequence of the K values from large to small K ；K 1 、K 2 、K 3 、K 4 、K 5 、K 6 And K 7 The corresponding K values are 2.4, 2.2, 2, 1.8, 1.6, 1.4 and 1.2 in sequence;
when | FN K(N) -FN K(N+1) |/[0.5×(FN K(N) +FN K(N+1) )]Stopping calculation when the content is less than or equal to 0.5%, wherein K (N) is the optimal K value, and the rheological times FN corresponding to the optimal K value K As the final rheological number FN; FN (FN) device K(N) FN corresponding to K having different values K And N is a positive integer from 1 to 7.
2. The method for improving the accuracy of the calculation of the rheological times of the asphalt mixture according to claim 1, wherein the repeated load permanent deformation experiment in the step one is carried out indoors by using a material testing machine UTM or MTS.
3. The method for improving the calculation accuracy of the rheological times of the asphalt mixture according to claim 2 is characterized in that the test piece used in the repeated load permanent deformation experiment in the step one is a cylindrical asphalt mixture test piece with the diameter of 10cm and the height of 15 cm.
4. The method for improving the accuracy of the calculation of the rheological times of the asphalt mixture according to claim 3, wherein the loading waveform of the repeated load permanent deformation experiment in the step one is a half sine wave, the loading frequency is 1Hz, the loading time is 0.1s, and the pause time is 0.9s.
5. The method for improving the accuracy of the calculation of the rheological times of the bituminous mixture according to claim 1, wherein a Hoerl strain rate model is adopted to fit a strain rate curve in the second step.
6. The method for improving the accuracy of the calculation of the rheological times of the bituminous mixture according to claim 1, wherein a Francken strain rate model is adopted to fit a strain rate curve in the second step.
7. The method for improving the accuracy of calculating the rheological times of the asphalt mixture according to claim 6, wherein the Francken strain rate model in the second step is as follows:
E(x)＝ABx B-1 +CDe Dx ，
in the formula, A, B, C and D are fitting parameters.
8. The method for improving the accuracy of calculating the rheological times of the asphalt mixture according to claim 5, wherein the Hoerl strain rate model in the second step is as follows: e (x) = AB x X C In the formula, A, B and C are fitting parameters.
9. The method for improving the accuracy of the calculation of the rheological times of the bituminous mixture according to claim 1, wherein the Hoerl strain rate model is used in the fourth step to fit the [ N ] with the abscissa in the third step KL ，N KH ]Strain rate curve within the range.
10. The method for improving the accuracy of the calculation of the rheological times of the bituminous mixture according to claim 1, wherein the Francken strain rate model is used in the fourth step to fit [ N ] with the abscissa in the third step KL ，N KH ]Strain rate curve within the range.
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| CN111781077A (en) | 2020-10-16 |
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