阅读说明：本技术 沥青路面龟裂演化的预测方法 (Method for predicting crack evolution of asphalt pavement ) 是由 肖敏敏 范霖 于 2021-09-16 设计创作，主要内容包括：一种沥青路面龟裂演化的预测方法,包括：基于统计量观测数据,描述因素统计量和研究对象之间的关系,明确变量之间相关关系的密切程度,得出因素统计量和研究对象之间的变量间回归数学方程；统计检验沥青路面龟裂演化预测模型的可信度,计算解释变量间回归数学方程的拟合优度,明确除此统计量以外的其他因素对研究对象的非线性影响效果；根据选定因素观测值的趋势走向,确定出因变量预测的取值,并通过回归预测模型给出未来几年沥青路面路面龟裂的预测区间,实现沥青路面龟裂演化行为的预测分析。通过沥青路面龟裂的回归预测,解决了当前施工部门对路面龟裂行为的监控缺乏合理性和精确性的缺陷,为优化路面龟裂修复养护方案提供了理论基础。(A method for predicting crack evolution of an asphalt pavement comprises the following steps: describing the relationship between the factor statistics and the study object based on the statistics observation data, and determining the closeness degree of the correlation relationship between the variables to obtain a regression mathematical equation between the variables between the factor statistics and the study object; carrying out statistical test on the credibility of the crack evolution prediction model of the asphalt pavement, calculating the goodness of fit of a regression mathematical equation among the explanatory variables, and determining the nonlinear influence effect of other factors except the statistical quantity on a research object; and determining the predicted value of the dependent variable according to the trend of the selected factor observed value, and giving a prediction interval of the crack of the asphalt pavement in the coming years through a regression prediction model to realize the prediction analysis of the crack evolution behavior of the asphalt pavement. Through the regression prediction of the cracking of the asphalt pavement, the defect that the monitoring of the cracking behavior of the pavement by the current construction department lacks reasonableness and accuracy is overcome, and a theoretical basis is provided for optimizing a pavement cracking repairing and maintaining scheme.)

1. The method for predicting the crack evolution of the asphalt pavement is characterized by comprising the following steps of:

step 1: determining the crack behavior evolution of the asphalt pavement as a research object, analyzing influence factors which influence the omnibearing characteristics of the research object in a list manner, determining the influence mechanism of the expression form of the influence factors on the research object, and constructing a preposed analysis frame for comprehensive evaluation of the crack behavior of the asphalt pavement;

step 2: according to the pre-analysis framework, any one of the influence factors of the omnibearing features is selected as a macroscopic statistic, and an explanation variable and an explained variable are determined according to the analysis judgment result of the actual problem on the basis of the macroscopic statistic;

and step 3: describing the relationship between the factor statistic and the study object based on the statistic observation data, and determining the closeness degree of the correlation between the interpretation variable and the interpreted variable to obtain a regression mathematical equation between the variables between the factor statistic and the study object;

and 4, step 4: carrying out statistical test on the credibility of the crack evolution prediction model of the asphalt pavement, calculating the goodness of fit of a regression mathematical equation among the explanatory variables, and determining the nonlinear influence effect of other factors except the statistical quantity on a research object;

and 5: and determining the predicted value of the dependent variable according to the trend of the selected factor observed value, and giving a prediction interval of the crack of the asphalt pavement in the coming years through a regression prediction model to realize the prediction analysis of the crack evolution behavior of the asphalt pavement.

2. The method for predicting the crack evolution of the asphalt pavement according to claim 1, characterized by comprising the following steps: in the step 1, all-round influence factors of asphalt pavement cracking caused by the listing are analyzed, and subjective factors and objective factors are determined.

3. The method for predicting the crack evolution of the asphalt pavement according to claim 2, characterized by comprising the following steps: subjective factors include: construction quality and maintenance quality.

4. The method for predicting the crack evolution of the asphalt pavement according to claim 2, characterized by comprising the following steps: objective factors include: traffic volume, climate environment, soil base compactness, surface course thickness and base course loose paving coefficient.

5. The regression prediction method for the crack evolution of the asphalt pavement according to claim 1, characterized in that: in the step 2, any influencing factor is selected as a macroscopic statistic, and the macroscopic statistic is used as an explanatory variable to predict the change of the cracking behavior of the asphalt pavement.

6. The method for predicting the crack evolution of the asphalt pavement according to claim 1, characterized by comprising the following steps: in step 3, the relationship between the factor statistic and the study object is described, the closeness degree of the correlation between the interpretation variable and the interpreted variable is determined, and a variable fitting mathematical equation between the factor statistic and the study object is obtained, which includes:

calculating a correlation coefficient between factor statistics and the cracking area of an asphalt pavement per kilometer, and performing significance test on the correlation coefficient; the formula is as follows:

wherein r is a correlation coefficient; t is the test statistic; n is the sample capacity of the statistical data; x is a factor statistic observed value; y is an observed value of the crack area of the pavement per kilometer;

the regression mathematical equation between the recurrence factor statistic and the variable between the regression mathematical equation and the cracking area of the asphalt pavement per kilometer is as follows:

wherein the content of the first and second substances,in order to be a regression parameter,is the observed mean of the independent variables,is the observed mean of the dependent variable;is a predictive variable, namely the cracking area of the asphalt pavement in the future kilometers.

7. The method for predicting the crack evolution of the asphalt pavement according to claim 1, characterized by comprising the following steps: in the step 4, the reliability of the crack evolution prediction model of the asphalt pavement is statistically tested, and the goodness of fit of the regression mathematical equation among variables is calculated, wherein the method comprises the following steps:

the method includes the steps of calculating a decision coefficient and explaining the goodness of fit of a regression mathematical equation between variables, wherein the formula is as follows:

r₁＝r²，

wherein r is₁Is a decision coefficient; r is a correlation coefficient;

secondly, calculating standard errors, explaining the nonlinear influence effect of other factors on the research object, and the formula is as follows:

8. the method for predicting the crack evolution of the asphalt pavement according to claim 1, characterized by comprising the following steps: in the step 5, according to the value of the prediction dependent variable, a prediction interval of the crack of the asphalt pavement in the next several years is given through a regression prediction model, so that the prediction analysis of the crack evolution behavior of the asphalt pavement is realized, and the formula is as follows:

wherein the content of the first and second substances,to predict the value x of the dependent variable₀Of a predictive variable, i.e. x₀Corresponding cracking area of asphalt pavement in future kilometers; t is t_α/2And (n-2) is a side position parameter value of the distribution of the statistic t.

Technical Field

The invention relates to the field of road engineering, in particular to a regression prediction method for crack evolution of an asphalt pavement.

Background

Based on 2010-2019 highway quality inspection data, the cracking percentage of the main types of asphalt pavement damage in China is the largest, and the cracking percentage of the main types of asphalt pavement damage in China is about 48.7% of the asphalt pavement damage in China. If the cracks which are mutually communicated and generated by the fatigue damage of the asphalt surface layer or the base layer are not treated in time, along with the repeated action of load and the long-time rainwater filling, the pavement crack can be rapidly expanded, so that the cost and the difficulty of pavement repair and maintenance can be increased, the service life of the road can be greatly shortened, and a potential threat to the driving safety can be formed. Therefore, based on the statistical data of the road quality inspection, the method can accurately predict the crack evolution behavior of the asphalt pavement, and becomes one of the main technical means pursued by the highway management and control department.

At present, the research on the crack through crack of the asphalt pavement mainly focuses on the specific cause of the crack and the mechanical analysis in the crack extension process, related departments focus main efforts on pavement crack repair and pre-maintenance, and constructors inherit the passive dynamics of 'with compensation and without monitoring' on the crack of the asphalt pavement.

The construction department has no sound technical scheme about the prediction of the crack evolution behavior of the asphalt pavement, lacks a normative theoretical basis, and even has the phenomenon that the maintenance scheme is provided by predicting the crack of the pavement according to the personal construction experience of a designer, so that the construction department lacks rationality and accuracy in monitoring the crack evolution behavior of the pavement, the crack penetration crack cannot be effectively prevented and controlled, the crack penetration crack is more serious, and the pavement repair, maintenance fund and maintenance period in the later period are increased.

Disclosure of Invention

In order to design an optimized asphalt pavement crack repairing and curing scheme, reduce repairing and curing funds and improve the service cycle of the whole service life of a road, the invention provides a regression prediction method of crack evolution of an asphalt pavement, which has scientificity, reliability and feasibility.

The invention provides a regression prediction method for crack evolution of an asphalt pavement, which comprises the following steps:

step 1: the cracks of the asphalt pavement appear at the bottom of the asphalt surface layer or the stable base layer firstly, and along with the fatigue action of repeated traffic load, the cracks are transmitted to the surface to form a plurality of staggered transverse and longitudinal cracks, and finally, the cracks develop into reticular or tortoiseshell-shaped cracks. In order to design an optimized asphalt pavement crack repairing and maintenance scheme, the method determines the prediction of the crack evolution of the asphalt pavement as a research object, comprehensively considers the factors which influence the crack development of the asphalt pavement in all directions, selects the construction quality and the maintenance quality as subjective factors, and selects the traffic volume, the climate environment, the soil foundation compactness, the surface course thickness and the base course loose paving coefficient as objective factors. The specific influence mechanism of the main factors on the cracking of the asphalt pavement is as follows:

traffic volume factors: the repeated traffic load of the road surface is used as the road surface contact action, and the stress response of the whole road surface structure is directly changed. When the strength of the pavement mixture is insufficient to bear traffic loads, the pavement structure layer is broken when it reaches its maximum plastic deformation. The pavement cracks are firstly found at the bottom of an asphalt surface layer or a stable base layer, the load bending tensile stress or strain is the largest, along with the repeated action of traffic load, the cracks are transmitted to the surface to form a plurality of staggered transverse and longitudinal cracks, and finally, the cracks develop into netty or tortoiseshell-shaped cracks;

construction quality factors: due to the influence of the traffic load and natural factors on the road surface, the service function of the road surface is gradually weakened along with the increase of the depth, and the road surface structure is generally paved in layers. The construction quality has poor strength and improper combination and function complementation combination, so that the structure function is weakened and the fracture occurs;

and (3) soil foundation factors: when the soil foundation has the quality defects of insufficient filling compactness and higher liquid limit of the filler, the difference of the soil foundation filler can be caused to generate uneven settlement, and finally, the pavement structure layer is damaged, so that the pavement is cracked. The cracked pavement accelerates the continuous cracking of cracks under the coupling action of repeated traffic load and environmental factors, and aggravates the phenomenon that the cracks of the pavement penetrate through the cracks;

basic layer factors: infrastructure defects are mainly due to uneven shrinkage of the material, especially temperature shrinkage and drying shrinkage. Due to improper design of aggregate grading of the base layer, overhigh water content, overhigh construction temperature and loose paving coefficient of the base layer, the water of the mixture of the base layer is unevenly diffused and permeated, uneven shrinkage deformation is generated in the base layer, and the base layer is cracked;

step 2: according to an evaluation system and a preposed analysis frame of the cracking behavior of the asphalt pavement, selecting any one of all factors (construction quality, maintenance quality, traffic, climate environment, soil foundation compactness, surface layer thickness and base course loose paving coefficient) as a macroscopic statistic, and predicting the change of the cracking behavior of the asphalt pavement as an explanatory variable;

and step 3: describing the relationship between the factor statistic and the cracking behavior of the asphalt pavement based on the statistic observation data, and determining the closeness degree of the correlation between the interpretation variable and the interpreted variable to obtain a variable fitting mathematical equation between the factor statistic and the cracking behavior of the asphalt pavement; the method specifically comprises the following steps:

calculating a correlation coefficient between factor statistics and the cracking area of an asphalt pavement per kilometer, and performing significance test on the correlation coefficient; the concrete formula is as follows:

wherein r is a correlation coefficient; t is the test statistic; n is the sample capacity of the statistical data; x is a factor statistic observed value; and y is an observed value of the crack area of the pavement per kilometer.

Recursion factor statistics and a regression prediction equation between the factor statistics and the cracking area of the asphalt pavement per kilometer are obtained; the concrete formula is as follows:

wherein the content of the first and second substances,is a regression parameter;is the observed mean of the independent (dependent) variables;is a predictive variable, namely the cracking area of the asphalt pavement in the future kilometers.

And 4, step 4: carrying out statistical test on the credibility of the crack evolution prediction model of the asphalt pavement, calculating the goodness of fit of a regression mathematical equation among the explanatory variables, and determining the nonlinear influence effect of other factors except the statistical quantity on a research object; the method specifically comprises the following steps:

calculating a decision coefficient and explaining the goodness of fit of a regression prediction equation among variables; the concrete formula is as follows:

r₁＝r² (6)

wherein r is₁Is a decision coefficient; r is a correlation coefficient.

Secondly, standard errors are calculated, and the nonlinear influence effect of other factors on the research object is explained; the concrete formula is as follows:

and 5: according to the trend of the selected factor observation value, determining the prediction value of the future dependent variable, and giving a prediction interval of the crack of the asphalt pavement in the coming years through a regression prediction model to realize the prediction analysis of the crack evolution behavior of the asphalt pavement; the concrete formula is as follows:

wherein the content of the first and second substances,to predict the value x of the dependent variable₀Of a predictive variable, i.e. x₀Corresponding cracking area of asphalt pavement in future kilometers; t is t_α/2And (n-2) is a side position parameter value of the distribution of the statistic t.

And (3) performing regression prediction on crack evolution of the asphalt pavement based on the steps 1-5, determining a prediction interval of the crack of the asphalt pavement in the next few years, solving the defect that the monitoring of the crack behavior of the pavement by the current construction department lacks reasonableness and accuracy, providing a scientific theoretical basis for optimizing a pavement crack repairing and maintaining scheme, and improving the full-life auxiliary cycle of the pavement to the greatest extent while reducing the pavement repairing and maintaining fund.

Description of the drawings:

FIG. 1 is a diagram of a pre-analysis framework of a model for predicting cracking behavior of an asphalt pavement according to an embodiment of the present invention;

Detailed Description

To describe the features and specific implementation steps of the present invention in detail, the following examples are given in conjunction with the accompanying drawings. The invention discloses a regression prediction method for crack evolution of an asphalt pavement, which comprises the following steps:

based on 2010-2019 national highway quality inspection data, selecting traffic volume of all factors (construction quality, maintenance quality, traffic volume, climate environment, soil foundation compactness, surface layer thickness and base course loose paving coefficient) influencing the cracking of the asphalt pavement as macro statistics. The detection data about the national highway traffic volume and the pavement crack area per kilometer in 2010-2019 are shown in the table 1.

Table 12010-2019 year national highway traffic volume and pavement crack area detection data per kilometer

Year of year	Average daily traffic volume (vehicle/day)	Road surface crack (m)2/km)
			2010	16045.977	47.6
2011	17126.288	53.7
			2012	18278.933	59.3
2013	19503.912	68.4
			2014	20801.225	64.9
2015	22170.872	72.6
			2016	23612.853	75.8
2017	25127.168	80.2
			2018	26713.817	84.4
2019	28372.8	87.5

Step 1: in order to design an optimized asphalt pavement cracking repairing maintenance scheme, the method determines the prediction of the asphalt pavement cracking evolution behavior as a research object, comprehensively considers the factors which influence the cracking development of the asphalt pavement in all directions, selects the construction quality and the maintenance quality as subjective factors, and selects the traffic volume, the climate environment, the soil foundation compactness, the surface course thickness and the base course loose paving coefficient as objective factors to construct a preposed analysis frame for the comprehensive evaluation of the asphalt pavement cracking behavior as shown in figure 1;

step 2: according to an evaluation system and a pre-analysis frame of the cracking behavior of the asphalt pavement, the traffic of all factors (construction quality, maintenance quality, traffic, climate environment, soil foundation compactness, surface course thickness and base course loose coefficient) is selected as a macroscopic statistic and used as an explanatory variable (x) to predict the change (y) of the cracking behavior of the asphalt pavement. Based on 2010-2019 national highway traffic volume and pavement crack area detection data per kilometer, x is calculated²、y²Xy correlation statistic function data are shown in table 2;

table 22010-2019 years of national highway traffic volume and pavement crack area detection per kilometer and related data

And step 3: describing the relationship between the traffic volume and the cracking behavior of the asphalt pavement based on the statistical observation data, and definitely interpreting the closeness degree of the correlation between the variables and the interpreted variables to obtain a variable fitting mathematical equation between the traffic volume and the cracking behavior of the asphalt pavement;

optionally, the step 3 includes:

3.1, calculating a correlation coefficient between the factor statistic and the crack area of the asphalt pavement per kilometer, and performing significance test on the correlation coefficient:

relevant coefficients:

carrying out significance test on the correlation coefficient:

calculating test statistics:

② the significance level is set as α 0.05, which can be obtained from the statistic t distribution table (see table 3):

TABLE 3 statistic t distribution side position parameter value

t_α/2(n-2)＝t_0.025(10-2)＝2.306

Because t is 13.336>t_α/2Since (10-2) is 2.306, the correlation between the annual average daily traffic volume and the crack-type road surface damage area per kilometer in the national highway quality inspection data in 2010-2019 is remarkable.

3.2 recursion of the regression equation of the average annual daily traffic volume and the crack type damage area of the pavement per kilometer:

according to the regression equation of the annual average daily traffic volume and the pavement cracking damage area per kilometer, the annual average daily traffic volume is increased by 1000 vehicles, and the pavement cracking damage area per kilometer is increased by 3.104 square meters.

And 4, step 4: carrying out statistical test on the credibility of the crack evolution prediction model of the asphalt pavement, calculating the goodness of fit of a regression mathematical equation among variables, and determining the nonlinear influence effect of other factors except the statistical quantity on a research object;

optionally, the step 4 includes:

4.1 calculating a judgment coefficient, and explaining the goodness of fit of the regression prediction equation among variables:

r²＝0.9782²＝0.9569

from the judgment coefficient, it is found that 95.69% of the variation in crack area per kilometer of the asphalt pavement is determined by the traffic volume. The annual average daily traffic volume and the cracking area of the asphalt pavement per kilometer have strong correlation linear relation, the regression prediction equation has high goodness of fit, and the regression prediction model has accurate prediction results on the cracking area of the asphalt pavement per kilometer.

4.2 calculating standard error, explaining the effect of other factors on the nonlinear influence of the study object:

according to the standard error, when the annual average daily traffic volume is used for predicting the crack diseases of the asphalt pavement per kilometer area, the result of the nonlinear influence of other factors on the crack diseases of the asphalt pavement per kilometer area is 2.902, namely the average error of the crack evolution prediction model of the asphalt pavement is 2.902m 2.

And 5: according to the trend of the selected factor observation value, determining the prediction value of the future dependent variable, and giving a prediction interval of the crack of the asphalt pavement in the coming years through a regression prediction model to realize the prediction analysis of the crack evolution behavior of the asphalt pavement:

according to the annual average traffic volume quality inspection data of the national roads in 2010-2019, the trend change (36.167 x) is fitted in a nonlinear way²+971.81x +15038, note that x is the corresponding serial number "1, 2, …"), and the values of average daily traffic in 2020-2025 years in the future are obtained, see table 4.

TABLE 42020-2025 average daily traffic volume fitting values

Year of year	Average daily traffic volume prediction value
		2020	30104.117
2021	31907.768
		2022	33783.753
2023	35732.072
		2024	37752.725
2025	39845.712

Because of the existence of standard errors, the pavement crack prediction area value per kilometer obtained by purely depending on the crack behavior of the asphalt pavement and a prediction formula is still slightly discrete, and in order to improve the prediction accuracy, a prediction interval of the pavement crack area per kilometer needs to be provided on the basis of a prediction value. Therefore, the predicted values of average daily traffic volume in 2020-2025 years are substituted into formulas (5) and (8), and the predicted area value of road surface cracks per kilometer in the current year and the predicted area reliability interval of road surface cracks per kilometer are calculated respectively and are shown in table 5.

TABLE 5 predicted area value of crack per kilometer of road surface and predicted area reliability interval of crack per kilometer of road surface in the same year

As can be seen from Table 5, the crack area per kilometer of the road surface increases with the increase of the traffic volume in the next 6 years, wherein an accurate prediction interval of the crack area per kilometer of the road surface is given in the next years, for example, when the traffic volume is 39845.712 in 2025 years, the accurate prediction interval of the crack area per kilometer of the road surface is (113.56, 137.51) m²The method and the device realize the prediction and analysis of the crack evolution behavior of the asphalt pavement, provide scientific basis for related departments to design an optimized asphalt pavement crack repairing and curing scheme, and furthest improve the service cycle of the whole service life of the road while reducing repairing and curing funds.