International Journal of Corrosion

Volume 2019, Article ID 2534794, 9 pages

https://doi.org/10.1155/2019/2534794

## Prediction Method of Asphalt Pavement Performance and Corrosion Based on Grey System Theory

^{1}School of Civil Engineering, Hubei Polytechnic University, Huangshi, China^{2}School of Civil Engineering, Changchun Institute of Technology, Changchun, China^{3}Civil Engineering Department, Tsinghua university, Beijing, China^{4}Chinese Railway Bridge Engineering Bureau Group Company South Engineering Co., Ltd., Guangzhou, China

Correspondence should be addressed to Ding-bang Zhang; moc.liamxof@bdzcire

Received 31 May 2018; Revised 14 August 2018; Accepted 21 November 2018; Published 1 January 2019

Academic Editor: Flavio Deflorian

Copyright © 2019 Ding-bang Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

The Grey system theory is a new mathematical method to predict data changes in the poor data integrity. As a branch of Grey system theory, the GM (1, 1) model is widely used because only small sample data and simple calculations are needed in prediction of engineering project. It is a critical problem to effectively predict the performance and corrosion of asphalt pavement of highway construction due to the inadequacy of highway performance monitoring data. The smoothness, rut, and pavement skid resistance are three important indexes to evaluate the performance and corrosion of asphalt pavement. This paper has established the prediction model and derived prediction equation of asphalt pavement performance according to the GM (1, 1) model method and then listed the calculation equation of residual and the gray absolute correlation degree. Based on the experience of constructed Dalian-Guangzhou expressway in China, the vectors “*a*” and “*b*” in the prediction equation of smoothness, rut, and pavement skid resistance have been calculated by using the original monitoring data. The field monitoring data are compared with the predictive data for residual and the gray absolute correlation. The results reveal that the predicted data of the smoothness, rut, and skid resistance are mostly consistent with the monitoring data, the biggest residual of the above three indexes is smaller than 8.09%, and the gray absolute correlation degrees all exceed 0.9, which means the accuracy of the predicted equation is excellent. The calculation method based on GM (1, 1) model can effectively predict the changing performance index of asphalt pavement.

#### 1. Introduction

The smoothness is an index to evaluate the deviation of the road surface longitudinal concave and convex volume, which reflects the vehicle driving comfort directly. The rut is a long deep track made by the repeated passage of the vehicle wheels; if the rut depth is deep, the road will be impassable. The skid resistance is an index to evaluate the slipper of pavement surface for stopping the typically sideways or oblique of vehicles. The above three indexes all reflect the economy, safety, and working life of a pavement [1–5]. The accurate prediction and evaluation of the above three pavement indexes have an important value, significance, and social benefit for pavement engineering [6, 7]. Therefore, time prediction of the asphalt pavement smoothness, rut, and skid resistance are necessary for improving and controlling the performance of asphalt pavement.

Nowadays, because of the heavy traffic volume, terrible weather, insufficient inspection funds, and other factors, the field monitoring data of the above performance indexes are limited. So some mathematical methods such as probability theory, fuzzy mathematics, and Grey system theory are adopted to predict the changing values of the above performance indexes. But the shortages of probability theory are the large sample size and the main factors of behavioral characteristics are difficult to be found [8, 9]. The fuzzy mathematics is no computation, and fuzzy set transformation is based on “max-min” algorithm and “if ⋯ then” fuzzy logical expert system [10]. The Grey system theory can overcome the deficiency of data shortage on prediction results; it can make accurate prediction in case of poor data integrity. Especially, as a branch of the Grey system theory, the GM (1, 1) model has the advantages of small sample, high precision, high efficiency, etc. [8, 11].

A comprehensive literature review is conducted to analyze and summarize the studies about asphalt pavement performance [1, 2, 5–7] and Grey system theory [8–15], especially the GM (1, 1) model.

In order to better explore the hazards caused by the reduction of asphalt pavement performance, domestic and foreign scholars have carried out extensive research [5–7]. Dougan C E, Aultman-Hall L., and Choi S. N. et al. [16] had found that the difference in smoothness between lanes is small and consistent (0.1 to 0.2) when averaged over longer sections, and it is not necessary to repeat measurements for all lanes along longer projects or whole routes. JW Li [17] had studied the severity and causes of pavement rut distress and crack distress combining with investigation of an expressway, and the corresponding treatment measures were proposed aiming at pavement distress characteristics. Nataadmadja A. D., Wilson D. J., and Costello S. B. et al. [18] had summarized several laboratory based test methodologies that have been trialled to predict the performance of chip seal surfaces in NZ and the correlation between the laboratory and in-field test results and discussed the advantages and disadvantages of these methodologies. TP Treatments [19] had studied the influence of moisture (wet or dry climate), temperature (freeze or no-freeze zone), subgrade type (fine grained or coarse grained), and traffic loading (low or high) to the pavement performance and put forward the maintenance measures of asphalt pavement about the above factors.

In 1989, Deng Julong [8, 20] had put forward the Grey system theory. The Grey system theory is a system that contains both known and unknown information, which focuses on the problem of “small sample” and “data deficiency”. As a branch of the Grey system theory, the GM (1, 1) model is a dynamic model to reveal the development of things and to predict their future development, which is based on the differential equation established by the original data.

Nowadays the Grey system theory, especially the GM (1, 1) model, is widely used in various fields, and the application in the civil engineering is more and more prominent. Liu Junyong [12] made use of the gray GM (1, 1) model to predict the settlement of the roadbed, and the predicted result was accurate, by comparing with monitoring data. Xia Yuanyou [13] studied the change of landslide by using the Grey system theory prediction model, and the reliability of the gray modeling theory in landslide prediction has been verified which played a guiding role in preventing landslide accident. Hu Qingguo [14] used the gray prediction model to predict the deformation of foundation pit accurately, which is very important for the safety construction of foundation pit. Zou Baoping [15] used GM (1, 1) model to predict the seepage flow of seabed tunnel accurately, and the reference for scientific and rational determination of seepage flow has been provided.

According to the literature review, it can be conducted that there are some problems in the current research: (1) many scholars have studied the influences of smoothness, rut, and skid resistance on asphalt pavement. But during the pavement working life, the changing performance of asphalt pavement about the above three indexes is difficult to predict and evaluate. (2) The application of GM (1, 1) model is used in many engineering project, but no scholar has used the GM (1, 1) model to predict the performance index (smoothness, rut, and skid resistance).

Therefore, firstly, this paper aims to establish a prediction model and equations for the smoothness, rut, skid resistance of asphalt pavement by using the GM (1, 1) model method. Secondly, the predicting equations are adopted to predict the changing characteristic of above three indexes of Dalian-Guangzhou expressway in China, respectively. Thirdly, the field monitoring data are compared with the predicted data for residual and the gray absolute correlation, and then the accuracy of the method can be evaluated.

#### 2. Prediction of Asphalt Pavement Performance

The prediction process of the GM (1, 1) model based method is as follows. Firstly, the existing data is processed and optimized to generate a new sequence. Secondly, we use the new sequence to generate a time function. Thirdly, predicting the future elements by using the time function and the changing rule of leading factors and the trend of future development would be revealed. Fourthly, we calculate the residual and the gray absolute correlation degree to evaluate the predicting accuracy.

##### 2.1. Prediction Model Establishment

Let the original data sequence be denoted by

where , ,* k* is the time serial number,* n* is the total number of monitoring data, and is the value of the pavement performance index (smoothness, rut, and skid resistance) in the No.* k* time according to the field monitoring.

Then the 1-AGO (accumulated generation operation) sequence can be obtained as follows:

where

The sequence can be obtained as follows:

where

The prediction model of pavement performance indexes can be constructed by establishing a first-order differential equation for as

where the vectors “*a*” and “*b*” of the differential (6) can be obtained by the least squares method as follows:

where

Then the solution of the differential equation (6) can be obtained:

where is the predicting 1-AGO (accumulated generation operation) sequence.

The prediction equation for the original data series can be obtained according to (10):

##### 2.2. Accuracy Test

*(**1) Residual Test.* The relative error and the absolute error between the initial data and can be obtained as follows:

If the relative error does not exceed 10%, then the accuracy of the predicting results is considered to meet the requirements.

*(**2) Correlation Test.* The gray absolute correlation is defined as follows:

where

The larger the correlation value is, the better the correlation between the predicted results and the original data is; the classification of relevance degree according to the absolute relevance is shown in Table 1.