Review of longitudinal pavement roughness prediction tools

Many road agencies use special tools for managing their assets. Article provides overview of most known pavement management systems. Most of all describing pavement management systems have special tools for prediction longitudinal roughness, rutting, friction, Pavement Conditional Index (PCI), Surface Distress Index (SDI), Structural Adequacy Index (SAI) and Ride Comfort Index (RCI) etc. Among the factors of performance deterioration the following external factors are the most frequently singled out: the number of freezing and thawing cycles, temperature, humidity, precipitation, ground water depth level, the number of traffic load repeats in daily average annual traffic intensity or equivalent single axle load (ESAL); internal factors: material type, structural strength and thickness, subgrade material, etc. There is an analysis of current longitudinal roughness prediction models, which are used on the project and network level, in the article. The article contains deterministic models of longitudinal roughness prediction suggested by Russian and foreign authors at different periods of times.

To ensure the most efficient asset management the highway agencies of developed countries use pavement management systems at network and project levels [1].The key element of many of those systems is the capability to predict the occurrence of critical state of pavement performance and/or functional parameters which determine the type and sequence of repair, preventive and other measures taking into account actual financing.The table 1 based on the analyzed literature references [2][3][4][5][6][7][8][9][10][11] contains data on the prediction tools of the best known pavement management systems.In the majority of the above management systems pavement management is carried out relying on performance indices which are the first and foremost to ensure comfortable driving.

Интернет
Among the factors of performance deterioration the following external factors are the most frequently singled out: the number of freezing and thawing cycles, temperature, humidity, precipitation, ground water depth level, the number of traffic load repeats in daily average annual traffic intensity or equivalent single axle load (ESAL); internal factors: material type, structural strength and thickness, subgrade material, etc.
Many pavement management systems make use mainly of the deterioration-time relation.The typical deterioration curve is shown in fig.1a.However, the nature of pavement deterioration is not always like this: inverted deterioration curves (fig.1b) were obtained by Haas [12] during monitoring of the pavements designed for heavier traffic load than the observed one.In this case the crucial influence during the change of performance was exerted primarily by climate and weather.а б

Figure 1. Pavement deterioration curves: a -when the traffic load corresponds to the design load, b -when the traffic load is lower than the design load
Raymond [13] points to high impact of local factors on performance deterioration.Some international models, including the World Bank's Highway Development and Management Model HDM-4 [14], allow the user to calibrate models according to local specific features.
In general, deterioration models may be divided into deterministic and probabilistic ones.
The deterministic model returns one state value for the predefined input data set [15].Deterministic models are usually shown as functions.The simplest ones are based on linear regression, however exponential functions and other more complicated ones may return more exact results.
Further, deterministic models are divided into mechanistic (theory-based), empirical (experiment-based), mechanistic-empirical (theory and experiment combined) or those based on expert evidence.
Mechanistic models are based on physical laws.For example, pavement deterioration may need application of relations between stresses, strains, and loads.Typically mechanistic models as is are not applied in pavement management.Moreover, it is believed to be impossible: in [16] it is mentioned that there are no solely mechanistic models for deterioration prediction, in [17] it is stated that mechanistic models are impractical for prediction, although in [18] it is assumed that there are no absolutely mechanistic models, however there are no reasons preventing from their designing.Nevertheless, mechanistic models are not used in prediction of pavement condition due to a great number of aspects.
Empiric models are developed to predict conditions depending on such variables as age, type of material, loading conditions, etc., typically via regression.This type of models is often used when deterioration cannot be explained mechanistically.Schram [19] found out that 91% of Canadian and American agencies used empirical models of performance deterioration.The majority of the countries of Northern Europe apply empirical linear extrapolation of the current condition of pavement in their management systems too [20].
Many deterioration models (prediction models) fall into the mechanical-empirical category.They include calculation of mechanical reactions (for example, stresses, strains, etc.) and other measured variables for prediction of conditions.This type of models is often applied for performance deterioration modeling [13,19,21,22].The models yield good results and it is believed that they model deterioration more precisely than empiric models.
The following approaches are used to achieve deterministic models [23]: straight (or simple??) linear extrapolation;  regression analysis (linear, multiple, special);  polynomial interpolation (least square method); Linear extrapolation is used for performance prediction when a limited survey data amount is available.It was ascertained [24] that the deterioration curve had not linear, but curvilinear shape; that is why this approach is used for specific road sections only.
Multiple linear regression is one of the simplest forms of the deterministic model and is used when more than one factor influences a dependent variable [15].The following equation conforms to the model: where  0 ,  1 …   are regression coefficients,  ̂ is a predicted value of the dependent variable,  1 …   are values of independent variables.Concerning pavement deterioration  ̂ is a parameter of performance,  1 …   are factors influencing the condition (age, materials, location, traffic intensity, etc.).To find coefficients  0 ,  1 …   the least square method is typically used.Exponential (S-curve) is usable in predicting of variable changes (for example, that pertinent to driving comfort) as function of the other variable (for example, age of road structure).
In probabilistic models the output parameter is probability that the asset (for example, road structure) is in a specific condition for the suggested input parameter set.There are many different types of models in this group.
One of the most popular probabilistic models used in asset deterioration modeling is Markov chain [15].Markov models give probability   that the element in  condition at  time step will be in  condition at  + 1 time step.These transition probabilities are arranged in the transition matrix: where   ≥ 0; ,  ≥ 1; ∑  , = 1.

𝑗 𝑘=1
Distribution of the asset (road structure) chain conditions at ( + ) time can be found through the product of the current distribution and transition matrixes: During deterioration modeling   is usually defined as probability of deterioration of  condition to  condition.While in the time homogeneous Markov model the prediction condition depends on the current condition only, in semi-Markov or nonhomogeneous models the independently distributed random values are used for time modeling between states.Thus, the model depends on time.From the point of view of the tangible asset deterioration it means that probability of deterioration to the next condition increases with the asset age.Semi-Markov models require more data for definition of additional parameters and are more complicated in implementation than the time-homogeneous Markov model [25].
The other commonly used probabilistic model is logistic regression.Unlike multiple linear regression where output characteristic is asset condition, logistic regression defines probability of the asset being in a specific condition with the predefined set of independent variables [15]: The literature shows various models of pavement longitudinal roughness deterioration.They may be classified into four categories: models related to structure effect; models based on temporal effect; models considering correlation between temporal and structure factors; and models where structure, surface and temporal effects define longitudinal roughness.
The table 2 contains deterministic models of longitudinal roughness prediction suggested by Russian and foreign authors at different periods of times.