pavement performance predicition models based on a factorial ...

PAVEMENT PERFORMANCE PREDICITION MODELS BASED ON A FACTORIAL EXPERIMENT IN THE STATE OF PARANA – BRAZIL “Directed to Committee A0010 for Review” by

Jose Leomar Fernandes, Jr. Professor Jose Kyinha Yshiba Professor

Engineering School of Sao Carlos - University of Sao Paulo Av. Trabalhador Saocarlense, 400 Sao Carlos, SP – 13566-590 – Brazil Tel: 55-16-3373-9598; Fax: 55-16-3373-9602 E-mail: [email protected] E-mail: [email protected]

Paper prepared for presentation and publication at the 85th Annual Meeting in January 22-26, 2006 of the Transportation Research Board, Washington, D.C.

Submission date: July 28, 2005 (Abstract: 158 words) (Text: 2596 words) (4 tables and 7 figures: 2750 word equivalents) (Total: 5504 words)

Fernandes Jr. & Yshiba

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ABSTRACT Pavement performance prediction models are important tools used by management systems, at both network and project levels, because they are essential for designing and planning maintenance and rehabilitation activities as well as for the estimation of the necessary budget. This work develops statistic models for the prediction of pavement performance, based on a factorial experiment and on an Analysis of Variance (ANOVA) of pavement evaluations performed in the highway network of the State of Parana, Brazil. The performance prediction models developed in the present work, which consider the effects of the factors age, traffic loading, and pavement structural capacity on the dependent variables roughness and pavement deflections, show better results than performance models developed by Brazilian and foreign highway agencies. There is evidence that the method used in this study can be applied to highway networks with different characteristics of climate, traffic, structural capacity, material types, construction techniques etc. Keywords: performance models; roughness; pavement deflection; management systems.


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INTRODUCTION The decision making in Pavement Management Systems (PMS) depends, within other factors, on the prediction of pavement deterioration, i.e., on the estimate of the evolution of pavement functional and structural conditions as a function of aging, traffic loading and environmental effects. Such estimates are obtained through causes and effects relationships, named performance models. The performance models are vital for the planning of maintenance and rehabilitation activities, for the estimation of the necessary budget to the pavement preservation, to the analysis of consequences of pavement condition under different financing scenarios, and also, to the life cycle economic analysis. One of the crucial tasks in the implementation of a PMS is, therefore, the decision about the type of performance prediction models to be used. The performance models can be classified in (1): • Mechanistic: models based on structural response parameters, such as, stress, strain, and displacements. Such models have not been developed yet because highway engineers do not use primary response parameters, but instead, they relate them with distresses or pavement properties; • Mechanistic-empirical: models that relate dependent variables of structural or functional deterioration with one or more independent variables, as bearing capacity of subgrade, traffic volume, layer thickness, pavement properties and so on. Examples of mechanistic/empirical models are the equations obtained from the Research on Interrelationships among Construction, Maintenance and Users Costs (2, 3). Those equations relate some structural responses to roughness and cracking; • Empirical: models in which the dependent variables that characterize the structural or functional condition are related to one or more independent variables, as bearing capacity of subgrade, equivalent single axle load (ESAL) applications, thickness and properties of pavement materials, age, environmental factors and their interactions. The empirical models are formulated from statistical analysis of performance data obtained from existing pavements. There some examples of empirical performance models obtained with data collected in the Brazilian highway network (2, 4, 5); • Probabilistic: models in which the experience of engineers and technicians is formalized through transition process, as for instance, Markov process, that allows the estimation of the future condition, usually in terms of an index of combined distresses, from matrices of transition probability. Several road organizations have implemented probabilistic performance models using Markov process (6, 7). This paper develops empirical performance models using field data collected in the paved highway network of the State of Parana, Brazil. It is performed factorial programming and analysis of variance (ANOVA) of pre-selected factors (i.e., independent variables: age, traffic, and pavement structure), that quantify the effects of those factors and their interactions on the pavement condition (i.e., dependent variables: roughness and pavement deflection). METHOD Factorial Experiment In this study, a factorial planning is used for the development of pavement performance models. Through an Analysis of Variance (ANOVA) the most significant factors and


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interactions are identified and regression equations are established. The factorial planning defines ‘which’ and ‘how’ the input variables are arranged in order to allow the observation and the identification of effects on the output variables. It must be emphasized that a well planned experiment enables to quantify the influence of each input variable and of their interactions on the system responses, with a number of field sections not superior to what is considered enough (8). Initially, it is necessary a priori definition of factors (independent variables) and their respective levels, as well as, the dependent variables to be measured. There are several factors that affect the pavement performance, but the inclusion of many factors would demand a huge database, not available in most of the Brazilian highway agencies. As a mean of comparison, HDM-III and HDM-4 consider pavement performance as a function of traffic loading, pavement age, climate (in a broad way) and structural capacity. The interval between lower and upper levels of those factors defines the inference space on which results are acceptable. The dependent variables are the results of evaluations performed on in-service pavement and represent its functional and/or structural condition. Usually, the evaluations carried out to attend a pavement management system requirements are the following: field survey of pavement surface condition (extension and severity of distresses); functional evaluation (roughness); structural evaluation (pavement deflection); skid resistance (micro and macro-texture characteristics). The replicates are important for the estimation of the experimental error probability. In this study, they consist of evaluations performed in pavement sections belonging to the same factorial matrix cell, being the results obtained with the same field team and with the same equipments, following the same procedures and in the same inference space (delimited region with similar geological and climatic conditions). The determination of the significance level of a factor or interaction is, usually, carried out through Snedecor F test, which compares the F value of a factor or interaction to a limit value of F (Flim), that can be found in statistics tables (9), according to the significance level adopted. The analysis of variance of a factorial experiment allows not only the identification of significant factors and interactions, but also the development of regression models, that relate the important factors (independent variable Xi) to the process response (dependent variable Y). A factorial experiment also allows the calculation of the determination coefficient (R2) of the model, from the sum of squares of significant factors and interactions. Characteristics of the Paved Highway Network in the State of Parana – Brazil The first step to the development of performance models was the identification and definition of the paved highway network, based on environmental information (climatic and geotechnical), pavement characteristics (type and structure), and traffic. Within the five geomorphologic regions into which the State of Parana is divided, the Basalt Region (Region III, in Figure 1) was chosen for this study due to socio-economic and climatic conditions that predominate in the region. It is the one that has the largest geographic area, with a surface equivalent to 42% of the total area of the State territory (approximately 200,000 km2), and in that area there is the concentration of the biggest part of the population, being also responsible for the largest percentage of agricultural production, commercial and industrial activities. Therefore, it generates considerable traffic volumes that transit in more


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than 5,300 km of paved roads, which correspond to more than 50% of the Parana State highway network. The selected area could not be considered a ‘climatic condition factor’ because the climate can be considered uniform in the Basalt Region (10), since there is a regular distribution of rainfalls during the year, in a total between 1,200 and 1,300 mm, and the Superpave PG Grade for asphalt binders is PG 64-10 in the whole region. Regarding the subgrade, clay latosoils originated from basalt are predominant (11). Those soils present a high bearing capacity (CBR between 9 and 17% and expansion inferior to 2%, when compacted at normal Proctor energy). Pavement sections with Hot Mix Asphalt (HMA) and base and sub-base of crushed stone were selected, in an extension of approximately 1,500 km (12). The structural capacity of the pavement sections was determined through the use of the corrected structural number (SNC), which takes into account the bearing capacity of the subgrade (2): SNC = SN + 3.51log CBR 0.85(log CBR ) 2 1.43 (1)

where: • SN is the structural number (13); • CBR is the California Bearing Ratio (%). The ESALs were estimated from daily average volumes of passenger cars, buses, light, medium and heavy trucks, and long combination vehicles. The data was obtained from weighing stations located in paved roads along the State of Parana (12). Comparing with data previously collected (14) it was possible to calculate traffic volume growing rates for each of the vehicle classes. In this work tt was considered Load Equivalence Factors established by AASHTO (13). Factors and Levels of the Independent Variables

Based on the inventory data, the selected factors and levels are: • Factor A – Age (years): o level a1: Al 8 years (“new pavement”); o level a2: 9 Am 16 years (“intermediate age pavement”); o level a3: Ah 17 years (“old pavement”). •

Factor T – Traffic loading, in terms of ESALs per year: o level t1: Tl 5×104 (light traffic); o level t2: Th > 5×104 (heavy traffic).

•

Factor S - corrected structural number (SNC): o level s1: Sl 5.5 (low); o level s2: Sh > 5.5 (high).

RESULTS

Performance parameters considered in this work are functional and structural. Tables 1 and 2 present the results of roughness, quantified in terms of IRI (International Roughness Index), and pavement deflection, obtained with Benkelman Beam (10-2 mm). Field test sections were

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selected to fill all cells of the factorial matrices and two replicates (r1 and r2) were considered (12). From analysis of variance (ANOVA) of the factorial matrices it is possible to identify significant factors and interactions (Tables 3 and 4). And with the regression coefficients of the analysis of variance it can be obtained statistical models that represent the effects of aging, traffic loading and structural capacity on the pavement performance, quantified in terms of roughness (IRI) and deflection (DEF). The statistic performance models obtained are: a)

Roughness (IRI, in m/km):

IRI = 2.8 + 0.38 × P ( A ) + 0.31 × P (T ) 0.16 × P (S ) + 0.09 × P ( A ) × P (T ) 0.08 × P ( A ) × P (S )

(2)

R2 = 0.75 b)

Pavement Deflection (DEF, in 0,01 mm):

DEF = 56.0 + 8.7 × P( A) + 4.25 × P(T ) 4.75 × P( S ) + 1.81× P( A) × P(S )

(3)

R2 = 0.62 where: P ( A) =

A 13 8

P(T ) =

T

5 × 10 4 10 5

P (S ) =

S

5,5 2

ANALYSIS OF THE RESULTS Residue and Correlation Coefficient Analysis

The residue analysis, as well as, the correlation coefficient analysis allow checking the efficiency of statistical models obtained through regression analysis. To do those analyses the predicted values by the statistical models are compared to observed values. It is important to point out that, in this study, the observed values of roughness and pavement deflections were taken in 1998 (15), in sections different from the ones considered in the development of performance prediction models. Satisfactory correlation coefficients were obtained for both models (r = 0.78, in Figure 2, and r = 0.86, in Figure 4). The results were also good in terms of the residue, since there is a random distribution around the zero (Figures 3 and 5). Therefore, the statistical aspects are favorable to the use of the roughness prediction model and the deflection prediction model developed in the present study. Comparison between the statistical models and other performance models

The statistical models developed in this study (IRI, Equation 2, and DEF, Equation 3) are compared to other performance models, used by highway agencies worldwide (Figures 6 and 7). The following models were selected to the comparisons: a) Empirical equation used by the Brazilian Department of Transportation Infrastructure in pavement rehabilitation projects (2):

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QI = 12.63 5.16 × RH + 3.31 × ST + 0.393 × A + 8.66 × log( NA / S ) + 7.17 × 10

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(DEFvB × log NA)2 (4)

R 2 = 0.52

b) Empirical equation use in the HDM-III (4):

[

IRI = 1.923 + 0.725(1 + S )

4.99

]

× YE 4 × e 0.0153 A

(5)

R 2 = 0.75

c) Equations obtained through regression analysis of data collected in the highway network of the State of Santa Catarina, Brazil (5):

QI = 18 .348 + 1 .1635 × A

(6)

R 2 = 0.29

DEFvB = 24.288 + 3.5458 × A

(7)

R 2 = 0.37

where: • QI: “quotient of irregularity”, an unit of roughness, very used in Brazil (counts/km); • RH: indicator of the rehabilitation condition; • ST: indicator of pavement surface type; • NA: cumulated ESALs until the date of the evaluation; • DEFvB: deflection obtained by Benkelman beam [0.01 mm]; • YE4: ESALs per year, calculated using AASHTO (13) Load Equivalent Factors. It can be observed in Figure 6 that the model developed in this work, considering the factors aging, traffic loading and corrected structural number, presents a higher correlation coefficient and a better fit to the observed roughness data than the other models considered (2, 4, 5). It can be observed in Figure 7 that the model developed in this work, considering the factors aging, traffic loading and corrected structural number, presents a higher correlation coefficient and a better fit to the observed pavement deflection data than the other model analyzed (5), that considers just the factor age. CONCLUSION

This work developed statistical performance models through the analysis of variance (ANOVA) of data collected in a survey carried out in 1995 along the paved highway network of the State of Parana. These models for predicting the evolution of roughness and pavement deflection show high determination coefficient values (R2), high correlation coefficient to observed data (r) and a random distribution of residual values. Compared to other performance prediction models, using data collected in different date and in different pavement sections than the ones considered in this study, the models developed in this paper presented a higher correlation to the observed values. It is important to mention that the same results were obtained by more recent studies (16, 17), considering the same performance models but using data obtained in the State of Santa Catarina, Brazil (5), and considering the same performance models and LTPP-FHWA


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data (18). Even so, it is recommended additional evaluations of the performance models presented in this study. It must also be emphasized that the method of this work, i.e., the use of factorial experiment techniques can be very helpful to the development of performance models, since they allow the identification not only of significant factors but also of significant interactions. It is a method that can be applied to highway network with different characteristics of climate, traffic, structural capacity, material type, construction quality etc., because the factorial matrix is defined to represent the intervals observed in the available data. ACKNOWLEDGEMENT

This work was developed with the financial support of CAPES (“Coordenadoria de Aperfeicoamento de Pessoal de Ensino Superior” – Brazilian Superior Teaching Personnel Development Coordination) in the form of a Ph.D. scholarship. REFERENCES [1]Haas, R; Hudson, W. R.; Zaniewski, J. – Modern pavement management. Malabar, Florida, Krieger Publishing. 1994. [2]Queiroz, C. A. V. – Performance Prediction Models for Pavement Management in Brazil. Austin. 317p. Dissertation for Degree of Doctor of Philosophy. The University of Texas at Austin. Texas. 1981. [3]GEIPOT – Brazilian Agency for Planning in Transportation – Research on Interrelationships among Construction, Maintenance and Users Costs – Final Report. Brasilia-DF, Brazil. 12 Volumes – 1981 (In Portuguese). [4]Paterson, W. D. O. – Road Deterioration and Maintenance Effects – Models for Planning end Management. The World Bank. Baltimore. The Johns Hopkins University Press. 1987. [5]Marcon, A. F. – Contribution to the Development of a Pavement Management System for the State of Santa Catarina Highway Network – Sao Jose dos Campos-SP, Brazil. 398 p. Ph.D. Dissertation. Technological Institute of Aeronautics. 1996. (In Portuguese). [6]Butt, A. A.; Shahin, M. Y.; Carpenter, S. H.; Carnahan, J. V. – Application of Markov process to pavement management system at network level. In: International Conference on Managing Pavements, 3. San Antonio, Texas, 1994. [7]Wang, K.C. P.; Zaniewski, J.; Way, G. – Probabilistic Behavior of Pavement. Journal of Transportation Engineering, v. 12, n. 3 – p.358. 1994. [8]Montgomery, D. C. – Design and analysis of experiments. John Wiley & Sons. 1991. [9]Box, G. E. P.; Hunter, W. G.; Hunter, J. S. – Statistics for experiments. New York, John Wiley. 1978. [10]IAPAR – Climatic Data of the State of Parana, Brazil. [email protected]. 2002. (In Portuguese). [11]Geographic Atlas of the State of Parana – Secretary of Agriculture, Lands and Cartography. Curitiba-PR, Brazil. 1987. (In Portuguese). [12]DER-PR – Department of Transportation of the State of Parana – Summary Report of the Pilot Study for Pavement Management System Implementation. Curitiba-PR, Brazil. 1995. (In Portuguese). [13]AASHTO – AASHTO Guidelines for pavement management systems. American Association of State Highway and Transportation Officials. 1993.


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[14]DER-PR – Department of Transportation of the State of Parana – Highway Traffic Parameters. Curitiba-PR, Brazil. 1990. (In Portuguese). [15]DER-PR – Department of Transportation of the State of Parana – Final Report of the Pavement Management System Implementation. Curitiba-PR, Brazil. 1998. (In Portuguese). [16] Nascimento, D.M.; Klein, F.C.; Yshiba, J.K.; Fernandes, Jr., J.L. – Comparative Analysis of Performance Prediction Models – 35th Annual Meeting of the Brazilian Paving Association. Rio de Janeiro-RJ, Brazil. 2004 (In Portuguese). 17]Nascimento, D.M.; Fernandes, Jr., J.L. – Using Performance Models as a Tool for Decision Making in PMS. 1st Brazilian-Portuguese Congress on Urban, Regional, Integrated and Sustainable Development. Sao Carlos-SP, Brazil. 2005. (In Portuguese). [18]FHWA – Federal Highway Administration – LTPP Data Pave – Online databank. In: http://www.datapave.com - 2004.


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LIST OF TABLES TABLE 1 Factorial Matrix with the functional evaluation results (roughness, IRI) TABLE 2 Factorial Matrix with the structural evaluation results (pavement deflection, 10-2 mm) TABLE 3 Summary of the analysis of variance (ANOVA): functional evaluation (roughness, IRI) TABLE 4 Summary of the analysis of variance (ANOVA): structural evaluation (pavement deflection, 10-2 mm)


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LIST OF FIGURES FIGURE 1 Geological regions of the State of Parana, Brazil FIGURE 2 Analysis of correlation between predicted and observed IRI values (Eq. 2) FIGURE 3 Analysis of residue of IRI values predicted by Equation 2 FIGURE 4 Analysis of correlation between predicted and observed DEF values (Eq. 3) FIGURE 5 Analysis of residue of DEF values predicted by Equation 3 FIGURE 6 Comparative analysis between Equation 2 and other models for predicting roughness FIGURE 7 Comparative analysis between Equation 3 and other model for predicting pavement deflection

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TABLE 1 Factorial Matrix with the functional evaluation results (roughness, IRI) Tl Th Sl

Sh

Sl

Sh

r1

r2

r1

r2

r1

r2

r1

r2

Al

2.5

2.1

2.1

2.0

3.2

2.4

2.7

2.3

Am

3.0

2.2

2.5

2.1

3.8

2.8

3.3

2.8

Ah

3.0

2.7

2.7

2.3

4.1

3.3

3.6

3.0

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TABLE 2 Factorial Matrix with the structural evaluation results (pavement deflection, 10-2 mm) Tl Th Sl

Sh

Sl

Sh

r1

r2

r1

r2

r1

r2

r1

r2

Al

58

42

43

25

61

54

57

39

Am

64

50

62

44

70

60

61

52

Ah

70

56

65

48

80

62

67

59

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TABLE 3 Summary of the analysis of variance (ANOVA): functional evaluation (roughness, IRI) Factors and Interactions SS(Alinear) SS(Aquadratic) SS(T) SS(S) SS(Al × T) SS(Aq × T) SS(Al × S) SS(Aq × S) SS(T × S) Replicates Residue SStotal

Sum of Squares (SS)

Regression Coefficients

2.326 0.000 2.282 0.602 0.141 0.010 0.106 0.025 0.007 1.602 0.194 7.293

0.38 0.00 0.31 -0.16 0.09 -0.01 -0.08 -0.02 0.02

2.78

Degrees of Mean Square (MS) Freedom (DF)

1 1 1 1 1 1 1 1 1 1 13 23

2.326 0.000 2.282 0.602 0.141 0.010 0.106 0.035 0.007 1.60 0.010 0.32

F

155.71* 0.01 152.76* 40.28* 9.42* 0.68 7.07** 1.69 0.45 107.21 21.23

Snedecor F Test: *Significance of 1%: 9.07; **Significance of 5%: 4.67; ***Significance of 10%: 3.14

where: • SS(Alinear): sum of squares of the linear component of Factor A; • SS(Aquadratic): sum of squares of the quadratic component of Factor A; • SS(T): sum of squares of the linear component of Factor T; • SS(S): sum of squares of the linear component of Factor S; • SS(Al × T): sum of squares of the interaction between the linear component of Factor A and Factor T; • SS(Aq × T): sum of squares of the interaction between the quadratic component of Factor A and Factor T; • SS(Al × S): sum of squares of the interaction between the linear component of Factor A and Factor S; • SS(Aq × S): sum of squares of the interaction between the quadratic component of Factor A and Factor S; • SS(T × S): sum of squares of the interaction between Factor T and Factor S; • SStotal: total sum of squares.

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TABLE 4 Summary of the analysis of variance (ANOVA): structural evaluation (pavement deflection, 10-2 mm) Factors and Interactions SS(Alinear) SS(Aquadratic) SS(T) SS(S) SS(Al × T) SS(Aq × T) SS(Al × S) SS(Aq × S) SS(T × S) Replicates Residue SStotal

Sum of Squares (SS)

Regression Coefficients

1027.563 42.188 433.500 541.500 33.063 22.688 52.562 31.688 2.677 1040.167 186.417 3594.000

8.69 -0.94 4.25 -4.75 -1.44 0.69 1.81 -0.81 0.33

56.00

Degrees of Mean Square (MS) Freedom (DF)

1 1 1 1 1 1 1 1 1 1 13 23

1207.56 42.19 433.50 541.50 33.06 22.64 51.56 31.69 2.67 1040.17 14.34 156.26

F

64.21* 2.94 30.23* 37.76* 2.31 1.58 3.67*** 2.21 0.19

Snedecor F Test: *Significance of 1%: 9.07; **Significance of 5%: 4.67; ***Significance of 10%: 3.14

10.90

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S

O

P

A

S

O

Ã

L

O

O

S

CAMBARA PARANAVAÍ

R

JACAREZINHO

O

G

LONDRINA

M

A

T

REGIÃO IV (ARENITO)

MARINGÁ

REGIÃO II (SEDIMENTAR)

GUAIRA

P A R A G U A I

U

REGIÃO I (CRISTALINO)

CASCAVEL

FOZ DO IGUAÇU

REGIÃO III (BASALTO)

CURITIBA GUARAPUAVA

PARANAGUÁ

S. LUIZ DO PURUNA

REGIÃO V AR

GE

NT

IN

A S A N T A

C A T A R I N A

FIGURE 1 Geological regions of the State of Parana, Brazil

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Predicted IRI (m/km)


5.0 4.0 3.0 2.0

r = 0.78

1.0 0.0 0.0

1.0

2.0 Observed

3.0

4.0

5.0

IRI

FIGURE 2 Analysis of correlation between predicted and observed IRI values (Eq. 2)

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Residue (m/km)

1 0.5 0 0 -0.5

1

2

3

4

5

-1 Predicted

IRI

FIGURE 3 Analysis of residue of IRI values predicted by Equation 2

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Predicted Deflection (0.01 mm)


100 80 60 40 20

r = 0.86

0 0 10 20 30 40 50 60 70 80 90 100 Observed Deflection (0.01

FIGURE 4 Analysis of correlation between predicted and observed DEF values (Eq. 3)

20


Residue (0.01 mm)

15 10 5 0 -5 0 -10

20

40

60

80

-15 Predicted

Deflection

(0.01

FIGURE 5 Analysis of residue of DEF values predicted by Equation 3

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Predicted

IRI


8.0 7.0 6.0 5.0 4.0 3.0 2.0 1.0 0.0

Queiroz: r = 0.68

Marcon: r = 0.57

Equation 2: r = 0.78

0

5

10

15

Paterson: r = 0.64

20

25

30

Age

Observed Paterson Marcon

Equation 2 Queiro

FIGURE 6 Comparative analysis between Equation 2 and other models for predicting roughness

22

Predicted

Deflection

(0.01


150 120

Marcon: r = 0.53

90 60

Equation 3: r = 0.86

30 0 0

5

10

15

20

25

30

Age

Observed Deflection Equation 3

Marcon

FIGURE 7 Comparative analysis between Equation 3 and other model for predicting pavement deflection