Research ArticleDevelopment of Pavement Distress Deterioration PredictionModels for Urban Road Network Using Genetic Programming

Tanuj Chopra ,1 Manoranjan Parida,2 Naveen Kwatra,1 and Palika Chopra 3

1Department of Civil Engineering, �apar University, Patiala, India2Department of Civil Engineering, Indian Institute of Technology, Roorkee, India3Department of Computer Science and Engineering, �apar University, Patiala, India

Correspondence should be addressed to Tanuj Chopra; tchopra@thapar.edu

Received 23 August 2017; Revised 5 December 2017; Accepted 14 December 2017; Published 29 March 2018

Academic Editor: Francesco Canestrari

Copyright © 2018 Tanuj Chopra et al.)is 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.

)e objective of the present study is to developmodels to predict the deterioration of pavement distress of the urban road network.Genetic programming (GP) has been used to develop five models for the prediction of pavement distress: Model 1 for the crackingprogression, Model 2 for the ravelling progression, Model 3 for the pothole progression, Model 4 for the rutting progression, andModel 5 for the roughness progression.)e data have been collected from the roads of Patiala City, Punjab, India; during the years2012–2015, the network of 16 roads have been selected for the data collection purposes. )e data have been divided into two sets,that is, training dataset (data collected during the years 2012 and 2013) and validation dataset (data collected during the years 2014and 2015). )e two fitness functions have been used for the evaluation of the models, that is, coefficient of determination (R2) androot mean square error (RMSE), and it is inferred that GP models predict with high accuracy for pavement distress and help thedecision makers for adequate and timely fund allocations for preservation of the urban road network.

1. Introduction

India’s road network is the second largest in the world,with the total road length increased from 0.399 millionkilometers as on 31 March 1951 to 4.698 million kilometersas on 31 March 2011 [1]. )e urban roads clutch huge trafficand bear the economic loss due to poor condition of theroads that accumulates to a gigantic sum. )e total trans-portation cost comprised two basic components, that is, roadcost and user cost. Researcher’s studies [2, 3] on variousaspects of road pavement and transportation have indicatedthat the road user cost constitutes a major part (around80–90% of the total transportation cost) which could besaved substantially with the help of a good decision supportsystem. )e utilization of urban roads and problems facedwhile maintenance are totally different than highway roadnetwork. In urban roads, the trip length is small, the numberof trips and diversion is large, and the intensity of traffic isheavy and nonuniform. In the last twenty years, themaintenance management systems have improved signifi-cantly due to the advances in technologies. Many researchers

are working on the development of pavement maintenancemanagement system (PMMS) and the effect of road surfacedeformations [4–17]. PMMS is one of such tools that assistengineers to maintain the roads in their serviceable con-ditions [17]. Mathew et al. [18] made efforts to develop thedeterioration models for performance of rural roads usingartificial neural network (ANN) and compared with re-gression techniques. )ey concluded that an ANN modelproved to be more suitable than the conventional regres-sion models because of its ability to adjust to a changingenvironment. Fwa et al. [19] presented a genetic algorithm-(GA-) based procedure for solving multiobjective networklevel pavement maintenance programming problems. )eyadopted the concepts of Pareto optimal solution set andrank-based fitness evaluation and two methods for selectingan optimal solution. Chan et al. [20] applied GA foroptimizing the resource allocation for pavement mainte-nance programming. )ey also compared the performanceof the various constraint handling methods, namely, pri-oritized resource allocation method, decode-repair method,and penalty method. Terzi [21] used ANN in modeling the

HindawiAdvances in Civil EngineeringVolume 2018, Article ID 1253108, 15 pageshttps://doi.org/10.1155/2018/1253108

Pavement Service Rating (PSR) for the flexible pavements.)ey developed an ANN model using input variables whichwere longitudinal cracking, total cracking, patching, rutdepth, slope variance, and output as panel data of PSR. )emodel was trained and tested using 74 datasets obtainedfrom AASHO test results. )e comparison of PSR had beendone with the ANN model and PCI had been obtained fromAASHO equation.)e values of coefficient of determination(R2) for the ANN model were 0.83 and 0.82 for the trainingset and testing set, respectively, and for PSI, the values of R2were 0.99 and 0.87 for the training and testing set, respec-tively. Reddy and Veeraragavan [22] developed deteriorationmodels and growth curves for rebound deflection, rut depth,and crack area for two types of pavement surfacing. )eydeveloped predictive models for deflection, rut depth, andcrack area progressionwith traffic. Bianchini and Bandini [23]proposed a neurofuzzy model to predict the performance offlexible pavements using the parameters routinely collected byagencies to characterize the condition of an existing pave-ment. )eir proposed hybrid model for predicting pavementperformance was characterized by multilayer feed-forwardneural networks that led the reasoning process of the IF-THEN fuzzy rules. Khraibani et al. [24] presented a nonlinearmixed-effects model for the evaluation and prediction ofpavement deterioration. Luo [25] proposed the application ofan auto regression method to pavement performance mod-eling to improve the predictive accuracy of predictions whenthere are only limited or incomplete data available.

)e literature reveals that there is successful imple-mentation of PMMS for maintaining the road network andmaking optimal use of resources in developed countries.However, still attempts are made to transfer such systems todeveloping countries from developed ones based on tech-niques, methodologies, and resources that are improper tolocal condition [26]. Successful implementation of PMMS fordifferent road categories in developing countries like India willlead to optimal use of resources and better and safer roads.)eobjective of the present study is to develop models for urbanroad network of Patiala (Punjab, India) using genetic pro-gramming (GP) to predict the pavement distress deterioration.

2. Data Collection

An efficient decision support system depends on accuracy,integrity, reliability, and the most important completeness ofthe database. )e data have been collected on the selected 16roads of Patiala, and the database has been organized in sucha manner that the data will be retrieved easily. A detaileddescription of the collected data and the procedure of datacollection and equipments used for the PMMS have beenpresented in the subsections.

2.1. Identification and Selection of Patiala City RoadSections. )e very first step is to identify the road networkand select the road sections. In the present study, Patiala City(Punjab, India) road network has been identified and 16road sections have been selected for developing pavementdistress models. Figure 1 shows a map of urban road

networks of Patiala city, and Table 1 consists of inventorydata of selected road sections. )e selected road sections arehomogeneous within them but vary considerably from eachother in terms of traffic and pavement width.

2.2. TrafficVolumeData. In the present study, traffic volumedata have been collected from Municipal Corporation,Patiala. Table 2 consists of the traffic volume of each roadsection, and Table 3 shows volume-to-capacity ratio of theselected road network. )e Equivalent Standard Axle (ESA)repetition in the analysis year (in millions) has been cal-culated as per IRC 37 [31].

2.3. Structural Evaluation of Pavements. )e structuralevaluation has been undertaken to assess the pavement’sstructural ability to receive wheel loads plying over it, that is,measurement of rebound deflection. )e normal practice isto use the Benkelman beam deflection (BBD) method forevaluating the structural condition of the flexible pavementas per the procedure laid down in IRC [27]. )e dual rearwheels of the truck are centered above the selected point.)eprobe of the Benkelman beam is inserted between the dualwheels and placed on the selected point. )e initial reading(D0) is recorded when the rate of deformation of thepavement is equal or less than 0.025mm/minute. )e truckis slowly driven a distance of 2.70m. An intermediatereading (Di) is recorded when the rate of recovery of thepavement is equal or less than 0.025mm/minute. )e truckis driven forward a further 9m. )e final reading (Df) isrecorded when the rate of recovery of pavement is equal to orless than 0.025mm/minute. )e rebound deflections havebeen calculated for all the selected road sections by takingthe initial, intermediate, and final deflection readings of theBBD test. )e rebound deflection value at any point is givenby the following two conditions:

(i) If (Di−Df) ≤ 0.025mm,

then rebound deflection� 2 (D0−Df).

(ii) If (Di−Df)> 0.025mm,

then rebound deflection� 2 (D0−Df) + 2.91[2 (Di−Df)].

Pavement temperature has been recorded at least onceevery hour by inserting thermometer in the standard hole andfilling up the hole with glycerol. )e rear axle weight of thetruck is 8170 kg with a tyre pressure of 5.6 kg/cm2, and spacingbetween the tyre walls is 35mm. Test points are taken ata distance of 60 cm from the pavement edge if the lane widthis less than 3.5m and at 90 cm distance from the pavementedge for wider lanes. For divided four lane stretch, themeasurement points should be at a distance of 1.5m fromthe pavement edge. Since the deflections measured by theBenkelman beam (BB) are influenced by the pavementtemperature and seasonal variations in different climates,pavement temperature and soil subgrade details have alsobeen collected at all observation points formaking subsequentcorrections to the deflection values. )e characteristic de-flection value is obtained as a sum of the mean and standard

2 Advances in Civil Engineering

Width above 100′ Width 80′–100′ Width 60′–80′ Width below 60′

Railway stationLevel crossing

Bus stand

Railway line

Truck terminal

Over bridges

Figure 1: Map of Patiala (Punjab, India) urban road network.

Table 1: Inventory data of selected road sections.

Section ID Name of the road Length(in kilometers)

Width of the carriageway(in meters)

Drainagecondition

UR01 �apar University–Bhadson Road 0.80 6.80 FairUR02 �apar University–Bhupindra Road 1.05 7.30 FairUR03 �apar University–Gurudwara Sahib (Passey Road) 2.50 7.50 GoodUR04 Passey Road–Civil Line (Ghuman Road) 1.00 7.20 Very poorUR05 Gurudwara Sahib Chowk–Sirhind Road 2.25 7.00 GoodUR06 Leela Bhawan Chowk–Cantonment 0.70 11.50 GoodUR07 Gurudwara Sahib Chowk–Bus Stand Road 0.90 7.50 PoorUR08 �ikriwala Chowk–Sangrur Road 1.00 7.50 GoodUR09 �ikriwala Chowk–Badungar Road 0.80 11.80 FairUR10 Bus Stand Chowk–Gurbax Colony 2.10 6.0 PoorUR11 Fountain Chowk–Leela Bhawan 0.70 12.5 GoodUR12 Fountain Chowk–Lower Mall 2.25 7.5 FairUR13 �apar University–Gurudwara Sahib 2.25 7.30 FairUR14 Leela Bhawan Chowk–No. 22 bridge 2.10 7.50 GoodUR15 Leela Bhawan Chowk–Gurudwara Sahib (Rajbaha Road) 1.46 10.0 FairUR16 Leela Bhawan Chowk–Baradari Garden 1.10 6.40 Good

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deviation for all the corrected rebound deflection values fora particular section. From the BBD values determined asabove, the modified structural number (MSN) for all thepavement sections has been calculated [30]:

MSN � 3.2 × D−0.63

. (1)

Figure 2 shows the BBD survey on UR02, and Figure 3presents the progressive variations of BBD observed during

Table 2: Traffic volume data of road sections.

Section ID Cycle Rickshaw/rehri Scooter/M-cycle Car/jeep/auto Bus/truck/tractor/trolly Cart Total ESA in the year 2013(in millions)

UR01 198 118 350 371 112 22 1171 0.28116.9 10 30 31.7 9.6 1.8 100

UR02 234 73 552 285 33 5 1182 0.07219.8 6.2 46.7 24.1 2.8 0.4 100

UR03 152 141 341 285 78 5 1002 0.11215.2 14.07 34.03 28.44 7.8 0.5 100

UR04 108 18 251 115 10 3 505 0.19421.7 3.5 49.7 22.7 1.9 0.6 100

UR05 110 69 272 317 120 12 900 0.42412.2 7.66 30.2 35.2 13.3 1.44 100

UR06 251 180 547 265 33 4 1280 0.14420 14 42 21 2.6 0.4 100

UR07 267 201 584 535 129 15 1731 0.23015.4 11.6 33.7 31 7.4 0.9 100

UR08 191 207 651 880 425 3 2357 0.1278.1 8.8 27.61 37.34 18.03 0.12 100

UR09 171 158 470 338 29 2 1168 0.22515 14 40 28.4 2.5 0.1 100

UR10 407 459 1104 65 5 — 2040 0.12920 22.5 54.1 3.2 0.2 — 100

UR11 583 247 705 864 438 5 2842 0.16621 9 25 29.8 15 0.2 100

UR12 464 358 722 878 34 12 2468 0.03619 14.5 29 35.6 1.4 0.5 100

UR13 404 92 548 347 196 5 1592 0.90225.4 5.8 34.4 21.8 12.3 0.3 100

UR14 554 349 1275 1106 112 8 3404 0.11516.3 10.2 37.5 32.5 3.3 0.2 100

UR15 381 319 1427 1179 714 20 4040 0.9289.4 7.6 35.2 29.2 17.6 1 100

UR16 371 180 580 144 2 3 1280 0.00329 14 45.3 11.3 0.15 0.25 100

Table 3: Volume-to-capacity ratio of selected road network.

Section ID Peak hour volume (PCU) “V” Capacity (PCU) “C” V/C Type of the carriagewayUR01 1635 1800 0.90 4-Lane undivided (two-way)UR02 611 2900 0.21 4-Lane divided (two-way)UR03 845 3200 0.26 2-Lane (two-way)UR04 750 2200 0.34 4-Lane divided (two-wayUR05 1355 2900 0.46 4-Lane divided (two-way)UR06 1433 1800 0.80 Undivided 4-Lane (two-way)UR07 2622 2900 0.90 4-Lane divided (two way)UR08 1934 2900 0.67 4-Lane divided (two-way)UR09 680 900 0.75 2-Lane (two-way)UR10 1156 900 1.28 2-Lane (divided) two-wayUR11 1992 4300 .46 6-Lane divided (two-way)UR12 1485 1200 1.2 6-Lane divided (two-way)UR13 2244 2200 1.02 4-Lane divided (two-way)UR14 1936 2900 0.66 6-Lane divided (two-way)UR15 2932 2900 0.10 4-Lane divided (two-way)UR16 529 1800 0.29 4-Lane undivided

4 Advances in Civil Engineering

the years 2012–2015 on the selected road sections of PatialaCity, that is, UR01 to UR16.

2.4. Functional Evaluation of Pavements. Functional evalu-ation of pavements consists of collection of road conditiondata related to surface distress including pavement distressin terms of cracks, potholes, rutting, and ravelling. In thepresent study, cracking, potholes, ravelling, rutting, androughness have been measured for all the selected roadsections for the development of prediction models forpavement distress. �e two other parameters, skid resistanceand mean texture depth, have been also measured. Skidresistance has been measured in terms of skid resistancevalue and sideways force coe�cient (SFC). But, there has notbeen any noticeable decrement in the value of SFC from theyear 2012 to 2015. Similarly, there has not been any sig-ni�cant change in the mean texture depth measured usingthe “Sand Patch Method.”

2.4.1. Cracking Measurement. A number of representativetest sections of length 100m have been selected for cracking

measurements for each pavement section. Cracking (alli-gator, longitudinal, and transverse) has been visuallyinspected. In case of alligator cracking, the area coveredunder the distress has been marked in the form of a rect-angular box with a chalk on the ground and is measured witha tape. In case of longitudinal and transverse cracks, e�ectivewidth has been taken as 50 cm and actual length has beenmeasured. Cracked area is expressed as the percentage of thetotal pavement area. Figure 4 shows the cracks present on theroad section UR09, and Figure 5 shows the progressivevariation of the cracking area for the road sections UR01 toUR16 during the years 2012–2015.

2.4.2. Pothole Measurement. Pothole means open cavity onthe pavement. Measurement of potholes for each roadsection has been done visually. Minimum diameter of150mm and minimum depth of 25mm of pothole havebeen taken [28]. Figure 6 shows the pothole on the sectionUR04, and Figure 7 shows the progressive variations ofpotholes for the road sections UR01 to UR16 during theyears 2012–2015.

2.4.3. Ravelling Measurement. Ravelling is the loss of ma-terial from wearing surface. �is distress type is associatedwith thin surfacing, such as, surface dressing, seal coat, andpremix carpet. �e a�ected area has been measured bytaking into account the area enclosed in regular geometricshapes, and then it has been expressed as the percentage ofthe total pavement area. Figure 8 shows the ravelling on thesection UR13, and Figure 9 shows the progressive variationsof ravelling for the road sections UR01 to UR16 during theyears 2012–2015.

2.4.4. Rutting Measurement. Rutting refers to permanentdeformation on the pavement surface in the wheel path.Permanent deformation is commonly de�ned as distortionswithin the individual layers of the pavement structure.Rutting is caused by structural and/or material failure thatcan lead to hazardous driving conditions. It is very commonin £exible pavements. �e rut depth has been measured with

Figure 2: BBD test in progress at chainage 0.350 km on the section UR02.

0

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lem

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eam

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Figure 3: Measured BBD for the road sections UR01 to UR16.

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2m straight edge placed in the transverse direction. Twelveobservations have been carried out for each selected roadsection. �e maximum rut depth (in mm) has been taken ineach observation slot. �e rut depths have been averaged toget the mean rut depth of the selected road section. Figure 10shows the rutting on the section UR01, and Figure 11 shows

the progressive variation of rutting for the road sectionsUR01 to UR16 during the years 2012–2015.

2.4.5. Roughness Measurement. Road roughness refers tosurface irregularities in the longitudinal direction. Roughness is

Figure 4: Cracks on the road section UR09.

02468

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king

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(%)

Section number20122013

20142015

Figure 5: Progressive variation of the cracking area for the road sections UR01 to UR16.

Figure 6: Pothole at chainage 0.300 km on the section UR04.

6 Advances in Civil Engineering

an important pavement evaluation parameter because it a�ectsnot only ride quality but also vehicle delay costs, fuel con-sumption, and maintenance costs. Roughness has been mea-sured with the �fth wheel bump integrator or simply known asroughometer. Unevenness Index (in cm/km) has been calcu-lated for each section with the following equation:

Unevenness Index (UI) � bumps in cm/length travelled in km.

(2)

Roughness has been calculated in the form of InternationalRoughness Index (IRI, m/km). Above Unevenness Index (UI)value has been converted into International Roughness Index(IRI in m/km) by using the following equation [28]:

IRI �1630

× UI( )1/1.12

, (3)

where UI is the Unevenness Index in mm/km. IRI is theInternational Roughness Index in m/km. Figure 12 showsbump integrator test (roughness test) in progress on thesection UR11, and Figure 13 shows the progressive variations

UR0

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Poth

oles

(no.

/km

)

Section number

Figure 7: Progressive variation of potholes for the road sections UR01 to UR16.

Figure 8: Ravelling at chainage 0.300 km on the section UR13.

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lled

area

(%)

Section number

Figure 9: Progressive variation of ravelling for the road sectionsUR01 to UR16.

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Figure 10: Rut depth measurement at chainage 0.200 km on the section UR01.

20122013

20142015

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epth

(mm

)

Figure 11: Progressive variation of rutting for the road sections UR01 to UR16.

Figure 12: Bump integrator test (roughness test) in progress on the section UR11.

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of IRI for the road sections UR01 to UR16 during the years2012–2015.

3. Methods

GP has commenced as an endeavor to discover howcomputers could be trained to solve problems withoutbeing explicitly programmed to do so. GP is an extension ofgenetic algorithms proposed by Koza [29] who de�nes GPas a domain independent problem solving impends inwhich computer programs are evolved to solve, or ap-proximately solve, problems based on Darwinian principlesof reproduction and analogs of naturally occurring geneticoperations such as reproduction, crossover, and mutation.�e �ve major prelude steps for the basic version of GPrequire the user to specify (a) the set of terminals for eachstem of the to-be-evolved program; (b) the set of primitivefunctions for each stem of the to-be-evolved program; (c)the �tness measure; (d) certain parameters for controllingthe run; and (e) the termination criterion and method fordesignating the result of the run.

3.1. Steps to Execute GP. �e execution steps of GP are asfollows:

(1) Select the dataset that has to be used as initialpopulation (generation 0) with the available func-tions and terminals.

(2) Apply the following steps iteratively on the populationuntil the termination criterion has been satis�ed:

(a) Execute each program in the population andascertain its �tness (explicitly or implicitly) usingthe problem’s �tness measure.

(b) Select one or two individual(s) from the pop-ulation based on the probability of �tnessmeasureto participate in the genetic operations in (c).

(c) Generate new individual(s) for the populationwith the help of following genetic operations:

(i) Reproduction: copy the selected individualto the new population.

(ii) Crossover: create new children for the newpopulation by recombining randomly cho-sen parts from two selected individuals.

20122013

20142015

UR0

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Roug

hnes

s, IR

I (m

/km

)

Figure 13: Progressive variation of IRI for the road sections UR01 to UR16.

Table 4: Architecture of the GP model.

Parameters Values Description

Initial population size Dataset Dataset-1 is of 16 instances consisting of datagathered in 2012 and 2013.

Function set +, −, ∗, /, sqrt(), tanh(), pow(x, y),log(), exp(), pow(x, 2), fabs() Set of functions used

Training percentage 70 —Selection method Tournament —Tournament size of replacement 3 —Maximum generations 100000 Maximum number of iterationsCrossover 0.8 Probability of crossoverMutation 0.04 Probability of mutationμ 200 Population sizeλ 250 Number of children producedFitness functions R2 Coe�cient of determination

RMSE Root mean square error

Advances in Civil Engineering 9

(iii) Mutation: create one new child for the newpopulation by randomly mutating a ran-domly chosen part of one selected individual.

(iv) Architecture-altering operations: chooseoperation from the available repertoire ofsuch operations and create one new child forthe new population by applying the selectedarchitecture-altering operation to one se-lected individual.

Table 6: Results of the proposed models for training dataset.

Dataset Model R2 RMSE

Training dataset (2013)

Model 1 0.96 0.48Model 2 0.84 0.53Model 3 0.90 0.93Model 4 0.97 0.27Model 5 0.79 0.04

y = 1.004xR2

= 0.96

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(% ar

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Observed total cracking (% area)

Figure 14: Scatter plot between observed versus predicted totalcracking for training.

y = 0.980xR2

= 0.84

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Observed ravelling (% area)

Figure 15: Scatter plot between observed versus predicted ravellingfor training.

Table 5: GP models for progression of cracking, potholes, ravelling, rutting, and roughness for urban roads.

Values

Model 1(crackingprogression)

CAj � (1/MSNi)((MSNi × CAi) + ((e((CAi×e−ESAi )/(AGEi)))/AGEi) + ((2MSNi + AGEi + eESAi )/CAi) + 1),

where CAj is the cracking of the next year, CAi is the cracking of the previous year, MSNi is the modi�ed structural numberof the previous year, AGEi is the age of the pavement before the start of the analysis year, and ESAi is the number of

equivalent standard axle repetitions in the analysis year (in millions)

Model 2(ravellingprogression)

RAj � 1 + RAi + ((AGEi(1 + ESAi) + 2(RAi + e����AGEi

√))/(RAi(ESAi + AGEi))) + tanh(AGE2

i ((AGEi × ESAi)−RAi)),where RAj is the ravelling area of the next year andRAi is the ravelling of the previous year, AGEi is the age of the pavement beforethe start of the analysis year, and ESAi is the number of equivalent standard axle repetition in the analysis year (in millions)

Model 3(potholesprogression)

POTj � tanh(etanh(CAi) + RAi + POTi) + POTi −ESAi − tanh(POTi − tanh(POTi − tanh(����������tanh(AGEi)√

)−AGEi)),where POTj is the pothole of the next year (number per km), POTi is the pothole of the next year (number per km), CAi isthe cracking of the previous year, RAi is the ravelling area of the previous year, AGEi is the age of the pavement before thestart of the analysis year, and ESAi is the number of equivalent standard axle repetition in the analysis year (in millions)

Model 4(ruttingprogression)

RDj � RDi +DF + tanh(RDi(MSN−DF− 1)/(log(MSN/ESAi) + CAi + AGEi + (RDi/2MSN + log(MSN)))),where RDj is the rutting of the next year, RDi is the rutting of the previous year, MSNi is the modi�ed structural number of theprevious year, AGEi is the age of the pavement before the start of the analysis year, DF is the drainage factor, CAi is the crackingof the previous year, and ESAi is the number of equivalent standard axle repetitions in the analysis period (in millions)

Model 5(roughnessprogression)

IRIj � 1.254(((ESAi × AGEi × IRIi)/((ESAi × RDi × dNPT × AGEi) + (12.048 × IRIi) + (ESA3i × AGEi)))

+(IRIi)����ESAi√

),where IRIj is the roughness of the next year, IRIi is the roughness of the previous year, ESAi is the number of equivalentstandard axle repetitions in the analysis year (in millions), AGEi is the age of the pavement before the start of the analysisyear, and dNPT is the change in the number of potholes during the analysis year, RDj is the rut depth in the previous year

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(3) When termination criterion has been satis�ed, thebest program in the population produced during therun has been designated as the result of the experi-ment. If the experiment is successful, the result may bea solution (or approximate solution) to the problem.

3.2. Development of the GP Model. �e control parametersas given in Koza [29] have been investigated in this study.�e population size (μ) and the number of children pro-duced (λ) have been taken as 200 and 250, respectively. �elarger is the number of generations, the greater are thechances of evolving a solution; hence, the number ofgenerations has been taken as 100000. �e values for theparameters, namely, crossover rate and mutation rate, havebeen selected as 0.80 and 0.04, respectively, after experi-mentations.�e values of other parameters, that is, training

y = 1.010xR2

= 0.90

0

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icte

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thol

es (n

umbe

r)

Observed potholes (number)

Figure 16: Scatter plot between observed versus predicted potholesfor training.

y = 0.985xR2

= 0.97

0

1

2

3

4

5

6

7

8

9

0 1 2 3 4 5 6 7 8 9

Pred

icte

d ru

t dep

th (m

m)

Observed rut depth (mm)

Figure 17: Scatter plot between observed versus predicted ruttingfor training.

y = 0.913xR2

= 0.79

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Pred

icte

d ro

ughn

ess,

IRI (

m/k

m)

Observed roughness, IRI (m/km)

Figure 18: Scatter plot between observed versus predicted roughnessfor training.

Table 7: Results of the proposed models for validation dataset.

Dataset Model R2 RMSE

Validation dataset (2014)

Model 1 0.77 0.60Model 2 0.78 0.62Model 3 0.84 0.71Model 4 0.80 0.86Model 5 0.81 0.76

Validation dataset (2015)

Model 1 0.75 0.89Model 2 0.75 0.90Model 3 0.90 0.70Model 4 0.81 0.90Model 5 0.73 0.09

0

2

4

6

8

10

12

14

16

0 2 4 6 8 10 12 14 16 18

Pred

icte

d to

tal c

rack

ing

(% ar

ea)

Observed total cracking (% area)

y = 0.942xR2

= 0.77

Figure 19: Scatter plot between observed versus predicted totalcracking for validation (2014).

Advances in Civil Engineering 11

percentage, selection method, and tournament size ofsubstitution, are taken as 70, “tournament” and 3, re-spectively, for the development of the GP model. Functionset (+, −, ∗, /, sqrt(), tanh(), exp(), log(), fabs(), pow(x, y),pow(x, 2)) has been taken for generation of model equa-tions. �e architectural details of the selected GP model aregiven in Table 4.

3.2.1. Models Generated Using GP. In the GP model de-velopment, the addition is chosen as the linking utility. �eprediction models generated using the GP are listed inTable 5. It consists of �ve models: Model 1, Model 2, Model

3, Model 4, and Model 5 for cracking, ravelling, potholes,rutting, and roughness, respectively.

4. Results and Discussions

�e results obtained from this approach have been used forthe quantitative assessment of the model’s predictiveabilities and are presented in Table 6. �e dataset gatheredduring the years 2012 and 2013 has been used for trainingmodels; that is, for the prediction of the year 2013 pavementdistress, the dataset of the year 2012 has been used. �epostregression �ts for the training dataset of all the models(Model 1, Model 2, Model 3, Model 4, and Model 5) arepresented in Figures 14–18, respectively. It can be observed

0

5

10

15

20

25

0 5 10 15 20 25 30

Pred

icte

d to

tal c

rack

ing

(% ar

ea)

Observed total cracking (% area)

y = 1.014xR2

= 0.75

Figure 20: Scatter plot between observed versus predicted totalcracking for validation (2015).

0

4

8

12

16

20

0 4 8 12 16 20

Pred

icte

d ra

velli

ng (%

area

)

Observed ravelling (% area)

y = 0.970xR2

= 0.78

Figure 21: Scatter plot between observed versus predicted ravellingfor validation (2014).

0

4

8

12

16

20

0 4 8 12 16 20

Pred

icte

d ra

velli

ng (%

area

)

Observed ravelling (% area)

y = 1.020xR2

= 0.75

Figure 22: Scatter plot between observed versus predicted ravellingfor validation (2015).

y = 0.992xR2

= 0.84

0

2

4

6

8

10

Pred

icte

d po

thol

es (n

umbe

r)

0 2 4 6 8 10Observed potholes (number)

Figure 23: Scatter plot between observed versus predicted potholesfor validation (2014).

12 Advances in Civil Engineering

from Figures 14–18 that the some deviation can be noticedbetween the observed and predicted values because of themodeling approach adopted and because of the assumednormal construction quality for the bituminous surfacingconsidering the use of optimum binder content in bi-tuminous base and wearing courses as per the routinepractice for maintaining the urban roads in India. But, thisdeviation is quite reasonable for the urban road sections ofdi�erent age and tra�c loading conditions.

4.1. Validation of GP Models. To further test the e�cacy andreliability of the models, the datasets collected during the years2014 and 2015 have been used for the validation purposes.�eresults of proposed models for validation dataset of year 2014and year 2015 are presented in Table 7. For the prediction of

pavement distress of the year 2014, the data gathered duringthe year 2013 has been used, and for the prediction ofpavement distress of year 2015, the data gathered during theyear 2014 has been used. �e postregression �ts for the val-idation datasets (2014–2015) of all themodels (Model 1,Model2, Model 3, Model 4, and Model 5) are presented in Figures19–28, respectively. All the GP models have been predictingwith good competence for both the datasets (2014 and 2015).�e results are revealing that these GP models can be appliedsuccessfully to the roads of Patiala City, Punjab, India.

5. Conclusions

(i) �e objective of this study was to explore the ap-plicability of GP models for pavement distress. Five

0

2

4

6

8

14

10

12

Pred

icte

d po

thol

es (n

umbe

r)

0 2 4 6 8 141210Observed potholes (number)

y = 1.012xR2

= 0.90

Figure 24: Scatter plot between observed versus predicted potholesfor validation (2015).

0

2

4

6

8

10

12

0 5 10 15

Pred

icte

d ru

t dep

th (m

m)

Observed rut depth (mm)

y = 1.040xR2

= 0.80

Figure 25: Scatter plot between observed versus predicted ruttingfor validation (2014).

0 5 10 150

2

4

6

8

10

14

12

Pred

icte

d ru

t dep

th (m

m)

Observed rut depth (mm)

y = 1.011xR2

= 0.81

Figure 26: Scatter plot between observed versus predicted ruttingfor validation (2015).

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Pred

icte

d ro

ughn

ess,

IRI (

m/k

m)

Observed roughness, IRI (m/km)

y = 1.016xR2

= 0.81

Figure 27: Scatter plot between observed versus predicted roughnessfor validation (0.1∗IRI in 2014).

Advances in Civil Engineering 13

models have been developed for the cracking pro-gression (Model 1), ravelling progression (Model 2),pothole progression (Model 3), rutting progression(Model 4), and roughness progression (Model 5).�e data collected during the year 2012 to year 2015on the 16 selected roads of Patiala, Punjab, India,have been used for the development of these models.

(ii) We can say that GP has built a good correlationbetween observed and predicted values and theparameters (like cracking, ravelling, pothole, rut-ting, and roughness) that have been taken in thepresent study are su�cient for the prediction ofpavement distress.

(iii) �e deviations between observed and predictedvalues are only because of the modeling approachadopted and because of the assumed normal con-struction quality for the bituminous surfacing con-sidering the use of optimum binder content inbituminous base and wearing courses, but this de-viation is quite reasonable for the urban road sectionsof di�erent age and tra�c loading conditions.

(iv) �ese models can be applied to other city roads witha range of tra�c varying from 0.1 to 0.85 equivalentstandard axle repetitions in the initial analysis yearand MSN in the range of 2 to 4.5.

(v) As an outcome, we can say that GP models providegood results for the prediction of pavement distressand may serve as a predictive model for the pre-diction of pavement distress for all the cities havinghomogeneous tra�c and climate conditions likePatiala, Punjab, India.

Conflicts of Interest

�e authors declare that there are no con£icts of interestregarding the publication of this paper.

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0

0.1

0.2

0.3

0.4

0.5

0.6

0.8

0.7

Pred

icte

d ro

ughn

ess (

IRI -

m/k

m)

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= 0.73

Figure 28: Scatter plot between observed versus predictedroughness for validation (0.1∗IRI in 2015).

14 Advances in Civil Engineering

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