DEVELOPMENT OF PAVEMENT MAINTENANCE MANAGEMENT SYSTEM FOR RURAL ROADS

Transcription

1 CHAPTER GENERAL DEVELOPMENT OF PAVEMENT MAINTENANCE MANAGEMENT SYSTEM FOR RURAL ROADS Development of Pavement Maintenance Management System for rural roads was attempted in three stages in this work. Firstly, a prioritisation technique was developed to prioritise the roads to be taken up for maintenance activity. Secondly, HDM-4 being a versatile pavement management tool, its applicability for rural roads was attempted after calibrating its deterioration models for conditions prevalent on Indian rural roads. Finally an effort was also taken to develop a deterministic optimisation model for the maintenance programming of rural roads incorporating the performance prediction model developed in this study. 5.2 PRIORITISATION OF ROAD SECTIONS USING FUZZY MULTI CRITERIA DECISION MAKING (FMCDM) APPROACH An effective Pavement Maintenance and Management System (PMMS) requires the prioritisation of the road stretches for logical disbursement of budget. In a Pavement Management System, prioritisation of road sections plays an important role, especially when budget available for road maintenance is limited. Though the optimisation of maintenance strategies for road network is considered to be a complete and an ultimate solution in PMMS, many a time it can be an impractical solution for rural roads due to the limitation on the budget. The assessment of pavement condition is mandatory for the prioritisation process and it necessitates the measurement of various distress parameters with respect to their extent and severity. Though the extent of distresses can be measured accurately, the severity of distresses has unavoidable uncertainty associated with it. Hence Fuzzy Multi Criteria Decision Making (FMCDM) 106

2 approach is a better option wherein the fuzzy logic is being applied to only those parameters which is predominantly uncertain in nature. The roughness on the study roads was found to be fairly high and it has significant influence on the user perspective about the condition of pavement. Hence in the present study, apart from the functional distresses, roughness of the road surface which is another parameter indicating riding comfort was also included as a parameter to define the condition of the pavement. Extent of distresses and roughness was proposed as a direct parameter and a fuzzy approach was suggested to assess the severity ofdistresses Methodology A fuzzy number 'A' is a fuzzy set, and its membership function is!lex): R ~ [0.1]. Triangular Fuzzy Numbers (TFN) are special class of fuzzy numbers which are generally used and corresponds to linear membership function Membership of TFN is defined by three real numbers, (1, m, n) as shown in Fig. 5.1 (Ross, T. J., 1997; Chen and Klein, 1997; Chen et ai., 2003). 1 o m n Fig. 5.1 Membership Function for Triangular Fuzzy Number 107

3 The TFN can be expressed as 11 A(x): ~ A (X) (x - 1) ~m - l~ 1 ~ X ~ m; n-x m ~ X ~ n; (n - m) 0 otherwise General operations involved between two TFNs, A (1, m, n) and B (P, q, r) are (Ross, T. J., 2003) : Addition oftwo fuzzy numbers (1, m, n) + (p, q, 1') = (1 + p, m + q, n + r) (5.1) Subtraction of two fuzzy numbers (1, m, n) e (p, q, r) = (1- r, m - q, n - p) (5.2) Multiplication of a real number with a fuzzy number K * (1, m, n) = (Kl, Km, Kn) (5.3) Prioritisation of pavement sections for the rural road network was attempted based on the methodology proposed by Chen and Klein (1997) and Chen (2001). Steps involved in prioritisation process using Fuzzy MCDM approach are: i) Preparation of a normalised distress data in a scale of 0 to 100. ii) Assigning rating for the extent ofdistresses and prepare a rating matrix, Rij where i = 1 to N, N is number of road stretches; j = 1 to M, M is the type of distress considered. iii) Replacing linguistic variables used for expressing severity of distresses by Triangular Fuzzy Numbers (TFN) and arranging TFNs in a weight matrix, Wjo iv) Calculation of fuzzy evaluation values 'Pi' by multiplying rating matrix, Rij with weight matrix, Wj. 108

4 m P. = "R.@W. I L..J IJ J j=i (5.4) Vi = 1, 2,..., N Vj =1, 2,..., M v) Arriving at the relative preference of road stretches by computing the difference between all combinations offuzzy values. (5.5) i = 1 to N k = 1 to N i :;t k vi) Preparation of a fuzzy preference relation matrix [P] to express the degree of preference of stretch Sj over Sk. where ejk is the real number which indicates the degree of preference of stretch Sj over Sk. s + e = -_--:..:.:..,------,- ik ik S ik + + Is ik -\ (5.6) Sik+ and Sjk- are positive and negative areas of difference between two fuzzy values viz., (Pi - Pk). Positives and Negative areas can be computed using the membership function IlA(X) of (Pi - Pk) as shown in Fig

5 1.0 Positive Area Negative --,...,... Area -I a m n Fig. 5.2 Estimation of Fuzzy Preference Relation Matrix Here eii = 0.5 and eik + eki = 1.0 Ifeik> 0.5, road stretch Si is to be given preference over road stretch Sk. vii) Priority index (PI) for all the road stretches are thus computed from the fuzzy preference relation matrix using the mathematical form. M (PI); =.2: (e;k -0.5) Vi = 1 to N J=I (5.7) Prioritisation Process using Fuzzy MCDM Approach Distresses considered in the prioritisation included ravelling, pothole and edge breaking with respect to three severity levels, low, medium and high. Definitions regarding severity of distresses are given in condition survey format in Appendix-I (B). Roughness (in terms of IRI in m/km) was also considered for the prioritisation, apart from the functional distresses. Roughness was categorised into three severity levels viz., low, medium and high based on the actual IRI values collected from the road stretches selected for the study. The influence of severity levels of various distresses 110

6 will have different impact on the condition of the pavement. Potholes of medium and high severity have much considerable influence on the deterioration of pavement than corresponding severity levels ofravelling and edge failure. The influence ofseverity of various distresses and roughness on the total deterioration of pavement was expressed in terms oflinguistic variables such as Low (L), Medium (M), High (H) and Very High (VH). Influence of severity levels of various distresses on the condition of pavement was arrived at based on their respective deduct values (Shahin, 1994) and hence the effect of various levels of distresses was arrived at in this approach by classifying the deduct values arbitrarily and expressed in terms of linguistic variables. A deduct value in the range of 0 to 40 for a particular severity level of a distress was assumed to have a low effect on the total deterioration of pavement and hence assigned a linguistic variable Low to express its influence. Similarly deduct values of 40 to 60, 60 to 80 and 80 to 100 corresponding to various severity levels of various distresses were assigned linguistic variables of Medium, Heavy and Very Heavy to express their influence on the total deterioration of pavement. Since roughness could not be assigned linguistic variables based on deduct values, the same was done based on the riding comfort offered by the road stretches. Roughness data collected from the study stretches in terms ofiri was found to vary between 6.5 and 11.0 m/km. The riding quality ofthose roads with IRI greater than 10 m/km was found to be very poor. Hence severity of roughness was classified as Low for IRI less than 6.5 m/krn, Medium for IRI between 6.5 & 10.5 rn/krn and High for IRI greater than 10.5 m/km respectively and linguistic variables of Low, Medium and Very High were assigned to them based on the riding comfort. Influence of severity of various distresses and roughness are shown in Table

7 Table 5.1 Effect of Severity of Distresses and Roughness Intensity ofvarious Distress Low Ravelling (LRa) Medium Ravelling (MRa) High Ravelling (HRa) Low Pothole (LP) Medium Pothole (MP) High Pothole ( HP) Low Edge Failure (LE) Medium Edge Failure (ME) High Edge Failure (HE) Low Roughness (LRo) Medium Roughness (MRo) High Roughness (HRo) Linguistic Variable Assigned Low Medium High Medium High Very High Low Low Medium Low Medium Very High Pavement condition data collected from the field for the development of deterioration model was used for the prioritisation procedure. Since the various distress data were observed to be in varying ranges, for example, pothole data was found to be in the range of 0 to 2%, but the ravelling data was in the range of 0 to 70%, hence a nonnalisation was done. Each distress data was normalised in the scale from 0 to 100 with respect to maximum value in the respective series through a simple normalisation process like, Normalised value = [(Actual Value x 100) I Maximum value in that series]. 112

8 Normalised values of distresses were arranged in ten groups with a uniform interval of loin ascending order and a rating of one to ten was assigned to each group ranging from 1 to 10 to 91 to 100 respectively. Depending on the quantity of each type of normalised distress on each road stretch, ratings from one to ten were assigned and were arranged in a rating matrix 'Rij', which is shown in Table 5.2. Each row of the matrix represents the rating assigned for each parameter of each road stretch and each column represents the parameter (either distress or roughness) considered. First element of '4' in the matrix corresponds to the first road stretch under the distress low ravelling which indicates that the value of low ravelling for that stretch is between 31 to 40 and in a similar manner all the entries were made in the matrix. Table 5.2 Rating Matrix (R ij ) for Distress and Roughness Parameters Road Rating Assigned for Various T r'pes of Distresses t Stretch LRa MRa HRa LP MP HP LE ME HE LRo MRo HRo ID t I

9 The linguistic variables assigned for expressing the influence of severity of distress parameters and roughness were expressed as Triangular Fuzzy Numbers (TFN) and are shown in Table 5.3. Table 5.3 Triangular Fuzzy Numbers (TFN) for Linguistic Variables Linguistic Triangular Fuzzy Numbers (TFN) Variable (1, m, n) Low Medium High Very high ,0 Effect of severity of distresses and roughness in terms of linguistic variables as given in Table 5.1 were converted into fuzzy numbers using TFNs given in Table 5.3 and were arranged in a weight matrix 'Wj' as shown in Table 5.4. Table 5.4 Fuzzy Weight Matrix (W j ) for Various Parameters Criteria Fuzzy Weights, Wj (1, m, n) LRa MRa HRa LP MP HP LE ME HE LRo MRo HRo

10 Fuzzy evaluation value 'Pi' was calculated by multiplying the rating matrix 'Rij' (Table 5.2) with weight matrix, 'W/ (Table 5.4) and was summed up for all the stretches and is shown in Table 5.5. Table 5.5 Fuzzy Evaluation Values (Pi) for Road Stretches Road Stretch Fuzzy Evaluation Value (Pi) ID (1, m, n) The relative preference between road stretches, were established by estimating the relative difference between fuzzy evaluation values. For example, in order to arrive at the relative preference of road stretch one over two, denoted as '1-2', the 115

11 difference between the fuzzy evaluation values ofthese road stretches was found out. For finding the difference of two fuzzy evaluation values, the subtraction operation of two TFNs as given in Equation 5.2 was adopted and the difference obtained was also a TFN. The relative preference of road stretch one over one, i.e., 1-1 was calculated as [( ), ( ), ( )] resulting in a TFN of (-14.4, 0, 14.4). Similarly the relative preference of road stretch one over two, i.e., 1-2 was calculated as [( ), ( ), ( )] which corresponds to a T.F.N of (-29.4, -13.4, 3.6). Similarly the relative preference of each road stretch over itself and all other stretches were worked out, and as an example, the relative preference of road stretch one over all road stretches is shown in Table 5.6. Table 5.6 Relative Preference of Road Stretch No.1 with respect to other Road Stretches TFN Corresponding to Relative Preference Relative Preference ofroad ofroad Stretches Stretches (1, m, n)

12 As the relative preference of each stretch over itself and all other roads were expressed by the Triangular Fuzzy Numbers as given in Table 5.6, the fuzzy preference relation matrix [P] was then developed to arrive at the degree of preference of each stretch over the other. As discussed in step-vi of Section 5.2, each element of the preference matrix [P] was calculated as the ratio of the positive area to the sum of positive and absolute value ofthe negative area. The positive and negative areas were computed using the membership function Il A (x) of 1-2. A sample computation of an element 'e12' ofthe fuzzy preference relation matrix is depicted in Fig Positive Area Negative -----'i-f-+ Area 1=-29.4 m=-13.4 n =+3.6 Fig. 5.3 Computation of Fuzzy Preference Relation Matrix The positive area in Fig. 5.3 is and total area is 16.5 and hence el2 is (0.3811/16.5), which is equal to Similarly the degree of preference of each stretch over itself and all other stretches were computed and the fuzzy preference relation matrix [P] thus developed is shown in Table 5.7. It can be seen from Table 5.7 that ejj is 0.5 which means the preference of road stretch 'i' over 'i' is equal and also that ejk+ eki = I, If ejk is greater than 0.5, then road stretch 'i' should be given 117

13 preference over road stretch 'k' and vice versa. In the matrix [Pi], el2 is and e21 is which indicates that road stretch No.2 should be given preference over road stretch 1. Finally the prioritisation process was done based on a single combined index for each stretch which was derived from all individual preference relations given in Table 5.7. A priority matrix was thus developed such that each element of the matrix was computed as (eik - 0.5) and represents the relative priority of a specific road stretch over another road Priority Index (PI) for each road stretch was computed from the priority matrix usmg the mathematical formula N (PI)j =L(e - ik 0.5) k=1 Vi = 1to N and are shown in Table 5.8. Thus, Priority Index (PI) ofthe road stretch No. 1 was calculated by taking the sum of all elements in the first row of the priority matrix and the PI of all road stretches were thus calculated. The road stretch with highest PI value was given the highest priority and the road stretch with lowest PI value was assigned the lowest priority. The priority rankings allotted accordingly are shown in Table

14 Road Stretch ID

15 Road Stretch ID II

16 Table 5.9 Ranking of Road Stretches Based on Priority Index (PI) from Fuzzy MCDM Approach Road Stretch Priority Index Rank based on ID (PI) PI ~ It can be observed from Table 5.9 that, road stretch No.13 has the highest PI of and hence the highest priority and road stretch No.ll has the smallest PI of and the least priority. A comparison was made between the prioritisation done for the road stretches based on the pel values and Priority Indices and is shown in Table

17 Table 5.10 Comparison of Ranking of Road Stretches Based on Priority Index (PI) and PCI Rank Based on Priority Index (PI) from Fuzzy MCDM Approach Road Stretch ID Rank Based on PCI Discussion It was observed that the ranking ofroad stretches based on both Priority Index from fuzzy approach and PCI values were almost similar, except the difference noticed in the case roads No. 7 and 10. This can be due to the effect of roughness of those roads which was taken into account in the fuzzy approach. But it can be expected that the fuzzy approach will yield a better result, since it not only made use of the deduct values (Shahin, 1994) to express the influence of various intensities of distresses on the total deterioration of pavement but also the uncertainty involved in assessing the severity of distresses was taken care of using fuzzy logic. Moreover, roughness which is a very important measure of the functional performance was also included as a 122

18 parameter in this prioritisation process unlike the ranking based on PCI, which includes only the influence of distresses. Further, any number ofparameters including structural criteria can be incorporated in the prioritisation process which will make the prioritisation more scientific. Hence Fuzzy MCDM approach can be used effectively and easily for the prioritisation of rural roads more advantageously over the prioritisation based on the PCI value. 5.3 OPTIMISATION OF MAINTENANCE STRATEGY FOR RURAL ROAD NETWORK USING HDM General Preventive Maintenance is needed to prevent fast deterioration ofthe pavement condition and to ensure the desired level of performance during the design life of the pavement. Early detection and repair of noticeable defects can prevent major breakdown of the pavement surface and consequently immense amount of savings in maintenance cost can be achieved. The most effective way to plan a maintenance programme is to carry out inspection of the road surface at suitable intervals. This is concerned with the evaluation of one or more road projects or investment options. HDM-4 has proved to be an effective, versatile tool for carrying out the economic analysis and arrive at the economic viability of alternative road projects, and to prepare road investment programme. However, road deterioration and work effect models used in HDM-4 should be properly calibrated to the regional, traffic and environmental conditions before its application. As mentioned in Section 2.6.1, HDM-4 has three analysis tools, viz., project analysis, programme analysis and strategy analysis. Project analysis deals with a road link or section with user-selected treatments, and associated costs and benefits, projected annually over the analysis period. Economic indicators are calculated for the different investment options. 123

19 Strategic planning involves an analysis ofthe road system as a whole, typically requiring the preparation of long term, or strategic planning estimates of expenditure for road development and preservation under various budgetary and economic scenarios. Predictions may be made of expenditure under selected budget heads, and forecasts ofhighway conditions in terms of key performance indicators, under a variety of funding levels. In strategy analysis, while defining M&R strategy, care is always taken to see that it includes the optimum strategy obtained as a result of project analysis. Calibration of HDM-4 deterioration models for rural roads and the application of calibrated HDM-4 to arrive at an optimum maintenance strategy by conducting a project analysis and strategy analysis are discussed in subsequent sections Calibration of HDM-4 Deterioration Models for Rural Roads General HDM-4 deterioration models are developed based on studies conducted on several countries, with varying environment and traffic conditions and hence it is extremely necessary that the these models are calibrated for rural road conditions to take care of the variation in model parameters. These models have provisions for adapting the relationships to local conditions, to take into account the variation in material characteristics, environment, type of surface etc. through the use of 'calibration factors'. Calibration should be done considering prevailing traffic conditions and actual deterioration mechanism. These factors are linear multipliers of predictions regarding the time of initiation and rate of progression of the different modes of distress such as cracking, ravelling, pothole and roughness. The calibration factors can be specified by the users and in the absence of any values by the user, the model adopts a default value for each deterioration factor. 124

20 Low volume roads are generally constructed with Pre-Mix Carpet course which is an open graded surface course. The distresses like ravelling and pothole are supposed to progress at a fast rate for open graded courses like Pre-Mix Carpet, consequently the calibration factors for these distresses should be high. Further, if the traffic and axle loads are low, the progression of load associated distresses shall be slow resulting in fairly low calibration factors for them. The calibration ofhdm-4 for rural conditions has been done by Jain et al. (2007) and the same has been reviewed in Section It has been observed that the calibration factors obtained in that study do not agree with the prediction done by the present deterioration models for rural roads. It is highly questionable that the calibration factors of cracking initiation and rut depth progression developed in this study are having higher values which mean that their rate of initiation and progression is high which can be expected from roads carrying high traffic volume and heavy axle loads. This finding is contrary to what is expected on rural roads where the traffic and axle loads of vehicles plying are very low. So also, the calibration factors ofravelling and pothole progression are having very low values which means that their rate of progression is very slow compared to that predicted by HDM-4 model which is contradictory to the findings from the present study. Hence it is essential that HDM-4 should be calibrated incorporating the actual rural conditions before application Methodology Calibration of a pavement performance model requires a group of distress data that expresses the real performance, preferably over a long span of time. The process of calibration consists of determining the adjustment factors which shows best agreement between the HDM-4 model's prediction and the actual field data. Calibration ofhdm-4 deterioration models mainly involves three steps: 125

21 i) Creating the Road Network Data In the road network folder a new road network has to be created. One section should be input in this folder by specifying the following Definition - Name, rd, speed flow type, traffic flow pattern, climate zones, road class, surface class, pavement type, length, carriageway width, shoulder width, number of lanes, flow direction, annual average daily traffic. Geometry - Rise and fall, horizontal curvature, speed limit, altitude and drain type. Pavement details - Previous surfacing done, year of previous surfacing, structural number and CBR ofsubgrade. Condition - Roughness, total area of cracking, ravelled area, number of potholes, edge break area, mean rut depth, texture depth, skid resistance and drainage condition ii) Creating the Vehicle Fleet Data The vehicles plying on the road section were input in the new vehicle fleet created. Vehicle types of motorcycle, car and heavy trucks were input by specifying the following details. Definition Basic Characteristics - physical details, tyre utilization and loading details Economic and financial unit costs - Vehicle resources, time value and maintenance values. iii) Calibration ofhdm-4 Models by Comparing the Predicted Distresses Calibration of HDM-4 to local condition requires good quality time-series data on the occurrence of distresses, for different pavement and traffic combinations. In the present study, calibration of HDM-4 models for rural roads was done using the pavement deterioration models developed in this study. Roads included in the study 126

22 were having the same pavement composition, traffic conditions and whose Structural Number lies in a range of 1.5 to 2.5. Deterioration models were developed for ravelling progression, pothole progression, edge failure progression and roughness progression. Using those models, the distresses were predicted and were compared with that of distresses predicted by HDM-4 models. The calibration factors in HDM-4 models for respective distress modes were varied and were again compared with the distress predicted using the developed models. Depending on the variation between the two distress values, the calibration factors were either increased or decreased from the default value of 'one'. The calibration factors which gave closer relationship with the predictions using the deterioration model developed in the study were selected as the calibration factor for the respective mode of distress. Calibration done for HDM-4 models for the present study included ravelling progression, pothole progression and roughness age-environment and roughness progression. For the distress edge failure, in HDM-4 calibration is confined to initiation only, hence was not included in the present calibration process. The default calibration factor in HDM-4 for all of these is one and the range of values for calibration factors provided in HDM-4 for various distress prediction models are given in Table Table 5.11 Range of Calibration Factors Provided in HDM-4 [HDM-4 Technical User Guide, 1999] Description Range Ravelling Initiation & Progression Factor Ravelling Retardation Factor Pothole Initiation & Progression Factor Roughness Age-Environment & Progression Factor

23 The condition of pavement at the end of year 2008 was given as input value and the distresses for next five years were predicted using the model developed in the study Validation of Calibration Factors The statistical significance of the calibration factor can be ascertained using Coefficient of Determination (R 2 value), Average Absolute Error (AAE) and Root Mean Square Error (RMSE), which were calculated by the following equations. (5.8) (5.9) (5.10) where, R 2 = Coefficient ofdetermination RMSE = Root Mean Square Error AAE = Average Absolute Error OJ = Predicted value ofdistress by developed model Pi = Predicted value ofdistress by HDM-4 model Oavg Average value of distress by developed model n Number of observations Calibration of Ravelling Progression Model Ravelling progression models developed in the present study (Equation 4.3, Section 4.3.3) was used to compare with the model in HDM-4. In HDM-4, the construction defects are input through two indicators, CDS and CDB. CDS indicates the Construction Defects for Bituminous Surfacing and CDB indicates Construction Defects for the Base course. Value of CDS ranges from 0.5 to 1.5 and CDB ranges from 0 to 1.5, the lower value corresponds to a case of no construction defects and 128

24 higher value corresponds to several defects. In this study since the pavements are considered to have fair construction quality, a value of 1.0 and 0.75 were assigned to CDS and CDB respectively. The present study is limited to Premix Carpet (FMC) surfaced pavements and hence calibrationwas done for PC surfaced pavements. The default calibration factor of one, predicted a lower value of ravelling than that predicted by the developed model. So values higher than one were tried till the predicted ravelling value agreed closely with the value predicted by the developed deterioration model. Comparison of predicted values by the deterioration models developed in this study and by HDM-4 models for various calibration factors is shown in Fig ~ 60 :a :S 50 Qj > III 40 ~ -+- Model Predicted HOM(1,1,1) HOM(1,1.3,1) 70 i 30 ~ ~HOM(1,1.6,1) -.-HOM (1,1.4,1) Year Fig. 5.4 Calibration Factor for Ravelling Progression Statistical parameters which were calculated to establish the fitness of the calibration factor are shown in Table

25 Table 5.12 Validation of Calibration Factor for Ravelling Progression Distress Calibration Coefticient of Average Root Mean Factors Determination Absolute Error Square (R 2 ) (AAE) Error (RMSE) 1,1, Ravelling 1,1.3, Progression 1,1.6, ,1.4, It can be observed from Table 5.12 that the calibration factor of 1.4 has the least values of R 2, AAE and RMSE values. Hence the calibration factor for ravelling progression was adopted as Calibration of Pothole Progression Model The prediction model developed for pothole progression in the present study (Equation 4.4, Section 4.3.4) was used for calibration of pothole progression model of HDM-4. Pothole data were collected in terms of percentage of carriageway affected area for the present study, but HDM-4 accounts potholes in number of units. In HDM-4 models an area of 0.1 m 2 of pothole area is considered as one pothole unit hence due conversion was done to bring both data to a single unit. The default calibration factor of one, predicted a higher value of distress than predicted by the developed model. So the calibration factor was decreased and the factor was selected when the variation between predicted values by both models was negligible. Comparison of predicted values by the prediction model and by HDM-4 models for various calibration factors is shown in Fig

26 r , , :;,.-==- 1 ";" ~ "'~7'""- I ~-a =---~--=,...;..~"--c_=..'"""""'-_l.c... ~ 'i ti :; Model Predicted -HDM(1,l) -~HDM (1,0.5)..-.'..- HDM(1,0.8) --tt-hdm (1,0.82) o -I----r----,-----,--..,----i Year Fig. 5.5 Calibration Factor for Pothole Progression Results of the statistical tests done to establish the significance of the calibration factor are shown in Table Table 5.13 Validation of Calibration Factor for Pothole Progression Calibration Coefficient of Average Root Mean Distress Factors Determination Absolute Error Square (R 2 ) (AAE) Error (RMSE) 1, Pothole 1, Progression 1, , From Table 5.13, it can be seen that the best calibration factor for pothole progression is Calibration of Roughness Progression Model Roughness progression model which was developed as a function of initial roughness, initial pothole, initial ravelling, modified structural number, construction quality and pavement age since last renewal, in the present study (Equation 4.6, 131

27 Section 4.3.6) was used to compare the roughness prediction model in HDM-4 for arriving at the calibration factors. Calibration factors for both roughness ageenvironment and roughness progression were arrived at. The default calibration factor of one, predicted almost comparable values as that predicted by the developed model. Then calibration factor was varied and the most suitable factor was selected when predicted values by both models showed very close relationship. Comparison ofpredicted values by the prediction model developed in the study and by thehdm-4 model for various calibrationfactors is shown infig , , E (..li: r-~--; ,.r--7p~--; II> ~ :~...s~----l.e :IIF--7~= (! o r--z.:!f ( a:: "a ~~ ( ~ =-:;~" ; :s ~ ; ~ I----r-----,----,--..,--...,.-----i ~Model Predicted --- HOM (1,1) -.- HOM (0.8,0.8) ~ HOM (0.85,0.85) '~ HOM (0.85,0.82) Year Fig 5.6 Calibration Factor for Roughness Progression Results ofstatistical tests done to establish the goodness ofthe best calibration factor is shown in Table

28 Table 5.14 Validation of Calibration Factor for Roughness Progression Calibration Coefficient of Average Root Mean Distress Factors Determination Absolute Error Square (R 2 ) (AAE) Error (RMSE) Roughness 1, , , , The calibration factors for roughness age - environment and roughness progression were obtained as 0.85 and 0.82 respectively. Results ofstatistical analysis shown in Table 5.12 to 5.14 establishes very good agreement between the distresses predicted by calibrated HDM-4 models and models developed in the study. The Coefficient of determination (R 2 ) values are either above or around 0.9 which shows a very good fitness for the evolved calibration constants. Further, the Average Absolute Error and Root Mean Square Error values are very low which confirms their goodness of fit Discussion Low volume roads are generally constructed with Pre-Mix Carpet course which is a thin and open graded bituminous course and hence functional distresses like ravelling and potholes are expected to progress at a fast rate for these roads compared to pavements with structural bituminous layers. Calibration of deterioration models of HDM-4 to rural road conditions done in the present study confined to surface distresses like ravelling and pothole and roughness using the pavement prediction models developed in the present study. Ravelling progresses at 24.2% faster, pothole and roughness progress at 11.46% and 1% slower than that predicted by HDM-4 prediction models. Proper calibration of HDM-4 models to actual rural conditions facilitates the 133

29 use of the tool for rural road pavement management which will be discussed in Section and Determination of Optimal Maintenance Treatment for Rural Road Sections using HDM-4 (Project Analysis) General Preventive Maintenance is needed to prevent fast deterioration ofthe pavement condition and to ensure the desired level of performance during the design life of the pavement. HDM-4 has proved to be an effective software tool for carrying out economic analysis for road investment options. Project analysis in HDM-4 deals with a particular road link or section with user-selected treatments, and strategic planning involves an analysis of the road system as a whole, typically requiring the preparation oflong term, or strategic planning estimates of expenditure for road development Methodology Project analysis is concerned with the evaluation of one or more road projects or investment options and deals with detailed technical information related to a specific pavement section. Typical projects include the maintenance and rehabilitation of existing roads, widening or geometric improvement schemes, pavement upgrading and new road construction. The methodology for finding optimal maintenance treatment using HDM-4 mainly includes: i) Creating the road network data ii) Creating the Vehicle Fleet Data iii) Creating the maintenance and improvement standards Steps i) and ii) were explained in Section iii) Creating the maintenance and improvement standards Maintenance treatments defined in this analysis include ensuring proper drainage at regular intervals, shoulder maintenance, patching, fog seal, slurry seal and 134

30 resurfacing with 20mm Pre-Mix Carpet. The do minimum action was taken as ensuring proper drainage and it was considered as the base option. The unit rate for each treatment was calculated using the Kerala P.W.D. Schedule of Rates and are shown in Table Table.S.lS Unit Rate for Maintenance Treatments S1. No. Maintenance Treatment Cost (Rs.in lakhs/lane/km) 1 Do minimum (Ensure proper drainage) Shoulder maintenance Pothole Patching Fog seal Patching and Fog seal Patching and Slurry seal Resurfacing with Pre-Mix Carpet (20 mm) The Internal Rate of Return (IRR) was calculated for the treatment application for each of the road section to establish the economic viability of the best maintenance alternative. In the economic appraisal of a road project, benefits were derived mainly from savings in road user costs and in road maintenance costs Project Analysis For the project analysis, initially a road network was created consisting of fifteen rural roads. Each road was subdivided into 20 sub sections and details regarding type of pavement, soil characteristics, condition of the road etc. for each of these sections were fed as input. 135

31 HDM-4 deterioration models calibrated as explained in Section for rural roads conditions of Kerala are used for the pavement performance prediction for the project analysis. A vehicle fleet with commercial vehicles, cars, two wheelers, cycles and auto rickshaws was created and the composition of the vehicles was also fed as input. Maintenance treatments included in the analysis were arrived at from the preliminary study conducted on the pavement condition data collected periodically from the study roads. Weighted average of each distress type was arrived at and these were classified into different ranges and the typical treatments needed were arrived at based on expert opinion. Various combinations of distress ranges that are possible on the rural roads were also considered based on the keen investigation of condition survey data collected. Possible combinations of treatments like patching and fog seal and patching and slurry seal etc. that can be applied on the roads based on the existing combination of distresses, was also incorporated in the analysis. Treatments assigned for edge failure was shoulder maintenance, for low range of ravelling was fog seal and for high range ravelling was slurry seal. For treating the potholes, patching was opted as the treatment. Resurfacing with Pre-Mix Carpet was selected as the treatment for treating the pavements with high roughness (expressed in terms ofiri in m/km) values. Thus six different maintenance treatments were considered in addition to the base option for the analysis to determine the optimal maintenance treatment for each road section. The maintenance standards for the maintenance treatments considered were created. Details like unit costs, intervention criteria, effects of the treatment etc. were given as input and analysis was conducted as responsive except for ensuring proper drainage which was conducted as scheduled. The optimal treatment was selected as the 136

32 one with maximum IRR value. The details of the maintenance treatments and the IRR values obtained for the twenty road sections of a typical road stretch is shown in Table 5.16 and results of project analysis for all other roads are shown in Appendix II (A). For certain road sections, IRR values obtained was negative and for certain other road sections, no solution was obtained. Such results imply that the base option is better when compared to the other treatments. Table 5.16 Maintenance Treatment Suggested for Road Stretch No.5 (Muslim Church) Road Section No. Optimal Treatment IRR value Section 1 Do Nothing (Drainage) * Section 2 Pre-Mix Carpet 75.3 Section 3 Pre-Mix Carpet 92.1 Section 4 Pre-Mix Carpet 72.5 Section 5 Pre-Mix Carpet 78.4 Section 6 Pre-Mix Carpet 75.3 Section 7 Pre-Mix Carpet 75.3 Section 8 Pre-Mix Carpet 72.5 Section 9 Slurry seal 74.9 Section 10 Pre-Mix Carpet 72.5 Section 11 Pre-Mix Carpet 72.5 Section 12 Pre-Mix Carpet 69.1 Section 13 Pre-Mix Carpet 55.2 Section 14 Pre-Mix Carpet 61.9 Section 15 Pre-Mix Carpet 65.6 Section 16 Pre-Mix Carpet 92.1 Section 17 Pre-Mix Carpet 72.5 Section 18 Pre-Mix Carpet 78.4 Section 19 Pre-Mix Carpet 72.5 Section 20 Pre-Mix Carpet 92.1 *No IRR value for the base option 137

33 Results of the project analysis was analysed so as to suggest the optimum maintenance treatment for each road section in a specific condition. Different types of distresses viz., ravelling and pothole and roughness observed on the study roads were classified into suitable ranges and the optimum maintenance treatments obtained from the project analysis for these ranges of distresses and ranges of roughness are shown in Table Table 5.17 Maintenance Options Suggested for Various Ranges of Distresses Type and Range of distress Maintenance Options IRR value Suggested range Ravelling < I0 % IRI < 6 m/km Pothole <0.5% Do Nothing (Ensure proper drainage)* Ravelling < 10 % IRI < 6 m/km Patching > 50 Pothole >0.5 % Ravelling between 10 % and 25 % IRI < 6 m/km Patching and Fog seal 70 to 200 Pothole> 0.5 % Ravelling between 25 % and 40 % IRI> 6m/km and < 8.5 m/km Slurry seal Pothole < 0.5 % Ravelling between 25 % and 40% Resurfacing with 20mm IRI > 8.5m/km Pre-Mix Carpet (PMC) Pothole < 0.5% Ravelling between 25 % and 40% Patching and IRI> 8.5 m/km Resurfacing with 20mm Pothole> 0.5% PMC Ravelling >40 % IRI> 8.5 m/km Pothole < 0.5% Preliminary treatment for ravelling and then Resurfacing with 20mm PMC * *No IRR value for the base option It can be seen from Table 5.17 that as far as the ravelling is less than 10%, IRI value is less than 6 m/km and potholed area is less than 0.5%, only revamping 138

34 drainage facilities every year is required. When the ravelling exceeds 10%, treatment of fog seal is required and when raveling exceeds 25% and is below 40%, slurry seal will be the best option provided the IRI value is less than 8.5 milan. Whenever potholed area exceeds 0.5%, patching is required along with other treatments. When the IRI value exceeds 8.5 milan, resurfacing is essential Optimal Maintenance Strategy for Rural Road Network using HDM-4 (Strategy Analysis) General The main objective of a road network optimisation is to formulate cost effective network preservation policies maintaining specific condition standards and to establish budget levels. Strategy analysis in HDM-4 deals with entire road networks or sub-networks managed by one road organisation. HDM-4 calculates economic benefits derived from maintenance or improvement options and finally select the set of investments to be made on a network comprising of a number of road sections which will optimise the objective function. Estimates are produced of expenditure requirements for medium to long term periods of usually 5-40 years Methodology In strategy analysis, HDM-4 generates medium to long term investment strategy for a road network comprising of a number of road section. For the analysis, budget constraint and optimisation criteria (objective function) should be defined. There are three optimisation criteria available, viz., maximise Net Present Value (NPV), maximise improvement in network condition i.e., reduction in IRI, (diri), minimise cost of road works to achieve a given target network condition in terms of IRI. The investment alternative is a combination of maintenance and improvement standards that can be applied to a section. Present strategy analysis was done with the 139

35 objective of maximising benefits, the problem can be defined as the selection of a combination of investment options applied on several road stretches which maximised the NPV for the whole network subject to the constraint of total financial cost being less than the budget available. A road network within the strategy was defined for the analysis. Strategy analysis includes following steps: i) Definition of strategy details Specification ofthe road network comprising ofroad sections Specification ofthe vehicle fleet Specification of general strategy information like start year for analysis, duration and output currency Specification ofthe optimisation criteria ii) iii) iv) Selection of road sections for analysis Selection ofvehicle types Definition of normal traffic which includes traffic composition and expected growth rate for both motorised and non-motorised traffic. v) Specification of standard assignments which includes definition of alternatives to be analysed. vi) Generation ofstrategy Customising the run setup, specifying the base alternative, selecting models to be included in the analysis Run the analysis. Time required to perform the analysis depends on the complexity ofstrategy. Generation of work programme is displayed. Work programmes to be included in the budget optimisation are manually selected. vii) Performing budget optimisation Definition of budget periods and amount Running the budget optimisation 140

36 Optimised work programme is displayed viii) Generation ofreports Strategy Analysis of the Rural Road Network In the definition of strategy details, a road network consisting of fifteen rural road sections was generated. Maximisation of Net Present Value was selected as the optimisation criteria and an analysis period of ten years was selected. Composition of pavements and details regarding their condition and traffic details were the same as that for the calibration process and project analysis discussed in Sections and In the specification of standard assignments, various M&R strategies were defined for each road section and for each strategy, different types of maintenance standards were assigned. In the present analysis, six maintenance standards as used in project analysis were assigned. While assigning strategy care was taken to ensure that it included the optimum strategy obtained from the project analysis. In the generation of strategy, one among the assigned strategies was selected as the base alternative. Ensuring proper drainage was selected as the base alternative in the present study. Life Cycle Cost Analysis was performed for the remaining strategies against the base alternative. Unconstrained work programme Le., without a budget constraint was available after the generation of strategy. In the optimisation using budget constraint, the optimisation setup was fixed first. Start year and end year of the analysis period and the capital budget were fed as input in the setup. Budget optimisation was performed for varying levels of budget from Rs. 10 lakhs to 40 lakhs for a ten year period. IRI value was selected as the criteria for intervention of maintenance action and optimisation was also performed by varying the IRI value from 6.5 m/km to 12.5 m/km for intervention of maintenance treatment for 141

37 the varying budget allocation. A typical optimised work programme obtained for an IRI value of 8.5 milan as intervention criteria and a budget level of Rs.20 lakhs for a ten year analysis period is shown in Table 5.18 and other strategy analysis results are given in Appendix II (B). Table 5.18 A Typical Optimised Maintenance Work Programme Maintenance Maintenance Road Stretch ID Year Cost Treatment (Rs.in lakhs) Slurry Seal Resurfacing Slurry Seal Slurry Seal Resurfacing Resurfacing Resurfacing Resurfacing Resurfacing Resurfacing Resurfacing Budget requirement for varying levels of IRI for maintenance intervention and budget allocation are shown in Table

38 Table 5.19 Effect of Varying Intervention Level of IRI and Budget Allocation on the Budget Requirement Budget Budget Requirement (Rs. in lakhs) for Varying levels ofiri Allocation (Rs. in lakhs) m/krn m/km m/km m/km m/km m/km rn/km It is seen from Table 5.19 that, for a budget allocation of Rs. 10 lakhs, the budget requirement remained same as Rs lakhs upto an IRI value of 10.5 rn/km and thereafter decreased to Rs lakhs for an IRI value of 12.5 m/km. For budget allocation of Rs. 15 and 20 lakhs, the budget requirement remained same as Rs lakhs and Rs lakhs respectively upto an intervention level of 8.5 rn/km and thereafter decreased upto an IRI of 12.5 m/km. For budget allocation of Rs. 25 lakhs, the budget requirement remained constant at Rs lakhs upto an IRI value of 7.5 rn/krn and for budget allocation of RsJO and 40 lakhs, the budget requirement remained constant at Rs lakhs upto an IRI of Rs.7.5 rn/km and thereafter decreased. It was also noted that for budget allocation of Rs. 30 and 40 lakhs, the budget requirement was the same for all levels of intervention and for an IRI value of 10.5 m/km and above, the budget requirement remained the same irrespective of the budget allocation. Optimum budget requirement for various levels of roughness (in terms of IRI) as maintenance intervention criteria obtained from the results of strategy analysis is shown in Table

39 Table 5.20 Optimum Budget Requirement for Various Levels ofiri as Intervention Criteria IRI( m/km) Optimum Budget (Rs. in lakhs) Discussion An optimised maintenance strategy for low volume rural road network was developed using HDM-4, after calibrating its deterioration and work effects models for low volume conditions. A project analysis was done for the fifteen rural roads in the network. Based on the analysis results, maintenance treatments were suggested for various ranges and combination of distresses and roughness. It was observed from results ofproject analysis that when the potholed area exceeded 0.5%, patching should be done, when ravelling was between 10% and 25%, fog seal was the suitable treatment and when ravelling was between 25% and 40% slurry seal was the best option. When the IRI value exceeded 8.5 m/km, resurfacing with 20mm PMC was identified as the suitable treatment. A strategy analysis was also done for the present rural road network incorporating the optimum maintenance strategy obtained from project analysis. For various levels of budget allocation, the optimum budget requirement for various values of IRI as intervention criteria for maintenance action was worked out. It was found that for intervention levels of IRI of 6.5 & 7.5 m/km, the budget requirements remained the same. For IRI values of 10.5, 11.5 and 12.5 m/km as the intervention criteria, the maintenance cost requirement remained at a constant value of Rs. 9.53,

40 and 2.89 lakhs respectively irrespective of the varying amounts of budget allocation. The results of the study can be a useful guide to the practising engineers in deciding optimal maintenance policy for rural roads. The set of investment options to be optimised by HDM-4 is user defined and hence it may not comprise all possible investment options for a particular road network. Hence the solution cannot be considered as a true optimisation since all the possible combinations ofsolutions were not considered. Further, HDM-4 is more concentrating on the roughness ofroad surface which was given as maintenance intervention criteria, as criteria for the functional performance of the roads. It was also observed that out of the various maintenance treatments considered, the treatments mainly suggested were either slurry seal or resurfacing with Pre-Mix Carpet. The application of these treatments on few roads exhausted the budget and deprived the maintenance of the rest of the roads in the network for lower levels of budget allocation. Based on these observations, an attempt was made to arrive at a true optimised maintenance strategy which will guarantee the maintenance of all roads in the network such that performance of all roads did not fall below at a minimum performance level and the same will be discussed in Section OPTIMISATION OF MAINTENANCE STRATEGY FOR RURAL ROAD NETWORK USING GENETIC ALGORITHM Introduction Major requirement of a Pavement Maintenance and Management System (PMMS) is to develop a multi-year pavement maintenance programme for the entire road network so as to maintain desirable performance within the available budget. Hence the main objective of the present study is to develop a multi-objective deterministic optimisation model to support the maintenance decision making process and to provide an optimal maintenance programme for the rural road network. 145

41 For multi-objective problems, the objectives are generally conflicting, thus preventing simultaneous optimisation of both objectives. Many of the realistic engineering problems do have multiple objectives, like minimisation of cost, maximisation ofperformance, maximisation ofreliability, etc. Genetic algorithm (GA) is an optimisation tool which is customised to accommodate multi-objective problems by using specialised fitness functions and introducing methods to promote solution diversity. Further GA can very well handle the combinatorial nature of network level pavement maintenance programming. Hence the multi-objective optimisation model in the present study is aimed at maximising the performance of the road network and minimising the maintenance cost and was solved using constraint based Genetic algorithm Methodology The main objective of the pavement maintenance programming is to maintain entire pavement network at a desirable condition within the available budget. A number of maintenance goals can be set to fulfill these objectives, such as maximising cost effectiveness of maintenance activities, minimising road user cost, minimising present worth of total maintenance cost and maximising road network performance. Prediction of future pavement conditions and quantification of impact of maintenance activities on the deterioration ofpavement are very critical in this regard. There are generally two approaches to solve multi-objective optimisation viz., combine the individual objective functions into a single composite function or move all but one objective into the constraint set. In the former case, determination of single objective is possible using methods such as utility theory or weighted sum method. But the real problem lies in the proper selection of weights or utility function to characterize the decision maker's preferences. In addition to this, proper scaling of 146

42 objectives is needed since small perturbations in weights can sometimes lead to quite varying results Pavement Performance Prediction Pavement performance prediction model is an important element used to estimate the maintenance requirements and to determine the road user costs and benefits of the maintenance implementation (Shahin, 1994). In order to simplify pavement condition analysis, and to ease the communication to higher level management, the composite performance index viz., Pavement Condition Index (PCI) which represent overall condition of pavement was used in the present study. Roughness of the road surface was not included as a performance indicator here so as to reduce the complexity of the model. Performance model developed in this study in terms of PCI as given in Equation 4.8 which is reproduced below was used as the pavement performance prediction model for the optimisation of the maintenance programme (0.55 x Page x CQ) PCI = PCI x (P age ) + e Formulation of the Problem The objective of the optimisation model IS to arnve at a cost effective maintenance strategy preserving the performance level of the road network at a desirable level. Hence a multi-objective optimisation model having two maintenance goals was adopted for the present study. The maintenance goals considered were maximisation of pavement performance and minimisation of maintenance cost, since the development of a multi-year pavement maintenance plan is mainly constrained by the available maintenance budget and minimum acceptable pavement condition. The formulation ofthe problem used integer numbers for both the decision variable Xkst and the maintenance action 'k st ', selected for road stretch's' at year 't'. 147

43 i) Maximisation of Pavement Performance The objective function aimed to maximise the performance of road network and the optimisation model was formulated as follows: T Maximize: Z1 = L PCI t t=1 s (5.12) Subject to (5.13) PCI st ~ PCI " '\I s =1to S, '\I t =1to T mm PCl st ~ 100 (5.14) (5.15) X kst {O, I}, 'lis = 1to S, t = 1to T, k = 1to K (5.16) where, PCl st = PCl st-i + X kst x ilpci k (5.17) pc! st = Mean (pel st ) - cr, '\Is = 1 to S (5.18) PClst & PCls(t-l) are the PCI of road stretch's' at tth and (t_1)th year respectively. Xkst is a decision variable, which is '0' when no action applied and '1' when an action 'k' is applied on road section's' at time '1'. Ckt is the cost ofcarrying out the maintenance action 'k' in the year '1' Btis the budget allocated for the tth year LiPCh is improvement in the PCI due to an action 'k' The maximisation of performance of the network as shown in Equation 5.12 was defined by the summation of the mean PCI among all pavement sections minus the standard deviation of the PCI values in each year, over the analysis period which is shown in Equation Equation 5.13 ensures that annual maintenance expenditure does not exceed the available budget allocated for each year. The maintenance actions should be done in such a way that the PCI of the road selections are above a minimum 148

44 acceptable level as explained in Equation Maintenance treatments should also be done in such a way that the PCl value ofthe road stretches do not exceed the maximum value of 100 as explained by Equation Equation 5.16 defines the decision variable Xkst to be an integer of value either 0 or 1 i.e., if a maintenance action 'k' is carried out on a road stretch's' in the year 't', then Xkst is one and otherwise zero. As different maintenance activities are implemented, the performance of pavement is affected in varying manner resulting in varying levels of improvement of PCI. Thus the performance of the pavement not only changes over time, but also with the type of maintenance actions applied on it. The effect of each maintenance action can be accounted in the performance ofthe pavement as given in Equation Pavement performance is dependent on many factors like traffic load carried, environment, age of pavement and previous maintenance activities. The effect of various maintenance actions on the condition of pavement is not consistent at different ages of the pavement. A routine maintenance could be very effective when applied at the early age of pavement, but its effectiveness reduces as the age of pavement increases. This variation of the effect of maintenance activity is not accounted in the formulation ofthe problem to avoid more complexity. (ii) Minimisation ofmaintenance Cost There is often a stringent limit on the availability of budget for rural road network, and hence minimisation of present worth of maintenance coast is an equally important objective as that of maximisation of pavement performance. Future maintenance cost was discounted to the present value by using the conversion factor (Itr)"t where 'r' is discount rate and "t' represents a specific year in the analysis period. The objective function for the minimisation of maintenance cost was formulated as follows: 149

45 K S T 1 Minimize: Z2 = L L L t X k t C kt k=1 s=1 t=1 (1 +r) s (5.19) subjectto the same constraints as given by Equations 5.13 to (iii) Multi-Objective Model Formulation The classical approach to solve a multi-objective optimisation problem is to assign a weightage 'Wi' to each normalised objective function 'Zi', so that the problem is converted into a single objective problem (Konak et ai., 2006). Hence a realistic approach to optimise the maintenance strategy was adopted by combining the above two objectives and both the maintenance goals were simultaneously optimised. As per the present bi-objective model, the overall performance of the road network was maximised and at the same time, the cost ofmaintenance ofthe road network was also minimised. Thus a maintenance programme that costs less and ensures maximum pavement performance was to be achieved. In order to combine the two objectives, which are of contrast nature, i.e., a maximisation and a minimisation, the minimisation problem was converted into a maximisation problem using the following transformation. _ 1 Z I+Z 2 (5.20) The second objective ofminimisation ofmaintenance cost takes the form as follows: _ K S T 1 t X k tckt k=1 s=lt=1 (1 + r) S (5.21) Maximise: Z2 = L L L Since both objectives were in non-comparable scales i.e., performance maximisation in terms of PCl which varies between 0 and 100, and the cost minimisation in terms of currency used, normalisation was required to combine both functions into a single objective function. Further, there can be chances of domination 150

46 of one over the other, if normalisation is not done (Fwa et al., 2000). The objective functions for the present problem were hence normalised between 0 and 1 as shown below. * z. -z.. Z = 1 Imm i Z -z imax Imm (5.22) * where, Zi' Zimin.' Zimax are the normalised objective function and the minimum and maximum possible values ofthe objective Zi.. In this study, due weightages, 'WI' and 'W2' were given to each objective function based on the priority assigned to them and combined to form a single objective function. Since the individual objective function value was normalised between zero and one, the maximum possible value each of the objective function is one. Similarly each of the weightages was also assigned a value ranging from zero to one such that the value of the sum of the two weightages is one. Consequently, the combined objective function had a maximum value ofone. If the maximisation ofthe pavement performance and the minimisation of maintenance cost are given equal priority, then the value of the weightages will each be equal to 0.5. If anyone of the objective is given higher priority over the other, then the former will have a value greater than 0.5 and the latter will have a value less than 0.5. The combined objective function was formulated as below: Maximize: wtz 1 * + W 2Z2* (5.23) Subject to: the constraints given in Equations 5.13 to where WI and W2 are the weightages given to the objective functions ofmaximisation of pavement performance (Z I) and minimisation ofmaintenance cost ( Z2 ) respectively. 151

47 Steps in Genetic Algorithm Various steps involved in solving the present optimisation problem usmg Genetic Algorithm (GA) are explained in the subsequent articles. i) Coding of Decision Variables First step of applying GA to any problem is the proper representation of chromosomes. Solution coding defines the way in which the attributes of a solution are represented. For the present pavement maintenance programming problem, each chromosome represents a maintenance activity for a particular road section for a particular year. Though the binary coding is generally adopted in GA, in this study an integer coding (0, 1, 2, 3,..., j) was adopted to represent the genes (representing a maintenance activity) so as to reduce the length of the strings. For each road stretch, there are 'T' genes, representing maintenance actions for 'T' years for that road stretch. Thus the solution string consists of (SxT) number of chromosomes, where os' is the total number of road stretches and 'T' is the analysis period. Coding of the solution is schematically represented in Fig Year Treatment I I YI Y2 Y3 Y4 Y5 Y6 Y7 Y8 Y9 YIO YII YI2 YI3 YI4 YI5 YI6 YI7 YI8 YI9 Y20 \. ~ 1 51 road stretch 2nd road stretch Yij -type ofmaintenance treatmentfor the i Ih road stretchfor the /h year Fig. 5.7 Coding of Solution for the Optimisation Model 152

48 ii) Constraint Handling Constraints of an optimisation problem which is being solved by GA should be handled carefully so as to ensure feasibility of solutions. Improper constraint handling will result in wastage of time in evaluating infeasible solutions. In the present optimisation problem those solutions which did not satisfy the constraints, especially the budget and pavement performance constraints (Equations 5.13 to 5.16) were handled by the 'Penalty and Repair' method. The penalty method converts a constrained problem into an unconstrained problem by penalising the objective function (Goldberg, 1989). Repair method initially tries to repair the infeasibility of a solution several times until the solution becomes a feasible one or till the repair becomes impossible. In this study the budget and pavement performance constraints were checked simultaneously for all individual genes for an infeasible solution and the position of genes which made the solution infeasible were identified. For any infeasible solution, for some pavement sections, for some particular year, either the minimum performance level may not be maintained or the budget may be exceeded. For a solution which did not satisfy the performance level, the maintenance action was upgraded by one step for a gene with lower actions and for a solution which exceeds the budget level, the maintenance action was lowered by one step for a gene with higher actions. The feasibility of the repaired solution was again checked and if not satisfied the repair process was repeated for a specified number of times till it became feasible. After the specified number of trials, if the solution still remained infeasible, then the fitness ofthe solution was penalised by a quantity proportional to the degree of constraint violation so as to make its rank low and consequently a less feasible solution. 153

49 iii) Fitness Function GA mimics the 'survival of the fittest' principle of nature to make a search process and hence suitable for solving maximisation problems. The objective of minimisation of maintenance cost was transformed into a maximisation problem and combined with the performance maximisation objective after assigning due weightages to each of the objectives as shown in in Equation Fitness in biological sense is a measure of the reproductive efficiency of chromosomes. Solutions with higher fitness values will have higher probability of being selected to successive generations. For maximisation problems, the fitness function can be considered to be the same as the objective function and the fitness value is the value ofthe objective function. IV) GA Operators GA uses mainly three basic operators to generate new solutions from existing ones viz., a) Reproduction b) Crossover c) Mutation. a) Reproduction The proportionate reproduction operator was used in the present study, where asolution string was selected for the mating pool with a probability proportional to its fitness. The sum of probability of each string being selected for the mating pool must be one since the population size is fixed in GA. The probability' pro ' of selecting i 1h string is 1 F. pro =_--.:1_ 1 N L F = where 'Fj' is the fitness value of jth string and 'N' is the population size. (5.24) Cumulative probability 'Prj' of any string 'i' was calculated by adding all the individual probabilities from top of the list. Thus the first string will have cumulative probability 154

50 between zero and Prj and the last string will have cumulative probability between Pr(i-I) and one. In order to select 'N' strings, 'N' random numbers were generated. A string that represented the chosen random number between the cumulative probability ranges was selected to the mating pool. Thus a solution string with higher fitness value will have a larger range in the cumulative probability range and therefore has ahigher chance ofbeing copied into the mating pool. b) Crossover As discussed in Section , a crossover operator was used to recombine two strings to get a better string. In crossover operation, generally two chromosomes, called parents, are combined together to form a new chromosome, called 'offspring'. The parents are selected among existing chromosomes in the population with preference towards fitness so that offspring is expected to inherit good genes which make the parents fitter. By iteratively applying the crossover operator, genes of good chromosomes are expected to appear more frequently in the population, eventually leading to convergence to an overall good solution. In order to preserve some of the good strings that are already present in the mating pool, all strings in the matting pool are not used in the crossover process. When a crossover probability, defined here as 'Pc' is used, only (l00 x Pc) percent strings in the population are used in the crossover operation and 100 (1 - Pc) percent of the population remains as they are in the current population. A one site crossover was adopted for the present study by randomly choosing a cross over site along the strings and by exchanging all bits on the right side of the site. The underlying objective of crossover is to exchange information between strings to get strings that is possibly better than the original pair ofstrings. 155

51 c) Mutation The mutation operator introduces random changes into the characteristics of chromosomes. Mutation is generally applied at the bit (gene) level. In typical GA Implementations, the mutation rate (probability of changing the properties of a gene) is very small and depends on the length of the chromosome. 'Pm' is used to decide the number of bits to be muted. The mutation probability A coin toss mechanism is employed to exercise mutation, i.e., a random number between 0 and 1 generated and if It is less than the mutation probability, then the bit is randomly changed. This helps in introducing a bit of diversity to the population by scattering the occasional points. The mutation causes movement in the search space restoring lost information to the population and also maintains diversity in the population. Simple genetic algorithm generally uses mutation rate between and 0.5. Application of these three operators on the current population creates a new population and this complete cycle is called a 'generation'. This new population was used to generate subsequent populations and finally yielding solutions that are close to the optimum solution. The values of the objective function express the fitness of the solution of the new generations. The process was repeated till convergence was achieved and the best solution of the last generation was stored as the optimal solution. The procedure of the optimisation problem using GA is shown in Fig

52 Start Define problem variables, Constraints and determine input parameter Define objective function (s) Generate initial pool of solutions Evaluate solutions for all objectives New Pool ofsolutions Select the best from parent pool and generate offspring solutions to form new pool Fitness assignment: Rank - based annroach Selection and formation of Parent Solution Pool Offspring Solution Generate offspring solutions by Crossover and Mutation from parent pool No Is stopping criterion met? Yes Print best selected Maintenance Fig. 5.8 Sequence of Operations in GA 157

53 5.4.3 Case Study The feasibility of the proposed model was established by conducting a case study for the rural road network shown in Table 3.1 which was used for the development of deterioration models. The road network consisted of fifteen road stretches, each of length 0.5 km with an average age of 5.7 years and construction quality varying from to The pavement condition data in the year 2009 was used to calculate the PCI values. Age and PCI values of the road stretches as on the year 2009 and the Construction Quality (CQ) are tabulated in Table Table 5.21 Details of Road Stretches Selected for the Case Study Road Stretch ID Age as on PCI ofthe Road Construction 2009 Stretches in the Year Quality (CQ) (years) Average Min Max

54 Maintenance treatments considered in this programme and their cost/lane/km as per Schedule ofrates (2008) ofkerala State P.W.D. are shown in Table Table 5.22 Maintenance Treatments Selected for the Study Maintenance Treatment Code Assigned Cost ( Rs. in lakhs/lane/km) Do Nothing Ko Shoulder Maintenance K} Pothole Patching K Patching and Slurry seal K Resurfacing with Pre-Mix Carpet (20 mm) lzl( The major distresses noticed in the study stretches were only functional and hence the maintenance treatments considered do not include pavement strengthening treatments. The discount rate for the present optimisation model was assumed as 4% (Priya, 2008) Increment in PCI due to Various Maintenance Actions Improvement in condition of pavement due to the maintenance activity may not be consistent between different ages of pavement. For instance, minor types of maintenance activities may be very effective when applied in the initial stages of pavement life and the effectiveness reduces as the pavement ages. Though much attention and effort of researchers have been focused on the study of rural roads for the past ten years, the effect on the PCI of a rural road due to a maintenance action has not been so far studied in India. Hence it was decided to conduct a survey among experts and collect the required information by 'Delphi technique'. In this approach, opinion was sought from experts to arrive at the effect of various maintenance actions on PCI 159

55 for roads in different conditions. Since the effect of a maintenance activity is varying for pavements in different conditions, firstly an effort was made to classify the pavements in different condition states based on PCI values. A questionnaire (shown in Appendix III) was prepared requesting the experts to classify the pavements into different condition states like excellent, very good etc. based on the PCI value. The experts were also requested to quantify the effect of four maintenance actions considered in the study on the pavements in different condition states. The effect of maintenance action was quantified in terms of improvements in PCI of pavements in different condition states. Average value of the improvements in PCI based on the expert opinion was worked out and is shown in Table Table 5.23 Effect of Maintenance Action on the Condition of Pavement in terms of PCI Based on Expert Opinion Improvements in PCI due to Various Maintenance Actions Present Pavement Condition Shoulder Pothole Patching and Resurfacing Maintenance Patching Slurry seal (Pre-Mix Carpet) (K]) (K 2 ) (K 3 ) (~) Very Good PCI >80 NA NA NA NA Good Fair Poor Very Poor PCI PCI PCI PCI PCI PCI PCI PCI <

56 An attempt was also made to work out the increments in PCI due to various maintenance actions using the available field data. For this exercise, PCI of the road stretches calculated corresponding to a set of condition data was made use of. Maintenance action of each type is generally carried out to reduce a specific type of distress. Pothole patching is done to remove potholes, hence after carrying out patching, potholes were assumed to be reduced to zero. When slurry seal was done, it was assumed that the ravelling reduced to a nominal value of 2% and when shoulder maintenance was done, edge breaking was set to zero keeping all other distresses as such. The improved PCI after carrying out each maintenance action selected for the study was calculated considering the reduction in the corresponding distress. The improvement in PCI value for all the roads thus obtained for each maintenance action was classified into different ranges and is shown in Table Table 5.24 Improvement in PCI due to Various Maintenance Actions Based on Field Data Maintenance Action Improvement in PCI Shoulder maintenance 1-2 Pothole Patching 8-20 Pothole Patching & Slurry seal Resurfacing with 20 mm Pre-Mix Carpet It can be observed from Table 5.24 that the increments in PCI as suggested by experts agree with the actual field condition and hence can be considered as a realistic judgment. Minimum targeted performance level of the road network was defined by selecting a minimum PCI value below which PCI of any of the road stretches was not supposed to fall. Since the study pertains to rural roads, while optimising the 161

57 maintenance strategy, a restriction was also imposed regarding the periodicity of Slurry seal and Re-surfacing with Pre-Mix Carpet as not more than once in two and four years respectively GA Parameters The number of solutions in each generation (population size) should be carefully chosen since, if the population size is too small, the risk of premature convergence to poor local optimum solution can occur. On the other hand, if the population size is too large, too much of effort and time will be needed to run the algorithm. Hence a parametric study was carried out on a sample road network to select the GA parameters. The population size was varied from 500 and the minimum population size which yielded the best result was found to be 800 and hence the population size was fixed as 800. The initial population was generated at random since it should contain solutions which vary in quality, so as to avoid premature convergence. Solutions in each generation were ranked as per their fitness value and the proportional selection was used for reproduction. Based on the results of parametric study, the crossover probability was fixed as 0.85 and mutation probability was selected as Both the budget and performance constraints were handled using 'Penalty and Repair' method. Total number of repairs was limited to lao and if the solution could not be repaired at this stage, the objective function was penalised heavily so that its fitness reduced drastically. Stopping criterion defines the condition of termination of search and was set as the moment when there is no further improvement in the best solution value for the last 10% ofthe total number of generations. 162

58 Effect of Maintenance Treatment on the Pavement Performance Deterioration mechanism of roads after a maintenance treatment differs from that of the roads for which no maintenance action has been done. The data regarding the deterioration of the roads after carrying out each maintenance treatment should be available to model the actual deterioration behaviour thereafter. Due to the absence of such a data an approximate procedure was adopted to model the post treatment deterioration of roads. Improved PCl of the roads after each maintenance treatment was worked out by adding the increments in PCl for each maintenance treatment as suggested in Table 5.23 to the present PCL Effect of maintenance action was accounted in terms of decrease in the age of pavement. The procedure adopted for accounting the effect of maintenance treatment on the further performance of the pavement is illustrated in Fig "--,_,-" ' '="'41.-,_, , 100..,.~=~ -\'>~"" " '",.,---: ~ ':p~"" I! 60 """" I. I ".'\, i 2 50 ""'"!: ,,- 40 -' '",\~9.0 ~, ' "'.,---- ~ ' O " o Age (Year) Fig. 5.9 Effect ofmaintenance Treatment on the Performance of Pavement in terms ofpci As seen from Fig. 5.9, the PCl ofa road section at an age offive years is 39.0 and if a treatment of slurry seal is done at this stage, its PCl increases by 35.0, and reaches a value of74.0. The effect ofthe maintenance treatment on the road section is 163

59 accounted as the reduction in age of the pavement and the new age is taken as the age corresponding to a PCI of 74, which is 3.2 years. Further deterioration of the road section was calculated using this new age as the basis. If there was no treatment done in any year, then the age at that time was simply incremented and the deterioration was estimated as before till any treatment was done for that stretch of the road. The age of the road corresponding to the new PCI after each maintenance treatment was back calculated in the algorithm using the same deterioration equation in terms of PCI (Equation 4.8) by trial and error process. Thus whenever some treatment was done for a road, its age thereafter has to be reset to an age corresponding to the improved PCI and the further deterioration was to be accounted from that age. The algorithm for the optimisation problem was coded using Net Beans IDE in Java environment Experimentation of the Program Main input parameters of the optimisation model developed include the age and construction quality of the roads in the network, the ratio of priority assigned to the two objectives of maximisation of performance and minimisation of maintenance cost, the minimum expected performance level of the network in terms of PCI value, maximum budget level allocated and the discount rate selected for the estimation ofthe present worth of maintenance cost. In order to study the influence of these input parameters on the maintenance decisions, several runs of the program was executed by varying each of these parameters. The program was run usmg the initial input parameters ViZ., age and construction quality of the road stretches of the rural road network used for the study in the development of deterioration models. The PCI of the roads were then calculated using Equation 4.8. The budget allocated, the minimum required performance level of the road network and the priority selected for the maximisation of pavement 164

60 performance and minimisation of maintenance cost were then specified. The initial population for the problem was generated by random process and the sequence of operations using genetic algorithm as shown in Fig. 5.8 was then performed. The optimised maintenance programme was selected as the best solution in the final pool of solutions when the stopping criterion of getting consistent best solutions for the last 10% of generations, was met. This stopping criterion for the search was found to be satisfied from 2200 to 2600 generations for various runs ofthe optimisation model. The effect of priority assigned to the two objectives of the decision support model was studied by varying the ratio of priority from zero to one as Oil, OJ/0.7, 0.5/0.5, 0.7/0.3 and 1/0 and the program was run for each of these priority ratios and the results were extracted. So also the effect of minimum required performance level. of the road network in terms of PCI was studied by running the program for three minimum values of PCI, i.e., 30, 40 and 50 respectively. An effort was also made to study the effect of delayed maintenance on the maintenance programme by delaying the maintenance of the road network from one to five years. Similarly the effect of varying age of roads in the road network was studied by varying the percentage of roads of varying age from one to five years in the network. Finally, the effect of construction quality was studied by varying the same as 0.25, 0.375, 0.5, and 0.75 and the influence of discount rate was studied by varying it as 3, 4, 5 and 6% respectively in each run ofthe program. Condition ofthe roads at the end ofyear 2009 was used as input to the optimisation model and the analysis period for the maintenance programme was chosen as ten years, i.e., from the year 2010 to Details of variation of input parameters to the optimisation program and the number of runs of the program executed for each case are shown in Table

61 Table 5.25 Details of Input Parameters used for the Experimentation of the Program Parameter Varied Ratio of Minimum Priority of PClofthe Other Input Parameters Objectives Network 0/1 Number ofruns of the Program Priority of Objectives 0.3/0.7 Budget: Rs. 25 lakhs/year, (Study Road Network) 0.5/0.5 30,40,50 15 Discount rate: 4 %. 0.7/0.3 1/0 1 year Budget: Rs. 20 lakhs/year, Delayed 2 Years CQ ofroad stretches: Maintenance (Hypothetical 3 Years 0.5/0.5 30,40,50 Same as that for the study network, 15 Road 4 Years Discount rate: 4 %. Network) 5 Years Budget: Rs. 20 lakhs/year, Construction Age and CQ of the roads kept same in a run, Quality (CQ) (Hypothetical Age of network was then 0.5/ varied from one to five Road years for each value of Network) CQ, Discount rate: 4 %. 3 Discount Rate (%) 4 Budget: Rs. 25 lakh/year, 0.5/ (Study Road 5 Discount rate: 4 %. Network) 6 Effect ofvarying Age of Budget Rs. 20 lakhs/ year, Roads in the Network CQ for all roads: Same as 0.5/ (Hypothetical Road 0.625, Network) Discount rate: 4 %. Total Number of Runs Analysis of Results Effect of Priority Assigned to Objectives and Minimum Required Pavement Performance Level on the Maintenance Programme A typical maintenance programme obtained for the road network keeping the minimum expected performance level of the road network at a PCI value of 40 and 166

62 assigning equal priority for both maximisation of performance and minimisation of maintenance cost is shown in Table The maintenance cost was set not to exceed Rs.25 lakhs for any year of the analysis period. Table 5.26 A Typical Optimised Maintenance Programme for the Rural Road Network Selected for the Case Study Rtretch Year (Minimum PCl: 40, Ratio of Priority: 0.5/0.5) Optimised Maintenance Actions for the Road Stretches where, 0- Do Nothing 1 - Shoulder Maintenance 2 - Pothole Patching 3 - Patching and Slurry seal 4 - Resurfacing with Pre-Mix Carpet The effect of priority of pavement performance to minimisation of maintenance cost on the maintenance decisions was studied by varying the priority of both objectives from zero to one as mentioned earlier. Analysis was conducted for varying levels of priorities for pavement performance to maintenance cost to arrive at 167

63 the suitable priority level for the rural road network and the results of the analysis are shown in Figs and 5.11 respectively iii ~ 100 t; 0 u 80 8 iii C.z: 60 1lI..ll: C III 41/-... C 'jij ~ ~ 0 0 I- 0/1 0.3/ / /0.3 1/0 Ratio of Priority of Performance to Cost Fig Variation of Total Maintenance Cost with Varying Priority ofpavement Performance and Maintenance Cost 80..,.- -;-- --=- ~.LL..ll: ~ 70 ~ "'-""""""---"'-""'""""'--- '2 50 o «: 40 41/.z: '0 o :0 10 f 0 ~ 0/1 0.3/ / /0.3 Ratio of Priority of Performance to Cost 1/0 Fig Variation ofthe AveragePCI of the Road Network with Varying Priority ofpavement Performance and Maintenance Cost A Comparison was made from Figs and 5.11 for various priority levels with respect to the cost minimisation model (ratio of priority 0/1) for the total 168

64 maintenance cost and average pe"rformance level of the road network and is shown in Table Table 5.27 Effect of Varying Ratio of Priority Levels of Pavement Performance to Cost Minimisation Ratio ofpriority of Performance to Maintenance Cost Percentage Increase in Total Maintenance Cost Percentage Improvement in Average PCI 0/ / OJ 0.5/ / / From Table 5.27, it can be observed that the percentage improvement in average PCI for a priority level of 0.5/0.5 is 16.3 for an increase in maintenance cost of 6.6%, but when the priority ofperformance was given a high weightage of 70% and the weightage to priority of maintenance cost was reduced to 30%, the maintenance cost increased to 19.6%, whereas the PCI increase was only 24.2% from 16.3% (Le., for an equal priority case). A question thus arises about the priority to be assigned for funding an optimised maintenance programme for a rural road network. The incremental increase in maintenance cost was quite high, when the priority of performance was assigned a weightage of 70% (ratio of priority: 0.7/0.3) and 100% (ratio of priority: 1/0), when compared with the case ofweightage of30% (ratio ofpriority: 0.3/0.7) and 50% (ratio of priority: 0.5/0.5). Hence it can be concluded that a weightage beyond 50% to the priority of pavement performance will require higher amount for maintenance and cannot be justified when resources are scarce. As mentioned earlier, analysis period for the maintenance programme was selected as ten years from the year 2010 to An analysis was done to observe the 169

65 distribution of the maintenance cost requirement over the analysis period for varying ratios of priorities and is shown in Figs to , 'Vi' :i 20.!!.5 g 15 1;; o u ~ 10 c Rl C QI... C.; 5 ~ o Year Fig Maintenance Cost Requirement over Years (Cost Minimisation Model: Ratio of Priority 0/1) 25 'Vi' J:. :; 20.5 vi ~ 15 1;; 8 ~ 10 c Rl C ~.~ 5 ~ o Year Fig Maintenance Cost Requirement over Years (Bi-objective Model: Ratio ofpriority 0.3/0.7) 170

66 25 'iii 20.c ~..!!!.5 III 15 a: -... III 0 u 10 lu U C111 C lu... c 'm ~ 5 o Year Fig Maintenance Cost Requirement over years (Bi-objective Model: Ratio ofpriority 0.5/0.5) 25 'iii.c ~ 20.5 en! 15 t: o u ~ 10 c 111 C S c 5 'm ~ o Year Fig Maintenance Cost Requirement over Years (Bi-objective Model: Ratio ofpriority 0.7/0.3) 171

67 30, iii : !!! c: iii 20 ~ 1;; 8 15 ~ c: :g c: OJ; 5 :!: o Year Fig Maintenance Cost Requirement over Years (Performance Maximisation Model: Ratio ofpriority110) Since no maintenance actions were carried out on these roads till the year 2009, many of the road sections were in a poor condition. Consequently the maintenance cost requirement for keeping the road network above the specified minimum performance level during the first year of analysis period was enormous compared to the rest of the years. As seen from Figs to 5.16, the maintenance cost requirement for the first year ofanalysis period is almost the same for all priorities as around Rs. 21 lakhs, except for the performance maximisation model which is Rs. 25 lakhs. The percentage of the total maintenance cost spent in each year of the analysis period for varying priorities and for a minimum performance level of PCI of 40 is shown in Table It is observed from Table 5.28 that the percentage maintenance cost requirement for the first year of analysis period is 20 to 26 %. The requirement in the subsequent years shows that the maintenance cost requirement is uniformly distributed 172

68 over the analysis period. The effect due to variation ofpriority on the maintenance cost requirement over the analysis period is not prominent as seen from the results. Table 5.28 Percentage Requirement of Maintenance Cost over the Analysis Period Year Percentage Requirement oftotal Maintenance Cost in each Year of Analysis Period for Varying Priorities Oil 0.3/ / /0.3 1/ An effort was also made to study the effect of minimum performance level selected on the total maintenance cost and the average PCI of the road network. Analysis was done for the minimum required PCI values of 30 and 50 also, in addition to the minimum PCI of 40 which was done earlier and the results are given in Table It can be seen from Table 5.29 that, the average PCI of the network is always higher than the minimum performance level selected and the difference between the achieved and minimum PCI value selected increases as the priority for performance increases from zero to one. It can also be seen from the results that the maintenance cost for a particular average PCI is not the same for different outputs of optimisation. 173

69 But the difference is around 10 to 15% and these variations can bound to happen in a bi-objective optimisation model. From the results obtained it can be inferred that a targeted minimum PCI value of either 30 or 40 is more desirable than 50 in terms of maintenance cost and performance. Table 5.29 Effect of Minimum Performance Level of the Road Network for Varying Ratios of Priority Ratio of Minimum PCI = 30 Minimum PCI = 40 Minimum PCI = 50 Priority of Pavement Average Total Average Total Average Total Performance PCIof Maintenance PCIof Maintenance PCIof Maintenance to Road Cost Road Cost Road Cost Maintenance Network (Rs. in lakhs) Network (Rs. in lakhs) Network (Rs. in lakhs) Cost 0/ / / /0.3 1/ A comparison was done with respect to a minimum PCI of 30 for higher levels of minimum performance of the road network and is shown in Table Table 5.30 Effect of Minimum Pavement Performance Level on the Performance of the Road Network and Maintenance Cost Ratio of Minimum PCI = 40 Minimum PCI = 50 Priority of Percentage Percentage Percentage Percentage Performance to Increase in Increase in Increase in Increase in Maintenance Maintenance Maintenance Average PCI Average PCI Cost Cost Cost 0/ OJ/O / / /

70 Effect of Delayed Maintenance on the Maintenance Programme As mentioned earlier, the road network which was used for the case study had all roads with practically no maintenance done for about five to six years as on the year 2009 and hence required surface renewal. This has resulted in the requirement of a higher maintenance cost in the first year of analysis period, i.e., in the year of Normally in a network of roads, the roads will be of different age and conditions. The effect of a delayed maintenance strategy will increase the maintenance cost. In order to study this effect clearly, a hypothetical road network with fifteen roads having varying construction quality was considered. For simplicity, the same construction quality as that for the roads in the network selected for the case study was adopted. A bi-objective model with a priority level of 0.5/0.5 for the performance and maintenance cost was selected for this analysis. The maximum maintenance cost was not supposed to exceed Rs. 20 lakhs in any year of the analysis period. Analysis was done for three minimum network performance levels, viz., PCl value of 30, 40 and 50. The maintenance programme obtained for the road network with a delayed maintenance of one year and five years for a minimum performance level ofpcl value of 40 are shown in Tables 5.31 and 5.32 respectively. 175

71 Table 5.31 Maintenance Programme for the Road Network with a Delayed Maintenance of One Year (Minimum PCI: 40, Ratio of Priority: 0.5/0.5) Optimised Maintenance Actions for the Road Stretches ~ tretch Year where, 0- Do Nothing 1 - Shoulder Maintenance 2 - Pothole Patching 3 - Patching and Slurry seal 4 - Resurfacing with Pre-Mix Carpet It is seen from Table 5.31 that, when the maintenance is delayed by one year only, no maintenance actions are required for the first two years and the maintenance programme for a ten year period consists of Patching and Slurry seal only. But when the maintenance is delayed or not done for five years as seen from Table 5.32, resurfacing is required to be done for six roads in the second year of the analysis period. 176

72 Table 5.32 Maintenance Programme for the Road Network with a Delayed Maintenance of Five Years (Minimum PCI: 40, Ratio of Priority: 0.5/0.5) Optimised ~ tretch Year Maintenance Actions for the Road Stretches where, o-do Nothing 1 - Shoulder Maintenance 2 - Pothole Patching 3 - Patching and Slurry seal 4 - Resurfacing with Pre-Mix Carpet The average performance of the road network and the total maintenance cost obtained for the road network when the maintenance was delayed by one to five years for minimum targeted PCI values of 30, 40 and 50 are shown in Table An analysis was also done to study the effect ofdelayed maintenance on the percentage increase in maintenance cost and percentage decrease in the average PCI value of the network for a minimum PCI value of40. The comparison was done with respect to the maintenance cost required and the average PCI value of the network with a delay in maintenance ofone year and is shown in Table

73 Table 5.33 Effect of Delayed Maintenance on Performance of Road Network and the Maintenance Cost (Ratio of Priority: 0.5/0.5) Minimum PCI = 30 Minimum PCI = 40 Minimum PCI = 50 Delay in Total Total Total Maintenance Average Maintenance Average Maintenance Average Maintenance (years) PCI Cost PCI Cost PCI Cost (Rs. in lakhs) (Rs. in lakhs) ( Rs. in lakhs) Table 5.34 Percentage Variation of Maintenance Cost and PCI for Delayed Maintenance (Minimum PCI: 40, Ratio of Priority: 0.5/0.5) Delay m Maintenance (years) Percentage Increase in Total Maintenance Cost with respect to Age ofone Year Percentage Decrease in Average PCI with respect to Age of One Year It is seen from Table 5.34 that not only the total maintenance cost almost doubles but also the average PCl of the road network decreases by 15.6% when the maintenance is delayed from one year to five years. The distribution of maintenance cost over the analysis period for the delayed maintenance is shown in Table It is seen from Table 5.35 that, when the maintenance is delayed by one year, the maintenance cost requirement for the first and second year of the analysis period is zero and when the maintenance is delayed by two years, no maintenance is required for the first year of analysis period. But when the maintenance is delayed by five years the maintenance cost required for second and third year is the maximum in the analysis period. 178

74 Table 5.35 Maintenance Cost Requirement over the Analysis Period for Delayed Maintenance (Minimum PCI: 40, Ratio of Priority: 0.5/0.5) Maintenance Cost (Rs. in lakhs) over Analysis Period for Delayed Year of Maintenance Analysis Period 1 Year 2 Years 3 Years 4 Years 5 Years Total Cost Effect of Variation of Age ofroads within the Network on the Maintenance Cost and Pavement Performance A road network may consist of roads of varying age, hence the effect of variation of age of roads within the network on the maintenance parameters was also studied. For this analysis a hypothetical road network which consisted of roads with varying age but with same medium construction quality of for all roads as shown in Table 5.36 was considered. The program was run for a minimum PCI value of 40 and equal priority for performance and maintenance cost. The budget allocated was selected as Rs. 20 lakhs/year and the results of the analysis are shown in Table A comparison was done for the average performance of the network and the total maintenance cost with respect to a network with all roads of equal age of one year and is shown in Table

75 Table 5.36 Effect of Variation of Age of Pavements within the Road Network on Maintenance Parameters (Minimum PCI: 40, Ratio of Priority: 0.5/0.5) Percentage ofroads ofvarious Age Maintenance Average 81. Cost Age Age Age Age Age PCI No. (Rs. in lakhs) 1year 2 years 3 years 4 years 5 years Table 5.37 Percentage Variation in Maintenance Parameters with Age of Roads within the Network Percentage ofroads ofvarious Ages Percentage 81. Age Age Age Age Age Decrease in No. 1year 2 years 3 years 4 years 5 years Average PCI Percentage Increase in Total Maintenance Cost

76 It is seen from Table 5.37 that, the average PCI decreases by 13.4%, but the total cost increases by 88.7% when the age of all roads in the network increases from one year to four years. When the percentage of roads of age one to five years is equal, the decrease in PCI is only 7.3%, but the percentage increase in cost is 56%. When the percentage of five year roads is 80 and four year roads is 20, the maintenance cost exceeds two times the cost required for all one year roads, but the average PCI value decreases by 12%. When the percentage of five year roads decreases to 60 and the percentage of four and three year roads are 20 each, then the cost again doubles but the performance level can be kept the same as that of all one year roads Effect ofconstruction Quality (eq) ofroads on the Maintenance Decision An analysis was also done to bring out the effect of construction quality on the optimum maintenance cost and performance level. The age of all roads in the network in a run was kept the same and the age of the network was then varied from one to five years. The construction quality was varied as 0.25, 0.375, 0.5, and 0.75 for each of this case and the minimum performance level was selected as a PCI value of 40 and the maximum budget was selected as Rs. 20 lakhs/year. The results of the analysis are shown in Table It can be observed that for a specific age of the network, the average value of the PCI remains almost consistent, but the maintenance cost decreases slightly with the increase ofcq from 0.25 to 0.75 except for some minor variations. As discussed in Section 4.6.2, the effect of construction quality on the condition of roads becomes prominent when the age of roads exceeds four years. Hence a typical variation of total maintenance cost and the average PCI of the road network with the construction quality for a road network of age four years is shown in Fig

77 Table 5.38 Effect ofconstruction Quality on the Pavement Performance and Maintenance Cost (Minimum PCI: 40, Ratio ofpriority: 0.5/0.5) Age Construction Average PCI of the Total Maintenance (Years) Quality Road Network Cost ( Rs. in Lakhs) It can be observed from Fig that the average PCI of the network remains almost uniform but there is a 25% decrease in the total maintenance cost, when the construction quality increases from 0.25 to It can also be observed from 182

78 Fig that for a construction quality between 0.5 and 0.75, the perfonnance of the network and the total maintenance cost requirement are comparable. Hence for an optimum performance ofthe road network and maintenance cost, a construction quality between this range shall be maintained. 80 QI U ~ 70 c.2l c 60 ftj ~ l! ls 40 {!.u '::::0 30 u 0. QI 20 lid III ~ 10 ~ o Construction Quality Fig Effect ofvariation ofconstruction Quality on Total Maintenance Cost and Average PCI of the Road Network (Age: 4 years, Minimum PCI: 40, Ratio ofpriority: 0.5/0.5) Maintenance cost requirement for the analysis period for varying construction quality for the road network ofage four years is shown in Fig It is observed from Fig that it is not possible to set any specific trend for the maintenance cost requirement for each year over the analysis period with regard to construction quality. 183

79 16 ]' 14.J/. III...I 12,5 ~ 10..~ 8 u ~ 6 c III ~ 4.. c 'm 2 ~ o - - f-- I-- - tnr ~ ~ ~ ~ Year.CQO.25.CQO.375.CQO.5.CQO.625.CQO.75 Fig Effect ofvariation of Construction Quality on Maintenance Cost over Analysis Period (Age: 4 years, Minimum PCl: 40, Ratio of Priority: 0.5/0.5) Effect of Discount Rate on Maintenance Cost An effort was made to study the effect of discount rate selected in estimating the present value of the maintenance cost on the total maintenance cost required. The road network selected for the case study was selected for this analysis also with the minimum expected performance level set at a PCI value of 40. The maximum budget allocated for each year was set at Rs. 25 lakhs per year and an equal priority was assigned to both pavement performance and maintenance cost. Generally a discount rate between 3% and 5% is selected for road investment options (priya, 2008). Hence to study its effect, the discount rate was varied from 3 to 6 % and the percentage increase in maintenance cost with respect to a discount rate of 3% was worked out and the results are shown in Table