development of pavement maintenance management system for...

CHAPTER 5

DEVELOPMENT OF PAVEMENT MAINTENANCE

MANAGEMENT SYSTEM FOR RURAL ROADS

5.1 GENERAL

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 MULTICRITERIA 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)

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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 of distresses.

5.2.1 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

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The TFN can be expressed as 11 A(x):

(x - 1)1 ~ X ~ m;

~m - l~~ A (X)

n-xm ~ 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 of two fuzzy numbers

(1, m, n) + (p, q, 1') = (1 + p, m + q, n + r)

• Subtraction of two fuzzy numbers

(1, m, n) e (p, q, r) = (1- r, m - q, n - p)

• Multiplication of a real number with a fuzzy number

K * (1, m, n) = (Kl, Km, Kn)

(5.1)

(5.2)

(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 of distresses 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.

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m

P. = "[email protected] L..J IJ J

j=I

Vi = 1, 2, ..... , N

Vj =1, 2, ..... , M

(5.4)

v) Arriving at the relative preference of road stretches by computing the difference

between all combinations of fuzzy values.

i = 1 to N

k = 1 to N

i :;t k

(5.5)

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.

eik

s +ik= -_--:..:.:..,------,-

S + Is -\ik + 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. 5.2.

109

1.0

Negative--,.......,......Area

-I a m n

Positive

Area

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

5.2.2 Prioritisation Process using Fuzzy MCDM Approach

(5.7)

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

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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 of ravelling and edge failure. The influence of severity 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 of those

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 5.1.

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Table 5.1 Effect of Severity of Distresses and Roughness

Intensity of Various Distress Linguistic Variable Assigned

Low Ravelling (LRa) Low

Medium Ravelling (MRa) Medium

High Ravelling (HRa) High

Low Pothole (LP) Medium

Medium Pothole (MP) High

High Pothole ( HP) Very High

Low Edge Failure (LE) Low

Medium Edge Failure (ME) Low

High Edge Failure (HE) Medium

Low Roughness (LRo) Low

Medium Roughness (MRo) Medium

High Roughness (HRo) 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] .

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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 (Rij) for Distress and Roughness Parameters

Road Rating Assigned for Various T r'pes of Distresses tStretch

LRa MRa HRa LP MP HP LE ME HE LRo MRo HRoID t

1 4 7 8 3 0 0 4 4 2 0 7 0

2 4 4 10 4 10 4 3 3 2 0 8 0

3 7 10 8 1 0 0 I 8 0 0 7 0

4 4 9 9 3 5 4 3 0 0 0 8 0

5 5 7 6 2 0 0 3 2 0 0 9 0

6 4 9 3 0 0 0 3 2 1 0 9 0

7 5 10 3 1 0 0 3 3 2 0 9 0

8 5 8 5 1 0 10 4 6 2 0 8 0

9 5 5 1 10 0 0 2 3 2 0 8 0

10 6 10 8 0 0 0 10 4 0 0 9 0

11 4 4 2 0 0 1 1 0 0 0 8 0

12 7 10 6 6 1 0 0 2 0 0 7 0

13 10 5 8 5 6 2 9 8 10 0 0 10

14 10 8 9 0 3 4 0 3 6 0 0 10

15 7 9 7 5 5 5 9 10 4 0 0 10

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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 0.0 0.0 0.3

Medium 0.3 0.5 0.7

High 0.6 0.8 1.0

Very high 0.9 1.0 1,0

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 (Wj ) for Various Parameters

Criteria Fuzzy Weights, Wj (1, m, n)

LRa 0.0 0.0 0.3

MRa 0.3 0.5 0.7

HRa 0.6 0.8 1.0

LP 0.3 0.5 0.7

MP 0.6 0.8 1.0

HP 0.9 1.0 1.0

LE 0.0 0.0 0.3

ME 0.0 0.0 0.3

HE 0.6 0.8 1.0

LRo 0.3 0.5 0.7

MRo 0.6 0.8 1.0

HRo 0.9 1.0 1.0

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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

RoadStretch Fuzzy Evaluation Value (Pi)

ID (1, m, n)

1 13.2 18.6 27.6

2 24.0 32.0 42.6

3 12.3 17.5 27.5

4 20.4 27.6 36.5

5 11.7 16.5 24.3

6 10.5 14.9 22.0

7 11.7 16.7 25.0

8 20.7 26.5 35.8

9 11.1 16.3 24.5

10 13.2 18.6 30.0

11 8.1 11.0 15.3

12 13.2 19.2 27.9

13 28.2 36.2 51.1

14 25.8 32.4 41.5

15 27.3 34.8 48.6

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

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difference between the fuzzy evaluation values of these 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

[(13.2 - 27.6), (18.6 - 18.6), (27.6 - 13.2)] 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 [(13.2 - 42.6), (18.6 - 32), (27.6 - 24.0)] 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 RoadStretches

Relative PreferenceTFN Corresponding to

of Road StretchesRelative Preference of Road

Stretches (1, m, n)1-1 -14.4 0.0 14.4

1-2 -29.4 -13.4 3.6

1-3 -14.3 1.1 15.3

1-4 -23.3 -9.0 7.2

1-5 -11.1 2.1 15.9

1-6 -8.8 3.7 17.1

1-7 -11.8 1.9 15.9

1-8 -22.6 -7.9 6.9

1-9 -11.3 2.3 16.5

1-10 -16.8 0.0 14.4

1-11 -2.1 7.6 19.5

1-12 -14.7 -0.6 14.4

1-13 -37.9 -17.6 -0.6

1-14 -28.3 -13.8 1.8

1-15 -35.4 -16.2 0.3

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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 of the 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' of the fuzzy preference relation matrix is depicted in Fig. 5.3.

1.0

Negative-----'i-f-+

Area

1=-29.4 m=-13.4

Positive

Area

n =+3.6

Fig. 5.3 Computation of Fuzzy Preference Relation Matrix

The positive area in Fig. 5.3 is 0.3811 and total area is 16.5 and hence el2 is

(0.3811/16.5), which is equal to 0.023. 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

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preference over road stretch 'k' and vice versa. In the matrix [Pi], el2 is 0.023 and e21

is 0.977 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

N

from the priority matrix usmg the mathematical formula (PI)j =L (eik - 0.5)k=1

Vi = 1to N and are shown in Table 5.8. Thus, Priority Index (PI) of the 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 5.9.

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Road1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

StretchID1 0.500 0.023 0.551 0.105 0.654 0.761 0.633 0.109 0.662 0.462 0.979 0.475 0.001 0.007 0.000

2 0.977 0.500 0.980 0.734 1.000 1.000 0.998 0.761 1.000 0.948 1.000 0.973 0.269 0.478 0.324

3 0.449 0.020 0.500 0.094 0.602 0.713 0.581 0.097 0.612 0.415 0.958 0.427 0.001 0.006 0.000

4 0.895 0.266 0.906 0.500 0.965 0.994 0.954 0.539 0.963 0.849 1.000 0.885 0.105 0.232 0.138

5 0.346 0.000 0.398 0.035 0.500 0.630 0.479 0.034 0.515 0.317 0.928 0.327 0.015 0.004 0.011

6 0.239 0.006 0.287 0.006 0.370 0.500 0.354 0.005 0.388 0.219 0.858 0.226 0.030 0.019 0.026

7 0.367 0.002 0.419 0.046 0.521 0.646 0.500 0.046 0.535 0.338 0.932 0.348 0.011 0.001 0.007

8 0.891 0.239 0.903 0.461 0.966 0.995 0.954 0.500 0.964 0.842 1.000 0.880 0.088 0.204 0.118

9 0.338 0.000 0.388 0.037 0.485 0.612 0.465 0.036 0.500 0.311 0.910 0.320 0.013 0.003 0.009

10 0.538 0.052 0.585 0.151 0.683 0.781 0.662 0.158 0.689 0.500 0.981 0.515 0.004 0.030 0.010

11 0.021 0.059 0.042 0.036 0.072 0.142 0.068 0.042 0.090 0.019 0.500 0.020 0.078 0.079 0.077

12 0.525 0.027 0.573 0.115 0.673 0.774 0.652 0.120 0.680 0.485 0.980 0.500 0.000 0.009 0.001

13 1.000 0.731 1.000 0.895 1.000 1.000 1.000 0.912 1.000 0.996 1.000 1.000 0.500 0.732 0.568

14 0.993 0.522 0.994 0.768 1.000 1.000 1.000 0.796 1.000 0.970 1.000 0.991 0.268 0.500 0.328

15 1.000 0.676 1.000 0.862 1.000 1.000 1.000 0.882 1.000 0.990 1.000 0.999 0.432 0.672 0.500

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RoadStretch 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

ID

1 0.000 -0.477 0.051 -0.395 0.154 0.261 0.133 -0.391 0.162 -0.038 0.479 -0.025 -0.499 -0.493 -0.500

2 0.477 0.000 0.480 0.234 0.500 0.500 0.498 0.261 0.500 0.448 0.500 0.473 -0.231 -0.022 -0.176

3 -0.051 -0.480 0.000 -0.406 0.102 0.213 0.081 -0.403 0.112 -0.085 0.458 -0.073 -0.499 -0.494 -0.500

4 0.395 -0.234 0.406 0.000 0.465 0.494 0.454 0.039 0.463 0.349 0.500 0.385 -0.395 -0.268 -0.362

5 -0.154 -0.500 -0.102 -0.465 0.000 0.130 -0.021 -0.466 0.015 -0.183 0.428 -0.173 -0.485 -0.496 -0.489

6 -0.261 -0.494 -0.213 -0.494 -0.130 0.000 -0.146 -0.495 -0.112 -0.281 0.358 -0.274 -0.470 -0.481 -0.474

7 -0.133 -0.498 -0.081 -0.454 0.021 0.146 0.000 -0.454 0.035 -0.162 0.432 -0.152 -0.489 -0.499 -0.493

8 0.391 -0.261 0.403 -0.039 0.466 0.495 0.454 0.000 0.464 0.342 0.500 0.380 -0.412 -0.296 -0.382

9 -0.162 -0.500 -0.112 -0.463 -0.015 0.112 -0.035 -0.464 0.000 -0.189 0.410 -0.180 -0.487 -0.497 -0.491

10 0.038 -0.448 0.085 -0.349 0.183 0.281 0.162 -0.342 0.189 0.000 0.481 0.015 -0.496 -0.470 -0.490

II -0.479 -0.441 -0.458 -0.464 -0.428 -0.358 -0.432 -0.458 -0.410 -0.481 0.000 -0.480 -0.422 -0.421 -0.423

12 0.025 -0.473 0.073 -0.385 0.173 0.274 0.152 -0.380 0.180 -0.015 0.480 0.000 -0.500 -0.491 -0.499

13 0.500 0.231 0.500 0.395 0.500 0.500 0.500 0.412 0.500 0.496 0.500 0.500 0.000 0.232 0.068

14 0.493 0.022 0.494 0.268 0.500 0.500 0.500 0.296 0.500 0.470 0.500 0.491 -0.232 0.000 -0.172

15 0.500 0.176 0.500 0.362 0.500 0.500 0.500 0.382 0.500 0.490 0.500 0.499 -0.068 0.172 0.000

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Table 5.9 Ranking of Road Stretches Based onPriority Index (PI) from Fuzzy MCDM Approach

Road Stretch Priority Index Rank based onID (PI) PI1 -1.578 9

2 4.440 4

3 -2.027 10

4 2.691 5

5 -2.959 12

6 -3.967 14

7 -2.781 11

8 2.505 6

9 ~3.072 13

10 -1.160 7

11 -6.156 15

12 -1.385 8

13 5.835 1

14 4.629 3

15 5.512 2

It can be observed from Table 5.9 that, road stretch No.13 has the highest PI of

5.835 and hence the highest priority and road stretch No.ll has the smallest PI of

-6.156 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 5.10.

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Table 5.10 Comparison of Ranking of Road Stretches Based on Priority Index (PI)and PCI

RoadRank Based on

Stretch IDPriority Index (PI) from Rank Based on

Fuzzy PCIMCDM Approach

1 9 7

2 4 4

3 10 9

4 5 6

5 12 11

6 14 15

7 11 8

8 6 5

9 13 13

10 7 12

11 15 14

12 8 10

13 1 3

14 3 1

15 2 2

5.2.3 Discussion

It was observed that the ranking of road 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

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parameter in this prioritisation process unlike the ranking based on PCI, which includes

only the influence of distresses. Further, any number of parameters 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 ROADNETWORK USING HDM-4

5.3.1 General

Preventive Maintenance is needed to prevent fast deterioration of the 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.

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Strategic planning involves an analysis of the 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 of highway 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.

5.3.2 Calibration of HDM-4 Deterioration Models for Rural Roads

5.3.2.1 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.

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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 of HDM-4 for

rural conditions has been done by Jain et al. (2007) and the same has been reviewed in

Section 2.4.3.3. 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 of ravelling 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.

5.3.2.2 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 of HDM-4 deterioration models mainly involves three steps:

125

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 of subgrade.

• 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

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 5.11.

Table 5.11 Range of Calibration Factors Provided in HDM-4

[HDM-4 Technical User Guide, 1999]

Description Range

Ravelling Initiation & Progression Factor 0.1-20

Ravelling Retardation Factor 1.0-4.0

Pothole Initiation & Progression Factor 0.1-20

Roughness Age-Environment & Progression Factor 0.1-20

127

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.

5.3.2.3 Validation of Calibration Factors

The statistical significance of the calibration factor can be ascertained using

Coefficient of Determination (R2 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,

R2 = Coefficient of determination

RMSE = Root Mean Square Error

AAE = Average Absolute Error

OJ = Predicted value of distress by developed model

Pi = Predicted value of distress by HDM-4 model

Oavg Average value of distress by developed model

n Number of observations

5.3.2.4 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

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 calibration was 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. 5.4.

80

70

- 60~:a....01

:S 50Qj>III 40~

i 30

~0.. 20

10

0

2009 2010 2011 2012 2013Year

-+- Model Predicted

___ HOM(1 ,1 ,1)

HOM(1,1.3,1)

~HOM(1,1.6,1)

-.-HOM (1,1.4,1)

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 5.12.

129

Table 5.12 Validation of Calibration Factor for Ravelling Progression

Distress Calibration Coefticient of Average Root MeanFactors Determination Absolute Error Square

(R2) (AAE) Error (RMSE)

1,1,1 0.684 8.37 9.707

Ravelling 1,1.3,1 0.966 2.818 3.140

Progression 1,1.6,1 0.901 3.630 5.420

1,1.4,1 0.979 2.456 2.440

It can be observed from Table 5.12 that the calibration factor of 1.4 has the

least values of R2, AAE and RMSE values. Hence the calibration factor for ravelling

progression was adopted as 1.4.

5.3.2.5 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 m2 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. 5.5.

130

r----------------------....- ..---.------

0.7 ..,.------------,

0.6 +-------------:;,.-==-__1

";" 0.5 +-------~__"'~7'""-__I~--a 0.4 +-=---~--=,...;..~"--c_=..'"""""'-_l

.c....~ 0.3 +------------1

'iti 0.2 +------------1:;£ 0.1 +-----------__1

o -I----r----,-----,--..,----i

2009 2010 2011 2012 2013

Year

-+-Model Predicted

-HDM(1,l)

-~HDM (1,0.5)

..-.' ..- HDM(1,0.8)

--tt-HDM (1,0.82)

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 5.13.

Table 5.13 Validation of Calibration Factor for Pothole Progression

Calibration Coefficient of Average Root MeanDistress Factors Determination Absolute Error Square


1,1 0.638 0.049 0.0026

Pothole1,0.5 0.39 0.064 0.037

Progression 1,0.8 0.794 0.0308 0.017

1,0.82 0.9571 0.0148 0.0148

From Table 5.13, it can be seen that the best calibration factor for pothole

progression is 0.82.

5.3.2.6 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

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 age-

environment 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 of predicted values by the prediction model developed in the

study and by the HDM-4 model for various calibration factors is shown in Fig. 5.6.

9.25 ..,---------------,

E 9.2 +-----------...----(..lI: 9.15 +-----------r-~--;

1 9.1 +-------------,.r--7P~--;II>~ 9.05 +-----------:~...s~----l

.E 9 +-------:IIF--7~=--------(!o 8.95 +-------r--z.:!F--------(a::"a 8.9 +----~~---------(

~ 8.85 +----=-:;~"-----------;:s~ 8.8 +--...........-----------;~ 8.75 -I----r-----,----,--..,--...,.-----i

2009 2010 2011 2012 2013

Year

~Model

Predicted

--- HOM (1,1)

-.- HOM (0.8,0.8)

~ HOM (0.85,0.85)

'~ HOM (0.85,0.82)

Fig 5.6 Calibration Factor for Roughness Progression

Results of statistical tests done to establish the goodness of the best calibration

factor is shown in Table 5.14.

132

Table 5.14 Validation of Calibration Factor for Roughness Progression

Calibration Coefficient of Average Root MeanDistress Factors Determination Absolute Error Square


Roughness 1,1 0.98 0.09 0.04

0.8,0.8 0.99 0.07 0.02

0.85,0.85 0.98 0.07 0.025

0.85,0.82 0.99 0.06 0.02

The calibration factors for roughness age - environment and roughness

progression were obtained as 0.85 and 0.82 respectively.

Results of statistical 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 (R2) 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.

5.3.2.7 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

use of the tool for rural road pavement management which will be discussed in Section

5.3.3 and 5.3.4.

5.3.3 Determination of Optimal Maintenance Treatment for Rural Road Sectionsusing HDM-4 (Project Analysis)

5.3.3.1 General

Preventive Maintenance is needed to prevent fast deterioration of the 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.

5.3.3.2 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 5.3.2.2.

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

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 - 2008 and

are shown in Table 5. 15.

Table.S.lS Unit Rate for Maintenance Treatments

S1. No. Maintenance TreatmentCost

(Rs.in lakhs/lane/km)

1 Do minimum (Ensure proper drainage) 0.250

2 Shoulder maintenance 0.250

3 Pothole Patching 0.500

4 Fog seal 0.785

5 Patching and Fog seal 1.913

6 Patching and Slurry seal 2.438

7 Resurfacing with Pre-Mix Carpet (20 mm) 4.310

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.

5.3.3.3 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

HDM-4 deterioration models calibrated as explained in Section 5.3.2 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 of IRI 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

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 9 Slurry seal 74.9












*No IRR value for the base option

137

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 5.17.

Table 5.17 Maintenance Options Suggested for Various Ranges of Distresses

Type and Range of distress Maintenance Options IRR value

Suggested range

Ravelling < I0 %Do Nothing (Ensure

IRI < 6 m/km *Pothole <0.5%

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 200Pothole> 0.5 %

Ravelling between 25 % and 40 %

IRI> 6m/km and < 8.5 m/km Slurry seal 25-75Pothole < 0.5 %

Ravelling between 25 % and 40%Resurfacing with 20mm

IRI > 8.5m/km 50 - 100Pothole < 0.5%

Pre-Mix Carpet (PMC)

Ravelling between 25 % and 40% Patching and

IRI> 8.5 m/km Resurfacing with 20mm 75-115

Pothole> 0.5% PMC

Ravelling >40 % Preliminary treatment for

IRI> 8.5 m/km ravelling and then50- 100

Pothole < 0.5% 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

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.

5.3.4 Optimal Maintenance Strategy for Rural Road Network using HDM-4(Strategy Analysis)

5.3.4.1 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.

5.3.4.2 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

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 of the road network comprising of road sections

• Specification of the vehicle fleet

• Specification of general strategy information like start year for

analysis, duration and output currency

• Specification of the optimisation criteria

ii) Selection of road sections for analysis

iii) Selection of vehicle types

iv) 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 of strategy

• 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 of strategy.

• 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

• Optimised work programme is displayed

viii) Generation of reports

5.3.4.3 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 5.3.2 and 5.3.3.

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

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

MaintenanceMaintenance

Road Stretch ID Year CostTreatment

(Rs.in lakhs)

6 2010 Slurry Seal 0.58

7 2010 Resurfacing 2.79










Budget requirement for varying levels of IRI for maintenance intervention and

budget allocation are shown in Table 5.19.

142

Table 5.19 Effect of Varying Intervention Level of IRI and Budget Allocation onthe Budget Requirement

Budget Budget Requirement (Rs. in lakhs) for Varying levels ofIRI

Allocation6.5 7.5 8.5 9.5 10.5 11.5 12.5

(Rs. in lakhs) m/krn m/km m/km m/km m/km m/km rn/km

10 9.53 9.53 9.53 9.53 9.53 5.1 2.89

15 14.44 14.44 14.44 13.38 9.53 5.1 2.89

20 19.44 19.44 19.44 13.38 9.53 5.1 2.89

25 23.87 23.87 21.66 13.38 9.53 5.1 2.89

30 26.08 26.08 21.66 13.38 9.53 5.1 2.89

40 26.08 26.08 21.66 13.38 9.53 5.1 2.89

It is seen from Table 5.19 that, for a budget allocation of Rs. 10 lakhs, the

budget requirement remained same as Rs. 9.53 lakhs upto an IRI value of 10.5 rn/km

and thereafter decreased to Rs. 2.89 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. 14.44 lakhs and Rs. 19.44 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. 23.87 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. 26.08 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 5.20.

143

Table 5.20 Optimum Budget Requirement for Various Levels ofIRI asIntervention Criteria

IRI( m/km) Optimum Budget (Rs. in lakhs)

6.5 26.08

7.5 26.08

8.5 21.66

9.5 13.38

10.5 9.53

11.5 5.10

12.5 2.89

5.3.5 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 of project 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, 5.1

144

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 of solutions were not considered. Further, HDM-4 is more concentrating

on the roughness of road 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 5.4.

5.4 OPTIMISATION OF MAINTENANCE STRATEGY FOR RURAL ROADNETWORK USING GENETIC ALGORITHM

5.4.1 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

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 of performance, maximisation of reliability, 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.

5.4.2 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 of pavement 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

objectives is needed since small perturbations in weights can sometimes lead to quite

varying results.

5.4.2.1 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.

C PCI 3 682 (P )1.822 (0.55 x Page x CQ)

P I = 0 -. x age + e

5.4.2.2 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 of the problem used integer numbers for both the decision variable Xkst

and the maintenance action 'kst ', selected for road stretch's' at year 't'.

147

i) Maximisation of Pavement Performance

The objective function aimed to maximise the performance of road network

and the optimisation model was formulated as follows:

TMaximize: Z1 = L PCI t

t=1 s

Subject to

PCI st ~ PCI " '\I s =1to S, '\I t =1to Tmm

PCl st ~ 100

Xkst {O, I}, 'lis = 1to S, t = 1to T, k = 1to K

where,

PCl st = PCl st-I + X kst x ilPCI k

pC! st = Mean (pel st ) - cr, '\Is = 1 to S

(5.12)

(5.13)

(5.14)

(5.15)

(5.16)

(5.17)

(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 of carrying out the maintenance action 'k' in the year '1'

Bt is 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 5.18. 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

acceptable level as explained in Equation 5.14. Maintenance treatments should also be

done in such a way that the PCl value of the road stretches do not exceed the maximum

value of 100 as explained by Equation 5.15. 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 5.17.

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 of the problem to avoid more complexity.

(ii) Minimisation of Maintenance 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

K S T 1Minimize: Z2 = L L L t X k t C ktk=1 s=1 t=1 (1 +r) s

subjectto the same constraints as given by Equations 5.13 to 5.16.

(iii) Multi-Objective Model Formulation

(5.19)

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 of maintenance of the 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.

_ 1Z --

2 - I+Z2

(5.20)

The second objective of minimisation of maintenance cost takes the form as follows:

_ K S T 1Maximise: Z2 = L L L t Xk tCkt

k=1 s=lt=1 (1 + r) S (5.21)

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

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 Immi Z -z

imax Imm

(5.22)

*where, Zi' Zimin.' Zimax are the normalised objective function and the minimum and

maximum possible values of the 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 of one. If the maximisation of the

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: wtZ1 + W 2Z2

Subject to: the constraints given in Equations 5.13 to 5.16.

(5.23)

where WI and W2 are the weightages given to the objective functions of maximisation of

pavement performance (Z I) and minimisation of maintenance cost ( Z2 ) respectively.

151

Year

Treatment

5.4.2.3 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. 5.7.

I 2 3 4 5 6 7 8 9 10 I 2 3 4 5 6 7 8 9 10

YI Y2 Y3 Y4 Y5 Y6 Y7 Y8 Y9 YIO YII YI2 YI3 YI4 YI5 YI6 YI7 YI8 YI9 Y20

\. ~

151 road stretch 2nd road stretch

Yij -type ofmaintenance treatment for the i Ih road stretch for the /h year

Fig. 5.7 Coding of Solution for the Optimisation Model

152

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 of the 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

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 5.23. 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 of the 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 i1h string is1

F.pro =_--.:1_

1 NL F.

. 1 11 =

(5.24)

where 'Fj' is the fitness value of jth string and 'N' is the population size. 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

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 of being copied into the mating pool.

b) Crossover

As discussed in Section 2.4.2.3, 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 of strings.

155

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. The mutation probability

'Pm' is used to decide the number of bits to be muted. 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 0.001 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. 5.8.

156

Start

New Pool of Solutions

Select the best from parentpool and generate offspringsolutions to form new pool

Define problem variables, Constraintsand determine input parameter

Define objective function (s)

Generate initial pool of solutions

Evaluate solutions for all objectives

Fitness assignment: Rank - basedannroach

Selection and formation of ParentSolution Pool

Offspring Solution

Generate offspring solutionsby Crossover and Mutationfrom parent pool

NoIs stopping

criterionmet?

Yes

Print best selected Maintenance

Fig. 5.8 Sequence of Operations in GA

157

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 0.5625 to 0.75. 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 5.21.

Table 5.21 Details of Road Stretches Selected for the Case Study

RoadAge as on

ConstructionPCI of the Road

Stretch ID2009

Quality (CQ)Stretches in the Year

(years) 2009

1 6.2 0.625 7.00

2 6.0 0.750 15.5

3 5.8 0.750 19.6

4 5.5 0.750 27.4

5 6.0 0.625 11.5

6 5.0 0.625 36.5

7 5.8 0.750 19.6

8 5.8 0.563 14.6

9 5.8 0.563 14.6

10 4.9 0.750 40.5

11 5.2 0.625 32.9

12 5.0 0.625 36.5

13 5.8 0.750 19.6

14 6.0 0.563 10.0

15 6.0 0.625 11.5

Average 5.7 0.6625 21.7

Min 4.9 0.5625 7.00

Max 6.2 0.750 40.5

158

Maintenance treatments considered in this programme and their cost/lane/km

as per Schedule of Rates (2008) of Kerala State P.W.D. are shown in Table 5.22.

Table 5.22 Maintenance Treatments Selected for the Study

Maintenance Treatment Code AssignedCost

( Rs. in lakhs/lane/km)

Do Nothing Ko 0.000

Shoulder Maintenance K} 0.250

Pothole Patching K2 0.500

Patching and Slurry seal K3 2.438

Resurfacing with Pre-MixlZL( 4.310

Carpet (20 mm)

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).

5.4.3.1 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

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. 5.23.

Table 5.23 Effect of Maintenance Action on the Condition of Pavement in terms ofPCI Based on Expert Opinion

Improvements in PCI due to Various Maintenance Actions

Present Pavement ConditionShoulder Pothole Patching and Resurfacing

Maintenance Patching Slurry seal (Pre-Mix Carpet)(K]) (K2) (K3) (~)

Very Good PCI >80 NA NA NA NA

PCI 70 - 80 2 510 15

Good

PCI 60 - 70 2 5 1025

PCI 50 - 60 2 1025 35

Fair

PCI 40 - 50 2 10 2545

PCI 30 - 40 2 1535 50

Poor

PCI 20 - 30 2 15 3560

PCI 10 - 20 2 2045 70

VeryPoor

PCI < 10 2 20 45 80

160

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 5.24.

Table 5.24 Improvement in PCI due to Various MaintenanceActions Based on Field Data

Maintenance Action Improvement in PCI

Shoulder maintenance 1-2

Pothole Patching 8-20

Pothole Patching & Slurry seal 16-50

Resurfacing with 20 mm Pre-Mix Carpet 28-70

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

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.

5.4.3.2 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 0.005.

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% of the total number of generations.

162

5.4.3.3 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. 5.9.

---------------------------------- ---------------------------------------,

100 ..,.~=~..."--,_,-"--------'----------90 +--------.. '="'41• .-,_,--------------

-\'>~"" "

80 +---------'" ,.,---:-------------

70 .~- - - - .. 74.0+-------------':p~"" I!

60 • """" I.I ".'\, i2 50 • ""'" !:------

40 • -'£'",\~9.0~ ,. ,,-20 +-----------'------------"'.,----. ~10 -+------------'-------------

O ...1..."o 1 2 3 3.2 4

Age (Year)

5 6 7

Fig. 5.9 Effect of Maintenance Treatment on the Performance ofPavement in terms of PCI

As seen from Fig. 5.9, the PCl of a road section at an age of five 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 of 74.0. The effect of the maintenance treatment on the road section is

163

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 6.9.1 IDE in Java environment.

5.4.3.4 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 of the

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

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 of the 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, 0.625 and

0.75 and the influence of discount rate was studied by varying it as 3, 4, 5 and 6%

respectively in each run of the program. Condition of the roads at the end of year 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 2019. 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 5.25.

165

Table 5.25 Details of Input Parameters used for the Experimentation of theProgram

Ratio of MinimumNumber

ParameterPriority of PClofthe Other Input Parameters

of Runs ofVaried theObjectives Network

Program0/1

Priority of Objectives 0.3/0.7 Budget: Rs. 25 lakhs/year,(Study Road Network) 0.5/0.5 30,40,50

Discount rate: 4 %.15

0.7/0.31/0

Delayed1 year Budget: Rs. 20 lakhs/year,2 Years CQ of road stretches:

Maintenance(Hypothetical 3 Years 0.5/0.5 30,40,50

Same as that for the study15network,

Road 4 Years Discount rate: 4 %.Network) 5 Years

0.250 Budget: Rs. 20 lakhs/year,Age and CQ of the roadsConstruction 0.375 kept same in a run,Quality (CQ)

(Hypothetical 0.500 0.5/0.5 40Age of network was then

25varied from one to five

Road 0.625 years for each value ofNetwork)

0.750 CQ,Discount rate: 4 %.

3Discount Rate

(%) 4 Budget: Rs. 25 lakh/year,(Study Road 5

0.5/0.5 40Discount rate: 4 %.

4

Network) 6

Effect of Varying Age of Budget Rs. 20 lakhs/ year,Roads in the Network

0.5/0.5 40CQ for all roads: Same as

12(Hypothetical Road 0.625,

Network) Discount rate: 4 %.

Total Number of Runs 71

5.4.4 Analysis of Results

5.4.4.1 Effect of Priority Assigned to Objectives and Minimum RequiredPavement 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

assigning equal priority for both maximisation of performance and minimisation of

maintenance cost is shown in Table 5.26. 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 RoadNetwork Selected for the Case Study

(Minimum PCl: 40, Ratio of Priority: 0.5/0.5)

ROptimised Maintenance Actions for the Road Stretches

tretch1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Year

2010 4 4 4 2 4 2 4 4 4 0 2 2 4 4 4

2011 1 1 0 4 1 2 2 2 2 4 4 4 2 1 1

2012 2 2 2 2 2 3 2 2 2 2 2 3 2 2 2

2013 2 2 2 3 3 2 2 2 2 2 3 2 2 3 3

2014 2 2 3 2 2 3 2 3 3 3 2 3 3 2 2

2015 2 2 2 2 3 2 2 2 2 2 3 2 2 3 3

2016 3 3 3 3 2 2 3 3 3 3 2 2 3 2 2

2017 2 2 2 2 2 3 2 2 2 2 3 2 2 3 3

2018 2 3 3 3 3 2 3 3 3 2 2 3 3 2 2

2019 3 2 2 2 2 3 2 2 2 3 3 2 2 3 3

where,

0- Do Nothing1 - Shoulder Maintenance2 - Pothole Patching3 - Patching and Slurry seal4 - 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

the suitable priority level for the rural road network and the results of the analysis are

shown in Figs. 5.10 and 5.11 respectively.

119.68

0/1 0.3/0.7 0.5/0.5 0.7/0.3 1/0

Ratio of Priority of Performance to Cost

140

120.5iii 100~t;

800u8 iii 60C.z:1lI..ll:C III

4041/-....C'jij

20~

~ 00I-

Fig. 5.10 Variation of Total Maintenance Cost with Varying Priorityof Pavement Performance and Maintenance Cost

1/00.7/0.30.5/0.50.3/0.70/1

80 ..,.- -;-- --=-__~.LL__

..ll:

~ 70

~ 60 +--"'-""""""---"'-""'""""'---

'2 50o«: 4041/

.z:.... 30'0o 200-

:0 10f 0

~Ratio of Priority of Performance to Cost

Fig. 5.11 Variation of the Average PCI of the Road Network with VaryingPriority of Pavement Performance and Maintenance Cost

A Comparison was made from Figs. 5.10 and 5.11 for various priority levels

with respect to the cost minimisation model (ratio of priority 0/1) for the total

168

maintenance cost and average pe"rformance level of the road network and is shown in

Table 5.27.

Table 5.27 Effect of Varying Ratio of Priority Levels of Pavement Performance toCost Minimisation

Ratio of Priority ofPercentage Increase in Total

PercentagePerformance to Improvement in

Maintenance CostMaintenance Cost

Average PCI

0/1 - -

0.3/0.7 0.3 OJ

0.5/0.5 6.6 1603

0.7/0.3 19.6 24.2

1/0 44.6 32.9

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 of performance 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 of weightage of 30% (ratio of priority: 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 2019. An analysis was done to observe the

169

distribution of the maintenance cost requirement over the analysis period for varying

ratios of priorities and is shown in Figs. 5.12 to 5.16.

25 ..,.--------------------

'Vi':i 20.!!.5

g 151;;ou~ 10cRlCQI...C.; 5~

o2010 2011 2012 2013 2014 2015 2016 2017 2018 2019

Year

Fig. 5.12 Maintenance Cost Requirement over Years

(Cost Minimisation Model: Ratio ofPriority 0/1)

25

'Vi'J:.:; 20

.5vi~ 151;;

8~ 10cRlC

~.~ 5~

o2010 2011 2012 2013 2014 2015 2016 2017 2018 2019

Year


(Bi-objective Model: Ratio ofPriority 0.3/0.7)

170

25

'iii 20.c~

..!!!.5

15IIIa:-...III0u 10lUUC111ClU

5...c'm~

o

25

'iii.c~ 20.5en!£ 15t:ou~ 10c111CSc 5'm~

o

2010 2011 2012 2013 2014 2015 2016 2017 2018 2019

Year

Fig. 5.14 Maintenance Cost Requirement over years


2010 2011 2012 2013 2014 2015 2016 2017 2018 2019

Year



171

30 ,---------------------

iii:§2 25..!!!c:iii 20~

1;;8 15

~c::g 1021c:

OJ; 5:!:

o2010 2011 2012 2013 2014 2015 2016 2017 2018 2019

Year


(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. 5.12 to 5.16, the maintenance

cost requirement for the first year of analysis 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 5.28.

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

over the analysis period. The effect due to variation of priority 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

Percentage Requirement of Total Maintenance Cost in each Year of

Year Analysis Period for Varying Priorities

Oil 0.3/0.7 0.5/0.5 0.7/0.3 1/0

2010 26.3 26.4 24.5 21.9 20.6

2011 6.0 5.2 10.8 11.5 14.6

2012 4.0 4.8 5.7 5.0 4.9

2013 7.1 8.2 8.3 7.0 6.7

2014 11.4 12.5 9.8 14.2 16.3

2015 9.1 8.2 6.8 12.1 11.3

2016 8.7 10.5 10.7 7.3 6.6

2017 10.9 7.5 6.3 6.3 9.3

2018 7.3 6.4 9.8 8.2 2.8

2019 9.2 10.3 7.3 6.5 6.9

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 5.29.

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

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 forVarying Ratios of Priority

Ratio of Minimum PCI = 30 Minimum PCI = 40 Minimum PCI = 50Priority ofPavement Average Total Average Total Average Total

Performance PCIof Maintenance PCIof Maintenance PCIof Maintenanceto Road Cost Road Cost Road Cost

Maintenance Network (Rs. in lakhs) Network (Rs. in lakhs) Network (Rs. in lakhs)Cost

0/1 46.1 66.28 56.1 82.77 60.4 91.66

003/0.7 51.1 67.1 56.2 82.99 61.4 92.32

0.5/0.5 62.2 77.2 65.2 88.25 66.9 95.58

0.7/0.3 69.5 96.33 70.0 99.85 71.3 114.25

1/0 71.7 104.94 74.5 119.68 75.5 127.14

A comparison was done with respect to a minimum PCI of 30 for higher levels

ofminimum performance of the road network and is shown in Table 5.30.

Table 5.30 Effect of Minimum Pavement Performance Level on the Performanceof the Road Network and Maintenance Cost

Ratio of Minimum PCI = 40 Minimum PCI =50Priority of Percentage

PercentagePercentage

PercentagePerformance to Increase in Increase inMaintenance

Increase inMaintenance

Increase inMaintenance

CostAverage PCI

CostAverage PCI

Cost

0/1 22 23 31 38

OJ/O.7 10 24 20 38

0.5/0.5 5 15 7.5 24

0.7/003 1 4 2 19

1/0 4 14 5 21

174

5.4.4.2 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 2010.

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 of PCl value

of 40 are shown in Tables 5.31 and 5.32 respectively.

175

Table 5.31 Maintenance Programme for the Road Network with a DelayedMaintenance of One Year (Minimum PCI: 40, Ratio of Priority: 0.5/0.5)

~Optimised Maintenance Actions for the Road Stretches

tretch1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Year

1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

3 1 0 0 0 0 1 0 1 1 0 0 0 0 0 0

4 1 0 2 2 2 0 0 0 1 0 2 2 0 1 1

5 2 2 1 1 2 2 1 2 2 2 2 2 2 2 2

6 3 3 3 2 2 3 3 3 2 3 2 2 3 2 3

7 2 2 2 2 3 2 2 2 3 2 2 2 2 3 2

8 2 3 3 3 2 2 3 2 2 3 3 3 3 2 3

9 3 2 2 2 2 3 2 3 3 2 2 2 2 3 2

10 2 2 2 3 3 2 2 2 2 2 2 3 2 2 2

where,

0- Do Nothing1 - Shoulder Maintenance2 - Pothole Patching3 - Patching and Slurry seal4 - 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

Table 5.32 Maintenance Programme for the Road Network with a DelayedMaintenance of Five Years (Minimum PCI: 40, Ratio of Priority: 0.5/0.5)

~Optimised Maintenance Actions for the Road Stretches

tretch1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Year

12 1 2 2 2 2 2 2 2 1 2 2 2 2 2

22 4 4 4 2 2 4 2 2 4 2 2 4 2 2

33 2 2 2 3 3 2 3 3 2 3 3 2 3 3

42 3 2 3 2 1 3 2 2 3 2 2 3 2 1

5 3 2 2 2 3 3 2 3 3 2 3 3 2 3 3

62 2 2 2 2 2 2 2 2 2 2 2 2 2 2

72 3 2 2 3 3 3 2 2 2 3 2 2 2 2

83 2 3 3 2 2 2 3 3 3 2 3 3 3 3

9 2 3 2 2 2 2 2 2 2 2 3 2 2 2 2

10 3 2 2 2 3 3 3 3 2 2 2 3 2 2 3

where,

o-Do Nothing1 - Shoulder Maintenance2 - Pothole Patching3 - Patching and Slurry seal4 - 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 5.33.

An analysis was also done to study the effect of delayed maintenance on the percentage

increase in maintenance cost and percentage decrease in the average PCI value of the

network for a minimum PCI value of 40. The comparison was done with respect to the

maintenance cost required and the average PCI value of the network with a delay in

maintenance of one year and is shown in Table 5.34.

177

Table 5.33 Effect of Delayed Maintenance on Performance of Road Networkand the Maintenance Cost (Ratio of Priority: 0.5/0.5)

Minimum PCI = 30 Minimum PCI = 40 Minimum PCI = 50Delay 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)1 60.8 31.84 64.7 38.85 67.9 51.492 55.4 37.10 61.3 49.80 63.4 55.393 52.0 43.78 57.7 58.06 61.5 69.304 52.8 54.41 56.1 66.28 57.9 74.255 51.0 69.80 54.6 75.85 57.0 88.03

Table 5.34 Percentage Variation of Maintenance Cost and PCI for DelayedMaintenance (Minimum PCI: 40, Ratio of Priority: 0.5/0.5)

DelayPercentage Increase in Total Percentage Decrease in

mMaintenance Cost with Average PCI with respect to

Maintenance(years)

respect to Age of One Year Age of One Year

1 - -2 28.2 5.03 49.4 11.04 70.6 13.25 95.2 15.6

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 5.35. 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

Table 5.35 Maintenance Cost Requirement over the Analysis Period for DelayedMaintenance (Minimum PCI: 40, Ratio of Priority: 0.5/0.5)

Maintenance Cost (Rs. in lakhs) over Analysis Period for DelayedYear of MaintenanceAnalysis

1 Year 2 Years 3 Years 4 Years 5 YearsPeriod1 0 0 1.44 2.36 3.322 0 1.39 1.48 3.05 14.003 0.36 2.22 2.84 8.45 11.014 1.41 2.56 11.38 9.77 7.05

5 2.71 9.39 6.90 8.61 10.186 9.79 6.75 6.76 7.52 2.967 5.04 9.41 5.77 5.77 6.498 9.05 6.24 8.35 6.95 9.759 6.01 6.68 7.35 8.03 3.9810 4.47 5.12 5.77 5.77 7.07

Total38.85 49.79 58.06 66.28 75.85

Cost

5.4.4.3 Effect of Variation of Age of Roads 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 0.625 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 5.36.

Acomparison 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 5.37.

179

Table 5.36 Effect of Variation of Age of Pavements within the Road Network onMaintenance Parameters (Minimum PCI: 40, Ratio of Priority: 0.5/0.5)

Percentage of Roads of Various Age AverageMaintenance

81. CostNo. Age Age Age Age Age PCI

(Rs. in lakhs)1year 2 years 3 years 4 years 5 years

1 100 0 0 0 0 64.2 37.552 0 100 0 0 0 59.1 43.963 0 0 100 0 0 57.7 57.234 0 0 0 100 0 55.6 64.885 0 0 0 0 100 50.4 70.866 20 20 20 20 20 59.5 58.647 40 20 20 20 0 61.2 52.088 60 20 20 0 0 62.9 46.789 80 20 0 0 0 64.1 42.7710 0 0 0 20 80 56.5 75.8211 0 0 20 20 60 63.4 79.8912 0 20 20 20 40 58.4 67.04

Table 5.37 Percentage Variation in Maintenance Parameters with Age of Roadswithin the Network

Percentage of Roads of Various AgesPercentage

81. Age Age Age Age AgePercentage

Increase in TotalDecrease in

No. 1year 2 years 3 years 4 years 5 years Average PCIMaintenance

Cost1 100 0 0 0 0 - -

2 0 100 0 0 0 7.90 17.09

3 0 0 100 0 0 10.1 52.41

4 0 0 0 100 0 13.4 72.79

5 0 0 0 0 100 21.5 88.71

6 20 20 20 20 20 7.30 56.15

7 40 20 20 20 0 4.70 38.70

8 60 20 20 0 0 2.00 24.60

9 80 20 0 0 0 0.10 13.91

10 0 0 0 20 80 12.1 101.91

11 0 0 20 20 60 1.30 112.76

12 0 20 20 20 40 9.10 78.53

180

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.

5.4.4.4 Effect of Construction Quality (eQ) of Roads 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, 0.625 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 5.38. 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 of CQ 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. 5.17.

181

Table 5.38 Effect of Construction Quality on the Pavement Performance andMaintenance Cost (Minimum PCI: 40, Ratio of Priority: 0.5/0.5)

Age Construction Average PCI of the Total Maintenance

(Years) Quality Road Network Cost ( Rs. in Lakhs)

0.25 64.52 44.34

0.375 63.65 40.96

1 0.5 65.40 40.67

0.625 64.88 40.63

0.75 64.89 38.06

0.25 61.13 54.73

0.375 60.05 53.89

0.5 60.16 51.782

0.625 61.11 48.88

0.75 61.34 47.35

0.25 57.98 61.38

0.375 57.41 60.10

3 0.5 57.81 59.87

0.625 57.98 59.46

0.75 56.63 58.29

0.25 54.54 71.48

0.375 55.12 69.82

0.5 53.26 61.77

4 0.625 55.36 63.71

0.75 54.23 62.83

0.25 52.90 77.30

0.375 52.33 76.75

0.5 51.21 70.865

0.625 53.03 74.75

0.75 52.48 72.65

It can be observed from Fig. 5.17 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 0.75. It can also be observed from

182

o

Fig. 5.17 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 of the road network and maintenance cost, a construction quality

between this range shall be maintained.

80QIU

~ 70c.2l 60cftj~ 50- ....l! lS 40{!.u'::::0 30u0.QI 20lIDIII~ 10~

0.25 0.375 0.5 0.625 0.75

Construction Quality

Fig. 5.17 Effect of Variation of Construction Quality on Total Maintenance Costand 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 of age four years is shown in Fig. 5.18. It is observed from

Fig. 5.18 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

16

]' 14.J/.III....I 12,5

~ 10..~ 8u~ 6cIII

~ 4..c'm 2~

o

-

-

f-- I-- -

•~ ~ ~ ~tnr

2010 2011 2012 2013 2014 2015 2016 2017 2018 2019

Year

.CQO.25

.CQO.375

.CQO.5

.CQO.625

.CQO.75

Fig. 5.18 Effect of Variation of Construction Quality on Maintenance Cost overAnalysis Period (Age: 4 years, Minimum PCl: 40, Ratio ofPriority: 0.5/0.5)

5.4.4.5 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 5.39.

184

Table 5.39 Effect of Discount Rate on the Average performance and TotalMaintenance Cost of the Road Network

Discount Rate Average PCI of the Maintenance CostPercentageDecrease in(%) Road Network (Rs. in lakhs)

Maintenance Cost3 65.3 94.41 -4 65.2 88.97 5.76

5 65.0 86.45 8.43

6 64.8 81.81 13.35

It is seen from Table 5.39 that the discount rate has a considerable effect on

the total maintenance cost requirement, however the discount rate selected should be in

pace with the economic scenario and consequently the prevailing inflation rate of the

country.

5.4.5 Discussion

A deterministic bi-objective optimisation model with the objectives of

maximising pavement performance and minimising maintenance cost was developed

for arriving at the optimum maintenance strategy for rural roads. When compared with

the minimisation of cost model, the bi-objective model with an equal priority for both

objectives yielded 16% increase in the PCI value with a 6.6% increase in cost. But for

the maximisation of performance model, the increase in performance level was 33%

but with a 45% increase in cost. Hence a bi-objective model, with an equal priority for

minimisation of maintenance cost and maximisation of performance can be considered

to be more reasonable for rural roads. The road network selected for the case study

consisted of roads with age ranging from 4.92 to 6.17 years without any maintenance

action being done till the start of the analysis period. Consequently, the maintenance

cost requirement for the first year of analysis period was as high as 20 to 26% of the

total maintenance cost and was uniformly distributed over the rest of years.

185

Any specific trend could not be set for the maintenance cost requirement over the years

with the varying priorities assigned to the objectives. Based on the results of the

analysis done to study the effect of minimum targeted performance level, any trend

could not be set for the variation of total maintenance cost and average performance

level with respect to the minimum performance level selected. But it was observed that

for priority level of 0.5/0.5 and above, for marginal increase in average PCI, the

percentage increase in cost was fairly high for a minimum PCI value of 50. Hence a

minimum required PCI value of either 30 or 40 will be more desirable for rural roads

than aminimum PCI value of 50.

From the analysis of the effect of delayed maintenance, it was observed that

the total maintenance cost almost doubled and the average PCI value of the road

network reduced by 16% when the maintenance was delayed by one to five years.

It was also observed that, when the maintenance was delayed by one year, the

maintenance cost requirement for the first and second year of the analysis period was

zero and when the maintenance was delayed by two years, no maintenance was

required for the first year of analysis period.

An analysis also was done to study the effect of varying age of roads within

the network by selecting a hypothetical network comprising of fifteen roads. It was

seen from the results of this analysis that the average PCI decreased by 13.4%, but the

total cost increased by 88.7% when the age of all roads increased from one year to four

years. When the percentage of roads in the network with age one to five years were

equal, the decrease in PCI was only 7.3%, but the percentage increase in cost was 56%.

When the percentage of five year roads was 80 and four year roads was 20, the

maintenance cost exceeded two times the cost required for all one year roads, but the

average PCI value decreased by 12%. When the percentage of five year roads

186

decreased to 60 and the percentage of four and three year roads were 20 each, then the

cost again doubled but the performance level could be kept the same as that of all one

year roads.

Construction quality, being an influential parameter affecting the performance

of rural roads, its effect on the maintenance decisions was also analysed. It can be

observed that the average PCI of the network remained almost uniform but there was a

25% decrease in the total maintenance cost, when the construction quality increased

from 0.25 to 0.75. It was also observed that for a construction quality between 0.5 and

0.75, the performance of the network and the total maintenance cost requirement are

comparable. Hence for an optimum performance of the road network at a reasonable

maintenance cost, a construction quality between 0.5 and 0.75 shall be maintained.

The discount rate selected in estimating the present value of maintenance cost

was also varied from 3 to 6% to study its effect on the maintenance cost requirement

and performance of the road network. It was observed that the average performance

level of the network remained consistent at a PCI value of 65, but the maintenance cost

decreased by 5.8%, 8.4% and 13.4% respectively when the discount rate was increased

from 3to 6%. Thus it can be concluded that discount rate also has a considerable effect

on the maintenance cost requirement.

187

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