SEPTEMBER 25 - 27, 2007psa2.kuciv.kyoto-u.ac.jp/lab/images/stories/gaikoku...Road Infrastructure...

Road Infrastructure Asset Management CourseRoad Infrastructure Asset Management Course

UNIVERSITY OF TRANSPORT AND COMMUNICATIONSUNIVERSITY OF TRANSPORT AND COMMUNICATIONS

SEPTEMBER 25 SEPTEMBER 25 -- 27, 200727, 2007

JOINTLY ORGANIZED BY:JOINTLY ORGANIZED BY:

UNIVERSITY OF TRANSPORT AND COMMUNICATIONSUNIVERSITY OF TRANSPORT AND COMMUNICATIONSKYOTO UNIVERSITYKYOTO UNIVERSITY

HANOI, VIETNAMHANOI, VIETNAM

Chaired by Prof. Kiyoshi Kobayashi, Kyoto UniversityChaired by Prof. Kiyoshi Kobayashi, Kyoto University

Nguyen Dinh Thao

Highways and Airfields Engineering Laboratory

Civil Engineering Department

University of Transport and Communications

E-mail : dinhthao200277@yahoo.com

Predict the deterioration process of road Predict the deterioration process of road

pavement using Stochastic modelpavement using Stochastic model

Contents

Part 1.

Introduction RoadSystem

Part 2.

DevelopPredictionModel

Part 3.

ApplicationPredictionModel

Part 4.

Conclusion

Part 1.

IntroductionRoad System

Contents

DO SEE

PROJECT LEVEL

Shares of different Roads

(Total length 224,482km)

55.68 %20.16 %

3.33 % 3.40 % 7.70 %9.73 %

National Roads

Provincial Roads

District Roads

Commune Roads

Urban Roads

Special Roads

Length of different Roads, km

17,295 21,840

45,250

124,994

7,476 7,627

140,000

The total number of bridges were 34,933 with the total length of

approximately 606,915m.

55.68 %20.16 %

3.33 % 3.40 % 7.70 %9.73 %

National Roads

Provincial Roads

District Roads

Commune Roads

Urban Roads

Special Roads

17,295 21,840

45,250

124,994

7,476 7,627

140,000

(Classes of roads are defined according to Highway Specification for Design, code TCVN 4054-1998)

Shares of different Roads in

term of percentage (Total length

224,482km)

30.80%20.30%

16.30%2.20%

30.40%

Class I and II - Roads Class III-Roads

Class IV-Roads Class V-Roads

Class VI-Roads

Shares of different Roads in term of

length (Total length 224,482km)

68,243

45,570

69,140

36,591

8 0 ,0 0 0

High Performance

9.89%0.50%49.37% 12.48%

27.76%

Cement Concrete

Asphalt Concrete

Bituminous Surface Treament

Macadam Stone

22,19428,017

62,324

110,835

140,000

NH.1 Haivan Pass

Management and Maintenance

Example:

Roads Operation without Maintenance

Rao Bridge in HaiPhong Province: Operated without any maintenance, so collapsed in 1987 with Life Time of 7 years 4 months.Railway Tunnels System: built by French in 1920’s, very poor maintenance for 70 years, so in 1993 Tunnel No.7 through HaiVan Pass collapsed.

War + Lack of Budget

By Reason ofServiceability

S initial

S critical

Actual

Life Time

Designed

Life Time

Elapsed Time

Problems:

? Elapsed

Lost of SI

SI initial

SI critical

Actual

Life Time

Designed

Life Time

Roads Operation with Maintenance/Problem of

Planning for Maintenance Work

SI restored after repairing

When, How ?

Lack of basics of

Sciences to determine !!!

Need building prediction model

Contents

Part 2.

Develop

Prediction

Part 3.

Application Prediction Model

Part 4.

Conclusion

Part 1.

IntroductionRoad System

Part 2.

Develop PredictionModel

Performance/Serviceability Index

Can you predict the condition of

pavement in the future?

Present

xtB (Future)

xtA (Present)

Condition

statesMaintenance

Status Quo

Do nothing

Developing Prediction

Model using Markov chain

of Stochastic process

based on investigated data

��

Forecasting/Predicting Deterioration of Facilities

A Markov chain is specified by :

1. A Set of States (S)2. Probability Transition Matrix (P)3. Probability Vector π

Markov Chain

Let’s study the change of condition states of a system within a set of condition states S.

A Markov chain is a sequence of random discrete variables having the property that, given knowledge of the present, the past is irrelevant for predicting the future.

In other words,

{ }1 0 0 1 1 1 1...n j n n n iPr X s X s X s X s X s+ − −= = ∩ = ∩ ∩ = ∩ =

{ }1n j n iPr X s X s+= = =

11 12 1K

21 22 2

1 2 KK

� � � �

Markov Transition Matrix

If the space of states is finite, the transition probability distribution can be represented as a matrix, called the

transition matrix P.

{ }1ij n j n ip Pr X s X s+= = =

Transitional Probabilities

Normal

Very worn

Pavement condition

24p33p

34p44p

Initial probability distribution (vector) on the set of states: π

1 Transitional Step

Probability Vector/Distribution

( )n nPπ π=

(1)Pπ π=

( ) ( ) ( ) ( )2 1 2P P P Pπ π π π= = =

( ) ( ) ( )( ) ( )3 2 1 3P P P Pπ π π π= = =

π : Initial probability distribution (vector): K components (Ex. K=4)

ith component of πmeans probability that facility is in state i at

the current time.

. . .. . .. . .. . .

ith component of π(n) means ?

Contents

Part 3.

Part 4.

Conclusion

Part 1.

Introduction Road System

Part 2.

Develop Prediction Model

Part 3.

Predict the deterioration of some highways in term of Roughness Index

(IRI) in Vietnam based upon the investigated data.

Application

The common IRI scale(http://training.ce.washington.edu/WSDOT/ )

Pavement roughness Ratings according to Vietnamese Standard (22TCN-277-01)

(8; 10](6 ; 8](4 ; 6](0 ; 4]40 ; 20

(7 ; 9](5 ; 7](3 ; 5](0 ; 3]60

(6 ; 8](4 ; 6](2 ; 4](0 ; 2]120 ;100 ; 80

Very PoorPoorFairGood

IRI (m/km)Design speed

(km/h)

(9; 11](7 ; 9](5 ; 7](0 ; 5]40 ; 20

(8; 10](6 ; 8](4 ; 6](0 ; 4]60

Very PoorPoorFairGood

IRI (m/km)Design speed

(km/h)

AC Pavement

Bituminous surface treatment Pavement

Selected pavement roughness Ratings

��Very PoorIRI > 7

��Poor6 < IRI ≤≤≤≤ 7

��Quite Fair5 < IRI ≤≤≤≤ 6

��Fair4 < IRI ≤≤≤≤ 5

��Good3 < IRI ≤≤≤≤ 4

��Very GoodIRI ≤≤≤≤ 3

Notation of statesStatesIRI

(m/km)

Data of Road condition investigated by VRA in 2001 and 2004

ID SECT_NAME . . .

[1] [2] . . .

1 QL18-I: 46.3-47 BAC NINH

2 QL18-I: 47-48 BAC NINH

. . . . . . . . .

319 QL4B: 77-78 LANGSON

ROUGHNESS (M/KM) . . . NMT_LTYPE

[76] . . . [159]

2.75 4

2.73 4

2.56 4

2.65 4

2.74 4

2.85 4

2.08 4

2.15 4

2.40 4

. . . . . .

3.93��IRI > 7

��6 < IRI ≤≤≤≤ 7

��5 < IRI ≤≤≤≤ 6

��4 < IRI ≤≤≤≤ 5

��3 < IRI ≤≤≤≤ 4

��IRI ≤≤≤≤ 3

Notation

of states

(m/km)

Classification of road conditions in 2001 and 2004 based on investigated data

319319Sum

561��

632��

8031��

8526��

35137��

0122��

20042001

Number of road sectionsState

How roads changes from states to states ?

Changes of condition states of selected road sections in term of IRI ratings from 2001 to 2004

31956638085350Sum

1100000��

2200000��

3116141000��

261366100��

1371919424890��

1225243136260��

Sum��State

319 sections (~ 319 kilometers) of 3 highways : NH10, NH18, NH4B

Transition matrix P in Tabular Form

100000��

0.5160.4520.032000��

0.5000.2310.2310.03800��

0.1390.1390.3070.3500.0660��

0.0410.1970.2540.2950.2130��

��State

Transition matrix P in Canonical Form

0 0.213 0.295 0.254 0.197 0.041

0 0.066 0.350 0.307 0.139 0.139

0 0 0.038 0.231 0.231 0.500

0 0 0 0.032 0.452 0.516

0 0 0 0 0 1

Transition matrix P in Canonical Form/Illustration

0 0.213 0.295 0.254 0.197 0.041

0 0.066 0.350 0.307 0.139 0.139

0 0 0.038 0.231 0.231 0.500

0 0 0 0.032 0.452 0.516

0 0 0 0 0 1

Classification of road conditions in 2001 and 2004 based on investigated data

319319Sum

561��

632��

8031��

8526��

35137��

0122��

20042001

Number of road sectionsState

Initial probability vector is the initial probability distribution on the set of states in 2004

( )0, 0.110, 0.266, 0.251, 0.197, 0.176π =

Calculation probability vector ππππ

0 0.213 0.295 0.254 0.197 0.041

0 0.066 0.350 0.307 0.139 0.139

0 0 0.038 0.231 0.231 0.500

0 0 0 0.032 0.452 0.516

0 0 0 0 0 1

( )0, 0.110, 0.266, 0.251, 0.197, 0.176= ×

0.176)0.197,0.251,0.266,0.110,(0.000,ππππ(0) (0) (0) (0) =

( )1Pπ π=

0.651)0.190,0.103,0.049,0.007,(0.000,ππππ(1) (1) (1) (1) =

. . .. . .. . .. . .

Given Transition Matrix P, Initial probability vector ππππ , and ( )n n

Pπ π=

Number of sections in state �� 319 x 0.651 = 208

Given Transition Matrix P, Initial probability vector ππππ , and ( )n n

Pπ π=

0.999)0.001,0.000,0.000,0.000,(0.000,ππππ(4) (4) (4) (4) =

0.989)0.009,0.002,0.000,0.000,(0.000,ππππ(3) (3) (3) (3) =

0.920)0.059,0.017,0.004,0.000,(0.000,ππππ(2) (2) (2) (2) =

0.651)0.190,0.103,0.049,0.007,(0.000,ππππ(1) (1) (1) (1) =

0.176)0.197,0.251,0.266,0.110,(0.000,ππππ(0) (0) (0) (0) =

Predicted number of road sections in each condition state in the future

1231261371222001

319000002016

316310002013

2931951002010

208613316202007

566380853502004Number of

road section in

��State

Absorbing State

Deterioration of selected road sections according to the first

maintenance scenario

2004 2007 2010 2013 2016

Time (Year)

State (1) State (2) State (3) State (4) State (5)

State (6) Total

Time RemainTime RemainTime RemainTime Remain

Maintenance & Repair Scenarios considered

The first scenario:

natural deterioration.

The third scenario: conducting

periodic maintenance or repair at

higher scale and wider scope to

avoid being in states 5555 and ��

The second scenario:

conducting periodic

maintenance or repair to

avoid being in state ��

Modelling 2nd Maintenance & Repair Scenario

0 0.213 0.295 0.254 0.197 0.041

0 0.066 0.350 0.307 0.139 0.139

0 0 0.038 0.231 0.231 0.500

0 0 0 0.032 0.452 0.516

0 0 0 0 0 1

0 0 0 0 0 0

0 1 0 0 0 0

0 0 1 0 0 0

0 0 0 1 0 0

0 0 0 0 1 0

1 0 0 0 0 0

Q1 = P. R1

0 0 0 0 0 0

0 1 0 0 0 0

0 0 1 0 0 0

0 0 0 1 0 0

0 0 0 0 1 0

1 0 0 0 0 0

0.041 0.213 0.295 0.254 0.197 0

0.139 0.066 0.350 0.307 0.139 0

0.500 0 0.038 0.231 0.231 0

0.516 0 0 0.032 0.452 0

1 0 0 0 0 0

��

��=

��

( t ) ( t' ) (t + 1) ( t ) (t + 1)P R1 Q1=PR1

0 0.213 0.295 0.254 0.197 0.041

0 0.066 0.350 0.307 0.139 0.139

0 0 0.038 0.231 0.231 0.500

0 0 0 0.032 0.452 0.516

0 0 0 0 0 1

Given Transition Matrix Q1 , Initial probability vector ππππ , and( )

nnQπ π= ×

0.000)0.200,0.167,0.152,0.089,(0.391,ππππ(7) (7) (7) (7) =

0.000)0.200,0.167,0.152,0.089,(0.391,ππππ(6) (6) (6) (6) =

0.000)0.199,0.168,0.153,0.089,(0.390,ππππ(5) (5) (5) (5) =

0.000)0.200,0.165,0.152,0.092,(0.391,ππππ(4) (4) (4) (4) =

0.000)0.205,0.169,0.143,0.072,(0.411,ππππ(3) (3) (3) (3) =

0.000)0.187,0.182,0.196,0.139,(0.295,ππππ(2) (2) (2) (2) =

0.000)0.190,0.103,0.049,0.007,(0.651,ππππ(1) (1) (1) (1) =

0.176)0.197,0.251,0.266,0.110,(0.000,ππππ(0) (0) (0) (0) =

0645349281252025

0645349281252022

0645449281242019

0645348291252016

0655446231312013

060586344942010

061331622082007

566380853502004

Number of

road sections in

��State

Steady State

Deterioration curves of selected road sections according to the

second maintenance scenario

2004 2007 2010 2013 2016 2019 2022 2025

Time (Year)

State (1) State (2) State (3) State (4)

State (5) State (6) Total

064534928125

��

Modelling 3rd Maintenance & Repair Scenario

0 0.213 0.295 0.254 0.197 0.041

0 0.066 0.350 0.307 0.139 0.139

0 0 0.038 0.231 0.231 0.500

0 0 0 0.032 0.452 0.516

0 0 0 0 0 1

0 0 0 0 0 0

0 1 0 0 0 0

0 0 1 0 0 0

0 0 0 1 0 0

1 0 0 0 0 0

Q2 = P. R2

0 0 0 0 0 0

0 1 0 0 0 0

0 0 1 0 0 0

0 0 0 1 0 0

1 0 0 0 0 0

0.238 0.213 0.295 0.254 0 0

0.277 0.066 0.350 0.307 0 0

0.731 0 0.038 0.231 0 0

0.968 0 0 0.032 0 0

1 0 0 0 0 0

��

( t ) ( t' ) (t + 1) ( t ) (t + 1)P R2 Q2=PR2

Modelling 3rd Maintenance & Repair Scenario

Given Transition Matrix Q2 , Initial probability vector ππππ , and

nnQπ π= ×

0.000)0.000,0.209,0.191,0.112,(0.489,ππππ(7) (7) (7) (7) =

0.000)0.000,0.209,0.190,0.112,(0.489,ππππ(6) (6) (6) (6) =

0.000)0.000,0.210,0.190,0.109,(0.491,ππππ(5) (5) (5) (5) =

0.000)0.000,0.209,0.195,0.120,(0.477,ππππ(4) (4) (4) (4) =

0.000)0.000,0.207,0.172,0.084,(0.538,ππππ(3) (3) (3) (3) =

0.000)0.000,0.230,0.253,0.180,(0.337,ππππ(2) (2) (2) (2) =

0.000)0.000,0.103,0.049,0.007,(0.841,ππππ(1) (1) (1) (1) =

0.176)0.197,0.251,0.266,0.110,(0.000,ππππ(0) (0) (0) (0) =

006761361562025

006761361562022

006761351572019

006762381522016

006655271712013

007481571082010

00331622682007

566380853502004

Number of road section

in year

��State

Steady State

Deterioration curves of selected road sections according to

the third maintenance scenario

2004 2007 2010 2013 2016 2019 2022 2025

Time (Year)

State (1) State (2) State (3) State (4)

State (5) State (6) Total

00676136156

��

Contents

Part 1. Part 2. Part 3.Part 1.

Introduction Road System

Part 2.

Develop Prediction Model

Part 3.

Part 4.

Conclusion

CONCLUSION

Predicting the deterioration process of road infrastructure is always the significant and challenging task for road management agencies to ensure the effectiveness of the maintenance and management work.

Using prediction model based upon Markov chain of stochastic process, future condition state of roads are definitely determined. Consequently, the most proper scenario of road maintenance should be established.

Given the required quality of the roads, the maintenance scenario of minimum life cycle cost should be specified. Otherwise, given the limit allocated budget, by using predictionmodel the maintenance scenario of highest quality gained also ispointed out.

Will be presentated in “Life Cycle Cost Analysis (2)”.

dinhthao200277@yahoo.com

Nguyen Dinh Thao, UTC

Thank you very much for your attention!

SEPTEMBER 25 - 27, 2007psa2.kuciv.kyoto-u.ac.jp/lab/images/stories/gaikoku...Road Infrastructure...

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