This document discusses using Markov chain theory to model the deterioration of bridge structures over time based on discrete condition data. It aims to improve bridge management systems by more accurately predicting deterioration rates. The document outlines current bridge inspection practices, limitations of existing condition rating schemes, and proposes using a Markov chain model with a transition probability matrix to better represent the probabilistic nature of deterioration. It describes collecting bridge condition data from inspections to analyze deterioration curves and inform maintenance planning.

1. Deterioration Forecasting of Bridge Structures Using Discrete
Condition Data
Tuan Minh Lac
RMIT University, Melbourne, Australia, 3001
Email: S3199687@student.rmit.edu.au
Abstract: Forecasting bridge deterioration is an important aspect of bridge management system in
term of optimising the maintenance phase by financial evaluation and risk analysis of infrastructure
asset. It helps to understand the current stage of bridge condition and develop an economical
decision to ensure sustained serviceability and safety of the structure. A main critical issue facing by
local government firm such as VicRoads in Victoria, Australia is the capability to predict with
reasonable accuracy of maintenance activities that may include total replacement of the structure.
Current use of level 2 bridge inspection poses high uncertainty from the condition rating scheme given
a rating between 1 and 4 where 1 is the best condition and 4 is the worst. The condition rating
scheme is largely dependent on the selection bias that possible contain measurement errors which
tend to weaken the accuracy of the result; that is unable to describe accurately the nature of
deterioration.
This paper will adopt Markov chain theory for deterioration modelling of bridge condition. The
application of this method will use data pool from earlier VicRoads “Level 2” inspection scheme in
order to present graphically the deterioration curve versus time.
Keywords: Bridge management system, Level 2 condition rating, Markov chain theory, Financial
evaluation.
INTRODUCTION
Bridges are part of transportation infrastructure and play an essential role in the development of the
economic and community welfare of the Victoria, Australia. There are large scale of existing concrete
bridges in Victoria continue to age at various stage (Steward, 2001). It is priority to conduct an
effective maintenance schedule for these bridges in order to keep the infrastructure facilities under
high grade condition at all times and satisfy public service under no interruption to the traffic. That is
accurately monitoring against any defect for appropriate repair and rehabilitation must carry out at the
right time. Bridge management system was introduced in the last few decades to assist with the
outline above. The system requires the following tasks: “condition assessment of the structure,
forecasting the rate of deterioration, cooperate maintenance schedule with corresponding financial
funding.
The condition assessment of a structure reveals its state in relation to the structure’s resistant to the
loading capacity and environment conditions. Overtime, the bridge will age to be different from the
original design and construction under deterioration behaviour. That is the rate of deterioration implies
the prediction of the remaining lives as well as future performance of the bridges or decay of the
bridge performance over time. Current use of the VicRoads Level 2 inspection rating scheme is limit
to represent the futuristic of the deterioration rate and quote a need to develop a model to meet the
requirement. Several methodologies were introduced to satisfy this objective and outline in the
literature review.

2.  Project Goals
The goal of this project is to escalate the performance of bridge management system by using an
appropriate methodology to overcome the limitation of existing Level 2 inspection condition rating
scheme. This methodology will allow VicRoads to implement bridge management system to develop a
model base on the historical data source from the inspection. The success of a bridge management
system is dependent largely of the precise estimation the nature of deterioration over time period
either as individual component or complete structural scanned.
PROPOSE METHODOLOGIES
This activity will establish the general background to gain sufficient knowledge and understanding on
the current issues and gaps in the development of VicRoads bridge management system. The review
will explore the existing available application of forecasting bridges deterioration. The application
includes the deterministic models, artificial intelligence models and stochastic models focusing
Markov approach method for this investigation.
Deterministic models:
A model using mathematical in which the outcomes represent through a known relationship between
the factors affecting facility deterioration and condition of the facility without the availability of random
variation. The model assumes that future bridge performance is known with certainty. A commonly
used deterministic model is the regression function obtains by doing a regression analysis on
historical bridge data (Veshosky et al 1994). This model can pull limitation from predicting the
average condition bypass the effect of condition of individual’s facilities (Madnat 1995, Jang and
Sinha 1989). The impact of deterioration mechanisms of bridge deck and the deck joints are not in
consideration of this model (Sianipar and Adams, 1997). Deterministic model will trouble to update
new data because of high difficulty. Also it underestimates model error from the cause of the
optimization best fit and that is any miss prediction indicates a model failure.
Artificial intelligence models:
Artificial intelligence (AI) models perform computer information-processing to develop forecast models
inspired by the densely interconnected, parallel structure of human brain process information
(Aleksander and Morton,. 1990). AI interacts with range of systems, artificial neural networks (ANN),
genetic algorithm (GA), and case based reasoning (CBR). A statistical analysis identify significant
factors influencing the deterioration where treating the deterioration as a pattern classification problem
and eleven parameters of the decks are identified to enhance the model(maintenance history, age,
previous condition, district, design load, deck length, deck area, environment, degree of skew,
number of spans, average daily traffic). An investigation has been made by Ying-Hua Huang (2000),
propose fully connected and layered feed-forward networks using back-propagation approach
multilayer perceptron (BP-MLP) classifier using the Artificial Neural Network prediction model for deck
deterioration. Using this method with the three ways cross validation from records of 942 concrete
decks of Wisconsin database, prediction model reaches classification rate of 84.66% and 75.39% for
training sets and the testing sets, respectively.
These results are highly significant that AI models adopt BP-MLP promise to be another possible
prediction tool.
Optimisation method follows the success of Artificial intelligence models was conducted associate
with high cost due to the computation process generating a large data output. An introduction of
hybrid optimisation method is to filter out feasible condition ratings as optimisation scheme for Neural
Network in predicting long term deterioration of the bridges (Callow D, Lee J., Blumenstein M., Guan

3. H., Loo Y. C. 2012). Case base reasoning is used to reduce the number of possible cases for a
bridge, but can still leave a large amount of possibilities. A hybrid process consisting of both Case
Base Reasoning – efficient in testing process and Genetic Algorithm – high systematic processes will
ensure that the possible cases are optimised to their best potential. The development of the hybrid
optimisation method of Case Based Reasoning and Genetic Algorithm ensures consistently optimised
bridges with accurate future predictions of deterioration. The advancement of the hybrid optimisation
method using both GAs and CBR techniques as in the following:
 Optimisation is performed at a much early stage where unreliable condition ratings are
eliminated thereby reducing the source of uncertainties;
 When an optimised set of condition ratings is used as input values for the current AI-based
deterioration model, the prediction errors will be greatly reduced;
 The computational time required for long-term prediction will also be reduced greatly.
This advancement aims to improve in the accuracy and reliability of current deterioration modelling
and to allow accurate future predictions to be calculated. And that is accurate future predictions were
made possible due to the optimised future validation values resembling the real input values. The final
result was a more reliable rate of deterioration. This means a more accurate Bridge Management
System could be developed. With future prediction decay rates being more reliable, it is easier to
calculate a bridge's expected life more accurately
Stochastic models (Markov approach method):
Markov models is recognised in modelling the deterioration of bridge structure as an effective solution
to support decision making on maintenance, whether individual component or complete structure in
rehabilitation. Using a Markov chain models, enable the ability to predict the bridge condition as a
probabilistic estimate base on Level 2 rating scheme resources and display a nature of deterioration
precisely with time interval. Most of the experienced researchers and infrastructure asset
management practitioner agreed upon the nature of deterioration of infrastructure facilities is not
deterministic (Mishalani and McCord, 2006). Because deterioration is uncertain over time, it should
ideally be represented as a stochastic processes base on the Markov chain theory (JIANG et al
1989).
The Markov modelling is considered together with an optimal maintenance strategy is developed by
using the Markovian transition probability matrix for individual bridges can be determined by
considering bridge features and circumstances such as environment, width and length of bridge, and
traffic quantity.
Markov property is founded on two fundamental rules for transition probability: past independency and
homogeneous (Ng S. K., Moses F. 1998). That is past independency suggest future states of the
process depend only on the current state and not how the current states had been reached.
Homogeneous requires a rate of transition from one state to another remain constant throughout the
time. Consider a set of states, S = {s1, s2,…,sT}. The process starts in one of these states and moves
successively from one state to another. The Markov-chain model assumes that a bridge can either
remain in the current state or deteriorate to the next lower state where the worst state space is
considered an absorbing state. By convention, all possible states and transitions have been included
in the definition of the processes, so there is always a next state and the process goes on forever If
the chain is currently in state si, then it moves to state sj at the next step with a probability denoted by
pij, and this probability does not depend upon which states the chain was in before the current state.
The probabilities pij are called transition probabilities. The process can remain in the state it is in
which is called holding time, and this occurs with probability pij.
The stochastic nature of deterioration process may be described as transition probability matrix (P) is
developed for the condition rating level 2 of individual bridge components and valid with one transition

4. matrix for the whole life span. The stochastic nature of the deterioration process can be described in
the format of:
[ ]
In order to develop a transition matrix, two approaches will be in consideration, the frequency
approach and the regression approach. By definition, frequency approach would require at least two
sets of inspection data pertaining to two different points in time. On the other hand, regression
approach only one set of bridge data is needed. The regression-based optimisation method is the
most-commonly used approach in estimating transition matrices for different types of facilities, such
as pavements and bridges (Bulusu and Sinha, 1997). This method uses a non-linear optimization
function to minimize the sum of absolute differences between the regression curve that best fits
the condition data and the conditions predicted. In this investigation, calculate the probability
transition matrix from condition data is the percentage prediction method. This approach is can be
obtained directly from the condition data.
Level 2 bridge inspection model
The process of apply an inspection to assess and rate the condition of the structure to identify the
current maintenance needs. These inspections carry out a visual inspection of bridge components
including measurement of crack width (according with Bridge inspection manual part 3.8.5) and an
assessment of condition using a standard condition rating system to represent the stage of
deterioration. As such fundamental requirement to produce consistent result shall be taken with state
description as table below and classification of the degree of deterioration with regard to environment
affecting.
Table1: Bridge Condition Rating:
Condition
State
Subjective
Rating
Description
1 GOOD
(as new)
0% - 20%
Free of defects with little or no deterioration evident
2 FAIR
20% - 45%
Free of defects affecting structural performance, integrity and durability.
Deterioration of a minor nature in the protective coating and/or parent
material is evident.
3 POOR
(monitoring
require)
45% - 60%
Defects affecting the durability/serviceability which may require
monitoring and/or remedial action or inspection by a structural engineer.
Component or element shows marked and advancing deterioration
including loss of protective coating and minor loss of section from the
parent material is evident. Intervention is normally required.
4 VERY
POOR
(Remedial
action
require)
> 60%
Defects affecting the performance and structural integrity which require
immediate intervention including an inspection by a structural engineer,
if principal components are affected. Component or element shows
advanced deterioration, loss of section from the parent material, signs
of overstressing or evidence that it is acting differently to its intended
design mode or function.

5. Individual Component Rating for Deck Units (component 8P) – Level 2 Inspection is recorded to
include:
 Widening
 Structure inventory and photographic record sheet.
 Condition rating sheet.
 Structure defect sheet.
 Structure information sheet.
Condition rating: The component 8P shall be inspected as description provide below and compare
against the accompanying photographs available. The general condition of the structure is including
any bridge widening.
Condition State 1:
The units are in good condition with minor moisture staining and white efflorescence powder visible in
the joints between units. The units may have minor faint cracking or minor edge chipping but no
spalling. The transverse tensioning rods are in good condition, and show no signs of corrosion.
Condition State 2:
The units may have moderate moisture staining with stalactite growths and efflorescence powder
visible but no rust staining due to corrosion of the transverse rods. There may be minor cracks and
spalls but no exposure of the stressing strands. Impact forces have caused minor damage but have
not exposed reinforcement. Fine longitudinal cracking of the soffit and edges of the units near the
supports may be evident as a result of ASR in deck units. The transverse tensioning rods may have
minor surface corrosion
Condition State 3:
The units may have medium moisture staining and efflorescence powder in the joints, along with
heavy rust staining due to corrosion of transverse tensioning rods. The asphalt surface may have
moderate cracking due to differential movement between the units or loss of tensioning force in the
transverse rods. However the anchorages are still tight in the recesses. There may be moderate
cracking and spalling with minor loss of section of the stressing strands due to corrosion. Non-
prestressed reinforcement may be heavily corroded with up to 20 % section loss.
Condition State 4:
The units may have heavy moisture staining and efflorescence powder in the joints with heavy rust
staining due to corrosion of the transverse tensioning rods. The asphalt surface may be badly cracked
or broken along the lines of the precast units. There may be severe cracking and spalling with
substantial loss of section of the non-prestressed reinforcement. Stressing strands may be broken or
have lost up to 10% of section due to corrosion. Transverse tensioning may be loose and the bar
anchorages may have popped clear of the recess.
Measurement of condition rating is carried out to estimate the condition as a percentage and to be the
sum of 100%. The percentage in each condition state is the area affected by the condition divided by
the total area of the component multiplied by 100.
Monitor structure inspection:
VicRoads implemented a monitoring scheme to regular program of engineering inspections to
determine if any signs of structural distress become apparent under repeated loading by traffic
loading condition (i.e heavy vehicle). This scheme was an additional layer of structure inspection
allows a consistent assessment of similar bridges across all regions and enables critical decisions to

6. be made about the important structures and priorities for replacing and rehabilitating bridge units.
Also, it enables Vicroads to undertake an upgrade and replacement program to an acceptable level of
safety.
This monitoring scheme is to verify:
 Sign of distress require short to medium term attention
 Cracking and similar that present for long period, is not considered to medium and long term
structural integrity of the bridge.
 Cracking and similar that is growing at a slow rate
Factors to consider including:
 Total traffic volumes.
 Load capacity assessment of structure.
 Bridge width and alignment.
 Environmental condition.
Data collection
The data was sourced from VicRoads of Victoria and includes the database of 3000 bridges ready to
be extracted detail of each critical component for the investigation. The assessment will then be
carried out for individual component and to display in the same plot of graph. The evaluation of the
behaviour in the graph concludes the pattern that allows a prediction over unit of time.
Bridge Condition Rating:
Table1: Sample data collection for bridge condition rating
Structure SB Chain Year
Constructed
Inspection Date: Inspector BCR
%
Age
229374 21366 35983 B.Kennedy 1 40
279189 21366 39608 JP 7 50
286476 22462 38571 KM 5 44
288841 22462 40167 RH 5 49
Individual Component 8P:
Table2: Sample data collection for individual component 8P
Structure ID Date Constructed Inspection Date: Inspection Condition Rating Age
1 2 3 4
SN5701 30/06/1960 16/12/2005 100 0 0 0 46
SN5714 30/06/1962 19/03/1997 50 50 0 0 35
SN7575 30/06/1961 07/04/1997 100 0 0 0 36
SN6038 30/6/1969 18/12/1999 0 100 0 0 31

7. RESULT AND DISCUSSION
 Overall Condition Rating (OCR)
Figure 1 OCR condition versus age data
An overall condition data was source from VicRoads for deck/slab precast concrete component (8P)
and is represented graphically in Figure-1. Due to the availability of the resource from monitoring
data, only structure ID 2918, 2988, 3216, 5520, 5562, 5585, 5700, 5701, 5714, 5715, 7575 are
reviewed for conditioning of the bridges. The deterioration of these structures was due largely to the
environmental factor as water caused deteriorated in concrete and expose reinforcement to rust.
Water acts as the transport system for nearly all mechanisms aggressive to concrete:
 Porous, water-saturated concrete that does not have adequate strength and entrained air is
prone to scaling, which is a deterioration mechanism caused by freezing of water in concrete
 Water can carry aggressive chemicals into the concrete surface such as acids, sulphates, or
chlorides
 Concrete that contains alkali-reactive aggregates is subject to deleterious expansion from
water
 Water that passes over the surface of concrete with a high velocity can erode the surface
over time
 As iron oxidizes(rusts) it expands, thus cracking the concrete from the inside out, the more it
cracks, the more water gets in and the more rust forms perpetuating a vicious cycle
1
1.2
1.4
1.6
1.8
2
2.2
2.4
2.6
2.8
3
3.2
3.4
3.6
3.8
4
0 10 20 30 40 50 60 70 80 90 100
Condition
Age in year
OCR condition vs age

8.  Markov Modelling
The application of Markov modelling is followed as outline in the literature review using percentage
prediction. The initial condition is assumed to be (1, 0, 0, 0) which represent the probability for 100 %
of the component will be in condition 1 at time zero. Apply the Markov chain prediction method over
100 years, and the result is shown as graph below
Individual Component Rating for Deck Units – component 8P:
Table2: Component 8P matrix transient probability
Matrix transition Initial input Optimisation input
CONDITION 1 2 3 4 1 2 3 4
1 0.93 0.06 0.01 0 0.993306 0.005104 4.0628E-05 0.001549
2 0.00 0.97 0.03 0 0 0.968614 0.03138605 0
3 0.00 0.00 0.95 0.05 0 0 0.93034237 0.069658
4 0.00 0.00 0.00 1.00 0 0 0 1
Figure 2: Transient probabilities for component 8P – Initial stage (left) and optimisation stage (right)
An initial slow deterioration rate with 90% majority remain in condition one and transition to condition
2 at 10% where very small population being in condition 3 and 4. The deterioration rate observed in
figure 2 after 100 year of age with approximately 85% 8P’s population will be in condition 1, 12%
chance of being in condition 2 and 3% being in condition 3, at upper bound of insignificant of staying
in condition 4.
Bridge Condition Rating (BCR):
Table 3: BCR matrix transient probability
Matrix transition Initial input Optimisation input
CONDITION 1 2 3 4 1 2 3 4
1 0.93 0.06 0.01 0 0.971302 0.009796 0.009774 0.009128
2 0.00 0.97 0.03 0 0 0.99931 0.00069 0
3 0.00 0.00 0.95 0.05 0 0 0.998681 0.001319
4 0.00 0.00 0.00 1.00 0 0 0 1

9. Figure 3: BCR transient probabilities – Initial stage (left) and optimisation stage (right)
The deterioration for BCR observe from figure 4 has a high deterioration rates up to approximately 50
years of age and converge saturated of being in all condition at approximately 25% break even.
Afterward the rate of deterioration gradually slow down and at 100 years of age which sharing less
than 10% in 0-20% condition and 30% evenly distributed in other conditions.
CONCLUSIONS
The Markov chain approach was used to derive a complete graphical model using percentage
prediction by develop transition matrix from the discrete rating data from VicRoads Level 2 Rating
Condition. Base on the available data for this investigation, some preliminary conclusion can be
withdrawn such Individual component 8P slab/deck unit is observed to have slower rate of
deterioration in comparison to overall Bridge Condition Rating (BCR) and have minimal effect on
planning maintenance of the overall bridge structure. On the other hand, the result of the model
shows a close relationship in comparison against monitoring report can further verify the effectiveness
of the Markov model.
Due to the limitation in the data resources, a better outcome can be archived where more inspection
data were provided, records of maintenance were available, and a separate monitoring report were
made available focus on the component 8P of over 50 remaining structures. (ie.SN9333, SN6038…)
CONSIDERATION FOR FURTHER WORK
 Expand the database by collecting data from other region in Victoria and improve accuracy of
the Markov model.
 Develop deterioration models for all bridge components to generate an overall bridge
condition rating.
 Prediction of cost - financial planning where cost can be seen by C
s
= from a
transition from one state “ ” to another state “j”. The cost of a transition is “m x m” matrix is C
R
= ( . Expected cost (Jensen and Bard 2003) given by:
∑
ACKNOWLEDGEMENT
This research paper would not have been possible without the help and support from my principal
supervisor, Dr Sujeeva Setunge and PhD student Md Saeed Hasan. It has been a valuable
experience on both an academic and a personal level, for which I am extremely thankful.

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