Modeling of Combined Deterioration of Concrete Structures by Competing
Hazard Model
Kiyoyuki KAITOAssociate Professor
Frontier Research Center
Osaka Univ., Osaka, Japan

Koichi SUGISAKI
Senior Reseacher
BMC Corp.
Chiba, Japan

Kiyoyuki KAITO, born 1972,
received his civil engineering
degree from the Univ. of Tokyo.

Koichi SUGISAKI, born 1976,
received civil engineering degreefrom Tokyo Institute ofTechnology.

kaito@ga.eng.osaka-u.ac.jp

sugisaki@hashimori.jp

Kiyoshi KOBAYASHI
Professor, Vice Dean
Graduate School ofManagement, Kyoto Univ.
Kyoto, Japankkoba@psa.mbox.media.kyotou.ac.jp
Kiyoshi KOBAYASHI, born
1952, received civil engineering
degree from Kyoto Univ.

Summary
In asset management of infrastructures, predicting deterioration of structures is one of an essential
technique. However, in order to estimate their deterioration process with high accuracy, not only
single cause deterioration but also combined deterioration appearing on for example concrete
structures has to be considered. Therefore this paper addresses the competing hazard model whichis possible to model complex deterioration by multiple causes, and especially focuses on that
deterioration by neutralization and salt attack on concrete bridges. Specially, separately
deteriorations by them are formulated by the Weibull hazard model that can express the timedependent deterioration phenomena. Employing this model, the phenomena of which deterioration
probability is increasing with time can be described. Furthermore, the complex deterioration isformulated by neutralization hazard rate’s linearly affecting salt attack one.
Keywords: Competing hazard mode; combined deterioration; corrosion; statistical deterioration
prediction; asset management.

1. Introduction
As a method for maintaining and managing social infrastructures efficiently, asset management is
attracting attention. At the first stage of asset management, it is extremely important to predict how
deterioration proceeds in structures from a macro perspective. In this circumstance, as deterioration
prediction technology, a statistical method, in which a prediction model is statistically developed
based on inspection data, has been proposed. Especially, in recent years, a large amount of data
have been accumulated through the research into deterioration prediction methods utilizing hazard
models[1], which indicates that their practicalities are high. However, the conventional deterioration
prediction model targets the damage caused by a single factor and describes its deterioration
process. Meanwhile, under the situation where structural and material characteristics are diversified
and the usage and environmental conditions vary like social infrastructures, there are many events
that have many factors in causing the same damage state. Moreover, such damaging events can beclassified into the following two events: (1) deterioration events in which each of several factors
proceeds independently and then the most rapid factor becomes significant, and (2) complex
deterioration events in which some of several factors are compounded during the deterioration
process and accelerate the deterioration process. As a representative complex deterioration, thecorrosion of reinforcing bars inside concrete structures can be enumerated. The corrosion ofreinforcing bars is considered due to salt damage and neutralization, and there are experimental
results that the process of neutralization accelerated the process of salt damage. In addition, thecracking due to the combination of freezing damage & salt damage or alkali aggregate reaction &salt damage can be said to be complex deterioration, because if one event proceeds, the other event
takes the catalytic role, accelerating the deterioration process. Furthermore, with respect to steel
materials, there is no fatigue limit in repeated stress under the corrosion condition, and so there is apossibility that corrosion will increase the probability of fatigue crack no matter the value of
repeated stress. Therefore, the development of a model of the deterioration process caused by morethan one factor independently or jointly can be said to be a useful technology that would contributeto the advance of asset management.

Considering the above mentioned issues, the objective of this study is to establish a deterioration
prediction model that takes into account compounded deterioration events, by using a competing
hazard model. In the following sections of this paper, Chapter 2 formulates a Weibull deterioration
hazard model that takes into account the competitive nature among several factors, by using twomodels that were classified based on whether or not the competitive nature depends on time.
Chapter 3 focuses on complex deterioration by the two competing factors: neutralization and salt
damage, targeting concrete structures, and estimates the timing of the corrosion of reinforcing bars,
using actual inspection data, and empirically analyzes the effectiveness of the proposed model. The
following chapters mention the reinforcement corrosion inside concrete structures as a specifictarget for a competitive deterioration hazard model. Needless to say, it is possible to apply thismodel to other damage and deterioration phenomena.

2. Competing Weibull hazard model
2.1 Formulation of a competitive hazard model
The authors construct a model of the complex deterioration phenomenon related to thereinforcement corrosion inside concrete structures, using a hazard model. The target concrete
members are represented by i ( i = 1,..., K ), and the elapsed time from the start of use of the member ito present is denoted by ti. In addition, it is assumed that there is more than one factor ( j = 1,..., J ) in
reinforcement corrosion at the concrete member i. Here, it is assumed that the elapsed time ζ i (lifespan) until reinforcement corrosion occurs at the member is a random variable and is subject to theprobability density function f j (ζ i ) and the distribution function F j (ζ i ) for each factor j. Here, thedomain of the life-span is [0, ∞ ) . In addition, the probability F~j (ζ i ) that reinforcement corrosion
will not occur for ti years can be expressed by the following equation:~
Pr ob{ ζ i ≥ t i } = F (ζ i ) = 1 − F j (ζ i )(1)

The conditional probability that reinforcement corrosion does not occur at the member i until thearbitrary timing ti and then reinforcement corrosion occurs due to the factor j during the period[t i , t i + Δt i ) can be expressed by the following equation:
λ j (t i )Δt i =f j (t i )Δt i~
F (t i )(2)

where λ j (t i ) represents the hazard function for each corrosion factor j, which is discriminated fromthe hazard function that takes into account all corrosion factors. This equation indicates that thehazard function is probability density. Furthermore, the partial survival distribution function andpartial density function for each corrosion factor can be expressed by the following equations, using
Equations (1) and (2), respectively [1]:t~(3)
F j (t i ) = exp − ∫ λ j (u )du

{

}

i

0

{

ti

f j (t i ) = λ j (t i ) exp − ∫ λ j (u )du
0

}

(4)

Next, the hazard~ function for all corrosion factors is defined. Since the survival distribution function
for all factors F (t i ) is the probability that any corrosion factor does not trigger~ corrosion, that is,
the joint probability of the partial survival distribution function for each factor F j (t i ) ( j = 1,..., J ) ,J~~
F (t i ) = ∏ F j (t i )

(5)

j =1

By substituting Equation (3) into Equation (5), the equation can be arranged as follows:

{

}

J
ti
⎧ ti J⎫~F (t i ) = ∏ exp − ∫ λ j (u )du = exp⎨− ∫ ∑ λ j (u )du ⎬
0
0
j =1
j =1
⎩
⎭

(6)

By defining the hazard function for all factors λ (t i ) like Equation (3) and comparing it with

Equation (6), the following equation is obtained.
Jλ (t i ) = ∑ λ j (t i )

(7)

j =1

Likewise, the probability density function of all factors can be expressed as follows, based on therelation of Equation (2).
J~~f (t i ) = λ (t i ) F (t i ) = (λ1 (t i ) + L + λ J (t i ) )F (t i ) = f 1 (t i ) + L + f J (t i ) = ∑ f j (t i )

(8)

j =1

2.2

Competing Weibull deterioration hazard model

2.2.1 Hazard model in which the competitive nature does not depend on time
A concrete functional form is provided for the hazard function, and the competing hazard model is
specified. In this study, the Weibull deterioration hazard model is applied, while assuming that theprobability of reinforcement corrosion increases with time. Here, the exponential deterioration
hazard model in which the probability of reinforcement corrosion does not depend on time is a
special form of the Weibull deterioration hazard model.
Here, as deterioration factors, neutralization (deterioration factor 1), salt damage (deterioration
factor 2), and complex deterioration are specified. Suppose that deterioration proceeds inside theconcrete structure i because of neutralization (deterioration factor 1) only. The hazard function for
deterioration factor 1 at arbitrary timing ti can be defined with the following equation as a general
Weibull deterioration hazard model.

λ1 (t i ) = γ 1m1t i m −1

(9)1

where γ 1 is the parameter representing the arrival rate of corrosion, and m1 is the acceleration
parameter representing the time dependency of the hazard function. When the acceleration
parameter m1 is equal to 1, the hazard function corresponds to the exponential deterioration hazard
model that does not depend on time. When the Weibull deterioration hazard function is used, thesurvival distribution function can be expressed by the following equation:
ti
~
m
(10)
F1 (t i ) = exp − ∫ λ1 (u )du = exp(−γ 1t i 1 )

{

0

}

Next, let us define the hazard function at the timing ti in the case where deterioration proceeds
because of salt damage (deterioration factor 2). In this case, the complex deterioration phenomenon
between salt damage and neutralization (deterioration factor 1) is also taken into account, and so thefollowing equation is defined:

λ 2 (t i ) = {γ 2 + δ iαγ 1 }m 2 t i m −1
2

(11)

In the above equation, that is, the hazard function for salt damage (deterioration factor 2), it isassumed that when complex deterioration is observed, the arrival rate parameter of thereinforcement corrosion due to deterioration factor 2 γ 2 is linearly influenced by the arrival rate
parameter due to deterioration factor 1 γ 1 . Namely, this formulation is made so that the hazard
functions for neutralization and salt damage do not influence each other, but neutralization
unilaterally influences salt damage. Here, δi is the dummy variable:⎧ 1 when complex deterioration occurs⎩ 0 otherwise

δi = ⎨(12)

As mentioned later, it is possible to obtain the information on whether or not complex deterioration
has occurred, through visual inspection or the like. In addition, α is the parameter representing thedegree of the influence of neutralization on the hazard function for salt damage. When thecompetitive nature is defined based on Equation (11), the competitive nature becomes constantregardless of time t. This basic model is hereinafter called “Model I.” In addition, the survival

distribution function for salt damage (deterioration factor 2) is expressed by the following equation:

{

}

{

ti
~
m2
F2 (t i ) = exp − ∫ λ 2 (u )du = exp − (γ 2 + αδ i γ 1 )t i 2
0

}

(13)

Accordingly, the unknown parameters, which are estimated by the competitive hazard model for
reinforcement corrosion, are the following five: the corrosion arrival rate parameters: γ 1 and γ 2 ,the acceleration parameters: m1 and m2, and the influence degree parameter: α.
2.2.2 Hazard model in which the competitive nature depends on time
It is assumed that the speed of the concentration of chloride ion, which is the determinant ofreinforcement corrosion, changes (increases) with time. Here, it is possible to define the hazard
model for salt damage (deterioration factor 2) taking into account the time dependency of thecompetitive nature as follows:
λ 2 (t i ) = {γ 2 + δ i αλ 1 (t i )}m 2 t i m −1

(14)

2

The hazard model in which the time dependency of the competitive nature is described is called
Model II. While Model I is constructed under the assumption that the influence of neutralization on
salt damage is represented by the corrosion arrival rate parameter γ 1 , Model II assumes that thisinfluence is represented by the hazard function λ1 (t i ) . In this case, the survival distributionfunction for salt damage is expressed by the following equation:

{

} {

}

m + m −1
⎧⎪
⎫⎪
ti
ti
ti 1 2~m2
m2 −1
F2 (t i ) = exp − ∫ λ 2 (u )du = exp − ∫ {γ 2 + αδ i λ1 (u )}m 2 u du = exp⎨− γ 2 t i − α 1δ i γ 1 m1 m 2⎬
00
m1 + m 2 − 1⎪⎭
⎪⎩

(15)
2.3

Estimation method

2.3.1 Contents of inspection data
Suppose that K visual inspection data regarding concrete structures have been obtained. The
inspection data is composed of mainly “inspection results” and “characteristic information.”
Inspection results have the information on whether or not reinforcement corrosion has occurred andthe factors in corrosion (neutralization, salt damage and complex deterioration) for each inspection
data sample i ( i = 1,..., K ). On the other hand, for characteristic information, the structural, usage,and environmental conditions that would influence reinforcement corrosion are recorded.
Firstly, inspection results are described. Out of K inspection data samples, the samples in which
reinforcement corrosion has occurred are classified as follows, for each factor: neutralization andsalt damage. (Since complex deterioration is expressed in the hazard function for salt damage, thisis included in the salt damage samples in this discussion.) The population of the samples in which
reinforcement corrosion has occurred due to the factor j is represented by Φ j , and the total numberof such samples is represented by K(j), and the k-th sample of Φ j is denoted by ( j , k ) . In theabove discussions, samples are distinguished by using “i” but in the following discussions, samples
are discriminated by using ( j , k ) . Accordingly, the population of the samples in which
reinforcement corrosion has occurred due to neutralization (deterioration factor 1, j = 1) isrepresented by Φ 1 , the total number of such samples is K(1); those for salt damage (deterioration
factor 2, j = 2) are Φ 2 and K(2), respectively. On the other hand, the sound condition samples inwhich reinforcing bars did not corrode are defined as j = 0. Obviously, there is the following
relation:
K (0) + K (1) + K ( 2) = K(16)

In this study, it is assumed that after the occurrence of reinforcement corrosion is confirmed,
corrosion factors are identified through inspection. In this assumption, ordinary visual inspection isconsidered. However, it is noteworthy that corrosion factors can be identified before the occurrenceof reinforcement corrosion through the core-sampling test or the like. Based on the above
mentioned definitions and assumptions, it is possible to describe the information on the occurrenceof reinforcement corrosion and the factors in corrosion (neutralization and salt damage), regardingconcrete structures ( j , k ) . In addition, the elapsed time of the sample ( j , k ) is represented by t jk .
With regard to complex deterioration, the dummy variable in Equation (12) is redefined as δ jk , andin the salt damage sample ( 2, k ) , it is possible to check whether or not complex deterioration is the
corrosion factor.
Next, characteristic information is described. It is assumed that the start timing of the corrosion ofreinforcing bars depends on the material and environmental characteristics of concrete structures.
Accordingly, the structural, usage, and environmental characteristics that would influence thecorrosion factors: neutralization and salt damage are specified. For each factor, the characteristic
vector is represented by x jk = ( x 1jk , x 2jk ) . Here, the subscripts 1 and 2 denote neutralization and salt
damage, respectively. In addition, x 1jk = ( x1jk ,...., x ejk1 ) , x 2jk = ( x1jk ,...., x ejk2 ) , and e1 and e2 represent
the total numbers of characteristic information that would influence respective factors. Accordingly,
the information on concrete structures ( j , k ) that can be obtained through visual inspection can be
expressed by ξ jk = (t jk , δ jk , x jk ) .
2.3.2 Estimation of unknown parameters with the maximum-likelihood method
In order to estimate the competing Weibull deterioration hazard model based on the inspection data
population ξ , it is assumed that the differences in corrosion occurrence due to the structural, usage,and environmental conditions can be expressed by the arrival rate of corrosion: γ jk , which isrepresented by a characteristic vector as follows:′

γ jk = exp(β j x jk )j = 1,2(17)

where β j = ( β j 1 , β j 2 , L , β j ej ) is the row vector composed of unknown parameters. The symbol ’ in
the above equation denotes transposition. Accordingly, the characteristic information on eachconcrete structure: x jk , which can be obtained through inspection, is reflected in the arrival rate
parameter. Therefore, the later-mentioned estimation of unknown parameters can be considered as
the estimation of β j rather than the direct estimation of the arrival rate parameter γ jk . Then, theunknown parameters that should be estimated are β1 , β 2 , m1, m2, and α. These are represented byθ = (β, m, α ) .
Next, when the k-th sample ( j , k ) in which corrosion factor j ( j = 1,2 ) induces reinforcement
corrosion is focused on, the likelihood function of the sample can be expressed by the following
equation, based on Equations (2) and (5).
J
~
~
~
~
L jk (θ ) = f j (t jk ) = λ j (t jk ) F (t jk ) = λ j (t jk ) F1 (t jk ) L F j (t jk ) = λ j (t jk )∏ Fh (t jk )

(18)

h =1

On the other hand, the likelihood function of the sound condition sample (either factor does not
induce damage; j = 0), in which reinforcement corrosion did not occur, is expressed as follows:J~~
L0 k (θ ) = F (t 0 k ) = ∏ Fh (t 0 k )

(19)

h =1

Furthermore, the sum of log likelihoods for all samples is expressed as follows:J

K ( j)ln L(θ ) = ∑ ∑ ln L jk (θ )(20)

j = 0 k =1

When the maximum-likelihood method is used, the maximum likelihood estimator of the parameterθ that maximizes the log likelihood function (20) can be obtained as θˆ that satisfies the following
relation:∂ ln L(θˆ)
=0
∂θ

(21)

Table 1 Overview of Used Data (total number of samples: 145)
AverageStandard Deviation

Age

46.2

19.4

Neutralization Depth [mm]

38.3

9.0

Chloride Ion Concentration at Reinforcing Bars [kg/m3]

1.1

1.4

Table 2 Reference Values for Estimating Reinforcement Corrosion
Neutralization
Salt damage
Complex deterioration

Used data

Reference Value

Neutralization residue
Chloride ion concentration(whole salt content)
Initial chloride ion amount

25mm
1kg/m3
1kg/m3

3. Empirical Study
3.1 Overview of inspection data
In this study, the authors could use the diagnostic data of the core extraction test, which is detailed
investigation, in addition to visual inspection. Table 1 shows the averages and variances of age,neutralization depth, and chloride ion concentration at reinforcing bars, which are considered toinfluence reinforcement corrosion, for all of 145 samples. The samples were taken from concrete
structures near the shoreline, and so chloride ion concentration is high as a whole. With regard toage, variation is relatively large. The necessary explained variables for this model are the twovalues representing whether or not reinforcement corrosion has occurred. However, in order toestimate the competing deterioration hazard model, it is necessary to clarify which is the factor in
reinforcement corrosion; neutralization, salt damage, or complex deterioration. In this study, inorder to infer the factor in reinforcement corrosion, the authors focused on “neutralization residue”
for neutralization, “chloride ion concentration” for salt damage, and “initial chloride ion amount”
for complex deterioration, and then obtained actual measurement values through the core extraction
method targeted at corrosion-seen samples. The factor in reinforcement corrosion was identified bycomparing the actual measurement values with the reference values (thresholds) shown in Table 2.
Practically, there are some cases in which it is impossible to conduct the core extraction test for all
samples. In such a case, the factor in reinforcement corrosion is determined based on the subjective
judgment by inspectors or engineers.
With regard to neutralization, the reference value of neutralization residue in the specification is 10
mm, but it is known that the actual measurement value of covering depth varies considerably.
Therefore, with regard to neutralization, considering safety and assuming that the specified value ofcovering depth varies from 15 mm to 40 mm, it was recognized that when neutralization residue
exceeds 25 mm, reinforcement corrosion occurs. With regard to salt damage, it was recognized thatreinforcement corrosion occurs when the salt content at reinforcing bars exceeds 1 kg/m3; this value
was specified considering that the samples were taken in the vicinity of the shoreline andemphasizing safety while the reference value in the specification is 1.2 kg/m3. With regard tocomplex deterioration, the authors judged by checking whether or not initial chloride ion
concentration is above the reference value by referring to the previous study. With regard tocomplex deterioration, it is acceptable to judge by seeing the distribution form of chloride ion
concentration, but it has been pointed out that complex deterioration is highly correlated with initialchloride ion concentration, and so the authors decided to adopt the former one in this study. In somecases, there were samples in which the values of neutralization and salt damage exceed therespective reference values. Such samples were classified into complex deterioration.

Table 3 Estimated Parameters
β1

m1

β21

β22

m2

α

Model I

-16.143.30-13.48

2.02

2.93

63.49

Model II

-33.55

7.36

-7.84

2.27

1.60

0.45

3.2 Estimation of competing hazard model
Utilizing inspection data, the authors conduct the estimation of the competing Weibull deterioration
hazard model, which was formulated in Section 2. From the information that can be obtained
through inspection, the explanatory variables of the hazard models for neutralization and salt
damage were selected through trial and error. As a result, there were no data that can be used as
explanatory variables for neutralization, and the surface chloride ion amount was adopted for salt
damage. Accordingly, the concrete hazard functions for neutralization γ 1 and salt damage γ 2 k can
be defined as follows:γ 1 = exp(β11 ) , γ 2 k = exp(β 21 + β 2 2 x 22 k )(22) (23)where x 2jk is the surface chloride ion concentration of the sample ( j , k ) that was normalized so thatits maximum is equal to 1. The neutralization hazard function: γ 1 is constant regardless of thesample ( j , k ) , because the explanatory variable is composed of a constant term only. It isnoteworthy that γ 1 does not have the subscript k. In addition, as mentioned in Section 2.2.1, when
the competitive deterioration hazard model in which the competitive nature does not depend ontime: Model I is adopted, the log likelihood for all samples becomes as follows:
K ( j)

K (0)

K (1)

j = 0 k =1

k =1

k =1

2

K (2)

ln L(θ : ξ ) = ∑ ∑ ln L jk = ∑ ln L0 k + ∑ ln L1k + ∑ ln L 2 k
K (0)

{

k =1

}

D (1)

{ [

= ∑ − γ 1 t 0 k 1 − (γ 2 k + αδ 0 k γ 1 )t 0 k 2 + ∑ ln γ 1 m1 t1k 1
k =1

D ( 2)m{ [m+ ∑ ln {γ 2 k + αδ 2 k γ 1 }m 2 t 2 k 2
k =1

m −1

]− γ t

1 2k

k =1
m1

m −1

]− γ tm1

1 1k− (γ 2 k + αδ 2 k γ 1 )t 2 km2− (γ 2 k + αδ 1k γ 1 )t1k 2
m

}

(24)

}

On the other hand, when the competing deterioration hazard model in which the competitive naturedepends on time: Model II is used, the log likelihood for all samples can be formulated as follows:ln L(θ : ξ ){ []m + m −1
K (0) ⎧
t 1 2 ⎫⎪ K (1)
⎪
m
m
m1 −1
m
m
= ∑ ⎨− γ 1t 0 k 1 − γ 2 k t 0 k 2 − αδ 0 k γ 1 m1 m 2 0 k− γ 1t1k 1 − (γ 2 k + αδ 1k γ 1 )t1k 2⎬ + ∑ ln γ 1 m1t1k
1
m1 + m 2 − ⎪⎭ k =1
k =1 ⎪⎩K ( 2){+ ∑ [ ln (γ 2 k + αδ 2 k γ 1 m1t 2 k
k =1

m1 −1

)m 2 t 2 k

m2 −1}− γ t1 2k}

m + m −1

m1

− γ 2k t 2k

m2

t 1 2
]
− αδ 2 k γ 1 m1 m 2 2 k
m1 + m 2 − 1(25)
The unknown parameters that maximize the above equations (24) and (25) are estimated with thedirect search method. The estimation results are shown in Table 3. Both of the acceleration
parameters are above 1. This indicates the characteristics of the Weibull deterioration hazard type
rather than the exponential deterioration hazard type. Especially, it is obvious that the influence of
the acceleration parameter for neutralization m1 becomes stronger with time. In addition, α in
Model I is larger than that in Model II. It can be considered that the time dependency of thecompetitive nature is taken into account in Model II, and so the complex deterioration process is
described even if α is small.

3.3 Analytical results
With the hazard model, it is possible to formulate survival probability. If the probability that

1.0
Survival Probability

Survival Probability

1.0
0.8
0.6
0.4

Neutralization
Salt Damage
Complex Deterioration

0.2
0.0
0

20

40

60

80

Elapesd Time [Years]

Fig. 1 Survival Probability: Model I

100

0.8
0.6
0.4
0.2

Neutralization
Salt Damage
Complex Deterioration

0.0
0

20

40

60

80

100

Elapsed Time [Years]

Fig.2 Survival Probability: Model II

reinforcement corrosion occurs due to the corrosion factor j at arbitrary timing τ i is called survival
probability, it can be calculated by solving the distribution function for each factor. Figs. 1 shows
the survival probabilities in Model I, which was calculated using the estimation results mentioned
in the previous section. Fig. 1 shows the survival curve calculated using the average of surface
chloride ion concentration. For the figure, the high factors in reinforcement corrosion are complex
deterioration, salt damage, and neutralization in this order. Therefore, it can be concluded that thecomplex deterioration proceeds more rapidly than the deterioration caused by a single factor ofneutralization or salt damage. In detail, the period until the survival probability against
reinforcement corrosion due to complex deterioration, salt damage, and neutralization reaches 0.5 isabout 17 years, about 83 years, and about 130 years, respectively in Fig. 1. It is noteworthy that thereason why neutralization is slow is that the samples used for this empirical analysis were takenfrom concrete structures near the shoreline and so there were few samples of neutralization.
Actually, the number of samples of neutralization was only 4 out of a total of 145 samples.
On the other hand, Figs. 2 shows Model II in which the competitive nature depends on time. With
regard to the survival curves calculated from the average of surface chloride ion concentration, thecomplex deterioration proceeds like the deterioration due to salt damage at the early stage, but theprobability of corrosion steeply increases from a certain age. In addition, as obvious from the resultsin Table 3, in the present model that takes into account the time dependency of the competitive
nature, the corrosion due to neutralization occurs earlier and its influence on complex deteriorationis larger. These are the reason why the corrosion due to neutralization is earlier and the corrosion
due to salt damage is slower in this figure than Fig. 1.

4. Conclusions
In this study, the authors proposed a competing hazard model taking into account the competitive
nature among several factors, targeting the complex deterioration phenomenon at infrastructures.
Focusing on the estimation of the timing of the start of reinforcement corrosion inside concrete, theauthors confirmed that the competitive nature between neutralization and salt damage accelerates
the start of reinforcement corrosion and studied when the effect of complex deterioration becomessignificant, through the empirical analysis using actual inspection data. Accordingly, it is expectedthat the proposed model will enable the description of the complex deterioration phenomenon atsocial infrastructures and contribute to the advance of asset management.
Part of this study was conducted at Frontier Research Base for Global Young Researchers, Graduate
School of Engineering, Osaka University, supported by Special Coordination Funds for Promoting
Science and Technology, Ministry of Education, Culture, Sports, Science and Technology.

Reference[1]TSUDA, Y., KAITO, K., AOKI, K. and KOBAYASHI, K.: Estimating Markovian Transition
Probabilities for Bridge Deterioration Forecasting, Journal of Structural Eng./Earthquake Eng.,
JSCE, Vol.23, No.2, pp.241s-256s, 2006.