The Effects Evaluation of The Deterioration of Bridge. Expansion Joints on The Corrosion at Steel Girder End Part

Transcription

1 Internet Journa of Society for Socia Management Systems Vo. 11 Issue 1 sms ORIGINAL ARTICLE The Effects Evauation of The Deterioration of Bridge Expansion Joints on The Corrosion at Stee Girder End Part Ryoichi Sakamoto 1*, Taku Onji 2, Kiyoyuki Kaito 3 and Kiyoshi Kobayashi 4 1 Undergraduate Student, Dept. of Civi Eng., Undergraduate Schoo of Eng., Osaka Univ. 2-1, Yamadaoka, Suita, Osaka, , JAPAN 2 Graduate Student, Dept. of Civi Eng., Graduate Schoo of Eng., Osaka Univ. 2-1, Yamadaoka, Suita, Osaka, , JAPAN 3 Ph.D., Assoc. Prof., Dept. of Civi Eng., Graduate Schoo of Eng., Osaka Univ. 2-1, Yamadaoka, Suita, Osaka, , JAPAN 4 Ph.D., Prof. Graduate Schoo of Management, Kyoto Univ. Yoshida-Honmachi, Sakyo-ku, Kyoto, , JAPAN * E-mai: r.sakamoto@civi.eng.osaka-u.ac.jp Abstract: The deterioration of stee girder end parts (stee components above abutment and pier) is the main factor for the administrators decision making of repair and repacement on the maintenance and management of bridges. Corrosion is one of the main deterioration phenomena at stee girder end parts. Moreover, the primary causes of corrosion are thought to be the water eakage from bridge expansion joint and the ponding on abutment/pier. Therefore, the ifetime improvement of bridges and the reduction of ifecyce costs coud be achieved by appropriatey estabishing the time interva of bridge expansion joints inspection and repacement. In this study, using regime switching mode and Markov deterioration hazard mode, regime switching Markov hazard mode is formuated. Using regime switching Markov deterioration hazard mode, the effects of the deterioration of bridge expansion joints on the deveopment of the corrosion at stee girder end parts are expressed. Moreover, the reation between the both deteriorations on the bridge expansion joints and the stee girder end parts is abe to be quantitativey vauated with the deterioration prediction resuts. Lasty, the effectiveness of the methodoogy proposed in this study is empiricay vaidated through the case study focusing on the visua inspection data of highway bridges. Keywords: asset management, bridge management, corrosion, regime switching mode, Markov deterioration hazard mode Received: / Accepted: Copyright 2017 Society for Socia Management Systems. Internet Journa of Society for Socia Management Systems Pubished Date: A Rights Reserved. 1

2 Internet Journa of Society for Socia Management Systems Vo. 11 Issue 1 sms Introduction In Japan, about 700 thousand highway bridges had been buit intensivey after the high economic growth period in the mid-1950s. Haf of these bridges wi be more than 50 years after constructions in the mid- 2020s, it is known that the aging of highway bridges wi rapidy deveop in the future. The increase in aged highway bridges is directy inked to socia unrest due to ower users safety and an increase in highway bridges maintenance/management costs. Therefore, it is necessary to regard highway bridges deterioration as not ony engineering probem but aso socia probem. Moreover, in Japan, the decining birthrate and aging of the popuation keep on going. Thus, it is thought to be an urgent issue to efficienty maintain and manage highway bridges in imited human resources and austerity finance. Therefore, by inspecting, repairing and renewa at appropriate intervas on the basis of the deterioration state and importance of the bridge, it is necessary to entend the ife of the bridge and reduce the ife cyce cost. In this study, the authors focus on the deterioration of the stee girder end parts (stee components above abutment/pier). The deterioration of the stee girder end parts is a main factor in the decision making of repair and renewa especiay in maintenance of stee bridge. Corrosion is one of the main deterioration phenomena at stee girder end parts. Moreover, the primary causes of corrosion are thought to be the water eakage from the bridge expansion joint and the ponding on abutment/pier. On the other hand, repair and renewa of the stee girder end parts invove carrying out traffic restrictions, and these repair and renewa are arge scae constructions with heavy machinery. As a resut, repair and repacement of stee girder end parts can ead to not ony reduction of road convenience but aso increase of ife cyce cost. Therefore, by keeping the bridge expansion joint good condition with the appropriate inspection interva and repacement interva of the bridge expansion joint, it is possibe to extend the ife of the stee bridge and to reduce the ife cyce cost. Under the above awareness of the issues, in this study, the authors propose a methodoogy for evauating the effect of water eakage caused by deterioration of the bridge expansion joint on corrosion of the stee girder end parts. Specificay, the presence or absence of water eakage from the bridge expansion joint above the stee girder end parts are considered as two types of regime. Moreover, Considering the infuence of water eakage from the bridge expansion joint on the girder end part, the deveopment process of corrosion at the girder end parts is represented by regime switching Markov deterioration hazard mode. In chapter 2., the basic idea of this study is expained. In chapter 3., regime switching Markov deterioration hazard mode is formuated. In chapter 4., the estimation method of regime switching Markov deterioration hazard mode is described in detai. In chapter 5., the effectiveness of the methodoogy proposed in this study is empiricay vaidated through the case study focusing on the visua inspection data of highway bridges. 2. Basic idea of this study 2.1 Statistica deterioration prediction method for infrastructure In this study, the occurrence process of water eakage from the bridge expansion joint and the deveopment process of corrosion at the girder end part are expressed with statistica method, and the mode is estimated by using visua inspection data of highway bridges. Administrators of infrastructure vary from nation to oca governments, and some faciities are managed by an infrastructure management company. Various inspections have been carried out on infrastructure faciities by each administrator. Thus, vast amounts of inspection data are accumuated. In the past, a ot of Studies on 2

3 Internet Journa of Society for Socia Management Systems Vo. 11 Issue 1 sms statistica deterioration prediction method using these inspection data has been accumuated. In particuar, in case of a faciity where deterioration state is observed in binary states (whether it is fauty or not), the deveoped deterioration prediction method (deterioration hazard mode) with surviva time anaysis 1) make it possibe to use not ony data which are obtained from the faciities renewed due to reaching contro imit but aso data which are obtained from the faciities which preventive repairs and renewas are carried out in the service period. Therefore, the accuracy of deterioration prediction consideraby improved 2). Furthermore, mutistage exponentia hazard mode (Markov deterioration hazard mode) 3) and mutistage Weibu hazard mode 4) express the deterioration process of faciities which are recorded with mutistage discrete condition state. These deveopments make it possibe to use the advantages of surviva time anaysis stated above for transitions of mutistage condition states. In addition, more compicated deterioration process (Benchmarking of deterioration process, prediction of composite deterioration process, etc.) can be estimated by mixed probabiity mode and hidden Markov deterioration mode which are formuated on the basis of those modes stated above 5)-6). In this study, the quantitative effect evauation of the presence or absence of water eakage by bridge expansion joint s deterioration on corrosion at stee girder end part is carried out. 2.2 Deveopment mechanism of corrosion Corrosion is the phenomenon that the stee materia tries to return to the stabe oxidized compound by combining with oxygen and water. In stee structures, corrosion is thought to be regarded as one of main deterioration. Corrosion of stee in water or in the atmosphere is caused by water and dissoved oxygen. This chemica reaction formua is expressed by the foowing Eq. (2.1). Fe O 2 + H 2 O Fe(OH) 2 Eq. (2.1) In addition, the extent of corrosion deveopment is greaty infuenced by the use environment and the type/shape/ocation of parts. For that reason, various methods for corrosion protection exist depending on each condition, such as painting, anti-corrosion stee and etc. However, painting is the most widespread method in consideration of the points of economic efficiency, andscape and workabiity. In painted structures, corrosion does not deveop as ong as paint is not deteriorated. On the other hand, if the paint is eft in a deteriorated state, the corrosion of the stee materia deveops. When corrosion of stee materia deveops, the cross section of the stee materia decreases. Thus, uness any measures are taken against corrosion occurring parts, the structura soundness is greaty affected. Based on this idea, in the case of taking into consideration the reduction of the ife cyce cost under the strict budget constraint, it may be more effective method to extend the ife of stee materia with preventive maintenance such as repainting at appropriate time points rather than breakdown maintenance such as repacement of stee materias. Furthermore, in order to prevent corrosion of stee materias, it is desirabe not ony to paint at appropriate time points but aso to prevent water, which is the cause of corrosion, from entering into the vicinity of the stee materia. That is, when maintenance and management of the stee bridge, appropriate repacements of the bridge expansion joint aimed at preventing the penetration of water to the stee girder end part are considered to be very important for extending the ife of the stee bridge and reducing the ife cyce cost. 2.3 Occurrence mechanism of water eakage Corrosion in the ower part of the girder end part is mainy caused by water eakage from the bridge 3

4 Internet Journa of Society for Socia Management Systems Vo. 11 Issue 1 sms Figure 2.1 non-drainage type s expansion joint Figure 2.3 damage to the bridge expansion joint Figure 2.2 drainage type s expansion joint expansion joint 7). The bridge expansion joint is roughy divided into two types such as non-drainage type and drainage type. In the bridge expansion joint of non-drainage type, as shown in Figure 2.1, a water stop is instaed at the bottom of the bridge expansion joint to prevent water from penetrating the ower parts of the girder end part. The causes of damage or faing off of water stop are considered to be sand deposit, repeated impacts by the passing vehices, excessive impacts by overoaded vehices, repeated expansions and contractions and aged deterioration as shown in Figure 2.3. When water stop is damaged, water such as rainfa penetrate into the girder end part. Thus, the girder end part becomes to the condition which corrosion tends to deveop. For these reasons, the presence or absence of the water stop s damage has deep reation to the corrosion of the girder end part. Therefore, water stop is reguary inspected. In the reguar inspections, the presence or absence of water eakage is judged from damage or faing off of the water stop, water traces from the water stop and ponding at the upper part of the abutment/pier. Moreover, the presence or absence of the water eakage is recorded as the inspection resuts. On the other hand, in the bridge expansion joint of drainage type, as shown in Figure 2.2, a water stop is not instaed at the bottom of the bridge expansion joint. Thus, the bridge expansion joint of drainage type has the structure which water penetrates from the seam of the bridge expansion joint into the ower part of the girder end part. Therefore, the inspection resuts concerning the water eakage are not recorded. From the above, it is conceivabe that the water eakage at the girder end part occurs because the water stops of the non-drainage type s bridge expansion joint damage or fa off. Moreover, corrosion deveops at points where the painting has peeed off. Therefore, in this study, the deterioration prediction mode for quantitative evauation of the reationship between the damage of the bridge expansion joint and the corrosion of the girder end part is proposed. 3. Formuation of mode 3.1 Presupposition for modeing The bridge administrator starts service of the bridge or renews at the caendar time a 0. Thereafter the administrator manages the girder end parts and the bridge expansion joints. ( = 1,, L) shows the girder end parts ID. Time series inspection data set (rating data representing corrosion deveopment state and binary data indicating the presence or absence of 4

5 Internet Journa of Society for Socia Management Systems Vo. 11 Issue 1 sms water eakage from the bridge expansion joint) is obtained for each. Discrete time axis t g which caendar time a 0 is set as initia time point t 0 = 0 is introduced. t G t g = t g 1 + z (g = 1, 2,, G ) Eq. (3.1) shows the end time point of the observation period of. In this study, the point on the discrete time axis is referred to as the time point. The time point is distinguished from the caendar time. The focusing deterioration process is the composite deterioration process with corrosion deveopment process and water eakage occurrence process. For the sake of simpicity, the girder end part is assumed to have never been renewed from the initia time point. When the girder end part is repaced, the caendar time is assumed to be the initia time point. The corrosion deveopment condition of the girder end part at the time point t g is expressed by using the discrete state variabe f(t g ) = i (i = 1,, I). Rating i (i = 1,, I) shows the corrosion deveopment conditions. Namey, the corrosion deveopment conditions are proportiona to the vaue of i. At the initia time point t 0 = 0, the discrete state variabe is shown as f(0) = 1. Furthermore, a state variabe representing the presence / absence of water eakage from the bridge expansion joint at time point t g is defined as water eakage management mode s g. s 1 abnorma mode g = { 0 norma mode Eq. (3.2) In this study, abnorma mode is defined as the state with water eakage. On the other hand, norma mode is defined as the state without water eakage. At the initia time point, the water eakage management mode is shown as s 0 = 0. In this study, the corrosion deveopment process and the water eakage occurrence process are respectivey expressed by Markov chain mode. The water eakage management mode is a risk management mode indicating whether the corrosion deveopment state which is affected by damage of the bridge expansion joint has occurred or not. Moreover, it is considered that the corrosion deveoping speed of the girder end part differs depending on the water eakage management mode. In the water eakage management mode s g = h (h = 0, 1), the state-dependent deveopment speed of the corrosion rating i at the girder end part is expressed by λ i,g deveopment speed λ i,g expressed ike Eq. (3.3). λ i,g. At this time, the corrosion in the period [t g, t g+1 ) is = s g λ i,1 + (1 s g )λ i,0 = s g x 1 β 1,i + (1 s g )x 0 β Eq. (3.3) 0,i Here, x h = (1, x 1,h,, x C,h ) (h = 0, 1) shows expanatory variabe vector. On the other hand, β h,i = (β 0,h,i,, β C,h,i ) shows unknown parameter vector. In the Eq. (3.3), the symbo " " represents a transposition operation. 3.2 Corrosion deveopment mode The Markov transition probabiity that the rating of corrosion transits from i to j (j = i + 1,, I 1) in the period [t g, t g+1 ) is expressed ike Eq. (3.4) 3). π ij (, g, z) j j 1 = λ r,g λ r,g λ m,g m=i r=i, m exp( λ m,g z) Eq. (3.4) Aso, π ii (, g, z) can be expressed by the foowing Eq. (3.5) with the condition of Markov transition probabiity. π ii (, g, z) I 1 = 1 π ij (, g, z) j=i (s = 0, 1) Eq. (3.5) As can be seen from these Markov transition probabiities, in this study, it is assumed that corrosion deveopment of the girder end part in the period [t g, t g+1 ) is determined by water eakage management mode s g at the beginning of the period t g. 5

6 Internet Journa of Society for Socia Management Systems Vo. 11 Issue 1 sms State variabe mode The transition of the water eakage management mode is thought to be independent of the deveopment of corrosion at the girder end part. The transition from 0 to 1 in the water eakage management mode indicates the deterioration of the water stop. On the other hand, the transition from 1 to 0 indicates the repair of the water stop. In this study, even when the repair records of the water stop are partiay accumuated, the transition from 1 to 0 of the water eakage management mode is stochasticay expressed. When the repair records of the water stop are competey accumuated, the transition from 1 to 0 shoud be deterministicay set. In this study, the transition probabiity of water eakage management mode is thought to be expressed by an exponentia hazard mode 1) formuated on the basis of information which is observed at the beginning of the period t g. Now, It is assumed that the norma mode s g = 0 is observed at the time point t g. At this time, the hazard ratio which the norma mode s g = 0 terminated during the period [t g, t g+1 ) is expressed by θ g,0. Simiary, when the abnorma mode s g = 1 is observed at the time point t g, the hazard ratio which the abnorma mode s g = 1 terminated during the period is expressed by θ g,1. The hazard ratio θ g,h (h = 0, 1) is expressed ike Eq. = (3.6) with the characteristic vector y g,h (1, y g,h,1,, y g,h,d ) such as the water eakage characteristic, etc. in the period t g. θ g,h = exp (y g,h α h ) Eq. (3.6) α h = (α h,0,, α h,d ) shows a D dimensiona row vector of unknown parameters. The water eakage management mode s g = h (h = 0, 1) is observed at the time point t g. Moreover, the probabiity which the water eakage management mode s g = h continues unti the time point t g+1 is expressed ike Eq. (3.7) with surviva probabiity F g,h (z) that the ifetime of each mode becomes z and over. F g,h (z) = exp ( θ g,h z) Eq. (3.7) Furthermore, the probabiity p g (θ g,0 ) which the water eakage management mode transits from the norma mode to the abnorma mode in the period [t g, t g+1 ) is expressed ike Eq. (3.8). p g (θ g,0 ) = 1 F g,0 (z θ g,0 ) Eq. (3.8) The probabiity q g (θ g,1 ) which the water eakage management mode transits from the abnorma mode to the norma mode in the period [t g, t g+1 ) is expressed ike Eq.(3.9). q g (θ g,1 4. Estimation of mode 4.1 Likeihood function ) = 1 F g,1 (z θ g,1 ) Eq. (3.9) It is assumed that rating i g of corrosion of the girder end part and the water eakage management mode s g are obtained at a time points t g. The symbo " " represents the observation vaue. At this time, the ikeihood function L(i, s, x, y, α, β) is expressed ike Eq. (4.1). L(i, s, x, y, α, β) L G 1 = π i g i g+1(, g, z) =1 g=0 [p g (θ g,0 ) δ g, {1 p g (θ g,0 )} 1 δ g, 1 s g ] [q g (θ g,1 ) δ g, {1 q g (θ g,1 )} 1 δ g, s g ] The dummy variabe δ g is defined as Eq. (4.2). δ g = { 0 (s g = s g+1) 1 (s g s g+1) Eq. (4.1) Eq. (4.2) i shows the observed rating data set, s shows the observed data set of water eakage management mode and x and y are the observed data sets of the characteristic variabes Here, the situation which rating i g of corrosion at the girder end part and the water eakage management mode s g are observed at a time points t g is not reaistic. Therefore, in this study, observed corrosion rating i g and the water eakage management mode s g the girder end part are used as observed vaues. On 6

7 Internet Journa of Society for Socia Management Systems Vo. 11 Issue 1 sms the other hand, unobserved rating and water eakage management mode are used as atent variabes. Namey, the ikeihood function (Eq. (4.1)) is regarded as the competion ikeihood function 8). In this way, unknown parameters of mode and atent variabes are simutaneousy estimated by using MCMC (Markov chain Monte Caro) method 9)-10). By using above method, the mode can be estimated in consideration of the partia unobservabiity of the rating and the water eakage management mode. 4.2 Unobservabe water eakage occurrence situation In the proposed regime switching Markov deterioration hazard mode, the atent variabe of water eakage management mode is expressed ike Eq. (4.3) because the transition of the water eakage management mode is not affected by rating of corrosion at the girder end part. Pr(s g+1 s g ) = [p g (θ g,0 ) δ g, {1 p g (θ g,0 )} 1 δ g, 1 s g ] Eq. (4.3) [q g (θ g,1 ) δ g, {1 q g (θ g,1 )} 1 δ g, s g ] The symbo "*" represents a atent variabe. The dummy variabeδ g, is expressed ike Eq. (4.4). δ, g = { 0 (s g = s, g+1 ) 1 (s g Eq. (4.4) s g+1 ) i i g represents a rating data set excuding i g. 4.3 Unobservabe corrosion deveopment situation The situation of corrosion deveopment is aso unobservabe data except the time point of inspection. However, atent variabes make it possibe to express the situation of corrosion deveopment at the oca time point. When rating of corrosion at the time point t g is not observed and the rating of corrosion is samped as the atent variabe i g,, the conditiona posterior probabiity of i, g {i g 1 expressed ike Eq. (4.5).,, i g+1 } is Tabe 5.1 The rating of corrosion Rating Depth Condition 1 No damage Area 2 Sma Sma 3 Sma Big 4 Big Sma 5 Big Big Tabe 5.2 The rating of water eakage Rating Condition 1 No damage 2 With Water eakage Pr (i g, i i g,, s, x, y, α, β) L (i i,, i, g g, s, x, y, α, β) = i g+1 L(i i, i, s, x, y, α, β) i=i g 1 5. Empirica anaysis 5.1 Overview of database Eq. (4.5) The effectiveness of the regime switching Markov deterioration hazard mode proposed in this study is discussed through the case study with actua bridge inspection data. An administrator which manages the bridges accumuates the visua inspection records such as the rating based on the corrosion deveopment of the stee girder end part and binary data of the presence or absence of water eakage. These visua inspection records are accumuated as rating data on the basis of Bridge periodica inspection guideine 11) as shown in Tabe 5.1 and Tabe 5.2. In this study, these rating data are used as information sampes to estimate the regime switching Markov deterioration hazard mode. In addition, the information sampes are extracted ony from the verticay corresponded bridge expansion joint and the main girder end parts. Namey, one of data set of information sampes consists of the rating of corrosion of the main girder 7

8 Internet Journa of Society for Socia Management Systems Vo. 11 Issue 1 sms Tabe 5.4 Estimation resut of corrosion deveopment process Constant term β 0 β 1 Painting specification Constant term Painting specification β 0,1 β 0,2 β 0,3 β 0,1 β 0,2 β 0,3 β 1,1 β 1,2 β 1,3 β 1,1 β 1,2 β 1,3 Estimate Upper imit 5% Lower imit 5% Geweke test statistic Tabe 5.3 Overview of database # of bridges 123 Sampe size 866 # of inspections 1~3 Inspection year 2004~2015 Construction 1926~2005 year Painting specification, Characteristics Sat damage area cassification, of bridge Traffic voume end part, the presence or absence of water eakage from the bridge expansion joint, the characteristics of each bridge and the time interva between the former inspection and the atter inspection. Based on the above assumptions, the overview of the database is shown in Tabe Estimation resut of corrosion deveopment process of main girder The information data sampes whish are described in section 5.1 are appied to the regime switching Markov deterioration hazard mode. In this study, painting specifications and sat damage area cassifications are considered as the candidates for expanatory variabes of Markov deterioration hazard mode because these characteristics are thought to have an effect on the corrosion. Painting specifications are cassified into three types such as A paint system, B paint system and C paint system. For these paint systems, A painting system and B painting system are generay cassified into genera painting system. On the other hand, C painting system is cassified into heavy-duty anticorrosion painting system. Thus, the infuence of painting specifications on the corrosion deveopment is considered by using binary dummy variabe. Tabe 5.4 shows the estimation resut of Markov deterioration hazard mode, which represents the deveopment of corrosion of the main girder. The sat damage area is 8

9 Internet Journa of Society for Socia Management Systems Vo. 11 Issue 1 sms Tabe 5.4 Estimation resut of state variabe mode α 0 α 1 Constant term Traffic voume Constant term α 0 1 α 0 2 α 1 1 Figure 5.1 Corrosion deveopment processes of the genera painting system cassified as A, B, C and D depending on the extent of necessity of taking measures against sat damage. Furthermore, the sat damage area is cassified as S, I, II and III depending on the distance from coastine. These detais are described in Specifications for highway bridges part III concrete bridge edition 12). The sampes used in this study are divided into four categories such as C-(S), C-(II), C-(III) and D. Therefore, C-(S), C-(II), and C-(III) are cassified as sat damage area and D is cassified as non-sat damage area. In this way, the infuence of sat damage area cassification on the corrosion deveopment is considered by using the binary dummy variabe. However, because the number of the sampes in the sat damage area is sma, the significance of sat damage area cassification is rejected by Geweke test 13) for the a processes of corrosion deveopment in the abnorma mode. Therefore, the resut is not shown in Tabe 4. Moreover, when paint specifications are adopted as expanatory variabe, statisticay significant resuts were obtained in the transitions of corrosion ratings in norma mode from 1 to 2, 2 to 3 and 3 to 4. On the other hand, statisticay significant resuts in the transitions of corrosion ratings in abnorma mode from 1 to 2 and 2 to 3. However, the 2 unknown parameter β 1,3 of the transition of corrosion ratings from 3 to 4 in the abnorma mode Estimated record Upper imit 5% Lower imit 5% Geweke test statistic was rejected by the Geweke test. Furthermore, the 2 unknown parameter β 0,1 of the transition of corrosion ratings in the norma mode from 1 to 2 was obtained as positive vaue. This resut indicates that the genera painting system is more resistant to corrosion than the heavy-duty anticorrosion painting system. However, this resut is contradictory to practica experiences. Therefore, the estimated 2 parameter β 0,1 was not adopted considering sign condition. By using the above estimation resuts, it is possibe to express the corrosion deveopment processes of the main girder in the norma mode and the abnorma mode as shown in Figure 5.1. However, Figure 5.1 shows the corrosion deveopment processes of the genera coating system as an exampe. Moreover, due to the sampe deficiency of corrosion rating 5, Tabe 5.4 and Figure 5.1 show the estimation resut up to corrosion rating 4. It is confirmed from Figure 5.1 that the corrosion in the abnorma mode deveops up to rating 4 about 11 years earier than that in the norma mode. In the future, when inspection data is continued to accumuate, it is specuated that further difference wi occur in the deterioration processes between the norma mode and the abnorma mode. 9

10 Internet Journa of Society for Socia Management Systems Vo. 11 Issue 1 sms Figure 5.2 Transition probabiity from abnorma mode to norma mode Figure 5.4 Corrosion rating occupancy in norma mode Figure 5.3 Transition probabiity from norma mode to abnorma mode Figure 5.5 Corrosion rating occupancy in abnorma mode 5.3 Estimate resut of state variabe mode In this study, the Markov deterioration hazard mode which expresses the corrosion deveopment process of the main girder and the Markov transition probabiity which expresses the water eakage management mode transition probabiity (norma mode and abnorma mode) are simutaneousy estimated. In addition to the estimation resuts of the corrosion deveopment processes of the main girder which are described in section 5.2, the estimation resuts of the state variabe mode are shown in Tabe 5.4. In this study, considering the traffic voume as the cause of water eakage from the bridge expansion joint, it was adopted as an expanatory variabe. The transition probabiities from abnorma mode to norma mode is shown in Figure 5.2 using this estimation resut. Figure 5.2 can be thought as the repair probabiity of the bridge expansion joint with the apse of time. The transition probabiity from norma mode to abnorma mode is shown in Figure 5.3. As shown in Figure 5.3, at 50% of the transition probabiity from norma mode to abnorma mode, the difference of about 0.8 years between the maximum traffic voume and the minimum traffic voume arise. Furthermore, the corrosion rating occupancy of the main girder in the norma mode is shown in Figure 5.4. In addition, the corrosion rating occupancy of the main girder in the abnorma mode is shown in Figure 10

11 Internet Journa of Society for Socia Management Systems Vo. 11 Issue 1 sms From this resuts, by setting the threshod (administration standard) for the occupancy of rating 4 depending on each water eakage management mode, the road administrator can make a decision for repacement of the bridge expansion joint. 6. Concusion In this study, regime switching Markov deterioration hazard mode on the based of the concept of Markov switching Poisson occurrence mode 14). Moreover, the effect of the presence or absence of water eakage on the corrosion deveopment of the stee girder end part is quantified. First, the water eakage management modes are defined by setting the norma mode for the case of no water eakage and the abnorma mode for the case of water eakage on the basis of the presence or absence of water eakage from the bridge expansion joint. Secondy, the corrosion deveopment process of the stee girder end part is expressed with Markov degradation hazard mode. Moreover, the transition probabiities of each water eakage management mode are expressed with the Markov switching mode. In this way, the corrosion deveopment processes in each water eakage management mode are formuated as a regime switching Markov deterioration hazard mode. Herewith, the processes of corrosion deveopment of the stee girder end part in each water eakage management mode can be distinguished. Thus, it is possibe to determine an appropriate repacement timing of the bridge expansion joint on the basis of the expected ifetime of the stee girder end part in each water eakage management mode. On the other hand, it is possibe to express the difference between deterioration processes by adopting the presence or absence of water eakage as an expanatory variabe of the conventiona Markov deterioration hazard mode. However, water eakage from the bridge expansion joint which is confirmed by visua inspection does not necessariy occur near the time point of inspection. Namey, the conventiona Markov deterioration hazard mode cannot adequatey consider the period which the stee girder end parts are exposed to water eakage from the bridge expansion joint. Therefore, the conventiona Markov deterioration hazard mode has a possibiity that the effect of water eakage from the bridge expansion joint on the corrosion deveopment of the stee girder end part may not be sufficienty evauated. From the above, the mode proposed in this study is more vauabe than the conventiona Markov deterioration hazard mode from the viewpoint of expressing the corrosion deveopment process of the stee girder end part in consideration of the probabistic occurrence state and occurrence timing of water eakage from the bridge expansion joint (water eakage management mode). Furthermore, when the traffic voume which is recorded as the time series data is adopted as the expanatory variabe of the transition probabiity in the Markov switching mode of the water eakage management mode and the regime switching Markov deterioration hazard mode is estimated, it becomes possibe to express the transition probabiity of each water eakage management mode of the bridge expansion joint in increase and decrease of the traffic voume. Thus, this mode can be very usefu for the bridge maintenance and management. On the other hand, there are sti some foowing future works in terms of this study. First, in the empirica anaysis of this study, the authors tried to appy the proposed methodoogy to imited highway bridges. Thus, the findings obtained from the empirica anaysis of this study can be used ony for the targeted bridges in this study. In the future, it is necessary to sequentiay improve the maintenance and management method of the stee girder end part and the bridge expansion joint at the time of water eakage occurrence by accumuating visua inspection data and the case studies of the mode proposed in this study. Secondy, using the 11

12 Internet Journa of Society for Socia Management Systems Vo. 11 Issue 1 sms corrosion deveopment processes of the stee girder end part in each water eakage mode anayzed in this study, ifecyce cost anaysis about the reduction of ife cyce costs between the periodic repacements of bridge expansion joint (preventive maintenance) and the breakdown maintenance accompanied by argescaed renewas needs to be conducted. At that time, it is necessary to consider the road users socia oss due to traffic reguations. Thirdy, at present, the deterioration of anti-corrosion function and the corrosion are cassified and recorded as separate deterioration phenomena. Therefore, it is necessary to integrate these deteriorations ratings by visua inspection because the deterioration of anti-corrosion function and the corrosion are thought to be sequentia deterioration phenomenon. References 1) Lancaster, T.: The Econometric Anaysis of Transition Data, Cambridge University Press, ) Kazuya Aoki, Kouji Yamamoto and Kiyoshi Kobayashi: Estimating Hazard Modes for Deterioration Forecasting, Journa of Japan Society of Civi Engineers, No.791/VI-67, pp , ) Yoshitane Tsuda, Kiyoyuki Kaito, Kazuya Aoki and Kiyoshi Kobayashi: Estimating Markovian Transition Probabiities for Bridge Deterioration Forecasting, Journa of Japan Society of Civi Engineers, No.801/I-73, pp.68-82, ) Kazuya Aoki, Koji Yamamoto, Yoshitane Tsuda and Kiyoshi Kobayashi: A Deterioration Forecasting Mode with Muti-Staged Weibu Hazard Functions, Journa of Japan Society of Civi Engineers, No.798/VI-68, pp , ) Kengo Obama, Koichi Okada, Kiyoyuki Kaito and Kiyoshi Kobayashi: Disaggregated Hazard Rates Evauation and Bench-Marking, Journa of Japan Society of Civi Engineers A, Vo.64, No.4, pp , ) Kiyoshi Kobayashi, Kiyoyuki Kaito, Akira Oi, Thao, N. D. and Naoki Kitaura: Estimating Composite Hidden Markov Deterioration Modes for Pavement Structure with Sampe Missing, Journa of Japan Society of Civi Engineers E1, Vo.71, No.2, pp.63-80, ) Masaki Tamura, Atsushi Kikuchi and Hiroshi Chiba: Investigation on Water Leakage Countermeasure of Expansion Joint of Highway Bridge: Journa of MLIT, pp , ) Daijiro Mizutani, Kiyoyuki Kaito, Kiyoshi Kobayashi, Eizo Hideshima, Yota Yamada and Satoshi Hirakawa: A Hidden Markov Deterioration Hazard Mode with Change of Inspection Criterion, Journa of Japan Society of Civi Engineers D3, Vo.71, No.2, pp.70-89, ) Yukito Iba, Masaharu Tanemura, Yasuhiro Omori, Hajime Wago, Seisho Sato and Akihiko Takahashi: Computationa Statistics II, Iwanami Shoten, ) Hajime Wago: Bayesian Econometric Anayses, Toyo Keizai Inc., ) Ministry of Land, Infrastructure, Transport and Tourism: Bridge Periodica Inspection Guideine, ) Ministry of Land, Infrastructure, Transport and Tourism: Specifications for Highway Bridges part I Common / part III Concrete Bridge,

13 Internet Journa of Society for Socia Management Systems Vo. 11 Issue 1 sms ) Geweke, J.: Evauating the Accuracy of Samping based Approaches to the Cacuation of Posterior Moments, Bayesian Statistics, Vo.4, pp , ) Daijiro Mizutani, Kiyoyuki Kaito, Kiyoshi Kobayashi and Satoshi Hirakawa: An Emergency Management Rue of Pothoes with Reference to Weather Conditions, Journa of Japan Society of Civi Engineers F4 (construction management), Vo.70, No.3, pp.63-80,