Bridge Deterioration Prediction Using Markov-Chain …docs.trb.org/prp/16-4744.pdf · 1 Bridge Deterioration Prediction Using Markov-Chain Model ... 54 different characteristics of

Li, Li, Chen and Sun

TRB 2016 Annual Meeting

Bridge Deterioration Prediction Using Markov-Chain Model Based 1

on the Actual Repair Status in Shanghai 2

3

4

Li LI 5

Associate Professor 6

Key Laboratory of Road and Traffic Engineering of the Ministry of Education 7

Tongji University 8

No. 4800 Cao’an Road, Jiading District, 201804, Shanghai, China 9

TEL:(+8621) 69580491, E-mail: [email protected] 10

11

Feng LI 12


Key Laboratory of Road Structure and Material of the Ministry of Transport 14

Research Institute of Highway, Ministry of Transport 15

No. 8 Xitucheng Road, Haidian District, 100088, Beijing, China 16


(Corresponding Author) 18

19

Zhang CHEN 20



Tongji University 23



26

Lijun SUN 27

Professor 28


Tongji University 30



33

34

35

Submitted for Presentation and Publication at the 2016 Annual Meeting of the 36

Transportation Research Board 37

38

39

Submission date: July 31, 2015 40

Revision date: November 15, 2015 41

Word count: 6977 with 3 tables and 4 figures 42

mailto:[email protected]

mailto:[email protected]



ABSTRACT 43

Bridge condition prediction is crucial in preparing future conservation budgets and five-year 44

capital programs for the construction and maintenance of bridges in Shanghai. A bridge 45

management system (BMS) has been formally used and promoted for urban bridge management 46

in Shanghai since 2004 and 16,623 bridge records have been accumulated. Although there are a 47

large amount of data records, predicting bridge deterioration precisely is difficult because the data 48

composition is complicated and the maintenance history is varied. Therefore, a Markov-chain 49

model was applied as a decision aid to consider the different conservation strategies. More than 50

66,000 data records were used to calibrate the model. The modeling considered two conservation 51

regimes: routine maintenance and minor repair, and medium and major repair. The repair rate was 52

obtained through an actual conservation survey. Besides the influence of spatial distribution, 53

different characteristics of bridges also were considered. Bridge conservation efforts were uneven 54

at the city level in Shanghai. The condition of bridges in the central city is much better than those 55

in suburban areas, although the proportion (55.6%, 2014) of suburban bridges is larger. 56

Furthermore, based on the present status of Shanghai bridges, conservation efforts have been 57

insufficient generally, and even worse in suburban areas. The medium and major repair level at 58

present has had a significant impact on deck systems and superstructure, but quite a small impact 59

on substructure and the whole bridge. Thus, the present conservation efforts cannot improve the 60

overall bridge condition fundamentally. As a result, the condition of bridges in Shanghai has 61

deteriorated rapidly. 62

63

Key words: Markov chains; Bridge deterioration; Bridge prediction; Bridge repair 64

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INTRODUCTION 85

The condition assessment and prediction of bridge infrastructure is crucial in preparing future 86

conservation budgets and five-year capital programs for the construction and maintenance of 87

bridges in Shanghai. A bridge management system (BMS) has been formally in use for urban 88

bridge management in Shanghai since 2004, following an initial trial of the BMS in 2002. At 89

present, the stable version of the BMS has successfully worked more than 11 years. All of the 90

bridges are inspected once a year and 16,623 bridge assessment records have been accumulated. 91

As small and moderately sized bridges make up the majority of the urban bridges, the data records 92

in the Shanghai BMS all describe bridges belonging to categories II to V according to the Chinese 93

technical code of urban bridges management CJJ 99-2003 [1], which excludes the super-large 94

bridges (bridges with total span more than 1000 meters or single span more than 100 meters.). 95

The technical status of bridges in the Shanghai BMS is quite complicated because bridges 96

with different structure types and different material properties are included in the same database. 97

Besides, the bridge age span is also large, as shown in Figure 1, which means that bridges at 98

different stages of development coexist. Any reasonable performance assessment method should 99

avoid the bias caused by this large span in bridge age. Apart from this, the bridge conservation 100

status also exists in various forms, including routine maintenance and minor repair, medium repair, 101

major repair and even reconstruction. Consequently, the precise prediction of bridge deterioration 102

has become a challenge. A meaningful prediction modeling approach for such infrastructure is 103

usually on the network-level, considering the necessary size of the data sample. The outcomes of 104

network-level deterioration models are the prediction of condition changes with time of the given 105

bridge network and can be used to plan maintenance, including repair and rehabilitation of bridges, 106

and to calculate bridge life cycle cost [2]. This study only considered network-level deterioration 107

modeling. Also, a prediction approach considering a variety of impact factors will be used. 108

109

110

Figure 1 Bridge Age Span in Shanghai, China (as of 2014) 111

112

A prediction approach was sought that was capable of considering a variety of impact factors. 113

Deterministic and stochastic methods are the most common ways by which to develop such a 114

prediction method. The deterministic model assumes that the bridge deterioration tendency is 115

certain, so regression analysis is commonly used to determine the infrastructure decay rate; an 116

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exponential regression model is widely used [3–5]. Typically, these models are relatively 117

convenient to calculate but fail to consider uncertainty and randomness of the bridge deterioration 118

process [6]. Besides, a high quality data set is also required for regression analysis, which is 119

usually hard to satisfy, and the preprocessing of data may cause too much risk of subjective 120

judgement [3]. Comparatively, stochastic models are better in such aspects. Engineering 121

experience can be used to describe the uncertain factors [7]. Although the deterioration processes 122

of bridge components are continuous, discrete condition ratings are often used to reduce the 123

complexity of continuous condition monitoring; this approach has been proved effective [8]. The 124

discrete probability models are represented by the Markov process, which is based on the concept 125

of probabilistic cumulative damage [9] and now commonly used in the performance prediction of 126

infrastructure facilities [10]. It is believed that models based on the Markov process have three 127

advantages [11]. Firstly, such models are able to reflect uncertainties of various aspects [12]. 128

Secondly, the prediction of a future state is based on the present state, so the model is incremental 129

[8]. And lastly, Markov-based models can be applied at network level with many facilities 130

involved, improving calculation efficiency [13, 14]. Some bridge management systems, such as 131

Pontis and BRIDGIT [15, 16], have adopted Markov models to predict the performance of 132

bridges. 133

Although the Markov process has been widely used in bridge performance prediction, most 134

applications focus only on a particular bridge component such as a deck, or directly consider the 135

bridge as a whole [11]. Besides, the sample size is not large enough in most applications [17]. 136

Some research has attempted to model the different deterioration characteristics of different bridge 137

components under certain maintenance regimes, but the bridge repair rates are all based on 138

assumption or empirical estimation, which is not rigorous enough to reflect the real performance 139

of bridges [18]. So there is often a performance gap between predictions and reality. Furthermore, 140

in some big cities or large infrastructure networks, infrastructure status in the central city and 141

suburban areas may be totally different due to the difference in the conservation investment level 142

or in the importance of traffic infrastructure. So it is not so reasonable to consider the bridges in 143

such situations as a whole even though the prediction is usually made on a network level. Rather, 144

the effect of infrastructure distribution should be taken into account. 145

The motivation of this study was to satisfy the need for a Markov-chain model that reflects 146

the real impact of actual bridge conservation status in Shanghai and that can predict the 147

performance deterioration tendency of different components of bridges in different areas (i.e., 148

central city and suburban areas). As for the Markov model, the key problem was to estimate the 149

transition probability matrixes (TPMs), a process also known as calibrating Markov models [19]. 150

A stationary Markov model uses time-independent TPMs by assuming a homogeneous 151

infrastructure deterioration pattern for a selected data set. Deterioration patterns of data sets with 152

similar characteristics, without medium or major repair in between, can be assumed to be 153

homogeneous when limited condition-rating data are available [2], and the stationary Markov 154

model could be considered in this situation. In other words, a single TPM can be used. 155

Therefore the actual objectives of this study were to calibrate a Markov-chain model using 156

bridge condition-rating records in Shanghai to predict the deterioration process of local bridge 157

infrastructures on a network level. To obtain actual bridge conservation data, a conservation 158



survey was also conducted by searching the BMS database and accessing the infrastructure 159

industry reports from 2004 to 2013 [20]. 160

161

162

MODEL AND ASSUMPTIONS 163

Markov-chain model 164

A Markov process describes a system that can be in one of several states. Each state can pass to 165

another at each time step according to fixed probabilities. A Markov-chain model is a special case 166

of the Markov process for which time and state parameters are both discrete. A Markov chain can 167

be treated as a series of state transitions based on certain probabilities. A stochastic process whose 168

transition probability of a future state depends only on the present state is defined as a first-order 169

Markov process [21]. For a stochastic process {𝑋(𝑡), 𝑡 ∈ 𝑇}, if the conditional probability can be 170

expressed as Equation (1), {𝑋(𝑡), 𝑡 ∈ 𝑇} is a Markov chain having discrete parameters. 171

172

𝑃(𝑋𝑡+1 = 𝑖𝑡+1|𝑋0 = 𝑖0, 𝑋1 = 𝑖1, ⋯ , 𝑋𝑡 = 𝑖𝑡) = 𝑃(𝑋𝑡+1 = 𝑖𝑡+1|𝑋𝑡 = 𝑖𝑡) (1) 173

174

In Equation (1), 𝑖𝑡 is the process state at time t; and P is the conditional probability of a 175

future event. There are two assumptions about Markov chains. First, the future state of a stochastic 176

process depends only on the present state and has nothing to do with the past. Second, the 177

transition probability between two states should be constant. So the time step needs to be 178

determined properly to assure simple-state transition. 179

As mentioned above, urban bridges in Shanghai are inspected once a year, so the time 180

interval for the model was set to one year. As the bridge condition is usually evaluated using 181

several rating levels, the transition probabilities should be expressed as a transition probability 182

matrix. A typical TPM, P, is shown in Equation (2). 183

184

𝑃 = [(

𝑝11 ⋯ 𝑝1𝑛

⋮ ⋱ ⋮𝑝𝑛1 ⋯ 𝑝𝑛𝑛

)] {𝑝𝑖𝑗 ≥ 0 𝑖, 𝑗 ∈ 𝐼

∑ 𝑝𝑖𝑗 = 1𝑗∈𝐼 𝑖 ∈ 𝐼 (2) 185

186

In Equation (2), n is the number of bridge condition states; matrix element 𝑝𝑖𝑗 represents the 187

probability that the bridge condition will pass from state 𝑖 to state 𝑗 during a certain time step. 188

Therefore, if the initial bridge condition is known, the future condition after t time intervals can be 189

obtained using Equation (3), where C is the condition vector [22]. 190

191

𝐶(𝑡) = 𝐶(0) × 𝑃𝑡 (3) 192

193

The TPM is the key of the Markov-chain model and is commonly obtained by statistically 194

analyzing the bridge condition data. Two methods can be used to calculate the transition 195

probability matrix: the regression method based on nonlinear optimization [17, 23], and the 196

percentage method [24]. The regression method is affected significantly by the prior maintenance 197

actions, for which records may not be readily available. In the percentage method, the transition 198

probability is estimated by the proportion of number of state changes to the total number of states 199



before the change. Thus, this method requires at least two consecutive condition records without 200

any maintenance interventions [11], which usually reduces the magnitude of data processing. 201

Because the requirement of the percentage method is comparatively easy to achieve, it was 202

selected for use in this study. 203

204

Model assumption and matrices simplification 205

In China, urban bridge conditions are graded by five levels for small and moderate bridges [1], as 206

shown in Table 1. For bridges with grades A to C, only routine maintenance and minor repair are 207

needed. According to the conservation requirements in the Chinese technical regulation [1], the 208

main work of the routine maintenance and minor repair is to mark the damaged area, find the 209

suspicious damage and keep the affected areas tidy. Thus, in such a situation, the condition rating 210

(CR) of a bridge should either maintain the original level or decay to the next lower level between 211

two consecutive years. In other words, the bridge CR grade cannot decay more than one grade in a 212

subsequent year. For bridges with grade D or E, more maintenance efforts are required, including 213

medium or major repair and even reconstruction. In this case, the bridge condition can be 214

improved, and thus the CR grade should be raised to any higher level according to the actual 215

repair efforts. According to the Shanghai bridge conservation investigation conducted in this study, 216

some universal principles can be summarized as follows: first, the medium repair is mainly for 217

D-grade bridges and the major repair is for E-grade bridges; second, both D- and E-grade bridges 218

will be improved to grade A after repair. However, there is also a situation that major repair is 219

implemented on grade D bridges if there is a surplus maintenance budget after all of the grade E 220

bridges are repaired. 221

222

Table 1 Urban Bridge Condition Ratings in China 223

Grade Definition Score

(100 mark system) Maintenance recommendations

A Intact 90-100 Routine maintenance

B Good 80-89 Routine maintenance and minor repair

C Qualified 66-79 Minor repair

D Unqualified/Bad 50-65 Medium or major repair

E Dangerous <50 Major repair or reconstruction

224

Therefore, three basic assumptions were made in this study based on the analysis above. 225

Assumption 1: in the circumstances of routine maintenance and minor repair, the CR of 226

a bridge should maintain the original level or decay to the next lower level between two 227

consecutive years. 228

Assumption 2: medium repair is mainly for grade D bridges and major repair is for 229

grade E bridges, but if there is a surplus maintenance budget, the major repair could be 230

implemented on grade D bridges. 231

Assumption 3: both D- and E-grade bridges will be improved to grade A after medium 232

or major repair. 233

Based on the CR definition in Table 1 and the assumptions above, the TPM in Equation (2) 234



can be simplified to Equation (4) and Equation (5), in which 𝑃𝑟𝑜𝑢𝑡𝑖𝑛𝑒 𝑎𝑛𝑑 𝑚𝑖𝑛𝑜𝑟 is the TPM 235

under routine maintenance and minor repair, and 𝑃𝑚𝑒𝑑𝑖𝑢𝑚 𝑎𝑛𝑑 𝑚𝑎𝑗𝑜𝑟 is the TPM under medium 236

and major repair. 237

238

𝑃𝑟𝑜𝑢𝑡𝑖𝑛𝑒 𝑎𝑛𝑑 𝑚𝑖𝑛𝑜𝑟 =

[ 𝑝55 1 − 𝑝55

𝑝44 1 − 𝑝44

𝑝33 1 − 𝑝33

𝑝22 1 − 𝑝22

1 ]

(4) 239

240

𝑃𝑚𝑒𝑑𝑖𝑢𝑚 𝑎𝑛𝑑 𝑚𝑎𝑗𝑜𝑟 =

[ 𝑝55 1 − 𝑝55

𝑝44 1 − 𝑝44

𝑝33 1 − 𝑝33

𝑝25 (1 − 𝑝25) ∗ 𝑝22 (1 − 𝑝25) ∗ (1 − 𝑝22)

𝑝15 1 − 𝑝15 ]

(5) 241

242

For ease of calculation, the state vector should be transformed from a qualitative rating [A, B, 243

C, D, E] in Table 1 to an ordinal system [5, 4, 3, 2, 1], in which elements of the state vector are 244

called status values. As urban bridges in Shanghai are inspected once a year, a one-year transition 245

probability can be determined. 246

In the circumstances of routine maintenance and minor repair, the probabilities for two (or 247

more) state changes in two consecutive years should be negligible, according to Assumption 1. 248

Besides, the rows of the transition matrix must sum to one. It follows that only five transition 249

probabilities are needed to fully define a particular TPM in such a maintenance circumstance, as 250

shown in Equation (4). 251

Comparatively, the case for medium and major repair circumstances is a little more complex, 252

as shown in Equation (5). For grades A to C (i.e., grades 5 to 3), only three transition probabilities 253

are needed, just as for the routine maintenance and minor repair, according to Assumption 2. For 254

grade D (grade 2), 𝑝25 is its actual repair rate according to Assumption 3 and correspondingly the 255

“unrepair” or neglect rate is 1 − 𝑝25. For these unrepaired grade D bridges, the probability of 256

maintaining a D grade is (1 − 𝑝25) ∗ 𝑝22, where 𝑝22 is already determined in Equation (4). And 257

the probability of that a grade D bridge will deteriorate to E grade is (1 − 𝑝25) ∗ (1 − 𝑝22). For 258

grade E (grade 1) bridges, 𝑝15 is the actual repair rate according to Assumption 3 and the neglect 259

rate is 1 − 𝑝15. 260

261

DATA PREPARATION AND CALCULATION OF TPMs 262

Data profiles 263

The stable operation of the Shanghai BMS started in 2004, thus bridge condition records for 2004 264

to 2014 were used in this study to calibrate the Markov-chain model. There are 16,623 bridge CR 265

records in the BMS; each has three sub-records because a bridge can always be divided into three 266

components: bridge deck system, superstructure and substructure. Each component is evaluated 267

separately and the CR grade for the whole bridge is obtained by summing the weighted grades of 268

all three components [1]. Thus, a single bridge actually has four data records and the available 269



data size is actually 66,492. All records had to be preprocessed before using them in TPM 270

calculations because (1) there may have been inspection errors in the BMS, and (2) all records had 271

to be subjected to the three assumptions used in this study to make sure the single TPM was valid 272

[2]. 273

The result of data preparation is shown in Table 2. The number of valid data records for the 274

bridge deck system was the smallest, probably because the deck inspections are based on visual 275

observation and this technique has the greatest variability. On the contrary, the number of records 276

for the inspection of substructure is steadiest over time, which means the decay of the substructure 277

is slow or the defects are hard to inspect. 278

279

Table 2 Number of valid data records 280

Bridge parts

Time interval

2004

2005

2005

2006

2006

2007

2007

2008

2008

2009

2009

2010

2010

2011

2011

2012

2012

2013

2013

2014

Deck system 627 859 879 1058 1227 1161 1153 1276 1366 1320

Superstructure 785 1094 1149 1227 1359 1386 1393 1410 1361 1499

Substructure 866 1133 1185 1309 1391 1480 1449 1499 1565 1632

281

It must be noted that although the bridge type and its material characteristics are varied in the 282

Shanghai BMS, data for concrete girder bridges comprise the majority (83.4% in terms of 283

structure type) of the entire data set, while records for reinforced concrete bridges and pre-stressed 284

concrete bridges accounted for 88.5% of the data set in terms of material type. Therefore the TPM 285

calculation based on these data could be considered homogeneous [2] and all the discussions in 286

this study mainly reflect the characteristics of such bridges in Shanghai. 287

288

TPMs Calculation 289

The 66,492 CR records of urban bridges in the Shanghai BMS from 2004 to 2014 (Table 2) were 290

used to calculate the TPMs. All of the data were preprocessed and validated before being used in 291

TPM calculations. 292

The analysis of Equations (4) and (5) above shows that the transition probabilities in the 293

circumstances of routine maintenance and minor repair are the basis of all calculations. Therefore 294

the calculation of TPMs started using Equation (4). Besides, as mentioned before, each bridge 295

component, as well as the whole bridge, usually has different deterioration characteristics, and the 296

bridge conditions in the central city and suburban areas may also be different in Shanghai; thus, 297

the TPMs should be calculated separately. 298

Circumstances of routine maintenance and minor repair 299

In this case, only four transition probabilities are needed for each situation. Every two-year 300

period (consecutive years) has a group of transition probabilities. However, the final TPMs under 301

routine maintenance and minor repair should be single for each bridge component and the whole 302

bridge [2]. So the calculation results need to be further processed. 303

As the distribution of transition probabilities for each grade is not uniform, the average value 304

and standard deviation were used in this study to analyze these data. The transition probabilities 305



that exceeded the valid range were excluded, and the final transition probabilities are the average 306

value of all valid values, as shown in Equation (6). This method has been proved effective for 307

obtaining stable transition probabilities [18]. 308

309

{𝑅𝑖 = 𝑝

𝑖𝑖± 𝑠𝑖

𝑝𝑖𝑖 = 𝑝𝑖𝑖𝑣𝑎𝑙𝑖𝑑 𝑝𝑖𝑖

𝑣𝑎𝑙𝑖𝑑 ∈ 𝑅𝑖

𝑖 ∈ [5,4,3,2] (6) 310

311

In Equation (6), 𝑅𝑖 is the valid range of transition probabilities for each grade i; 𝑝𝑖𝑖 and 312

𝑠𝑖 are the average value and standard deviation, respectively, of transition probabilities through all 313

years for each grade i; 𝑝𝑖𝑖 is the final transition probabilities for each grade i; and 𝑝𝑖𝑖𝑣𝑎𝑙𝑖𝑑 is the 314

valid probabilities for each grade i. The data processing results can be found in Table 3. 315

316

Table 3 Final transition probabilities under routine maintenance and minor repair and 317

under medium and major repair 318

Category

Final probability

(routine maintenance and minor repair )

Final probability

(medium and major repair )

Element Entire

city

Central

city Suburbs Element

Entire

city

Central

city Suburbs

Bridge

deck

system

𝑝55 0.856 0.860 0.847 𝑝25 0.148 0.244 0.048

𝑝44 0.670 0.693 0.598 𝑝15 0.814 1.000 0.167

𝑝33 0.771 0.773 0.797 - - - -

𝑝22 0.865 0.887 0.887 - - - -

Super-

structure

𝑝55 0.945 0.945 0.943 𝑝25 0.148 0.244 0.048

𝑝44 0.789 0.764 0.823 𝑝15 0.814 1.000 0.167

𝑝33 0.803 0.810 0.821 - - - -

𝑝22 0.836 0.824 0.807 - - - -

Sub-

structure

𝑝55 0.943 0.932 0.956 𝑝25 0.148 0.244 0.048

𝑝44 0.903 0.914 0.892 𝑝15 0.814 1.000 0.167

𝑝33 0.982 1.000 0.944 - - - -

𝑝22 1.000 1.000 1.000 - - - -

Whole

bridge

𝑝55 0.920 0.900 0.917 - - - -

𝑝44 0.885 0.898 0.904 𝑝25 0.148 0.244 0.048

𝑝33 0.923 0.952 0.900 𝑝15 0.814 1.000 0.167

𝑝22 0.925 0.973 0.986 - - - -

319

Circumstances of medium and major repair 320

The case for medium and major repair is a little more complex because the probabilities of 321

CR grades D and E for more than two state jumps in two years must be taken into consideration 322

based on the actual repair rate. As noted previously, a conservation investigation was conducted to 323

acquire the actual repair rate [20]. The transition probabilities for grades A to C are same as those 324

under routine maintenance and minor repair, while the transition probabilities for grades D and E 325

were calculated based on the actual repair rate. The final probabilities reflecting medium and 326

major repair can also be found in Table 3. As shown in Table 3, the transition probabilities for 327

bridges in the central city were much higher than those for bridges in suburban areas, indicating 328



that the bridge conservation intensity in the central city was greater than that in the suburban areas. 329

The better economic development state of the central city may be the main reason for this result. 330

It is should be noted that the transition probabilities named 𝑝25 and 𝑝15 in Table 3 were 331

calculated based only on the survey results of whole bridge repair because more detailed 332

conservation data about individual bridge components were not available. Thus, in this study all 333

bridge components were considered to have the same repair rate as the whole bridge. 334

335

BRIDGE DETERIORATION PREDICTION 336

CR prediction based on present status of Shanghai 337

Using the Markov TPMs and present status of urban bridges, the future status of bridge conditions 338

at any year can be predicted. Taking the bridge condition in 2014 as the present status 𝐶(0), the 339

status vector is defined by Equation (7), in which bridges in different locations are considered 340

separately. Then the bridge condition during next t years 𝐶(𝑡) can be predicted using Equation 341

(8), in which 𝑃𝑐𝑖𝑟is the Markov TPM in a particular circumstance. 342

343

𝐶(0) = {

[0.617, 0.289, 0.083, 0.011, 0] (𝑖𝑓 𝑒𝑛𝑡𝑖𝑟𝑒 𝑐𝑖𝑡𝑦 )[0.531, 0.336, 0.111, 0.021, 0] (𝑖𝑓 𝑡ℎ𝑒 𝑠𝑢𝑏𝑢𝑟𝑏)[0.685, 0.251, 0.060, 0.004, 0] (𝑖𝑓 𝑐𝑒𝑛𝑡𝑟𝑎𝑙 𝑐𝑖𝑡𝑦)

(7) 344

𝐶(𝑡) = 𝐶(0) × (𝑃𝑐𝑖𝑟)𝑡 𝑡 = 1, 2, 3, 4, 5 (8) 345

346

The prediction results of all three bridge components and the whole bridge for the two 347

conservatism regimes are displayed in Figure 2 and Figure 3. The prediction period is 10 years 348

(i.e., 2014–2024). 349

350



351

Figure 2 Bridge prediction results under routine maintenance and minor repair. Letters A, B, 352

C, D and E represent bridge grades according to the Chinese technical regulation. 353

354



355

Figure 3 Bridge prediction results under medium and major repair. Letters A, B, C, D and E 356

represent bridge grades according to the Chinese technical regulation. 357

358

CR prediction for a new bridge 359

The deterioration process under different conservation regimes can be predicted using the 360

Markov-chain model above for a new bridge with intact condition status in Shanghai. The 361



calculation method is described in Equation (9). In Equation (9), 𝐶(𝑡)∗ is the bridge CR grade 362

(status value) after t years; 𝐶(0)∗ is the status vector of the initial condition; 𝑃𝑚𝑎𝑖𝑛𝑡𝑎𝑖𝑛 is the 363

TPM in certain conservation circumstance; and CR is the bridge condition rating vector, which is a 364

constant vector in the case of new bridge. In this study CR= [5; 4; 3; 2; 1]. 365

366

𝐶(𝑡)∗ = 𝐶(0)∗ × (𝑃𝑚𝑎𝑖𝑛𝑡𝑎𝑖𝑛 )𝑡 × 𝐶𝑅 (9) 367

368

It was assumed that new bridges will deteriorate from the intact state during the forecast 369

period of 20 years. Thus, the initial status vector 𝐶(0)∗ was [1, 0, 0, 0, 0]. The bridge condition 370

deterioration tendency for different components and for the whole bridge can be found in Figure 4, 371

in which the ordinate scale 5 to 1 represents CR grades A to E, respectively. 372

373



374

Figure 4 Deterioration prediction over 20 years for a new bridge in Shanghai. The ordinate 375 scale 5 to 1 (y axis) represents CR grades A to E, respectively. 376

377

DISCUSSION 378

Figure 2 and Figure 3 show that the bridge condition will deteriorate rapidly if only routine 379

maintenance and minor repair are implemented. Comparatively, the bridge deck system has the 380

fastest decline of the three bridge components analyzed. At the end of the prediction period (2024) 381

the proportion of bridge deck systems with grade A will be less than 20%, while the proportion of 382

grade E deck systems will be as much as 20%. This finding is quite worrying because the safety 383

rating of a grade E bridge is “dangerous”. Medium and major repairs seem to have a significant 384

positive impact on the bridge deck status in the central city, as shown in Figure 3(a) to Figure 3(f), 385



but this positive impact is not apparent for the suburban bridges. The latest data in the Shanghai 386

BMS show that the proportion of suburban bridges is 55.6% (2014), thus their conditions have a 387

large impact on the overall state of transport infrastructure in the city. Because the medium and 388

major repair rate is too low in suburban areas of Shanghai (see Table 3), the bridge conditions in 389

these areas cannot be improved significantly. The cases for the superstructure, substructure and the 390

whole bridge are almost the same as for the bridge deck system. Bridges in the central city always 391

have a better performance than their suburban counterparts, and the suburban bridges reduce the 392

overall bridge quality level of the entire city, reflecting that investment on the repair of suburban 393

bridges in Shanghai is very insufficient. Even in the central city, the present repair rate cannot 394

fundamentally improve the technical condition of existing bridges. 395

The results portrayed in Figure 2 and Figure 3 indicate that bridges in Shanghai have entered 396

a rapid deterioration stage, and if the repair efforts cannot be strengthened from now, the future 397

state of these bridges will be quite worrying. This conclusion is also consistent with the empirical 398

findings of the Shanghai bridge management investigation conducted as part of this study. 399

Figure 4 displays the predicted deterioration of a new bridge based on the present bridge 400

conservation strategy in Shanghai. The medium and major repair efforts at present seem to have a 401

significant impact on the bridge deck system and the superstructure, as shown in Figure 4(a) and 402

Figure 4(b), and the impact will be apparent in 6–8 years. Regarding routine maintenance and 403

minor repair, the location of a new bridge seems to have no influence on the bridge deterioration 404

process. However, in the case of medium and major repair, the location effect is obvious and the 405

performance decline of new suburban bridges is predicted to be far more rapid than that of new 406

bridges in the central city. As with existing bridges, the present repair efforts are insufficient to 407

improve the state of the substructures and the whole bridges, as shown in Figure 4(c) and Figure 408

4(d). 409

410

CONCLUSIONS 411

Bridge condition data spanning approximately 11 years in the Shanghai BMS were used in this 412

study to calibrate a Markov-chain model to forecast the bridge condition, and also to find the 413

deterioration tendency, of urban bridges in Shanghai. The bridge CR grades were used to generate 414

the state vector space and the time step was set to one year, matching the bridge inspection 415

frequency and simplifying the form of Markov TPMs. 416

The modeling process considered two conservation strategies, and the actual repair rate was 417

obtained through a conservation survey. The influence of bridge location also was considered. 418

Results from the study support the following conclusions. 419

Bridge conservation efforts (or investment levels) are uneven across the city, with those in the 420

central city being much better than those in suburban areas, although the proportion of suburban 421

bridges is higher (55.6%). Furthermore, the present level of bridge conservation efforts in central 422

Shanghai is insufficient, and the condition in suburban areas is even worse. The medium and 423

major repair efforts at present have a significant positive impact on the deck system and the 424

superstructure of central city bridges, but the impact of these efforts on the substructure and the 425

whole bridge is quite small, indicating that the present conservation strategy cannot improve the 426

bridge conditions fundamentally. The positive impacts of conservation efforts on central city 427



bridges do not extend to suburban bridges. Overall, bridges in Shanghai have entered a rapid 428

deterioration stage, and existing repair efforts need to be strengthened immediately. 429

430

ACKNOWLEDGEMENTS 431

This study was funded by The Ministry of Science and Technology of China (Grant Number: 432

2013DFA81910) and National Natural Science Foundation of China (Grant Number: 51378242 433

and 51508411). The authors would like to acknowledge this financial support. 434

435

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