Value of additional traffic data in the context of bridge service-life management

NSIE#1857795, VOL 0, ISS 0 Value of additional traffic data in the context of bridge servicelife management Dominik Skokandi c and Ana Mandi c Ivankovi c QUERY SHEET This page lists questions we have about your paper. The numbers displayed at left are hyperlinked to the location of the query in your paper. The title and author names are listed on this sheet as they will be published, both on your paper and on the Table of Contents. Please review and ensure the information is correct and advise us if any changes need to be made. In addition, please review your paper as a whole for typographical and essential corrections. Your PDF proof has been enabled so that you can comment on the proof directly using Adobe Acrobat. 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Q9 The year of publication has been changed as per Crossref details both in the list and in the text for this reference. Please check. Q10 Please provide the volume number. Q11 Please provide the publisher location. Q12 Please provide the publisher location. PROOFONLY Value of additional traffic data in the context of bridge service-life management Dominik Skokandi c and Ana Mandi c Ivankovi c Department of Structures, Faculty of Civil Engineering, University of Zagreb, Zagreb, Croatia ABSTRACT The assessment of existing road bridges as parts of infrastructure networks is required in consideration of their deterioration and age. Advanced monitoring and management tools are mainly used for landmark bridges while the decision making process for small to medium bridges, which constitute the majority of the bridge network, mainly relies on condition assessment based on experience and conservative analysis related to design codes. In the analysis of the load-carrying capacity of theses bridges, loads imposed by the passing traffic are predominant due to their variable nature and level of uncertainties. The research presented in this paper outlines the value of additional traffic data, collected with both traffic counters and Weigh-in-Motion (WIM) method in the scope of assessment procedures for these bridges. Adequate processing of collected traffic data is crucial for subsequent extrapolation of maximum load effects on a particular bridge over a certain period in time. By taking into account all related costs, the purpose of this paper is to prove the benefits of employing traffic load monitoring data in structural assessment and subsequent decision-making process in service life management of bridges. ARTICLE HISTORY Received 27 April 2020 Revised 22 September 2020 Accepted 29 September 2020 KEYWORDS Assessment; decisionmaking; existing bridges; service-life management; Value of information; weigh-in-motion 1. Introduction Vast majority of civil infrastructure in the USA and Western Europe has been constructed in the 1960s and 1970s and is currently at the risk of ageing and in dire need of assessment and rehabilitation. The deterioration and ageing process is especially evident on the existing road bridges, which represent a critical part of global transportation networks, as the consequences of their potential failure would be severe, from both social and economic aspects. Therefore, the safety assessment of these bridges is required for the evaluation of their reliability levels, as they have been designed and constructed according to old codes, which were not as strict as current standards, in terms of loading and resistance modelling (Skokandi c, 2020). One of key steps in the design or assessment process for new or existing bridges is the determination of total load effects at critical sections of the bridge. Due to their variable nature, most significant effects are induced by the traffic passing over the bridge itself (O’Connor & O’Brien, 2005). Practical application of traffic load models from current design codes for new bridges (Eurocode, 2005) in the assessment procedure for existing ones may provide conservative results suggesting that majority of these bridges need to be strengthened or even replaced. On the other hand, more recent research has proven that the application of site-specific traffic load models, derived from Structural Health Monitoring (SHM) data, results in increased reliability levels and, consequently, in an unrestricted use of the bridge over a much longer remaining service life (Skokandi c, 2020). In addition, extreme traffic loads can be quantified from collected data so as to numerically evaluate bridge response under extreme load scenarios and compare them with alarm levels established by bridge designers (Sousa, Costa, Henriques, Bento, & Figueiras, 2015). These load models are developed from the collected real-life traffic data obtained using the Weight-in-Motion (WIM) technology, a measurement procedure for the collection of traffic data as a part of SHM tools. WIM devices installed outside the bridge length are particularly interesting from the network-level perspective since, if well designed, they allow characterisation of traffic load patterns for a set of bridges within a roadway network (Mandi c Ivankovi c, Strauss, & Sousa, 2020). In addition to these studies, a number of research projects, both in Europe and worldwide, have focused over the last two decades on the topics of bridge assessment, inspection, and Structural Health Monitoring (SHM) in the context of the bridge management process. One of these projects is the recently concluded COST Action TU1402 “Quantifying the Value of Structural Health Monitoring”. The project was initiated to address the challenges of validation and quantification of the SHM data from the perspective of stakeholders and infrastructure owners (Th€ ons et al., 2017) and it resulted in the decision-supporting guidelines for operators, practicing engineers and scientists (Diamantidis, Sykora, & Sousa, 2019; Helder Sousa, Wenzel, &Th € ons, 2019;Th € ons, 2019). The theoretical framework developed within the TU1402 action is based on implementation of the Value of Information (VoI) analysis and decision tree method in the decision-making process regarding the utilization of SHM data. In the current state of practice, 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 CONTACT Dominik Skokandi c[email protected] Department of Structures, Faculty of Civil Engineering, University of Zagreb, Zagreb, Croatia ß2020 Informa UK Limited, trading as Taylor & Francis Group STRUCTURE AND INFRASTRUCTURE ENGINEERING https://doi.org/10.1080/15732479.2020.1857795 PROOFONLY SHM is more used for research purposes than for real structures. This is mainly due to the lack of understanding of the value of additional information that is gained using SHM tools, as even in the cases when SHM is implemented, its information is often disregarded by bridge owners and engineers in charge, and the decisions are based on experience, frequently with conservative assumptions (Zonta, Glisic, & Adriaenssens, 2014). Unfortunately, such practices can result in unnecessarily high maintenance and rehabilitation costs for bridges and viaducts, which are therefore deemed critical elements of the transport infrastructure networks. Furthermore, every partial or complete closure of these bridges leads to both direct losses incurred by bridge owners and indirect losses to bridge users, not to mention socioeconomic costs for the local community. These indirect costs can be significant and, for important bridges, they can even be higher than the direct ones (Thoft-Christensen, 2009, Thoft-Christensen, 2012). Nonetheless, if bridge monitoring could be designed and implemented as a complement to visual inspection, to enhance its effectiveness and improve on its shortcomings, bridge owners could decide to recognise its advantage (Mandi c Ivankovi c et al., 2020). In order to address these issues in the context of bridge management process, a detailed algorithm for validation of additional SHM data in bridge assessment procedures has been developed in (Skokandi c, 2020), based on theoretical framework defined in the COST TU1402 Action. The work presented in this paper aims to quantify the value of incorporating bridge assessment results based on traffic load monitoring data into the decision-making process for bridge maintenance and management, using the VoI methodology developed in (Skokandi c, 2020). Although traffic measurements discussed in the paper are recorded regularly, they are currently only used for traffic analysis and selection of overloaded vehicles. In this research, they are implemented in the procedure for bridge assessment. The benefits of the assessment results from the owner’s point of view in terms of reduced overall maintenance costs are also investigated. By doing so, results of posterior VoI (based on available data from traffic counters in the country and WIM measurements on a road leading to a certain bridge) could convince the operator to invest in more traffic load analysis and WIM measurements (at different locations) and to use the existing and subsequently collected traffic load and WIM data in bridge management, and not only for traffic counting and weight limitations as it has been done so far. In the first part of the paper, the emphasis is placed on the WIM technology, development of traffic load models, and reliability analysis of the Case Study bridge. Three distinct assessment levels (strategies) will be considered: at the initial level, the assessment is performed without any additional traffic information, using the codified Load model 1. At the second level, the assessment is conducted based on Load model 1 adjusted in respect to heaviest traffic measurements in the country and, at the third level, the assessment is based on specific traffic load related to continuous WIM measurements on a road leading to a bridge. Development of the posterior VoI analysis algorithm and estimation of all related costs and benefits are provided in the second part of the paper for the three assessment strategies (S0 related to level 1 assessment, S1 related to level 2 assessment, and S2 related to level 3 assessment). The analysis of VoI results, and recommendations for future research, are given in the concluding section that presents benefits of employing traffic load monitoring data in structural assessment and subsequent decision-making process within the service life management of bridges. 2. Importance of traffic load modelling in assessment of existing bridges 2.1. Overview Reliability analysis for both new and existing structures is a procedure in which structural resistance is evaluated in relation to the total effect of the applied loads, in order to quantify the safety level or reliability of the structure. For bridges, dominant loads are described as permanent loads, consisting of the structure self-weight and additional dead loads (road surfacing, railings, etc.), and live loads induced by the passing traffic. Regardless of the reliability analysis method (deterministic, semi-probabilistic, probabilistic), traffic loads are associated with the highest level of uncertainties, due to their variable and unpredictable nature. Additionally, for existing bridges, which have reduced reliability levels when compared to new bridges, permanent loads can be accurately calculated based on the on-site geometry measurements and material testing, thus further reducing their uncertainty levels. On the other hand, loads induced by the passing traffic can be either estimated using codified load models for the design of new bridges, or developed using the recorded traffic data. Some countries, such as Netherlands, Denmark, Switzerland, and Slovenia, have developed specific bridge assessment codes based on the reduced traffic load models or site-specific models (Skokandi c, 2020;Wi  sniewski, Casas, & Ghosn, 2012). Principles of weighing vehicles in motion using bridges, which are valid to this day, were first established by Moses in the USA (Moses, 1979). In the late 1990s, research interest in B-WIM intensified as two research projects supported by the European Commission were initiated based on the BWIM work from Slovenia and studies from Ireland: COST Action 323 –Weigh in Motion of Road vehicles (Jacob, 2002) and FP4 project WAVE –Weighing of Axles and Vehicles (Jacob, 2002) in Europe. More recent improvements in B-WIM technology were achieved as a part of two FP7 research projects, TRIMM (Ralbovsky et al., 2014) and BRIDGEMON (Corbaly,  Znidari c, Leahy, Hajializadeh, & Zupan, 2014; Favai et al., 2014). In Croatia, there are still no official codes or guidelines for modelling traffic loads in the assessment process for the existing road bridges, and this modelling is also not included in official EU standards Eurocodes. On the other hand, traffic data measurements have been conducted regularly on Croatian state roads for over two decades, using 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 2 D. SKOKANDIĆAND A. M. IVANKOVIĆ PROOFONLY both WIM and B-WIM technology (Skokandi c, Mandi c Ivankovi c,  Znidari c, & Srbi c, 2019). Research focusing on the use of recorded traffic data in the assessment procedures for road bridges in Croatia has been conducted at the University of Zagreb over the last decade, as reported in several papers (Mandi c Ivankovi c, Skokandi c,  Znidari c, & Kreslin, 2019; Mandi c, Radi c, &  Savor, 2009; Skokandi c, Mandi c Ivankovi c, & D zeba, 2016) and PhD thesis (Mandi c Ivankovi c, 2008; Skokandi c, 2020). This paper focuses on the quantification of measured traffic data from the perspective of bridge owners and bridge users. In general, traffic load on road bridges can be divided into congested traffic, basically a traffic jam situation, and free-flow traffic, which is a steady traffic flow of 60-100 km/ h. Furthermore, from the engineering point of view, the traffic load is divided into the static and dynamic components. Most of the current design codes have the dynamic part already integrated with the specified load models but, in older codes, dynamic factor was calculated manually depending on bridge characteristics (Bruls, Croce, & Sanpaolesi, 1996; Bruls, Mathieu, Calgaro, & Prat, 1996; Dawe, 2003; Eurocode, 2005; Skokandi c et al., 2019). More detailed historical review of traffic load models developed over the years can be found in the book by Dawe (2003). In Croatia, a majority of existing state road bridges have been designed according to older codes, mainly PTP-5 (valid until 1973) and the codes based on the German DIN 1072 (valid until 2002). The Case Study bridge analysed in this paper was built in the 1960s according to PTP-5 code. Significant increase in the average annual daily traffic (AADT) over the last two decades of the past century caused the revision of design codes and acceptance of European standards in the 2000s (Mandi c & Radi c, 2004; Skokandi c et al., 2019). The basic approach to the development of traffic loads, both site-specific and modern codified ones, is to collect a certain amount of traffic data, including axle loads and spacings, and to apply one of statistical methods to extrapolate the collected data and estimate the maximum expected load effects. There is a number of traffic data collection methods available, but most widely accepted ones are based on the WIM and B-WIM methods ( Znidari c, Kreslin, Lavri c, & Kalin, 2012). Codified traffic load models have been developed for the design of new bridges and, therefore, they may provide conservative results in the assessment procedure for existing bridges. The application of localised, adjusted or site-specific traffic load models in the assessment of existing bridges is crucial for making optimum management decisions. 2.2. Current traffic load models for the design of new bridges The European code EN 1991-2:2003 (Eurocode, 2005) defines imposed loads, both models and representative values, associated with road traffic, which includes dynamic effects, centrifugal, braking, and acceleration actions to be used for the design of new bridges. These load models were developed based on traffic data collected with WIM technology on a motorway in France in the 1980s. The data were used for calculating load effects using influence lines and areas, and extrapolations were made to evaluate reference values of representative traffic loads. A more detailed review on the background and development of EN 1991-2 codes can be found in (Bruls, Croce, et al., 1996; Bruls, Mathieu, et al., 1996). The Load Model 1 (LM1), defined as a general traffic model that already takes into account dynamic amplification due to vehicle-bridge interaction, is used in the majority of bridge designs for every road and bridge type and is therefore implemented in the assessment procedure for the Case Study bridge in this paper. It is comprised of two tandem systems (TS) representing concentrated axle loads and uniformly distributed load (UDL) across the entire width of the carriageway. Graphical representation of LM1 for state road bridges (with the total width wunder 9.0 m) is given in Figure 1 (Skokandi c et al., 2019). Adjustment factors (Figure 1)aQ,i,aq,iand aq,rare used for the adjustment of total traffic loads depending on the road category and expected traffic density and weight. Values of these factors are defined in National Annex for each country, or if not specifically indicated, they can be taken equal to 1.0 for all new bridges, as it is the case in the majority of EU countries. Nevertheless, some countries, such as France, Germany, and Netherlands apply increased values of adjustment factors to take into account predicted increase in traffic growth. A detailed list with values of these specific adjustment factors for selected EU countries can be found in (Skokandi c et al., 2019). Adjustment factors from Figure 1 can also be used for the reduction of total traffic load effects in the assessment procedure for existing road bridges, by reducing their initial value of 1.0 based on the measured traffic data. For example, Switzerland defined national assessment codes for existing bridges and implemented reduced adjustment factors based on bridge type and span length (SIA, 2011). The procedure for calibration of adjustment factors based on WIM data, defined by O’Brien et al. (2012), can be used for a single bridge or the local transport network. In Croatia, the traffic load effects calibration based on measured traffic data was conducted by Mandi c Ivankovi c(2008, 2009), through analysis of national traffic records. As a result, reduced values of adjustment factors are calibrated and will be used in this paper as one of assessment strategies in the analysis of the Case Study bridge. Reduced factor values, depending on bridge type and span length, are given in Table 1. 2.3. WIM and B-WIM as a part of structural health monitoring Traffic data collected using both WIM and B-WIM systems constitute an unbiased traffic sample as the measurement is conducted in uncontrolled conditions and without the need for vehicle to slow down or stop. The data set obtained for each vehicle passing over the measurement site includes its gross weight (GVW), axle load, number and spacing, vehicle 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 STRUCTURE AND INFRASTRUCTURE ENGINEERING 3 PROOFONLY speed, and timestamp of the passage. Post-processing of collected traffic data is required for their extrapolation and subsequent estimation of maximal load effects on the selected bridge over a certain time period, as it was done based on collected WIM data for the Case Study bridge in this paper. Additionally, B-WIM systems also provide supplemental structural data on bridge response to the effect of the passing traffic, such as measured influence lines, load distribution, and dynamic factors. This additional information can be used as a key input in assessment procedures for existing road bridges, applied for calibration of numerical models, as presented in (Mandi c Ivankovi c, Skokandi c, et al., 2019; Znidari c, Kalin, & Kreslin, 2018). For the presented Case Study bridge, continuous traffic data measurements were conducted using the pavement WIM system on the road leading to the bridge. Therefore, the VoI analysis presented in the second part of the paperwillbeconductedinordertoquantifybenefitsresulting from incorporation of recorded traffic data in the assessment of existing road bridges. In general, there are two main approaches for the postprocessing of collected traffic data, either using statistical methods, i.e. extrapolating the data by fitting it to a certain distribution, or using a very large number of long-run simulations like the Monte Carlo method. For example, in the development process for current design load models from EN 1991-2, the post-processing was conducted using three distinct methods, two based on statistical approach (fitting the upper data tail to a half-normal and a Gumbel distribution) and Monte Carlo (MC) simulation for the validation of obtained results (Bruls, Croce, et al., 1996). Other commonly used methods include Block Maxima, Peaks over Threshold (POT), Box-Cox approach (O’Brien et al., 2015), and convolution method ( Znidari c, 2017). While statistical methods are subject to a certain level of subjectivity and can, therefore, have a considerable margin of error, MC simulations are not practical for general use, as they require a certain level of knowledge and high computational power. Further details on the most widely used post-processing methods for the extrapolation of traffic data can be found in the review paper by O’Brien et al. (2015). Along with the selection of a statistical extrapolation method, the selection of a reference time period is essential in the post-processing of traffic data and subsequent calculation of maximum expected traffic load effects. For example, characteristic values of LM1 (Figure 1) were extrapolated for a 50-year reference period during the development of EN 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 Figure 1. Example of LM1 on a two-lane state road bridge. Table 1. Reduced adjustment factors for assessment of state road bridges in Croatia - research-based proposal (Mandi c et al., 2009). Span [m] 10 10 –20 20 –30 30 –40 40 –50 Simply supported bridge aq,2¼aq,r¼1,0 aQ,10,80 0,80 0,80 0,80 0,80 aQ,2;aQ,3;aq,10,30 0,38 0,51 0,58 0,62 Continuous bridge aq,2¼aq,r¼1,0 aQ,10,80 0,80 0,80 0,80 0,80 aQ,2;aQ,3;aq,10,48 0,72 0,78 0,81 0,82 4 D. SKOKANDIĆAND A. M. IVANKOVIĆ PROOFONLY 1991-2 (Bruls, Mathieu, et al., 1996). In order to apply the LM1 for shorter time periods, two approaches can be used. The first one is to shift the Gumbel distribution to lower reference periods in order to obtain a lower mean value for traffic load effects. Additionally, EN 1990 (Eurocode, 2002) provides simplification for reduction of characteristic values of LM1 to a one-year period by simply reducing initial values (Figure 1) by 20%. The first approach is used for the reliability analysis of the Case Study Bridge as the simplification provided by EN 1990 is relatively conservative. Chosen approach utilizes the property of the Gumbel distribution that the standard deviation is independent of the considered reference period and that the mean value depends on the period Tin the following way (Faber, 2012): l50 ¼l1þ0, 78 r1lnðT50Þ(1) where: l50,l1–are the traffic load effects mean values for 50and 1year reference periods; r1–is the traffic load standard deviation for 1year reference period (r1¼r50Þ; T–is the chosen reference period. The extrapolation method chosen for this research, called convolution method, has proven to provide similar results like long-run simulations and, at the same time, it is computationally less complex and more suitable for practical application. It was first proposed by Moses and Verma (1987), and has been used and constantly improved in Slovenia ( Znidari cetal., 2012) for over two decades with data recorded from SiWIMV R B-WIM system ( Znidari c, 2017). The convolution method is based on assumptions that the traffic in two adjacent lanes on the bridge is independent and that the highest load effects are achieved when two vehicles in each lane meet side by side at a critical section of the selected bridge. The described method was developed around the fact that, due to the typical length of heavy vehicles, critical loading scenarios for short to medium size bridges occur in the free flow traffic (while the traffic jam situations typically represent critical loading scenarios for long bridges). Such an approach is justified on a majority of simply supported continuous bridges whose influence-line lengths between supports are up to 30 meters, and has therefore been chosen for the Case Study bridge analysed in this paper. The convolution method applies the influence line theory for the calculation of traffic load effect of each vehicle, followed by generation of load effects histograms for each independent lane, the convolution of these histograms to simulate the presence of vehicles in both tracks simultaneously, and subsequent extrapolation of maximum values to certain time periods. For further details, this can be found elsewhere (Skokandi c,  Znidari c, Mandi c Ivankovi c, & Kreslin, 2017; Znidari c, 2017). 3. Case study bridge 3.1. Overview The Case Study bridge used in this research was built in 1961 as a continuously reinforced concrete (RC) slab bridge over three spans. It is located on a Croatian state road, near the town of Posedarje, and features a total deck width of 8.50 meters, and two traffic lanes, one for each direction of travel. Thebridgeiscontinuousacrossthreespans,9.0þ15.0 þ9.0 m, divided with RC piers and abutments, and supported on RC foundations and wooden piles. The bridge setup involving a larger central span has been selected due to heavy rainfall, which caused the collapse of the old concrete arch bridge that had been built on the same location in the 1960s. The original documentation and design plans, along with the built-in reinforcement, are available from the archives ( Sram, 2002). The longitudinal and transverse sections of the bridge are presented in Figures 2 and 3. The numerical FE model of the bridge was used for calculation of total load effects for the load-carrying capacity assessment. It was developed using Sofistik software (Sofistik & Sofistik, 2014) for structural analysis, using 2D quad elements, with finite element size of 0.2 0.2 m, presented in Figure 4. Material characteristics and additional permanent load values (road surfacing, railings etc.) were obtained from the original documentation, as presented in Tables 2 and 3. In addition to self-weight and additional permanent load, only traffic load effects were taken into account in structural analysis, as dominant variable loads on road bridges. Based on the preliminary visual inspection, documentation review and linear analysis, the critical failure mode for the selected bridge was defined as a flexural failure due to bending moment in the middle of the central span (resistance to load ratio 0,836 –section 2-2 in Figure 4), and failure at internal bridge supports due to hogging moment (resistance to load ratio 0,742 –section 1-1 in Figure 4). The limit state equation (LSE) for the cross-sectional bending capacity was defined for both critical sections based on the geometry, material characteristics, and built-in reinforcement. 3.2. Assessment strategies The multi-level assessment of the Case Study bridge was conducted in order to quantify the value of additional traffic data obtained using the previously described WIM measurements, with each level representing one of the defined assessment strategies. Multi-level assessment procedures are suitable for existing bridges as the complexity and accuracy increase consecutively throughout the levels. At the initial level, the assessment procedure is performed without any additional information, using the codified procedure and Load model 1 for the design of new bridges from EN 19912. The results obtained at this level are considered as a reference value, which will be used for comparison and quantification of additional traffic data implemented at subsequent levels. The re-assessment of the Case Study bridge is performed at the second level of the defined procedure, using reduced values of adjustment factors for codified LM1, as based on traffic measurements conducted on the heaviest loaded road in Croatia and presented in Table 1 (Mandi c et al., 2009). Traffic load effects are developed in the final step of the assessment procedure using the convolution 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 STRUCTURE AND INFRASTRUCTURE ENGINEERING 5 PROOFONLY method based on continuous WIM measurements on the road leading to the Case Study bridge. The reliability analysis of the Case Study bridge is conducted for each level using a fully probabilistic approach, as recommended in the Probabilistic Model Code (JCSS, 2002), and the results are presented in terms of calculated probabilities of failure p f and the corresponding reliability indices b. The basic limit state equation for reliability analysis is 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 Figure 2. Longitudinal section of Case Study bridge (units in m). Figure 3. Cross-section of Case Study bridge (units in m). Figure 4. FE numerical model of Case Study bridge –deformation under permanent load (developed in the Sofistik software for structural analysis). Table 2. Parameters for modelling cross-sectional resistance –statistical characterisation. Variable Symbol [Units] Distribution Nominal Value Mean Value (m) St.Dev. (r) Source Effective depth of bars d[m] Normal 0.56 0.56 0.10 m(JCSS, 2001b) Number of bars per slab section n b Deterministic 14 14 / Yield strength of reinforcing steel f y [kN/cm 2 ] Normal 22.0 24.46 0.05 m Area of rebar A s [cm 2 ] Normal 3.14 3.14 0.02 m Resistance uncertainty hRLognormal / 1.00 0.06 m(Fib, 2016) 6 D. SKOKANDIĆAND A. M. IVANKOVIĆ PROOFONLY developed based on the defined critical failure mode and JCSS recommendations (JCSS, 2001b). Design codes for new bridges (Eurocode, 2002) propose a semi-probabilistic procedure based on the partial safety factors method (PSFM), but it has been proven that probabilistic approach provides improved assessment results in terms of load-carrying capacity (Lauridsen, Jensen, & Enevoldsen, 2007). The flow chart of the multi-level assessment procedure defined for the Case Study bridge, as based on the one developed in (Skokandi c, 2020), is given in Figure 5. 3.3. Assessment procedure and results The basic limit state equation (LSE) for the reliability analysis of the Case Study bridge is defined as: Z¼hRRhEE(2) where: R–is the cross-sectional resistance to selected load effect (bending moment, shear force, etc.); E–is the value of the corresponding load effect at critical cross-section; hR;hE–are additional model uncertainty distributions accounting for deviations between the model and reality (JCSS, 2002). Further derivation of Equation (2) is conducted based on the selected critical failure mode for which the assessment procedure is performed. For the Case Study bridge, based on the preliminary condition assessment the cross-sectional flexural failure due to negative bending moment on both inner supports is defined as the critical failure mode. Furthermore, as the Case Study bridge is a continuous system, flexural failure in the middle of the central span is also considered in the assessment. Therefore, Equation (2) can be re-written as: Z¼hRMRhEME(3) where: MR–is the cross-sectional bending moment resistance; ME–is the total bending moment load effect at a critical cross-section; The cross-sectional bending resistance of the Case Study bridge M R can be calculated based on original documentation and built-in reinforcement, as follows: hRMR¼hR0:9dnbAsfy(4) where: d–is the effective depth of reinforcing bars; nb–is the total number of reinforcing bars in the critical cross-section; As–is the cross-sectional area of a single reinforcing bar; fy–is the yield strength of reinforcing steel, available from original documentation. Bending moment values as the total load effect in critical cross-sections M E can be defined as: hEME¼hE,GðMGþMDGÞþhE,QMQ(5) where: MG–is the portion of total bending moment induced by self-weight of the bridge; MDG–is the portion of total bending moment induced by additional dead load (e.g., road surfacing, railings, etc.); MQ–is the portion of the total bending moment induced by traffic load; hE,G–is the permanent load model uncertainty function; hE,Q–is the traffic load model uncertainty function. Finally, the fully derived LSE for the Case Study bridge can be defined as: Z¼hR0:9dnbAsfyhE,GðMGþMDGÞhE,QMQ (6) All parameters in Equations (2)–(6) are modelled as stochastic variables (or random variables –i.e., parameters whose values depend on certain uncertainty or an outcome in their quantifications) with the corresponding statistical parameters and distribution types, as presented in Tables 2 and 3. Values of statistical parameters and recommended distribution types are taken from the Probabilistic Model Code (JCSS, 2002) and fib guidelines (Fib, 2016), while nominal values for resistance variables are obtained from original documentation ( Sram, 2002) and from the numerical model analysis for load effect variables. Both load effects and cross-sectional resistance are calculated in the middle of the middle span (section 2-2, Figure 4) and at inner supports (section 1-1, Figure 4). Based on structural analysis of the Case Study bridge numerical model (Figure 4), the critical failure mode is defined as flexural failure due to the negative bending moment on the supports above the piers. The corresponding values are shown in Tables 2 and 3. The total traffic load effect M Q is calculated separately for each of the three assessment strategies as explained in the flowchart shown in Figure 5. For the first two assessment levels, it is derived from the numerical model for a reduced LM1 compatible with the one-year reference period based on Equation (1). As for the final level, M Q is derived directly from WIM measurements for various time periods using the convolution method. Mean values for WIM traffic 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 748 749 750 751 752 753 754 755 756 757 758 759 760 761 762 763 764 765 766 767 768 769 770 771 772 773 774 775 776 777 778 779 780 781 782 783 784 785 786 787 788 789 790 791 792 793 794 795 796 797 798 799 800 801 802 803 804 805 806 807 808 809 810 811 812 813 814 815 816 817 818 819 Table 3. Parameters for modelling total load effects for a reference period of one year –statistical characterisation. Variable Symbol [Units] Distribution Nominal Value Mean Value (m) St.Dev. (r) Source Self-weight load effect M G [kNm/m] Normal / 253.60 0.04 m(JCSS, 2001a) Additional dead load effect M DG [kNm/m] Normal / 51.70 0.05 m Traffic load effect –level 1 M Q,1 [kNm/m] Gumbel / 216.10 0.14 m(Eurocode, 2005) Traffic load effect –level 2 M Q,2 [kNm/m] Gumbel / 163.97 0.14 m Traffic load effect –level 3 M Q,3 [kNm/m] GEV / 67.10 0.13 m(ARCHES D10,10,2009) Dynamic amplification factor DAF Gumbel / 1.25 0.10 m Dead load uncertainty hE,GNormal / 1.00 0.05 l(JCSS, 2001b) Traffic load uncertainty hE,QNormal / 1.0 0.10 l STRUCTURE AND INFRASTRUCTURE ENGINEERING 7 PROOFONLY load effects are defined as median values of cumulative distribution functions (CDFs) for various time periods, as presented in Figure 6. The initial CDF of traffic load effects f(x) (Figure 6a) is developed with the convolution method from actual WIM measurements recorded for a period of over two months, in both summer and winter seasons. CDFs for other time periods are extrapolated using the extreme value theory (Ang & Tang, 1975) by exponentiating the initial distribution f(x) to a certain power.  Znidari c (2017) proposes the variable Nfor exponentiation, whose value is based on three parameters: number of days taken into consideration (e.g. number of working days per year), selected time periods for extrapolation, and the number of multiple presence events on the bridge expected in a chosen time period. The last of these parameters presents the most influencing parameter for the value of Nand is explained in more detail in ( Znidari c, 2017). For the reliability analysis of the Case Study bridge, the maximum expected traffic load effects from WIM measurements are extrapolated for a reference period of one year only, to be compatible with the target reliability index. The value of Nis calculated directly from the obtained data and the CDF is presented in Figure 6b. It is clear from Figure 6 that the CDF for the time period of 1 year has shifted to the right compared to the initial one, resulting in increased mean and characteristic values, but is also steeper, meaning that the variability is decreasing. For longer time periods, the variability decrease even more, as the parameter Nincreases exponentially and the CDFs will be more and more steeper, as described in ( Znidari c et al., 2012). Expected bending moment values shown in Figure 6 are derived from WIM measurements for the total width of the bridge cross-section and are therefore expressed in kNm. The absolute value from Figure 6 must be modified as the LSE in Equation (5) is defined for the reliability analysis of the critical bridge-deck section, with the total width of 100 cm, based on recommendations given in design codes (Eurocode, 2004). Before their implementation in Equation (6) their absolute value is multiplied with the factor (LDF), which defines the proportion of total load transferred to the critical slab section. For the Case Study bridge, the LDF factor is derived directly from the numerical model, as a ratio of absolute value of total load effects [kNm] to their proportion transferred on the critical section [kNm/m] is equal to 0.167. Furthermore, to take into account the dynamic proportion of load effects due to bridge-vehicle interaction, the values from Figure 6 need to be multiplied with the dynamic amplification factor (DAF). In the absence of additional traffic data, the value from design codes for new bridges is used for the DAF (Bruls, Mathieu, et al., 1996; Eurocode, 2005). Its value depends on the bridge type, span and selected load effect, and for the Case Study Bridge, it is equal to 1.25. The traffic load effects presented in the Table 3are calculated for one-year reference period, using Equation (1) for levels 1 and 2, while n level three they are derived directly from WIM measurements (Figure 6). The reliability analysis for the Case Study bridge is conducted for each of the three defined assessment strategies using Monte Carlo simulation with 10 8 runs, based on the defined LSE (6) and the values from Tables 2 and 3. The number of simulations is calculated from the recommendations given by Nowak and Collins (2007) based on the expected probability of failure (10 5 ) and the coefficient of variance (0.05). The probability of failure is selected approximately based on recommendations for new structures while the coefficient of variance is approximated to take statistical error into account. Results in terms of calculated probabilities of failure, and the corresponding reliability indices, are presented in Table 4. Results presented in Table 4, on one hand, clearly point to the benefits of additional data in both second and third assessment levels, validating the additional data with the reduction of probability of failure and increase in the corresponding reliability index. However, on the other hand, obtained reliability indices are too low compared to the minimum required value of 3.3, based on the consequence class and relative cost of safety measures (JCSS, 2002). Therefore, the conclusion can be made that the Case Study bridge is not suitable for traffic loads prescribed in the 820 821 822 823 824 825 826 827 828 829 830 831 832 833 834 835 836 837 838 839 840 841 842 843 844 845 846 847 848 849 850 851 852 853 854 855 856 857 858 859 860 861 862 863 864 865 866 867 868 869 870 871 872 873 874 875 876 877 878 879 880 881 882 883 884 885 886 887 888 889 890 891 892 893 894 895 896 897 898 899 900 901 902 903 904 905 906 907 908 909 910 911 912 913 914 915 916 917 918 919 920 921 922 923 924 925 926 927 928 929 930 931 932 933 934 935 936 Figure 5. Multi-level assessment strategy supported by full-probabilistic analysis. 8 D. SKOKANDIĆAND A. M. IVANKOVIĆ PROOFONLY time is around 5 minutes, based on available alternate routes. The same parameters are used for the bridge repair period when costs of bridge repair are over 200% of the bridge value (Equation (17)). Costs in the event of total bridge failure C FAIL are taken as 400% of the bridge total value C BV (section 4.2.2.). Costs of unavailability in cases when bridge repair or failure occurs are calculated using Equation (18) and Eurostat data. The average cost per weekend days is estimated at 50% of the workday cost, while the total cost per vehicle per month for every minute of prolonged time is calculated as 12.75 EUR. With an average AADT of 9500 (taking into account both summer and winter seasons) obtained by bridge owner, costs are calculated as follows: CN AREP ðÞ ¼NCN A,vehicle tN A ¼9500 12, 75 1:5min 3months ¼545:062, 00 EUR CN AFAIL ðÞ ¼NCN A,vehicle tN A ¼9500 12, 75 5:0min 12months ¼7:267:500, 00 EUR VoI analysis is conducted using the algorithm developed in the Excel spreadsheet software for the assessment results given in Table 4. Summarized input data for VoI analysis for 1-year reference period are presented in Table 7, with benefits for each outcome Bi calculated using Equation (7) as negative total costs C TOT, assessment using Equation (14). The VoI analysis is performed by means of data from Table 8 and the decision tree concept presented in Figure 7, using numerical model developed in the Excel spreadsheet software. The results are presented in Figures 9 and 10. The optimum assessment strategy branch is presented with a thick dashed line, as the one resulting in maximized benefits B i (negative costs C TOT,assessment which are presented as percentage of the total bridge value C BV ). 4.3.2. Voi analysis including both bridge owner and user’s costs Results of VoI analysis given in Figure 9 show that the assessment strategy S2 at level 3 (dark shaded cell on Figure 9), using site-specific traffic load model developed from WIM data, is an optimum strategy for assessment of the Case Study bridge, in terms of costs and benefits for both bridge owner and user. Furthermore, strategy S 1 , based on reduced codified traffic load model using the recorded traffic data, is also feasible, compared to the initial strategy S 0 in which no additional data is used in the assessment. The relative value of additional information in both strategies using additional data, S 1 and S 2 is calculated with Equation (12) and (13), and total benefits for each strategy (light shaded cells on Figure 9): VS1,relative ¼B1S1 ðÞ B0S0 ðÞ B0S0 ðÞ jj ¼1:3188ð3:7849Þ 3:7849 jj ¼0:6515 ¼65:15 % VS2,relative ¼B2S2 ðÞ B0S0 ðÞ B0S0 ðÞ jj ¼0:1340ð3:7849Þ 3:7849 jj ¼0:9646 ¼96:46 % The difference between strategies S1 and S2 is not large as it is between S1 and the prior strategy S0, which is mainly due to the difference in the mean value and standard deviation of the bending moments related to traffic action at level 2 and level 3, respectively. But the difference could get larger for bridges with lower specific traffic loads. Results of the Strategy S1 with the adjusted Load model 1 are also very important as these adjustment factors are based on traffic count in the country in general, although a more localised traffic load could be of greater importance for a specific bridge. Furthermore, as it is clear from results given in Figure 9 and separate C REP cost values from Table 7, the results of each branch show that the repair of the Case Study bridge is not optimum maintenance approach due to high costs of bridge repair as the reliability indices are very low (choice a 0 –do nothing values are closer to 0 than a i –repair bridge values). However, it is also visible from Figure 9 that the VoI results strongly depend on calculated user costs arising from bridge unavailability (C N/A specified in Table 7)in case of repair works or its failure. This proves the assumptions made in previous research (Koch et al., 2002; Skokandi c, 2020; Thoft-Christensen, 2009) that user costs quickly become dominant in the global cost function even for smaller bridges when the unavailability period is prolonged. These results could be of key interest for decision makers at the government level. Nevertheless, as these costs are commonly not taken into account by some road and bridge owners in the scope of bridge management systems, VoI from Figure 9 is re-performed by taking into account only direct costs incurred by bridge owner. These results, aimed particularly at bridge owners, in which all unavailability costs are equal to zero, are presented in the form of a decision tree in Figure 10. 1639 1640 1641 1642 1643 1644 1645 1646 1647 1648 1649 1650 1651 1652 1653 1654 1655 1656 1657 1658 1659 1660 1661 1662 1663 1664 1665 1666 1667 1668 1669 1670 1671 1672 1673 1674 1675 1676 1677 1678 1679 1680 1681 1682 1683 1684 1685 1686 1687 1688 1689 1690 1691 1692 1693 1694 1695 1696 1697 1698 1699 1700 1701 1702 1703 1704 1705 1706 1707 1708 1709 1710 1711 1712 1713 1714 1715 1716 1717 1718 1719 1720 1721 1722 1723 1724 1725 1726 1727 1728 1729 1730 1731 1732 1733 1734 1735 1736 1737 1738 1739 1740 1741 1742 1743 1744 1745 1746 1747 1748 1749 1750 1751 1752 1753 1754 1755 Table 6. Costs of SHM measurements for Case Study bridge. Assessment strategy C SHM per lane C SHM –total No additional data –Level 1 0 0 Reduced adjustment factors based on heaviest measured traffic in the country–Level 2 / 10.000 EUR Site-specific traffic load model based on measured WIM data on the road leading to the bridge –Level 3 20.000 EUR 40.000 EUR STRUCTURE AND INFRASTRUCTURE ENGINEERING 15 PROOFONLY 4.3.3. Voi analysis including only direct costs by bridge owner The results of re-performed VoI analysis given in Figure 10 present a similar trend as the ones in Figure 9, as the assessment strategy S 2 is still the most optimal one, followed by the strategy S 1 . VS1,relative ¼B1S1 ðÞ B0S0 ðÞ B0S0 ðÞ jj ¼0:3335ð0:9200Þ 0:9200 jj ¼0:6375 ¼63:75 % VS2,relative ¼B2S2 ðÞ B0S0 ðÞ B0S0 ðÞ jj ¼0:0840ð0:9200Þ 0:9200 jj ¼0:9086 ¼90:86 % 4.3.4. Case study bridge VoI results –discussion Results presented in this case study clearly emphasize the benefits of incorporating bridge assessment results based on traffic load monitoring data in the decision-making process for bridge maintenance and management. The implementation of country specific traffic load measurements (strategy S1) should be included in the assessment of existing bridges as they reduce direct costs of the bridge owner (Figure 10 and result with 63.75% relative benefit). Additionally, although the Case Study bridge is not iconic and is relatively small, the investment in site specific WIM measurements (with the strategy S2) would benefit the bridge owner even more (90.86%). When direct cost for the owner and indirect user costs due to bridge unavailability are considered, both traffic load collection methods (country specific traffic load measurements as a part of strategy S1, and site-specific WIM measurements at the road leading to the certain bridge as a part of strategy S2) result in even higher benefits for society in general (65.15% and 96.46% respectively). The difference of the benefits for two strategies would become even larger for bridges with lower specific traffic loads. Additionally, in order to present the dominant effect of indirect user costs in total cost reduction (in EUR), the absolute values of additional SHM information are given in Table 9, as total savings for both bridge users and its owner (calculated using Equations (10) and (11)). 5. Conclusions The assessment procedure of the Case Study bridge described in this paper is based around the implementation of additional traffic information, obtained with vehicle weighing process and WIM technology. The purpose was to prove that traffic data, regularly collected by most road directorates worldwide mainly for traffic analyses and selection of overloaded vehicles, can additionally be used as a basis for site-specific assessment of existing road bridges, which will consequently lead to a more efficient bridge management. The benefit for both the bridge owner and bridge user is presented, and both the relative and absolute value of additional information for each assessment strategy are summarized in Tables 8 and 9. It is important to note that the calculated relative values of additional SHM information are very dependent on the input parameters (probabilities of failure and corresponding reliability indices from Table 4). In cases when bridges have higher reliability levels, the difference between relative values when only direct costs are taken into account and when user costs are added is much larger, as presented on two newer bridges in (Skokandi c, 2020). 1756 1757 1758 1759 1760 1761 1762 1763 1764 1765 1766 1767 1768 1769 1770 1771 1772 1773 1774 1775 1776 1777 1778 1779 1780 1781 1782 1783 1784 1785 1786 1787 1788 1789 1790 1791 1792 1793 1794 1795 1796 1797 1798 1799 1800 1801 1802 1803 1804 1805 1806 1807 1808 1809 1810 1811 1812 1813 1814 1815 1816 1817 1818 1819 1820 1821 1822 1823 1824 1825 1826 1827 1828 1829 1830 1831 1832 1833 1834 1835 1836 1837 1838 1839 1840 1841 1842 1843 1844 1845 1846 1847 1848 1849 1850 1851 1852 1853 1854 1855 1856 1857 1858 1859 1860 1861 1862 1863 1864 1865 1866 1867 1868 1869 1870 1871 1872 Table 7. Input data for VoI analysis of the Case Study Bridge. Choice S i Choice a i Total costs C TOT C REP C SHM C N/A C FAIL S 0 –reference strategy with no additional traffic data a 0 –do nothing 0.000C BV 0.000 0.000 0.000 0.000 16.456C BV 0.000 0.000 12.456 4.000 a 1 –bridge repair 14.456C BV 2.000 0.000 12.456 0.000 18.456C BV 2.000 0.000 12.456 4.000 S 1 –strategy with reduced load model based on traffic measurements a 0 –do nothing 0.0171 C BV 0.000 0.0171 0.000 0.000 16.473 C BV 0.000 0.0171 12.456 4.000 a 1 –bridge repair 14.473C BV 2.000 0.0171 12.456 0.000 18.473 C BV 2.000 0.0171 12.456 4.000 S 2 –strategy with site-specific traffic load model based on WIM measurements a 0 –do nothing 0.068 C BV 0.000 0.068 0.000 0.000 16.524 C BV 0.000 0.068 12.456 4.000 a 1 –bridge repair 1.589 C BV 0.587 0.068 0.934 0.000 17.111 C BV 0.587 0.068 12.456 4.000 Table 8. Summarized results –VoI analysis of additional data –relative value [%]. Assessment strategy The relative value of additional SHM information [%] Including both bridge owner and user’s costs Including only direct costs by bridge owner Strategy S1: Reduced adjustment factors based on heaviest measured traffic in the country – Level 2 65.15 63.75 Strategy S2: Site-specific traffic load model based on measured WIM data on the road leading to the bridge –Level 3 96.46 90.86 16 D. SKOKANDIĆAND A. M. IVANKOVIĆ PROOFONLY The added value of the presented research can be summarized as follows: 1. the global cost function is developed with detailed modelling of each cost parameter as a percentage of the total bridge value 2. the trade-off between the bridge owner perspective (smaller total benefits) and society perspective (higher total benefits) for both strategies S1 and S2 3. the critical influence that indirect costs have on the outcomes of the VoI analysis is identified –the dominance of users’costs in global cost function –difference between the total costs reduction with and without users’costs in Table 9 VoI based case studies, as the one presented in this paper, can convince bridge operators, and consequently decision makers at the government level, about benefits of employing traffic load monitoring data in structural assessment of existing bridges and, consequently, in making knowledge-based maintenance decisions for an optimum bridge network management. In this way, the practical value of proactive bridge management is clearly demonstrated – embracing innovative tools and methods, as opposed to reactive management –employing visual inspection-based condition assessment. Further study, in continuation of the presented research, is aimed at creating the database with multiple various bridges and the corresponding measured traffic data. By doing so, the likelihoods of SHM indication used could be estimated with sufficient reliability to be applied in the preposterior analysis. Consequently, uncertainties in the analysis (bridge carrying capacity, traffic load effect variability, and estimated costs) would be reduced as more and more bridges are analysed. In order to conduct pre-posterior analysis using the presented algorithm, the decision tree (Figure 7) can easily be modified by adding the probabilistic chance node labelled WIM outcome (SHM Indication) prior to action choice node on branches S 1 and S 2 . By doing so, prior probability of failure, obtained without any additional traffic information, and the defined SHM likelihoods, will be sufficient for reliable estimation of probabilities of failure and the corresponding costs and benefits on subsequent branches (with additional traffic information). The estimation procedure can be conducted using the Bayesian updating theory, and will thus provide decision-makers with a value of additional WIM information for selected bridges or bridge network before the information is actually obtained. 1873 1874 1875 1876 1877 1878 1879 1880 1881 1882 1883 1884 1885 1886 1887 1888 1889 1890 1891 1892 1893 1894 1895 1896 1897 1898 1899 1900 1901 1902 1903 1904 1905 1906 1907 1908 1909 1910 1911 1912 1913 1914 1915 1916 1917 1918 1919 1920 1921 1922 1923 1924 1925 1926 1927 1928 1929 1930 1931 1932 1933 1934 1935 1936 1937 1938 1939 1940 1941 1942 1943 1944 1945 1946 1947 1948 1949 1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 Figure 9. VoI analysis of additional traffic data in assessment of the Case Study bridge, including both direct and indirect costs. STRUCTURE AND INFRASTRUCTURE ENGINEERING 17 PROOFONLY Additionally, the presented algorithm can be used for priority ranking of bridges in the network based on urgency of repair. By implementing the time-variant analysis, it is possible to estimate the time period for the realisation of maintenance activities. In order to do so, the estimated costs need to be modified as they are based on present-day values and currently available knowledge. The discounting model proposed by Rackwitz (2006) for industrial countries can be used for modification of future-investment costs. It is important to note that the accuracy and robustness of the presented algorithm for estimation of all costs and benefits related to the bridge management procedure is closely related to the selection of method and statistical parameters for reliability analysis (Tables 2 and 3), and to the estimation of total costs. Therefore, creation of a database with realistic parameters for selected bridges would reduce deviation of estimated characteristics and costs from reality, making the proposed method even more suitable for implementation in bridge management systems. Notations list AADT Average Annual Daily Traffic B-WIM Bridge Weigh-in-Motion CDF Cumulative distribution function DAF Dynamic Amplification Factor FORM First Order Reliability Method GSW Gross Vehicle Weight JCSS Joint Committee for Structural Safety LDF Load Distribution Factor LM1 Load Model 1 LSE Limit State Equation MC Monte Carlo method NCHRP National Cooperative Highway Research Program POT Peaks over Threshold RC Reinforced Concrete 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 2020 2021 2022 2023 2024 2025 2026 2027 2028 2029 2030 2031 2032 2033 2034 2035 2036 2037 2038 2039 2040 2041 2042 2043 2044 2045 2046 2047 2048 2049 2050 2051 2052 2053 2054 2055 2056 2057 2058 2059 2060 2061 2062 2063 2064 2065 2066 2067 2068 2069 2070 2071 2072 2073 2074 2075 2076 2077 2078 2079 2080 2081 2082 2083 2084 2085 2086 2087 2088 2089 2090 2091 2092 2093 2094 2095 2096 2097 2098 2099 2100 2101 2102 2103 2104 2105 2106 Table 9. Summarized results –VoI analysis of additional data –absolute value [EUR]. Assessment strategy The absolute value of additional SHM information [EUR] Summarized savings of both bridge owner and its users Direct savings of bridge owner Strategy S1: Reduced adjustment factors based on heaviest measured traffic in the country – Level 2 1.438.821,00 342.187,00 Strategy S2: Site-specific traffic load model based on measured WIM data on the road leading to the bridge –Level 3 2.130.081,00 476.087,00 Figure 10. VoI analysis of additional traffic data in assessment of the Case Study bridge, taking into account only direct costs incurred by bridge owner. 18 D. SKOKANDIĆAND A. M. IVANKOVIĆ PROOFONLY SHM Structural Health Monitoring SiWIMV RSlovenian Weigh-in-Motion TS Tandem System (concentrated traffic load) UDL Uniformly Distributed Load (distributed traffic load) VoI Value of Information WIM Weigh-in-Motion List of Symbols a 0 ;a 1 Actions regarding the bridge (no repair; repair) aQ,i;aq,i;aq,rAdjustment factors for traffic load model LM1 bReliability index hE,GRandom variable of model uncertainties for permanent load effect hE,QRandom variable of model uncertainties for traffic load effect hRRandom variable of model uncertainties for resistance lMean value rStandard deviation BiTotal benefits for strategy S i C 0 Bridge construction costs C BV Total value of the bridge C FAIL Cost of bridge failure C SHM Cost of bridge monitoring C N/A Cost of bridge non-availability C REP Cost of bridge repair C TOT, assessment Total costs for bridge assessment fBFactor for multiplication of bridge value due to its importance fCConstruction factor fREP Factor for complexity of bridge repairs G AADT Grading factor –AADT G DD Grading factor –Detour distance G LS Grading factor –Largest span G RC Grading factor –road category G TL Grading factor –Total bridge length p f Probability of failure S 0 ;S 1 ;S 2 Assessment strategies regarding additional SHM data X 1 ;X 2 System outcomes (system safe; system not safe) Acknowledgements This article is based upon work conducted in the scope of COST Action TU 1402 –Quantifying the Value of Structural Health Monitoring, supported by COST (European Cooperation in Science and Technology), and on the Croatian national project Performance Indicators for the Assessment of Existing Bridges, supported by the University of Zagreb. 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