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Downloaded from ascelibrary.org by RMIT UNIVERSITY LIBRARY on 01/03/19. Copyright ASCE. For personal use only; all rights reserved. Resilience Engineering for Urban Tunneling Edited by Michael Beer, Dr.-Ing. Hongwei Huang, Ph.D. Bilal M. Ayyub, Ph.D., P.E. Dongming Zhang, Ph.D. Brian M. Phillips, Ph.D. Downloaded from ascelibrary.org by RMIT UNIVERSITY LIBRARY on 01/03/19. Copyright ASCE. For personal use only; all rights reserved. INFRASTRUCTURE RESILIENCE PUBLICATION NO. 2 Resilience Engineering for Urban Tunnels Edited by Michael Beer, Dr.-Ing. Hongwei Huang, Ph.D. Bilal M. Ayyub, Ph.D., P.E. Dongming Zhang, Ph.D. Brian M. Phillips, Ph.D. Sponsored by Center for Technology and Systems Management, University of Maryland Institute for Risk and Reliability, Leibniz Universität Hannover Tongji University China Civil Engineering Society Institute for Risk and Uncertainty, University of Liverpool Infrastructure Resilience Division of the American Society of Civil Engineers Published by the American Society of Civil Engineers Downloaded from ascelibrary.org by RMIT UNIVERSITY LIBRARY on 01/03/19. Copyright ASCE. For personal use only; all rights reserved. Library of Congress Cataloging-in-Publication Data Names: International Workshop on Resilience of Urban Tunnels (2016 : College Park, Md.) | Beer, Michael, editor. | Huang, Hongwei, editor. | Ayyub, Bilal M., editor. | Zhang, Dongming, editor. | Phillips, Brian M., editor. | Center for Technology and Systems Management, sponsoring body. Title: Resilience engineering for urban tunnels / sponsored by Center for Technology and Systems Management, University of Maryland, Institute for Risk and Reliability, Leibniz Universitt Hannover, Tongji University, China Civil Engineering Society, Institute for Risk and Uncertainty, University of Liverpool, Infrastructure Resilience Division of the American Society of Civil Engineers ; edited by Michael Beer, Dr.-Ing, Hongwei Huang, Ph.D., Bilal M. Ayyub, Ph.D., P.E., Dongming Zhang, Ph.D., Brian M. Phillips, Ph.D. Description: Reston, Virginia : American Society of Civil Engineers, [2018] | Series: Infrastructure resilience publication ; no. 2 | Includes bibliographical references and index. Identifiers: LCCN 2018028802 | ISBN 9780784415139 (soft cover : alk. paper) | ISBN 9780784481813 (pdf) | ISBN 9780784481820 (epub) Subjects: LCSH: Tunnels–Design and construction–Congresses. | Tunnels–Reliability— Congresses. | Urban transportation–Congresses. Classification: LCC TA800.I73 2016 | DDC 624.1/93–dc23 LC record available at https://lccn.loc.gov/2018028802 Published by American Society of Civil Engineers 1801 Alexander Bell Drive Reston, Virginia 20191-4382 www.asce.org/bookstore | ascelibrary.org Any statements expressed in these materials are those of the individual authors and do not necessarily represent the views of ASCE, which takes no responsibility for any statement made herein. No reference made in this publication to any specific method, product, process, or service constitutes or implies an endorsement, recommendation, or warranty thereof by ASCE. The materials are for general information only and do not represent a standard of ASCE, nor are they intended as a reference in purchase specifications, contracts, regulations, statutes, or any other legal document. ASCE makes no representation or warranty of any kind, whether express or implied, concerning the accuracy, completeness, suitability, or utility of any information, apparatus, product, or process discussed in this publication, and assumes no liability therefor. The information contained in these materials should not be used without first securing competent advice with respect to its suitability for any general or specific application. Anyone utilizing such information assumes all liability arising from such use, including but not limited to infringement of any patent or patents. ASCE and American Society of Civil Engineers—Registered in U.S. Patent and Trademark Office. Photocopies and permissions. Permission to photocopy or reproduce material from ASCE publications can be requested by sending an e-mail to [email protected] or by locating a title in the ASCE Library (http://ascelibrary.org) and using the “Permissions” link. Errata: Errata, if any, can be found at https://doi.org/10.1061/9780784415139. Copyright © 2018 by the American Society of Civil Engineers. All Rights Reserved. ISBN 978-0-7844-1513-9 (print) ISBN 978-0-7844-8181-3 (PDF) ISBN 978-0-7844-8182-0 (ePub) Manufactured in the United States of America. 24 23 22 21 20 19 18 1 2 3 4 5 Photo credit: Front cover photograph courtesy of Dongming Zhang. Downloaded from ascelibrary.org by RMIT UNIVERSITY LIBRARY on 01/03/19. Copyright ASCE. For personal use only; all rights reserved. Contents Preface................................................................................................................................................. v Acknowledgments .......................................................................................................................vii Attendees and Affiliations ........................................................................................................ ix Introduction ..................................................................................................................................... xi Keynote Speaker Papers Enhancing Civil Infrastructure Resilience with Structural Health Monitoring ............................................................................................. 3 Yunfeng Zhang, Bilal Ayyub, and Hongwei Huang Reliability Analysis and Real-Time Predictions in Mechanized Tunneling .......................................................................................................... 13 Günther Meschke, Ba Trung Cao, and Steffen Freitag Non-intrusive Inspection and Real-Time Monitoring for Tunnel Structural Resilience........................................................................................ 29 Hongwei Huang and Dongming Zhang Efficient Reliability and Risk Analysis of Complex Interconnected Systems .............................................................................................................. 43 J. Behrensdorf, M. Broggi, and M. Beer Enhancing Resilience of Traffic Networks with a Focus on Impacts of Neuralgic Points Like Urban Tunnels ..................................................... 55 Katharina Klemt-Albert, Robert Hartung, and Sascha Bahlau Reliability of Critical Infrastructure Networks: Challenges...................... 71 Konstantin M. Zuev and Michael Beer Decision Aids for Tunneling .......................................................................... 83 Herbert H. Einstein Breakout Session Reports Topic 1: Monitoring for Resiliency of Urban Tunnels .............................. 89 Topic 2: Robust Design of Tunnels .............................................................. 95 Topic 3: Modeling and Management of Uncertainties............................. 99 iii iv CONTENTS Downloaded from ascelibrary.org by RMIT UNIVERSITY LIBRARY on 01/03/19. Copyright ASCE. For personal use only; all rights reserved. Research Recommendations 1. Monitoring for Resiliency of Urban Tunnels .......................................105 2. Robust Monitoring and Maintenance for Durability..........................107 3. Resilience Engineering at System Scale ...............................................109 Index................................................................................................................................................115 Downloaded from ascelibrary.org by RMIT UNIVERSITY LIBRARY on 01/03/19. Copyright ASCE. For personal use only; all rights reserved. Preface This report addresses the area of resilience engineering with specific emphasis on urban tunnels and their embedding into civil infrastructure systems. It provides bases for developing a comprehensive overall approach to resilience of urban tunnels. The contributions in this report cover the state of the art from various relevant perspectives, as well as conclusions made for perspective developments. As such, this report provides a source for students and researchers interested in resilience of urban tunnel and infrastructure to get a quick impression on the state of development. It may also serve as a resource for practitioners to adopt recent developments for current and future engineering projects to address and increase resilience. Eventually, the report will increase awareness of the significant importance of resilience among authorities to implement requirements to ensure sustained societal and economic benefits. The state of the art is represented in seven invited papers. The paper by Zhang and Ayyub describes pathways for using integrated structural health monitoring to enhance the resilience of civil infrastructure. Meschke, Cao, and Freitag report on recent developments for controlling mechanized tunneling using real-time predictions for ensuring structural reliability. An advanced technology for real-time monitoring of tunnels is presented by Huang and Zhang, where non-intrusive inspections are used to ensure tunnel resilience. These three contributions demonstrate the current level of achievement in the area using advanced engineering models and technologies. In addition, they provide a perspective for further developments expanding from this platform. The remaining papers address selected specific challenges and ideas for solution that seek their synergetic marriage with the broad powerful platform to form a comprehensive overall framework to address resilience of urban tunnels at large. Behrensdorf, Broggi, and Beer explore a numerical concept for assessing the reliability of complex interconnected systems. Klemt-Albert, Hartung, and Bahlau discuss the criticality of neuralgic points in traffic networks in view of enhancing resilience. Zuev and Beer highlight issues and potential solutions when assessing reliability of networks of critical infrastructure. Eventually, Einstein documents the importance of decision aids in tunneling with respect to risk and resilience. The second part of this report is built on the discussions from the First International Workshop on Resiliency of Urban Tunnels (Reston, Virginia, USA, September 1, 2016) and the conclusions drawn for perspective developments. This part is structured in conclusions from three breakout session reports, and three structured research recommendations on the key topics are identified. The first breakout session report concerns the monitoring for resiliency of urban tunnels. The second report refers to robust design of tunnels. Third, the modeling and v Downloaded from ascelibrary.org by RMIT UNIVERSITY LIBRARY on 01/03/19. Copyright ASCE. For personal use only; all rights reserved. vi PREFACE management of uncertainties is considered. The reports in these three topic areas summarize synergetic findings and advice from expert discussions as a guide for future developments. They were used as a basis to develop three structured research recommendations, which were rolled out after the breakout session reports. The first recommendation is focused on developments on monitoring for resiliency of urban tunnels. The second concerns robust monitoring and maintenance for durability. The third is devoted to resilience engineering at a system scale. These recommendations are intended to be developed into large-scale research programs. All materials presented in this report were peer reviewed according to the standards of ASCE. Downloaded from ascelibrary.org by RMIT UNIVERSITY LIBRARY on 01/03/19. Copyright ASCE. For personal use only; all rights reserved. Acknowledgments The organizers of the First International Workshop on Resiliency of Urban Tunnels, held in Reston, Virginia, USA, September 1, 2016, Michael Beer, Leibniz Universität Hannover, Germany Hongwei Huang, Tongji University, Shanghai, China Bilal M. Ayyub, University of Maryland, College Park, USA would like to express their sincere appreciation to the keynote speakers Yunfeng Zhang, University of Maryland, College Park, USA Günther Meschke, Ruhr Universität Bochum, Germany Loic Galisson, Soldata Group, USA Charng Hsein Juang, Clemson University, USA Sez Atamturktur, Clemson University, USA Konstantin M. Zuev, California Institute of Technology, USA Herbert H. Einstein, Massachusetts Institute of Technology, USA Bill Bergeson, Federal Highway Administration, USA Brian Wolfe, Maryland Transportation Authority, USA for their inspiring contributions. Highly appreciated are the contributions by all authors of the invited papers and of the breakout session reports. For providing high-quality service we thank our reviewers and the facilitators of the breakout sessions. Particular thanks are conveyed to Brian Phillips, University of Maryland, College Park, USA Dongming Zhang, Tongji University, Shanghai, China for their marvelous preparation of this report. For the financial support we thank the American Society of Civil Engineers and for supporting organization, travel, and attendance we thank Leibniz Universität Hannover, Germany University of Liverpool, UK University of Maryland, College Park, USA Tongji University, China China Civil Engineering Society National Natural Science Foundation, China Shanghai Science and Technology Committee, China Peak Discipline Construction on Civil Engineering of Shanghai, China. vii Downloaded from ascelibrary.org by RMIT UNIVERSITY LIBRARY on 01/03/19. Copyright ASCE. For personal use only; all rights reserved. This page intentionally left blank Downloaded from ascelibrary.org by RMIT UNIVERSITY LIBRARY on 01/03/19. Copyright ASCE. For personal use only; all rights reserved. Attendees and Affiliations Last First Amare Ariaratnam Atamturktur Ayyub Beer Bergeson Broggi Butry Tekeste Samuel Sez Bilal Michael Bill Matteo David Einstein Herbert Galisson Gong Huang Irias Juang Klemt-Albert McLeod McPherson Meschke Nie Ning Phillips Saadat Sansavini Shou Topa Gomes Wu Xie Xiong Zhang Zhang Zhang Zhang Zhou Zuev Loic Wenping Hongwei Xavier Hsein Katharina Marshall David Günther Xingyao Zhangwei Brian Yalda Giovanni Kehjian (Albert) António Jingzhe Xiongyao Haocheng Dongming Jie Yunfeng Yinning Biao Konstantin Affiliation Maryland Transportation Authority Arizona State University Clemson University University of Maryland Leibniz Universität Hannover Federal Highway Administration Leibniz Universität Hannover National Institute of Standards and Technology (NIST) Massachusetts Institute of Technology (MIT) Soldata Northern America Clemson University Tongji University East Bay Municipal Utility District Clemson University Leibniz Universität Hannover East Bay Municipal Utility District HDR, Inc. Ruhr University Bochum Tongji University Soldata Northern America University of Maryland University of Maryland ETH Zurich National Chung-Hsing University University of Porto University of Maryland Tongji University Virginia Tech Tongji University Clemson University University of Maryland Virginia Tech Tongji University California Institute of Technology ix Downloaded from ascelibrary.org by RMIT UNIVERSITY LIBRARY on 01/03/19. Copyright ASCE. For personal use only; all rights reserved. This page intentionally left blank Downloaded from ascelibrary.org by RMIT UNIVERSITY LIBRARY on 01/03/19. Copyright ASCE. For personal use only; all rights reserved. Introduction Urban tunnels nowadays play a quite significant role in transportation systems, not only to make transportation more efficient avoiding congestions but also to improve the quality of life in metropolitan areas by removing traffic from the living environment. As the number of urban tunnels increases incredibly, questions and concerns regarding their safe operation, potential vulnerability and recovery after intentional or unexpected disruption have become central issues not only among engineers and stakeholders but also in the society and governmental administration. Clearly, this situation is calling for a generalized structured approach not only for assessing, mitigating and managing risk but actually for a comprehensive resilient design and operation. However, in practice, operation and maintenance of tunnels is largely realized through heuristic approaches. Current research and practice show a key deficiency: while significant efforts have been made on risk assessment, only little has been done for risk control including resilience of underground structures, thus resulting in unexpected economic losses. An application-oriented method for dynamic risk control and resilient design is of great necessity for the safe operation of our underground systems. As a particular technical challenge, this approach needs to combine elements from structural engineering and systems engineering. Moreover, it needs to include a large monitoring component, and it needs to be dynamic to account for rapid changes in system states and conditions. In operating such ever-growing infrastructure systems, the risk associated with tunnels has become a focus of the government and the public in the world. Since this situation does not only apply to one country or society but is a global problem, it can be addressed best with joint forces. With this mission in mind, we have brought together more than 30 selected researchers in the areas of geotechnical, structural and system risk from the United States, China, Germany, and with diverse responsibilities from academic, industrial, and governmental perspectives. To identify a clearly structured research agenda for the development of a dynamic risk control and resilient design approach, the workshop covered three major topics including smart sensing, robust design and uncertainty modeling. Seven keynotes covering the aforementioned three topics were delivered by distinguished researchers in each area. After a seed discussion, seven subtopics were identified with the goal of driving projects in global collaborations. The first topic covers monitoring for urban tunnel resilience. The second topic addresses robustness against uncertainties in the construction. The third topic puts efforts on the integrated robust design through modularity and adaptability. The fourth topic is devoted to robust monitoring and maintenance for durability. The fifth topic concerns generalized modeling for xi Downloaded from ascelibrary.org by RMIT UNIVERSITY LIBRARY on 01/03/19. Copyright ASCE. For personal use only; all rights reserved. xii INTRODUCTION resilience engineering with a component scale and a systems scale perspective. The sixth topic covers resilience-informed decision making, and the last topic addresses multisector interdependencies in the resiliency modeling. With this structure the workshop was cumulated in the development of largescale research proposals by the attendees, which are all synchronized. In combination of the developments we then aim for a comprehensive overall approach to resilience of urban tunnels to be established within a reasonably short time. To monitor the developments and their interaction, this workshop is expanded into a series of annual meetings around the world, rotating between America, Europe, and Asia. Michael Beer, Chair Downloaded from ascelibrary.org by RMIT UNIVERSITY LIBRARY on 01/03/19. Copyright ASCE. For personal use only; all rights reserved. KEYNOTE SPEAKER PAPERS Downloaded from ascelibrary.org by RMIT UNIVERSITY LIBRARY on 01/03/19. Copyright ASCE. For personal use only; all rights reserved. This page intentionally left blank Downloaded from ascelibrary.org by RMIT UNIVERSITY LIBRARY on 01/03/19. Copyright ASCE. For personal use only; all rights reserved. CHAPTER 1 Enhancing Civil Infrastructure Resilience with Structural Health Monitoring Yunfeng Zhang* Bilal Ayyub* Hongwei Huang† Abstract: In natural hazardous events such as strong earthquakes, engineers are usually faced with many competing priorities in making safety and occupancy decisions about large inventories of civil infrastructure building and bridge assets and usually there is shortage in experienced engineers available for inspection and repair work. For structural members hidden behind drywall or ceilings, inspection is particularly time consuming and costly because those nonstructural components have to be removed first. One of the ultimate goals in inspection is to quickly and accurately determine the residual capacity (in strength and deformation) of structural members to assure structural safety in future events such as aftershocks. Structural health monitoring (SHM) technologies are useful for rapid structural condition assessment especially for many hidden locations after major hazardous events. This paper describes a strategy for enhancing structural resilience by integrating innovative SHM technologies focused on limited number of structural fuse members within resilient structures. The proposed framework will be helpful in facilitating the implementation of SHM technologies into civil infrastructures by quantifying and comparing the resilience metrics of different SHM options. INTRODUCTION After natural hazardous events such as strong earthquakes, engineers are usually faced with many competing priorities in making safety and occupancy decisions about large inventories of building and bridge assets and usually there is shortage * Department of Civil & Environmental Engineering, University of Maryland at College Park, USA † Department of Geotechnical Engineering, Tongji University, Shanghai, China 3 Downloaded from ascelibrary.org by RMIT UNIVERSITY LIBRARY on 01/03/19. Copyright ASCE. For personal use only; all rights reserved. 4 RESILIENCE ENGINEERING FOR URBAN TUNNELS in experienced engineers available for inspection and repair work. However, most of the post-hazard inspections and structural condition assessment are performed manually at present. Intensive labor, high cost and variable results are typical of manual operation. In buildings, structural members are often hidden behind fireproof coating and drywalls, and thus buckling or yielding of these hidden steel members are difficult to detect, often requiring removal of coverings and thus time consuming and costly. For example, a steel tube brace hidden behind drywalls in a 4-story office building buckled and then fractured in the 1994 Northridge earthquake (Tremblay et al. 1994; Sabelli et al. 2013). Tremblay et al. (1995) reported that “The building remained plumb following the earthquake : : : the initial assessment of the structure by the owner’s representative prior to the review engineer arriving on site was that the structure had not sustained much damage (only one window had been broken). Only after the preliminary assessed cosmetic damage to the dry wall was removed, at the order of the engineer, was the extent of damage revealed and proper assessment of the structure could begin.” In a more recent event, the 22-story Pacific Residential Tower in Christchurch was green-tagged following the MW 6.2 Christchurch earthquake of February 2011, indicating that they were safe to occupy but would require some minor repairs of non-structural components (Clifton et al. 2012). In the 2011 Christchurch earthquake, numerous eccentrically braced frames (EBFs) buildings were found to yield in the link beam that typically exhibits paint flaking and Luder lines (Grilli et al. 2012, Clifton et al. 2012). For a 12-story EBF building damaged in this 2011 earthquake, estimates of the peak inelastic demand in the active link were made through visible assessment of the active link yielded web metal and secondly through estimation of the peak inter-story building drift and conversion of this to a peak inelastic demand in the EBF active links (Clifton et al. 2012). If the link beam were instrumented, peak shear strain in the links would have been determined much faster and more accurately. Clearly from these two real examples, it can be concluded that visual signs of minor cosmetic damage in non-structural elements do not give reliable results in revealing the actual severe damage sustained by hidden structural members. SHM technologies are useful for rapid structural condition assessment especially for many hidden locations after major hazardous events. Under extreme loading such as strong earthquakes or winds, structural members in steel structures could fail in buckling or yielding. However, assessment by inexperienced workers is subject to a high degree of uncertainty and may lead to misleading judgment on structural condition and safety. Civil structures could be more effectively managed through automated inspection and computerized condition assessment information processing. The replacement of our present-day manual inspection with automated condition assessment would substantially reduce the associated costs/downtime and enhance community resilience. Sensor data from SHM systems provides the base data for real-time updating of the structural condition and reliability. Downloaded from ascelibrary.org by RMIT UNIVERSITY LIBRARY on 01/03/19. Copyright ASCE. For personal use only; all rights reserved. ENHANCING CIVIL INFRASTRUCTURE RESILIENCE WITH STRUCTURAL HEALTH MONITORING 5 Structural health monitoring (SHM) is also helpful to understand the safety state of the geostructures, in particular for large-scaled distributed geo-systems such as metro tunnel networks (O’Rourke, 2010). It is recognized that sensing and monitoring systems could support engineering judgement and even complement it especially for the case of a ductile performance response but will not attempt to replace it (Huang and Zhang 2016). New design trends for seismic resistant structures is to incorporate fuse members (sacrificial elements to dissipate energy) into structures so that damage is concentrated to fuse members while other parts of the structure remain undamaged during design level earthquakes. Few implementations of the structural fuse concept have been rigorous in emphasizing easy replaceability of the sacrificial elements and absence of damage to the primary structural system (El-Bahey and Bruneau 2011). Examples of structural fuses are buckling restrained braces (BRBs), steel shear links and slit steel plate wall with buckling restrain cover plate. Such structure design concept is also appealing to SHM since condition assessment or monitoring work can now be focused on a limited number of fuse members. For such smart fuse members instrumented with sensors, automated structural health monitoring of fuse zone for possible damages inflicted by earthquakes or strong winds could be performed in a very efficient way and this practice would greatly accelerate condition assessment and thus enhance resilience through shorter and more accurate inspection. Consequently, decision on whether to do structural repair or no need for evacuation could be made after extreme events. In certain types of structural fuses such as BRBs (El-Bahey and Bruneau 2011) and buckling restrained slit steel plate wall (Sun et al. 2011), crack was seen to develop, and the steel core plate eventually fractured when they sustain severe plastic deformation in order to dissipate energy. An important question to address is how to detect the crack before the steel core plate completely fractures, but this has been found to be very difficult because the steel core plate is hidden behind the buckling restraining members and direct access to the interior steel core plate for visual inspection is not an option before those buckling restraining members can be removed. Therefore, SHM technology that can remotely monitor the plastic deformation development and cracks is desired for condition assessment of such structural fuse members. This paper presents preliminary research work toward integrating SHM technologies with resilient civil infrastructure design and establishing a resilience metric for rating candidate SHM technologies. As a demonstration of SHM feasibility in resilience enhancement by reducing post-hazard inspection and recovery time, wireless scanning for strain information using RFID based passive wireless sensor without the need for battery, is described. Preliminary experimental results have suggested this method is very promising for structural condition assessment. This novel BT sensor is developed for detection of surpassing prespecified threshold strain level and thus can be used for monitoring steel yielding and buckling occurrence. The BT sensor uses a special design of trigger device to activate the sensor and RFID tag for wireless damage scanning. 6 RESILIENCE ENGINEERING FOR URBAN TUNNELS Downloaded from ascelibrary.org by RMIT UNIVERSITY LIBRARY on 01/03/19. Copyright ASCE. For personal use only; all rights reserved. RESILIENCE METRICS FOR RATING STRUCTURAL HEALTH MONITORING TECHNOLOGY Most of the post-hazard inspections and structural condition assessment are performed manually at present. Intensive labor, high cost and variable results are typical of manual operation. The replacement of our present-day manual inspection with automated condition assessment would substantially reduce the associated costs/downtime and enhance community resilience. SHM technology targeting such fuse members are thus of importance in the context of rapid posthazard structural condition inspection and recovery. With the advancement in this field, several SHM techniques will be proposed for a specific type of structural fuse and how to rate the performance of these SHM technique candidates becomes an important issue in the process of choosing the cost-effective SHM technology for the fuse condition assessment application. This practice would greatly accelerate condition assessment and thus enhance resilience through shorter and more accurate inspection, as shown in Figure 1. Consequently, decision on whether to do structural repair or no need for evacuation could be made after extreme events. Resilience may be defined as a function indicating the capability to sustain a level of functionality, or performance, for a given building, bridge, lifeline network, or community, over a period defined as the control time (Renschler et al. 2010). The change in functionality due to strong earthquake or wind events is characterized by a drop, representing a loss of functionality and a recovery as shown in Figure 1. The following resilience metrics was proposed by Ayyub (2014) based on this definition that meet logically consistent requirements drawn partly from measure theory and provide a basis for the development of effective decision-making tools for multi-hazard environments. ResilienceðRe Þ = T i þ FΔT f þ RΔT r T i þ ΔT f þ ΔT r (1-1) Figure 1. Resilience enhancement through rapid structural condition assessment 7 ENHANCING CIVIL INFRASTRUCTURE RESILIENCE WITH STRUCTURAL HEALTH MONITORING Downloaded from ascelibrary.org by RMIT UNIVERSITY LIBRARY on 01/03/19. Copyright ASCE. For personal use only; all rights reserved. where for any failure event (f ) as illustrated in Figure 8, the corresponding failure profile F and the corresponding recovery profile R are measured as follows: R tr R tf FailureðFÞ = t i f dt , R tf t i Qdt tf rdt tf Qdt RecoveryðRÞ = R t r (1-2) The failure-profile value (F) can be considered as a measure of robustness and redundancy; whereas the recovery-profile value I can be considered as a measure of resourcefulness and rapidity. Q is defined as the system’s performance in terms of its strength (S) minus the corresponding load effect (L) in consistent units, i.e., Q = S − L. Both L and S are treated as random variables, the time to failure (Tf) can be characterized by its probability density function that can be found in the work by Ayyub (2014). The primary basis for evaluating Eqn. 1 is the definition of performance (Q) at the system level with meaningful and appropriate units, followed by the development of an appropriate breakdown for this performance, using what is termed herein as performance segregation. In previous definition of resilience metrics, SHM is not explicitly considered; rather structural condition assessment (inspection or SHM) is implicitly included in the recovery phase. In order to rate the performance of civil infrastructures that might be designed with different candidate SHM systems, the above resilience metric is proposed by explicitly considering the inspection phase of the recovery process. This becomes an important issue in the process of choosing the most costeffective SHM technology for practical implementation. ResilienceðRe Þ = FailureðF m Þ = R tm t R tmi ti t i þ F m ΔT m þ Rm ΔT r t i þ ΔT m þ ΔT r Q · ΔT m = Rtrue , tm Qdt t i Qdt f dt (1-3) R tr t rdt tm Qdt RecoveryðRm Þ = R trm (1-4) where f = Qtrue, a random variable that represents the true condition of civil infrastructures (see the horizontal green line in Figure 2); ΔTm = total inspection (or SHM) time taken to get closer enough (error between Qphase_i and Qtrue < acceptable value) to the true condition Qtrue. Qphase_i is a random variable that represents the condition assessment result from the ith phase in SHM process. For certain hazardous events such as earthquakes, ΔTf ( = Tf − Ti) is typically very short (often less than a minute) and thus neglected here for simplicity. ti is thus approximately equal to Time to failure (tf), which has the following density function: d ti = − dt Z∞ c=0    Zt 1 exp −λt 1 − F L ðαðτÞsÞdτ f S0 ðsÞds t τ=0 (1-5)
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