PSI - Issue 22
First International Symposium on Risk Analysis and Safety of Complex Structures and Components (IRAS 2019)
Volume 2 2 • 201 9
ISSN 2452-3216
ELSEVIER
First International Symposium on Risk Analysis and Safety of Complex Structures and Components (IRAS 2019)
Guest Editors: A bí lio M .P. de J esus , Ant ó nio A b el H enri q ues J osé A . F .O. C orreia J osé M . F . C astro P edro Montenegro R ui A . B . C al ç ada
Available online al www.sciencedirect.com ScienceDirect
Available online at www.sciencedirect.com ScienceDirect Structural Integrity Procedia 00 (2019) 000 – 000 Available online at www.sciencedirect.com ScienceDirect Structural Integrity Procedia 00 (2019) 000 – 000
www.elsevier.com/locate/procedia
www.elsevier.com/locate/procedia
ScienceDirect
Procedia Structural Integrity 22 (2019) 1–9
© 2019 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) Peer-review under responsibility of the First International Symposium on Risk and Safety of Complex Structures and Components organizers Abstract The First International Symposium on Risk Analysis and Safety of Complex Structures and Components (IRAS 2019) was organised in-teamed with the ESIS/TC12 Technical Committee on Risk Analysis and Safety of Large Structures and Components, which took place between 1-2 July 2019 at the Faculty of Engineering of the University of Porto (FEUP), in the City of Porto, located at seaside in the northwest region of Portugal. The guest editors of the IRAS 2019 deeply acknowledges all members of the International Scientific Committee, Thematic Sessions Organizers, Keynote Speakers and authors that contributed to the success of this event, that gathered more than 126 participants presenting more than 168 papers and posters. Sponsors are also fully acknowledged for their important contributions. The ESIS/TC12 2019 winners of the Robert Moskovic Award, Award of Merit TC12, and ESIS/TC12 Young Scientist Award were announced during the conference. Additionally, the guest editors (conference chairs) sincerely thank the tireless efforts of the Organizing Committee members as well as students and other FEUP and Construction Institute staff involved in the organization. Finally, the guest editors are pleased to inform that the second edition of the IRAS event will be organised by Prof. Aleksandar Sedmak (University of Belgrade, Serbia) which will take place in Belgrade in Serbia in the year 2021. © 2019 The Authors. Published by Elsevier B.V.This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) Peer-review under responsibility of the First International Symposium on Risk and Safety of Complex Structures and Components organizers First International Symposium on Risk and Safety of Complex Structures and Components Editorial of the 1 st IRAS conference José A.F.O. Correia a,b, *, Abílio M.P. De Jesus a,b , António A.R. Henriques a , José M.F. Castro a , Pedro Montenegro a , Rui A.B. Calçada a a CONSTRUCT - LESE, Faculty of Engineering, University of Porto, Rua Dr. Roberto Frias, Campus FEUP, 4200-465 Porto, Portugal b INEGI - LAETA, University of Porto, Rua Dr. Roberto Frias, Campus FEUP, 4200-465 Porto, Portugal Abstract The First Inter ational Symposium on Risk Analysis and Safe y of Complex Structur s a d Components (IRAS 2019) was organised in-teamed with the ESIS/TC12 Technical Committe on Risk Analysis and Safety of Large Structures and Com onents, which took place tween 1-2 July 2019 at the Faculty f Engineering of the Un versity of Po to (FEUP), in the City of Port , loc ted a seasi e in the northwest region of Portugal. The guest editors of the IRAS 2019 deeply acknowledges all member of the I ternational Scientific Committee, Thematic Sessions O ganizer , Keynote Speakers and authors that contributed to the success of this event, that gathered more than 126 parti pants presenting more than 168 papers and post rs. Sponsors are also fully acknowledged for their important contributions. The ESIS/TC12 2019 win ers of the Robert Moskovic Award, Awar of Merit TC12, and ESIS/TC12 Young Scientist Award wer an ounced during the conferenc . Additionally, the guest editors (conference chairs) sincerely ank the tir less efforts f the Organizing Committee members as well as udents and other FEUP and Construction Institute staff involved in the organiz tion. Finally, the guest editors are pleased to inform that the second edition of the IRAS event will be organised by Prof. Aleksandar Sedmak (University of Belgrade, Serbia) which will take place in Belgrade in Serbia in the y ar 2021. © 2019 The Authors. Published by Elsevier B.V.This is an open access article under the CC BY-NC-ND li ense (http://cr ativecommons.org/licenses/by-nc-nd/4.0/) Peer-review under responsibility of the First International Symposium on Risk and Safety of Complex Structures and Components org nizers First International Symposium on Risk and Safety of Complex Structures and Components Editorial of the 1 st IRAS conference José A.F.O. Correia a,b, *, Abílio M.P. De Jesus a,b , António A.R. Henriques a , José M.F. Castro a , Pedro Montenegro a , Rui A.B. Calçada a a CONSTRUCT - LESE, Faculty of Engineering, University of Porto, Rua Dr. Roberto Frias, Campus FEUP, 4200-465 Porto, Portugal b INEGI - LAETA, University of Porto, Rua Dr. Roberto Frias, Campus FEUP, 4200-465 Porto, Portugal Keywords: Risk analysis; Safety criteria; Structural integrity; Fatigue; Fracture mechanics; Complex structures; Structural components.
Keywords: Risk analysis; Safety criteria; Structural integrity; Fatigue; Fracture mechanics; Complex structures; Structural components.
* Corresponding author. Tel.: +351-966-559-442. E-mail address: jacorreia@inegi.up.pt * Corresponding author. Tel.: +351-966-559-442. E-mail address: jacorreia@inegi.up.pt
2452-3216 © 2019 The Authors. Published by Elsevier B.V.This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) Peer-review statement: Peer-review under responsibility of the First International Symposium on Risk and Safety of Complex Structures and Components organizers 2452 3216 © 2019 The Autho s. Published by Elsevier B.V.This is an open acc ss rt cle under the CC BY-NC-ND license (http://c ativecommons.org/licenses/by-nc-nd/4.0/) Peer-review statement: Peer-review under responsibility of the First International Symposium on Risk and Safety of Complex Structures and Components organizers
2452-3216 © 2019 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) Peer-review under responsibility of the First International Symposium on Risk and Safety of Complex Structures and Components organizers 10.1016/j.prostr.2020.01.001
José A.F.O. Correia et al. / Procedia Structural Integrity 22 (2019) 1–9 Author name / Structural Integrity Procedia 00 (2019) 000 – 000
2
2
1. Introduction The ESIS Executive Committee decided to change the name of TC 12 in November 2016. The current name of the ESIS TC12 is Risk Analysis and Safety of Large Structures and Components (Correia et al., 2019a). One of the tasks of the ESIS TC12 Technical Committee is the organization of events for the dissemination of the technical and scientific knowledge of its members as well as other participants. The TC12/ESIS co-chairs and scientific managers have participated in the organization of various scientific events and technical meetings with similar topics (Correia et al., 2019b, 2019c; Correia et al., 2018a; Rebelo et al. 2018; Correia et al. 2017; Pariente et al., 2016; Correia et al., 2018b, 2018c, 2018d). The First International Symposium on Risk Analysis and Safety of Complex Structures and Components (IRAS 2019) was organised by ESIS TC12 on Risk Analysis and Safety of Large Structures and Components, which took place between 1-2 July 2019 at the Faculty of Engineering of the University of Porto, in the City of Porto, located at seaside in the northwest region of Portugal, (see Figure 1). This conference was intended to be a forum for discussion of the recent advances in maintenance, safety, risk analysis, probabilistic assessment, life-cycle performance, fatigue, fracture, damage mechanics, numerical simulation of a wide range of infrastructures, such as, engineering technical systems, transportation systems, bridges, buildings, dams, railways, underground constructions, wind and transmission towers, offshore platforms, pipelines, naval vessels, oceanic structures, nuclear power plants, airplanes and other types of structures including aerospace and automotive structures are considered. The IRAS 2019 event was opened with a plenary talk given by Prof. Guian Qian (Chinese Academy of Sciences, China) entitled “Application of weakest link concept to fatigue and fracture assessment” (see Figure 2a)). Invited keynote presentations were given by Prof. Hojjat Adeli (Ohio State University, USA) on “Machine Learning and Structural Health Monitoring” (see Figure 2b)), Prof. Milan Veljkovic (Delft University of Technology, Netherlands) on “Overview of TUD - Stevin Laboratory fatigue research and recent results” (see Figure 2c)), Prof. Tomasz Nowakowski (Wroclaw University of Science and Technology, Poland) on “From Reliability to Resilience: Advanced Challenges for Technical System Performances” (see Figure 2d)), and by Prof. Shun-Peng Zhu (University of Electronic Science and Technology of China, China) on “Advances in st ructural fatigue reliability design and assessment under uncertainty” (see Figure 2e)). Within 10 technical sessions, 168 talks were presented by 126 participants on various aspects of risk analysis and safety of complex structures and components (Correia et al. 2019d). The first edition of the IRAS 2019 event gathered participants from more than 20 nationalities demonstrating the worldwide acceptance of this first event. The Organizing Committee of the IRAS 2019 deeply acknowledges all authors that contributed to the success of this event, with their exciting presentations. The members of the International Scientific Committee are also fully acknowledged for their support to the IRAS 2019 event. Special thanks are also addressed to the Thematic Sessions Organizers and Plenary Speakers for their dedication and knowledge and energy brought to this event. Sponsors are also fully acknowledged for their important contributions. Finally, the guest editors sincerely thank the tireless efforts of Organizing Committee members as well as students and other FEUP (Faculty of Engineering of the University of Porto) and IC (Construction Institute) staff.
Fig. 1. Opening session of the IRAS 2019 event.
3
José A.F.O. Correia et al. / Procedia Structural Integrity 22 (2019) 1–9 Author name / Structural Integrity Procedia 00 (2019) 000 – 000
3
a)
b)
c)
d)
e)
Fig. 2. Keynote speakers: a) Prof. Guian Qian (Chinese Academy of Sciences, China); b) Prof. Hojjat Adeli (Ohio State University, USA); c) Prof. Milan Veljkovic (Delft University of Technology, Netherlands); d) Prof. Tomasz Nowakowski (Wroclaw University of Science and Technology, Poland); e) Prof. Shun-Peng Zhu (University of Electronic Science and Technology of China, China). 2. Organizing Committee The First International Symposium on Risk Analysis and Safety of Complex Structures and Components (IRAS2019), in-teamed with the ESIS/TC12 Technical Committee, was organized by the following members from the Faculty of Engineering of the University of Porto (Portugal): - José António Fonseca de Oliveira Correia; - Abílio Manuel Pinho De Jesus; - António Abel Ribeiro Henriques; - José Miguel de Freitas Castro; - Pedro Aires Moreira Montenegro e Almeida; - Rui Artur Bártolo Calçada. 3. Scientific Committee The honorary chair of this IRAS 2019 event was Prof. Hojjat Adeli from the University of Ohio, USA.
José A.F.O. Correia et al. / Procedia Structural Integrity 22 (2019) 1–9 Author name / Structural Integrity Procedia 00 (2019) 000 – 000
4
4
The international scientific committee was composed of the following members:
A. Fernández Canteli A. Martín-Meizoso Abílio M.P. de Jesus Adão da Fonseca Alain Nussbaumer Aleksandar Sedmak Alessio Pipinato Andréas Andersson Andrei Kotousov António Abel Henriques
Dmitry Neganov Dmitry Reznikoff Ehsan Noroozinejad Elena Fedorova Elias Kassa Enrique Castillo Evgeniia Georgievskaia Filippo Berto Francesco Iacoviello Gilbert Hénaff Grzegorz Lesiuk Hermes de Carvalho Hernán Pinto Arancet Hryhoriy Nykyforchyn Humberto Varum Jesús Toribio Jianfeng Wen João Pedro Martins John Leander José António Correia José Esteves Jose Maria Goicolea Guian Qian Haohui Xin Helder Craveiro Helena Gervásio Henk Kolstein
José Miguel Castro José Xavier Katarzyna Pietrucha-Urbanik Laszlo Toth Linamaría Gallegos Mayorga Lothar Kroll Ludmila Botvina Luis Simões da Silva Majid Ayatollahi Makoto Tanabe María Jesús Lamela María Nogal Matthew Hebdon Mieczysław Szata Miguel Calvente Milan Veljkovic Mirosław Bocian Nicholas Fantuzzi Nicole Apetre Nikolay Makhutov Paul Caiza Paulo Tavares de Castro Pedro Montenegro Peter Huffman Raied Karoumi Raimundo Freire Júnior Roberto Brighenti
Rodrigo Falcão Moreira Rui Calçada Rui Carneiro de Barros Rui Liu Rui Martins Sabrina Vantadori Sergio Cicero Gonzalez
Sérgio Tavares Shengchuan Wu Shun-Peng Zhu Snežana Kirin Stanislav Seitl Stéphane Sire
António Reis Atillio Arcari Ayhan Ince Behrooz Keshtegar Carlos Oliveira Carlos Rebelo Carlos Sousa Chao Jiang Chengwei Fei Cristian Delamarian Cristina Reis Dariusz Rozumek David Rocuba Debiao Meng Dianyin Hu Dimitrios Pavlou Diogo Ribeiro
Sviatoslav Timashev Thomas Ummenhofer Tiago Ferradosa Tomasz Nowakowski Vladimir Moskvichev Wanming Zhai Wojciech Błażejewski Xavier Romão Xiancheng Zhang Yury Matvienko
Yury Petrov Z. Marciniak Zhongxiang Liu
4. Topics of the conference Contributions were accepted covering the following topics:
- Methods for reliability and probabilistic safety assessment; - Sensitivity analysis; - Data collection and analysis; - Design and evaluation of technical systems and structures; - Design innovation for safety and reliability; - Codes, standards and safety criteria; - Engineering Structures; - Structural Integrity and durability;
- Management and life-cycle performance; - Models for ageing and life extension; - Fatigue, fracture and damage mechanics; - Damage evaluation and fatigue design; - Dynamic and fatigue reliabilities; - Safety assessment (loads and environmental effects; material properties; prediction of response and performance); - Analytical and numerical simulation; - Structural health monitoring; - Rock and soil structural integrity.
José A.F.O. Correia et al. / Procedia Structural Integrity 22 (2019) 1–9 Author name / Structural Integrity Procedia 00 (2019) 000 – 000
5
5
5. Thematic Sessions The thematic sessions and their organizers were the following: - A – Probabilistic Fatigue & Fracture Approaches Applied to Materials and Structures organized by: Shun-Peng Zhu, University of Electronic Science and Technology of China, Chengdu, China Guian Qian, Institute of Mechanics, Chinese Academy of Sciences, Beijing, China Chengwei Fei, Department of Aeronautics and Astronautics, Fudan University, China José A.F.O. Correia, Faculty of Engineering, University of Porto, Portugal Abílio De Jesus, Faculty of Engineering, University of Porto, Portugal Alfonso Fernández-Canteli, University of Oviedo, Spain Miguel Muniz-Calvente, University of Oviedo, Spain - B – Vibrations, fatigue and fracture problems in safety of engineering structures organized by: Grzegorz Lesiuk, Wroclaw University of Science and Technology, Poland José A. F. O. Correia, Faculty of Engineering, University of Porto, Portugal Abílio M. P. de Jesus, Faculty of Engineering, University of Porto, Portugal - C – Structural Integrity of Renewable Energy and Oceanic Structures organized by: Dimitrios Pavlou, University of Stavanger, Norway Miguel Correia, Force Technology, Norway Nicholas Fantuzzi, University of Bologna, Italy Tiago Ferradosa, Faculty of Engineering, University of Porto, Portugal - D – Structural Integrity of Lightweight Structures – experimental, theoretical and numerical approach organized by: Lothar Kroll, Technical University of Chemnitz, Germany – Chair Wojciech Błażejewski, Wroclaw University of Science and Technology, Poland – Co-chair José António Correia, Faculty of Engineering, University of Porto, Portugal José Miguel Castro, Faculty of Engineering, University of Porto, Portugal Ehsan Noroozinejad, Graduate University of Advanced Technology, Iran – Chair Abbas Sivandi-Pour, Graduate University of Advanced Technology, Iran - F – Safety and Structural Integrity of Railway Structures and Rolling Stock organized by: Pedro A. Montenegro, Faculty of Engineering, University of Porto, Portugal – Chair Rui Calçada, Faculty of Engineering, University of Porto, Portugal – Co-chair Araliya Mosleh, Faculty of Engineering, University of Porto, Portugal Diogo Ribeiro, Faculty of Engineering, University of Porto, Portugal Shengchuan Wu, State Key Lab. of Traction Power, Southwest Jiaotong University, China - G – Failure mechanism and life assessment under defects organized by: Dianyin Hu, Beihang University, Beijing, China – Chair Jianxing Mao, Beihang University, Beijing, China Dianyin Hu, Beihang University, Beijing, China Yunxia Chen, Beihang University, Beijing, China Shengchuan Wu, Southwest Jiaotong University, Chengdu, China Grzegorz Lesiuk, Wroclaw University of Science and Technology, Poland José A.F.O. Correia, Faculty of Engineering, University of Porto, Portugal Abílio M.P. De Jesus, Faculty of Engineering, University of Porto, Portugal - E – Lifelines and Infrastructures Safety Evaluation organized by:
José A.F.O. Correia et al. / Procedia Structural Integrity 22 (2019) 1–9 Author name / Structural Integrity Procedia 00 (2019) 000 – 000
6
6
Shun-Peng Zhu, University of Electronic Science and Technology of China, Chengdu, China Guian Qian, Institute of Mechanics, Chinese Academy of Sciences, Beijing, China Jianfeng Wen, Key Laboratory of Pressurized System and Safety, Shanghai, China José A.F.O. Correia, University of Porto, Portugal Abílio M.P. De Jesus, University of Porto, Portugal - H – Environmental effect on structural integrity organized by: Elena Fedorova, Polytechnic Institute of Siberian Federal University, Institute of Computational Technologies SB RAS, Russia – Chair Evgeniia Georgievskaia, JSC “NPO CKTI”, Saint -Petersburg, Russia – Co-chair - I – Fatigue of Steel and Composite Structures organized by: Milan Veljkovic, Delft University of Technology, Netherlands – Chair Haohui Xin, Delft University of Technology, Netherlands – Co-chair Henk Kolstein, Delft University of Technology, Netherlands José Correia, University of Porto, Portugal - J – Degradation and Conservation of Ancient (Historical) Materials and Structures organized by: 6. TC12/ESIS 2019 awards During the year 2019, the TC12/ESIS technical committee decided to create three awards (refer to Correia et al. (2019)): Robert Moskovic Award; Award of Merit TC12; and ESIS/TC12 Young Scientist Award. Each year, the ESIS/TC12 technical committee will attribute these awards during associated ESIS events. During the IRAS 2019, the Robert Moskovic Award was attributed to the following researchers in recognition of their outstanding contributions: - Prof. Hojjat Adeli, University of Ohio, USA, for contributions in the Computational Intelligence and Smart Structures field (Figure 3a)); - Prof. Alfonso Carlos Fernández-Canteli, University of Oviedo, Spain, for contributions in the Unified Probabilistic Fatigue Methodology field (Figure 3b)); and, - Prof. Aleksandar Sedmak, University of Belgrade, Serbia, for contributions in the Structural Integrity and Failure Analysis field (Figure 3c)). The Award of Merit TC12 was attributed to the following researchers in recognition of their contributions to IRAS 2019 event as well as for the ESIS-TC12 technical committee: - Dr. Grzegorz Lesiuk, Wroclaw University of Science and Technology, Poland (Figure 4a)); - Dr. Dianyin Hu, Beihang University, China (Figure 4b)); - Dr. Pedro Montenegro, University of Porto, Portugal (Figure 4c)); and, - Dr. Shun-Peng Zhu, University of Electronic Science and Technology of China, China (Figure 4d)). The ESIS/TC12 Young Scientist Award was attributed to the following young researchers in recognition of their scientific works (see Table 1) presented in the IRAS 2019 event: - Kodai Matsuoka, Railway Technical Research Institute, Japan (Figure 5a)); - Rita Dantas, University of Porto, Portugal (Figure 5b)); - Teresa Magoga, University of Tasmania, Australia (Figure 5c)); - Vítor Gomes, University of Porto, Portugal (Figure 5d)); and, - Yaroslav Dubyk, IPP-Centre Ltd. and National Academy of Sciences of Ukraine, Ukraine (Figure 5e)). Cristina Reis, University of Trás-os-Montes and Alto Douro, Portugal – Chair Paula Braga da Silva, University of Trás-os-Montes and Alto Douro, Portugal Carlos Oliveira, Polytechnic Institute of Viana do Castelo, Portugal
José A.F.O. Correia et al. / Procedia Structural Integrity 22 (2019) 1–9 Author name / Structural Integrity Procedia 00 (2019) 000 – 000
7
7
Table 1. ESIS/TC12 Young Scientist 2019 Awards.
Authors
Title
Kodai Matsuoka, Tsutomu Watanabe and Shindo Yoshinori Rita Dantas, José A.F.O. Correia, Grzegorz Lesiuk, Slobodanka Jovašević, Dariusz Rozumek, Carlos Rebelo, W. Wisniewski and Abílio M.P. De Jesus Teresa Magoga, Roberto Ojeda, Stuart Cannon, and Giles Thomas Vítor M.G. Gomes, Abílio M.P. De Jesus, Miguel A.V. Figueiredo, José A.F.O. Correia, Lenin Abatta, Grzegorz Lesiuk and António A. Fernandes
Analysis of a Snow Shelter on a High Speed Railway Bridge Evaluation of biaxial (axial+torsional) high-cycle fatigue behavior of S355 structural steel Interdependencies between Variables in Fatigue Analysis of a Weight Optimised Warship Fatigue Behaviour of Bolted Connections Applied in Racking Structures. Experimental and Numerical study
Dubyk Yaroslav
Application of Probabilistic Leak Before Break for WWER-1000 Unit
a)
b)
c)
Fig. 3. Robert Moskovic 2019 award winners: a) Prof. Hojjat Adeli, University of Ohio, USA; b) Prof. Alfonso Carlos Fernández-Canteli, University of Oviedo, Spain; c) Prof. Aleksandar Sedmak, University of Belgrade, Serbia.
a)
b)
c)
d)
Fig. 4. Award of Merit TC12 winners: a) Dr. Grzegorz Lesiuk, Wroclaw University of Science and Technology, Poland; b) Dr. Dianyin Hu, Beihang University, China; c) Dr. Pedro Montenegro, Faculty of Engineering of the University of Porto, Portugal; d) Dr. Shun-Peng Zhu, University of Electronic Science and Technology of China, China.
José A.F.O. Correia et al. / Procedia Structural Integrity 22 (2019) 1–9 Author name / Structural Integrity Procedia 00 (2019) 000 – 000
8
8
a)
b)
c)
d)
e)
Fig. 5. ESIS/TC12 Young Scientist 2019 Award winners: a) Kodai Matsuoka, Railway Technical Research Institute, Japan; b) Rita Dantas, University of Porto, Portugal; c) Teresa Magoga, University of Tasmania, Australia; d) Vítor Gomes, University of Porto, Portugal; e) Yaroslav Dubyk, IPP-Centre Ltd. and National Academy of Sciences of Ukraine, Ukraine. Acknowledgements The guest editors would like to express a special thanks to Professor Francesco Iacoviello, Editor-in-Chief of Procedia Structural Integrity journal, and to Elsevier staff for their support during the preparation of this issue. Additionally, thanks to all the sponsors of the event: FCT (Portuguese Science Foundation – FiberBridge project – POCI-01-0145 FEDER-030103); CONSTRUCT Unit (Institute of R&D in Structures and Construction – UID/ECI/04708/2019); IC (Construction Institute, Porto, Portugal); SIKA (SIKA AG); VESTAS (Vestas Wind Systems); EDP (Electricidade de Portugal); University of Electronic Science and Technology of China (China); ESIS (European Structural Integrity Society); SPFIE (Portuguese Structural Integrity Society); Associação de Turismo do Porto e Norte (Portugal). References Correia, J.A.F.O., De Jesus, A.M.P., Muniz-Calvente, M., Sedmak, A., Moskvichev, V., Calçada, R., 2019a. The renewed TC12/ESIS technical committee - Risk analysis and safety of large structures and components. Engineering Failure Analysis, 105, pp. 798-802. Correia, J.A.F.O., Berto, F., Ayatollahi, M., Marsavina, L., Kotousov, A., Sedmak, A., 2019b. Guest editorial: Advanced design and fatigue assessment of structural componentes. Fatigue and Fracture of Engineering Materials and Structures, 42(6), pp. 1217-1218.
José A.F.O. Correia et al. / Procedia Structural Integrity 22 (2019) 1–9 Author name / Structural Integrity Procedia 00 (2019) 000 – 000
9
9
Correia, J.A.F.O., Ferradosa, T., Castro, J.M., Fantuzzi, N., Jesus, A.M.P.D., 2019c. Editorial: Renewable energy and oceanic structures: Part I. Proceedings of the Institution of Civil Engineers: Maritime Engineering, 172(1), pp. 1-2. Correia, J.A.F.O., Lesiuk, G., De Jesus, A.M.P., Calvente, M., 2018a. Recent developments on experimental techniques, fracture mechanics and fatigue approaches. Journal of Strain Analysis for Engineering Design, 53(8), pp. 545. Rebelo, C., Correia, J., Baniotopoulos, C., De Jesus, A., 2018. Wind energy technology (WINERCOST). Wind Engineering, 42(4), pp. 267. Correia, J.A.F.O., De Jesus, A.M.P., Pariente, I.F., Belzunce, J., Fernández-Canteli, A., 2017. Mechanical fatigue of metals. Engineering Fracture Mechanics, 185, pp. 1. Pariente, I.F., Belzunce, J., Canteli, A.F., Correia, J.A.F.O., De Jesus, A.M.P., 2016. Editorial of the ICMFM Conference. Procedia Engineering, 160, pp. 1-4. Correia, J.A.F.O., De Jesus, A.M.P., Calçada, R.A.B., 2018b. Editorial. Proceedings of the Institution of Civil Engineers: Forensic Engineering, 171(2), pp. 47-48. Fonseca de Oliveira Correia, J., Jesus, A.M.P., Varum, H., Calçada, R., Romão, X., 2018c. CINPAR2016–strengthening and repair of structures. International Journal of Structural Integrity, 9(3), pp. 278-280. De Oliveira Correia, J.A.F., Calvente, M.M., De Jesus, A.M.P., Fernández-Canteli, A., 2018d. Guest editorial. International Journal of Structural Integrity, 8(6), pp. 614-616. Correia, J.A.F.O., De Jesus, A.M.P., Henriques, A.A.R., Castro, J.M.F., Montenegro, P., Calçada, R.A.B., 2019d. Proceedings of the First International Symposium on Risk Analysis and Safety of Complex Structures and Components, Book of Abstracts, ISBN 978‐972‐752‐259‐0 , Faculty of Engineering of the University of Porto, Portugal.
Available online at www.sciencedirect.com ScienceDirect Structural Integrity Procedia 00 (2019) 000 – 000 Available online at www.sciencedirect.com ScienceDirect Structural Integrity Procedia 00 (2019) 000 – 000
www.elsevier.com/locate/procedia
www.elsevier.com/locate/procedia
ScienceDirect
Procedia Structural Integrity 22 (2019) 189–193
© 2019 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) Peer-review under responsibility of the First International Symposium on Risk and Safety of Complex Structures and Components organizers © 2019 The Authors. Published by Elsevier B.V.This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) Peer-review under responsibility of the First International Symposium on Risk and Safety of Complex Structures and Components organizers important to minimize heir occurrence and know how to prevent and act in ach ype of accident. Understanding th causes and went wrong in previous accidents, is an essential step to tak corrective ac ons, to define strategies and safety plans. This study aims at performing a statistical analysis, by creating a database of rail accidents that happened in Po tu al in the years of 2014 and 2017. Th results will make it possible to understand the a cidents ’ crit factors, patterns, a d details. Portugal has one of the low st accident rates from Europe and the most common accident type is “accident with people triggered by railway rolling stock” . The results from this research can be added to other accidents historical registers, amplifying the existing data to support safety decision-makers. © 2019 The Autho s. Publ shed by Elsev er B.V.This is an open access article u er th CC BY-NC-ND li ense (http://creativecommons.org/licenses/by-nc-nd/4.0/) Peer-review under responsibility of the First International Symposium on Risk and Safety of Complex Structures and Components organ z rs First International Symposium on Risk and Safety of Complex Structures and Components Accidents on railway lines in Portugal Cristina Reis a,b,c, *, José Correia b,c , Carlos Oliveira c,d , Nuno Tomaz a a Department of Engineering, University of Trás-os-Montes and Alto Douro, Quinta de Prados, 5000-801 Vila Real, Portugal b CONSTRUCT, Faculty of Engineering of the University of Porto, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal c INEGI, University of Porto, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal d Department of Civil Engineering, Polytechnic of Viana do Castelo, Viana do Castelo, Portugal Abstract The railway system is essential for urbanization and social development. Despite it is considered one of the safest transports means worldwide, rail accidents are complex to approach and may induce to catastrophes with several fatalities. Thus, it is important to minimize their occurrence and know how to prevent and act in each type of accident. Understanding the causes and went wrong in previous accidents, is an essential step to take corrective actions, to define strategies and safety plans. This study aims at performing a statistical analysis, by creating a database of rail accidents that happened in Portugal in the years of 2014 and 2017. The results will make it possible to understand the accidents ’ critical factors, patterns, and details. Portugal has one of the lowest accident rates from Europe and the most common accident type is “accident with people triggered by railway rolling stock” . The results from this research can be added to other accidents historical registers, amplifying the existing data to support safety decision-makers. First International Symposium on Risk and Safety of Complex Structures and Components Accidents on railway lines in Portugal Cristina Reis a,b,c, *, José Correia b,c , Carlos Oliveira c,d , Nuno Tomaz a a Department of Engineering, University of Trás-os-Montes and Alto Douro, Quinta de Prados, 5000-801 Vila Real, Portugal b CONSTRUCT, Faculty of Engineering of the University of Porto, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal c INEGI, University of Porto, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal d Department of Civil Engineering, Polytechnic of Viana do Castelo, Viana do Castelo, Portugal Abst ct The ailway syste is essential for urb izati n and s cial development. Despi e it is considered on of the safest transports m ans worldwid , rail ac idents are complex to ap r ach and may induce to catastrophes with several fatalities. u , it is Keywords: Railway lines; Accidents; Statistical analysis; Portugal.
Keywords: Railway lines; Accidents; Statistical analysis; Portugal.
* Corresponding author. Cristina Reis E-mail address: crisreis@utad.pt * Corresponding author. Cristina Reis E mail address: crisreis@utad.pt
2452-3216 © 2019 The Authors. Published by Elsevier B.V.This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) Peer-review statement: Peer-review under responsibility of the First International Symposium on Risk and Safety of Complex Structures and Components organizers 2452 3216 © 2019 The Autho s. Published by Elsevier B.V.This is an open acc ss rticle under the CC BY-NC-ND license (http://c ativecommons.org/licenses/by-nc-nd/4.0/) Peer-review statement: Peer-review under responsibility of the First International Symposium on Risk and Safety of Complex Structures and Components organizers
2452-3216 © 2019 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) Peer-review under responsibility of the First International Symposium on Risk and Safety of Complex Structures and Components organizers 10.1016/j.prostr.2020.01.052
Cristina Reis et al. / Procedia Structural Integrity 22 (2019) 189–193 Author name / Structural Integrity Procedia 00 (2019) 000 – 000
190
2
1. Introduction The railway is one of the most important transportation methods worldwide. With land urbanization, the necessity for accessibilities and mobility have emerged. Every day, there are thousands of train travels, transporting people, products, chemicals, fuels, etc. (Oggero, et al., 2006). The European railway network was formed by a different kind of networks, according to the country, each with its own characteristics. When built, central governments aimed at unifying their people and cities, often ignoring the connections out of boundaries. The result, was an incompatible European network, leading several governments to build new tracks or modernize the existing ones (Martí-Henneberg, 2013). In Portugal, the railway implementation follows similar patterns as other European countries. The first Portuguese railway was built in 1856 between Lisboa and Carregado, served by a British second-hand locomotive. The attention was given by the society and the amount of money involved, private entities started investing in building new tracks across the country. Therefore, twenty years later, Portugal ’s main railway was already designed. Although, the construction cost was higher than expected and the traffic estimation was overrated, forcing investors to dismiss their investments. Portuguese central government was enforced to take over the costs from three essential lines: Alentejo, Linhas do Sul e Sueste; Linha do Norte and; Linha do Douro. At the beginning of the twenty century, every Portuguese cities were served by the railway system. The train carriages were built with wood and stops were frequent to refill the locomotive with water (Expresso, 2016). However, since the 1990 decade, the Portuguese government has closed several lines and stations across the country, deactivating over than 1300 km from the existing 3658 km. The Portuguese railway can be summarized in the coastline axis Braga-Lisboa-Faro, with few complementary lines. Nowadays, the Portuguese government has announced and started some modernizations works in specific routes until 2020, but the tracks will not be able to allow high-speed trains, unlike the reaming European countries (Expresso, 2016). Despite the railway is considered one of the safest transportations means, the railway demands constant investment in accident prevention and studies about accidents causes. In 2017, Europe witnessed 1855 railway accidents, some of them with several fatalities. According to the former Railway Transport National Institute (INTF), now included in the Portuguese Transportation and Mobility Institute (IMT), the following concepts are important to understand (INTF, 2006): “Serious accident” – Any accident involving, at least, a moving rail vehicle that causes deaths or serious injuries at least, one-person, or considerable damage to the material, roads, other installations, or to the environment, or prolonged disruption of circulation. Accidents in workshops and warehouses are excluded; “Accident” – A sudden, unwanted or involuntary event or chain of events with harmful consequences. Accidents fall into the following categories: collisions, derailments, level crossing accidents, accidents with people caused by moving rolling stock, fires and others; “Incident” – Any occurrence, other than accident or serious accident, associated with the operation of the railway and affecting the operation safety. All events (broken rails, tourniquets, signaling failures, overshooting of the most restrictive aspect (SPAD), broken wheels and axle breakdowns) must be reported. If one of these events leads to an accident, it must also be reported. In the railway systems, there are 7 types of accidents that can happen (INTF, 2006): Derailment – When the train goes off the track. Getting off a track into another which isn’ t desired, may also be a derailment. It means any situation in which, at least, one wheel of a train leaps from the rail; Collision – Train collision, including collisions with obstacles in the jig, means a collision which may be frontal between trains, between the front and the tail of two trains, between a train and any part of another train, or the collision of a train with maneuvering movements, fixed objects (such as line ends), objects temporarily present on or near the track (such as rocks, landslides, trees, rail vehicles lost parts or road vehicles) and railway maintenance machinery or equipment; Fire – rolling stock fires concerns to fires and/or explosions that happen on railway vehicles during their travel or operations; Structural collapse – Not directly related to railway accidents are the ones resulting from structural collapses, like bridges, tunnels or the permanent way. These collapses are mainly due to structural failures in engineering works, landslides, soil erosion, among others;
Cristina Reis et al. / Procedia Structural Integrity 22 (2019) 189–193 Author name / Structural Integrity Procedia 00 (2019) 000 – 000
191
3
Equipment’s fatigue – Another aspect that can also be related with railway accidents is the equipment structural fatigue, from broken rails, track deformation (withers or warps), wheel and axle ruptures, among others; Signaling equipment failure – Any failure of the signaling system, which results in a less restrictive signal than required; Human failure – Risk of human failure associated with the performance of locomotive operators and management companies’ employees. Probably, this is one of the most difficult types of occurrence to prevent, as focuses on human action, which depends on many factors: fatigue, sudden illness, distraction, ignorance, among others. In Europe, in the year of 2009, 1391 people have died in rail accidents (Evans, 2011). In 2017, the most regular accident in Europe was “Accidents with people triggered by railway rolling stock” with 1080 occurrences (Pordata, 2019). Portugal is one of the European countries with few railway accidents. According to the Pordata portal (Pordata, 2019), in 2017, have happened in Portugal 29 railway accidents, 13 more than the previous year. The most recurrent type of accident was “Accidents with people triggered by railway rolling stock” with 19 occurrences, followed by 7 accidents in railroad crossings and derailment accidents with 3. To minimize the accident rate or impact is important to modernize tracks, train people and define safety plans. To correctly do so, it is necessary to know where to act and what to improve. These are recognized by analyzing previous accidents and what went wrong. Thus, the present study aims to analyze railway accidents that happened in Portugal, in order to learn from them and to minimize their occurrence. A database will be created to perform a statistical analysis, making it possible to know accidents critical factors and deeply understand patterns and details. 2. Methodology The adopted methodology for the elaboration of the present study consists, initially, by making bibliographical research about the railway theme, with a special focus on the Portuguese context. Thus, it will be possible to characterize its current state, as well as identify all types of occurrences recorded in 2014 and 2017. Railway accidents data from those years were collected by analyzing the List of Significant Accidents from the Railway Annual Security Reports produced by the IMT (IMT, 2014; IMT 2017). All of the occurrences and/or accident characteristics and circumstances were identified, such as their category, severity, period of the day, among others, for the selected years. To perform the information collection for the database, the following aspects and assumptions were considered and identified: Month of the year, subdivided by quarter; Month day; Weekday; Hour, subdivided by day period:
o Morning – 6 am -12 am; o Afternoon – 12 am - 6 pm; o Evening – 6 pm - 0 am; o Night – 0 am - 6 am.
Severity: o Mortal - in the existence of the fatalities;
o Serious - serious or minor injuries and/or prolonged road interruptions; o No severity - in case of road interruption and/or emergency plan activation; o Incident - in the case of “near -accident".
Accident classification: o Collisions; o Derailment;
o Accident on the level crossing; o Accident with persons caused by moving rolling stock; o Equipment Fatigue;
Cristina Reis et al. / Procedia Structural Integrity 22 (2019) 189–193 Author name / Structural Integrity Procedia 00 (2019) 000 – 000
192
4
o No Signaling; o Human failure; o Others.
Road interruption period, in minutes;
Type of emergency plan, defined by the emergency coordinator and by the local emergency manager: o Red /Category A;
o Yellow /Category B; o Orange /Category C.
Accident with or without people. With this data, accident variables were characterized, in order to identify accidents critical factors and patterns. 3. Results The created database allowed to perform a series of calculations sets, in order to identify accident patterns and most common factors. Table 1 shows the summary values for the occurrences and/or accidents occurred in 2014 in Portugal, according to the criteria defined above. In total 282 occurrences were registered in Portugal during the year of 2014, but only the 50 accidents with high impact will be considered. Table 2 presents the summary values for the occurrences and/or accidents that were registered in Portugal in 2017. In total, 29 accidents were recorded in Portugal, 19 of which were personal accidents caused by the movement of rolling stock, 7 at level crossings and 3 derailments.
Table 1. Data on accidents in Portugal, 2014.
Variable Month with most occurrences Weekday with most occurrences
January (8) Monday (13) Afternoon (20) 216.375 Minutes Accident with persons caused by moving rolling stock (31) Category C (22)
Most frequent day period Average interruption time Most frequent accident
Most common emergency plan type Most common accident severity Number of accidents with people
Serious (19)
43
Table 2. Data on accidents in Portugal, 2017.
Variable Month with most occurrences Weekday with most occurrences
May (8)
Tuesday (8)
Most frequent day period Average interruption time Most frequent accident
Afternoon (10) 608 Minutes
Accident with persons caused by moving rolling stock (19)
Most common emergency plan type Most common accident severity Number of accidents with people
Orange (24) Mortal (18)
27
Cristina Reis et al. / Procedia Structural Integrity 22 (2019) 189–193 Author name / Structural Integrity Procedia 00 (2019) 000 – 000
193
5
4. Conclusions The analysis of previous railway accidents is an important step to understanding what went wrong and to develop new safety strategies and solutions that mitigate or reduce the impact of future occurrences. In total, there were 282 occurrences (50 accidents) in 2014 and 29 accidents in 2017 registered in the Portuguese territory. The most common type of accident, in both years, was caused by rolling movement stock, responsible for 31 accidents in 2014 and 19 accidents in 2017. At the other extreme, are the rolling stock fire accidents, with no accidents during the analyzed period. This work is of great importance for the railway sector, namely in the prevention and mitigation of accidents, in improving rescue methods and in increasing the general safety of railway transportation. Understanding the causes and impacts of past accidents is essential to ensure that the same mistakes are not made and to improve assistance methods in different types of situations. Acknowledgements This work was financially supported by: Project POCI-01-0145-FEDER-007457 - CONSTRUCT - Institute of R&D In Structures and Construction funded by FEDER funds through COMPETE2020 - Programa Operacional Competitividade e Internacionalização (POCI) – and by national funds through FCT - Fundação para a Ciência e a Tecnologia; UID/ECI/04708/2019 - CONSTRUCT - Instituto de I&D em Estruturas e Construções funded by national funds through the FCT/MCTES (PIDDAC); and, FiberBridge – Fatigue strengthening and assessment of railway metallic bridges using fiber-reinforced polymers (POCI-01-0145-FEDER-030103) by FEDER funds through COMPETE2020 (POCI) and by national funds (PIDDAC) through the Portuguese Science Foundation (FCT/MCTES). References A cidentes ferroviários: total e por tipo de acidente . Pordata. https://www.pordata.pt/Europa/ Instituto da Mobilidade e dos Transportes (IMT). Relatório Anual de Segurança Ferroviária 2014 (Railway Annual Security Report 2014), ed 01/2015. Lisboa, 2015. Instituto da Mobilidade e dos Transportes (IMT). Relatório Anual de Segurança Ferroviária 2017 (Railway Annual Security Report 2017), ed 01/2018. Lisboa, 2018. Instituto Nacional do Transporte Ferroviário (INTF). Relatório Anual de Segurança de 2006 (Annual Security Report 2006), ed. 1.1. Lisboa, 2007. 160 na linha . Rui Cardoso in Expresso. https://expresso.pt/sociedade/2016-10-22-160-anos-na-linha, 2016 [last access 10/07/2019] Oggero, A., Darbra, R. M., Muñoz, M., Planas, E., Casal, J., 2006. A survey of accidents occurring during the transport of hazardous substances by road and rail. Journal of Hazardous Materials 133, 1-7. Martí-Henneberg, J., 2013. European integration and national models for railway networks (1840 – 2010). Journal of Transport Geography 26, 126-138. Evans, A. W., 2011. Fatal train accidents on Europe's railways: 1980 – 2009. Accident Analysis & Prevention 43, 391-401.
Available online at www.sciencedirect.com
Available online at www.sciencedirect.com Available online at www.sciencedirect.com
ScienceDirect Structural Integrity Procedia 00 (2018) 000–000 Structural Integrity Procedia 00 (2018) 000–000 Procedia Structural Integrity 22 (2019) 345–352
www.elsevier.com / locate / procedia
www.elsevier.com / locate / procedia
2452-3216 © 2019 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) Peer-review under responsibility of the First International Symposium on Risk and Safety of Complex Structures and Components organizers 10.1016/j.prostr.2020.01.043 ∗ Corresponding author. Tel.: + 86-18761654420 E-mail address: mahdishadabfar@tongji.edu.cn 2210-7843 c 2019 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http: // creativecommons.org / licenses / by-nc-nd / 4.0 / ) Peer-review under responsibility of the First International Symposium on Risk and Safety of Complex Structures and Components organizers. Slope stability is a critical problem in civil engineering projects, which is encountered in many geotechnical struc tures including dams, embankments, and structures constructed along the slopes. The main objective of slope stability analysis is to identify the most unstable slip surface that may cause failure in the slope. In conventional methods, instability potential is evaluated by calculating the factor of safety (FS), and the critical slip surface is the one with the lowest FS. Mathematically, the problem is to find the position vector of the slip surface, v ( x 1 , x 2 , ..., x n ), which ∗ Corresponding author. Tel.: + 86-18761654420 E-mail address: mahdishadabfar@tongji.edu.cn 2210-7843 c 2019 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http: // creativecommons.org / licenses / by-nc-nd / 4.0 / ) Peer-review under responsibility of the First International Symposium on Risk and Safety of Complex Structures and Components organizers. © 2019 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) Peer-review under responsibility of the First International Symposium on Risk and Safety of Complex Structures and Components organizers Abstract Slope stability analysis is one of the most challenging problems in geotechnical engineering. Due to the uncertainty involved in the problem, probabilistic methods are recently utilized to estimate the probability of slope failure. In this study, the slope stability is presented as an optimization problem and the Simulated Annealing (SA) method is used to identify the slip surface with the minimum safety factor. The SA algorithm is then integrated with the Monte Carlo sampling method to calculate the probability of slope failure. Next, the groundwater level is added to the problem formulation as a random variable to model the uncertainty for cases where the groundwater table is not accurately determined. The results of the analysis showed that for slopes with low safety factors, the uncertainty of the groundwater table worsens the condition and increases the failure probability. Moreover, the parametric study showed that the insu ffi cient understanding of groundwater level distribution and the assumption of uniform distribution further increases the failure probability. The results of this study are presented in the form of a probability curve against the groundwater table. This presentation has practical applications in real projects. c 2019 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http: // creativecommons.org / licenses / by-nc-nd / 4.0 / ) Peer-review under responsibility of the First Internatio al Symposium on Risk a d Safety of Complex Structures and Components organizers. Keywords: Type your keywords here, separated by semicolons ; First International Symposium on Risk and Safety of Complex Structures and Components A hybrid Monte Carlo-Simulate A nealing approach for reliability analysis of slope stability considering the uncertainty in water table level Mahdi Shadab Far a, ∗ , Hongwei Huang a a Department of Geotechnical Engineering, Tongji University, No. 1239, Siping Road, Shanghai, 200092, China Abstract Slope stability analysis is one of the most challenging problems in geotechnical engineering. Due to the uncertainty involved in the problem, probabilistic methods are recently utilized to estimate the probability of slope failure. In this study, the slope stability is presented as an optimization problem and the Simulated Annealing (SA) method is used to identify the slip surface with the minimum safety factor. The SA algorithm is then integrated with the Monte Carlo sampling method to calculate the probability of slope failure. Next, the groundwater level is added to the problem formulation as a random variable to model the uncertainty for cases where the groundwater table is not accurately determined. The results of the analysis showed that for slopes with low safety factors, the uncertainty of the groundwater table worsens the condition and increases the failure probability. Moreover, the parametric study showed that the insu ffi cient understanding of groundwater level distribution and the assumption of uniform distribution further increases the failure probability. The results of this study are presented in the form of a probability curve against the groundwater table. This presentation has practical applications in real projects. c 2019 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http: // creativecommons.org / licenses / by-nc-nd / 4.0 / ) Peer-review under responsibility of the First International Symposium on Risk and Safety of Complex Structures and Components organizers. Keywords: Type your keywords here, separated by semicolons ; First International Symposium on Risk and Safety of Complex Structures and Components A hybrid Monte Carlo-Simulated Annealing approach for reliability analysis of slope stability considering the uncertainty in water table level Mahdi Shadab Far a, ∗ , Hongwei Huang a a Department of Geotechnical Engineering, Tongji University, No. 1239, Siping Road, Shanghai, 200092, China 1. Introduction 1. Introduction Slope stability is a critical problem in civil engineering projects, which is encountered in many geotechnical struc tures including dams, embankments, and structures constructed along the slopes. The main objective of slope stability analysis is to identify the most unstable slip surface that may cause failure in the slope. In conventional methods, instability potential is evaluated by calculating the factor of safety (FS), and the critical slip surface is the one with the lowest FS. Mathematically, the problem is to find the position vector of the slip surface, v ( x 1 , x 2 , ..., x n ), which
Made with FlippingBook Digital Publishing Software