An innovative SHM solution for earthquake- induced damage identification in historic masonry structures

Alban Kita abril de 2020 UMinho | 2020 An Innovative SHM Solution for Earthquake-Induced Damage Identification in Historic Masonry Structures Alban Kita An Innovative SHM Solution for EarthquakeInduced Damage Identification in Historic Masonry Structures Universidade do Minho Escola de Engenharia Università degli Studi di Perugia abril de 2020 Tese de Doutoramento Engenharia Civil Trabalho efetuado sob a orientação de Professor Doutor Filippo Ubertini (Unipg) Professor Doutor Paulo B. Lourenço (UMinho) Alban Kita An Innovative SHM Solution for EarthquakeInduced Damage Identification in Historic Masonry Structures Universidade do Minho Escola de Engenharia Università degli Studi di Perugia DIREITOS DE AUTOR E CONDIÇÕES DE UTILIZAÇÃO DO TRABALHO POR TERCEIROSS Este é um trabalho académico que pode ser utilizado por terceiros desde que respeitadas as regras e boas práticas internacionalmente aceites, no que concerne aos direitos de autor e direitos conexos. Assim, o presente trabalho pode ser utilizado nos termos previstos na licença abaixo indicada. Caso o utilizador necessite de permissão para poder fazer um uso do trabalho em condições não previstas no licenciamento indicado, deverá contactar o autor, através do RepositóriUM da Universidade do Minho. Licença concedida aos utilizadores deste trabalho Atribuição-NãoComercial-SemDerivações CC BY-NC-ND https://creativecommons.org/licenses/by-nc-nd/4.0/ Date and place Guimarães 24/02/2020 Signature Acknowledgement The present Thesis was developed within a joint international doctoral programme between the Departments of Civil and Environmental Engineering of the Universities of Florence and Perugia, Italy, and the Department of Civil Engineering of the University of Minho, Portugal. This research was carried out under the joint supervision of Prof. Filippo Ubertini and Prof. Paulo B. Lourenço. First and foremost, I am very grateful to my supervisor Prof. Filippo Ubertini for giving me the opportunity and the tools to undertake and complete my Ph.D. programme in the University of Perugia, as well as for sharing knowledge, providing permanent support, careful teaching and advice, suggestions and motivation along with all the research. Without his guide the research work could not have been accomplished. I would like to express my gratitude to my supervisor Prof. Paulo B. Lourenço for providing all the necessary resources to attend doctoral studies in the University of Minho, in Guimarães, welcoming me into the Historical and Masonry Structures UMinho research group, and for sharing experience, interest and support, encouragement and valuable discussions. I would like to thank heartily my co-supervisors: Dr. Nicola Cavalagli for the indispensable help, the fruitful wellspent discussions, assistance, patience and availability; and Dr. Maria Giovanna Masciotta for the continuous encouragement, valuable suggestions, productive conversations, careful reading and precious comments on the dissertation. I have very sincere thanks to extend to Prof. Ilaria Venanzi from the University of Perugia for the great possibility of collaboration we exploited, her support and interest in my work. I would like to thank the staff and secretariats of the Universities of Perugia, Florence and Minho. Moreover, I express my appreciation to all my friends and colleagues from Perugia and Guimarães for their support and friendship during this adventure. I would like to express my gratefulness to my Family for their love and unconditional support that they have always showered on me. In conclusion, I wish to thank my best half, Dori, for her unwavering patience, love and encouragement. You’ve always believed in me. Thank you! To Dori! Thank you for being (in) my Life. III STATEMENT OF INTEGRITY I hereby declare having conducted this academic work with integrity. I confirm that I have not used plagiarism or any form of undue use of information or falsification of results along the process leading to its elaboration. I further declare that I have fully acknowledged the Code of Ethical Conduct of the University of Minho. Date and place Guimarães 24/02/2020 Signature IV Resumo da Tese de Doutoramento O principal objetivo deste trabalho de investigação dizia respeito ao desenvolvimento e validação de uma metodologia inovadora para a deteção, localização e quantificação de danos causados por sismos em estruturas históricas de alvenaria. A metodologia proposta, designado por DORI, baseia-se na combinação de métodos baseados em dados e métodos inovadores baseados em modelos, abordando a identificação de dano com base na análise modal operacional (OMA), modelação rápida de substitutos e análise dinamica incremental (IDA) para edifícios de alvenaria do Património Cultural (CH) sujeitos a sismos. Mais detalhadamente, a metodologia DORI propõe a fusão de dados estáticos e dinamicos no método de deteção de dano baseado em OMA e estende a OMA através da introdução e implementação de dois métodos inovadores independentes e complementares baseados em modelos, para localização e quantificação de danos induzidos por sismos em construções históricas de alvenaria com monitorização permanente: o primeiro método é baseado num modelo substituto, uma ferramenta rápida que combina dados de monitorização de vibração a longo prazo (ou seja, OMA) e a modelação numérica, enquanto o segundo método é baseado em IDA não linear sísmica. A Tese está focada na validação de diferentes aspetos da metodologia DORI, através da aplicação a quatro estruturas que servem de casos de estudo: uma estrutura de alvenaria ensaiada em laboratório e reconhecida internacionalmente, designada por Brick House, e tres edifícios de alvenaria de CH equipados com sistemas permanentes de monitorização de saúde estrutural, nomeadamente o Palácio de Consoli, a Torre Sciri e a Torre sineira de San Pietro. Em conclusão, a metodologia DORI proposta nesta Tese para deteção, localização e quantificação de danos induzidos por sismos é uma nova abordagem metodológica, aplicada e validada com sucesso em estruturas históricas de alvenaria, constituindo uma ferramenta promissora para a rápida avaliação de danos pós-sismo das estruturas de CH sob monitorização SHM a longo prazo. Palavras-chave: Identificação de danos induzidos por sismos; Monitorização da Saúde Estrutural; Estruturas históricas de alvenaria; Herança cultural; Modelação por elementos finitos; Monitorização de longo prazo; Modelação substituta; Análise Dinamica Incremental; Sismo; Medida de intensidade; Medida de dano; Torre de alvenaria; Torre sineira de alvenaria; Palácio de alvenaria. V Abstract The main objective of this research work concerned the development and validation of an innovative methodology aimed at the detection, localization and quantification of earthquake-induced damages in historic masonry structures. The high cultural, economic and political value set upon historic buildings spread out all over the world has made the earthquake-induced damage identification, as well as preservation and conservation of architectural heritage, a subject of outstanding importance. The proposed methodology, called DORI, is based on the combination of data-driven, as well as innovative model-based methods, addressing the Damage identification based on Operational modal analysis (OMA), Rapid surrogate modeling and Incremental dynamic analysis (IDA) for Cultural Heritage (CH) masonry buildings subjected to earthquakes. More in detail, the DORI methodology proposes the static-and-dynamic data fusion in the OMA-based damage detection method, and extends it through the introduction and implementation of two independent and complementary innovative model-based methods, for localization and quantification of earthquake-induced damage in permanently monitored historic masonry buildings: the former is a surrogate model-based method, a rapid tool which combines long-term vibration monitoring data (i.e. OMA) and numerical modeling, while the latter is based on non-linear seismic IDA. The Thesis focuses on the validation of different aspects of the DORI methodology, through application to four case study structures: an internationally well-known laboratory masonry structure, called the Brick House, and three CH masonry buildings equipped with permanent Structural Health Monitoring systems, namely the Consoli Palace, the Sciri Tower and the San Pietro Bell Tower. In conclusion, the DORI methodology proposed for earthquake-induced damage detection, localization and quantification is a novel methodological approach, successfully applied and validated in historic masonry structures, constituting a promising tool for rapid post-earthquake damage assessment of CH structures under long-term SHM monitoring. Keywords: Earthquake-induced damage identification; Structural Health Monitoring; Historic masonry structures; Cultural Heritage; Finite Element modeling; Long-term monitoring; Surrogate modeling; Incremental Dynamic Analysis; Earthquake; Intensity measure; Damage measure; Masonry tower; Masonry bell tower; Masonry palace. VI Contents 1 Introduction and the new proposed DORI methodology 1 1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Literature review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.3 The proposed DORI methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.4 Novel aspects of the proposed DORI methodology . . . . . . . . . . . . . . . . . . . 12 1.5 Outline and organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2 Data-driven damage detection 16 2.1 Theory background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2.2 The proposed method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 2.3 Application example: the Consoli Palace . . . . . . . . . . . . . . . . . . . . . . . 22 2.3.1 Introduction to the case study . . . . . . . . . . . . . . . . . . . . . . . . 23 2.3.2 Data fusion for enhancing statistical reconstruction of natural frequencies . . . . 27 2.3.3 Application of enhanced vibration-based SHM damage detection . . . . . . . . 30 2.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 3 FEM-based damage localization using surrogate modeling 37 3.1 Theory background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 3.2 The proposed method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 3.3 Application example: the Sciri Tower . . . . . . . . . . . . . . . . . . . . . . . . . 44 3.3.1 Introduction to the case study . . . . . . . . . . . . . . . . . . . . . . . . 44 3.3.2 Continuous SHM and FE modeling . . . . . . . . . . . . . . . . . . . . . . 47 3.3.3 Detection and localization of simulated damage . . . . . . . . . . . . . . . . 54 3.3.4 Localization of earthquake-induced damage . . . . . . . . . . . . . . . . . . 60 3.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 VII Contents 5.13 Three real seismic events used for earthquake-induced damage localization and quantification in the San Pietro Bell Tower: ground motion records of CSA station during Accumoli earthquake (a), Ussita shock (b) and Norcia earthquake (c). . . . . . . . . . . . . . . 132 5.14 Belfry: IDA-based tensile damage (minimum, maximum and mean values) estimated with Accumoli, Ussita and Norcia earthquakes by means of the eleven (11) selected seismic input IMs. For comparative purposes actual damage (dt) is also reported. . . . . . . . . . . . 133 5.15 Comparison between actual damage (dt) and IDA-based estimated tensile damage, considering different combinations of IMs for the three selected real ground motion records: Accumoli (a), Ussita (b) and Norcia (c). Note that IDA-based damage is expressed in terms of weighted average ranges and mean values obtained from the IDA curve sets and corresponding mean curves, respectively. . . . . . . . . . . . . . . . . . . . . . . . . . 135 5.16 Comparison between actual damage (dt) and weighted mean IDA-based estimated tensile damage, considering different combinations of IMs (Scenarios 1, 2 and 3) for Accumoli, Ussita and Norcia earthquakes. Zoom plots have range of axis from 0 to 0.05. . . . . . . 136 5.17 The IDA curve sets (shaft, belfry and cusp) and corresponding mean curves: plots of tensile damage, dt, versus PRA (a), RMSRA (b), RIC(c) and RIA(d). . . . . . . . . . . . . . . 138 5.18 The IDA curve sets (shaft, belfry and cusp) and corresponding mean curves: plots of tensile damage, dt, versus PRV (a) and RMSRV (b). . . . . . . . . . . . . . . . . . . . . . 139 5.19 The IDA curve sets (shaft, belfry and cusp) and corresponding mean curves: plots of tensile damage, dt, versus PRD. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 5.20 Dispersion of the IDA curve sets (shaft, belfry and cusp) by means of RMSEi,j (Eq. (4.2)): tensile damage Vs PRA, RMSRA, RIC, RIA, PRV, RMSRV and PRD. . . . . . . . . . 140 5.21 Three real seismic events used for earthquake-induced damage localization and quantification in the San Pietro Bell Tower: measured dynamic response on top of the bell tower in terms of acceleration during the three main shocks of the seismic sequence, Accumoli earthquake (a), Ussita earthquake (b) and Norcia earthquake (c). . . . . . . . . . . . . 141 5.22 Belfry: IDA-based tensile damage (minimum, maximum and mean values) estimated with Accumoli, Ussita and Norcia earthquakes by means of the seven (7) selected seismic response IMs. For comparative purposes actual damage (dt) is also reported. . . . . . . . 143 XIV Contents 5.23 Comparison between actual damage (dt) and IDA-based estimated tensile damage, considering different combinations of seismic response IMs for the three selected real ground motion records: Accumoli (a), Ussita (b) and Norcia (c). Note that IDA-based damage is expressed in terms of weighted average ranges and mean values obtained from the IDA curve sets and corresponding mean curves, respectively. . . . . . . . . . . . . . . . . . . . 144 5.24 Comparison between actual damage (dt) and weighted mean IDA-based estimated tensile damage, considering different combinations of seismic response IMs (Scenarios 1, 2 and 3) for Accumoli, Ussita and Norcia earthquakes. Note that zoom plots have range of axis from 0 to 0.05. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 5.25 Belfry: IDA-based tensile damage (minimum, maximum and mean values) estimated with Accumoli, Ussita and Norcia earthquakes by means of their eighteen (18) (eleven (11) seismic input and seven (7) seismic response) IMs into Eq. (4.3). For comparative purposes actual damage (dt) is also reported. . . . . . . . . . . . . . . . . . . . . . . . . . 146 5.26 Comparison between actual damage (dt) and IDA-based estimated tensile damage, considering different combinations of seismic input and seismic response IMs for the three selected real ground motion records: Accumoli (a), Ussita (b) and Norcia (c). Note that IDA-based damage is expressed in terms of weighted average ranges and mean values obtained from the IDA curve sets and corresponding mean curves, respectively. . . . . . . . . . . . . 148 5.27 Comparison between actual damage (dt) and weighted mean IDA-based estimated tensile damage, considering different combinations of IMs (Scenarios 1, 2 and 3) for Accumoli, Ussita and Norcia earthquakes: using only seismic input IMs (a), using only seismic response IMs (b) and using seismic input and seismic response IMs combined (c). . . . . . . . . 149 A.1 Plots of earthquake magnitude versus epicentral distance (a), subsoil category (b), hypocentral depth (c), faulting mechanism (d) and time (e) for all strong ground motions used in the statistical correlation analysis of IMs. . . . . . . . . . . . . . . . . . . . . . . . . . 160 B.1 Tensile damage dtcontour plots on the Brick House obtained at the last step of the IDAs with IT0806xa_m earthquake with increasing levels of the seismic input. . . . . . . . . . 166 B.2 The IDA curve sets and corresponding mean curves for the ten (10) parts of the Brick House: plots of tensile damage (dt) versus PGA (a-j). . . . . . . . . . . . . . . . . . . . . . 167 B.3 The IDA curve sets and corresponding mean curves for the ten (10) parts of the Brick House: plots of tensile damage (dt) versus IC(a-j). . . . . . . . . . . . . . . . . . . . . . . 168 XV Contents B.4 The IDA curve sets and corresponding mean curves for the ten (10) parts of the Brick House: plots of tensile damage (dt) versus IA(a-j). . . . . . . . . . . . . . . . . . . . . . . 169 B.5 The IDA curve sets and corresponding mean curves for the ten (10) parts of the Brick House: plots of tensile damage (dt) versus Sa(T1) (a-j). . . . . . . . . . . . . . . . . . . . . 170 B.6 The IDA curve sets and corresponding mean curves for the ten (10) parts of the Brick House: plots of tensile damage (dt) versus ASI (a-j). . . . . . . . . . . . . . . . . . . . . . . 171 B.7 The IDA curve sets and corresponding mean curves for the ten (10) parts of the Brick House: plots of tensile damage (dt) versus PGV (a-j). . . . . . . . . . . . . . . . . . . . . . 172 B.8 The IDA curve sets and corresponding mean curves for the ten (10) parts of the Brick House: plots of tensile damage (dt) versus Sv(T1) (a-j). . . . . . . . . . . . . . . . . . . . . 173 B.9 The IDA curve sets and corresponding mean curves for the ten (10) parts of the Brick House: plots of tensile damage (dt) versus IH(a-j). . . . . . . . . . . . . . . . . . . . . . . 174 B.10 The IDA curve sets and corresponding mean curves for the ten (10) parts of the Brick House: plots of first principal plastic strain (εpl 1) versus PGA (a-j). . . . . . . . . . . . . . . . . 175 B.11 The IDA curve sets and corresponding mean curves for the ten (10) parts of the Brick House: plots of first principal plastic strain (εpl 1) versus IC(a-j). . . . . . . . . . . . . . . . . . 176 B.12 The IDA curve sets and corresponding mean curves for the ten (10) parts of the Brick House: plots of first principal plastic strain (εpl 1) versus IA(a-j). . . . . . . . . . . . . . . . . . 177 B.13 The IDA curve sets and corresponding mean curves for the ten (10) parts of the Brick House: plots of first principal plastic strain (εpl 1) versus Sa(T1) (a-j). . . . . . . . . . . . . . . . 178 B.14 The IDA curve sets and corresponding mean curves for the ten (10) parts of the Brick House: plots of first principal plastic strain (εpl 1) versus ASI (a-j). . . . . . . . . . . . . . . . . 179 B.15 The IDA curve sets and corresponding mean curves for the ten (10) parts of the Brick House: plots of first principal plastic strain (εpl 1) versus PGV (a-j). . . . . . . . . . . . . . . . . 180 B.16 The IDA curve sets and corresponding mean curves for the ten (10) parts of the Brick House: plots of first principal plastic strain (εpl 1) versus Sv(T1) (a-j). . . . . . . . . . . . . . . . 181 B.17 The IDA curve sets and corresponding mean curves for the ten (10) parts of the Brick House: plots of first principal plastic strain (εpl 1) versus IH(a-j). . . . . . . . . . . . . . . . . . 182 B.18 Tensile damage dtcontour plots on the San Pietro Bell Tower obtained at the last step of the IDAs with IT0788 earthquake with increasing levels of the seismic input. . . . . . . . 183 B.19 The IDA curve sets (shaft, belfry and cusp) and corresponding mean curves: plots of ELDMD versus PGA (a), RMSA (b) and IC(c). . . . . . . . . . . . . . . . . . . . . . . . . . 184 XVI Contents B.20 The IDA curve sets (shaft, belfry and cusp) and corresponding mean curves: plots of ELDMD versus IA(a), Sa(T1) (b) and ASI (c). . . . . . . . . . . . . . . . . . . . . . . . . . 185 B.21 The IDA curve sets (shaft, belfry and cusp) and corresponding mean curves: plots of ELDMD versus PGV (a), RMSV (b), Sv(T1) (c) and IH(d). . . . . . . . . . . . . . . . . . . . . 186 B.22 The IDA curve sets (shaft, belfry and cusp) and corresponding mean curves: plots of ELDMD versus Sd(T1). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187 XVII List of Tables 2.1 Frequency and crack amplitude shifts according to eight (8) damage scenarios, obtained from different combinations of shifts A=-1.5%, B=-0.5% and C=+1.0%. Outliers percentages resulted from corresponding control charts are also reported. . . . . . . . . . . . . . . 31 3.1 Experimental identified natural frequencies and damping ratios from AVT and frequencies estimated through MLR at 20◦C. . . . . . . . . . . . . . . . . . . . . . . . . . . 47 3.2 Mechanical parameters of the FE model before tuning. . . . . . . . . . . . . . . . . . 50 3.3 Comparison between experimental and numerical modal parameters after tuning. . . . . 52 3.4 Uniaxial stress-strain values and scalar tension damage values utilized in the CDP model for masonry. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 3.5 Relative frequency decays obtained for the considered damage scenarios (in percentage). . 57 3.6 Results of the localization obtained for the simulated damage scenarios D1 and D2. Note that if components ki(i= 1, ..., 4) of Uare equal to 1, it means no damage occurred to the macroelement. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 3.7 Synthetic information regarding the four main shocks of January 18th 2017 seismic sequence as recorded by seismic stations placed nearby epicenters (PGAE-W, PGAN-S, PGAZ denote PGA values in E-W, N-S and vertical directions, respectively). . . . . . . . . . . . 61 3.8 Results of localization of the earthquake-induced damage. Note that if components ki(i= 1, ..., 4) of Uare equal to 1, it means no damage occurred to the macroelement. . . . . 63 3.9 Comparison between experimental (Exp) and dynamic non-linear FE model Peak Response Accelerations (PRAs) at level 3 of the Sciri Tower (see Fig. 3.3b). . . . . . . . . . . . . 64 4.1 General classification of IMs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 4.2 Acceleration-related IMs (A: amplitude, F: frequency content, D: duration). . . . . . . . . 82 4.3 Velocity-related IMs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 4.4 Displacement-related IMs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 XVIII Contents 4.5 Mixed/hybrid IMs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 4.6 Mechanical parameters adopted on the Brick House FE numerical model. . . . . . . . . 93 4.7 Uniaxial stress–strain and scalar tensile damage values utilized in the CDP model for the masonry material. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 4.8 CDP parameters defining flow potential, yield surface and viscosity. . . . . . . . . . . . 93 4.9 Original characteristics of the selected strong ground motions subsequently matched to the Christchurch response spectrum for IDA. PGAs refer to spectrum-matched accelerograms. 95 5.1 Mechanical parameters assumed in the San Pietro Bell Tower FE model after calibration. . 122 5.2 Uniaxial stress–strain (tension stiffening) and scalar tensile damage values utilized in the three parts of the numerical model. . . . . . . . . . . . . . . . . . . . . . . . . . 122 5.3 Main characteristics of strong ground motions used for Incremental Dynamic Analysis of the FE model of the San Pietro Bell Tower. . . . . . . . . . . . . . . . . . . . . . . . . 125 5.4 Scale factors (SFs) applied to the unscaled accelerograms used for Incremental Dynamic Analysis of the San Pietro Bell Tower. . . . . . . . . . . . . . . . . . . . . . . . . . 126 5.5 Scaling factors applied to the ground motion records of Castelnuovo-Assisi station in the three main earthquakes of the 2016 Central Italy seismic sequence. . . . . . . . . . . . 132 A.1 The main information of selected ground motions. . . . . . . . . . . . . . . . . . . . 161 XIX List of acronyms/abbreviations/symbols αi,j Weight coefficients ϵFlow potential eccentricity γSpecific weight µViscosity parameter νPoisson’s ratio ψDilation angle in the p–q plane σcCompressive strength σtTensile strength ASINH Nau and Hall P-Acceleration Spectrum Intensity ASIVT Von Thun Acceleration Spectrum Intensity A95 Acceleration parameter CaAmplification of acceleration CdAmplification of displacement CvAmplification of velocity DSINH Nau and Hall Displacement Spectrum Intensity EIInput Energy XX Contents IAArias Intensity IaRiddell and Garcia compound acceleration index ICCharacteristic Intensity IDCosenza and Manfredi Damage Factor IdRiddell and Garcia compound displacement index IFFajfar index IHHousner P-Velocity Spectrum Intensity ISSandi instrumental intensity IvRiddell and Garcia compound velocity index MwMoment magnitude PDDestructive Potential Factor RIAResponse Arias Intensity RICResponse Characteristic Intensity Sa,avg The geometric mean of spectral acceleration Sa(T1) Spectral acceleration at T1 Sd(T1)Spectral displacement at T1 SpaC Inelastic spectral acceleration Sv(2T1) Spectral velocity at 2T1 Sv(T1) Spectral velocity at T1 VSIHC Hidalgo and Clough P-Velocity Spectrum Intensity VSIKKappos P-Velocity Spectrum Intensity VSINH Nau and Hall P-Velocity Spectrum Intensity XXI Contents VSIVT Von Thun Velocity Spectrum Intensity ˜εpl cEquivalent plastic strain ˜εck tCracking strain εpl 1First principal plastic strain εtTotal strain εel 0tElastic strain of undamaged material AV T Ambient Vibration Test CAD Cumulative Absolute Displacement CAV Cumulative Absolute Velocity CBM Condition-Based Maintenance CDP Concrete Damage Plasticity CH Cultural Heritage CSA Castelnuovo-Assisi seismic monitoring station dtTensile damage variable DM Damage Measure DOF Degree of freedom DORI Damage identification based on Operational modal analysis & Rapid surrogate modeling & Incremental dynamic analysis for CH masonry buildings subjected to earthquakes EYoung’s modulus EDA Effective Design Acceleration EFDD Enhanced Frequency Domain Decomposition EPA Effective Peak Acceleration XXII Contents EPD Effective Peak Displacement EPRI Electrical Power Research Institute EPV Effective Peak Velocity ESD European Strong Motion FDD Frequency Domain Decomposition FE Finite Element FEM Finite Element Method FEMU FEM Updating GMPE Ground Motion Prediction Equation HERACLES HEritage Resilience Against CLimate Events on Site IDA Incremental Dynamic Analysis IM Intensity Measure ITACA ITalian ACcelerometric Archive LCL Lower Control Limit LDA Linear dynamic analysis LNEC Laboratorio Nacional de Engenharia Civil (in Portuguese) LSA Linear static analysis LV DT Linear Variable Displacement Transducer MAC Modal Assurance Criterion MID Maximum Incremental Displacement MIV Maximum Incremental Velocity MLR Multivariate Linear Regression XXIII Chapter 1 Introduction and the new proposed DORI methodology by earthquakes or by other types of dynamic loadings, allows cost-effective management of maintenance and restoration (post-earthquake) interventions. In this context, SHM systems can improve protection and conservation of structures by providing real-time diagnostic and prognostic data, thus enabling condition-based maintenance instead of periodic or breakdown-based maintenance, with a significant optimization of economic expenses (Farrar and Worden 2007). Vibration-based systems are very attractive in SHM due to the possibility of obtaining reliable modal parameter estimates from in-service response data through automated Operational Modal Analysis (OMA) techniques (Magalhães et al. 2009; Rainieri and Fabbrocino 2010; Reynders et al. 2012; Ubertini et al. 2013; Brincker and Ventura 2015), typically using a small number of sensors. Powerful tools allow tracking the evolution in time of the parameters associated with a specific structural mode (modal tracking). Furthermore, recent developments in the field have led to the definition of statistical tools that permit to remove the variance in the data associated with changing environmental conditions (typically temperature and humidity) and to detect anomalies in the structural behavior corresponding to very small variations in frequencies. These techniques are based on multivariate statistical analysis, such as Multivariate Linear Regression (MLR) (Worden et al. 2002), Principal Component Analysis (PCA) (Yan et al. 2005a; Yan et al. 2005b; Bellino et al. 2010) and novelty detection by means of statistical process control tools such as control charts (Worden et al. 2002; Farrar and Worden 2012; Magalhães et al. 2012; Mosavi et al. 2012; Dackermann et al. 2014; Dervilis et al. 2015). In this way, small changes in the structural behavior occurring after an earthquake can be automatically detected or, conversely, the same techniques assume the structure in the healthy state after the event if no significant deviations of the data from normal conditions are observed. If applied to a multitude of structures, it would be possible giving priority to those constructions that have exhibited the largest deviations from normal conditions after an earthquake. While SHM systems can potentially offer the possibility to obtain accurate condition screenings of the structural health, problems, critical aspects and technical limitations for applications to CH structures still exist. The selection of the proper sensing hardware and signal processing tools, the minimum number of sensors, their appropriate configuration, just to mention a few, make the damage identification task very challenging. Damage, by its nature, is a highly localized phenomenon, thus the careful selection and deployment of sensors are critical for its spacial detection. To obtain reliable and high-quality structural information, it is important to monitor the structural behavior at the fine-grained level, ensuring a sufficiently large number of sensors (Masciotta et al. 2019). Recently, wireless technologies have emerged aiming at providing relatively inexpensive and densely distributed sensor platforms for autonomous SHM and damage detection. However, 5 Chapter 1 Introduction and the new proposed DORI methodology although these considerable advancements, wireless SHM systems still present several limitations which are preventing the full realization of their potential, such as inappropriate instrumentation and sensor overload, reliable network topology, data compression and transmission, data mining, energy consumption and storage cost, environmental and noise effects, and more (Brownjohn 2007). Nevertheless, they possess all the advantages of both Ambient Vibration Tests (AVT) and OMA that make them particularly attractive for applications, such as their fully non-destructive nature and the relatively inexpensive equipment that is necessary for testing, resulting in historical and architectural respect conforming to international criteria and protocols on cultural heritage preservation. Moreover, continuous tracking of the actual structural conditions, typically using a limited number of sensors, is enabled in a fully automated way (Overschee and Moor 1996; Reynders et al. 2012). Although vibration-based SHM and damage detection have unavoidable limitations in those cases where seismic damages affect only very limited portions of the structure scarcely influencing global vibration modes, they are useful for detecting different types of damages, including very small ones that do not affect the safety of the structure. In this context, considering the pros and cons, more widespread applications of continuous SHM for historic constructions are however having constantly growing interest. The first significant developments in SHM originated from major construction projects in civil infrastructure, such as large dams (Comerford et al. 1992), large-scale bridges (Ko and Ni 2005), offshore platforms (Brederode et al. 1986), nuclear installations, tunnels and excavations, and more. The primary scope was to gain a better insight into the structural behaviour of such systems during construction activities, normal operation and extreme events (earthquakes, strong winds and floods), by tracking specific parameters suitable for the extraction of information regarding the structural response and for the identification of possible anomalous changes (Masciotta et al. 2019). In the context of SHM for historic structures, several applications of AVT and OMA, aimed at vulnerability assessment through calibration of Finite Element (FE) models, can be found in the literature in the case of historic bridges (Calcada et al. 2002; Spyrakos et al. 2004; Brencich and Sabia 2008; Limongelli et al. 2018; Gkoktsi et al. 2019; An et al. 2019), monumental buildings (Bartoli et al. 1996; Jaishi et al. 2003; Casarin and Modena 2008; Pau and Vestroni 2008; Ramos et al. 2010; Ramos et al. 2011; Aras et al. 2011; Formisano et al. 2012; Ramos et al. 2013; Clementi et al. 2017; Formisano et al. 2018a; Lorenzo et al. 2019) and historic towers (Bennati et al. 2005; Ivorra and Pallares 2006; Gentile and Saisi 2007; Pena et al. 2010; Oliveira et al. 2012; Foti et al. 2012; Pieraccini et al. 2014; Gentile et al. 2015; Pellegrini et al. 2018; Bru et al. 2019; Ivorra et al. 2019), including applications as tools for non-destructive evaluation of the severity of damages caused by earthquakes (Tashkov et al. 2010; Krstevska et al. 2010). 6 Chapter 1 Introduction and the new proposed DORI methodology While the applications of long-term permanent vibration-based SHM systems can be mentioned in the literature considering bridges, critical infrastructures (Materazzi and Ubertini 2011; Magalhães et al. 2012; Ubertini et al. 2013) and public buildings (Dolce et al. 2017), the implementation of multivariate statistical analysis techniques to historic and monumental constructions equipped with permanent vibration-based SHM systems is not yet widespread, with only a few examples (Bartoli et al. 1996; Ramos et al. 2010; Saisi et al. 2015; Ubertini et al. 2018; Kita et al. 2019b; Gentile et al. 2019). Most of the under monitoring structures have dealt with field data artificially modified for simulating damage effects (Ntotsios et al. 2008; Magalhães et al. 2012; Comanducci et al. 2015; Comanducci et al. 2016) and only few applications have experienced earthquake field data recorded on real structures undergoing actual damage (Saisi et al. 2015; Gentile et al. 2016; Ubertini et al. 2018; Gentile et al. 2019), also including the Osservatorio Sismico delle Strutture (OSS), an Italian network of permanent seismic monitoring systems installed in public buildings in Italy (Dolce et al. 2017; Cattari et al. 2019). A practical demonstration of the ability of a permanent vibration-based SHM system to efficiently detect an early stage earthquake-induced damage (not detected by a mere visual inspection), presenting to some extent, also damage quantification in the form of permanent variations in natural frequencies, can be found in (Ubertini et al. 2018). 7 Chapter 1 Introduction and the new proposed DORI methodology 1.3 The proposed DORI methodology The DORI methodology proposed in this Thesis consists of an enhanced data-driven vibration-based method combined with two independent innovative model-based methods, aimed at the detection, localization and quantification of earthquake-induced damages in historic masonry structures. Specifically, DORI addresses the Damage identification based on Operational modal analysis & Rapid surrogate modeling & Incremental dynamic analysis for CH masonry buildings subjected to earthquakes. The general framework of the DORI methodology is summarized in the flow chart illustrated in Fig. 1.1, while the description is provided in the next paragraphs. The very first activities to be carried out concern detailed preliminary investigations such as geometrical survey, on-site inspection and structural condition assessment (visual and instrumental/analytical), damage survey with the mapping of material degradation and structural crack pattern analysis, material characterization and so forth (Lourenço 2006; Ubertini et al. 2016). All these activities provide the necessary information for carrying out AVT, whose main objective is evaluating the baseline dynamic characteristics of the structure and, in particular, its natural frequencies, mode shapes and damping ratios. The overall results and information from these preliminary investigations and AVT serve as the basis for the development and installation of the permanent vibration-based SHM system, choosing, in particular, the best sensor’s location for long-term SHM purposes, as well as for the construction and calibration of numerical models. The development of long-term structural health monitoring systems for preventive conservation of historic masonry buildings has received increasing scientific interest. In this context, validated data-driven OMA-vibrationbased SHM methods for damage detection combine automated mode tracking, multiple data regression and novelty detection. In light of these considerations, the first goal of this Thesis is to implement an enhanced OMA-vibration-based SHM tool for automated earthquake-induced damage detection. The DORI methodology proposes a data-driven damage detection method with a significant improvement in the removal of the effects of changes in environmental and operational conditions from identified natural frequencies, in other words, an enhanced data cleansing, which represents a key step for damage detection. The introduction of static measures (in addition to temperatures) as predictors to the statistical tools for the extraction of damage-sensitive features is proposed in this Thesis in the case of an historic stiff masonry building. The method is tested and validated on the Consoli Palace, an iconic monumental masonry building located in Gubbio, Italy, which is being continuously monitored by a permanent long-term static and dynamic SHM system since July 2017. First, the continuous modal identification is not common in the literature in the context of long-term monitor8 Chapter 1 Introduction and the new proposed DORI methodology Figure 1.1: General framework of the DORI methodology: Damage identification based on Operational modal analysis & Rapid surrogate modeling & Incremental dynamic analysis. 9 Chapter 1 Introduction and the new proposed DORI methodology ing of stiff masonry structures such as palaces, given the majority of validated modal tracking applications essentially concerning slender towers. In addition, the availability of continuous static features in the present case study, in particular, crack amplitude data, allows an enhancement of the dynamic MLR model, achieving a more accurate damage detection. The continuous monitoring data acquired over a sufficient time window, enable rapid and automated damage detection, even for small damages at an early stage (not yet detectable by visual inspections) caused by moderate earthquakes, thus constituting an effective low-cost tool for CBM and preventive conservation of historic masonry structures. Subsequently to the OMA-based data-driven damage detection, methods addressing higher levels of damage identification with a certain accuracy represent a major challenge and are yet to be defined, especially when dealing with earthquake-induced damages. In this context, the second goal of this Thesis is to address the earthquake-induced damage localization and quantification task in historic masonry structures, by combining two innovative independent model-based methods, the former consisting in the use of a calibrated Surrogate Model (SM), while the latter based on Incremental Dynamic Analysis (IDA). The SM-based method relies on the use of long-term OMA-vibration-based monitoring data, dynamic MLR models and numerical model updating. While damage detection can be essentially considered a data-driven process, damage localization typically requires the construction and the calibration of a FE model of the structure, in order to link identified modal parameters to variations of damage-related mechanical parameters. The tuned numerical FE model is ideally subdivided into distinctive macrostructural elements to discriminate such damage-dependent structural parameters belonging to different zones and bound the localization of damage. The real-time damage detection and localization are performed by using long-term monitoring data and by solving an inverse FE model calibration problem on a SM. To minimize the computational effort, a simple SM consisting of a quadratic expression relating natural frequencies and modal shape components to elastic parameters is considered. In this context, equivalent elastic properties of macrostructural elements are identified by minimizing an objective function considering experimentally identified and numerically predicted damageinduced decays in natural frequencies and changes in eigenvector components. In particular, the continuous identification of these damage-dependent properties is carried out by the online minimization of the relative differences between experimental and numerical modal parameters. The innovative aspect of the proposed method of DORI is represented by defining the objective function that combines both natural frequencies and mode shapes, and not only natural frequencies. It allows increasing the number of degrees of freedom of the inverse problem, thus permitting to investigate the robustness of the obtained optimization solution and avoid false positive results. The SM-based method is applied and validated in the case of another medieval 10 Chapter 1 Introduction and the new proposed DORI methodology heritage masonry building, i.e. an historic civic tower in Perugia, Italy, called the Sciri Tower, which has been continuously monitored since December 2017. The validation is carried out by using simulated damage scenarios (artificially imposed damage-induced frequency decays) and a set of real far-field earthquake data, and considering the FE model of the tower including surrounding buildings, calibrated based on the obtained results from AVT. The proposed procedure is capable of correctly detecting and localizing earthquake-induced damages. The IDA-based method completes the DORI methodology. It is based on multidimensional non-linear seismic IDA simulations carried out using a numerical FEM model together with seismic data recorded via long-term vibration-based SHM. IDA simulations are carried out at increasing levels of the earthquake input and relate a certain damage parameter to the intensity of the dynamic input. The construction and tuning of the numerical model representative of the structure under analysis are required, while the seismic/response intensity parameter is measured by the monitoring system and, through the IDA curves, is used to estimate the damage. The key aspect is the introduction of local multidimensional IDA curve sets, so as to allow a local estimation of damage with confidence intervals. In particular, IDA curves are built with reference to different specific portions of the structure, relating a set of meaningful local Damage Measures (DMs) against one or more selected earthquake ground motion Intensity Measures (IMs). A suitable damage parameter for masonry structures and a suitable seismic intensity measure should be defined on the basis of both theoretical considerations and numerical modeling in such a way to reduce as much as possible the variability of IDA curves so limiting the uncertainty in the estimated damage. In particular, a thorough overview of all IMs proposed in the literature is provided, since the use of the most efficient IMs represents an important aspect of IDA results and effectiveness. To this end, wide literature research, definition, classification and statistical correlation analysis considering one hundred (100) seismic records allow selecting the most suitable, uncorrelated and efficient intensity measures for IDA purposes. Multidimensional local IDA curve sets are constructed and used in the way that, when an earthquake occurs, the seismic/response intensity parameter is measured by the monitoring system or directly computed from the measurements, and local damage conditions are immediately estimated using the prior multidimensional IDA analysis. The IDA-based method is validated through applications to the FE numerical model of a laboratory reduced-scale masonry structure, called the Brick House, and subsequently to the FE model of an iconic medieval masonry building located in Perugia, Italy, the San Pietro Bell Tower. Earthquake-induced damage localization and quantification are achieved with an acceptable level of approximation considering real earthquake acceleration records for both structures. 11 Chapter 1 Introduction and the new proposed DORI methodology More in-depth descriptions of the innovative methods constituting the DORI methodology are presented in each Chapter, in particular, the enhanced data-driven method for damage detection in Chapter 2, the surrogate modeling in Chapter 3 and the IDA-based method in Chapter 4. 1.4 Novel aspects of the proposed DORI methodology It should be emphasized that the proposed DORI methodology constitutes the original contribution of this Thesis. DORI incorporates several innovative aspects, aimed at earthquake-induced damage detection, localization and quantification in historic masonry buildings. The first innovative aspect of the Thesis concerns the proposal of data fusion in data-driven damage detection method, in particular, the use of static measures as predictors in the dynamic MLR model for removing environmental effects from identified natural frequencies, in addition to temperature data. The second and main innovative aspect proposed by the DORI methodology regards the introduction of two innovative independent model-based methods in the context of long-term OMA-based monitoring for localization and quantification of earthquake-induced damage. The surrogate model-based method is based on a linear finite element model and combines long-term vibration monitoring data (i.e. OMA) and numerical modeling. Given the simplicity and limited computational costs, it is a rapid tool for damage detection and localization. In particular, the innovative quadratic SM exploits an objective function which is based also on variations in mode shapes, in addition to natural frequencies changes (damage-induced decays). On the other hand, the seismic IDA-based method is newly proposed for earthquake-induced damage localization and quantification, not observed so far in the literature. Unlike the SM, the IDA requires a non-linear model. Several benefits can be exploited by putting together OMA, SM and IDA-based methods. First of all, damage detection achieved by continuous OMA, e.g. in terms of frequency shifts and control chart (novelty detection), can be used for comparative purposes with damage identified with SM and IDA, allowing to avoid false positive results. Second, the combination of linear (SM), as well as non-linear (IDA) models can certainly enrich the accuracy of the DORI methodology. Afterwards, IDA uses the seismic response of an earthquake, whereas OMA and SM are based on long-term vibration monitoring data, thus, combining two independent approaches for damage identification purposes. Also, the combination of the SM with the IDA-based methods can be exploited for comparative and/or complementary scopes, in particular, it allows reducing the uncertainties related to IDA, together with the mitigation of the uncertainties in the localization task and the focus on the consistency between these two independent methods. 12 Chapter 1 Introduction and the new proposed DORI methodology Overall, the proposed DORI methodology enables a rapid post-earthquake damage assessment of long-term monitored CH structures for condition-based maintenance and preventive conservation. After the occurrence of a seismic event, DORI allows to immediately reveal the presence of damage and to subsequently localize and quantify it with an acceptable level of confidence. 1.5 Outline and organization This Thesis is organized in six (6) Chapters. The main contents of each Chapter are summarized as follows: •Chapter 1 provides an introduction to the work, with the motivation for innovative SHM solutions in CH masonry structures, the literature review on SHM basic concepts and a particular focus on vibrationbased SHM damage detection. Afterwards, a general description of the proposed DORI methodology is provided, as well as, the outline of the Thesis. •Chapter 2 presents the basic theoretical background as well as the enhanced vibration-based SHM method for earthquake-induced damage detection, consisting in the novel use of static features as predictors in the data cleansing statistical tool (a dynamic MLR model), in particular, crack amplitude data, resulting into a clearly improved statistical reconstruction of natural frequencies aimed at damage-sensitive features extraction, a key aspect for novelty analysis by means of control chart. The proposed method is validated through the application to the Consoli Palace, an historic stiff masonry building, where a long-term permanent mixed static and dynamic SHM system is implemented since July 2017 and a vibration data automated modal analysis procedure has allowed to effectively track the evolution in time of the natural frequencies of six (6) identified modes, a novelty in the literature in the context of long-term monitoring of stiff masonry buildings such as palaces, whereas the majority of modal tracking applications to masonry structures are essentially concerned to slender towers. It is demonstrated that the adopted vibration-based SHM tool on the Consoli Palace enable rapid and automated earthquake-induced damage detection, even for small damages, simulated by artificial insertion of small frequency and crack amplitude shifts in the monitoring data, conceivably associated to a small structural damage at an early stage (caused by a moderate/light seismic event), thus constituting an effective low-cost tool for condition-based maintenance and preventive conservation of the stiff monumental palace. 13 Chapter 1 Introduction and the new proposed DORI methodology •Chapter 3 presents a detailed description of the surrogate model-based method aimed at real-time damage detection and localization using long-term vibration-based monitoring data and FE model updating. Damage localization is performed by solving an inverse model calibration problem on a surrogate model, based on variations of modal parameters observed through the processing of monitoring data. A simple surrogate model consisting of a quadratic expression relating natural frequencies and modal shape components to elastic parameters is considered, minimizing the computational effort. The surrogate model-based method is validated through application to the Sciri Tower, an historic civic masonry tower, where a simple permanent vibration-based SHM system is installed. A tuned numerical model of the structure is constructed and ideally subdivided into distinctive macrostructural elements to discriminate the damage-dependent structural parameters belonging to different zones. Simulated damage-induced natural frequency variations and frequency decays observed through the processing of monitoring data after a far-field earthquake have been used to detect and localize possible earthquake-induced damages. Using artificial damage scenarios have demonstrated that the proposed procedure is effective for both earthquake-induced damage detection and localization. Furthermore, the results obtained using field data and the real earthquake response have been validated through non-linear dynamic analysis and visual inspections. •Chapter 4 presents a detailed description of the innovative IDA-based method aimed at rapid localization and quantification of earthquake-induced damages in masonry structures. It is based on IDA carried out from a numerical model (non-linear finite element analysis) and using data recorded during seismic events, relying on the introduction of local multidimensional IDA curve sets relating meaningful local damage parameters to selected seismic intensity measures. An in-depth specific study consisting of wide literature research, definition, classification and statistical correlation analysis is carried out to investigate their interdependence and to subsequently select the most suitable, uncorrelated and meaningful intensity measures for IDA purposes. The proposed method is numerically validated through application to a reduced-scale masonry structure, namely the Brick House, a notable benchmark, object of previous studies by several authors. Ten (10) IDA curve sets, one for every part of the FE model, have been constructed considering tensile damage, plastic strain magnitude and first principal plastic strain as damage measures. Additionally, an in-depth investigation of dispersion, using root mean square errors of IDA curve sets, allowed identifying the most efficient intensity parameters in the case of tensile damage and first principal plastic strain. Finally, considering three acceleration records of the 2016 Central Italy seismic sequence, earthquake-induced damage localization and quantification (in terms of overall weighted average estimation of damage ranges and 14 Chapter 2 Data-driven damage detection havior of the structure. The coefficients of the statistical model contained in matrix βare estimated in a least-square sense by minimizing the norm of the prediction error, E, in Eq. (2.4), in the reference tt. PCA is another well-known technique that can address the removal of environmental effects from identified natural frequencies when statistical correlations between natural frequencies and environmental parameters are linear (Yan et al. 2005a; Bellino et al. 2010). The main advantage of PCA is that it does not require to measure environmental conditions. PCA consists of remapping the original data into the more convenient vectorial space generated by the Principal Components (PCs) and only some of the PCs are retained to turn back to the original space. PCs are statistically independent variables that constitute an orthogonal basis and provide different contributions to the variance of the original data. The basic idea behind this operation is that the PCs that provide the largest contributions to the variance represent the independent environmental and operational factors that have to be retained for estimating ˆ Yin Eq. (2.1). Remaining PCs are instead associated with residual errors and are neglected. Several improvements to classic PCA have been proposed in the literature to handle the more general case of non-linear correlations between damage-sensitive features, such as Kernel PCA and local PCA (Kambhatla and Leen 1997; Yan et al. 2005b). Nevertheless, the PCA technique is not the focus of this work, where, instead, the attention is devoted to the MLR technique. 21 Chapter 2 Data-driven damage detection 2.2 The proposed method The development of long-term SHM systems for preventive conservation of CH buildings is receiving a growing trend of scientific interest. Nevertheless, the damage detection effectiveness of these systems is still debated, especially for complex masonry buildings where both local and global failure mechanisms can be activated, whereby the majority of the documented successful applications are limited to masonry towers. The methodology proposes an enhanced version of the data-driven earthquake-induced damage detection method presented in Section 2.1. With reference to the general framework illustrated in Fig. 2.1, particular focus is devoted to the 3rd step, i.e the removal of environmental and operational conditions from identified natural frequencies and the extraction of damage-sensitive features. An enhanced data cleansing is proposed by introducing static measures as predictors to the statistical tools for the extraction of damage-sensitive features (e.g. MLR). The availability of continuous static features in permanently monitored structures can lead to significant refinement of the dynamic regression model. The proposed method is applied to the Consoli Palace, a masonry CH structure that has been under continuous static and dynamic monitoring for more than two years. The effectiveness of the adopted dynamic MLR tool, using past values of predictors, is investigated for removing temperature effects from identified natural frequencies and, in particular, catching delayed temperature-induced effects related to the thermal inertia. Also, the introduction of measured crack amplitude data is proposed to be used in addition to temperature data as predictors for the construction of dynamic MLR models, aiming at improving the statistical modeling of natural frequencies. Finally, the effectiveness of the adopted SHM tool with particular focus on the results of control charts is investigated by simulating earthquake damage effects in terms of frequency shifts artificially imposed to natural frequencies time histories. 2.3 Application example: the Consoli Palace The implementation of a long-term static-dynamic SHM system in the Consoli Palace and the application of the proposed method are reported in this Section. The case study is briefly presented in Section 2.3.1 while results on data fusion are discussed in Section 2.3.2. Section 2.3.3 is devoted to the validation of the enhanced damage detection method. The main conclusions are summarized in Section 2.4. 22 Chapter 2 Data-driven damage detection 2.3.1 Introduction to the case study The Consoli Palace (in Italian Palazzo dei Consoli) is the most representative monument of the medieval town of Gubbio, Italy, and is located in the heart of its historical center (see Fig. 2.2). Several studies have been carried out on the Consoli Palace in the framework of Horizon 2020 European HERACLES (HEritage Resilience Against CLimate Events on Site) project, devoted to enhancing resilience of historic buildings against harmful events, with reference to various types of hazards. It concerns a wide research programme planned to develop effective SHM methodologies and protocols for application to historic masonry palaces, a structural typology that has been rarely investigated in an SHM perspective (Kita et al. 2018; Kita et al. 2019b; Cavalagli et al. 2019a; Cavalagli et al. 2019b; Garcia-Macias et al. 2019). It constitutes the first example in the literature where continuous modal identification and SHM based on frequency tracking has been applied to the case of a stiff masonry palace, with the purpose of early detecting any damage or change in its structural behavior following an earthquake. Built in gothic style between 1332 and 1349, it presents an articulated internal distribution of volumes and an elevation of more than 60 m (from the street level up to the top of the small bell tower). The Palace is built in calcareous stone masonry and has a rectangular plan of about 40x20 m, with foundations placed on two different levels. Geometrical and structural damage surveys have highlighted existing cracks associated to a moderate state of structural damage. Revealed to be an effective diagnostic tool also in the case of the Figure 2.2: The Consoli Palace, historic pictures and today: unknown authors in 1907 (a) and 1912 (b) and front view today (c). 23 Chapter 2 Data-driven damage detection monumental stiff palace, AVT allowed the identification of six (6) modes of vibration within the range from 0 to 10 Hz: three global and three local (involving mostly the bell tower placed on the top) (Kita et al. 2019b). Overall, results on damage survey, AVT and numerical modeling have provided the necessary information for the conceptual development and installation of a simple low-cost mixed static and dynamic long-term SHM system in the Consoli Palace on July 5th 2017, which is currently active (see Fig. 2.3). It consists of two crack meter sensors (LVDT1 and LVDT2), two surface temperature sensors (T1 and T2) and three high sensitivity accelerometers (A1, A2 and A3) to track the evolution of modal properties of the structure. The application Figure 2.3: Long-term static-dynamic SHM system installed on the Consoli Palace: LVDTs and temperature sensors’ layout with detailed view of positioning in correspondence of the 1st and 2nd main crack ((a) and (b), respectively, where the double arrows indicate the direction of opening of the monitored crack) and accelerometers locations (c). 24 Chapter 2 Data-driven damage detection of an automated Stochastic Subspace Identification (SSI) modal analysis procedure (Ubertini et al. 2013) has allowed to effectively track the evolution in time of the natural frequencies of the six (6) identified modes of the Palace, which represents a novelty in the literature in the context of long-term monitoring of stiff masonry buildings such as palaces, whereby previous applications of modal tracking to masonry structures were essentially limited to slender towers. Results of continuous modal identification and frequency tracking are presented in Fig. 2.4, while Fig. 2.5 shows the plot of the evolution in time of two monitored crack amplitudes and temperature data of the Consoli Palace. The static and dynamic response of the Consoli Palace under ambient loading conditions have been continuously monitored for more than two years. Investigation of significant temperature effects for the first year of monitoring can be found in (Kita et al. 2019b). Differently from what observed in other literature works on vibration-based monitoring of masonry buildings, an unexpected negative correlation between natural frequencies and temperature has been found for the Consoli Palace. This negative correlation is indeed observed for the first time, compared to positive natural frequencies-temperature correlations of masonry structures such as slender towers and stiffer structures such as churches and/or cathedrals (Masciotta et al. 2016; Figure 2.4: Time series of identified natural frequencies during the monitoring period (daily fluctuations are also evidenced with a detailed view). 25 Chapter 2 Data-driven damage detection Figure 2.5: Evolution in time of two monitored crack amplitudes (LVDT1 and LVDT2) and temperature data (T1 and T2) of the Consoli Palace during the monitoring period (daily fluctuations are also evidenced with a detailed view). Masciotta et al. 2017). Fig. 2.6 shows plots of 2nd and 5th natural frequencies versus temperature measured by sensor T1. The increase in natural frequencies of global vibration modes of the Palace with decreasing ambient temperature has been attributed to an increase in global structural stiffness due to strengthening effects of metallic reinforcements (tie rods shortening at lower temperatures) and the presence of a moderate structural damage state in the Palace. Also, remarkable freezing effects on natural frequencies have been observed during some exceptional cold days between February and March 2018 (see Fig. 2.4), resulting in sharp increases, conceivably caused by the stiffening effect produced by ice crystals forming within the masonry micro-pores. 26 Chapter 2 Data-driven damage detection Figure 2.6: Correlation between natural frequencies and temperature: plots of frequencies of modes Fy1 (a) and T1 (b) versus temperature data T1. 2.3.2 Data fusion for enhancing statistical reconstruction of natural frequencies As already introduced in the context of vibration-based SHM in Section 2.1, the effects of changes in environmental conditions can be removed from identified natural frequency data using statistical techniques (Yan et al. 2005a; Yan et al. 2005b; Bellino et al. 2010). In the case of the Consoli Palace, MLR filters have been adopted for the removal of temperature effects on identified natural frequencies, where linear correlations between a set of rdependent variables (natural frequencies) and a set of pindependent variables (temperatures), called predictors, are exploited (see Eq. (2.4)). In particular, continuously tracked modal frequencies are the dependent variables, measured crack amplitudes can be regarded as either dependent or independent variables, while temperatures are independent variables. Due to some non-linear correlations observed between natural frequencies and temperature data (Kita et al. 2019b), whose effects are conceivably attributed to the thermal inertia of the masonry resulting in a time shift between changes in air temperature and changes in natural frequencies, a dynamic MLR model resulted very useful. In fact, the adopted dynamic MLR tool, using past values of predictors, has proved quite effective for removing temperature effects from identified natural frequencies and, in particular, catching delayed temperature-induced effects related to the thermal inertia. Moreover, the use of crack amplitudes as predictors have allowed to further improve the statistical modeling of natural frequencies, which is a key aspect and innovative in the SHM. The MLR model in Eqs. (2.3) and (2.4) is referred to as ”static” when independent and dependent variables are sampled at the same time (contemporary), while it is referred to as ”dynamic” when arrays of past observations of temperatures and/or crack amplitudes are used to construct a set of independent variables. 27 Chapter 2 Data-driven damage detection In order to show the effectiveness of the adopted dynamic MLR model, Fig. 2.7 shows plots of the relative prediction errors of natural frequencies versus the length of the training period. In this way, the effect of a change in the length of the training period on the prediction error of the statistical model is investigated. Three types of model are presented, namely: (i) a static model considering temperatures T1 and T2 as predictors at time t (model Static_T), (ii) a dynamic model considering temperatures T1 and T2 at time t, t-6h, t-12h, t-24h and t-48h (considering the past 48 h with steps of single hours) as predictors (model Dynamic_T) and (iii) a dynamic model considering temperatures T1 and T2 and crack amplitudes C1 and C2 at time t, t-6h, t-12h, t-24h and t-48h as predictors (model Dynamic_T+C). The results clearly highlight that the prediction errors of the MLR models are almost minimized after about 4−5months of training period length. In particular, the use of a dynamic model is seen to highly improve the quality of the prediction for the natural frequencies, getting more reliable damage-sensitive features. Furthermore, the advantage of including crack amplitudes as predictors is also quite evident in Fig. 2.7, which is conceivably attributed to the role of the existing moderate damage state of the Palace. In addition, Fig. 2.8 shows time series of identified as well as predicted (using the model Dynamic_T+C) natural frequencies, considering a training period of twelve months. It is shown that dynamic MLR models are able to catch daily and long-term fluctuations in dependent variables, therefore being well suited to be used to remove temperature effects from monitoring data and to derive damage sensitive features. Overall, it Figure 2.7: Relative error between identified and predicted natural frequencies for increasing training period length: Fx1 (a), Fy1 (b), L1 (c), L2 (d), T1 (e) and L3 (f). 28 Chapter 2 Data-driven damage detection is noteworthy to mention that introducing crack amplitudes as predictors, in addition to temperatures, for the statistical reconstruction of natural frequencies time histories constitutes a novelty in the literature context, not observed in Structural Health Monitoring of historic masonry structures. In order to further understand the advantage of using crack amplitudes as predictors, control charts with one year training period have been investigated, by applying Eq. (2.2). Fig. 2.9 shows control charts obtained with only temperatures as predictors (Figs. 2.9a-b) and control charts when also crack amplitudes are considered (Figs. 2.9c-d). The number of outliers above the UCL line in the 2nd case is reduced with respect to the 1st one. Indeed, the percentage has decreased from 5.5% to 4.42%. Moreover, UCL has passed from 41 to 34. Overall, including crack amplitudes as predictors significantly improve the quality of the control chart. It reduces the probability to observe an outlier when the structure is in the healthy state (false alarm) and concentrates them at lower values of T2. As a final remark in the presented results, it should be mentioned Figure 2.8: Statistical reconstruction of natural frequencies in the monitoring period after twelve months of training period: Fx1 (a), Fy1 (b), L1 (c), L2 (d), T1 (e) and L3 (f). 29 Chapter 2 Data-driven damage detection Figure 2.9: Control charts of the undamaged condition with only temperatures as predictors (a-b) and with temperatures and crack amplitude data as predictors (c-d). that the presence of ice on the structure results in outliers even in normal conditions without damage. 2.3.3 Application of enhanced vibration-based SHM damage detection The acquired long-term monitoring data have been processed by means of the vibration-based SHM tool implemented for the Consoli Palace, based on the four (4) steps defined in Fig. 2.1, in order to detect deviations of the structural behaviour from normal conditions, as described in Section 2.1. In order to demonstrate the ability of the SHM system and the effectiveness of the adopted SHM tool to enable rapid and automated earthquake-induced damage detection, some frequency shifts have been imposed to natural frequencies time histories, thus, artificially inserting earthquake damage effects in the continuous monitoring data. 30 Chapter 3 FEM-based damage localization using surrogate modeling In this Chapter, the application and validation of the proposed surrogate model-based method are presented with reference to an historic civic masonry tower located in Perugia, Italy, called the Sciri Tower. The main theoretical aspects are first addressed, followed by a detailed description of the proposed method. After introducing the tower, together with AVT and long-term SHM data analysis, the calibration and the characteristics of the linear and non-linear FE models representative of the structure are presented. Finally, after the construction of a quadratic surrogate model, the remaining part of the Chapter is devoted to the detection and localization of simulated damage scenarios, as well as real earthquake-induced damage, the latter successfully validated also by non-linear FEM analysis. 37 Chapter 3 FEM-based damage localization using surrogate modeling 3.1 Theory background Vibration-based SHM methods are eminently efficient for damage detection and, to some extent, damage quantification in the form of permanent variations in natural frequencies (Ubertini et al. 2018; Gentile et al. 2019). While damage detection can be considered an essentially data-driven process, damage localization, on the contrary, can require the inverse calibration of a FE model of the structure, also called FEM Updating (FEMU). This procedure aims to minimize the mismatch between the numerical and experimental responses (typically natural frequencies and mode shapes) by the calibration of the model uncertain damage-related parameters (e.g. material properties, connectivity, or boundary conditions). Thus, changes on the modal features can be related to damage-induced variations in the mechanical parameters of the structure (Atamturktur and Laman 2012; Sehgal and Kumar 2016). However, given the complexity of the geometry of most historic buildings, along with the large number of simulations that are usually required in the minimization problem associated with the FEMU, the computational burden poses a major limitation in practice. On the other hand, the use of surrogate models offers great potential to bypass time demanding and costly numerical models when performing FEMU-based damage localization, thereby enabling continuous model updating to be performed in a computationally efficient way and compatible with continuous SHM systems (Cabboi et al. 2017; Torres et al. 2017; Venanzi et al. 2019). In this way, the model updating procedure for damage identification can be conducted in a computationally inexpensive way. Surrogate-assisted strategies suggest the use of efficient models, such as Response Surface Methods (RSMs), allowing an explicit relationship between FEM responses and structural parameters in a computationally efficient way. There are only a few experiences in the literature on the application to model updating of historical structures (Cabboi et al. 2017; Torres et al. 2017; Venanzi et al. 2019). It is worth noting the work (Cabboi et al. 2017) who conducted an automated surrogate-based model updating of the San Vittore bell-tower in Milan (Italy), where the RSM for the real-time updating of a 3D FEM of the tower has been used. Also, (Torres et al. 2017) proposed an RSM-based FEM updating of the Metropolitan Cathedral of Santiago (Chile). The localization task can be performed by solving an inverse FEM calibration problem, where equivalent elastic properties of macrostructural elements are identified by minimizing an objective function considering experimentally identified and numerically predicted damage-induced decays in natural frequencies as well as changes in eigenvector components. This can be performed by an efficient response surface meta-model, which allows minimizing the computational effort of the calibration procedure. 38 Chapter 3 FEM-based damage localization using surrogate modeling In general, the scope of a surrogate model is to bypass in a cost-effective way the input/output relationship of a computationally demanding model. Let us define mdamage-sensitive parameters, xi∈R,i= 1, .., m, determining the response yof a FEM. A surrogate model serves as a black-box representation of the response of the FEM as y(x), with xbeing the vector of design parameters x= [x1, ..., xm]T. To construct the surrogate model, it is often necessary to obtain a training population by Monte Carlo simulations (MCS) using the FEM. A training population of Nindividuals is defined by a mxNmatrix of design sites X= [x1, ..., xN], and an observation vector Y= [y1, ..., yN]T, with yi∈Rbeing the system’s response to the input xi. Specifically, the modal properties obtained by linear modal analysis of the FEM can be assumed as outputs. The Response Surface Method (RSM) constitute a collection of statistical tools for fitting empirical models and so alleviate the computational effort of iterative processes (Myers et al. 2016). The second-order quadratic RSM formulation can be written as follows: y(x) = α0+ m X j=1 αjxj+ m X j=1 αjjxj2+ m X j=1 m X i≥j αjixjxi+ϵ(3.1) where coefficients α0,αj,αjj and αji represent the intercept, linear, quadratic and interaction coefficients, respectively. The term ϵis a normally distributed statistical error with zero mean, independent, and identically distributed at each observation. 39 Chapter 3 FEM-based damage localization using surrogate modeling 3.2 The proposed method The proposed method for earthquake-induced damage assessment is based on real-time damage detection and localization using long-term vibration monitoring data, which is performed by solving an inverse calibration problem on a quadratic surrogate model, to track variations of modal parameters observed through the processing of monitoring data. It concerns an enhanced version of the method proposed in (Cabboi et al. 2017), whereby the innovative aspects are presented next. The outline of the procedure is summarized in the following steps: • Step 1: Construction of a reliable numerical linear FE model, tuned based on AVT, and a surrogate model linking frequency shifts and eigenvector components to elastic parameters of macrostructural elements; • Step 2: Perform OMA at time intervals δtid by using monitoring data; • Step 3: Removal of the fluctuations of natural frequencies caused by changing environmental and/or operational conditions through a dynamic MLR model; • Step 4: Novelty analysis: construction of a control chart to detect the damage at time δtid; • Step 5: If the damage is detected at step 4, localization of such damage at time δtid by inspecting the time series of equivalent elastic parameters of macrostructural elements continuously obtained through the solution of an optimization problem using the surrogate model. The optimization problem may be solved by assigning different weights to natural frequencies and mode shape components to test the robustness of the solution and avoid false positives. The procedure is detailed in the following lines. Continuous modal identification is needed for the 2nd step of the procedure. Within the monitoring process, modal properties are continuously identified by means of an automated SSI technique (Ubertini et al. 2013). The monitored structure is modeled in by the following equations: x(k+ 1) = Ax (k) + w(k) y(k) = Cx(k) + v(k) (3.2) 40 Chapter 3 FEM-based damage localization using surrogate modeling in which kis the time step, x∈Rq×1is the state vector (with qorder of the identified model), y∈RL×1is the vector collecting the Loutput measurements, A∈Rq×qis the system matrix from which modal information can be retrieved, C∈RL×qis the corresponding output matrix, w∈Rq×1and v∈RL×1are white noise vector processes representing the external input and the noise affecting the measurements, respectively. In order to remove the effects of environmental conditions from identified natural frequencies (3rd step), a dynamic MLR model has been adopted, found to be crucial for catching delayed temperature-induced effects (see Section 2.1 and Section 2.3.2). With reference to Eqs. (2.3) and (2.4), dependent variables are stored in the observation matrix Y(the natural frequencies identified by eigenvalue analysis of matrix Ain Eq. (3.2)), while their estimates in ˆ Y. Residuals in Eq. (2.4) can be used to obtain the time series of cleansed natural frequencies, contained in matrix Fcleansed according to Eq. (3.3), by summing the vector containing average values of the natural frequencies observed in the training period, Fmean tt, to the vector of statistical model residuals, E. Fcleansed =Fmean tt+E(3.3) The 4th step concerns the construction of a control chart for detecting the occurrence of damage at time δtid, after removing the effects of environmental conditions. The control chart is the time history of the T2statistic computed on the basis of the residuals of the MLR model according to Eqs. (2.2) and (2.4). A continuous model updating is carried out by optimizing a set of parameters of the FE model of the tower. Experimental natural frequencies and mode shapes, obtained from continuous monitoring as well as depurated/cleansed from thermal effects (only in the case of natural frequencies), are preliminarily evaluated at time intervals δtid. Frequency changes, ∆fexp, with respect to reference values are also computed at the same time δtid. The parameters to be updated, i.e. the design variables of the optimization problem, are collected into a vector U= (U1, ..., Un, Un+1, ..., U2n, U2n+1, ..., Un·m), where nis the number of uncertain parameters (e.g. the elastic modulus) and mis the number of different zones in which the tower can be ideally divided (macroelements). To assess the continuous variations of damage-related parameters, a functional Jis defined as follows: J(U) = l X i=1 (αiϵi(U) + βiδi(U)) (3.4) where 41 Chapter 3 FEM-based damage localization using surrogate modeling ϵi= ∆fexp i fexp i −∆fFEM i(U) fFEM i(U) δi= 1 −MACii(U) (3.5) The optimization problem is stated as follows: find U that minimizes J(U) subjected to Ulb ≤U≤Uub (3.6) where Ulb and Uub are the vectors storing the lower and upper bound values of the components of U. In Eq. (3.4) and Eqs. (3.5), MAC represents the Modal Assurance Criterion between the identified mode shapes and those obtained by the model, ∆fFEM iare the natural frequencies variations estimated with the FEM model with respect to the nominal values fFEM i,lis the number of identified modes and αiand βiare weighting coefficients that establish the relative importance of the two addends in Eq. (3.4). A gradient-based minimization technique can be used for convex objective space while a random optimization algorithm can be employed otherwise. The optimization problem is solved continuously for each set of identified modal data (natural frequencies and mode shapes) in order to track in time the damage-dependent parameters. As the choice of the weighting coefficients can significantly affect the localization results, a preliminary parametric analysis has to be carried out in order to determine the most appropriate sets of αiand βi. In order to limit the computational time required by the optimization problem and allow an online estimation of equivalent parameters of macrostructural elements, a surrogate model is adopted to estimate fFEM iand their corresponding mode shapes. To this aim, a simple quadratic formulation is adopted (Douglas and Reid 1982): fFEM i(U) = n X j=1 Ai,jU2 j+ n X j=1 Bi,jUj+Ci ΦFEM i(U) = n X j=1 Di,jU2 j+ n X j=1 Ei,jUj+Fi (3.7) where Ai,j ,Bi,j,Ci,Di,j,Ei,j and Fi, are coefficients relating the ith identified modal properties to the jth uncertain parameter (j= 1, .., n). With reference to Eq. (3.1), it can be noted that the quadratic surrogate model used in the case of the Sciri Tower does not consider the mixed term. When the control chart 42 Chapter 3 FEM-based damage localization using surrogate modeling highlights the presence of damage, this is expected to be localized in the macrostructural region experiencing decays in equivalent elastic constants obtained from the above presented continuous model tuning procedure. As already stated at the beginning of this Section, the proposed method is an enhanced version of the method proposed in (Cabboi et al. 2017). Innovative aspects concern, in particular, the objective function in Eq. (3.4) which includes two terms: one related to resonant frequencies variations and the other one related to mode shapes variations. This leads to improve the accuracy of the results, as damage can influence not only the resonant frequencies but also the mode shapes. This can also improve the solution’s robustness because a multi-objective optimization allows studying the stability of the solution with respect to changes in the weighting coefficients, distinguishing non-physical solutions from robust ones. Moreover, the term of the objective function related to natural frequencies (ϵi) is expressed in terms of relative changes, instead of using absolute changes. This makes relative changes ϵiassume similar values for every natural frequency and allows using a single weighting coefficient for all the resonant frequencies. Instead of a linear PCA approach adopted in (Cabboi et al. 2017), a dynamic MLR model is proposed. The latter uses present and past observations of measured temperature data, being effective in removing temperature effects also in the case of significant delays between changes in air temperature and changes in structural behavior due to the high thermal capacity of the structure. The proposed method is applied to the Sciri Tower, an historic civic masonry tower located in Perugia, Italy, that has been continuously monitored for about two years. A complete FE model of the tower and the surrounding building aggregate is adopted to construct the surrogate model, instead of using a simplified model where the interaction between the tower and the surrounding building is modeled by local constraints. 43 Chapter 3 FEM-based damage localization using surrogate modeling 3.3 Application example: the Sciri Tower 3.3.1 Introduction to the case study The 2nd case study structure considered in this dissertation is the 41 m high civic tower located in Via dei Priori in the historical center of Perugia, Italy, named Torre degli Sciri (Garcia-Macias et al. 2019; Venanzi et al. 2020). Built in the 13th century for defensive purposes, the Sciri Tower represents today the only intact remaining tower of around 70 medieval towers of the city. Fig. 3.1 shows some historical medieval paintings and a current aerial view of the tower. Being incorporated into a building aggregate with approximate crosssection dimension of 20 x 25 m (plan view depicted in Fig. 3.2c), it is surrounded by neighboring masonry buildings up to the first 17 m on three sides, while the fourth side is free and facing Via dei Priori towards North (Figs. 3.1e and 3.2b). East and North fronts are shown in Figs. 3.2a-b, respectively. The masonry is homogeneous and regular and it is made of squared white limestone blocks. The tower has a quadrangular cross-section (7.15 x 7.35 m, as depicted in 3.2d) and it can be ideally divided into two structural portions, as depicted in Fig. 3.2: the lower and the upper parts. The lower part, up to a height of 8.4 m, is characterized by about 2.1 m thick walls with some small openings and a stone masonry vaulted slab which stands above the rooms of an old chapel. The upper part, rising up to 41 m, has slender continuous walls (thickness from 1.6 to 1.4 m) with four 1.5 m wide brick masonry vaulted slabs at different heights. Moreover, a brick Figure 3.1: The Sciri Tower over the centuries, historic paintings and today: technical drawings of Augusta Perusia by Eusebio in 1602 (a) and Mortier in 1724 (b), unknown author in 1880 (c), photo by Raniero Gigliarelli in 1908 (d) and aerial view today (e). 44 Chapter 3 FEM-based damage localization using surrogate modeling Figure 3.2: The Sciri Tower: East front (a), North front (b), plan view at 12 m height (c) and cross section of the tower (d). masonry ceiling vault completes the tower on the top. Consolidated by the Municipality of Perugia in 2015, aiming at its seismic improvement and the conservative restoration of the entire complex, the Sciri Tower is in a very good state of preservation without any significant and visible damage pattern. Finally, no damages were observed after major earthquakes occurred in Italy in recent years: L’Aquila Earthquake, 2009, Emilia Earthquake, 2012, and Central Italy seismic sequence, 2016 (Cattari et al. 2019). An AVT was carried out on the Sciri Tower on May 22nd 2017 with the main purpose of evaluating the baseline dynamic characteristics of the building and, in particular, its natural frequencies, mode shapes and damping ratios (Venanzi et al. 2020). It was conducted on the building using a total of 12 high sensitivity (10 V/g) uniaxial accelerometers, model PCB 393B12, installed on the structure to measure micro tremors induced by traffic and wind (operational conditions). The layout of the accelerometers (progressively denoted as A1, A2,... A12) is depicted in Fig. 3.3b. Modal parameters from ambient vibration data have been estimated through two different tools: classical and enhanced version of Frequency Domain Decomposition (FDD and EFDD) and SSI. Seven (7) vibration modes have been identified within the range from 0 to 11 Hz: two flexural modes in 45 Chapter 3 FEM-based damage localization using surrogate modeling NW direction (x direction as depicted in Fig. 3.3, denoted as Fx1 and Fx2, respectively), two flexural modes in SW direction (y direction, denoted as Fy1 and Fy2, respectively), one torsional mode, namely Tz1, and, finally, two higher-order flexural modes, Fx3 and Fy3. In particular, Figs. 3.3c-d show the first three singular values of the power spectral density matrix obtained from the AVT by means of the FDD technique, where seven (7) resonant peaks are clearly identified, and mode shapes obtained from the AVT data by means of the SSI technique, respectively. It can be noticed that the first two mode shapes are bending modes that are not classically oriented according to the main directions of the square cross-section. In fact, given the configuration within the building aggregate yielding restraints in two sides of the tower (see Fig. 3.2c), the direction of the first bending mode shapes is along the diagonal of the tower cross-section. The natural frequencies (fFDD i,fEFDD iand fSSI i) and damping ratios (ξEFDD iand ξSSI i) of the seven (7) identified modes from AVT are Figure 3.3: Accelerometers layout for continuous monitoring (a) and AVT (b). First three singular values (SV) of the power spectral density matrix (FDD) obtained from the AVT and identified resonant peaks with related modes of vibration (c) and mode shapes identified by automated SSI technique (d). 46 Chapter 3 FEM-based damage localization using surrogate modeling Ed= (1 −d)E0(3.11) The solution algorithm for non-linear dynamic analysis has been based on the classical Newton-Raphson formulation. In particular, the cracking strain, ˜εck t, is defined as ˜εck t=εt-εel 0t, where εtis the total strain and εel 0tthe elastic strain corresponding to the undamaged material, εel 0t=σt/E0(see Fig. 3.8). For tension stiffening, the description of the failure condition and of the post-peak behavior depends upon the tensile stresses, σt, the cracking strains, ˜εck t, and the tensile damage variable, dt. The behavior of the masonry has been reproduced up to the ultimate limit state, considering damage in tension only. Given the lack of results of specific on-site tests, the mechanical properties assigned to the materials have been estimated based on the Italian technical standard code, NTC08 and NTC18 (NTC08 2008; NTC18 2018), and from the literature (Gams et al. 2017; Cavalagli et al. 2018). Tab. 3.4 summarizes the adopted damage parameters in Figure 3.8: Stress-strain relationships of the Concrete Damage Plasticity (CDP) constitutive model: tension curve (a), compression curve (b) and uniaxial load cycle assuming default values for the stiffness recovery factors (wt=0 and wc=1) (c). 53 Chapter 3 FEM-based damage localization using surrogate modeling tension for the Sciri Tower. Table 3.4: Uniaxial stress-strain values and scalar tension damage values utilized in the CDP model for masonry. σt˜εck tdt [kN/m2] [−] [−] 160 0.00e-00 0.00 120 1.75e-04 0.55 84 3.77e-04 0.80 16 7.59e-04 0.90 3.3.3 Detection and localization of simulated damage For the purpose of continuously assessing and localizing the damage, the FE model has been subdivided into four (4) macroelements, as illustrated in Fig. 3.9a: • Macroelement 1 (M1): the building aggregate and a portion of the tower up to the top height of the roof of the same aggregate (0-18.9 m); • Macroelement 2 (M2): the portion of the tower between the height of 18.9 and 26.8 m; • Macroelement 3 (M3): the portion of the tower between the height of 26.8 and 33.8 m; • Macroelement 4 (M4): the portion of the tower between the height of 33.8 and 41.0 m. According to this partition of the structure, the parameters to be identified have been discriminated for each macroelement and collected in the vector of the design variables of the optimization problem U, as follows: U= (k1, k2, k3, k4)(3.12) where ki(i= 1, ..., 4), are coefficients that multiply the elastic moduli of materials belonging to M1, M2, M3 and M4, respectively. The variation of the components of vector Uwith respect to initial values, identified by the damage localization procedure, is related to the occurrence of damage in the structure. A more significant decrease in one component of Uwith respect to the others indicates that the damage is concentrated 54 Chapter 3 FEM-based damage localization using surrogate modeling Figure 3.9: Macroelements M1, M2, M3 and M4 defined for damage localization (a) and zones Z1 and Z2 in which damage is simulated according to damage scenarios D1 and D2, respectively (b). in that specific portion of the structure. A surrogate quadratic model has been adopted in the online optimization procedure, as introduced in Eqs. (3.7). To compute the coefficients of the quadratic model, Ai,j,Bi,j,Ci,Di,j,Ei,j,Fi, with i= 1, ..., l, (lis the number of identified modes) and j= 1, ..., n, (nis the total number of uncertain parameters), each component of Uhas been varied by ±5% and the corresponding natural frequencies and mode shapes have been computed from the FE model. The coefficients of the quadratic models (see Eqs. (3.7)) have been calculated by imposing equivalence between the first and second derivative of fFEM iand ΦFEM i, expressed in terms of the unknown coefficients, with the first and second-order finite differences obtained from the analysis. The assumption of quadratic equations to describe the relationship between the design variables (Ui) and the modal parameters (fFEM iand ΦFEM i) is acceptable in a range around the initial values. To demonstrate the acceptability of the hypothesis, a parametric analysis has been carried out by varying individually each component of U. The natural frequencies and modal displacements have been obtained for both the full 3D FE model and the surrogate model. The results of the parametric analysis in terms of natural frequencies and mode shapes demonstrate that the surrogate model is reasonably suitable to represent the variation 55 Chapter 3 FEM-based damage localization using surrogate modeling Figure 3.10: First two natural frequencies (a, c) and MAC (b, d) obtained with the FE model and the surrogate model. of the modal parameters of the structure, in the neighborhood of the initial value of U. In particular, Figs. 3.10a-c show the first and second natural frequencies obtained with the surrogate model (fs 1and fs 2) and the FE model (fFEM 1and fFEM 2), while Figs. 3.10b-d show the MAC of the first and second mode obtained with the surrogate model (MACs 1and MACs 2) and the FE model (MACFEM 1and MACFEM 2). The maximum relative difference between the two models concerns f1and is equal to 0.54% in the range of k=±3%, that is considered acceptable for the purpose of early-stage damage localization. Once the surrogate model is set, in order to demonstrate the effectiveness of the procedure, two damage scenarios have been simulated: • Damage scenario 1 (D1): localized damage at Z1 - the contact between the tower and the aggregate/roof, possibly related to deformations between the tower and the surrounding building, obtained with a 20% reduction of the elastic modulus; • Damage scenario 2 (D2): damage in Z2/M3 (possible crack formation due to the presence of two openings) simulated with a 40% reduction of the elastic modulus. 56 Chapter 3 FEM-based damage localization using surrogate modeling Table 3.5: Relative frequency decays obtained for the considered damage scenarios (in percentage). D1 D2 ∆f1-0.99 -1.11 ∆f2-0.88 -1.41 ∆f3-0.25 -1.75 ∆f4-0.54 -2.97 ∆f5-0.96 -4.35 ∆f6-0.46 -4.28 The portions Z1 and Z2 in which damage occurs for the two damage scenarios are shown in Fig. 3.9b. Tab. 3.5 summarises the numerical relative frequency decays obtained for the two damage scenarios, while Fig. 3.11 shows the corresponding control charts obtained by calculating the T2statistical distance on the residuals of the first two natural frequencies (Eqs. (2.2) and (2.4)), after artificially applying such damage-induced frequency shifts corresponding to D1 and D2. The frequency shifts have been artificially inserted in the time series of the identified natural frequencies assuming that damage occurred in the middle of the observation period after one year of training period. These results show how D1 and D2 can be detected from the control charts and how the damage localization is triggered. In order to localize damage, the optimization problem in Eqs. (3.4) and (3.5) has been solved, by exploiting the surrogate model in Eqs. (3.7). The lower and upper bounds vectors in Eq. (3.6) are Ulb = (0,0,0,0) Table 3.6: Results of the localization obtained for the simulated damage scenarios D1 and D2. Note that if components ki(i= 1, ..., 4) of Uare equal to 1, it means no damage occurred to the macroelement. Damage scenario α β k1k2k3k4 D1 1 0 1.00 0.86 1.00 1.00 D1 10 1 1.00 0.86 1.00 1.00 D1 1 1 1.00 0.86 1.00 1.00 D1 1 10 0.99 0.97 1.00 0.39 D1 0 1 0.68 1.00 1.00 0.36 D2 1 0 1.00 0.93 0.05 0.89 D2 10 1 1.00 0.93 0.06 0.80 D2 1 1 1.00 0.92 0.09 0.55 D2 1 10 1.00 0.98 0.08 0.09 D2 0 1 1.00 1.00 0.02 0.06 57 Chapter 3 FEM-based damage localization using surrogate modeling Figure 3.11: Control chart of the observation period with no damage and with damage scenarios D1 and D2 applied on January 13th 2019. and Uub = (1,1,1,1), respectively, with 0meaning complete damage and 1meaning no damage occurred to the macroelement. The selected optimization algorithm is a classical genetic algorithm that has been chosen for its computational effectiveness. The parameters of the genetic algorithm have been established through a preliminary parametric analysis: the population size has been set to 1000 in order to achieve good repeatability of the results. The optimization has been repeated by adopting different values of the coefficients αand β, in order to weight differently the two terms of Eq. (3.4) and search for stable solutions in order to avoid unfeasible results. Tab. 3.6 shows the results of the localization for D1 and D2, considering one single data set. When α≥β, for damage type D1 the coefficient k2is smaller than one, indicating that damage has occurred on M2, at the contact between the tower and the surrounding buildings. 58 Chapter 3 FEM-based damage localization using surrogate modeling The coefficient k3experiences the highest variation for D2, denoting that damage has occurred in M3. In the cases when α≤βsome solutions that significantly deviate from the others are observed. This highlights that considering the term related to MAC in addition to the term related to frequency in the objective function of the inverse identification problem, it allows investigating the robustness of the solution with respect to the weighting coefficients variation, distinguishing between the solutions that significantly differ from the expectations and the robust ones. It is also clear from the results in Tab. 3.6 that the contribution of the term related to MAC to the solution accuracy is limited due to only 3 mode shape components available (only 3 sensors are used for continuous monitoring). Nonetheless, the contribution can substantially increase with data from a larger number of sensors at different levels of the tower. The localization method has also been applied to track the variation in time of the damage-dependent parameters. To this aim, frequency decays obtained for damage scenario D1 and D2, reported in Tab. 3.5, have been Figure 3.12: Tracking in time of the components of Uafter the end on the training period considering damage condition D1 simulated on January 13th 2019. 59 Chapter 3 FEM-based damage localization using surrogate modeling applied to identified natural frequencies cleansed by thermal effects (Fig. 3.6) one month after the end of the training period of one year (December 2017-December 2018). Fig. 3.12 shows the tracking in time of the components of vector U(see Eq. (3.12)) for damage D1. It is possible to observe that the coefficient k2experiences the highest and clearest variation as a consequence of the simulated frequencies decays, confirming that damage is mainly localized in M2. After damage occurs, an increase in k4is also observed. Since a damage is never expected to increase stiffness, this change has to be attributed to numerical reasons related to the solution of the inverse problem and should not be considered as a damage indicator. In this regard, the use of a regularization term in the objective function may help in limiting possible numerical problems. A similar trend would, however, need some tuning and calibration to avoid masking damage effects. 3.3.4 Localization of earthquake-induced damage In the previous Section, the damage localization procedure has been validated with reference to simulated damage scenarios, D1 and D2, by numerically applying frequency shifts, corresponding to specific damage events. In the present Section, the procedure is further validated using real frequency shifts, measured after a seismic sequence occurred in January 2017, during a preliminary monitoring period of the structure. In the context of an initial dynamic investigation, preliminary to the continuous monitoring, the tower has been monitored for one week, from January 16th to January 23rd 2017, through a simple vibration-based SHM system which comprised accelerometers A4, A5 and A6 (see Fig. 3.3b). In this period, an important seismic sequence occurred on January 18th 2017 with epicenters close to L’Aquila, in central Italy, at about 100 km distance from the Sciri Tower (Venanzi et al. 2020). Four (4) main shocks with moment magnitude higher than Mw= 5 were recorded from 09:25 to 13:33 UTC. Moreover, four (4) additional shocks with 4≤Mw ≤5occurred in the same period of time. The acceleration time histories of these earthquakes have been taken from the strong motion network database provided by the Department of Civil Protection (DPC) and by the Italian seismic network of the National Institute of Geophysics and Vulcanology (INGV). Tab. 3.7 reports moment magnitude Mw, time and distance from epicenters of the four main shocks measured by the seismic stations closest to epicenters, together with E-W, N-S and vertical components denoted as PGAE-W, PGAN-S and PGAZ, respectively. Fig. 3.13 shows the E-W and N-S components of the time histories of horizontal accelerations recorded by accelerometers A5 and A6, respectively, during the first two shocks, those that led to the higher seismic responses of the tower, together with the geographic location of the epicenters with respect to Perugia. It is noted that, due to the large distance (about 100 km) between Perugia and the epicenter of the earthquake sequence, the response acceleration levels of the tower were relatively low. Acceleration in the 60 Chapter 3 FEM-based damage localization using surrogate modeling Table 3.7: Synthetic information regarding the four main shocks of January 18th 2017 seismic sequence as recorded by seismic stations placed nearby epicenters (PGAE-W, PGAN-S, PGAZdenote PGA values in E-W, N-S and vertical directions, respectively). Epicenter Mw Time UTC Distance PGAE-W PGAN-S PGAZ [-] [hour] [km] [cm/s2] [cm/s2] [cm/s2] Montereale 5.3 09 : 25 95 195.39 361.17 124.24 Capitignano 5.4 10 : 14 98 442.64 566.15 188.35 Capitignano 5.3 10 : 25 102 407.89 591.07 161.58 Cagnano Amiterno 5.1 13 : 33 102 272.61 284.87 101.74 Figure 3.13: Seismic accelerations recorded during the main seismic events of January 18th 2017 (a-b) and geographic location of the epicenters with respect to Perugia (c). E-W direction was predominant in both shocks, with peak values equal to 18.86 cm/s2and 16.66 cm/s2, respectively. The seismic events did not produce any visible damage to the structure but led to non-negligible variations of its natural frequencies. Figs. 3.14a-b show the time histories of the natural frequencies of vibration of six (6) modes of the tower continuously identified and tracked during the preliminary monitoring period (modes Fx1, Fy1, Fx2, Fy2, Tz1 and Fy3) from January 16th to January 23rd 2017. As it is visible from the figures, the seismic events clearly led to small frequency decays. The vertical dashed lines in all plots represent the date and hour of the major earthquakes of the seismic sequence, highlighting the instantaneous decays in natural frequencies induced by the same events. In addition, Fig. 3.14c reports the relative frequency decays after the 61 Chapter 3 FEM-based damage localization using surrogate modeling Figure 3.14: Frequency tracking around the seismic event of January 18th 2017 (a-b), with the indication of the percentage values of the relative frequency decays (c) first two seismic events. Only the first six (6) frequency decays have been computed since the SSI continuous identification was able to detect the first six (6) natural frequencies during that week of monitoring, as a consequence of the adopted sensors configuration in the preliminary monitoring system. They have been computed considering the average of 5 frequency samples measured before the event occurred at 09:25 UTC and 5 frequency samples after the shock occurred at 10:14 UTC. It is noteworthy to stress that, during the day-night of the seismic sequence, positive temperature has been recorded, ranging from 1.7to 3.7◦C. In these conditions, with positive frequency-temperature correlations, a small thermal recovery of the frequency shifts has to be expected, leading to slightly lower decays. However, considering very limited temperature fluctuations, this effect is neglected. It is worth mentioning that earthquake-induced effects on the dynamic response of the tower could have been also highlighted by the control chart generated as the output of the vibration-based SHM system, but given the short preliminary monitoring period, there was not enough data for its construction. The experimental frequency decays reported in Fig. 3.14 have been used to run the localization procedure. The analyses have been repeated for different weights αand βof the two terms in Eq. (3.4). Tab. 3.8 reports the results of the damage localization, highlighting that all the analyses, except the one with α= 1, β = 10, provide consistent outputs and locate damage at macroelement M2. This is probably due to the fact that, 62 Chapter 4 Damage localization and quantification via IDA 4.1 Theory background The development of computer processing power and structural analysis software has made possible a continuous drive towards increasingly accurate but at the same time more complex analysis methods. The state of the art holds the use of several analysis methods for the design and assessment of masonry buildings, from (elastic) linear static analysis (LSA) to linear dynamic analysis (LDA), and from non-linear static (NLSA) to non-linear dynamic analysis (NLDA). The NLSA (or pushover, SPO), with suitable scaling of the static force pattern, allows to obtain a ”continuous” picture as the complete range of structural behavior is investigated, from elasticity to yielding and finally collapse (Cattari and Lagomarsino 2013; Cattari et al. 2015; Lagomarsino and Cattari 2015a; Lagomarsino and Cattari 2015b). The NLDA consists of running several different records, each producing several ”single-point” analyses, and may be performed either by using a large number of records (Cloud Method and/or Multiple Stripe Analysis (MSA)) or considering a proper selection of time histories, scaled in order to perform IDA (Lagomarsino and Cattari 2015b). Passing from a single static analysis to the incremental SPO provides the basic conceptual development of the extension of a single time-history analysis into an incremental one, where the seismic loading is scaled. This concept has been first mentioned in 1977 (Bertero 1977), and subsequently considered in many researchers’ works (Bazzurro and Cornell 1994a; Bazzurro and Cornell 1994b; Luco and Cornell 2000; Psycharis et al. 2000). Adopted by the U.S. Federal Emergency Management Agency guidelines (FEMA 2000a; FEMA 2000b) as the incremental dynamic analysis, it has been established as the state-of-the-art method to determine the global collapse capacity. Despite the potential information that can be derived by the IDA, the application to CH masonry structures is comparatively less common with respect to other types of structures, such as RC frames, due to the high computational costs (Basone et al. 2017; Masaeli et al. 2018). (Vamvatsikos and Cornell 2002) proposed a computational-based methodology called Incremental Dynamic Analysis (IDA), which involves a series of non-linear dynamic time-history analyses, a powerful, multi-purpose and widely applicable parametric analysis method, capable of thoroughly estimating the structural performance under increasing seismic intensity. It considers the numerical model of a structure subjected to one (or more) ground motion record(s), the latter scaled to multiple levels of intensity, thus producing one (or more) curve(s) of response parameterized versus the intensity level itself. An IDA study allows a thorough understanding of the range of response or ”demands” versus the range of potential levels of a ground motion record, as well as a better comprehension of the structural response/implications as the ground motion intensity increases to more severe levels and its stability considering the record-to-record variability. However, recently, the procedure of scaling (up) accelerograms is sometimes seen as a critical aspect and/or drawback 69 Chapter 4 Damage localization and quantification via IDA of the IDA approach. In this context, very high scaling factors are not encouraged. Finally, in the framework of Performance-Based Earthquake Engineering (PBEE), the assessment of demand and capacity is viewed through the lens of an IDA study. The IDA curve contains the necessary information to assess performance levels or limit states. IDA’s fundamental hierarchical concepts (Vamvatsikos and Cornell 2002) are defined below: • Unscaled ground motion record: time history representing a seismic event (generally accelerogram), a1, defined as a vector a1(ti), ti=0,t1,...,tn−1. • Scale Factor (SF): the non-negative scalar λ∈[0,+∞) that produces a scaled accelerogram aλ= λ·a1. • Intensiy Measure: the non-negative scalar IM ∈[0,+∞) of the scaled accelerogram, that constitutes a function IM=fa1(λ). • Damage Measure: DM ∈[0,+∞), non-negative scalar representing the output of IDA on the structural model. • Single-Record IDA Study: a dynamic analysis study of a given structural model parameterized by the SF applied to a1(ti). • IDA Curve: plot of a DM recorded in an IDA study versus one or more IMs that characterize aλ(+2D plot). • Multi-Record IDA Study: a collection of Single-Record IDA Studies of the same structural model, under different accelerograms. • IDA Curve Set: a collection of IDA Curves of the same structural model under different accelerograms, all parameterized by the same IMs and DM. The selection of appropriate ground motion records or seismic inputs is of significant importance since an IDA study is accelerogramand structural model-specific. In fact, given the record-to-record variability of structural responses, the choice of suitable strong ground-motions represents a first key aspect for IDA. Several studies dealt with the selection of suites of real ground-motions (Bommer and Acevedo 2004; Iervolino and Cornell 2005). Seismic action can be represented through different types of time histories: (i) natural accelerograms; (ii) artificial and (iii) simulated time histories. In recent years, the increasing availability of online databases 70 Chapter 4 Damage localization and quantification via IDA of strong-motion records has shifted the focus towards the use of natural accelerograms, recorded during real earthquakes and considering information like seismic hazard, site conditions, target spectrum, etc. The input ground-motions to IDA can be either representative of earthquake scenarios that control the site hazard or compatible with a target elastic response spectrum. Technical standards suggest the use of a suite of ground motion records, aimed at covering a full range of responses and with different seismic characteristics in terms of amplitude, energy or frequency content. According to the Italian (NTC08 2008; NTC18 2018) and European (EN 1998-1 2005) codes, at least seven (7) time-history analyses need to be performed and mean output values are to be considered (Karanikoloudis and Lourenço 2018). Alternatively, if fewer analyses are conducted (e.g. with three groups of accelerograms), one can consider the maximum output values. Also, the combination of the used accelerograms should present an average response spectrum consistent with the prescribed elastic one. In general, the combination of at least seven (7) accelerograms is highly recommended for structural analysis, with effects on the structure represented by the averages of the maximum values obtained from the analyses. Usually, the seismic input for IDA is represented by spectrum-matched accelerograms, in other words, acceleration time series whose response spectra result compatible with a specific target response spectrum (Atik and Abrahamson 2010; Pena et al. 2010). Previous works gave a description of the rationale and advantages of using spectrum-matched accelerograms (Atik and Abrahamson 2010), demonstrating that spectrum matching does not lead to bias in structural analysis results (Grant and Diaferia 2012). The next key aspect for IDA analysis concerns the choice and/or definition of representative and efficient intensity measures (IMs) and reasonable and meaningful damage measures (DMs) (Vamvatsikos and Cornell 2002; Riddell 2007). There is a relatively large number of parameters or IMs of a ground motion proposed over the years in the literature (Housner 1952; Arias 1970; Kramer 1996; Cosenza and Manfredi 2000; Riddell and Garcia 2001; Riddell 2007; Douglas et al. 2015). In general, a single parameter cannot successfully and fully characterize the strength and intensity of ground motions. In this context, a thorough overview of the IMs proposed in the literature followed by an in-depth analysis is needed. In order to thoroughly characterize an earthquake, an IM should be able to describe three main ground motion characteristics/features of earthquake engineering significance, such as amplitude, frequency content and duration. All of these characteristics can scientifically influence the earthquake damage. The selection of IMs should consider their capability in providing information about one or more of these characteristics. Generally speaking, IMs can be classified as peak or integral parameters, and as seismic input measures or response measures. Peak parameters are based on the computation of one single value while integral measures take into account also the duration of an earthquake. Seismic input measures are considered as structure independent, because 71 Chapter 4 Damage localization and quantification via IDA of their computation directly from the ground motion record, whereas response measures depend on the structure’s characteristics. Moreover, taking into consideration specific period ranges, IMs can further be categorized into three subgroups: acceleration-related, velocity-related and displacement-related measures. A detailed analysis of IMs for IDA-based damage assessment is reported in Section 4.3. A wise choice of IMs concerns investigating their main property: the efficiency for predicting DM and/or the structural response (Vamvatsikos 2002). An efficient IM is defined as one that yields relatively small variability of DMs for a given IM level, in other words, the one that provides a relatively low dispersion of values of DMs. In this context, the comparison among different IMs, in particular, the investigation of the dispersions of the DMs associated with various IMs, is needed. An efficient IM leads to less dispersion in an IDA curve set. Another advantage of using an efficient IM, i.e. having lower dispersion of DM given IM, is reflected in the smaller sample of records and fewer non-linear IDA runs necessary. Therefore, a desirable property of a candidate IM is to yield a small dispersion. The Damage Measure (DM) represents an observable quantity that is part of the output (or can be deduced from) of the corresponding non-linear dynamic analysis (Vamvatsikos 2002). There are different possible choices such as maximum base shear, inter-story drift ratio, floor peak inter-story drift angles, Park & Ang index (Park and Ang 1985), and so forth. Other DMs can be quantities and/or numerical outputs of the non-linear constitutive model used in the specific application. A very interesting constitutive model is the wellknown Concrete Damage Plasticity, previously described in Section 3.3.2. It is widely used in the literature in the case of non-linear dynamic analyses (Valente and Milani 2016; Valente and Milani 2018; Cavalagli et al. 2018; Ubertini et al. 2018; Formisano et al. 2018b; Sarhosis et al. 2018; Valente et al. 2019; Valente and Milani 2019a; Valente and Milani 2019b; Abbati et al. 2019). In particular, tensile damage, as a cumulative parameter, can certainly represent a reasonable DM. Moreover, selecting a suitable DM depends on the application and the structure itself. It may be useful to use two or more DMs (all resulting from the same analyses) to assess different response characteristics. 72 Chapter 4 Damage localization and quantification via IDA 4.2 The proposed method The proposed method is based on non-linear seismic Incremental Dynamic Analysis (IDA) (Vamvatsikos and Cornell 2002) combined with earthquake data, aimed at damage localization and quantification. It requires the construction and tuning of a numerical model of the structure under analysis. In this regard, IDA simulations are carried out from the calibrated numerical model at increasing levels of the earthquake input, considering a suitable non-linear constitutive model for the masonry material, and relate a set of reasonable local damage measures (DMs) against one or more selected earthquake ground motion intensity measures (IMs). Each IDA curve is referred to individual specific parts of the structure (numerical model). The introduction of local IDA curves (i.e. generated with reference to different portions of the structure) represents a key aspect, allowing a local estimation of damage with confidence intervals. To this end, an in-depth analysis of the IMs proposed in the literature is needed since the use of the most suitable IMs represents a pivotal aspect of IDA effectiveness. Suitable parameters for damage in masonry structures and for intensity measures should be considered on the basis of both theoretical considerations and numerical modeling in such a way that the variability of the IDA curves is reduced as much as possible, so limiting the uncertainty in the estimated damage. Finally, multidimensional IDA curve sets are constructed, where multidimensional indicates that during any IDA, each analysis point conceptually contains a vector of DMs that corresponds to a vector of IMs for that scaled incarnation of the single record. In practical terms, when an earthquake occurs, IMs computed from the seismic data (e.g. the base acceleration and/or seismic response measured by the monitoring system installed on the structure or measurements from a nearby seismic station) are used and local damage conditions are immediately estimated using the mathematical relation obtained through prior multidimensional IDA analyses. The outline of the proposed seismic IDA-based SHM procedure, whose sketch is depicted in Fig. 4.1, is summarized in the next steps: • Step 1: Construction and calibration of a detailed FE model; • Step 2: Ideal subdivision of the model into nmeaningful parts for damage localization purposes; • Step 3: Selection of seismic input: given the record dependency of IDA and the record-to-record variability of structural responses, a suite of ground motion records is considered (learthquakes for IDA); • Step 4: Incremental Dynamic Analyses run; 73 Chapter 4 Damage localization and quantification via IDA • Step 5: Selection of the most relevant mIMs by means of an appropriate correlation study and decision on significant DMs; • Step 6: Construction of multidimensional IDA curve sets: DM =f(IM)(4.1) where DM = (DM1, DM2, ..., DMn)and IM = (IM1, IM2, ..., IMm), with nindicating the number of parts in which the structure is subdivided and mthe total number of considered IMs. Assuming monotonic IMs, the IDA curves in Eq. (4.1) become multidimensional functions (R∗m→ R∗n), being R∗the set of non-negative real numbers; • Step 7: Investigation of the dispersion of IDA curve sets and the most efficient m∗IMs through the mean values of the Root Mean Square Errors (RMSE) of single curves computed with respect to the mean curve: RMSEi,j =1 l l X k=1 sPq p=1 ∆DMk,p i,j 2 q(4.2) where ∆DMk,p i,j =DMk,p i,j −DMmean,p i,j represents the difference between the kth and mean damage (obtained from the kth and mean curve, respectively), while i= 1, .., n (nparts), j= 1, .., m∗ (m∗≤m), k= 1, .., l (lthe number of earthquakes considered for IDA) and p= 1, .., q (qis the number of samples of the mean curves). • Step 8: Regression analysis of IDA curves: DMi,j =gi,j(IMj) + εi,j (4.3) where gi,j represents an appropriate analytical function (e.g. a polynomial function and/or a spline), εi,j indicates the error terms, while i= 1, .., n and j= 1, .., m∗; • Step 9: Occurrence of a seismic event and computation of earthquake-specific IM∗= (IM∗ 1, IM∗ 2, ..., IM∗ m∗) using seismic records; • Step 10: Damage identification: use of intensity measures contained in IM∗into Eq. (4.3) for IDAbased localization and quantification of earthquake-induced damage in each i-th part, denoted as 74 Chapter 4 Damage localization and quantification via IDA DM∗ i,j. The latter is averaged in terms of weighted mean ranges (maximum and minimum value) and weighted mean values by the following equation: DM∗ i=Pm∗ j=1 αi,jDM∗ i,j Pm∗ j=1 αi,j (4.4) where the coefficients αi,j, representing the weights of the m∗most efficient IMs, depend on the IDA curve sets dispersion and are computed as the inverse of RMSEi,j defined in Eq. 4.2. The final equation for weighted average damage quantification becomes: DM∗ i=Pm∗ j=1 1 RMSEi,j DM∗ i,j Pm∗ j=1 1 RMSEi,j (4.5) 75 Chapter 4 Damage localization and quantification via IDA Figure 4.1: Scheme of the proposed method based on multidimensional non-linear seismic IDA: localization and quantification of earthquake-induced damage in ndistinct parts of the structural model, DM∗= (DM∗ 1, DM∗ 2, ..., DM∗ n), by using the IMs of a seismic event, IM∗= (IM∗ 1, IM∗ 2, ..., IM∗ m), within a priori built IDA curve sets relating nlocal DMs to mIMs. 76 Chapter 4 Damage localization and quantification via IDA 4.3 Analysis of intensity measures for IDA-based damage assessment One of the most important aspects of a multi-record IDA study concerns the definition and choice of IMs (Vamvatsikos and Cornell 2002). The relationship between DM and IM is multidimensional, whereby the results of an IDA study expressed by Eqs. (4.1) and (4.3) can be presented in a multitude of different IDA curves, depending on the choices of IMs. A particular focus is here dedicated to the in-depth analysis of the IMs proposed in the literature since the use of the most suitable IMs represents an important aspect of the IDA results and effectiveness. To this end, a statistical correlation study between IMs has been carried out, considering one hundred (100) seismic records from the ITalian ACcelerometric Archive (ITACA) strong motion database (Pacor et al. 2011). The objective of this specific study is to avoid the use of highly correlated independent variables, providing a robust justification of the choices made in the selection of IMs used in the rest of the work. In order to thoroughly characterize an earthquake, an IM should be able to describe three main ground motion characteristics/features of earthquake engineering significance: amplitude, frequency content and duration. A relatively large number of intensity parameters has been proposed in the literature, each of them providing information about one or more of these characteristics. In practice, it is usually necessary to resort to more than one IMs to adequately characterize a ground motion, an aspect of particular importance for IDA. Ground motion amplitude is measured based on acceleration, velocity and displacement time series, as the size of the oscillations on an earthquake recording. In general, peak ground motion parameters result to be particularly poor for characterizing the overall nature of the motion because they only reflect the amplitude of a single isolated peak. The most common IMs used to describe ground motion amplitude include Peak Ground Acceleration (PGA), Peak Ground Velocity (PGV) and Peak Ground Displacement (PGD). The simplest and most worldwide used measure is PGA, which corresponds to the largest absolute value of acceleration in the time-series (the horizontal peak amplitude is considered separately from the peak vertical motion). It concerns a basic measure of earthquake potential but not totally reliable. Although the inertial force is directly related to the acceleration, from an engineering perspective PGA does not capture the frequency content, duration and energy of the acceleration time history, all features that can strongly influence the earthquake shaking damage. In fact, a large PGA recorded during a short duration impulse can conceivably cause a smaller amount of structural damage with respect to a more moderate PGA associated with a long duration impulse. PGV is an additional general parameter for characterization of ground motion amplitude, with the additional advantage 77 Chapter 4 Damage localization and quantification via IDA of being associated with a period range of more general importance to earthquake response. For buildings sensitive to loadings in this intermediate-frequency range (e.g., tall or flexible structures), the peak velocity may provide much more accurate evidence of the damage potential with respect to the peak acceleration. Finally, PGD is generally associated with ground motions of very long period, not a particularly helpful measure of the potential effects of strong shaking. Also, its reliability is questionable due to the double-integration from acceleration. As a result, peak displacement is less commonly used as a measure of ground motion in comparison to its acceleration or velocity counterparts. The frequency content of an earthquake concerns identifying the amount of energy imparted at different frequencies. The dynamic response of structures is very sensitive to the frequency at which they are subjected to. The resonance effect, tend to amplify the response of the structure when the frequency contents of the ground motion are concentrated around its natural frequency (the ground motion and the building are in resonance with one another). In this context, buildings suffer the greatest damage from ground motion at a frequency close or equal to their own natural frequency. Generally, the frequency content is measured by the response spectrum and the Fourier spectrum. In the present study, the main frequency content measures selected are response spectra-based (spectral parameters). Another frequency content measure is the frequency ratio PGV/PGA, generally used to emphasize the effects of local site conditions. It provides information on the frequency content and the strong-motion duration of the ground motion (Zhu et al. 1988). The strong motion duration of an earthquake is another obviously important property. It represents the time interval in which a strong ground motion occurs and can remarkably affect the amount of damage due to an earthquake or its potential. Many physical processes in certain types of structures, such as the degradation of stiffness and strength or the presence of minor cracks, can progress to major failures, being sensitive to the number of load or stress reversals that occur during an earthquake. Experience has confirmed that a motion of short duration may not produce enough load reversals to damage a structure, even with a high amplitude of the motion. On the other hand, a strong ground motion with moderate amplitude but long duration can result in more load reversals and cause substantial damage, aspect of utmost importance in terms of structural stiffness degradation. The duration of a seismic event is related to the time required for the release of accumulated strain energy by the rupture along the fault. In general, an earthquake accelerogram contains all acceleration impulses from the time the earthquake begins until the time the motion has returned to the level of background noise. For earthquake engineering purposes, only the strong motion portion of the accelerogram is of interest. Different approaches have been considered in the literature for evaluating the duration of strong motions in accelerograms. The main definitions of earthquake duration are represented by 78 Chapter 4 Damage localization and quantification via IDA Peak seismic input parameters are PGA, PGV, PGD. Other measures can be Sustained Maximum Acceleration (SMA) and Sustained Maximum Velocity (SMV) defined as the third highest absolute peak value of acceleration and velocity time history, respectively, (Nuttli 1979), and Effective Design Acceleration (EDA) (Reed et al. 1988). While PGA is not totally reliable, the PGV seems to be a more representative measure of earthquake intensity as it is directly connected with the energy content (Housner and Jennings 1982). In addition, Riddell and Garcia found that compound parameters could minimize the dispersion of hysteretic energy-dissipation spectra of inelastic single-degree-of-freedom (SDOF) systems (Riddell and Garcia 2001): Ia, Ivand Idare considered as ground motion measures with respect to fundamental periods in the lower, intermediate and higher period range, respectively. Also, Fajfar proposed a compound IM, IF, for structures with fundamental periods in the intermediate-period range (Fajfar et al. 1990). Notations, definitions, as well as amplitude, frequency content and duration characterizations, are reported in Tabs. 4.2, 4.3, 4.4 and 4.5. Integral seismic input parameters can be the Root Mean Square Acceleration (RMSA), Velocity (RMSV) and Displacement (RMSD). They are much more effective for engineering purposes for incorporating the effect of frequency content and duration and for measuring the energy content of a seismic event. Two measures of earthquake destructiveness based on the RMSA are the Arias intensity, IA, and the Saragoni Factor, PD. IA, is defined as the time integral of the square of the seismic ground acceleration and can be related to the energy content of an earthquake given the proportionality to the square of acceleration (Arias 1970). A plot of the build-up of IAwith time is known as a Husid plot (Husid 1969). Arraya and Saragoni have shown that IApredicts the destructiveness capacity in an appropriate mode only when the frequency content of different earthquakes is similar (Araya and Saragoni 1980; Araya and Saragoni 1984). They have introduced a sort of normalization of IA, defined as Destructive Potential Factor, PD, a more effective measure which can be expressed as a function of the duration, maximum ground acceleration and frequency content of the strong ground motion. PDis computed as the ratio between IAand the square of zero crossings of the record in the time unit (ν2), the latter incorporating the frequency content. Acceleration parameter, A95, represents the level of acceleration which contains up to 95% of IA(Sarma and Yang 1987). Another integral parameter is the Characteristic Intensity, IC, based on the total duration and the RMSA (Park et al. 1985). It has been shown to be linearly related with measures of observed damage for both experimented and actual damaged buildings. Cosenza and Manfredi have proposed a damage factor, ID, that is related to the energy content of the earthquake (Cosenza and Manfredi 1997). In addition, Maximum Incremental Velocity (MIV) and Displacement (MID) have been proposed for characterizing the damage potential of earthquake motions in the near-fault region (Anderson and Bertero 1987). MIV and MID are computed as the maximum area under an acceleration and velocity pulse (between two consecutive zero acceleration and velocity crossings), respec85 Chapter 4 Damage localization and quantification via IDA tively. Moreover, the Cumulative Absolute Velocity (CAV), originally proposed by Kennedy and Reed (EPRI 1988) in a study sponsored by the Electrical Power Research Institute (EPRI), is defined as the area under the absolute ground acceleration during the total duration of the record, also interpreted as incremental velocities sum. RMSA, RMSV, RMSD, IC, IA, PD, MIV, MID and CAV, besides integral parameters, are concerned also as seismic input IMs. Notations, definitions, as well as amplitude, frequency content and duration characterizations, are reported in Tabs. 4.2, 4.3, 4.4 and 4.5. Intensity measures based on the response of a linear elastic SDOF system are identified as spectral parameters, considered as structure-specific IMs. Acceleration, velocity and displacement response spectra represent the response of SDOF systems. The response spectrum represents the most basic tool of earthquake engineering and most of the design standards define hazard intensity based on the spectral acceleration of the ground motion. The response spectrum describes the frequency content of ground motions in a manner that is more fundamental to earthquake response than the traditional Fourier spectrum, because of the inclusion of the damping effects. The fundamental period and the damping ratio (generally 5%) are the only parameters needed to characterize dynamically a SDOF system. The most widely used spectral IM is the acceleration response at the first mode period of vibration of the structure (5% damped), Sa(T1). It represents a measure of the maximum strength demand of the earthquake, being proportional to the maximum seismic force acting on the structure. Other spectral IMs are the velocity and displacement response at the first mode period of vibration of the structure, Sv(T1) and Sd(T1), respectively. In addition, the Effective Peak Acceleration (EPA), Velocity (EPV) and Displacement (EPD) were firstly introduced in the code design previsions (ATC 1978, BSSC 1984) by Applied Technology Council (Kramer 1996) to characterize the intensity of design ground motions. They are defined as the average spectral acceleration, velocity and displacement over a certain period range divided by 2.5 (the standard response amplification factor for a 5% damping spectrum). EPA considers a period range 0.1≤T≤0.5seconds, EPV the period range 0.7≤T≤2.0seconds while EPD is computed over the period range from 2.5 to 4.0 seconds. Sa(T1), Sv(T1), Sd(T1), and EPA, EPV, EPD constitute peak seismic response IMs. Notations, definitions, as well as amplitude, frequency content and duration characterizations, are reported in Tabs. 4.2, 4.3, 4.4 and 4.5. Spectrum intensity measures evaluated by the integration of the response spectrum in a given period range (spectrum intensity parameters) can explicitly account for higher modes effects as well as period lengthening due to structural softening. Although the elastic response spectrum cannot directly define damage on a structure (which is essentially inelastic deformation), it captures in one curve the amount of elastic deformation for a wide variety of structural periods and, therefore, may be a good overall measure of ground motion intensity. 86 Chapter 4 Damage localization and quantification via IDA On this basis, Von Thun Acceleration Spectrum Intensity, ASIVT, has been proposed by (Thun et al. 1988), whereas for velocity-spectrum-sensitive structures, Housner defined a measure for expressing the destructiveness severity of earthquakes computed as the area under (integral) the pseudo-velocity spectrum in the period range 0.1≤T≤2.5seconds (Housner 1952). Housner Intensity, IH, has such integration limits in a way that a range of typical periods of vibration of urban buildings has been taken into account. Accordingly, IHmay be considered as an overall measure of the capability of an earthquake to excite a population of buildings with fundamental period between 0.1 and 2.5 seconds. There are other definitions of Velocity Spectrum Intensity (VSI) suggested by several Authors. Hidalgo and Clough considered IHand a new definition of spectrum intensity, defined as VSIHC, where the upper integration limit was reduced to 1.0 second (Hidalgo and Clough 1974). Kappos proposed another definition of spectrum intensity, VSIK, where the integration limits are depended on the natural eigenperiod of the structure T1 (Kappos 1991): the suggested period-intervals are t1 = 0.8T1 and t2 =1.2T1. Other examples of VSI can found in the literature (Nau and Hall 1984; Thun et al. 1988). These spectrum intensity parameters, ASIVT, ASINH, IH, VSIVT, VSIK, VSIHC, VSINH, can be classified as integral seismic response IMs. Notations, definitions, as well as amplitude, frequency content and duration characterizations, are reported in Tabs. 4.2, 4.3, 4.4 and 4.5. 87 Chapter 4 Damage localization and quantification via IDA With a complete overview on many IMs, a statistical correlation study has been carried out considering about fifty (50) intensity measures, aimed at investigating the interdependence among them and at understanding the most suitable and reasonable measures for IDA purposes. To this end, a total of one hundred (100) strong ground motions from earthquakes with moment magnitude Mw≥5 have been selected from the ITACA strong motion database (Pacor et al. 2011), taking into consideration: (i) normal, thrust and strike-slip faulting mechanisms, (ii) ordinary and pulse-like near-fault ground motions, (iii) epicentral distance range of 2-80 km and (iv) all subsoil categories (A, B, C, D, E). Detailed information about ground motions is reported in Appendix A. It is noteworthy to stress that, although input acceleration, velocity and displacement time histories are given in East and North directions, IMs have been computed using their mean direction. Considering the aforementioned ground motions, correlation coefficients Rhave been computed between acceleration-related (Fig. 4.2a), velocity-related (Fig. 4.2b), displacement-related (Fig. 4.2c) and mixed IMs (Fig. 4.2d), allowing to rate their degree of interdependence: high correlation (1 > R > 0.9), medium correlation (0.9 ≥R > 0.6) and low correlation (0.6 ≥R). In general, a high degree of correlation inside each subgroup can be observed. These results are in clear agreement with those presented by (Riddell 2007). IMs belonging to different subgroups are badly correlated between them, as shown in Fig. 4.2e. Besides the selection of the most uncorrelated measures, at least one seismic peak and one seismic integral IM, as well as one response peak and one response integral parameter, have been chosen as pivot parameters from each subgroup for IDA purposes. Considering (as an example) the case of response integral velocity-related parameters, the applied rule aimed at uncorrelated IMs selection would imply the following steps: first the pivot IM is chosen (IH) and then the ones featuring R≤0.9 with respect to the pivot are taken into account, while the others with R > 0.9 are discarded (VSIVT, VSIK, VSIHC, VSINH). Only Ca, Cv, Cdand IDmade an exception to this selection rule because they remain almost constant with increasing seismic intensity, thus being not useful for IDA purposes. Finally, the most uncorrelated, meaningful and representative IMs that have been selected and used for the construction of IDA curves are: PGA, RMSA, IC, IA, PD, CAV, Sa(T1), ASIVT, PGV, RMSV, SED, CAD, Sv(T1), IH, PGD, RMSD, Sd(T1), DSINH and EI(m=19 with reference to Eq. (4.1)). They are highlighted in Figs. 4.2a-d, whereas correlation coefficients between them are reported in Fig. 4.2e. 88 Chapter 4 Damage localization and quantification via IDA Figure 4.2: Correlation between IMs: correlation coefficients Rbetween acceleration-related (a), velocityrelated (b), displacement-related (c) and mixed IMs (d); correlation coefficients between the selected IMs for IDA (e). Note that the latter are highlighted with red color. 89 Chapter 4 Damage localization and quantification via IDA 4.4 Application example: the Brick House The proposed method in Section 4.2 is applied and validated through the Finite Element (FE) model of a wellknown case study, the Brick House. It is a benchmark tested on the National Laboratory for Civil Engineering (LNEC) shaking table in Lisbon, Portugal, whose experimental results act as a reference for calibration of the numerical counterpart. The tests, carried out in the scope of the workshop “Methods and Challenges on the Out-of-Plane Assessment of Existing Masonry Buildings” (Lourenço et al. 2017), aimed at assessing the out-of-plane performance of the mock-up under seismic loading. A detailed FE model of the structure is developed and non-linear dynamic analyses are carried out to obtain numerical insight into the seismic response of the building specimen, identifying its most vulnerable parts. Section 4.4.1 presents the case study, including the validation of the FE model of the structure. The selection of seismic input used for non-linear dynamic analysis is reported in Section 4.4.2 while non-linear seismic IDA curve sets are illustrated in Section 4.4.3. Finally, Section 4.4.4 is devoted to presenting the results on earthquake-induced damage localization and quantification via non-linear seismic IDA. Main conclusions are summarized in Section 4.5. 4.4.1 Experimental testing and FE modeling The Brick House was built using regular fired clay bricks with an English bond masonry arrangement, yielding a wall thickness of around 23.5 cm. The house presented three walls arranged according to a U shape layout (see Fig. 4.3): the façade wall with a central opening and a gable on top, and the two orthogonal sidewalls acting as abutments, of which only one was pierced by a window. Unidirectional seismic loading in the perpendicular direction to the façade was applied with an increasing input intensity testing protocol up to collapse. The pre-processed N64E strong ground motion component of the Christchurch (New Zealand) earthquake of February 21st 2011 was used. In this way, the façade was loaded in the out-of-plane direction, while the sidewalls were loaded in-plane but, given the presence of a window in one of them, an asymmetric dynamic behavior was observed, leading to significant torsion of the structure. The seismic test sequence included eight (8) steps of increasing intensity, where the last one reached a PGA of about 12.47 m/s2. The collapse mechanism observed at the end presented partial collapse of the gable top of the façade and the lateral wall with window, while the other sidewall remained almost intact (see Figs. 4.3a-c). The instrumentation included twenty (20) unidirectional accelerometers and six (6) linear variable displacement transducers (LVDTs), placed in different locations for measuring the absolute acceleration responses of the structure as well as the input signals on the shake table, and the out-of-plane displacements of 90 Chapter 4 Damage localization and quantification via IDA Figure 4.3: Experimental results: brick masonry prototype after shaking table test (a) and collapse mechanism schemes (b, c) (Candeias et al. 2017). Numerical model validation: damage obtained by the corresponding FE model after the Christchurch (N64E component) earthquake simulation (d-f). the façade, respectively. Further details concerning the mock-up, seismic testing campaign, instrumentation setup, damage pattern and observed collapse mechanisms are presented in (Candeias et al. 2017). A 3D FE model of the Brick House mock-up has been built using the ABAQUS 6.10 platform (Simulia 2010). A free meshing of solid eight-node linear brick elements C3D8R with the mean dimension of about 10 cm (two elements in thickness) has been adopted, resulting into a total of 5595 nodes, 16785 DOFs and 3460 elements. The choice of such a mesh dimension has been determined based on a preliminary sensitivity analysis, here omitted for the sake of brevity, looking for a compromise between accuracy of the solution and control of computational costs. The model has been assumed as fixed to the ground. At the constitutive level, the same material has been assigned to the whole structure as homogeneous, assuming an isotropic behavior. Linear mechanical parameters of the masonry can be found in (Candeias et al. 2017), as estimated after in-situ characterization experimental tests on six (6) wallets. 91 Chapter 4 Damage localization and quantification via IDA The numerical prediction of the behavior of masonry structures still represents a complex issue due to the difficulties to adequately simulate the non-linear cyclic response of the masonry material. In this regard, the non-linear FE modeling and mechanical behavior of the masonry material have been here reproduced, as suggested in literature works on seismic vulnerability analysis (Valente and Milani 2016), using the CDP constitutive model proposed by Lubliner (Lubliner et al. 1989) and subsequently modified by Lee and Fenves (Lee and Fenves 1989) for cyclic loading and damage implementation. More information on CDP model is detailed in Section 3.3.2 with the principal scheme illustrated in Fig. 3.8 and description of main equations (Eqs. (3.10) and (3.11)). In the case of the Brick House mock-up, despite the absence of data to accurately describe the non-linear behavior of the material in tension and the failure of experimental diagonal compression tests, the post-elastic material response (with specific reference to the mortar) in tension and compression (assumed to be exponentially decreasing) has been suggested in (Gams et al. 2017). For the present numerical model, the proposed linear (Candeias et al. 2017) and non-linear (Gams et al. 2017) parameters resulted very useful for the calibration process. It should be emphasized that, for obtaining full consistency between numerically predicted and experimentally recorded response accelerations, an additional manual tuning was needed. The following linear parameters are adopted: Young’s modulus E, Poisson’s ratio ν, specific weight γ, and tensile and compressive strength (σtand σc), as reported in Tab. 4.6. The ratio between σtand σcis equal to about 0.1. Regarding CDP, with reference to the suggested values, slightly different but reasonable damage parameters in tension have been adopted (see Tab. 4.7). The description of the failure condition and of the post-peak behavior depends upon the tensile stresses, σt, the cracking strains, ˜εck t, and the tensile damage variable, dt. The behavior of the masonry has been reproduced up to the ultimate limit state, considering damage in tension only. CDP complementary parameters for defining flow potential, yield surface and viscosity are reported in Tab. 4.8. In detail, ψrepresents the dilation angle in the p–qplane. The flow potential eccentricity, ϵ, is a small positive number that defines the rate at which the hyperbolic flow potential approaches its asymptote. The parameter σb0/σc0represents the ratio of initial equibiaxial compressive yield stress to initial uniaxial compressive yield stress. Kcis the ratio between second stress invariants on the tensile and compressive meridians at initial yield for any given value of the pressure invariant, such that the maximum principal stress is negative. Finally, µindicates the viscosity parameter, which is set equal to 0 (default value in ABAQUS/Explicit). 92 Chapter 4 Damage localization and quantification via IDA Table 4.6: Mechanical parameters adopted on the Brick House FE numerical model. Eν γ σtσc [kN/m2][-] [kN/m3] [kN/m2] [kN/m2] 3.62e+06 0.3 18.9 250 2480 Table 4.7: Uniaxial stress–strain and scalar tensile damage values utilized in the CDP model for the masonry material. σt˜εck tdt [kN/m2] [−] [−] 252 0.0e-00 0.00 198 3.0e-05 0.20 99 8.0e-05 0.40 45 1.1e-04 0.70 22 1.8e-04 0.90 Table 4.8: CDP parameters defining flow potential, yield surface and viscosity. ψ ϵ σb0/σc0Kcµ [deg] [−] [−] [−] [−] 30 0.1 1.16 0.667 0 The validation of the Brick House FE model has been performed by investigating its damage pattern predicted after the Christchurch earthquake numerical simulation, using the same input motion of the experimental tests (Kita et al. 2019a). Figs. 4.3d-f illustrate the numerically obtained damage pattern, which is consistent with the experimental collapse mechanism observed during the shaking table test and shown in Figs. 4.3ac. Furthermore, as displayed in the plots of Fig. 4.4, numerically predicted and experimentally measured response accelerations have been compared in five (5) strategic and meaningful reference points. Given the consistency of damage pattern and plots of PRAs, the model can be considered validated, hence ready for IDA. The DMs used in the present case study are output variables obtained from ABAQUS numerical model, namely: tensile damage parameter, dt, plastic strain magnitude, PEMAG, and first principal plastic strain, εpl 1. For damage localization purposes, the Brick House FE model has been partitioned into ten (10) parts (see Fig. 4.5), thus allowing a local IDA-based estimation of DMs, computed as average values weighted over the volume of the numerical elements of every single part of the FE model (volume-averaged damage 93 Chapter 4 Damage localization and quantification via IDA Figure 4.4: Numerical model validation: plots of experimental versus numerical PRAs, with reference to the top accelerometers (A07, A18, A03, A16 and A02). Note that PGA is measured at the base reference point. parameter). Also, the direction of the application of the seismic loading is indicated with a double-sided arrow. Figure 4.5: The ten (10) parts of the Brick House numerical model defined for damage localization purposes through IDA. The double-sided arrow indicate the direction of application of the seismic loading (applied as base excitation). 94 Chapter 4 Damage localization and quantification via IDA Figure 4.10: The IDA curve sets: plots of first principal plastic strain (εpl 1) versus IC(a-j). Contour plots obtained in the last step of the non-linear dynamic analysis with IT0788xa_m earthquake scaled at SF=3 (k). pattern evolution with increasing levels of earthquake input is illustrated in Fig. B.1 in terms of dtcontour plots obtained at the last step of the IDAs with IT0806xa_m earthquake. 101 Chapter 4 Damage localization and quantification via IDA 4.4.4 IDA-based damage identification After the construction of the IDA curve sets, higher levels of identification (localization and quantification) of earthquake-induced damage have been achieved for the ten (10) parts of the structural model, by using Eqs. (4.4) and (4.5) and IMs of arbitrary real seismic events. For this purpose, three near-field ground motion records belonging to the 2016 Central Italy seismic sequence (Chiaraluce et al. 2017), appropriately scaledup in the present case, have been used: (i) the acceleration recorded at Castelluccio station (North-South component) of Norcia Mw6.5 earthquake occurred on October 30th; (ii) the East-West component of the acceleration recorded in Amatrice station, close to the epicenter of Accumoli Mw6.0 earthquake occurred on August 24th; (iii) the acceleration recorded at Campi station (North-South component) of Ussita Mw5.9 shock of October 26th (Ubertini et al. 2018). With regard to the Brick House, the first record, scaled with SF=1.25, has been considered as low seismic intensity; the second record has been scaled with SF=1.75, representing a medium seismic intensity; and the last one with SF=2.75 represents a high seismic intensity. Scaled-up acceleration time histories are shown in Fig. 4.11. Some very preliminary results of damage identification on the Brick House can be found in (Kita et al. 2019a). Taking advantage of the least dispersed IDA curve sets, obtained with PGA, IC, IA, Sa(T1), ASI, PGV, Sv(T1) and IH, and illustrated more in detail in Appendix B.1 (from Fig. B.2 to Fig. B.9), the set of eight (8) IMs has allowed to firstly localize and subsequently quantify earthquake-induced damages. These IMs have been computed from the three seismic records depicted in Fig. 4.11. With reference to part 6 only, Fig. 4.12 illustrates IDA-based estimated damages using IMs contained inside vectors IM∗N,IM∗Aand IM∗Ufor Norcia, Accumoli and Ussita, respectively, on the sets of seven (7) curves and the corresponding mean curves (see Figure 4.11: Scaled acceleration records of seismic events used for earthquake-induced damage localization and quantification: SF=1.25 scaled-up Norcia earthquake (a), SF=1.75 scaled Accumoli shock (b) and SF=2.75 scaled-up record of Ussita earthquake (c). 102 Chapter 4 Damage localization and quantification via IDA Figure 4.12: Part 6: IDA-based tensile damage (minimum, maximum and mean values) estimated with Norcia, Accumoli and Ussita earthquakes by means of the eight (8) selected IMs into Eq. (4.3). For comparative purposes, actual damage (dt) is also reported. 103 Chapter 4 Damage localization and quantification via IDA Eq. (4.3)). IDA-based damages have been estimated in terms of minimum, maximum and mean values, the latter obtained from the mean curve. An IDA-based damage estimation zone, delimited by the minimum and maximum damages obtained with the eight (8) IMs, is highlighted by an infilled area with light grey color. Also, for comparative purposes, actual damages have been reported in the plots. They represent numerically computed mean damage parameters in different portions, in particular, the tensile damages dtobtained from the non-linear dynamic analyses carried out considering the three seismic records plotted in Fig. 4.11. In general, a relatively good consistency between numerical actual damages and IDA-based ones can be observed. A first important aspect concern the agreement between actual damage and weighted mean IDA-based estimation. Besides consistency between mean values, another important condition regards the estimation of the range of damage, i.e. the difference between the maximum and minimum IDA damage: obviously the smaller the better. As an example, in the case of Ussita earthquake (see Fig. 4.12c), the best consistency between mean damages can be if ASI is used for IDA-based damage estimation. On the other hand, the estimated range of damage is very small using IC. Both considerations, consistency between mean damages and reduced as much as possible damage ranges, are of particular importance in earthquake-induced damage quantification. In this spirit, the idea of using not all IMs, but carefully selecting only some of them, taking into account a compromise of the aforementioned two considerations, can lead to a better IDA-based damage estimation. For this purpose, IDA-based damages obtained from every single IM have been averaged by using combinations of these IMs, namely Scenarios 1, 2 and 3. Scenario 1 comprises all m∗IMs, while the 2nd and the 3rd combine only some parameters, aiming at reducing the estimated mean ranges and obtaining a better consistency with actual damages. The abovementioned eight (8) IDA curve sets (obtained with PGA, IC, IA, Sa(T1), ASI, PGV, Sv(T1) and IH) have been considered. The weighting coefficients of the corresponding m∗=8 best IMs, αi,j, have been computed as the inverse of RMSEi,j (see Eq. (4.2)), thus depending on the IDA curve sets dispersion. Mean values of IDA-estimated damage obtained from every single IM have been averaged through these weighting coefficients αi,j according to Eqs. (4.4) and (4.5). In this context, by using the set of the m∗IMs in Eq. (4.5), IDA-based tensile damages have been estimated, in terms of weighted average ranges (maximum and minimum) and weighted mean values for all the ten (10) parts of the model. Fig. 4.13 shows IDA-based tensile damages in the case of three earthquakes and three Scenarios of combinations of IMs. In general, a good agreement between actual damages and IDA-based estimated damages can be highlighted. The dt values of the ten (10) regions fall within the corresponding IDA-based estimated average ranges. The proper combinations of only a few IMs (e.g. Scenario 3) have allowed full consistency between actual damages and IDA-based damages for the ten (10) parts of the structure. In addition, for a better understanding of the 104 Chapter 4 Damage localization and quantification via IDA damage pattern obtained via IDA, contour plots of numerically computed actual damage dtobtained at the last step of the non-linear dynamic analysis are positioned on the side of each plot, highlighting increasing damage with increasing seismic intensity (contour range from 0 to 1.0). By increasing the seismic intensity from low to high, it is clearly demonstrated that earthquake-induced damages concentrate in specific parts of the structural model, such as parts 7, 5 and 8, whereas parts 1 and 10 present the lowest values of estimated tensile damage (maximum dt≤0.1-0.2). Finally, for a more direct comparison, Fig. 4.14 illustrates weighted mean IDA-based tensile damages plotted versus actual damages, dt, for the three seismic events for all parts of the model. It can be highlighted that, passing from Scenario 1 to 3, there is a clear trend of improvement in matching, with a closer allocation along the diagonal. 105 Chapter 4 Damage localization and quantification via IDA Figure 4.13: Comparison between actual damage (dt) and IDA-based estimated tensile damage, considering different combinations of IMs for the three selected real ground motion records. Note that IDA-based damage is expressed in terms of weighted average ranges and mean values obtained from the IDA curve sets and corresponding mean curves, respectively. 106 Chapter 4 Damage localization and quantification via IDA Figure 4.14: Comparison between actual damage (dt) and weighted mean IDA-based estimated tensile damage, considering different combinations of IMs (Scenarios 1, 2 and 3) for the three selected real ground motion records. 107 Chapter 4 Damage localization and quantification via IDA In addition to tensile damage, the same procedure has been applied in the case of first principal plastic strain, εpl 1, for IDA-based damage localization and quantification. The least dispersed IDA curve sets, illustrated more in detail in Appendix B.1, have been considered. The set of eight (8) IMs has allowed to firstly localize and subsequently quantify earthquake-induced first principal plastic strain damages. With reference to part 6 only, after applying Eq. (4.3), Fig. 4.15 illustrates IDA-based estimated damages, in terms of minimum, maximum and mean values, the latter obtained from the mean curve. Both aspects, agreement between actual damage and weighted mean IDA-based estimation as well as the minimum possible estimated damage range, have been taken into account also for first principal plastic strain as DM. As an example, in this case, considering the Ussita earthquake (see Fig. 4.15c), the best consistency between mean damages can be if ICis used for IDA-based damage estimation. On the other hand, the estimated range of damage is very small using PGV. Subsequently, by carefully using only some of IMs (Scenarios 1, 2 and 3) a better IDA-based damage estimation has been achieved. Considering weight coefficients αi,j, (see Eq. (4.4)), averaged mean values of IDA-based first principal plastic strain damages have been estimated, in terms of weighted average ranges and weighted mean values for all the ten (10) parts of the model. After applying Eq. (4.5), Fig. 4.16 shows IDA-based estimated first principal plastic strains against εpl 1actual damages obtained from the non-linear dynamic analyses carried out with the three seismic records of the 2016 Central Italy seismic sequence. Also in the case of εpl 1, a good agreement between actual damages and IDA-based estimated damages can be highlighted, as well as proper combinations of only a few IMs have allowed full consistency for the ten (10) parts of the structure. Contour plots of εpl 1actual damage are illustrated in the same figure, highlighting increasing damage with increasing seismic intensity (contour range from 0 to 0.045). Fig. 4.16 further confirms that part 7 (top gable) is the most damaged portion of the model, while parts 1 and 10 are the safest ones. Both in the case of dtand εpl 1, the estimation of weighted average ranges and mean values resulted to be more accurate than the simple average estimation (not weighted), due to narrower damage ranges themselves. Fig. 4.17 concludes the results illustrating weighted mean IDA-based εpl 1plotted versus actual damages, for the three seismic events for all parts of the model. Switching from Scenario 1 to 3, there is a clear trend of improvement in matching, with a closer allocation along the diagonal. 108 Chapter 4 Damage localization and quantification via IDA Figure 4.15: Part 6: IDA-based first principal plastic strain (εpl 1) (minimum, maximum and mean values) estimated with Norcia, Accumoli and Ussita earthquakes by means of the eight (8) selected IMs into Eq. (4.3). For comparative purposes, actual damage is also reported. 109 Chapter 4 Damage localization and quantification via IDA Figure 4.16: Comparison between actual damage and IDA-based estimated first principal plastic strain (εpl 1), considering different combinations of IMs for the three selected real ground motion records. Note that IDAbased damage is expressed in terms of weighted average ranges and mean values obtained from the IDA curve sets and corresponding mean curves, respectively. 110 Chapter 5 IDA-based damage identification in the San Pietro Bell Tower 5.2a represents a solid representation of the structure consisting of a sectional view, where the three aforementioned structural portions are clearly visible. The shaft is characterized by thick walls made of regular calcareous stone masonry blocks. The external surface of the belfry, including its columns, is made of mixed travertine-calcareous stone masonry with some brick replacements, while the internal surface is made of brick masonry. Finally, the cusp consists of mixed travertine-calcareous stone masonry with an external cover in brick masonry (Ubertini et al. 2016; Cavalagli et al. 2018; Ubertini et al. 2018). The dynamic behavior of the tower was assessed by means of an AVT carried out on February 15th 2015, which allowed identifying the first seven (7) modes of vibration (natural frequencies, damping ratios and mode shapes) of the structure in the range from 0 to 8 Hz (Ubertini et al. 2016). Afterwards, with the purpose of monitoring the structural integrity of the bell tower and of promptly detecting damages caused by low-return period earthquakes, a simple low-cost vibration-based SHM system was installed in the tower for preventive conservation and CBM, currently active since December 9th 2014. Fig. 5.2b shows the configuration of the permanent vibration-based SHM system: three high-sensitivity uni-axial piezoelectric accelerometers (model PCB 393B12 with 10 V/g sensitivity) are installed at the base of the cusp and two others at the basement (on the ground level). In addition, two temperature sensors (K-type thermocouples, one at the base of the belfry and one at the base of the cusp) and various environmental monitoring sensors were also installed and included in the monitoring system since October 2015. The data acquisition system is located inside the tower and connected via the INTERNET to a dedicated remote server in the Laboratory of Structural Dynamics of the Department of Civil and Environmental Engineering of the University of Perugia, where continuous data are processed through an ad hoc developed MatLab code, using each stored 30-minute windows for automated modal identification. The analysis of continuous dynamic monitoring data highlighted the main characteristics of the response of the tower to wind, swinging bells and low return period earthquakes. Despite the very low levels of vibration in operational conditions, five (5) modes are successfully and continuously identified in most of the data sets. Fig. 5.3 shows the time histories of the natural frequencies identified since the beginning of the monitoring, for about five (5) years, every 30 minutes, using a fully automated SSI output-only modal identification technique (Ubertini et al. 2013). Significant seasonal increases from winter to summer conditions, as well as daily fluctuations, are clearly visible in the plots and are conceivably associated with changes in environmental conditions, primarily in ambient temperature (Ubertini et al. 2017). 117 Chapter 5 IDA-based damage identification in the San Pietro Bell Tower The adopted SHM procedure for the San Pietro Bell Tower comprises four (4) consecutive steps, as sketched in Fig. 2.1. A fully automated vibration-based SHM procedure was implemented. It is based on output-only fully automated modal parameters tracking and on a multivariate statistical analysis criterion for damage detection. All five (5) modal frequencies, first tracked and then cleansed, are used to build the statistical models for novelty analysis (see Section 2.1), in order to detect anomalous deviations from normal conditions, thus, revealing changes in the structural behavior. The procedure comprises SSI-based automated modal identification, modal tracking, removal of environmental and operational effects from identified modal frequencies and damage detection (see Fig. 2.1). The removal of environmental effects (temperature and humidity) is carried out via a multivariate statistical analysis technique based on MLR. Damage detection is accomplished by application of the tool of control charts based on a well-known statistical distance and with one year of data as a training period. Despite the presence of significant environmental effects on identified natural frequencies of the San Pietro Bell Tower (Ubertini et al. 2017), the proposed SHM method proved effective in detecting very small stationary variations in identified modal frequencies and automatically revealing any anomaly in the structural behavior, typically occurring after an earthquake and possibly related to a developing damage patFigure 5.3: Plots of five (5) years continuously identified natural frequencies of the San Pietro Bell Tower since December 2014 (daily fluctuations are also evidenced with a detailed view). 118 Chapter 5 IDA-based damage identification in the San Pietro Bell Tower tern (Ubertini et al. 2016; Ubertini et al. 2017; Cavalagli et al. 2018; Ubertini et al. 2018; Giordano et al. 2019). The vibration-based SHM system allowed an automated rapid earthquake-induced damage detection of the bell tower after the main shocks of the 2016 Central Italy seismic sequence. Despite the relatively low intensity of the sequence in Perugia (due to the distance from the epicenters equal to about 80 km) and no clear relevant structural damages were observed in any part of the structure, above all in the belfry, the analysis of long-term monitoring data clearly highlighted that small permanent changes in the structural behavior of the bell tower occurred after the earthquakes, with decreases in all identified natural frequencies (Ubertini et al. 2018; Giordano et al. 2019). Such natural frequency decays were fully consistent with what predicted by non-linear finite element simulations and, in particular, with the development of microcracks at the base of the columns of the belfry. Moreover, besides consistent decays in natural frequencies, the long-term vibration-based SHM clearly detected earthquake-induced damage through control charts. The control chart, built according to Eq. (2.2) by using five (5) years of time series of identified natural frequencies after removal of the effects of changing environmental conditions (Eqs. (2.1) and (2.4)), is illustrated in Fig. 5.4. A clear deviation of the structural behavior from normal conditions can be highlighted after Accumoli earthquake, with a notable increase in the relative frequency of outliers, and also later after Ussita and Norcia shocks. In the present case, it can be associated to small damages induced by the three earthquakes, consisting of microcracks at the base of the columns of the belfry, as well as in some key sections of the pointed arches in the same structural portion. Microcracks in these regions are however hardly distinguishable from pre-existing ones and from the physiological cracking of a masonry structure, which validates the effectiveness of the SHM system in detecting earthquake-induced damage at a stage where this is not yet detectable by visual inspections (Ubertini et al. 2018). The implemented vibration-based continuous monitoring system in the San Pietro Bell Tower resulted in a low-cost tool for automated rapid earthquake-induced damage detection for a full-scale structure, even at an early stage, thus contributing to condition-based maintenance and cost-effective preservation. In order to carry out non-linear incremental dynamic analyses, a detailed 3D numerical model of the structure has been built in the framework of the Finite Element Method (FEM) by using solid hexahedral and tetrahedral elements, in the ABAQUS 6.10 platform (Simulia 2010). In particular, a structured mesh has been adopted in the shaft and the basement regions, while a free mesh has been employed in the belfry and the cusp (see Fig. 5.5). At the constitutive level, the model of the tower has been subdivided into three regions: the shaft, the belfry and the cusp. Stones and brick masonry in different portions of the structure have been modeled as homogeneous and orthotropic, with different mechanical properties depending on the material and texture detected in the various parts of the structure. Such modeling strategy has been exploited in order to obtain 119 Chapter 5 IDA-based damage identification in the San Pietro Bell Tower Figure 5.4: Control chart of five (5) years of monitoring period (a) and detailed view showing increased number of outliers after the three main shocks of the 2016 Central Italy seismic sequence (b). a more accurate calibrated model, particularly, in terms of mode shape’s consistency (Lourenço 2002). The numerical model has been calibrated by varying the values of uncertain mechanical parameters through a modal sensitivity analysis and a proper optimization procedure, and on the basis of the experimentally identified natural modes of vibration, in particular, using natural frequencies at the reference temperature of 20◦C as the target frequencies (Cavalagli et al. 2018). In order to obtain consistency between numerically and experimentally identified mode shapes, also a proper modeling of the restraints given by the neighboring con120 Chapter 5 IDA-based damage identification in the San Pietro Bell Tower structions in the lower part of the bell tower and, primarily, the basilica and the abbey, was found to be crucial. It is worth noting that there is an excellent agreement between experimentally identified natural frequencies at the reference temperature of 20◦C (f20◦C) and numerical ones predicted by FEM analysis (fFEM), with an average relative difference, ∆fmean, between the two quantities lower then 3%. For more details on the model and the calibration procedure, the interested reader is referred to (Cavalagli et al. 2018). The main tuned mechanical parameters of the constituent materials (Young’s modulus E, shear modulus G, Poisson’s ratio νand specific weight γ) are summarized in Tab. 5.1. Above all for running numerical non-linear analysis, FEM materials have been modeled with isotropic constitutive behavior. This modeling assumption allows to release the mutual dependence of E, G and ν. In this context, independent values of E, G and ν, have been assigned without any directional criterion (E11=E22=E33=E, G12=G23=G13=G) in order to achieve good results without losing simplicity and accuracy of the FE model (Gentile et al. 2015). Figure 5.5: Parts of the numerical model defined for damage localization purposes through IDA: Shaft, Belfry and Cusp (a), mesh discretization of the FE numerical model of the San Pietro Bell Tower (b) and detailed view of mesh on the Belfry (c). 121 Chapter 5 IDA-based damage identification in the San Pietro Bell Tower The CDP model (Section 3.3.2, Fig. 3.8) has been also adopted in the case of the San Pietro Bell Tower allowing to perform non-linear seismic incremental dynamic analyses. The use of such a damaging model has required the adoption of an isotropic formulation for the material. It is worth noting that CDP masonry strength parameters have been earlier estimated on the basis of a sensitivity analysis on the input variables required for the constitutive models to define the failure surfaces and the post-peak behavior. For this purpose, the good agreement between the damage scenario observed on the structure after the Umbria-Marche seismic event of 1997 and the same damage predicted by the numerical model using the seismic record of the same earthquake have allowed a reliable estimation of strength parameters (Cavalagli et al. 2018). The CDP material properties are summarized in Tab. 5.2, in terms of tension stiffening and tension damage. The description of the failure condition and of the post-peak behavior depends upon the tensile stresses, σt, the cracking strains, ˜εck t, and the tensile damage variable, dt. The behavior of the masonry has been reproduced up to the ultimate limit state, considering damage in tension only. Table 5.1: Mechanical parameters assumed in the San Pietro Bell Tower FE model after calibration. Structural part E G ν γ [kN/m2] [kN/m2][-] [kN/m3] Shaft 4.274E+06 1.238E+06 0.25 26.0 Belfry 4.335E+06 1.787E+06 0.25 17.5 Cusp 1.800E+06 0.563E+06 0.25 18.9 Table 5.2: Uniaxial stress–strain (tension stiffening) and scalar tensile damage values utilized in the three parts of the numerical model. Shaft Belfry Cusp σt˜εck tdtσt˜εck tdtσt˜εck tdt [kN/m2] [−] [−] [kN/m2] [−] [−] [kN/m2] [−] [−] 400 0.00E-00 0.00 220 0.00E-00 0.00 220 0.00E-00 0.00 300 1.75E-04 0.55 140 7.39E-05 0.45 140 1.66E-05 0.55 210 3.77E-04 0.80 70 1.65E-04 0.60 70 3.86E-04 0.70 40 7.59E-04 0.90 20 2.44E-04 0.90 20 5.83E-04 0.90 122 Chapter 5 IDA-based damage identification in the San Pietro Bell Tower 5.2 IDA-based earthquake-induced damage localization and quantification 5.2.1 Seismic input selection As already introduced in Section 4.1, seismic input selection represents a key issue in non-linear dynamic analysis of structures. Certainly, among different types of acceleration time-histories, natural accelerograms are the best for seismic action representation. The increasing presence of numerous online databases of strong-motion records has shifted the focus mainly towards the use of natural accelerograms. A suite of ground motion records is used also in the case of the San Pietro Bell Tower, aimed at covering a full range of responses and with different seismic characteristics in terms of amplitude, energy or frequency content. The seismic input for IDA of structures is usually defined in terms of acceleration time series whose response spectra result compatible with a specific target response spectrum. The implementation of code provisions for record selection can be very useful. To address this issue, the commercial software REXEL was developed to provide computer-aided ground-motion selection, consistent with the design spectrum and seismic hazard at the site of interest (Iervolino et al. 2009). It is a tool for the selection of ground-motion records, in particular, the automatic selection and scaling of spectrum compatible ground-motions for dynamic analysis of structures (available at the website of the Rete dei Laboratori Universitari di Ingegneria Sismica, ReLUIS – www.reluis.it). REXEL allows the search for combinations of compatible natural accelerograms, in other words, record sets matching either user-defined target spectra or design spectra according to the Italian technical standard code, NTC08 and NTC18 (NTC08 2008; NTC18 2018), and the EC8. The REXEL accelerometric recordings rely on several databases: the ITalian ACcelerometric Archive (ITACA), the European Strong Motion Database (ESD) and Selected Input Motions for Displacement-Based Assessment and Design (SIMBAD). In the case of the San Pietro Bell Tower, seven (7) natural spectrum-compatible seismic groups of accelerograms (two horizontal components) have been obtained by REXEL and used as seismic inputs for non-linear incremental dynamic analysis. As stated in Section 4.1, natural accelerograms (earthquake records) represent the best ones for running IDA. After a search on the ITACA database by REXEL, Fig. 5.6 shows the combination of fourteen (14) spectra compatible with the site of the bell tower, compared to the Perugia target elastic response spectrum, the latter generated according to NTC08. The Perugia site conditions and the other parameters necessary to define the target response spectrum related to the Ultimate Limit State have been taken into account. As displayed in the plot, there is a good consistency between the target and the 123 Chapter 5 IDA-based damage identification in the San Pietro Bell Tower Figure 5.6: Plots of fourteen (14) response spectra compatible with the target response spectrum (site of the San Pietro Bell Tower). Average spectrum is depicted in blue thick line. average spectrum of the seven (7) groups of accelerograms found by REXEL. The corresponding spectrummatched accelerograms are defined in terms of two-components acceleration time series whose response spectra result compatible with the Perugia (bell tower site) response spectrum. The main original characteristics of the seven (7) natural selected ground motions used for IDA on the San Pietro Bell Tower are synthesized in Tab. 5.3, while the time histories of the corresponding unscaled spectrummatched acceleration time histories (both horizontal components) are plotted in Fig. 5.7. It is worth noting that the present seismic loading is bidirectional, whereby components are applied in the two horizontal directions to the FE model of the bell tower: x component in East-West and y in North-South direction. They have been scaled at increasing levels for IDA by means of appropriate SFs synthesized in Tab. 5.4 (λ,aλ=λ·a1, as suggested in (Vamvatsikos and Cornell 2002)). 5.2.2 Non-Linear Seismic IDA Curve Sets with seismic input IMs The most uncorrelated, meaningful and representative IMs, that have been identified by means of the statistical correlation study and whose results are summarized in Section 4.3 (see Fig. 4.2e), are PGA, RMSA, IC, IA, PD, CAV, Sa(T1), ASIVT, PGV, RMSV, SED, CAD, Sv(T1), IH, PGD, RMSD, Sd(T1), DSINH and EI(m=19 with 124 Chapter 5 IDA-based damage identification in the San Pietro Bell Tower Figure 5.7: Plots of the seven (7) spectrum-compatible unscaled seismic records (acceleration time series) used for IDA of the San Pietro Bell Tower: x component is input in East-West direction while y in North-South direction. Table 5.3: Main characteristics of strong ground motions used for Incremental Dynamic Analysis of the FE model of the San Pietro Bell Tower. EQ. ID Station ID EQ. name Date Mw Fault PGAxPGAy [−] [−] [−] [dd/mm/yyyy] [−] [−] [m/s2] [m/s2] IT0014 TLM1 Friuli 06/05/1976 6.4 Thrust 3.390 3.090 IT0164 ALT Irpinia 23/11/1980 6.9 Normal 0.549 0.564 IT0169 BSC Irpinia 23/11/1980 6.9 Normal 0.946 0.810 IT0390 NCR Umbria-Marche 23/09/1997 6.0 Normal 4.922 4.150 IT0788 ANT L’Aquila 06/04/2009 6.3 Normal 0.260 0.197 IT0789 AQA L’Aquila 06/04/2009 6.3 Normal 4.339 3.950 IT0806 FMG L’Aquila 06/04/2009 6.3 Normal 0.263 0.235 125 Chapter 5 IDA-based damage identification in the San Pietro Bell Tower Table 5.4: Scale factors (SFs) applied to the unscaled accelerograms used for Incremental Dynamic Analysis of the San Pietro Bell Tower. EQ. ID Scale factor IT0014 0.01 0.05 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 IT0164 0.01 0.05 0.10 0.20 0.30 0.50 0.70 1.00 2.00 3.00 5.00 6.00 IT0169 0.01 0.05 0.10 0.20 0.30 0.50 1.00 1.50 2.00 2.50 3.00 3.50 IT0390 0.01 0.05 0.10 0.15 0.20 0.25 0.30 0.40 0.50 0.60 0.70 0.80 IT0788 0.10 0.20 0.30 0.50 1.00 3.00 5.00 7.00 9.00 10.00 12.00 14.00 IT0789 0.01 0.05 0.10 0.15 0.20 0.25 0.30 0.40 0.50 0.60 0.70 0.80 IT0806 0.10 0.20 0.30 0.50 0.80 1.00 3.00 5.00 7.00 10.00 12.00 13.00 reference to Eq. (4.1)). These seismic input IMs have been used in the case of the San Pietro Bell Tower for the construction of IDA curves. In this context, the obtained IDA curve sets relate the local DMs (with reference to shaft, belfry and cusp parts) to the preselected IMs. Similarly to the Brick House (a second selection step based on a rapid visual investigation of the dispersion), the curve sets presenting a relatively large dispersion have been discarded and only the less scattered have been subsequently used for damage identification. In the case of the San Pietro Bell Tower, the definitive most efficient seismic input IMs considered for IDA are the following eleven (11): PGA, RMSA, IC, IA, Sa(T1), ASI (computed limiting the integral of Tab. 4.2 from 0 to the tower’s first-mode period), PGV, RMSV, Sv(T1), IHand Sd(T1). With reference to Eq. (4.3), m∗=11 IMs can be collected in the vector IM∗= (PGA,RMSA,IC,IA,Sa(T1),ASI,PGV,RMSV,Sv(T1),IH,Sd(T1)). While the seismic loadings for IDA are bidirectional, with components applied in the two horizontal directions to the FE model of the bell tower, the IDA curve sets are graphically represented as mean IMs computed using their mean direction versus numerically computed mean DMs, the latter represented by average values weighted over the volume of the numerical elements of each single part of the FE model (volume-averaged damage parameter). The IDA curve sets of the San Pietro Bell Tower (each containing seven (7) curves plus their mean curve) obtained from tensile damage dt(for instance) versus the aforementioned eleven (11) seismic input intensity measures have been investigated for the shaft, belfry and cusp. The IDA curves in terms of dtversus acceleration-related intensity measures are depicted in Fig. 5.8 (PGA, RMSA and IC) and Fig. 5.9 (IA, Sa(T1) and ASI). Fig. 5.10 shows the three plots of the curves obtained with the best velocity-related IMs, such as PGV, RMSV, Sv(T1) and IH. Finally, curves for the shaft, belfry and cusp obtained with Sd(T1) are illustrated in Fig. 5.11. In each graph, in addition to the set of curves, mean curves are depicted with a thick black line. 126