Evaluation of seismic Vulnerability and Strengthening of heritage Buildings. Case Study: The Giralda of Seville

EVALUATION OF SEISMIC VULNERABILITY AND STRENGTHENING OF HERITAGE BUILDINGS. CASE STUDY: THE GIRALDA OF SEVILLE EVALUACIÓN DE LA VULNERABILIDAD SÍSMICA Y REFUERZO DE EDIFICIOS PATRIMONIALES. CASO DE ESTUDIO: LA GIRALDA DE SEVILLA Emilio Romero Sánchez Seville, 2024 Supervisors / Directores Dr. Antonio Morales Esteban Dr. Jaime Navarro Casas PHD DISSERTATION TESIS DOCTORAL EVALUATION OF SEISMIC VULNERABILITY AND STRENGTHENING OF HERITAGE BUILDINGS. CASE STUDY: THE GIRALDA OF SEVILLE / EVALUACIÓN DE LA VULNERABILIDAD SÍSMICA Y REFUERZO DE EDIFICIOS PATRIMONIALES. CASO DE ESTUDIO: LA GIRALDA DE SEVILLA. Emilio Romero Sánchez. Seville, 2024. Ph.D. dissertation made in the Department of Building Structures and Geotechnical Engineering of the Higher Technical School of Architecture in the University of Seville. Also, it has been endorsed by the research group PAIDI TEP-107 “Structures and Geotechnic”, assigned to the University Institute of Architecture and Construction Sciences (IUACC). I AGRADECIMIENTOS Me gustaría dedicar las primeras palabras de este documento en agradecer a todas las personas que han hecho posible el desarrollo de esta tesis doctoral. A mis directores, los Drs. Antonio Morales Esteban y Jaime Navarro Casas, les agradezco profundamente. Sus conocimientos y consejos me han ayudado como guía en este largo recorrido. En particular, quiero expresar mi gratitud a Antonio Morales por haber apostado por mí desde mis inicios como investigador hasta la actualidad. Gracias por su continua confianza, por las horas dedicadas y por su constante preocupación y apoyo. También quiero agradecer a la Dra. Doña Rita Bento por acogerme y compartir sus conocimientos sobre ingeniería y vulnerabilidad sísmica. Su colaboración durante los meses de estancia en el Instituto Superior Técnico de la Universidade de Lisboa ha sido de gran ayuda para el desarrollo de este trabajo. A mis compañeros del grupo TEP-107 “Estructuras y Geotecnia”, donde se enmarca esta investigación, por su ayuda y ánimos durante todo este periodo. Gracias por hacerme sentir como uno más desde el primer momento. Agradezco también a mis compañeros de la Sala de Investigadores por los buenos ratos tan necesarios para desconectar durante el trabajo. Agradecer a Jaime de Miguel por los buenos momentos de risas y ánimos. Gracias María Victoria por tus consejos, estrecha colaboración y amistad. A mis compañeros y amigos del Instituto Superior Técnico de Lisboa, especialmente, a Madalena Ponte, por su cálida acogida desde el primer momento y por hacerme sentir parte del grupo. Quiero expresar mi profundo agradecimiento a todas aquellas personas que me han apoyado y ayudado directa o indirectamente. En este sentido, me gustaría hacer especial relevancia a mis amigos Manuel Alejandro, Miguel y José Carlos, por sus ánimos y apoyo constante. Manuel Alejandro agradezco tu ayuda, apoyo y consejos en todo momento, compartiendo tu experiencia en el mundo de la investigación. Y, por supuesto, agradecer a mi familia por su apoyo incondicional, consejos y ánimos desde el primer momento. Especialmente, a mis padres por creer en mí dese el inicio, apoyarme y animarme siempre. A mi hermana, por sus ánimos. A Irene, por su apoyo constante y sus valiosos consejos desde el inicio de este trabajo. II III FINANCIAL SUPPORT The author of this document wishes to express explicit gratitude to the different institutions that have contributed to the financial support of this Ph.D. dissertation: - The author of this work has been the beneficiary, for four years, of a predoctoral contract for University Teacher Training (FPU), in the 2019 call (ref. FPU2019/03597), financed by the Ministry of Universities of the Government of Spain. Likewise, linked to programme, an aid was obtained to carry out a three-month research stay at the Higher Technical Institute of Lisbon (ref. EST23/00025). - Furthermore, since its inception, this thesis has been supported and closely linked to the objectives set out in the research project of the Andalusian FEDER Programme entitled “Project for a cultural heritage resilient to earthquakes. Case studies: the Mosque of Córdoba and the Giralda of Seville” (ref. US-1380730). - To the “University Institute of Architecture and Construction Sciences” (IUACC) of the University of Seville. SOPORTE ECONÓMICO El autor de este documento desea expresar un explícito agradecimiento a las diferentes instituciones que han contribuido a la financiación de la presente tesis doctoral:  El autor de este trabajo ha sido beneficiario, durante cuatro años, de un contrato predoctoral de Formación del Profesorado Universitario (FPU), en la convocatoria de 2019 (ref. FPU2019/03597), financiado por el Ministerio de Universidades del Gobierno de España. Igualmente, ligada a dicha programa, se obtuvo una ayuda para la realización de una estancia de tres meses en el Instituto Superior Técnico de Lisboa (ref. EST23/00025).  Además, desde sus inicios, esta tesis ha estado financiada y estrechamente ligada a los objetivos expuestos en el proyecto de investigación del Programa FEDER de Andalucía, “Proyecto para un patrimonio cultural resiliente a los terremotos. Casos de estudio: la Mezquita de Córdoba y la Giralda de Sevilla” (ref. US-1380730).  Al “Instituto Universitario de Arquitectura y Ciencias de la Construcción” (IUACC) de la Universidad de Sevilla. IV INDEX Abstract 1 Resumen 3 PART A I. Introduction / Introducción 7 II. Objectives 27 III. Methodology 28 IV. Case Study Building: Giralda Tower of Seville 31 V. Summary of the Results and their Discussion 41 Section 1: Analysis of the historical settlements. 41 Section 2: Numerical modelling, seismic assessment and damage analysis. 52 Section 3: Impact of the soil-foundation-structure interaction in the seismic behaviour of the tower. 68 Section 4: Strengthening methods. 78 VI. Conclusions / Conclusiones 83 References 91 List of Figures and Tables 101 V PART B I. Publications in JCR/SJR Journals 107 SECTION 1 Article 1: Analysis of the Historical Settlements of the Giralda. Article 2: Analysis of the Giralda tower geotechnical profile and its settlements. SECTION 2 Article 3: Numerical modelling for the seismic assessment of complex masonry heritage buildings: the case study of the Giralda tower. Article 4: Failure and damage analysis of the Giralda tower of Seville under different non-linear static and dynamic seismic loadings. SECTION 3 Article 5: Impact of the soil-foundation-structure interaction in the seismic behaviour of a heritage masonry tower. II. Book chapters Book chapter: Preliminary evaluation of the soil-structure interaction on the seismic behaviour of a complex masonry tower: the Giralda tower of Seville. III. Conferences Communications Conference 1: Seismic assessment of historic complex towers. The case study of the Giralda tower. Conference 2: Preliminary seismic analysis of Giralda tower applying a finite element model. Conference 3: Preliminary seismic assessment of the soil-structure interaction effects of a complex masonry tower. ANNEX A. Scientific Relevance of the Indexed Journals BLOQUE A 6 INTRODUCTION / INTRODUCCIÓN 7 1. INTRODUCTION General aspects Europe is characterised by a rich and diverse variety of cultural heritage buildings. Among its numerous types of ancient buildings, masonry towers are one of the fundamentals of its cultural richness as they embody the history and the development of several regions. They can be found widespread in quite a few countries in Europe and they represent one of the main sources to understand the fortress construction. Therefore, preserving its cultural heritage is a current and challenging issue for the European Union (EU). In that sense, all the countries are committed to preserving and to improving their cultural heritage through policies and programmes. The structural security assessment of heritage buildings is a paramount task. Generally, ancient towers were constructed with masonry walls and they were designed to withstand just gravity loads (Formisano & Ademovic, 2022). As a result, they present several features that reduce their horizontal resistance (Casolo et al., 2013): i) limited ductility and low tensile strength of the masonry; ii) heterogeneity of the structural and constructive materials; iii) complex and irregular geometries; iv) leaning phenomena; and iv) a slender configuration. Also, they can be found indistinctly in regions with low to high seismic hazard in Europe. Consequently, masonry towers suffered from serious damage during past earthquakes. Such is the case of the effects of the 2012 Emilia earthquake (Mw=6.1), which resulted in serious damage to the belfry of towers, churches and several masonry fortresses (Cattari, Degli Abbati, et al., 2014; Sorrentino et al., 2014), the 2016 Amatrice earthquake (Fiorentino et al., 2018) or the 2009 L’Aquila earthquake (Augenti & Parisi, 2010). Furthermore, a recent seismic event, the 2023 Marrakesh’s earthquake, seriously affected heritage buildings, particularly the Islamic minaret of the Koutubia Mosque. This is one of three largest Almohad minarets in the world, as discussed in (Jiménez Martín, 2018). Thus, if located in areas prone to earthquakes, masonry towers can be potentially affected to seismic damage. In some cases, if affected, it could be highly important for the cultural, social and economic development of the region as they represent the iconic symbol of regions and cities. Therefore, assessing their seismic behaviour seems crucial to guarantee their structural safety so that their historical and cultural value can be preserved. By doing so, it is also possible to prevent the loss of such part of the culture but also to minimize the loss of fatalities and economic income. This has been the main goal of past scientific and engineering works on the seismic assessment of masterpiece buildings as presented in (Micelli & Cascardi, 2020; Rossi et al., 2015; Vuoto et al., 2022). Assessing the seismic performance of heritage buildings is particularly important in earthquake-prone regions like the south of the Iberian Peninsula (M. Requena-Garcia-Cruz et al., 2023). This region is characterised by a moderate seismic activity due to the near convergence between the Eurasian and African tectonic plates (Amaro-Mellado, Morales- Esteban, Asencio-Cortés, et al., 2017). Furthermore, Seville is located on soft alluvial strata that is known to increase the effects of earthquakes (Amaro-Mellado, Morales-Esteban, & Martínez-Álvarez, 2017; M. v. Requena-Garcia-Cruz et al., 2022). Therefore, this area may be affected by large earthquakes (Mw>7) with a long-return period, which makes the population unacquainted with them (Fazendeiro Sá et al., 2016). The city of Seville (Spain) has suffered from several past earthquakes, such as that of Lisbon in 1755 (Mw=8.5) and later of San Vicent cape in 1969 (Mw=8) (Sá et al., 2018). These historical earthquakes caused severe damage BLOQUE A 8 to several masonry towers of the city, including the Giralda tower as mentioned in (Gentil, 1989). The cultural heritage has a great wealth and diversity in Seville. It is a reference of the historical and social identity for its population. It is also one of the bases of the economic and cultural development of the city. In this sense, the Giralda tower of the Cathedral of Seville is one of most representative buildings of the city and the country. It was declared as a Word Heritage Site by the UNESCO owing to its patrimonial value in 1987. It has the maximum level of protection as well: Outstanding Universal Value. Historical settlements analysis and foundations of heritage buildings The analysis and prediction of damage that can be caused by the differential settlements in masonry buildings is an important issue in the behaviour and retrofitting analysis of this type of structures (Giardina et al., 2020). Other works analyse the behaviour of the masonry buildings under the effect of different types of settlements and soils (Ferlisi et al., 2020), such as soft soils (Peduto et al., 2019). After an exhaustive search of similar works, a lack of studies about the soil, the foundation and the historical settlements of heritage buildings has been noted. The analysis of the damage caused by historical settlements (Micelli & Cascardi, 2020) and the incidence of the soil in this type of buildings is necessary (Ivorra et al., 2010). In the analysis of the structural behaviour of these buildings it is important to bear in mind account the historical movements of the foundations to detect future damage and vulnerabilities. These buildings have generally had several constructions phases which have caused movement in the foundation due to load increases. Numerous research works have recently investigated the structural behaviour of heritage buildings, using different structural analysis methods (Malcata et al., 2020). In this study, the non-linear analysis method and two-modelled approach were employed to assess the results obtained from two software tools. Most of these studies have focused on the assessment of the seismic behaviour of these buildings (Degli Abbati et al., 2019a) (D’Ayala & Paganoni, 2011). Very few have applied the soil-structure interaction for this analysis (De Silva et al., 2015). In (de Silva, Ceroni, et al., 2018) a non-linear static (push-over) analysis was applied in the model which considered the soil and the boundary conditions of the building. Then, the results were compared with a non-linear dynamic analysis taking into account the soilfoundation interaction. In (de Silva, Pitilakis, et al., 2018), several types of interaction (surrounding buildings and soil-structure) were analysed comparing numerical models with insitu dynamic surveys. In that work, the soil model was simplified by means of springs, simulating the soil-foundation impedance. Also, some previous studies worked on the structural assessment of the heritage bell towers (Milani & Clementi, 2019)(Hadzima-Nyarko et al., 2017). Furthermore, other studies were centred on the characterisation of the buildings’ materials (Pineda, 2016). In this study, an increase in the fundamental period of the structure owing to the structural material was identified. It therefore analysed the utilisation of traditional materials in order to optimise future repair works. It can be observed that there is some research concerning the structural and soil-structure interaction for heritage buildings. However, to the author´s knowledge, there are not many studies that analyse in detail the foundation and its behaviour for these historical structures. Focusing on the case study building of this this research, several previous works about the case study building and the nearby area have been used to carry out an accurate definition of the geotechnical model, the foundation, the construction phases and the boundary conditions. According to the definition of the geotechnical model, several works performed at the base of INTRODUCTION / INTRODUCCIÓN 9 the tower (Barrios Padura et al., 1997) and in the nearby area (Diz-Mellado et al., 2021) have been used. A thorough and proper characterisation of the tower foundation has been done taking into account the different historical hypothesis (P. R. Pérez, 1988), borehole studies (VORSEVI, 1988) and the archaeological campaigns (1996-1998) (Tabales Rodríguez, 1998; Tabales Rodríguez et al., 1996). In addition, the different modifications that the buildings have undergone over time have been considered, based on the studies realised and the literature published (Jiménez Martín, 1993, 1998). Numerical modelling and seismic assessment of heritage buildings Structural assessment plays an essential role in the diagnosis and safety analysis of ancient buildings (Lagomarsino & Cattari, 2015). Knowledge about the evolution of the building in its history is essential: geotechnical properties, phases of construction, rehabilitation interventions, materials and the geometry of the structure. In that sense, the seismic vulnerability has been studied in a vast number of research works due to the uncertainties in the performance and in the complexity of this type of buildings (Degli Abbati et al., 2019b). Seismic assessment plays an important role in the preservation and in the safety of architectural heritage, allowing the development and implementation of appropriate retrofitting strategies. These buildings were not constructed considering seismic actions and they are very vulnerable to lateral loads. In that sense, the ancient towers are very remarkable case study because they have some geometrical features that increment the seismic vulnerability (Sarhosis et al., 2018; Valente & Milani, 2018). Furthermore, past earthquake damage assessments have shown that ancient buildings are very vulnerable in a seismic event (Cattari, Abbati, et al., 2014; Parisi & Augenti, 2013; Saisi & Gentile, 2015). The main difficulty in the structural assessment of ancient buildings is to obtain the mechanical properties of the materials, especially in masonry buildings, due to their heterogeneous properties and the numerous parameters (Cattari, Calderoni, et al., 2021; Kržan et al., 2015). Due to the uncertainties in the mechanical parameters of ancient masonry buildings, an in situ survey campaign is required to calibrate the numerical model (Ponte et al., 2021). These surveys campaigns are composed of Non-Destructive Test (NDT) due to the high level of protection of the ancient buildings. In this regard, the NDT have been discussed and illustrated in the literature (Boschi et al., 2019; McCann & Forde, 2001). The ambient vibration test is the main experimental method used to evaluate the dynamic behaviour of the structures and to calibrate the numerical models (Gentile & Saisi, 2007; Nohutcu, 2019). Moreover, several research works analyse the different mechanical properties of masonry walls with the aim of being able to be used as reference values. In (Boschi et al., 2019) the results of 105 in situ tests performed in a great number of brick masonry typologies were shown. In (Kržan et al., 2015), a range of mechanical properties reference parameters was provided for a great variety of stone and brick masonry, based on experimental tests and data from the literature. The numerical modelling of historic monuments, generally characterised by large dimensions and complex and irregular geometric features, is a difficult task. As suggested in (Cattari, Calderoni, et al., 2021), robust nonlinear numerical models are required to perform accurate and reliable seismic analyses. The Equivalent Frame Method (EFM) and the Finite Element Method (FEM) are the most used approaches in this type of analysis (M. V. Requena-Garcia- Cruz, Cattari, et al., 2023). The EFM discretises the URM walls in piers and spandrels connected with rigid links since seismic damage is observed to be concentrated in these two elements (Lagomarsino, 2006). Given that, the FEM is the most widely used for heritage masonry buildings due to provide a more detailed damage analysis for more exhaustive analyses (Cattari, Calderoni, et al., 2021; Cattari, Camilletti, et al., 2021; Cattari & Magenes, BLOQUE A 10 2022). In fact, due to the complex and irregular geometry of such structures of masonry towers, the FEM is particularly recommended for the analysis of such structures as used in (Bartoli et al., 2016, 2019; D’Ambrisi et al., 2012; Micelli & Cascardi, 2020; Pieraccini et al., 2014; M. V. Requena-Garcia-Cruz, Romero-Sánchez, et al., 2023; Vuoto et al., 2022). In this context, different modelling approaches and analysis methods are considered for the seismic assessment depending on the characteristics of the structure and the level of accuracy of the analysis and the results: micro-modelling, macro-modelling and homogenisation (Cattari, Calderoni, et al., 2021; D’Altri et al., 2020; Pineda et al., 2010). In that sense, the correct definition of the modelling strategy is essential. Macro-modelling is more commonly used for the global behaviour of a full-scale structure. Moreover, this is applied in the case of solid thick walls so that the stress across or along the macro length will be fundamentally uniform (Pineda, 2016). In this regard, the masonry is modelled as an isotropic or anisotropic homogeneous continuum (Degli Abbati et al., 2019b). One of the most complex tasks in this type of modelling is to define the anisotropic inelastic behaviour of the material (Petracca, Pelà, Rossi, Oller, et al., 2017). Employing solid 3D FE, which represents the mechanical behaviour of the masonry in a continuous form, allows the maintenance of cost-effective computational efficiency (Tiberti et al., 2016). In this context, there are a great number of research works in which different types of modelling are applied (Milani et al., 2012; Milani & Clementi, 2021). Furthermore, as suggested in (Valente & Milani, 2016), the FE method provides the most reliable results in the case of slender towers with a predominant bending behaviour, which could be particularly important in the case of the Giralda tower. The seismic vulnerability of ancient buildings is generally performed considering nonlinear analyses: static pushover and/or incremental dynamic, e.g. (Lagomarsino & Cattari, 2015). Furthermore, the different failure mechanisms can be assessed applying the kinematic limit analysis approach (Milani, 2019). Static and dynamic analyses have been widely used in research and engineering works. Furthermore, the different seismic codes propose both as valid test methods for the analysis of existing buildings (Aggiornamento Delle ‘Norme Tecniche per Le Costruzioni’» Di Cui al Decreto Ministeriale 17 Gennaio 2018. (Italian Guideline), 2018; Eurocode-8: Design of Structures for Earthquake Resistance. Part 3: Assessment and Retrofitting of Buildings, 2005). The implementation of the nonlinear static analysis (NLSA) in 3D numerical models is an overwhelming method to correctly predict the global damage in the numerical model and active failure mechanisms (Milani & Clementi, 2021). Comparing both of such well-known types of analyses can offer useful information on how to address the seismic assessment of masonry heritage buildings as suggested in (Milani & Valente, 2015; Valente & Milani, 2016). The NLSA results represent the envelope of all possible structural responses and it is possible to apply in case of global behaviour analysis, taking into account the inherent limitations (Milani et al., 2012). The nonlinear dynamic analysis (NLDA) are more accurate methods to simulate the structural behaviour of ancient masonry buildings. It should be noted that dynamic excitation activates a higher vibration mode, which could be associated with damage in the weak upper levels of the tower, especially in towers with large hollows at the top (Valente & Milani, 2018). However, the NLDA needs a high computational effort and calculation time, compared to the NLSA. The seismic behaviour of masonry towers is an important issue due to the large number of structures of this typology in the built heritage around the word. In this respect, many works employ the FEM for the analysis of masonry towers, such as (Valente & Milani, 2016), where eight masonry towers were analysed, using detailed 3D FEM. This work showed a good agreement between the results of the nonlinear pushover and the dynamic analyses. However, the results of the pushover analysis are more conservative. In (Torelli et al., 2020), the seismic assessment methods proposed by the Italian codes for the assessment of the seismic vulnerability in cultural heritage buildings were analysed in a masonry tower. In (Shehu, 2021), INTRODUCTION / INTRODUCCIÓN 11 the limitations and the possibilities of the pushover analysis with the FEM, using three masonry towers as a case study, were discussed. In (Peña et al., 2010), three different numerical FEM of old masonry towers were carried out with several complexity levels, to compare the results. In that sense, several differences in the damage patterns were detected for an irregular masonry tower by applying both types of non-linear analyses. It should be noted that the Spanish seismic code (Spanish Seismic Code [Norma de Construcción Sismorresistente: Parte General y Edificación (NCSE-02)], 2002) does not provide any specific regulations or guidance for the seismic safety analysis of heritage buildings. Soil-foundation-structure interaction in the seismic behaviour of heritage buildings Boundary conditions are also particularly important in the assessment of ancient buildings. Generally, the seismic analyses of such buildings were carried out considering the fixed-based condition due to its simplicity (Milani & Valente, 2015). However, as it was obtained in several works, the soil-foundation-structure interaction (SFSI) could highly affect the seismic performance of buildings, particularly high-rise over soft strata (M. V. Requena-Garcia-Cruz, Romero-Sánchez, et al., 2022), since (Can Altunışık et al., 2023; Mylonakis & Gazetas, 2000): i) settlements can affect the structural behaviour; ii) soft layers of soil with high deformability can amplify the seismic waves; and, iii) the dynamic behaviour of the structures could be modified by the presence of the soil. To account for the SFSI, several modelling approaches were employed in the literature. However, the most used ones are the Nonlinear Winker (BNWM) and the direct methods (Anand & Satish Kumar, 2018; Bayraktar & Hökelekli, 2020; M. V. Requena-Garcia-Cruz, Bento, et al., 2022). The BNWM simulates the soil as nonlinear springs, leading to several simplifications and assumptions. Nevertheless, as presented in (M. V. Requena-Garcia-Cruz, Bento, et al., 2022), it can provide a preliminary approach to the effects of the SFSI in the seismic performance of a building. Contrariwise, the direct method assumes the continuum modelling of the complete system, soil + foundation + structure, based on the FEM. In (Fathi et al., 2020), modal, static and dynamic analyses were carried out to assess the SFSI on an ancient masonry building. Compared to the fixed-based results, it was obtained that the damage was higher if the SFSI was accounted for. In (Özmen & Sayın, 2023; Tongaonkar & Jangid, 2003) masonry bridges were assessed to evaluate the influence of the soil. It was obtained that the surrounding soil showed significant effects on the response of the bridge, particularly in the values of horizontal displacements. Particularly, on URM ancient towers, some works evaluated the effects of the SFSI on these buildings. In (Piro et al., 2020), 2D analyses were carried out to evaluate the dynamic performance of a URM tower using the FEM. In (Shabani et al., 2022), linear dynamic analyses were carried out to calibrate a URM tower numerical model based on OMA and considering the SFSI. In (De Silva et al., 2015), the dynamic behaviour of a similar building in Italy was assessed though an equivalent oscillator and the FEM. It was concluded that the simplified method provided results in good agreement with the FEM. In (de Silva, Ceroni, et al., 2018), this last work was improved by performing both static and dynamic analyses to assess the seismic safety of the URM tower. It was obtained that, although the collapse mechanisms did not differ from static and dynamic analyses, the effects of the soil amplified the seismic loading. All of these works on ancient URM buildings concluded that detailed numerical models are needed to properly account for the SFSI effects. Also, despite the influence of the SFSI on the BLOQUE A 12 dynamic behaviour of these structures, a lack of guidance in the literature and in the codes can be found to properly quantify the SFSI. Structural strengthening methods of heritage buildings To stregtening ancient masonry structures, several requirements aim to safeguard the cultural heritage’s authenticity. The retrofit solutions implemented must fulfil several requirements: preserving the monument´s authenticity, minimize the visual impact through minimal intervention and ensure compatibility and durability (Ponte et al., 2023). This research focuses on the calibration of the retrofitting techniques applying a masonry panel numerical model. The numerical simulations can be latter applied to the heritage building numerical model. There is insufficient data for nonlinear characterization of the ancient masonry and its strengthening methods. Consequently, it is crucial to develop this type of analysis that combines laboratory test results with numerical modelling (Ponte et al., 2019). This way, a 3D FE model has been implemented using the macro-modelling approach. This numerical model has been used to reproduce numerically a cyclic laboratory test. It has been used to simulate the original masonry walls and that with the different retrofitting methods. In this regard, the numerical simulation was carried out withing the framework of OpenSees software (McKenna et al., 2000), using the pre- and post-processor STKO (Petracca, Candeloro, et al., 2017). A similar procedure was applied in (Garcia-Ramonda et al., 2023), where a simple 2D numerical model was developed to validate the experimental results of retrofitting techniques. In this study, (Garcia-Ramonda et al., 2023) analysed the in-plane shear behaviour of double-leaf historic clay brick masonry wall. The aim is to provide new insights into understanding these experimental tests. It investigates both unreinforced walls and those retrofitted with textilereinforced mortar and steel-reinforced grout, focusing on low-strength mortar joints. In (Ponte et al., 2019), a numerical model applying macro-modelling approach were carried out to compare the previous laboratory test under cyclic in-plane loading. In this work, the calibration procedure for the model involves adjusting its behaviour to match the outcomes of experimental tests conducted on rubble stone masonry piers using air lime mortar. The force– displacement diagram, damage pattern, failure mode, and dissipated energy show strong agreement between the experimentally tested piers and their numerical simulations. In this context, in (Sharma et al., 2022), several cyclic in-plane shear-compression laboratory test on rubble stone masonry piers, which are highly representative of historical construction in Portugal, were numerically reproduced. This study involver conducting a parametric analysis and comparing the results with relevant existing research. Due to the importance of characterizing the retrofit solutions for ancient masonry structures, there are many studies that experimentally test these solutions. In (Garcia-Ramonda et al., 2022) several samples of brick masonry with different configurations were tested: unreinforced, repaired and retrofitted. Basalt Textile Reinforced Mortar were applied and tested. This retrofitting technique is composed by bidirectional grid of basalt fiber embedded in hydraulic lime mortar on both faces of wall. This work concluded that this technique is sustainable for retrofitting the brick masonry wall and postearthquake repair. In (Ponte et al., 2023), several specific retrofit solutions for historic masonry buildings were teste applying in-plane quasi-static cyclic test. These strengthening methods are the following: the injection of mortar and FRCM systems, with glass and carbon meshes. The experimental results were compared with the other literature results of equivalent strengthening solutions. In this context, an accurate review of the different research works about the textile-reinforced mortar for masonry walls was carried out in (Boem, 2022). The study compares the main features of several experimental INTRODUCTION / INTRODUCCIÓN 13 test, addressing both in-plane and out-of-plane behaviour. Furthermore, numerical modelling strategies and design approaches were discussed. Conclusions The literature review revealed that there are very few previous studies carried out in which the soil and the structure are jointly considered for the analysis of the seismic behaviour of heritage buildings. Although these types of studies exist, most of them focused on buildings of lower cultural value, in relation to the building under study, or they implement very simple evaluation models. Furthermore, the previous work carried out in the Giralda of Seville, with the aim of evaluating its seismic vulnerability, are practically non-existent. Main contributions of this Thesis The main contributions of this thesis are:  Development of a new methodology for the seismic evaluation of heritage buildings based on the application of the OpenSees open-source framework. It has been able to perform the dynamic analysis in an acceptable computational time, despite being a very complex numerical model.  Assessment of the seismic vulnerability of the Giralda tower of Seville, which had not been performed to date.  Modelling of the complete system of the tower, soil + foundation + structure, to develop a detailed FEM model. To achieve this, URM macro-mechanical elements and the direct method have been used within the OpenSees framework. A lack of research focusing on this specific type of modelling using the OpenSees framework can be found to date. Furthermore, this calibrated numerical FEM can be used in future analyses of the tower.  This study provides useful information and knowledge about the seismic security of one of the most iconic masonry towers in the world, declared as UNESCO Word Heritage Site of exceptional value. This data could be useful for the enhancement of its conservation and for future rehabilitation activities. In fact, the digital information generated (geometrical and numerical FEM) will be important for the development of future works and in the scope of scientific research activity.  Dealing with an open issue in earthquake engineering, which is the consideration of the effects of the soil and the foundation in seismic analyses, particularly in heritage ones.  Comparison between the effects of historic earthquakes in the past on the tower and the results from numerical analysis considering historical records.  Development of a methodology to account for the SFSI. Assessment of the impact of the SFSI on heritage towers. The SFSI is not usually considered in the seismic analyses of such buildings, despite being proved to affect in certain cases the seismic performance of slender URM buildings.  Analysis of the seismic response and the potential risk of damage of the tower under an earthquake probabilistic scenario based on ground motions considering the seismic action of the Spanish code. BLOQUE A 14 Organization and Structure of the Thesis This thesis has been prepared in accordance with the regulatory requirements set by the University of Seville for Ph.D. Dissertations under the modality of a compendium of publications. Along these lines, this document is structured in two main sections, followed by a final annex that compiles all the bibliography used, as well as the scientific relevance of the publications included in this Thesis. Along these lines, block A includes a brief introduction justifying the work, the definition of the objectives of the Thesis, as well as the methodology proposed to achieve them. After this, a presentation of the building under study is conducted, continuing with a brief summary of the results obtained in the different publications included in the compendium. The chapter ends with the definition of the main conclusions obtained in this work, as well as future lines of research. For its part, Block B is made up of the different indexed scientific articles included in this compendium, as well as several conference proceedings linked to the Thesis, all of them indexed in WoS and/or Scopus. These articles have been published (or are in an advanced state of review) in high-impact journals indexed in the Journal Citation Reports (JCR): Bulletin of Earthquake Engineering (Q1), International Journal of Architectural Heritage (Q2) and Engineering Failure Analysis (Q1). The results achieved by this thesis have been grouped into four differentiated sections, which respond to the different specific objectives defined in chapter 2 of this first block: Section 1: Analysis of the historical settlements. In this section, the historical settlements of the Giralda tower have been analysed. With this aim, a detailed characterisation of the foundation and its geotechnical profile has been carried out. Furthermore, a historical analysis of the different construction phases, the loads, the time of execution and consolidation between phases has been conducted. For that, several 2D Finite Element Models (FEM) has been developed in order to define the different important soil profiles in the settlements of the tower. Then, an accurate 3D FEM has been created to accurately analyse the historical settlements. Finally, the relation between the historical settlement and the verticality of the tower has been explored. The following section contain the following publications:  Article 1: Romero Sánchez, E., Morales Esteban, A., Navarro Casas, J. (2022). Analysis of the Historical Settlements of the Giralda. International Journal of Architectural Heritage, 17(8), 1312-1330.  Article 2: Romero Sánchez, E., Morales Esteban, A., Navarro Casas, J. (2022). Analysis of the Giralda tower geotechnical profile and its settlements. International Journal of Computational Methods and Experimental Measurements, 10(1), 1-12. INTRODUCTION / INTRODUCCIÓN 15 Section 2: Numerical modelling, seismic assessment and damage analysis. In this section, the 3D Finite Element Model (FEM) of the Giralda tower has been developed. To achieve this, the structure and material have been accurately analysed. The available information of previous characterization projects and the graphic information of the building have been tested and completed with different in-situ surveys. In this regard, a sensitivity analysis has been conducted on several variables that affect the FEM. Subsequently, a rigorous calibration of the numerical model has been performed. Finally, both nonlinear static and dynamic analyses have been carried out in order to assess the seismic safety and the damage patterns in the tower. The results of the second section are summarized in the following sections:  Article 3: Romero-Sánchez, E., Morales-Esteban, A., Bento, R., Navarro-Casas, J. (2023). Numerical modelling for the seismic assessment of complex masonry heritage buildings: the case study of the Giralda tower. Bulletin of Earthquake Engineering, 21(9), 4669-4701. JCR (Q1).  Article 4: Romero-Sánchez, E., Requena-García Cruz, M. V., Morales-Esteban, A. Failure and damage analysis of the Giralda tower of Seville under different non-linear static and dynamic seismic loadings. Bulletin of Earthquake Engineering. Under second revision in 15-05-2024. JCR (Q1).  Conference 1: Romero-Sánchez, E., Requena-García Cruz, M. V., Morales-Esteban, A. Seismic assessment of historic complex towers. The case study of the Giralda tower. COMPDYN Proceedings. 2023.  Conference 2: Romero-Sánchez, E., Requena-García Cruz, M. V., Morales-Esteban, A. Preliminary seismic analysis of Giralda tower applying a finite element model. CITE. 2023. Section 3: Impact of the soil-foundation-structure interaction in the seismic behaviour of the tower. This section focuses on investigating the influence of the Soil-Foundation-Structure Interaction (SFSI) on the seismic performance of the ancient Giralda tower. To achieve this, a complex numerical model considering the soil, foundation and structure have been developed and calibrated. The characterization of the soil layers has been completed through several in-situ test carried out in the nearby area. A preliminary nonlinear static analysis has been carried out to verify the numerical model and obtain a first approximation of the SFSI effects. Subsequently, nonlinear dynamic analysis has been applied to assess the influence of the SFSI on the tower. The results for both fixed and SFSI conditions have been analysed and compared. The results of the third section are summarized in the following contributions:  Article 5: Romero-Sánchez, E., Requena-García Cruz, M. V., Morales-Esteban, A. Impact of the soil-foundation-structure interaction in the seismic behaviour of a heritage masonry tower. Engineering Failure Analysis. Under second review in 13-05-2024. JCR (Q1). BLOQUE A 22 supone el modelado continuo del sistema completo, suelo + cimentación + estructura, basado en el FEM. En (Fathi et al., 2020), se llevaron a cabo análisis modales, estáticos y dinámicos para evaluar el SFSI en un antiguo edificio de mampostería. En comparación con los resultados de base fija, se obtuvo que el daño era mayor si se contabilizaba el SFSI. En (Özmen & Sayın, 2023; Tongaonkar & Jangid, 2003) se evaluaron puentes de mampostería para evaluar la influencia del suelo. Se obtuvo que el suelo circundante presentó efectos significativos en la respuesta del puente, particularmente en los valores de los desplazamientos horizontales. En particular, en las torres antiguas de la URM, algunos trabajos evaluaron los efectos del SFSI en estos edificios. En (Piro et al., 2020), se realizaron análisis 2D para evaluar el desempeño dinámico de una torre URM utilizando el FEM. En (Shabani et al., 2022) se aplicaron análisis dinámicos lineales para calibrar un modelo numérico de torre de mampostería basado en OMA y considerando el SFSI. En (De Silva et al., 2015), se evaluó el comportamiento dinámico de un edificio similar en Italia mediante un oscilador equivalente y el FEM. Se concluyó que el método simplificado proporcionó resultados en buena concordancia con el FEM. En (de Silva, Ceroni, et al., 2018b), este último trabajo se mejoró realizando análisis tanto estáticos como dinámicos para evaluar la seguridad sísmica de la torre URM. Se obtuvo que, aunque los mecanismos de colapso no difirieron de los análisis estáticos y dinámicos, los efectos del suelo amplificaron la carga sísmica. Todos estos trabajos en edificios antiguos de URM concluyeron que se necesitan modelos numéricos detallados para tener en cuenta adecuadamente los efectos del SFSI. Además, a pesar de la influencia del SFSI en el comportamiento dinámico de estas estructuras, se puede encontrar una falta de orientación en la literatura y en las normativas vigentes para cuantificar adecuadamente el SFSI. Métodos de refuerzo de edificios patrimoniales Para reforzar las antiguas estructuras de mampostería, existen varios requisitos que tienen como objetivo salvaguardar la autenticidad del patrimonio cultural. Las soluciones de refuerzo implementadas deben cumplir varios requisitos: preservar la autenticidad del monumento, minimizar el impacto visual mediante una mínima intervención y garantizar la compatibilidad y durabilidad (Ponte et al., 2023). Esta investigación se centra en la calibración de técnicas de rehabilitación aplicando un modelo numérico a escala panel. Las simulaciones numéricas se pueden aplicar posteriormente al modelo numérico global del edificio patrimonial. No hay datos suficientes para la caracterización no lineal de la mampostería antigua y sus métodos de refuerzo. En consecuencia, es crucial desarrollar este tipo de análisis que combine resultados de ensayos de laboratorio con modelado numérico (Ponte et al., 2019). De esta manera, se ha implementado un modelo 3D FEM utilizando el método de macromodelado. Este modelo numérico se ha utilizado para reproducir numéricamente un ensayo cíclico de laboratorio, simulando los muros de mampostería originales y los diferentes métodos de refuerzo. En este sentido, la simulación numérica se realizó aplicando el software OpenSees (McKenna et al., 2000), utilizando el pre- y postprocesador STKO (Petracca et al., 2017). En este contexto, se aplicó un procedimiento similar en (García-Ramonda et al., 2023), donde se desarrolló un modelo numérico 2D simple para validar los resultados experimentales de las técnicas de refuerzo. En este estudio, (García-Ramonda et al., 2023) analizó el comportamiento a cortante en el plano de un muro histórico de mampostería de ladrillos de arcilla de doble hoja. El objetivo es proporcionar nuevos conocimientos para comprender estas pruebas experimentales. Investiga tanto los muros no reforzados como los rehabilitados con INTRODUCTION / INTRODUCCIÓN 23 mortero reforzado con textiles y lechada reforzada con acero, centrándose en las juntas de mortero de baja resistencia. En (Ponte et al., 2019), se llevó a cabo un modelo numérico aplicando un enfoque de macro modelado para comparar el ensayo de laboratorio anterior bajo carga cíclica en el plano. En este trabajo, el procedimiento de calibración del modelo implica ajustar su comportamiento para que coincida con los resultados de ensayos experimentales realizados sobre muestras a escala panel de mampostería utilizando mortero de cal aireada. El diagrama de fuerza-desplazamiento, el patrón de daño, el modo de falla y la energía disipada muestran una fuerte concordancia entre los paneles ensayados experimentalmente y sus simulaciones numéricas. En este contexto, en (Sharma et al., 2022), se reprodujeron numéricamente varios ensayos cíclicos de laboratorio de compresión y cortante en el plano sobre paneles de mampostería de piedra, muy representativos de la construcción histórica en Portugal. Este estudio implica realizar un análisis paramétrico y comparar los resultados con investigaciones relevantes existentes. Debido a la importancia de caracterizar las soluciones de rehabilitación para estructuras de mampostería antiguas, existen muchos estudios que prueban experimentalmente estas soluciones. En (García-Ramonda et al., 2022) se probaron varias muestras de mampostería de ladrillo con diferentes configuraciones: sin reforzar, reparada y rehabilitada. Se aplicaron y ensayaron morteros de basalto reforzados con textiles. Esta técnica de rehabilitación está compuesta por una rejilla bidireccional de fibra de basalto embebida en mortero de cal hidráulica en ambas caras del muro. Este trabajo concluyó que esta técnica es sostenible para la rehabilitación del muro de mampostería de ladrillo y la reparación posterior al sismo. En (Ponte et al., 2023), se probaron varias soluciones de refuerzo específicas para edificios históricos de mampostería aplicando ensayos cíclicos en el plano. Estos métodos de refuerzo son los siguientes: la inyección de mortero y sistemas FRCM, con mallas de vidrio y carbono. Los resultados experimentales se compararon con otros resultados de la literatura sobre soluciones de refuerzo equivalentes. En este contexto, se realizó una cuidadosa revisión de los diferentes trabajos de investigación sobre el mortero reforzado con textil para muros de mampostería en (Boem, 2022). El estudio compara las características principales de varias pruebas experimentales, abordando el comportamiento tanto dentro como fuera del plano. Además, se discutieron estrategias de modelado numérico y enfoques de diseño. Conclusiones De la revisión bibliográfica realizada se observa que son muy escasos los estudios previos desarrollados en los que se considere de manera conjunta el suelo, cimentación y la estructura para el análisis del comportamiento sísmico de edificios históricos. Si bien existen este tipo de estudios, la mayoría se centran en edificios de un menor valor patrimonial en relación con el edificio objeto de estudio o implementan modelos de suelo muy básicos. Además, son prácticamente inexistentes los trabajos previos elaborados en la Giralda de Sevilla con el objeto de evaluar su vulnerabilidad sísmica. Principales contribuciones de la tesis Las principales contribuciones de esta tesis son:  Desarrollo de una nueva metodología para la evaluación sísmica de edificios patrimoniales basada en la aplicación del programa de código abierto OpenSees. En este sentido, se ha podido realizar el análisis dinámico en un tiempo computacional aceptable, a pesar de ser un modelo numérico muy complejo.  Evaluación de la vulnerabilidad sísmica de la Giralda de Sevilla, la cual no se había realizado hasta la fecha. BLOQUE A 24  Modelado del sistema completo de la torre, suelo + cimentación + estructura, para desarrollar un modelo FEM detallado. Para conseguirlo se han utilizado elementos macro mecánicos URM y el método directo dentro del programa OpenSees. Hasta la fecha, se puede encontrar una falta de investigación centrada en este tipo específico de modelado utilizando el marco OpenSees. Además, este FEM calibrado se podrá utilizar en futuros análisis de la torre.  Este estudio proporciona información y conocimientos útiles sobre la seguridad sísmica de una de las torres de mampostería más emblemáticas del mundo, declarada Patrimonio Mundial de la UNESCO de valor excepcional. Estos datos podrían ser útiles para mejorar su conservación y para futuras actividades de rehabilitación. De hecho, la información digital generada (geométrica y numérica FEM) será importante para el desarrollo de futuros trabajos y en el ámbito de la actividad científica.  Consideración de los efectos del suelo y la cimentación en los análisis sísmicos, particularmente en los patrimoniales. Lo cual, se trata una de las cuestiones pendientes en la ingeniería sísmica como es la  Comparación entre los efectos sobre la torre de terremotos históricos pasados y los resultados del análisis numérico considerando registros históricos.  Desarrollo de una metodología para considerar el SFSI. Evaluación del impacto del SFSI en las torres patrimoniales. El SFSI no suele considerarse en los análisis sísmicos de este tipo de edificios, a pesar de que se ha demostrado que afecta en ciertos casos el comportamiento sísmico de edificios URM esbeltos.  Análisis de la respuesta sísmica y el riesgo potencial de daño de la torre bajo un escenario probabilístico de terremoto basado en acelerogramas seleccionados considerando la acción sísmica del código español. Organización y estructura de la tesis Esta tesis se ha elaborado siguiendo con las exigencias normativas marcadas por la Universidad de Sevilla para la redacción de Tesis Doctorales bajo la modalidad de compendio de publicaciones. En esta línea, el presente documento se estructura en dos grandes bloques más un anexo final que recopila toda la bibliografía utilizada, así como la relevancia científica de las publicaciones incluidas en esta Tesis. En esta línea, el bloque A incluye una breve introducción justificativa del trabajo, la definición de los objetivos de la Tesis, así como la metodología planteada para alcanzarlos. Tras ello, se realiza una presentación del edificio objeto de estudio para pasar a mostrar un resumen de los resultados obtenidos en las diferentes publicaciones incluidas en el compendio. El capítulo finaliza con la definición de las principales conclusiones obtenidas en este trabajo, así como futuras líneas de investigación. Por su parte, el Bloque B lo componen los diferentes artículos científicos indexados incluidos en este compendio, así como las distintas comunicaciones a congresos indexadas en WoS y/o Scopus. Dichos artículos han sido publicados (o están en un avanzado estado de revisión) en revistas de alto índice de impacto indexadas en el Journal Citation Reports (JCR): Bulletin of Earthquake Engineering (Q1), International Journal of Architectural Heritage (Q2) y Engineering Failure Analysis (Q1). Además, se incluye un artículo publicado en la revista International Journal of Computational Methods and Experimental Measurements perteneciente al Q4 de SJR. Los resultados alcanzados por esta tesis se han agrupado en cuatro secciones diferenciadas, que dan respuesta a los diferentes objetivos específicos definidos en el capítulo 2 de este primer bloque: INTRODUCTION / INTRODUCCIÓN 25 Sección 1: Análisis de los asientos históricos. En este apartado se han analizado los asientos históricos de la Giralda. Para ello, se ha realizado una caracterización detallada de la cimentación y su perfil geotécnico. Además, se ha hecho un análisis histórico de las diferentes fases constructivas, las cargas, el tiempo de ejecución y la consolidación entre fases. Con esta información, se han desarrollado varios Modelos de Elementos Finitos (FEM) 2D con el fin de definir los diferentes perfiles de suelo importantes en los asentamientos de la torre. A continuación, se creó un FEM 3D detallado para analizar con precisión los asientos históricos. Finalmente, se ha explorado la posible relación entre los asientos históricos y la verticalidad de la torre. La siguiente sección contiene las siguientes publicaciones:  Artículo 1: Romero Sánchez, E., Morales Esteban, A., Navarro Casas, J. (2023). Analysis of the Historical Settlements of the Giralda. International Journal of Architectural Heritage, 17(8), 1312-1330.  Artículo 2: Romero Sánchez, E., Morales Esteban, A., Navarro Casas, J. (2022). Analysis of the giralda tower geotechnical profile and its settlements. International Journal of Computational Methods and Experimental Measurements, 10(1), 1-12. Sección 2: Modelado numérico y evaluación sísmica de edificios patrimoniales. En este apartado se ha desarrollado el Modelo 3D FEM de la torre Giralda. Para conseguirlo se ha analizado minuciosamente la estructura y los materiales. La información disponible de proyectos de caracterización anteriores y la información gráfica del edificio han sido analizadas y completadas con diferentes estudios in situ. En este sentido, se ha ejecutado un análisis de sensibilidad sobre varias variables que afectan al modelado FEM. Posteriormente se ha realizado una rigurosa calibración del modelo numérico. Finalmente, se han aplicado análisis estáticos y dinámicos no lineales para evaluar la seguridad sísmica y los patrones de daño en la torre. Los resultados de la segunda sección se resumen en las siguientes secciones:  Artículo 3: Romero-Sánchez, E., Morales-Esteban, A., Bento, R., Navarro-Casas, J. (2023). Numerical modelling for the seismic assessment of complex masonry heritage buildings: the case study of the Giralda tower. Bulletin of Earthquake Engineering, 21(9), 4669-4701. JCR (Q1).  Artículo 4: Romero-Sánchez, E., Requena-García Cruz, M. V., Morales-Esteban, A. Failure and damage analysis of the Giralda tower of Seville under different non-linear static and dynamic seismic loadings. Bulletin of Earthquake Engineering. Under second revision in 15-05-2024. JCR (Q1).  Congreso 1: Romero-Sánchez, E., Requena-García Cruz, M. V., Morales-Esteban, A. Seismic assessment of historic complex towers. The case study of the Giralda tower. COMPDYN Proceedings. 2023.  Congreso 2: Romero-Sánchez, E., Requena-García Cruz, M. V., Morales-Esteban, A. Preliminary seismic analysis of Giralda tower applying a finite element model. CITE. 2023. BLOQUE A 26 Sección 3: Interacción suelo-cimentación-estructura en el comportamiento sísmico de edificios patrimoniales Esta sección se centra en investigar la influencia de la Interacción Suelo-Cimentación- Estructura (SFSI) en el comportamiento sísmico de la torre de la Giralda. Para lograrlo, se ha desarrollado y calibrado un modelo numérico complejo que considera el suelo, los cimientos y la estructura. La caracterización de las capas del suelo se ha completado mediante varios ensayos in situ ejecutado en la zona cercana. Se ha realizado un análisis estático no lineal preliminar para verificar el modelo numérico y obtener una primera aproximación de los efectos SFSI. Posteriormente, se ha aplicado un análisis dinámico no lineal para evaluar la influencia del SFSI en la torre. Se han analizado y comparado los resultados tanto para condiciones fijas como SFSI. Los resultados de la tercera sección se resumen en las siguientes contribuciones:  Artículo 5: Romero-Sánchez, E., Requena-García Cruz, M. V., Morales-Esteban, A. Impact of the soil-foundation-structure interaction in the seismic behaviour of a heritage masonry tower. Engineering Failure Analysis. En Segunda Revisión a 13-05-2024. JCR (Q1).  Capítulo de libro: Preliminary evaluation of the soil-structure interaction on the seismic behaviour of a complex masonry tower: the Giralda tower of Seville. Seismic Behaviour and Desing of Irregular and Complex Civil Structures V. Springer. 2024  Congreso 3: Romero-Sánchez, E., Requena-García Cruz, M. V., Morales-Esteban, A. Preliminary seismic assessment of the soil-structure interaction effects of a complex masonry tower. WCEE. 2024. Sección 4: Métodos de refuerzo de edificios patrimoniales. En la segunda estancia de investigación en el Instituto Superior Técnico IST de la Universidad de Lisboa se analizaron varias técnicas de rehabilitación sísmica de mampostería antigua. El objetivo de este trabajo es obtener la calibración del modelo numérico y los parámetros mecánicos actualizados. En particular, este apartado tiene como objetivo analizar el comportamiento del modelo numérico aplicado para simular el material en el FEM. El proceso de calibración implicó la simulación de ensayos cíclicos de laboratorio a escala de panel mediante un modelo numérico. Los coeficientes propuestos en el Código italiano se han utilizado para simular las propiedades mecánicas actualizadas en el FEM. Una vez obtenidos los parámetros mecánicos calibrados se aplicarán al modelo numérico real de la torre. OBJETIVES 27 2. OBJETIVES The main objective of the Thesis is to analyse the seismic behaviour of heritage buildings and their subsequent reinforcement, thereby enhancing the resilience of cultural heritage. To achieve this goal, the study focuses on assessing the seismic vulnerability of the Giralda of Seville. The failure mechanisms and potential damage that the building could suffer in the event of an earthquake have been identified, considering the soil, foundation, and structure interaction. Additionally, specific seismic retrofitting solutions have been analysed to mitigate expected seismic damage. These can then be integrated into the building’s conservation activities. The following specific objectives has been stablished to accomplish the main objective:  Developing an accurate study of the case study building, including the foundation and soil, in order to obtain its constructive, structural and geotechnical characteristics.  Studying the seismic hazard of the city to determine the seismic action. The spectral acceleration of the code in function of the seismic acceleration. Selection of the best fit spectral acceleration of the European database.  Development of numerical models through the finite element method, applying macromodelling approach. To do so, the complete structural system will be considered: soil + foundation + superstructure.  Assessment of the seismic vulnerability of the ancient tower, considering the soil, foundation, structure interaction. Non-linear static and dynamic analyses will be applied keeping in mind the structural and the complete system (soil, foundation and structure).  Analysing the seismic safety of the heritage building.  Numerical analysis of seismic strengthening strategies based on laboratory test results. BLOQUE A 28 3. METHODOLOGY The methodology followed to develop the Thesis is presented in this section. The flowchart applied is shown in Figure 1. I. Analysis of the literature, information and bibliography. The building information has been gathered (characterization projects, geometrical information, archaeological projects, documentary studies, etc). As part of this process, a historic analysis of the tower and its surroundings has been developed. During this phase, different research documents and projects have been consulted and evaluated. This phase is important to understand the historic evolution of the building, detecting the different construction phases and interventions carried out. Furthermore, the bibliography about the state of art has been compiled and analysed. II. Accurate analysis of the case study building. Assessment of the building through the information gathered and in-situ surveys. These surveys include visual inspection, laser measurement and digital image analysis. Additionally, an ambient vibration test campaign has been done to obtain the dynamic characterisation of the building. During this step, different variables have been identified to be applied in the sensitivity analysis and in the calibration of the numerical model. III. Analysis of the seismic hazard of the city and determination of the seismic action. For this, a probabilistic scenario has been assessed. The Seville city’s acceleration values for the 95, 475 and 975 years return periods, obtained from the updated Spanish seismic hazard maps have been employed. The spectral acceleration (SA) has been calculated using the provisions established in the EC8-3, based on the previous mentioned values. Then, the SA is used for the analysis of the seismic safety based on the results of the pseudo-static calculations. Also, the best real accelerograms (which are more realistic than artificial records) that match the SAs have been selected from the European database. These accelerograms have been used in the dynamic analysis. To achieve this, a specific method developed by the research group has been employed. IV. Development of the numerical models. Firstly, creation of 3D CAD models for the definition of the geometry by applying several specifics CAD Software: the commercial software Autodesk Civil3D and Rhinoceros software were employed for the soil profiles and for the structure, respectively. Subsequently, the development of the 3D Finie Element Numerical models (FEM) accounting for the continuous modelling by using several specifics software: PLAXIS 2D and 3D for soil profiles (historical settlements) and the OpenSees open-source software using the pre- and postprocessor STKO software for the structure and soil-foundation-structure numerical model. Macroelement approaches have been employed to develop the 3D FEM. Furthermore, the direct method has been used to develop the soil-foundation-structure (SFSI) numerical model. Sensitivity analysis to test the different uncertainties in the models (mesh size, boundary conditions, constitutive laws of materials, among others) was conducted. Finally, the calibration of the numerical models was performed based on the in-situ surveys results. V. Analysis of the structural behaviour, seismic vulnerability and the seismic safety. For this purpose, first, an evaluation of the historic settlements suffered by the building throughout its history was conducted. Next, a nonlinear static analysis was performed based on the Eurocode-8 requirements to provide a preliminary seismic performance of the structure. Subsequently, nonlinear dynamic analysis (Time-history) was carried out, considering the accelerograms selected in the previous section III. These analyses have been carried out using the calibrated 3D FEM from the previous METHODOLOGY 29 section IV. Then, a seismic safety evaluation was performed at a global scale considering the different types of analyses conducted and the corresponding results obtained. An accurate damage distribution in the tower was determined using the result from different analyses and the conditions defined in the FEM (fixed and SFSI). VI. Assessment of retrofitting strategies. First, study of the retrofitting techniques that could be applied to improve seismic performance of the masonry structure has been conducted. Additionally, the coefficients proposed by the Italian Code to apply in the mechanical parameters for simulating the strengthening techniques have been evaluated. Subsequently, the calibration of the retrofitting materials and elements have beeb performed through cyclic laboratory test results. In this context, the behaviour of the material model applied in the 3D FEM was assessed. The calibration process involved evaluating different techniques by numerically simulating cyclic laboratory test at panel scale. Figure 1. Schematic diagram of the methodology BLOQUE A 30 CASE STUDY BUILDING: THE GIRALDA TOWER 31 4. CASE STUDY BUILDING: THE GIRALDA TOWER In this section, the Giralda tower of Seville, which is using as case study building in this Thesis, is presented. The information is presented in function of the location, the historical data, and geometrical and structural features. 4.1. Location of the tower Seville is located in the southwestern Iberian Peninsula. It has a moderate seismic activity, but it is located on soft alluvial strata that is known to increase the effects of earthquakes (Amaro- Mellado, Morales-Esteban, & Martínez-Álvarez, 2017; M. v. Requena-Garcia-Cruz et al., 2022). The city is affected by large earthquakes (Mw>7) of long-return periods, which makes the population unacquainted with them (Fazendeiro Sá et al., 2016). The regional seismicity of Iberia is produced by the contact between the Eurasian and the African tectonic plates (Sá et al., 2016, 2021) located in the south. Also, there is an intraplate seismic activity generated by local faults. The first source causes large earthquakes with very long return periods and the second produces a moderate seismic activity. Seville, situated in the southwestern Iberian Peninsula (IP), is affected by frequent small earthquakes and infrequent moderate magnitude earthquakes. However, it should be noted, that Seville was notably affected by three of the most destructive events that have ever hit the Iberian Peninsula: the 1504, the 1755 Lisbon (MW=8.5) and the 1969 (MW=8) earthquakes (Sá et al., 2021). The city is situated in the centre of a wide river plain formed by the Guadalquivir valley. Its soil deposits have a different geological constitution. The west soil deposit is a scarp that has a slope of 60-100 m composed of tertiary age materials (Pliocene-Miocene): marl, silt and sands. The east soil deposit has a soft slope with a larger altitude, formed by calcareous cement sand (pipeclay). Hence, the east soil deposit, on which the tower is placed, has fluvial sediments of the Guadalquivir River and tributary streams more than 18 m thick (Soler Arias et al., n.d.), due to the presence of a superficial layer composed by fluvial filling. The cultural heritage in Seville is rich and diverse. It is a reference of the historical and social identity for its population. Additionally, it plays a crucial role in the economic and cultural development of the city. In this regard, the Giralda tower of the Cathedral of Seville is one of most representative buildings of the city and the country. 4.2. Historic data During the Almohad period (1147-1248), Seville was considered the capital of Al-Andalus, especially in the epoch of the caliphs Abū Ya’qūb and his son Abū Yūsuf. The construction of the Major Mosque, which was started in 1172 by Almad ibn Bāsu, was considered the most important event regarding the religiosity of the city (Molins, 1998). It was constructed on swampy ground due to the Guadalquivir riverbed passing through this area, where a group of buildings (houses, a chapel, markets and gardens) were built extramural during the Cordoba caliphate. These buildings were expropriated and demolished by the Almohads in order to build the Major Mosque. Ahmad ibn Bāsu ordered that the ground in this area be levelled by means of a mortar wedge, which ensured the stability and the regularity of the mosque (Jiménez Martín, 2007), due to the soil in this area sloping to the southeast. The remains of these buildings were found in the different archaeological projects carried out on the east side of the Cathedral and the Virgen de los Reyes square (Tabales Rodríguez et al., 1996). BLOQUE A 38 Figure 8. Giralda tower foundation, east façade elevation and plan (based on the archaeological studies carried out by Tabales (Tabales Rodríguez, 1998)). North elevation of the Islamic minaret of the Major Mosque (based on the hypothesis of A. Almagro (Almagro & Zúñiga, 2007)(Almagro, 2012)). Dimensions in metres. The slab is composed of mortar made of lime, sand, Islamic and Roman ceramic bricks, fragments of ceramic vessels, fragments of stone blocks, etc. (M. A. Tabales et al., 1998). It has also been enlarged 1.00 m to the east and to the north and 2.30 m to the south. However, to the west, it has been attached over two pre-existing walls (one pre-Almohad (Emiral) and other of the Mosque, earlier than 1184) (Figure 8) (Tabales Rodríguez, 1998). Therefore this mortar base has a dimension of 18.60 m (north-south direction) and 15.40 m (east-west direction), with an area of 287 m2 (Figure 8) (M. Á. Tabales et al., 1998). The mortar of the footing slab has lost lime due to the presence of a large concentration of organic detritus in the south façade. This is owing to the presence of septic tanks and sewer pipes of the XIII and XVIII Century (M. A. Tabales et al., 1998). This has caused the loss of cohesion in the mortar of this area (Figure 9). The tower´s foundation is composed of four courses of sandstone ashlars, which have a height of 0.48-0.58 m (Figure 9). The first course stands out 0.70 m with respect to the south façade. CASE STUDY BUILDING: THE GIRALDA TOWER 39 The other courses widen, with their depth being around 0.08-0.10 m each. The base reaches a depth of 2.50 m with regards to the current level. The first and the second course were carried out with bend, which was used as a levelling technique during the construction of the minaret. There is a course of ceramic bricks, which was used as a wedge to regularise the surface in the contact with the footing slab under the first course (Tabales Rodríguez, 1998). It is important to highlight that the joint between stone blocks in the first course was executed with the use of ceramic bricks, mud and wood ribbons in order to have less rigidity (Figure 9). As can be seen in Figure 9, the foundation has been attached over two pre-existing walls in the west façade. It was built against the existing Pre-Almohad wall and the first mosque wall (1176-1184) (Figure 9). Accordingly, it is important to highlight that there is a joint between the tower and the old mosque, as it was built as a structurally independent building. Figure 9.Giralda tower foundation, south and north façade elevation (based on the archaeological studies carried out by Tabales (Tabales Rodríguez, 1998)). BLOQUE A 40 SUMMARY OF THE RESULTS AND THEIR DISCUSSION 41 5. SUMMARY OF THE RESULTS AND THEIR DISCUSSION SECTION 1: ANALYSIS OF THE HISTORICAL SETTLEMENTS [ARTICLES 1 Y 2] 1.1. Phases and loads Several historical phases have been defined to accurately simulate the different stages that the tower has undergone. In consequence, three relevant phases have been selected for the analysis (foundation and base construction / Islamic minaret / Renaissance bell tower). These match historical moments where its weight increased substantially. It is important to define the time of each construction phase and the length of the periods of non-construction in order to consider the settlements caused by the consolidation effects. In the case of the Giralda tower, the construction of its foundation and its base was stopped for four years, between 1184 to 1188 with the same goal (M. Á. Tabales et al., 1998). Later, there was a period of nonconstruction of 360 years between the construction of the Islamic minaret and the renaissance bell tower. The following phases have been considered in the calculation:  P1. Construction of the foundation (-2.50 m) and its base (2.50 metres of stone blocks). This was finished in 1184.  P2. Phase of consolidation, which corresponds to the time between the foundation and the base of the minaret with sandstone. This took place between 1184 and 1188 (4 years).  P3. Construction of the Alminar, which was built with ceramic brick. This took place between 1188 and 1198 (10 years).  P4. Phase of consolidation, which corresponds to the time later than the construction of the Alminar. The phase of consolidation which corresponds to the periods of nonconstruction, which has a great importance in this building, has been taken into account as well. This stage corresponds to the time between the end of the Islamic minaret construction in 1198 and the beginning of the construction of the bell tower in 1558 (360 years).  P5. Construction of the bell tower, which took place from 1558 to 1568. It raised the total height of the tower to 94,69 m. This was finished in 1568.  P6. Phase of consolidation, which corresponds to the subsequent time of the construction of the Renaissance bell tower. The load of each of the three phases has been determined from the specific weight of each material, which has been obtained from other works (Barrios Padura et al., 2012) and the Spanish code CTE-DB-SE-AE (Basic Document. Building Actions. Spanish Technical Building Code, 2009). In addition, due to their relevance, the weight of the bells (24 710 kg), of the Giraldillo (1 500 kg) and the four bronze lilies (1 200 kg) has been borne in mind. In Table 1, the pressure and the cumulative pressure of each construction phase has been calculated. Table 1. Pressure applied to the base of the foundation for the construction phases. Construction phase Year Pressure (kPa) Cumulative pressure (kPa) 1 Construction of the foundation and the base of stone blocks 1184 75.30 75.30 2 Construction of Islamic minaret 1188-1198 529.5 604.80 3 Construction of the belfry 1558-1568 47.80 652.60 BLOQUE A 42 1.2. Geotechnical model Seville is placed on recent alluvial materials from the Quaternary. These were transported by the Guadalquivir river and they were put on the Guadalquivir blue marls (Manuel Vázquez Boza, Percy Durand Leyra, Antonio Morales Esteban, 2015). The geotechnical model is composed of infill, sand, clay, gravel and marls (Soler Arias et al., n.d.). The geotechnical strata under the tower have been defined in Table 2 and Table 3. Table 2. Stratigraphy of the soil and layer thickness. Level Layer thickness Stratigraphy I 3.00 m (0.00 m to 2.50-3.00 m) Composed of several layers of infill. Under the pavement, there is a sandy subbase with gravel of a brown tonality. Next, there are several silty marl layers with traces of sand, gravel, ceramic and organic matter. II 5.00 m (2.00-3.00 m to 7.00-9.00 m) Fine and soft alluvial infill. This is just under the tower foundation and it is composed of an anthropic fill with ceramic traces, clayey sand, silts, ceramic brick traces and organic matter. III 4.00 m (7.00-9.00 m to 11.00-12.00 m) Composed of grey clays with sands, gravel and ceramic traces. IV 6.00 m (11.00-12.00 m to 17.90-18.40 m) Alluvial substrate composed of sandy gravel with traces of silt and clay. V (17.90-18.50m / --) The Tertiary substrate. The blue Guadalquivir marls. The physical and mechanical properties of the strata used for the calculations are listed in Table 3. These have been obtained from the geotechnical studies carried out on samples extracted from the boreholes drilled at the tower foot in 1988 (Barrios Padura et al., 1997) and other boreholes drilled in the nearby area. Furthermore, these data have been compared and completed with the archaeological study carried out in the area in 1996-1998 (Tabales Rodríguez, 1998; Tabales Rodríguez et al., 1996), the Basic geotechnical maps of Seville (Soler Arias et al., n.d.), the Geological and Mining Institute of Spain (IGME) and the Spanish code CTE DB-SE-C (Ministerio de Fomento, 2007). In addition, other research of the Giralda tower (Barrios Padura et al., 2012) and the nearby area (Barrios, Borja, et al., 1997) (Diz- Mellado et al., 2021) has been taken into consideration. Table 3. Geotechnical properties of the strata. LEVEL I LEVEL II LEVEL III LEVEL IV LEVEL V Drainage type Drained Undrained Undrained Drained Undrained Unit weight γ (kN/m3) 20 19.2 19.1 19 19.2 Saturated unit weight γsat (kK/m3) 20.9 20.8 20.4 20 19.6 Permeability kx (m/s) 10E-04 10E-07 10E-10 10E-03 10E-12 Water content w (%) 20 28.8 26.8 7.5 24.9 Compression Index Cc (-) 0.119 0.153 0.172 - 0.12 Recompression index Cs (-) 0.0119 0.0153 0.0172 - 0.012 Void ratio e0 (-) 0.5 0.5 0.5 - 0.5 Effective cohesion c´ (kPa) 10 29.4 22 10 100.5 Angle of internal friction Փ (º) 28° 30° 26° 32° 20° Dilatance angle ψ (º) 0 0 0 2º 0 Elastic oedometer modulus Eoed (kPa) 5 000 5 428 6 165 50 000 90 000 SUMMARY OF THE RESULTS AND THEIR DISCUSSION 43 Morh-Coulomb model Shear Modulus G (kN/m2) 1428.6 1550.9 1761.4 14285.7 25714.3 Effective Young´s modulus E´ (kPa) 3714.3 4032.2 4579.7 37142.9 66857.1 Effective Poisson´s ratio ʋ (-) 0.30 0.35 0.35 0.30 0.25 Soft Soil model Modified compression index λ* (-) 0.034 0.044 0.050 - 0.035 Modified swelling index k* (-) 0.007 0.009 0.010 - 0.007 The water table is at a depth of 6.00 m. Its depth changes according to the rainy season. The Guadalquivir River level also affects it. Due to that, its depth can change from 2.00-3.00 m to 9.00-10.00 m (Soler Arias et al., n.d.). In this work the water table have been considered at its average level. The tower base is composed of mortar made of lime, sand, ceramic brick, fragments of vessels, fragments of stone blocks, etc. Its characteristics (Table 4) have been determined according to other works (Barrios Padura et al., 2012) (Barrios, Borja, et al., 1997) and the Spanish code CTE-DB-C (Ministerio de Fomento, 2007). Table 4. Properties of the foundation base. γ (kN/m3) γsat (kN/m3) γd (kN/m3) w (%) qu (kPa) c´ (kPa) Փ (º) E (kN/m2) G (kN/m2) E´ (kN/m2) υ Mortar Base 19 20 15.6 28 5 070 15 40 500 000 228 900 526 470 0,15 The accurate definition of the dimensions of the geotechnical model under the tower has been done considering the boreholes carried out in 1988, in the base of the tower. The top surface of each layer has been plotted through a point cloud, using the commercial software Autodesk Civil3D (Autodesk, Inc., 2020). What is more, four 2D geotechnical profiles have been depicted in order to analyse the depth and the possible irregularities of each layer under the tower (Figure 10). It should be noted that the depth of the soft alluvial infill layer (Level II) is not uniform. It is 2.00- 3.00 m thicker in the south-east corner of the tower. This is a soft layer which could have caused a larger settlement in this area. This layer has a heterogeneous composition with silty clay sand alternating with ceramic traces, ceramic brick traces and organic matter. In some zones there is a great content of organic matter, possibly caused by the presence of several cesspits of the old mosque (M. A. Tabales et al., 1998). BLOQUE A 44 Figure 10. Geotechnical profiles (GP) under the tower. Dimensions in metres. 1.3. Numerical model of the soil The deformation and stability of the foundation have been analysed using PLAXIS 3D v20 (Bentley Systems, 2020a), which is a FEM software used to analyse the deformation and stability of geotechnical problems. In the case of the 3D FEM, the soil has been defined in the software through the definition of several boreholes, where the depth of each layer and the water table are specified. The base of mortar can be also considered in the schematic profile because it is an essential aspect in the composition of the tower’s foundation. Finally, the SUMMARY OF THE RESULTS AND THEIR DISCUSSION 45 different construction phases have been defined according to the calculation phases in the software. For each of them, the pressure applied, its length and the time between phases has been considered to calculate the consolidation settlements. In order to define the behaviour of the soil in the FEM, two models have been considered in the analysis of the foundation settlements. First, the Mohr-Coulomb model (MC) (Labuz & Zang, 2012), which is an elastic perfectly-plastic model. The behaviour of the foundation has been considered to model and to obtain a first estimation of the tower’s settlement. The computation time is short due to the consideration of a constant average stiffness of the soil layer. This model requires five parameters in order to define the behaviour of the soil: two stiffness parameters (Effective Young’s modulus and Effective Poisson’s ratio) and three strength parameters (Effective cohesion, effective friction angle and dilatancy angle). These parameters are obtained from a basic laboratory test of soil samples. Second, the Soft Soil model (SS) (Bentley Systems, 2020b) has been used to do a more accurate analysis. This method is used for the analysis of soils such as normally consolidated clays, which can be found in the geotechnical model under the tower. The volumetric strain in this model is considered in the formulation of the compression and the swelling lines. To this effect the parameters of stiffness are defined by the modified compression index (λ*) and the modified swelling index (k*). These indexes have been obtained in function of the compression (λ) and the swelling index (k), respectively. Parameters obtained from the oedometric test can also be employed: the compression index Cc, the swelling index Cs and the initial void ratio e0. 1.4. Historical settlements The settlements for each construction phase, considering the consolidation effects, are listed in Table 5. The results of both analyses (MC and SS models) are also presented. The settlements have been measured in five different points, which are located in the centre and under each corner of the foundation (Figure 11). In order to evaluate the accuracy of the results, the different settlements in each point in the 3D FEM have been compared with other previous works and the real measurement of the verticality of the tower. Figure 11. Discretisation and measurement points of the 3D FEM: a) axonometric view and b) plan. BLOQUE A 46 The 3D FEM has an area of 36x36 m and is 20 m deep (Figure 11). The thickness of the different layers has been defined by means of several boreholes in the software. The depth of each layer has been determined by means of a cloud point as aforementioned. The FEM has been defined from the contact area between the stone blocks and the mortar base (-2.50 m level). The settlements have been measured in this level, where the foundation rests on the mortar base. The fill layer (up to 0.00 m level) has been defined as a superficial load. The tower foundation of four courses of sandstone ashlars has been defined by means of a plate. The tower foundation has been situated in the centre of the FEM. The cohesive strata (Levels II, III and V) have been defined with undrained conditions in order to analyse the movements caused by the consolidation effects. Table 5. Settlement for each point and construction phase. Results in centimetres (cm). P1 P2 P3 P4 P5 P6 MC SE -4.1 -13.8 -49.1 -78.3 -80.2 -82.6 NE -4.0 -13.4 -47.0 -75.6 -77.5 -79.8 NW -3.8 -12.2 -46.8 -73.7 -75.5 -77.6 SW -3.8 -12.6 -48.9 -76.5 -78.2 -80.5 C -4.0 -13.1 -48.6 -76.6 -78.5 -80.8 SS SE -2.0 -28.1 -61.7 -102.7 -103.2 -105.5 NE -2.0 -28.1 -57.2 -97.1 -97.6 -99.8 NW -2.1 -26.8 -57.0 -94.0 -94.6 -96.5 SW -2.1 -26.8 -61.5 -99.7 -102.0 -102.2 C -2.0 -27.5 -60.0 -99.1 -99.7 -101.8 It can be observed that the settlements are more uniform in the early phases. The largest increase of settlements is produced in the phase of the construction of the Islamic minaret (P3) and its consolidation phase (P4). This is in agreement with the big increase of the pressure applied (529.5 kPa) and the long time of consolidation (370 years). Finally, the settlements only increased in 2-4 cm with the construction of the bell tower (1568) and its consolidation (P5 and P6, respectively). It can also be noted that the settlements in the SS model are larger than the ones achieved in the MC model. These results are in accordance with the fact that the SS FEM is more accurate as it considers the compression index (Cc), the swelling index (CS) and the porosity (e0) of each layer. In this regard, it is expected that the deformation of the soft strata (Level II and III) will be more accurately calculated. Figure 12 shows the total mesh displacement (uz) of the MC model in the section GP2 (southnorth under the east façade) and GP4 (west-east under the south façade). These sections have been selected due to the larger depth of the soft strata. As can be seen, the settlement of the foundation is larger under the south-east corner (SE). In these sections the differential settlements are larger than in the central profiles. This is due to the irregularity of soft strata. The deformation, which is larger under the south-east corner, is similar in both. SUMMARY OF THE RESULTS AND THEIR DISCUSSION 47 Figure 12. Total mesh displacement of the MC model. Section GP2 (a) and GP4 (b). Figure 12 shows the total mesh displacement in a section from the south-east (SE) to the north-west (NW) corner. It can be observed that the settlement under the south-east corner is larger than the north-west corner. The tower has the largest settlement (-82.60 cm) under the south-east corner. This is due to an increase of 2.4 m in the depth of the soft layer (Level II) in that zone. It is important to highlight that the largest differential settlements have been obtained in this direction (NW to SE): 5.0 cm in the MC FEM (Figure 12) and 9.0 cm in the SS FEM (Figure 16). This differential settlement coincides with the direction of the largest inclination measurement of the tower (Barrios Padura et al., 1997)(Barrios, Valverde, et al., 1997). Figure 13. Total displacement of the MC model. Section from the south-east to the north-west corner. Also, the evolution of settlements in the four corners of the tower as a function of time are presented in Figure 14 for the MC model and in Figure 17 for the SS model. In that sense, the time has been plotted in a logarithmic scale in graphic (a), and the time has been plotted in linear scale in the construction (P3) and consolidation of the Alminar (P4) graphic (b). Generally, the largest settlements have been achieved for the P3 and P4 phases, which show the construction and consolidation of the Islamic Minaret. By contrast, the smallest settlements have been obtained for the Bell tower construction (P5 an P6 phases). BLOQUE A 54 strengths, the strain (εcp) at peak compressive strength and the peak tension strength (ft). Furthermore, Young´s modulus (E), the poison ratio (v) and the density (ρ) of the material have been defined as elastic mechanical parameters. In this material model, the fracture energies in tension (Gt) and compression (Gc) are divided by the characteristic length of the finite element (lch) to achieve mesh size independence (M. V. Requena-Garcia-Cruz, Romero- Sánchez, et al., 2023; Romero-Sánchez et al., 2023). Under uniaxial tension and compression, the stress-strain follows an elastic relation up to ft and fc0, respectively, which represents the micro-cracking of the material. Once achieved ft, a soft stress-strain response is obtained. However, for compression, a plastic range is achieved up to fcp and, later, it decreases following a soft phase up to fcu. In this regards, four different materials have been considered: the unreinforced ceramic brick masonry wall, the stone masonry located at the base of the tower, the stone masonry of the belfry and the upper body, and another for the ramp’s elements. Figure 22. Uniaxial constitutive law of the masonry material in tension and compression adapted from (Petracca, Pelà, Rossi, Zaghi, et al., 2017). 2.2. Calibration of the FEM 2.2.1. Sensitivity analysis of mesh size A mesh-sensitivity analysis was developed, by modelling the tower with the same solid models but different structured mesh sizes. The structural element size and the number of tetrahedron solid elements in the thickness of the outer wall have been considered to define these mesh sizes (Figure 23). The coarse mesh size has been defined to deal with at least three tetrahedron elements in the thickness of outer wall, as in (Castellazzi et al., 2018). Figure 24 plots the capacity curves in the X-direction with different mesh sizes. The numerical models with mesh sizes between 30 and 60 cm have a stable behaviour. It can be observed that the difference in the results among these is negligible. The 70 and 80 mesh sizes are unstable. Moreover, their capacity has increased proportionally to the mesh size because of its higher dimension. Furthermore, the computation time increases considerably with the refinement of the mesh size (Figure 24b). In addition, the damage distribution has been analysed and compared. As can be seen in Figure 25, the damage distribution considering the 40 cm mesh (Figure 25 b) is more accurate than the 60 cm mesh (Figure 25 a). In this regard, the location of the damage in the 60 cm mesh is more irregular, appearing very dispersed damage near the belfry. Due to that, the 40 cm mesh has been adopted for this analysis for its balance between accuracy and computational effort. Furthermore, in the case of the 40 cm mesh, there are, at least, three tetrahedron elements in the thickness of the inner masonry wall. The average calculation time for the NLSA with the 40 cm mesh is 1h and 9 min. The model has SUMMARY OF THE RESULTS AND THEIR DISCUSSION 55 been calculated with the parallel option in OpenSees, using multiprocessors. Due to the characteristics of the computer used, the model has been divided into 24 parts. It has been calculated on a computer with an AMD Ryzen 9 5900X 3.70 GHz processor. Figure 23. Different mesh sizes applied in the sensitivity analysis (number of elements and nodes). Figure 24. Sensitivity analysis of mesh size in the numerical model. a) Pushover curves, b) time required. Figure 25. Damage distribution, a) mesh of 60 cm and b) mesh of 40 cm. BLOQUE A 56 2.2.2. Modal analysis A modal analysis has been performed to obtain the main vibration modal shapes and the frequencies to analyse them. In this respect, three fundamental global modal shapes have been identified in the numerical analysis. Modes 1 and 2 are translational in the X and the Y direction, respectively. The third vibration mode is rotational (Figure 26 and 27). The 3D FEM of the tower has been calibrated using the results of the in-situ survey. With this aim in mind, the values of the periods and frequencies of the numerical FEM have been compared with the ambient vibration test. The calibration of the FEM model has been carried out by applying an OMA test. For this purpose, the Artemis Modal Pro software (Structural Vibration Solutions A/S, 2019) has been used. The experimental dynamic parameters of the tower have been extracted employing the Enhanced Frequency Domain Decomposition (EFDD) and the Stochastic Subspace Identification (SSI) technique. The vibration modes are determined by selecting peaks in the response spectral density functions for the set of performed tests. The different modal shapes obtained in the OMA test have been compared with the numerical ones in order to calibrate the 3D FEM (see Figure 26 and 27). Three global modal shapes have been identified in both analyses: two bending modes and a torsional mode. With a view to calibrating the numerical model, the three vibration modes have been compared (Figure 26 and 27). Figure 27 shows that the calibrated and the experimental frequencies are closely related. Furthermore, it is important to highlight that the three modal shapes obtained from the calibrated FEM and the OMA deformed in the same direction. The first two modal shapes have very similar frequencies due to the square-shaped plan of the tower. Furthermore, the third vibration mode is torsional with a period smaller than the first two. These results are similar to those obtained under several masonry towers in (Valente & Milani, 2018). The updated FEM of the tower has been modelled with the boundary conditions and an elasticity modulus, obtained from E=800·fcp, in the masonry brick. Figure 26. Frequencies of the first three vibration modes. Experimentally OMA (ARTeMis) and numerically FEM (OpenSees). B (Boundary) and I (Isolated) SUMMARY OF THE RESULTS AND THEIR DISCUSSION 57 Figure 27. Main vibration modes of the tower. Experimental OMA analysis (up); numerical analysis (down). 2.2.3. Strength domain The strength domain method (D’Altri et al., 2022) has been used for the definition of the strength behaviour of the masonry panels. The calibration at a panel scale is generally recommended in masonry buildings since the strength parameters are associated with shear and bending failure. A numerical benchmark masonry panel has been considered to perform the sensitivity analysis. Both the shear (Vt) and flexural (Mu) behaviour have been borne in mind. The empirical behaviour for both types of failure has been computed according to the prescriptions established in the Italian NTC-18. As established in the NTC-18, the Turnšek and Čačovič (T&C) criterion has been used (Turnšek & Čačovič, 1971). BLOQUE A 58 Figure 28. Strength domain of the masonry panel and maximum shear strength (Vt) computed for different models by varying a) the tensile and b) the compressive constitutive laws. Damage plots (tension, d+, and compression, d-) and cracks patterns for the CL A numerical model. The panel considered has been of 6 m and 6 m of width and height, respectively and of 1.30 m of thickness. It has been fixed at the base (all 6 degrees-of-freedom). Both the cantilever (CA) and the fixed-fixed (FF) conditions have been considered at the top of the panel for the analyses as in (Requena-García-Cruz et al., 2023). Similarly to (D’Altri et al., 2022), several axial load ratios have been accounted for to perform the analysis: 5%, 12%, 18%, 30%, 40% and 50%. The sensitivity analysis has been divided into different phases. First, the tensile strength (ft) of the masonry has been varied and the rest of the mechanical parameters have been fixed. For this purpose, different values of ft have been defined according to fcp: 0.025fcp; 0.035fcp and 0.05fcp. Concerning fcp, this value has been firstly obtained from the previous characterisation project conducted in 1685, which used several masonry samples from different locations of the tower (J. Pérez, 1985). This is why this value is kept constant during the calibration process as it was obtained from experimental testing. Once the ft has been calibrated, several variations of the uniaxial nonlinear compressive behaviour have been borne in mind, keeping the identified value of fcp fixed: i) CL A, the compressive elastic limit (fc0) has been set equal to fcp, while the rest of the parameters have been fixed; ii) CL B, the linear elastic behaviour has been set to fcp without considering the hardening branch; iii) CL C, a different shape of the uniaxial compressive curve has been considered by defining a horizontal branch after reaching fcp. The variations considered in the uniaxial compression constitutive law have been similar to those defined in (Torelli et al., 2020). SUMMARY OF THE RESULTS AND THEIR DISCUSSION 59 In Figure 28, the results of the sensitivity analysis are shown. As can be observed, some models present a similar behaviour to the empirical one. Furthermore, when comparing the plots with the damage and the cracks (strain) expected, the results seem to be in a good agreement. Concerning the tensile strength, the model that best fits both the empirical strength criteria (which is closer to the diagonal cracking behaviour) and the damage models is the one that set ft as 0.035fcp. Concerning the compressive strength, the best model has been the CL A configuration, where fc0 has been set as fcp. The continuous domains in have been plotted for damage plots of tensile strength (d+), compressive strength (d-) and material strain (Figure 28). It is important to highlight that these patterns have been plotted for the CL A model with the final calibrated mechanical parameters adopted in the numerical model. In Table 6, the final mechanical parameters selected after the calibration procedure are shown for each of the materials considered in the numerical model. Table 6. Mechanical properties used in the 3D FEM model. Attribute Brick masonry Stone Masonry belfry Stone masonry base Lime concrete ramp Units Bottom Middle Upper Mass ρ 1,800 1,800 1,800 2,200 2,500 2,500 kg/m 3 Elasticity E 2.90 2.27 1.81 2.50 2.50 3.00 GPa ν 0.2 0.2 0.2 0.25 0.25 0.2 Tension f t 129 100 80 143.8 130.2 312 kN/m 2 Compression f c0 2,441 1,988 1,582 1,677 1,519 2,600 kN/m 2 f cp 3,630 2,840 2,260 2,396 2,170 5,200 kN/m 2 f cr 363 284 226 239 217 520 kN/m 2 2.3. Non-linear static analysis Different pushover analyses have been carried out in the X and the Y direction in the positive and negative ranges, applying different load patterns. Also, the tower model isolated and the model with the boundary conditions have been analysed and compared. All the capacity curves obtained in the NLSA analysis have been plotted in Figure 29. Significant differences have been found between the different load patterns. The models with a uniform horizontal load have a higher capacity than the pseudo-triangular models. This is due to the fact that the horizontal load is applied uniformly throughout the cane, that is more massive than the upper bodies. Furthermore, the resultant of the triangular load is higher. Generally, the capacity is greater in the X direction than in the Y direction. This increase is likely caused by the irregular distribution of the hollows in the outer and the inner walls. In addition, the irregular distribution of the ramps can also affect it. Despite the difference in the maximum strength between the different load patterns, it is worth mentioning that in both load patterns, the maximum deformation capacity is similar (i.e. deformation at the collapse). As can also be observed, the models with boundary conditions have a higher stiffness in the elastic range in the positive analysis. Anyway, the capacity is similar in both models (isolated and boundary condition). Nevertheless, in the case of +X with both load patterns (T and U), the capacity is lower in the case of the model with boundary conditions (B). This may be due to the irregularity in the damage distributions provided by the boundary conditions. However, the capacity is greater in the B models than in the isolated (I) model in the negative range analysis. In that way, the Cathedral walls provide a higher rigidity in this direction. In these models, the ultimate displacement is higher than in the isolated models. BLOQUE A 60 Figure 29. Pushover curves of the model in the X and the Y direction, positive and negative orientation. Triangular (T) (proportional to the mass and the height) and Uniform (U) (proportional to the mass). Isolated (I) and with boundary conditions (B). The different damage patterns obtained from the FEM in the X and Y directions have been analysed and compared. In this vein, in this manuscript the tensile damage models have been plotted because they are more severe than the compressive ones (Figure 30-33). These damage patterns have been plotted in the ultimate displacement. It is possible to identify the areas of damage concentration. Besides, the damages in both FEM (isolated tower and with boundary conditions) have been compared to identify which is the most accurate numerical model. Generally, the greatest damage is concentrated near the belfry because it is weaker than the cane of the tower. In addition, the damages are located near the openings in the outer walls as it is its weakest area. The presence of openings is an important issue for local collapse, as demonstrated in (Valente & Milani, 2018). The severe and extensive damage is concentrated mainly near the openings. In that sense, the main geometrical feature of the bell towers is the large hollows at the top level. This issue causes considerable damage near the opening of the belfry, suggesting that the most vulnerable part of the structure may have collapsed partially. It should be noted that the ramps would be seriously damaged given that they are weak elements between two rigid bodies. Furthermore, there are greater damages near the belfry in the models with boundary conditions. These walls are not symmetric (being only located in the south and west façades). Therefore, they introduce more irregularity into the model. In addition, there is great damage in the contact between these walls and the tower. As can be seen in Figure 30-33, the upper body does not show significant damage. However, in the model with boundary conditions Figure 31 (b) this body presents some damages. The inner wall does not show significant damage. It is important to highlight that these damage patterns are similar to those described in the testimonies of past earthquakes. In that sense, several testimonies of the 1755 earthquake described that the tower presented the most serious cracks in its upper levels. Besides, a great number of ramps were in a state of ruin. SUMMARY OF THE RESULTS AND THEIR DISCUSSION 61 Figure 30. Damage pattern. Push +X direction: a) Isolated tower and b) tower with boundary condition. Figure 31. Damage pattern. Push -X direction: a) Isolated tower and b) tower with boundary condition. BLOQUE A 62 Figure 32. Damage pattern. Push +Y direction: a) Isolated tower and b) tower with boundary condition. Figure 33. Damage pattern. Push -Y direction: a) Isolated tower and b) tower with boundary condition 2.4. Seismic safety The capacity-demand performance method has been used to assess the seismic safety following the N2-method (Fajfar 2000). This is the procedure established in the EC8. For this purpose, the capacity curves obtained from the NLSA and the inelastic demand spectrum have SUMMARY OF THE RESULTS AND THEIR DISCUSSION 63 been used. In this regard, the NLSA capacity curves with the different damage limits (DLs) have been plotted in Figure 34. The analysis has been carried out in the ±X (East-West) and ±Y (North-South) directions. As can be observed, a horizontal displacement of around 1 cm has been recorded at the initial step of the NLSA. This can be related to a possible horizontal failure of the building during the application of the gravity loads due to the irregularity of the building (ramps in spiral and boundary conditions). As seen, a slightly worse behaviour has been obtained for the Y direction than for the X one, which can be also related to the irregularities of the tower. The DLs and the displacement demand (dtb) have been computed to assess the seismic safety of the tower. As can be seen, the dtb for PR=95 years ranges between DL2-DL3. This PL means that the tower could be slightly damaged in some parts, but it could be easily repaired. In the case of PR=475 years, the seismic demand is near DL3, but it will not comply with the capacity/demand ratio proposed by the EC8-3. In this case, the ratio is higher than 1, being on average (considering the ± results) 1.03 for the X and 1.10 for the Y direction, respectively. For this DL, the damage might be significant but could be repairable. For PR=975 years, the tower could be in the DL of near collapse. Figure 34. NLSA capacity curves obtained and seismic safety assessment. 2.5. Non-linear dynamic analysis The results of NLDA considering ten real GMs selected of the European database have been analysed and compared. The horizontal top displacements have been analysed for the most severe GM of each PR (Figure 35 (b)). To do that, the time-history horizontal displacements of the control nodes located at the top, the rooftop and the belfry levels have been plotted to assess the possible local collapse of upper bodies due to dynamic excitation. Furthermore, the GM accelerations, in both directions, have been compared with the accelerations obtained at the top node (Figure 35 (a)). There have been certain cases where the analysis has been interrupted when the displacements of the control node are incompatible with the capacity of the tower. This is a clear sign of the emergent collapse of the structure as proved in (Valente & Milani, 2016). It has been obtained that the upper bodies will collapse in most of the analyses carried out for the PR of 975 years, obtaining high incompatible displacements (higher than 1% of the tower height). In the case of PR of 975, the top horizontal displacements are compatible only for accelerograms two accelerograms. Furthermore, there is an important difference BLOQUE A 70 Figure 42. SA (Soil type A) according to the EC8-1, for a PR of 95 (a), 475 (b) and 975 (c) years, including the GM selected. Table 9. Real accelerograms selected (Soil type C), standard deviation (S) and factor of scale (f) for the 95 (0.04 g), 475 (0.09 g) and 975 (0.13 g) years of return period (PR) for the Giralda site. PR Accelerogram S f PR Accelerogram S f PR Accelerogram S f 95 GM-95C-1 0.01 1.00 475 GM-475C-1 0.08 1.04 975 GM-975C-1 0.16 0.92 GM-95C-2 0.01 1.00 GM-475C-2 0.08 0.96 GM-975C-2 0.20 0.91 GM-95C-3 0.04 1.02 GM-475C-3 0.13 0.94 GM-975C-3 0.20 0.91 GM-95C-4 0.12 1.06 GM-475C-4 0.19 0.91 GM-975C-4 0.50 0.77 GM-95C-5 0.15 1.08 GM-475C-5 0.20 1.04 GM-975C-5 0.54 1.32 GM-95C-6 0.17 1.10 GM-475C-6 0.39 0.82 GM-975C-6 0.58 0.75 GM-95C-7 0.26 0.92 GM-475C-7 0.28 1.15 GM-975C-7 0.60 1.35 Figure 43. SA (Soil type C) according to the EC8-1, for a PR of 95 (a), 475 (b) and 975 (c) years, including the GM selected. 3.3. Numerical model of soil-foundation-structure interaction (SFSI) The direct approach considering the different stratum of the soil is applied to model the towerfoundation-soil interaction system. The dimension of the soil domain has been defined up to 180 m in the transverse and the longitudinal directions. Furthermore, the vertical dimension of the soil domain has been defined up to 30 m deep (Altunişik et al., 2023). The 3D FE numerical model has been defined up to reaching H800, which is the depth of the seismic bedrock formation (Paolucci et al., 2021). This is identified when the soil reaches Vs≈800 m/s. In this regard, this Vs value is obtained in the Blue Guadalquivir marl stratum (Manuel Vázquez Boza et al., 2015). As can be seen in Table 7 and Figure 44(c), this layer has been split into 3 sublayers until reaching the Vs≈800 m/s. The procedure suggested by STKO developers on mesh size has been applied in order to achieve a balance between the computational cost and the consistency of the results (M. V. Requena-Garcia-Cruz, Bento, et al., 2022). In this regard, an iterative procedure has been applied, in function of the mechanical parameters and the absorbing boundary conditions, to define the mesh size. The soil domain region close to the foundation has been meshed with SUMMARY OF THE RESULTS AND THEIR DISCUSSION 71 the same finite element size of the structure and the foundation, 0.5 m. Furthermore, the finite element size has been increased to 1 m to define the far region soil domain to reduce the computational effort. A four-node tetrahedron element has been used to define the solid domain mesh. In this way, the ‘EqDOF’ has been applied to the interaction between the soil and the foundation surfaces (Figure 45). The 3D FE mesh is composed by 1,104,735 solid elements and 166,216 nodes (Figure 45(a)). Figure 44. Numerical model: a) 3D CAD model; b) 3D FE Superstructure + foundation and c) complete SFSI system (Superstructure + foundation + soil) The ‘PressureIndependMultiYield’ material (PIMY) has been implemented to define the constitutive model of the soil (M. V. Requena-Garcia-Cruz, Bento, et al., 2022; M. V. Requena- Garcia-Cruz, Romero-Sánchez, et al., 2022). This is an elastoplastic material that aims to characterise the nonlinear stress-strain reaction of the soil. The numerical model was developed by the University of San Diego and they used OpenSees to implement various soil models (Yang & Elgamal, 2003). The Von Mises' multisurface plastic theory is used to define the failure criterion of this material. It was implemented in OpenSees to simulate an undrained clay-type elastoplastic shear response, because this type of soil is insensitive to compression change (pressure-dependent material). Furthermore, the “upgradestagematerial” has been used to define the plastic behaviour of the soil material (M. V. Requena-Garcia-Cruz, Bento, et al., 2022). It should be noted that the definition of the updated command of the soil was executed prior to the beginning of the gravitational analysis, similar to (M. V. Requena-Garcia- Cruz, Bento, et al., 2022). This is due to non-convergence issues occurring if the soil behaviour is modified following this analysis because of the significant gravitational loads of the structure. The soil may become suddenly non-linear and may not be able to adjust the elastic stress immediately to the yield surface. This could be because stresses beyond its linear limit might be produced during the application of the gravitational loads. The numerical model, based on the definition of a finite region, requires suitable conditions for implementation at artificial numerical limits. In dynamic analysis, it is crucial to define appropriate boundary conditions to avoid the wave propagations reflection. Large numerical models can address this issue but require significant computational resources. An alternative solution is to incorporate absorbing boundaries into the 3D FEM. In this study, the viscous boundaries suggested by Lysmer and Kuhlemeyer (Lysmer & Kuhlemeyer, 1969) have been BLOQUE A 72 applied (Figure 45(b)). These boundaries employ independent dashpots in both normal and shearing directions along the model boundary, with properties varying for each layer. The components of the ground motions have been applied in both orthogonal directions (X and Y), as well as the corresponding vertical component (Z). The interaction between the soil domain and the viscous boundary has been developed by applying zero-length material with properties that vary depending on the soil stratum. The method effectively absorbs waves near the boundary and operates within the time domain. The Rayleigh damping command implemented in OpenSees has been used to implement the damping. The fundamental frequencies obtained for the vibration shapes have been used to define the α and the β parameters of the Rayleigh damping. In this regard, the first six vibration modes have been considered for that. Figure 45. Numerical model of the SFSI: a) Boundary conditions of 3D FEM and b) Free field boundary condition based on Lysmer and Kuhlemeyer (Lysmer & Kuhlemeyer, 1969). 3.4. Non-linear dynamic analysis of SFSI In this section, the results of the NLDA have been analysed and compared, considering both fixed and SFSI conditions. Several real GMs have been selected for soil types A and C to assess the SFSI and the FB models, respectively. The results have been obtained for eleven central nodes, selected in each level (the seven inner cameras, the belfry, the rooftop, the Well body and the top. The average of the maximum time-history acceleration values associated with various PR have been displayed in Figure 46 (the results of fixed conditions have been plotted in dots). A significant difference has been found between the accelerations considering the fixed and the SFSI condition. The results show that the accelerations in the shaft levels of the tower are higher in the case of the fixed conditions, for PR 475 and 975. However, the amplification is higher in the upper bodies when considering the SFSI effects. In this regard, for the SFSI model, the acceleration has increased around 5 m/s2 at the top levels with respect to the belfry level (+50.8 m). Therefore, the acceleration values for the SFSI model are higher than those of the fixed one for the top node. SUMMARY OF THE RESULTS AND THEIR DISCUSSION 73 Figure 46. Average accelerations of each level node for different PR and conditions. Figure 47 shows the average values of the maximum time-history displacements corresponding to the different PR (the results of fixed conditions have been plotted in dots). It should be noted that the SFSI results have been moved to 0 at the base (relative displacements) to compare both results. As can be seen, the displacements in ±X direction (west-east) are similar to the ±Y direction (north-south) in the fixed situations. However, in the SFSI models, the displacements are slightly higher in the direction ±Y direction. The higher displacements have been obtained with the PR 975 accelerograms under both conditions. These are more irregular in the case of considering the SFSI effects (all of these are in the negative range). This may be because the ground effects cause a certain collapse in the tower at the end of the NLDA. The Well body collapses in the GM of PR 475 and 975, considering the effects of SFSI. In the case of fixed conditions, the upper body only collapses in the GM of PR 975. Figure 47. Average displacement of each level node for different PR and conditions. BLOQUE A 74 Due to the amplification of the accelerations and the horizontal displacements in the top levels, in Figure 48, some significant output of time-history accelerations and displacement in top section nodes (bell, clock and top) have been plotted to analyse the seismic behaviour of the upper bodies. Analysing the displacement time-histories of nodes near the top of the tower is crucial for understanding the dynamic behaviour of such structures (Casolo et al., 2013). These displacement records offer valuable quantitative data on the tower’s deformations during seismic events (Figure 48(b)). Figure 48. NLDA results of the upper bodies for different PR: a) accelerations and b) displacements. (Time s) A significant amplification of the acceleration has resulted in the upper bodies’ levels with respect to the belfry. This could potentially be the result of a partial collapse of the upper bodies. These results indicate that a slight amplification is observed between the GM applied and the belfry level in all PR. The horizontal displacement history (Figure 48(b)) shows a clear local collapse of the Well body, in the case of a PR of 475 and 975. In that sense, as an initial approximation, if the displacement near the top of the structure exceeds 0.5 – 1% of its height, it could indicate a local or global collapse mechanism (Casolo et al., 2013). The horizontal displacement of the nodes at the top and the base of the bell cell exhibit a marked difference due to the partial collapse of the upper bodies, as the final deformed shapes show. Generally, SUMMARY OF THE RESULTS AND THEIR DISCUSSION 75 it should be noted that a significant inelastic residual deformation has been detected at the end of each dynamic analysis, considering the SFSI effects. A residual displacement of around 14 cm at the top of the tower has been obtained for some GM of PR 95. In case of accelerograms of PR 475 and 975, the residual horizontal displacements in the clock body are 50 cm and 65 cm, respectively. In the case of PR 475 and 975, the residual displacement has been analysed at the clock body level since the top body has collapsed, as observed in Figure 48(b). According to (Valente & Milani, 2016), the residual deformation is defined as the ratio between the horizontal residual displacement and the height of the tower. As stated, if the residual deformation is higher than the range of 0.4-0.8%, the structure is expected to present an incipient state of collapse. It should be noted that this procedure is used as a first approximation of the state of the structure, as stated in the work cited. Nevertheless, as a preliminary assessment, for PR 95, it has been obtained that the residual deformation is 0.17%. Therefore, the residual deformation is not important for the PR 95. For PR 475, the residual deformation has been 0.68%. Hence, it can be stated that the clock body level presents a high residual deformation, but between the limit range provided. However, for the PR 975, a residual deformation of 0.87% has been measured at the clock body level. Thus, it results in an incipient state of collapse after the application of this ground motion. As aforementioned, this is an approximation and one of the few quantitative indicators as mentioned in (Valente & Milani, 2016). Therefore, the analysis of the damage pattern is required to check these results. 3.5. Damage analysis In this section, the different tension damage plots (d+) have been plotted at the end of each GM. They have been depicted in tension owing to their being more severe than in compression. Figure 49-51 show the damage patterns of GM for a PR of 95, 475 and 975. Generally, it should be noted that the damage distribution is different for both conditions (fixed and SFSI). In this regard, these results enabled the identification of damage patterns and the most susceptible areas at different levels of seismic intensity. Generally, significant damage is primarily focused near the belfry and in the upper bodies across all PRs. Minor damage is seen in the outer shaft of the tower, concentrating around its openings. In this way, the inner body does not exhibit substantial damage. However, the ascent ramps would suffer serious damage for all the PRs, considering the fixed conditions. In the case of SFSI FEM, only the upper ramps would be damaged. As it can be seen in these figures, the damage increases in the upper bodies in all PRs when the SFSI effects are considered. This issue can be explained by the acceleration amplification detected in the upper bodies in the SFSI FEM. Thus, the Well body experiences more significant damage and deformations, and several columns of it collapse in multiple GMs of 475 and 975 PR. In the case of PR 975, the damage in the belfry level is similar, but the upper bodies suffer a significant increase of damage, intensified at the top body. These damages in the upper body align with the historical transcriptions of the damage inflicted on the tower during the Lisbon earthquake of 1755. BLOQUE A 76 Figure 49. Damage plots in tension (d+) for the PR 95 years: a) Fixed conditions and b) SFSI conditions. It should be noted that the damage in the belfry level have been concentrated in the base and in the upper part of the brick pilasters in case of PR 475 and 975. This issue has been increased in the numerical model of the SFSI condition. This may be a sign of a possible local collapse mechanism in the brick pilasters of the belfry level. In case of the ramps, the damage obtained in the SFSI model is very close to the transcriptions of the damage suffered by the tower during the 1755 Lisbon earthquake. Figure 50. Damage plots in tension (d+) for the PR 475 years: a) Fixed conditions and b) SFSI conditions. SUMMARY OF THE RESULTS AND THEIR DISCUSSION 77 Figure 51. Damage plots in tension (d+) for the PR 975 years: a) Fixed conditions and b) SFSI conditions. BLOQUE A 78 SECTION 4: STRENGTHENING METHODS The main objective of this study is to obtain the calibration of the numerical models and update the mechanical parameters for the seismic retrofitting solutions. To achieve this, the experimental quasi-static cyclic test developed in (Ponte et al., 2023) has been numerically tested to obtain a preliminary analysis of the strengthening methods. Furthermore, the coefficients proposed by the Italian code (NTC. Norme Tecniche per Le Costruzioni, 2018) to consider the retrofit solutions has been applied and analysed. These coefficients adjust the mechanical parameters of the masonry material to simulate the retrofitting methods in the numerical model. Once the calibrated mechanical parameters are obtained, they will be applied to the real numerical model of the tower. The specimen has a dimension of 120 x 120 x 40 cm3 of stone masonry representative in Portuguese heritage building (Ponte et al., 2023). In this regard, reinforced concrete footing and beam with a dimensions 0.5 x 1.25 x 0.10 m3 and 0.5 x 1.25 x 0.10 m3, respectively, were built in the specimens to apply the different boundary conditions (Figure 52). Two unreinforced masonry walls (URM) have been used as base. Furthermore, several retrofitting specimens have been analyzed with different solutions: mortar injection and Fabric Reinforced Cementitious Matrix system (FRCM) applying glass FRP mesh. It is important to highlight that the FRP mesh has been applied to only one face of the wall. The 3D FEM has been developed using the macro-modelling approach like the real numerical model of the tower, explained in the Section 2. A four-tetrahedron element have been used to mesh the model. In this regard, the numerical simulation was carried out using the framework of OpenSees software (McKenna et al., 2000), using the pre- and post-processor STKO (Petracca, Candeloro, et al., 2017). A specific material named ASDConcrete3D (Petracca et al., 2023) has been implemented to simulate the nonlinear behaviour of the masonry material. It is a plastic-damage model implemented in OpenSees to simulate masonry like materials. The quasi-static cyclic test has been performed numerically with the same step and characteristic that the laboratory one. In that sense the test has been divided in two main steps: i) a uniform vertical stress has been imposed on the top concrete beam and ii) imposed cyclic horizontal displacement pattern has been implemented. The cantilever system has been considered as boundary condition. Figure 52. The numerical model of the masonry specimen: a) material properties and b) tetra-mesh. SUMMARY OF THE RESULTS AND THEIR DISCUSSION 79 In first place, a calibration of the unreinforced masonry specimen (URM) has been depicted. For the calibration, the mesh size, mechanical parameters and the top vertical load have been considered. In this regard, the experimental and numerical results have been compared to fit the cyclic results in function of the horizontal displacement and base shear. As can be observe in the Figure 53, the numerical results are very close to the experimental ones. In this regard, the peak capacity is around 50 kN in both cases. However, the strength decay after reaching the peak capacity. This issue is more significantly in the laboratory test compared to the 3D FEM analysis (Figure 53 (a)). Furthermore, the damage patterns obtained are very similar in both analyses, indicating a shear failure damage (Figure 53 (b) (c)). Figure 53. Calibration of the specimen URM1: a) Force-displacement of cyclic analysis, b) damage distribution from the study by (Ponte et al., 2023) and the damage pattern of 3D FEM. In case of the URM 2 (Figure 54), the base shear-displacement results are very similar comparing the numerical and experimental ones (Figure 54 (a)). In this case, the decreasing of the capacity is more similar in both analyses and the ultimate displacement (around 25 mm) is the same. Shear failures have been identified in both analyses, with closely aligned damage patterns (Figure 54 (b)(c)). The higher damage is concentrated in the lower half of the specimen wall masonry. BLOQUE A 86 CONCLUSIONS / CONCLUSIONES 87 VI. CONCLUSIONES C.1. Conclusiones finales Esta tesis tiene como objetivo analizar la vulnerabilidad sísmica de los edificios patrimoniales y su posterior refuerzo, potenciando así la resiliencia del patrimonio cultural. En particular, este estudio se ha centrado en evaluar la vulnerabilidad sísmica de la Giralda de Sevilla. Para lograrlo, se ha desarrollado un modelo numérico complejo que considera la interacción suelocimentación-estructura. En este apartado se han presentado las principales conclusiones derivadas de los resultados de los diferentes apartados. Además, se han comentado los futuros trabajos de investigación derivados de esta tesis. A partir de los resultados obtenidos en apartados anteriores, se han obtenido las siguientes conclusiones específicas:  Los grandes asientos obtenidos se debieron a los estratos blandos bajo la cimentación de la torre, que presentan un gran espesor. Estos estratos tienen un módulo elástico (E) muy bajo, 5.428 kPa y 6.165 kPa, respectivamente. Sin embargo, los asientos diferenciales fueron causados por la profundidad irregular del estrato blando, que aumenta su espesor en 2,50 m en la esquina sureste. Debido a esto, los mayores asientos se obtuvieron en la esquina sureste para todos los modelos de suelo.  El mayor incremento de asiento se ha obtenido en la construcción del alminar y su consolidación. Esto puede deberse al mayor aumento de la presión aplicada (529,5 Kpa) y al largo tiempo de consolidación (370 años). Por el contrario, el asentamiento diferencial sólo aumentó entre 2,0 y 3,0 cm con la construcción del campanario y su consolidación.  La inclinación de la torre provocada por los asientos diferenciales es muy similar a las medidas de verticalidad reales. Sin embargo, se ha detectado una pequeña variación en la inclinación obtenida en algunos modelos. Esto podría deberse a irregularidades en la construcción y al margen de error en las simulaciones FEM.  Según los análisis, se puede afirmar que la carga de la cercana Catedral tiene un efecto insignificante sobre los asentamientos de la torre. Es importante destacar que las cargas de la Catedral son menores, más repartidas y más superficiales que las de la torre de la Giralda. De hecho, se puede observar que el peso de la torre ha provocado asientos inducidos en la Catedral, los cuales son visibles en la puerta del Lagarto.  El terreno ya se ha consolidado, como se puede comprobar en el análisis de la evolución de los asientos en función del tiempo y el análisis de la presión intersticial. En ese sentido, el suelo ha disipado todas las presiones de la construcción del Campanario. Además, han pasado más de 450 años desde sus construcciones.  Cabe señalar que, aunque el análisis no lineal de edificios patrimoniales complejos de mampostería suele requerir un alto esfuerzo computacional, el software OpenSees ha sido capaz de realizar este análisis en un tiempo computacional aceptable. En este sentido, ha sido posible calcular el modelo complejo de elementos finitos, cuya malla está compuesta por 1.104.735 elementos sólidos y 166.216 nodos, utilizando la metodología propuesta.  Los resultados obtenidos en este trabajo enfatizan la importancia de modelar las condiciones de contorno de edificios antiguos para evaluar un comportamiento sísmico. Los patrones de daño de la torre han variado ligeramente, aumentando el daño cerca del nivel del campanario. BLOQUE A 88  Los diagramas de daños por tracción han demostrado que las principales características geométricas de las torres campanario aumentan su vulnerabilidad sísmica. Las aberturas son un área débil en la que se concentra el daño. Por tanto, el nivel del campanario es la zona más vulnerable debido a los grandes huecos que pueden provocar mecanismos de colapso local.  Los resultados de los desplazamientos absolutos en el nodo superior han sido similares en ambos análisis (NLSA y NLDA). Sin embargo, las irregularidades obtenidas en el NLDA para los desplazamientos en cada uno de los nodos no han sido detectadas en el NLSA.  Teniendo en cuenta los límites de deriva establecidos en normativas y directrices, se ha determinado que, a escala global, la torre no superará los valores especificados para cada límite de daño, ni siquiera para los mecanismos de colapso fuera del plano. Sin embargo, los patrones de daño muestran que la torre presentará daños. De hecho, es evidente que ciertas partes de la torre sufrirán daños moderados y mecanismos de colapso locales. En consecuencia, se puede afirmar que los límites de deriva descritos en las normativas y directrices pueden dar lugar a evaluaciones sísmicas inexactas y peligrosas de edificios históricos.  Cabe señalar que la distribución de daños obtenida para la NLDA ha sido muy similar a la transcripción histórica de terremotos pasados que afectaron a la torre. De lo anterior, se puede concluir que las características geométricas de la torre, en este caso la adición del campanario, las irregularidades en altura y la variación de sección transversal han sido muy influyentes en el comportamiento sísmico del edificio. Sus efectos se han observado en la amplificación significativa de los desplazamientos obtenidos en el nudo superior respecto al nivel de la terraza de las azucenas y de campanario.  El comportamiento sísmico de la torre ha cambiado considerablemente con la adición de los efectos SFSI. Esto resultó en un mejor ajuste con las transcripciones de terremotos pasados. En el caso del terremoto de Lisboa de 1755, el cuerpo del Pozo quedó en ruinas, donde se derrumbaron dos columnas. Además, se detectó un desplazamiento residual en los niveles superiores con todos los acelerogramas analizando el 3D FEM con el modelo SFSI. El comportamiento de la caña de la torre es rígido ya que su desplazamiento es constante y homogéneo en ambas condiciones.  Se detectaron mayores diferencias en la amplificación de la aceleración a través de los niveles de la torre, considerando diferentes modelos (base fija y SFSI). La amplificación es proporcional a la altura en el caso de la condición de base fija. Sin embargo, en el caso del SFSI se detecta una amplificación mayor desde el nivel del campanario hasta el cuerpo superior. Esto destacó la importancia de considerar los efectos del SFSI en el análisis sísmico de torres patrimoniales debido al cambio en su comportamiento bajo excitaciones sísmicas.  Generalmente, el daño es mayor en los cuerpos superiores con condiciones SFSI según el análisis de los patrones de daño. Sin embargo, los daños son menores en la caña de la torre. Las rampas de ascenso presentan menos daños cuando se consideran las condiciones SFSI. Se detectó claramente un mecanismo de fallo parcial de los cuerpos superiores debido a los considerables desplazamientos horizontales en la parte superior. Esto enfatiza la debilidad de cuerpos superiores ante esfuerzos de corte, ya que son más delgados que la masiva caña.  El modelo numérico utilizado para simular la no linealidad del material de mampostería funcionó bien en la evaluación de técnicas de refuerzo a escala de panel.  La eficacia de los coeficientes propuestos por el código italiano para simular métodos de rehabilitación en estructuras antiguas de mampostería ha sido verificada. CONCLUSIONS / CONCLUSIONES 89 C.2. Futuras líneas de investigación La investigación realizada en esta Tesis ha sentado una base científica para analizar y mejorar la vulnerabilidad sísmica de los edificios patrimoniales. Como resultado, los investigadores del grupo ahora cuentan con las herramientas y procedimientos necesarios para explorar más a fondo la ingeniería sísmica y analizar este tipo de estructuras antiguas. En este sentido, de este estudio ha surgido un nuevo tema de investigación dentro del grupo, donde se continuará en futuros proyectos. Además, están previstos varios estudios para un futuro próximo, tales como:  El análisis dinámico de la torre se realizará aplicando el escenario determinista. Se recopilarán los terremotos más dañinos que afectaron a Sevilla en el pasado. Luego, estos se simularán utilizando ecuaciones de predicción del movimiento del suelo (GMPE). Se utilizará el GMPE para representar las aceleraciones espectrales y se seleccionarán acelerogramas reales.  Aplicación del análisis cinemático para evaluar los mecanismos de fallo local detectados en el nivel del campanario.  Evaluación de nuevas técnicas de refuerzo símico a escala de panel, comparando ensayos cíclicos experimentales y numéricos. Los parámetros mecánicos actualizados obtenidos se aplicarán en el 3D FEM de la torre y evitarán modernizar solo la superestructura.  Evaluación de métodos de refuerzo del terreno considerando el complejo 3D FEM para evaluar sus efectos en el comportamiento sísmico de la torre y evitar el refuerzo sólo de la estructura.  Elaboración de un modelo numérico FEM más definido del campanario renacentista y de los cuerpos superiores, debido a la elevada concentración de daños en esta parte. Analizar en detalle la distribución de los daños en esta zona. Para ello se aplicarán las aceleraciones amplificadas medidas en el nivel del campanario. Además, varias partes se modelarán aplicando un enfoque de micromodelado. Simulación de los materiales de contacto entre elementos estructurales para tener en cuenta sus efectos sobre el comportamiento de la estructura.  En este trabajo se han aplicado restricciones 'EqDOF' para vincular el suelo y las superficies de cimentación, ya que permiten realizar análisis en un tiempo computacional aceptable. Sin embargo, en trabajos futuros, se deberían explorar vínculos más complejos, como los materiales de contacto, para evaluar exhaustivamente el SFSI, a pesar de su mayor demanda computacional. BLOQUE A 90 REFERENCES 91 REFERENCES Aggiornamento Delle ‘Norme Tecniche per Le Costruzioni’» Di Cui al Decreto Ministeriale 17 Gennaio 2018. (Italian Guideline), 20 Roma (2018). Almagro, A. (2012). Alminares de Al-Andalus y Al-Magrib. Laborarotiro de arqueología y arquitectura de la ciudad. Escuela de estudios Arabes, CSIC. Almagro, A., & Zúñiga, J. I. (2007). 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Seismic vulnerability assessment of an old historical masonry building in Osijek, Croatia, using Damage Index. Journal of Cultural Heritage, 28, 140–150. https://doi.org/10.1016/j.culher.2017.05.012 Ivorra, S., Pallarés, F. J., Adam, J. M., & Tomás, R. (2010). An evaluation of the incidence of soil subsidence on the dynamic behaviour of a Gothic bell tower. Engineering Structures, 32(8), 2318–2325. https://doi.org/10.1016/j.engstruct.2010.04.007 Jiménez Martín, A. (1993). Tres torres en la vida de IBM´Arabi. 282, 671–677. Jiménez Martín, A. (1998). Notas sobre el Alminar de la Aljama de Isbiltya. In VIII Centenario de la Giralda (1198-1998) (pp. 31–43). REFERENCES 95 Jiménez Martín, A. (2007). Notas sobre la mezquita mayor de la Sevilla almohade. Antigrama, 22, 131–154. Jiménez Martín, A. (2018). Tres torres en la vida de Ibn´Arabi. In Ibn Arabi y su época (pp. 77–99). Jiménez Martín, A., & Cabeza Méndez, J. M. (1988). 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Bulletin of Earthquake Engineering, 13(1), 13–47. https://doi.org/10.1007/s10518-014-9674-1 Lysmer, J., & Kuhlemeyer, R. L. (1969). Finite Dynamic Model for Infinite Media. Journal of Engineering Mechanics Division, 95, 859–878. Malcata, M., Ponte, M., Tiberti, S., Bento, R., & Milani, G. (2020). Failure analysis of a Portuguese cultural heritage masterpiece: Bonet building in Sintra. Engineering Failure Analysis, 115(May), 104636. https://doi.org/10.1016/j.engfailanal.2020.104636 Manuel Vázquez Boza, Percy Durand Leyra, Antonio Morales Esteban, J. L. de J. A. (2015). La marga azul del Guadalquivir. CIE Inversiones Editoriales DOSSAT 2000. Manuel Vázquez Boza, Percy Durand Neyra, Antonio Morales Esteban, & José Luis de Justo Alpañés. (2015). La marga azul del Guadalquivir. CIE Inversiones Editoriales DOSSAT 2000. McCann, D. M., & Forde, M. C. (2001). Review of NDT methods in the assessment of concrete and masonry structures. NDT and E International, 34(2), 71–84. https://doi.org/10.1016/S0963-8695(00)00032-3 McKenna, F., Fenves, G. L., & Scott, M. H. (2000). OpenSees: Open system for earthquake engineering simulation. University of California. McKenna, F., Fenves, G.L., Scott, M. H. (2000). OpenSees: Open system for earthquake engineering simulation. Pacific Earthquake Engineering Research Center. University of California, Berkeley. Pacific Earthquake Engineering Research Center. https://opensees.berkeley.edu/ McNeer, R. (2021). Rhino - Rhinoceros 3D. https://www.rhino3d.com/. https://www.rhino3d.com/. BLOQUE A 102 Figure 23. Different mesh sizes applied in the sensitivity analysis (number of elements and nodes). .................................................................................................................................55 Figure 24. Sensitivity analysis of mesh size in the numerical model. a) Pushover curves, b) time required. .......................................................................................................................55 Figure 25. Damage distribution, a) mesh of 60 cm and b) mesh of 40 cm. ...........................55 Figure 26. Frequencies of the first three vibration modes. Experimentally OMA (ARTeMis) and numerically FEM (OpenSees). B (Boundary) and I (Isolated) ...............................................56 Figure 27. Main vibration modes of the tower. Experimental OMA analysis (up); numerical analysis (down). ...................................................................................................................57 Figure 28. Strength domain of the masonry panel and maximum shear strength (Vt) computed for different models by varying a) the tensile and b) the compressive constitutive laws. Damage plots (tension, d+, and compression, d-) and cracks patterns for the CL A numerical model. .58 Figure 29. Pushover curves of the model in the X and the Y direction, positive and negative orientation. Triangular (T) (proportional to the mass and the height) and Uniform (U) (proportional to the mass). Isolated (I) and with boundary conditions (B). .............................60 Figure 30. Damage pattern. Push +X direction: a) Isolated tower and b) tower with boundary condition. ..............................................................................................................................61 Figure 31. Damage pattern. Push -X direction: a) Isolated tower and b) tower with boundary condition. ..............................................................................................................................61 Figure 32. Damage pattern. Push +Y direction: a) Isolated tower and b) tower with boundary condition. ..............................................................................................................................62 Figure 33. Damage pattern. Push -Y direction: a) Isolated tower and b) tower with boundary condition ...............................................................................................................................62 Figure 34. NLSA capacity curves obtained and seismic safety assessment. ........................63 Figure 35. NLSA results for the different PR: a) accelerations and b) displacements. ..........64 Figure 36. NLSA results for the different PR: a) accelerations and b) displacements. Acceleration recorded at each of the levels considered for the ±X (a) and ±Y (b) directions and for each PR. ..........................................................................................................................65 Figure 37. Displacement recorded at each of the levels considered for the ±X (a) and ±Y (b) directions and for each PR. ...................................................................................................66 Figure 38. Comparison between the damage in tension (d+) plots obtained for PR = 95 years for a) NLSA and b) NLDA. ....................................................................................................66 Figure 39. Comparison between the damage in tension (d+) plots obtained for PR = 475 years for a) NLSA and b) NLDA. ....................................................................................................67 Figure 40. Comparison between the damage in tension (d+) plots obtained for PR = 475 years for a) NLSA and b) NLDA .....................................................................................................67 Figure 41. a) Geotechnical profile; b) VS profiles resulting from different in-situ SPT and DPSH tests. ....................................................................................................................................68 Figure 42. SA (Soil type A) according to the EC8-1, for a PR of 95 (a), 475 (b) and 975 (c) years, including the GM selected. .........................................................................................70 Figure 43. SA (Soil type C) according to the EC8-1, for a PR of 95 (a), 475 (b) and 975 (c) years, including the GM selected. .........................................................................................70 Figure 44. Numerical model: a) 3D CAD model; b) 3D FE Superstructure + foundation and c) complete SFSI system (Superstructure + foundation + soil) .................................................71 Figure 45. Numerical model of the SFSI: a) Boundary conditions of 3D FEM and b) Free field boundary condition based on Lysmer and Kuhlemeyer (Lysmer & Kuhlemeyer, 1969).........72 Figure 46. Average accelerations of each level node for different PR and conditions. ..........73 Figure 47. Average displacement of each level node for different PR and conditions. ...........73 Figure 48. NLDA results of the upper bodies for different PR: a) accelerations and b) displacements. (Time s) .......................................................................................................74 FIGURES AND TABLES LIST 103 Figure 49. Damage plots in tension (d+) for the PR 95 years: a) Fixed conditions and b) SFSI conditions. ............................................................................................................................76 Figure 50. Damage plots in tension (d+) for the PR 475 years: a) Fixed conditions and b) SFSI conditions. ............................................................................................................................76 Figure 51. Damage plots in tension (d+) for the PR 975 years: a) Fixed conditions and b) SFSI conditions. ............................................................................................................................77 Figure 52. The numerical model of the masonry specimen: a) material properties and b) tetramesh. ...................................................................................................................................78 Figure 53. Calibration of the specimen URM1: a) Force-displacement of cyclic analysis, b) damage distribution from the study by (Ponte et al., 2023) and the damage pattern of 3D FEM. .............................................................................................................................................79 Figure 54. Calibration of the specimen URM2: a) Force-displacement of cyclic analysis, b) damage distribution from the study by (Ponte et al., 2023) and the damage pattern of 3D FEM. .............................................................................................................................................80 Figure 55. URM1. Retrofit with FRCM system. Carbon FRP mesh: a) Force-displacement of cyclic analysis, b) damage distribution from the study by (Ponte et al., 2023) and the damage pattern of 3D FEM. ...............................................................................................................81 Figure 56. URM2. Retrofit with FRCM system. Glass FRP mesh: a) Force-displacement of cyclic analysis, b) damage distribution from the study by (Ponte et al., 2023) and the damage pattern of 3D FEM. ...............................................................................................................81 Figure 57. URM2. Retrofit with injection: a) Force-displacement of cyclic analysis, b) damage distribution from the study by (Ponte et al., 2023) and the damage pattern of 3D FEM. .......82 Table list Table 1. Pressure applied to the base of the foundation for the construction phases … 39 Table 2. Stratigraphy of the soil and layer thickness ……………………………………... 40 Table 3. Geotechnical properties of the strata…………………………………………….. 40 Table 4. Properties of the foundation base ………………………………………………… 41 Table 5. Settlement for each point and construction phase. Results in centimetres (cm) …………………………………………………………………………………………….. 44 Table 6. Mechanical properties used in the 3D FEM model……………………………... 57 Table 7. Geotechnical parameters of the strata: γ (unit weight), Vs (wave velocity), E (dynamic elastic modulus), v (Poisson ratio), G (shear modulus), B (bulk modulus), c (cohesion) and Φ (friction angle)……………………………………………………………. 67 Table 8. Real accelerograms selected (Soil type A), standard deviation (S) and factor of scale (f) for the 95 (0.04 g), 475 (0.09 g) and 975 (0.13 g) years of return period (PR) for the Giralda site ……………………………………………………………………… 67 Table 9. Real accelerograms selected (Soil type C), standard deviation (S) and factor of scale (f) for the 95 (0.04 g), 475 (0.09 g) and 975 (0.13 g) years of return period (PR) for the Giralda site ……………………………………………………………………… 68 BLOQUE A 104 FIGURES AND TABLES LIST 105 BLOQUE B I. Publications in indexed journals SECTION 1 Article 1: Analysis of the Historical Settlements of the Giralda. Article 2: Analysis of the giralda tower geotechnical profile and its settlements. SECTION 2 Article 3: Numerical modelling for the seismic assessment of complex masonry heritage buildings: the case study of the Giralda tower. Article 4: Failure and damage analysis of the Giralda tower of Seville under different non-linear static and dynamic seismic loadings. SECCIÓN 3 Article 5: Impact of the soil-foundation-structure interaction in the seismic behaviour of a heritage masonry tower. II. Book chapters Book chapter: Preliminary evaluation of the soil-structure interaction on the seismic behaviour of a complex masonry tower: the Giralda tower of Seville. III. Communications published in conference proceedings Conference 1: Seismic assessment of historic complex towers. The case study of the Giralda tower. Conference 2: Preliminary seismic analysis of Giralda tower applying a finite element model. Conference 3: Preliminary seismic assessment of the soil-structure interaction effects of a complex masonry tower. BLOQUE B 106 PUBLICATIONS IN INDEXED JOURNALS 107 I. PUBLICATIONS IN INDEXED JOURNALS BLOQUE B 108 PUBLICATIONS IN INDEXED JOURNALS 109 SECTION 1 ARTICLE 1 Analysis of the Historical Settlements of the Giralda. Romero Sánchez, E., Morales Esteban, A., Navarro Casas, J. (2022) International Journal of Architectural Heritage, 17(8), 1312-1330. https://doi.org/10.1080/15583058.2022.2034070 ABSTRACT. The preservation of the cultural heritage is a current challenge for modern societies. Thus, it is important to analyse the structural behaviour of historical buildings in order to detect and prevent future damage. This paper analyses the historical settlements of the Giralda tower of the Cathedral of Seville. Currently, it has a tilt which might have been caused by a differential settlement. With this aim, a detailed characterisation of the foundation and its geotechnical model has been carried out. An accurate 3D Finite Elements Model (FEM) has been used to analyse the settlements, taking into account the different construction phases, the loads, the time of execution and consolidation between phases. Finally, the 3D FEM results have been compared with other previous works and the in-situ measurements of the verticality of the tower. Therefore, the authors have found that the tilt to the south-east direction has been caused by the thicker, soft strata under this corner, which has caused differential settlement in this direction. Moreover, it should be highlighted that a good agreement between the settlements of the model and its real top displacements has been obtained. BLOQUE B 110 PUBLICATIONS IN INDEXED JOURNALS 111 SECTION 1 ARTICLE 2 Analysis of the Giralda tower geotechnical profile and its settlements. Romero Sánchez, E., Morales Esteban, A., Navarro Casas, J. (2022) Journal of Computational Methods and Experimental Measurements, 10(1), 1-12. 10.2495/CMEM-V10-N1-1-12 ABSTRACT. The preservation of the cultural heritage is a current and challenging issue for the sustainable development of countries, such is the case in the European Union. Seville is a Spanish city located in the southern Iberian Peninsula, and it is well-known for the importance of its cultural heritage. It is one of the main sources for its economic growth, employment and cultural development. The Giralda tower of the Cathedral of Seville is its most representative building. It has been declared as World Heritage Site by the UNESCO due to its patrimonial value. The Giralda was constructed in 1384 as the Aljama of the major mosque of Seville. However, it has undergone different construction phases over time. One of the most relevant modifications was the addition of the bell tower designed by the architect Hernán Ruíz in the Renaissance. Moreover, the tower has been affected by several historic earthquakes. The goal of this study is to define the geotechnical profile of the soil under the tower and to analyse its settlements. This study will focus on the several modifications that the building has suffered throughout its history. Moreover, it will properly and exhaustively characterise the foundation, which has not been carried out to date. To do so, the geotechnical profile has been defined accurately with the information of the boreholes drilled at its base. Then, finite elements have been used to model the different load phases, which correspond to the different construction phases. Finally, this analysis has shown a great agreement between the settlements of the tower and its real top displacements. BLOQUE B 118 BOOK CHAPTERS 119 II. BOOK CHAPTERS BLOQUE B 120 BOOK CHAPTERS 121 SECTION 3 BOOK CHAPTER Preliminary evaluation of the soil-structure interaction on the seismic behaviour of a complex masonry tower: the Giralda tower of Seville. Romero-Sánchez, E., Requena-García Cruz, M. V., Morales-Esteban, A. (2024) Seismic Beihaviour and Desing of Irregular and Complex Civil Structures V. Springer ABSTRACT. The soil structure interaction is usually omitted in the seismic analyses of ancient historical buildings, considering the fixed base condition. However, usually, these buildings present a poor foundation, and they are over soft strata, making the as-sumption of the fixed base condition unrealistic. This paper aims to assess the seismic behaviour of the well-known Giralda tower (Seville, Spain) considering the soilstructure interaction (SSI). It was built with unreinforced brick masonry walls in the XII century. A 3D nonlinear numerical model based on the finite element method has been developed, considering the foundation and the soil. Nonlinear static and dynamic analyses have been carried out in the OpenSees framework. The SSI has been simulated through the direct method. The interaction with the Cathedral has been borne in mind. The results have shown that, if the soil struc-ture interaction is considered, the peak strength is similar to the fixed base model, but the displacement is approximately doubled. This leads to an increase of the damage expected. BLOQUE B 122 COMMUNICATIONS PUBLISHED IN CONFERENCE PROCEDDINGS 123 III. COMMUNICATIONS PUBLISHED IN CONFERENCE PROCEEDINGS BLOQUE B 124 COMMUNICATIONS PUBLISHED IN CONFERENCE PROCEDDINGS 125 CONFERENCE 1 Seismic assessment of historic complex towers. The case study of the Giralda tower. Romero-Sánchez, E., Requena-García Cruz, M. V., Morales-Esteban, A. (2023) COMPDYN 2023 doi: 10.7712/120123.10793.20092 ABSTRACT. The Giralda tower of Seville is an ancient complex tower. It is composed of an inner and an outer wall connected by an ascending ramp that varies with its height. The ascending ramp makes every façade be different in height and composition. Also, the unreinforced masonry var-ies and it has some parts made of stone. Moreover, the western façade partly connects with the cathedral and the southern area. It reaches a total height of 95 m and it is one of the most an-cient buildings in Seville. It was listed as a World Heritage Site by the UNESCO in 1987 with the maximum level of protection: Outstanding Universal Value. The tower is located in a seis-mically-prone area and it is known to have been severely damaged during past historic earth-quakes. Therefore, a complete and adequate seismic analysis of its seismic behaviour is manda-tory. This work has focused on a refined analysis of its seismic performance to provide reliable results. A detailed 3D architectural model of the monument has been created in the Rhinoceros software. The seismic assessment has been carried out following the Finite Element Method (FEM) with the OpenSees software. This approach is based on a numerical procedure ground-ed on the use of nonlinear static analysis. Equivalent boundary conditions have been intro-duced to assess the interaction among the different parts of the tower with the cathedral. To minimise the uncertainties in complex masonry buildings and to calibrate the numerical model in situ experimental tests have been carried out. Finally, different horizontal load patterns have been considered in the analyses to assess its seismic behaviour. BLOQUE B 126 COMMUNICATIONS PUBLISHED IN CONFERENCE PROCEDDINGS 127 CONFERENCE 2 Preliminary seismic analysis of Giralda tower applying a finite element model. Romero-Sánchez, E., Requena-García Cruz, M. V., Morales-Esteban, A. (2023) CITE 2023 ABSTRACT. La Giralda es uno de los edificios más importantes de la ciudad de Sevilla (España). Su valor cultural e histórico es indudable, ya que integra varios estilos arquitectónicos construidos en varias fases. Fue catalogada por la UNESCO como Patrimonio de la Humanidad en 1987 y, posteriormente, alcanzó el máximo nivel de protección: Valor Universal Excepcional. El objetivo principal de este trabajo es el desarrollo de un modelo numérico pormenorizado de la torre mediante elementos finitos. La configuración de este se ha realizado en el software STKO, empleando OpenSees como motor de cálculo. La calibración se ha realizado aplicando ensayos in situ no destructivos. Por último, un análisis estático no lineal se ha empleado para la evaluación del comportamiento sísmico global del edificio. Para ello se han aplicado varios patrones de carga. Como resultado, este trabajo muestra que los daños pueden concentrarse alrededor de los huecos, en las rampas y en el nivel del campanario.