Preliminary structural and seismic performance assessment of the Mosque-Cathedral of Cordoba: The Abd al-Rahman I sector

Engineering Structures 291 (2023) 116465 Available online 16 June 2023 0141-0296/© 2023 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/bync-nd/4.0/). Preliminary structural and seismic performance assessment of the Mosque-Cathedral of Cordoba: The Abd al-Rahman I sector M.V. Requena-Garcia-Cruz a , * , E. Romero-S´ anchez b , M.P. L´ opez-Pi˜ na b , A. Morales-Esteban b , c a Department of Mechanical Engineering and Industrial Design, University of Cadiz, Spain b Department of Building Structures and Geotechnical Engineering, University of Seville, Spain c Instituto Universitario de Ciencias de la Construcci´ on, University of Seville, Spain ARTICLE INFO Keywords: Structural and seismic performance Finite element method Nonlinear analyses UNESCO World Heritage Site Numerical modelling Masonry buildings ABSTRACT This manuscript discusses some preliminary results on the structural and the seismic performance of the Mosque- Cathedral of Cordoba, a UNESCO World Heritage. The area is characterized by a moderate seismic hazard. The building was built from the 8th to the 16th century and it has undergone several transformations. Owing to the complexity of the building, this work has focused on the assessment of the Abd al-Rahman I sector, which is the most aged part of the complex. For that, first, a 3D numerical finite element model of the sector has been done in the OpenSees framework and calibrated. To do so, an experimental non-destructive campaign has been carried out. Second, the model has been used to evaluate the structural behaviour, under vertical and horizontal loads, considering different scenarios. Finally, the crack patterns and the seismic safety have been obtained. The results showed that the numerical damage obtained for the gravitational loads is in good agreement with the data collected from the in situ surveys. Also, particular attention should be paid to the cymatiums, as they are the most demanded part of the system. Regarding its seismic performance, the building presents a higher capacity in the direction of the arcades. For the seismic demand, slight damage is expected in both principal directions of the building, which could be easily repaired. Damage concentration is expected in the contact between the perimetral wall and the arcades. This work has expanded the study of the features of the Mosque-Cathedral of Cordoba to the structural and seismic analysis with advanced numerical FE computing, which has not been done to date. To the authors’ knowledge, this is the first time that a macro-modelling approach with solid elements is presented for the seismic assessment of heritage buildings using the OpenSees framework. The methodology to do so is also presented. Apart from showing how advanced numerical analyses can provide useful information to assess the existing damage on monumental buildings, this work aims at contributing to the assessment of the vulnerability and the safety of one of the most emblematic mosque-like buildings of the world. 1. Introduction 1.1. Importance of the structural assessment of heritage buildings Built cultural heritage embodies the identity of cultures and regions. It provides information on the technical and the cultural achievements of a specific period or population [1]. These features characterise the Great Mosque-Cathedral of Cordoba, located in the region of Andalusia, in southern Spain. The complex was declared by the UNESCO as a World Heritage Site in 1984 [2]. This protection was extended to its surroundings, the Historic Centre of Cordoba, in 1994. In 2014, the UNESCO awarded the complex with the recognition of ‘Site of Outstanding Universal Value’. The Mosque-Cathedral of Cordoba is one of the most important monuments in Spain. Its construction started in the 8th century and it was completed in the 16th, undergoing several extensions and transformations. The building is characterized by the wideness of its space, its size and its building techniques. It is composed of parallel naves made of masonry walls and arches with shafts and capitals of stone, following a mosque-like configuration. Owing to its features, it has greatly influenced Western and Eastern Islamic and Christian architectures [2]. Therefore, the preservation of such a monumental asset is crucial. In the case of the Mosque-Cathedral of Cordoba, several features have been studied, such as its proportions and distribution [3,4], columns organisation system [5] or its acoustic properties [6]. As pointed * Corresponding author at: Department of Mechanical Engineering and Industrial Design, University of Cadiz, Spain (M.V. Requena-Garcia-Cruz). E-mail addresses: [email protected] (M.V. Requena-Garcia-Cruz), [email protected] (E. Romero-S´ anchez), [email protected] (M.P. L´ opez-Pi˜ na), ame@ us.es (A. Morales-Esteban). Contents lists available at ScienceDirect Engineering Structures journal homepage: www.elsevier.com/locate/engstruct https://doi.org/10.1016/j.engstruct.2023.116465 Received 10 January 2023; Received in revised form 3 May 2023; Accepted 9 June 2023 Engineering Structures 291 (2023) 116465 2 out in [5], owing to the complexity of the asset, most of these previous studies focused on sectors into which the building is divided. Although many researchers have evaluated this complex building, none of them has studied in depth its structural features. Structural analysis plays a key role in the diagnosis and the safety assessment of historic buildings [7]. It enables characterising their current state, better understanding their structural features and determining their level of structural safety. Furthermore, structural analysis is essential in monumental buildings built following old techniques in seismic areas such as Cordoba. This region has a moderate seismic activity, due to the convergence between the Eurasian and the African tectonic plates [8]. It is distinguished by intraplate close earthquakes of moderate magnitude and far away earthquakes of large/very large magnitude with long return periods [9,10]. Studies focused on the conservation and the restoration of historic buildings are complex from the structural and seismic analysis point of view [11]. This is mainly due to [12]: i) their aseismic design; ii) the transformations undergone; and iii) the difficulty of acquiring as built information of the structural elements and the materials. Nevertheless, improving assessment methodologies and the level of knowledge of cultural assets is key to guarantee their conservation and to carry out future interventions [13,14]. On this basis, the careful analysis of case studies or sectors provides helpful information that can be analogically applied for its rehabilitation and reconstruction [15]. 1.2. Modelling strategies for heritage buildings There are several methods and modelling strategies to assess the structural and the seismic behaviour of masonry heritage buildings. In [16], a critical review of the different strategies, ranging from the Equivalent Frame EF) method (commonly used in engineering practice) to more refined techniques like 2D and 3D Finite Element (FE) procedures based on continuous, discrete, and micro-mechanical approaches is presented. Above all, the FE method is the most powerful and frequently used modelling approach for the structural and the seismic response of heritage buildings. The EF has been used to model mosque-like buildings in 3D [17,18]. However, it leads to certain simplifications, such as the impossibility to obtain the concentrated damage for small deformations, among others, that the FE method does not present [19,20]. Focusing on the FE method, two distinct modelling approaches can be found as presented in [21]: the continuous or the discrete approaches. The continuous approach discretizes the masonry’s walls using beam, shell and solids elements. The discrete approach, considers the masonry as an assembly of blocks that can impact and slide between them. The continuous or macro modelling technique uses a homogeneous and isotropic material to simulate the behaviour of the structural elements. It is usually a damage-plasticity model that allows representing the different masonry capacities in tension and compression through different constitutive laws. Contrariwise to the discrete approach, a homogenization between the bricks and mortar characteristics is considered [22]. Despite its limitation compare to the discrete approach, the continuous method has been proved sufficiently efficient and a robust method to obtain the response of different typologies of historical constructions, as discussed in [23]. Furthermore, this is the approach that is commonly used to model singular heritage buildings such as domes [24–26], towers [27,28], palaces [20], churches [21,29] or mosques [18,30]. In order to provide a reliable safety assessment, it is necessary to obtain numerical models validated and calibrated [31]. This is usually done through an in situ investigation plan based on non-destructive tests (NDT). NDT enable surpassing the difficulty/impossibility of carrying out destructive tests on historic buildings. These allow gathering information about the most relevant parameters, such as the mechanical properties of the materials and the stiffness of the system. The operational modal analysis (OMA) is one of the most used NDT to calibrate numerical models, particularly for complex ancient buildings [7,32–34]. 1.3. Performance assessment of heritage buildings The behaviour of heritage buildings can be either obtained through nonlinear static analyses (NLSA) and/or dynamic analyses, such as timehistory or incremental. The type of analysis is a very critical point since the type of result obtained has a direct consequence in the decisionmaking of both the assessment and latter retrofitting of the asset [35]. Dynamic analyses are a more accurate method to simulate the behaviour of buildings, especially heritage ones. In dynamic analyses, the contribution of all modes is considered. Also, the effect of the vertical component of the input motions is contemplated which, in special structures like heritage buildings, cannot be omitted. Furthermore, this method does not need to perform the conventional transformation to an equivalent nonlinear single degree of freedom system, since the seismic demand is directly described in terms of acceleration time history, obtaining more accurate results. Contrariwise, NLSA does not consider the seismic input, as the displacement demand is evaluated later by applying capacity-demand methods, like the N2-method. Despite such pros, dynamic analyses are more time consuming and require a high computational burden. In spite of some inherent limitations of NLSA, as mentioned above, Nomenclature Mechanical parameters of materials f c Compressive strength. Subindexes ‘0′, ‘p’ and ‘r’ refer to elastic, peak and residual strength f Mc Compressive strength of masonry f M,k Characteristic compressive strength of masonry f bc Compressive strength of brick or stone f mc Compressive strength of mortar f t Tensile strength f Mt Tensile strength of masonry ε c Compressive strain. Subindex ‘p’ refers to peak strength ε t Tensile strain Analyses and parameters computed EF Equivalent frame FE Finite element NDT Non-destructive test NLSA Nonlinear static analysis OMA Operational modal analysis PBA Performance-based approach G fc Compressive fracture energy G ft Tensile fracture energy l ch Element characteristic length E Young’s modulus v Poisson ratio G Shear modulus ρ Density σ Standard deviation PL Performance level DL Damage level V b Basal shear force W Weight of the system d top Displacement of the control node on the top d tb Seismic demand displacement M.V. Requena-Garcia-Cruz et al. Engineering Structures 291 (2023) 116465 3 NLSA represents an effective and feasible tool for the analysis of heritage structures. In fact, NLSA is nowadays extensively used not only at research level but also in the engineering practice. Compared to dynamic analyses, NLSA allows an easier formulation of the monotonic behaviour of URM panels (it does not require to simulate their cyclic behaviour and a lower computational burden is required). The performance of NLSA requires proper choices concerning: the seismic load pattern, the selection of the control node and the representative displacement to be considered in the pushover curve. All of them affect the pushover curve obtained and they are particular important in irregular buildings without rigid diaphragms. In [27], the results obtained with both types of analysis exhibited a satisfactory match, suggesting similar conclusions for the seismic vulnerability of the heritage buildings analysed. Furthermore, as concluded in [36], NLSA can be used as a first attempt to assess the seismic behaviour of complex heritage buildings, bearing in mind that more complex dynamic analyses are needed to compare the results. Further information on the pros and cons of each type of analyses on heritage structures, particularly URM ones, was presented in [37]. For the evaluation of the seismic safety of heritage buildings, the performance-based approach (PBA) is commonly adopted. This is grounded on the fulfilment of some target performance levels in correspondence to predefined seismic actions [12]. The performance of the buildings can be obtained via NLSA and the verification of the capacitydemand method (among other methos as listed in [12]). NLSA and the PBA have been effectively used to assess the structural and the seismic performance of heritage buildings like minarets [38], old mosques [17,18] and churches [39]. 1.4. Scope of this work This work aims to assess, as a preliminary study, the structural and the seismic performance of the Great Mosque-Cathedral of Cordoba. Given the recent historiography of the Mosque-Cathedral of Cordoba pointed out in the state of the art, this work expands the study of its features to the structural and the seismic analysis. This work has not been done yet on this building, despite its cultural value and the seismic hazard of the area. Owing to the complexity of the building, as a preliminary study, this work has focused on the assessment of the Abd al- Rahman I sector in detail. This is the oldest part of the building, which was finished in the 8th century. Apart from studying the structural features of this building for the first time with advanced methods, the main novelty of this work is the methodology presented to achieve the goal established. The analyses have been carried out in the OpenSees framework. This is an opensource software, specific for earthquake-engineering issues. This type of buildings has not been developed in depth in this framework. Hence, as a novelty, an integrated methodology for a mosque-like building is presented, specifically developed to be used in the OpenSees framework. The methodology combines FE analysis, macro-mechanical modelling and experimental NDT for the validation of analytical analyses. Given the state-of-the-art analysis, above all, the FE method is the most powerful and frequently used modelling approach for the structural and seismic assessment. For this reason, the results obtained in this paper can be used in future research works but also for practitioners, especially for the maintenance and the retrofitting plans of the complex. Furthermore, the results obtained have allowed to assess and to discuss both the building’s internal damage and its cracking pattern. The numerical model has been subsequently employed to provide a first evaluation of the seismic behaviour of the building. Apart from showing how advanced numerical analyses can provide useful information to assess the existing damage of monumental buildings, this work aims at contributing to the assessment of the vulnerability and the safety of one of the most emblematic mosque-like buildings of the world. On this basis, this document is divided as follows. In §2, a summary on the history, the features and the historic transformations of the Mosque-Cathedral of Cordoba has been presented. In §3, a preliminary assessment of the current state of the Abd ’al-Rahman I sector has been performed. Knowledge of the structure evolving in the in situ NDT experimental campaign (according to the state of the art review), the material parameters and the structural identification has been provided. In §4, the PBA has been presented together with the selected Performance Levels (PL) and the seismic input. In §5, the nonlinear FE numerical modelling has been developed, validated and calibrated through the experimental results derived from the NDTs and the available data. In this work, the FE method has been chosen since it is the most powerful modelling method. It has been combined with the macro-mechanical modelling approach. It allows obtaining robust results for a preliminary and a global analysis with a fair computational burden and time. In §6, the NLSA have been carried out under vertical and horizontal loads considering different scenarios. Since, in this research, it is intended to develop a calibrated and validated model, NLSA have been chosen, bearing in mind the limitations and the simplifications of this type of analysis. These limitations and implications are intrinsic to the method. Hence, to obtain reliable results, proper choices concerning the load pattern, the control node and the representative displacement have been considered. As pointed out, all of them affect the pushover curve and are particular important. A study concerning the effects of different horizontal load patterns and different control nodes on the structural response has been shown. Simultaneously, the crack patterns obtained from the numerical analysis have been discussed. Afterwards, the seismic safety assessment has been presented. In §7, the conclusions and the future developments have been presented. A flowchart to summarize the methodology path followed in this work is presented in Fig. 1. 2. The Great Mosque-Cathedral of Cordoba 2.1. General information and extensions Located in southern Spain, the Great Mosque-Cathedral of Cordoba constitutes one of the most representative buildings of Andalusian architecture and of emblematic Hispano-Muslim Umayyad art [2]. It is a diaphanous structure that has gone through various extensions, finally reaching an overall dimension of 130 m in length and 50 m in width. The building was constructed for a religious purpose and it has three differentiated elements (Fig. 2(a)): the minaret, a rectangular hypostyle hall or liu´ an conceived as a prayer room with naves perpendicular to the qibla (where the mihrab is placed) and a proportionally harmonic patio or sahn. In the design of the Great Mosque-Cathedral of Cordoba, elements hitherto unheard-of in Islamic religious architecture were used [2]. Such is the case of the double arches (the lower one in the form of a horseshoe and the upper one semi-circular) to create the parallel naves (Fig. 2(b)) or the ‘honeycomb’ capital (Fig. 2(c)), which differs from the Corinthian capital, typical of the caliph art [40]. The Great Mosque-Cathedral of Cordoba has been in constant evolution, subjected to reforms and extensions to be adapted to the needs of the period, like transitioning from Islamic to Christian worship [40]. The construction of the Abd al-Rahman I mosque was started in 785 and it was formed by eleven naves to house eleven thousand worshippers. The original mosque was enlarged three different times following the original design [6] (Fig. 3): by Abd al-Rahman II in 852, Al Hakam in 970 and Al Mansour in 988 [41]. In the 13th century, Cordoba’s Great Mosque was transformed into a cathedral, which also involved the construction of different defensive structures in the Historic Centre. In the 16th century, the Renaissance cruciform basilica was built in a Plateresque style [40]. Over the years, different chapels and domes were added within the reticula of columns and arcades. The building, with its juxtaposition of cultures and architectural styles, has grown organically and continuously over two millennia, maintaining its material integrity, as the UNESCO report stated [2]. The first mosque adopted the orientation of a previous Christian church, which was convenient due to its orientation towards the M.V. Requena-Garcia-Cruz et al. Engineering Structures 291 (2023) 116465 4 Guadalquivir River [41] (Fig. 2(a)). The successive extensions followed the same scheme, resulting in a South-West oriented mosque (Fig. 4(a)). The construction of the primitive part of the mosque (the Abd al- Rahman I, the Abd al-Rahman II and the Al Hakam sectors) was made by reusing existing materials (or plunder). Their bases, shafts and capitals come from existing and dismantled buildings (Roman, Catholic and Arabic) in the region. Consequently, materials vary from marble, granite to limestone. The double arches were made with stone voussoirs and bricks, creating its characteristic bichromatism (Fig. 4(b)). By contrast, the Al Mansour sector was constructed using mainly new materials. It followed a slightly different and more sophisticated building methodology, based on Byzantine architecture [40]. In this sector, the voussoirs were built entirely with stone. The levels of the different elements vary to achieve a global homogenous horizontal line on top of the capitals. 2.2. The Abd ’al-Rahman I sector The Abd ’al-Rahman I sector is composed of eleven longitudinal naves, with different widths ranging from 6.83 m to 7.83 m. In total, the sector is 90 m wide and 20 m long. In Fig. 5, a plan of the sector analysed is shown, pointing out the interaction/contact with other sectors. There are stone columns formed by bases, shafts, capitals and cymatiums that date from the Roman and the Visigothic period [5] (Fig. 6). On the top of the arches, the ‘aqueducts’ evacuate the rainwater and support the timber roofing (Fig. 7(a)). These walls are made of brick limestone masonry. Below, there is a coffered ceiling composed of timber beams of 80–90 cm span, which are lightly embedded on top of the walls. Most of the timber roofing of the naves was changed for steel trusses in the early 20th century (Fig. 7(b)). In this sector, only N14 still has the timber roofing. The rest of the naves N9-N13 and N15-N19 have the 20th century steel trusses. The walls on the perimeter are composed of limestone masonry. Some openings of the north wall were filled. 3. Preliminary assessment of the current state The Great Mosque-Cathedral of Cordoba is characterised by its complexity and size. Depending on the date of construction, each sector presents different configurations and materials. Therefore, they are Fig. 1. Methodology followed in this study. Fig. 2. (a) General view of the complex and the Guadalquivir River. Internal photographs, taken by the authors, of the Mosque with particular emphasis on the naves configuration and the coffered ceiling (b), and the double arches (c). M.V. Requena-Garcia-Cruz et al. Engineering Structures 291 (2023) 116465 5 expected to perform differently structurally and in the case of an earthquake. Given this, the careful analysis of the different sectors and elements that compose the asset is essential for its overall understanding. Accordingly, as suggested by [12], reliable models are needed for historic buildings to guarantee their conservation and to avoid exceeding calculations. On that premise, a detailed structural and seismic performance assessment is carried out on the Abd ’al-Rahman I sector. To do so, a thorough analysis of its structural features and particularities for a robust modelling and calibration has been performed. This is the primitive area, which, therefore, contains most of the reused material. Furthermore, this sector has been chosen to be analysed as a first step for the study of the entire complex. In this section, the procedure followed for the assessment of the current state of the Abd ’al-Rahman I sector is presented. A comprehensive inspection and diagnosis campaign has been performed to distinguish its main structural aspects. The activities carried out on site included the structural identification and characterisation, the visual inspection and the NDT. For the analyses and the construction of the 3D model, the historic drawings (plans and cross sections) belonging to the studies of [41] were used as the main reference. In §3.1, the results of the visual inspection are presented. In §3.2, the in situ testing campaign is described along with the analysis of the mechanical properties of the materials. 3.1. Visual inspection According to the literature and the information provided by the maintenance group of the building, there is no apparent damage in any of the sectors of the building. The building has an exhaustive monitoring and conservation plan. Hence, it is in constant refurbishment. If there had been damage, it was automatically repaired. Hence, it is not possible to analyse visually the damage that the building has had. The identification of the material of the columns has been performed by means of a visual inspection and this has been corroborated with the work developed in [5]. 3.2. In situ testing and available data revision 3.2.1. Schmidt Hammer tests The Schmidt Hammer Method test has been carried out to extract Fig. 3. Plan view with the indication of the extensions in the building adapted from [41] M.V. Requena-Garcia-Cruz et al. Engineering Structures 291 (2023) 116465 6 some preliminary results on the compressive strength of the materials (Fig. 8(a)). This is one of the most used NDT to quickly recognise the condition of building structures. Despite being mainly used for concrete elements, specific devices have been developed to evaluate masonry walls, which have been used in the characterisation of old buildings [42]. In this study, two different Schmidt Hammer devices of Proeti SA [43] have been used. They have a rebound energy of 2.207 Nm and a low rebound energy of 0.735 Nm, to specifically obtain the stone and the masonry compressive strength, respectively (Fig. 8(b)). Fig. 9 shows the identification of the material of the columns as well as the elements tested, which have been highligthed in red. The number of the columns (C i ) has been identified. For each element tested, nine different tests were performed, separated by 10/15 cm. As can be observed, the columns are mainly composed of marble, granite and limestone. The predominant materials of the columns are Lumachella carnina marble (53 %), grey granite (21 %) and Estremoz marble from Fig. 4. Façade to the patio (a) and north–south section of the Abd al-Rahman I, Abd al-Rahman II and Al Hakam sectors (b), both drawings adapted from [41]. Fig. 5. Plan of the Abd ’al-Rahman I sector, pointing out in red the adjacent sectors (contact sections) and the number of the naves (N i ). This is the nomenclature established by the maintenance plan to refer to the naves of the complex. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) M.V. Requena-Garcia-Cruz et al. Engineering Structures 291 (2023) 116465 7 Portugal (10.4 %). Table 1 lists the maximum (max), the minimum (min) and the average (aver) compressive strength (f c ) obtained from the Schmidt Hammer tests on the columns according to the material. Also, the standard deviation ( σ ) of the test results is provided. In general, the statistics analysis of the samples shows that the results are in good agreement. The results obtained for the Estremoz marble and the violet limestone have been the most disperse. The column made of Antique Nero marble was protected by glass and it could not be tested. In the case of the limestone masonry walls, the results performed on the stone have resulted in values of maximum, minimum and average compressive strength (f bc ) of 46 MPa, 22 MPa and 30.20 MPa, respectively, with a ± 4.7 σ . For the bricks of the vaults and the ‘aqueducts’, a f bc of 27 MPa with a ±1.1 σ has been obtained. 3.2.2. Ambient vibration tests With the aim of a more reliable modelling and assessment, an OMA has been performed. This is used to identify the overall dynamic behaviour (the natural frequencies and the vibration modes) of the sector and the connection between elements. The dynamic response of the arcades was measured with force-balance triaxial accelerometers, called GMSplus measuring system from GeoSIG Inc (Fig. 10(a)). The sensors are of high sensitivity, reaching an individual low noise of 24-bit Δ −Σ ADC. All the equipment used belongs to the Department of Building Structures and Geotechnical Engineering of the University of Seville. The ARTeMIS Modal software [44] has been used to calculate the frequencies for the later calibration of the numerical model. To do so, and following previous works [20,45], the Enhanced Frequency Domain Decomposition (EFDD) method has been employed. A surrogate model was firstly created considering some preliminary Fig. 6. In detail sections of the Abd ‘al-Rahman I sector identifying the type of roof in its current state. (a) Longitudinal section of a nave with the 20th century steel roof; (b) transversal section, being N14 in the centre with timber roofing; (c) longitudinal section of the main nave N14 with the old timber roof. Drawings adapted by the authors from [41], including the foundation. Fig. 7. (a) Detail of the ‘aqueducts’ that gather the rainwater and support the two different types of roofing. (b) Photographs of the timber and the steel trusses roofing taken by the authors. M.V. Requena-Garcia-Cruz et al. Engineering Structures 291 (2023) 116465 8 values obtained from the experimental campaign. The mechanical values considered in this surrogate model are listed in Table 2. This model was used to define the position of the triaxial devices for the free ambient vibration test. To do so, a preliminary modal analysis was performed. The measurement points were located considering the deformed modal shape of each mode of vibration obtained. These were placed in the arcades where they presented a considerable deformation in order to obtain good results while taking the measurement. Two measurements have been performed. First, the global behaviour of the building has been obtained. To do so, the corners of the building have Fig. 8. (a) Performing the Schmidt Hammer test on columns of the sector. (b) Schmidt Hammer devices used for the stone and for the masonry. Fig. 9. Plan view of the Abd ’al-Rahman I sector with the identification of the material of the columns and the elements tested (highlighted in red). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) Table 1 Results from the Schmidt Hammer test on the stone materials of the columns. Material Group N◦columns ƒ c,max (MPa) ƒ c,min (MPa) ƒ c,aver (MPa) σ Lumachella carnina Marble 61 (53 %) 83.5 50 72 4.5 Estremoz marble Marble 12 (10.40 %) 80 35 60 8.7 Red breccia Marble 3 (2.60 %) 84 83 83.5 1.5 Green-blue marble Marble 1 (0.87 %) 75 67 70 5.2 Antique Nero marble Marble 1 (0.87 %) – – – – Yellow Breccia Marble 1 (0.87 %) 82 73 77 4.5 Grey granite Granite 25 (21.74 %) 80 70 61 5.5 Sargo granite Granite 3 (2.60 %) 80 80 80 0 Troade granite Granite 2 (1.74 %) 89 57 77.6 4.3 Violet limestone Limestone 3 (2.60 %) 89 67 77.8 7.3 Black limestone Limestone 2 (1.74 %) 80 59 75.5 1.2 Dark limestone Limestone 1 (0.87 %) 89 64 78 1.7 M.V. Requena-Garcia-Cruz et al. Engineering Structures 291 (2023) 116465 9 been measured (the north-western corner was used as reference). Second, two arcades were assessed to obtain their modal behaviour as individual elements. The vibration modes have been determined by selecting peak values in the response of the spectral density functions of the set of the tests performed. In Fig. 10(b), the layout of the sensors in the arcades is shown, pointing out the reference sensor (in dark blue in a fixed position) and the different measurement points (in pink) considered. The reference-fixed sensor, for the global analysis, has been depicted in orange. The results obtained from the OMA and the calibration of the model have been presented in §5.3. After the OMA, no good results have been obtained for the global analysis. Hence, for the calibration, only the second set of measurements has been considered. 3.2.3. Morphology and mechanical properties The materials that compose the building are masonry, stone, steel and timber. In this building, masonry walls are either composed of ceramic bricks or limestone and lime mortar. According to the classification on the morphology of masonry [46], the walls are single leaf, where stone and ceramic elements are bound together using mortar. In the case of the stone elements, these are characterised by a regular cut and they are staggered and placed on horizontal courses with thin mortar joints. According to the masonry typologies established in [47], these have been classified as soft stone masonry. In [48], reference values of soft stone masonry are provided for its mechanical properties: f Mc =1.40–2.40 MPa, f Mt =0.042–0.063 MPa, E =900–1700 MPa, G =300–420 MPa and ρ =1.8 T/m 3 . According to the NDT, the average f bc obtained has been 30.2 MPa. According to the EC6 provisions [49], the characteristic compressive strength of stone masonry can be calculated using f M,k =Kf bc 0.7 f mc 0.3 . However, as pointed out in [48], this formulation is proposed for contemporary buildings. Consequently, in the case of old masonry, the value should be modified by a reduction factor of 0.70. For stone ashlar masonry, K is equal to 0.45 and the compressive strength of the lime mortar (f mc ) has been defined as 0.5 MPa [48]. As a conclusion, a f Mc equal to 2.78 MPa has been obtained, slightly higher than the reference values. In the case of the ceramic brick masonry walls, the mortar joints are thick, commonly known as Byzantine brickwork. These walls have been classified as full brick masonry with lime mortar. In [48], reference values of this type of masonry were provided for its mechanical properties: f Mc =2.00–4.00 MPa, f Mt =0.040–0.140 MPa, E =240–1800 MPa, G =80–600 MPa and ρ =1.8 T/m 3 . According to the NDT, f bc is 27 MPa. According to the EC6, K is 0.6 for brick work masonry and lime mortar f mc can be considered as 1.5 MPa, resulting in a reduced f Mc equal to 4.76 MPa. Nevertheless, as suggested by [48], the properties of very think mortar joints masonries should be reduced by 0.75, resulting in a f Mc equal to 3.57 MPa, in agreement with the reference values. Considering the values of f Mc , the rest of the parameters have been defined by interpolating the values defined in [48] and paying attention to the following considerations: i) regarding the referenced values of E and G, these relate to the uncracked masonry (it has been checked that E ranges between 200–350f Mc , as suggested by [50]); ii) following the provisions of [48], for uncracked sections, it has been considered that G equals to 1/3–2/5 E as a realistic ration; iii) the f t is assumed to be equal to 5 % of the compressive strength [1]; iv) the Poisson’s ratio has been defined according to [48]. The state of conservation is good and, therefore, no reduction factor for the strength and elastic properties has been considered, as suggested in [51]. For the Mediterranean region, different types of stone units have been defined (depending on their source) and characterised in [48]. According to the NDT campaign, in this building, several stone units have been identified (marble, granite and limestone) and their f c has been experimentally obtained. It has been checked that the values of f c , obtained for each unit, have been within the ranges proposed in [52,53]. Hence, the rest of the mechanical properties have been defined considering the values of f c and interpolating the ranges proposed in these works. These results have been also aligned with the experimental values obtained for another historical building in Andalusia [54]. G has been defined as 0.4E, which is the ratio presented in almost all national building codes. The f t has been assumed to be, at least, equal to 5 % of f Mc . Fig. 10. (a) OMA set-up and (b) location of the accelerometers. Table 2 Mechanical properties of the materials used in the preliminary analysis. Material ρ (T/ m 3 ) E (GPa) G (GPa) v ƒ c (MPa) ƒ t (MPa) Clay bricks and lime mortar masonry 1.8 1.7 0.55 0.2 3.57 0.120 Limestone and lime mortar masonry 1.8 1.7 0.42 0.3 2.78 0.063 Marble 2.8 15 6 0.25 60–83.5 3–4.17 Granite 2.8 35 14 0.25 61–80 3.05–4 Limestone 2.7 10 2 0.25 75.5–78 3.77–3.9 Timber (old roof) 0.45 11 4 0.4 40 10 Steel (new roof) 7.8 210 81 0.3 410 275 M.V. Requena-Garcia-Cruz et al. Engineering Structures 291 (2023) 116465 16 6.4. Damage assessment Considering the DLs computed for each global curve (Fig. 19), it can be seen that for the seismic demand displacement (d tb ), the PL expected is limited in both directions, ranging between DL2-DL3. As presented in [12], this level of damage means that some parts of the building might be slightly damaged but could be easily repaired. Particularly, in the case of the Y-direction, since the behaviour is slightly worse than in the X-direction, the seismic demand is closer to the DL3. The safety verification has been checked following the EC8-3 prescription. According to this, the ration between the DL3 and the seismic demand displacements d DL3 /d tb should be higher than 1. In this case, it has been obtained that for the +X-direction, it is 1.14 and for the +Y-direction, it is 1.11. Detailed meshing models with the concentration of the damage and the possible crack patterns are discussed. These have been plotted for the two principal directions of the building and for the pushover step when the d tb is attained in each direction. In Fig. 20, the damage concentration for the +X direction is shown in tension (a) and in compression (b). As can be observed, for the tension, the damage is mainly concentrated in the low part of the north wall, reaching values close to 1 (completely damaged). In the highest part of this wall, some cracks could also appear. Nevertheless, the highest values of damage can be found in the contact between the north wall and the arcades. This can be due to the different materials that compose both walls: limestone and ceramic bricks masonry for the perimeter and inner walls, respectively. Furthermore, the horizontal connection between both walls could not be completely rigid. As seen in Fig. 21, additional damage in tension es expected in the first row of the arches of all the arcades. Also, excessive damage in tension is expected at the low parts of the columns shafts and bases. In the case of the compression, no excessive damage has been seen apart from a few cymatiums being excessively demanded and some parts of the arches, as seen in Fig. 21. However, in the contact between the north wall and the arcades, significant damage is expected, reaching values close to 0.8–0.9. Hence, bearing in mind the excessive damage obtained in tension, this contact can be considered as one of the weakest parts of the structural system. This is in agreement with the historical records of the reinforcements carried out in this wall. In Fig. 22, the damage concentration for the +Y direction is shown in tension and in compression. As can be seen, the damage expected is higher in this direction compared to the other one. As previously commented, this can be due to the bracing effect of the arcades in the other direction. In this case, for the tension, the western wall would be significantly damaged, presenting more parts with excessive damage than the north wall. Damage is concentrated in the lower parts and, to some extent, in the upper part. Similarly to the X direction, a significant damage is also concentrated in the contact between the north wall and the arcades (Fig. 23). Also, as seen in Fig. 23, in tension, the cymatiums are expected to present excessive damage. In the case of compression, no excessive damage is observed since just the north-western wall is expected to be damaged in the upper part. Fig. 19. Capacity curves obtained in the NLSA. Fig. 20. Damage pattern for the +X direction in tension (a) and in compression (b). M.V. Requena-Garcia-Cruz et al. Engineering Structures 291 (2023) 116465 17 7. Conclusions and future developments This paper has addressed the preliminary structural and the seismic assessment of the Mosque-Cathedral of Cordoba, located in the Spanish earthquake-prone region of Andalusia. The UNESCO declared this building as a World Heritage Site of Outstanding Value due to its historic, architectural and artistic value. Given the complexity of the asset, this work has focused on the assessment of the Abd al-Rahman I sector, which is the oldest part of the complex, dating from the 8th century. A comprehensive investigation for the structural and the seismic assessment of the sector has been performed. Refined macro-modelling FE-based models have been calibrated through an experimental campaign based on NDT and the available data to obtain the behaviour and the dynamic characteristics of the asset (frequencies and modes of vibration). Quasi-static analyses have been performed, based on gravitational and horizontal load patterns. This has allowed obtaining the damage and the crack patterns. Also, its seismic safety has been assessed. Particularly, this work has drawn some conclusions: •The OMA has allowed calibrating the numerical model, obtaining, at the end of the iterative procedure, relative errors between frequencies of ±3.8 %. •Generally, the numerical damage for the gravitational load pattern seems in good agreement with the data collected from the in situ survey. It was obtained that particular attention should be paid to the cymatiums, since the damage in compression and in tension reaches values close to 0.7 and 0.9, respectively. •Pushover analyses resulted in a different capacity for the +X and +Y directions of the building. In this case, the building presents a higher capacity in the +X direction, which might be due to the bracing effects of the arcades. A sensitivity analysis on the position of the control node was performed. It was concluded that the most vulnerable curves are those obtained for a control node located in the centre of masses of the building. Fig. 21. Lateral view of the damage pattern for the +X direction in tension (a) and in compression (b). Fig. 22. Damage pattern for the +Y direction in tension (a) and in compression (b). M.V. Requena-Garcia-Cruz et al. Engineering Structures 291 (2023) 116465 18 •It has been established that the PL of the sector is expected in both directions to range between DL2-DL3. Hence, for the seismic demand, light damage is expected, but it could be easily repaired. According to the prescriptions of the EC8, it has been found that the seismic safety is satisfied considering the ground acceleration prescribed by the current Spanish seismic code. It should be highlighted that the worst results were obtained for the +Y-direction. •For the seismic demand, damage in tension is expected to be concentrated in the contact between the arcades and the north wall for both principal directions. Additional damage in tension is expected in the first row of arches of all the arcades. Given the recent historiography of the Mosque-Cathedral of Cordoba, pointed out in the state of the art, this work expands the study of its features to the structural and the seismic analysis. The main novelties of this work are: •Studying the structural features of this building for the first time with advanced methods. •Developing a methodology in the OpenSees framework based on FE analysis, macro-mechanical modelling and experimental results for the validation of the analytical model. To the authors’ knowledge (after an exhaustive review of the literature), this is the first time that a macro-modelling approach with solid elements is presented for the seismic assessment of heritage buildings using the OpenSees framework. •Performing NDT on a masterpiece building that had not been done to date. These have allowed identifying the materials and the mechanical properties of the structural elements as well as the dynamic behaviour the system. •Obtaining some preliminary results that can be used in future research works but also for practitioners, especially for the maintenance workers. •Obtaining the structural behaviour of a specific structural configuration (the double horse-shoe arch) and identifying the weakest elements of a mosque-like building. •According to the results obtained, both the internal damage and the cracking pattern of the building have been depicted. This study shows how advanced numerical analyses can provide useful information to assess the existing damage on monumental buildings. Also, this work aims at contributing to the assessment of the vulnerability and the safety of one of the most emblematic mosque-like buildings of the world. This work represents the first attempt to study the structural and the seismic performance of the Mosque-Cathedral of Cordoba using advanced numerical modelling. It has allowed to draw some preliminary results and conclusions. However, as seen, this is a very complex building and, therefore, more specific and exhaustive studies are needed to properly assess the structural and seismic behaviour. Despite its feasibility and simplicity, as discussed in this research, NLSA present several limitations and simplifications for heritage building. Therefore, as a continuation of this work, in the near future, the authors are encouraged to develop dynamic analyses, such as timehistory or incremental dynamic analysis. Also, in this work, the macromechanical modelling approach is used. However, as concluded in [74], in ancient building, the stereotomy has greatly influenced the dynamic response of ancient masonry structures. Therefore, a discrete-element behaviour assessment can be of great interest to provide some insight on the specific behaviour of this mosque-like configuration. Finally, special interest is also taken by the authors in the specific study of the effects of the soil structure-interaction in the building [75,76]. CRediT authorship contribution statement M.V. Requena-Garcia-Cruz: Conceptualization, Methodology, Data curation, Investigation, Formal analysis, Software, Validation, Writing – original draft, Writing – review & editing. E. Romero-S´ anchez: Methodology, Investigation, Software, Validation, Writing – review & editing. M.P. L´ opez-Pi˜ na: Software, Validation. A. Morales-Esteban: Conceptualization, Supervision, Writing – review & editing, Funding acquisition, Project administration. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Data availability Data will be made available on request. Acknowledgements This work has been supported by the “Fondo Europeo de Desarrollo Regional” FEDER_US-1380730 project. The authors would like to thank the Cathedral of Cordoba’s Chapter for the support and for enabling the study of the monument. Specially, we would like to thank Prof. Gabriel Rebollo Puig, the architect in charge of the building, for his support and willingness to help. The funding provided by the Instituto Universitario de Arquitectura y Ciencias de la Construcci´ on is also acknowledged. Also, the help provided by Dr. Enrique V´ azquez and Dr. ´ Alvaro Serrano with the OMA analysis is acknowledged. Fig. 23. Lateral view of the damage pattern for the +Y direction in tension. M.V. Requena-Garcia-Cruz et al. 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