Non-destructive testing and finite element method integrated procedure for heritage diagnosis: the Seville Cathedral case study

Journal of Building Engineering 37 (2021) 102134 Available online 6 January 2021 2352-7102/© 2020 Elsevier Ltd. All rights reserved. Non-destructive testing and Finite Element Method integrated procedure for heritage diagnosis: The Seville Cathedral case study Eduardo Diz-Mellado a , Emilio J. Mascort-Albea b , Rocío Romero-Hern´ andez b , Carmen Gal´ an-Marín a , Carlos Rivera-G´ omez a , * , Jonathan Ruiz-Jaramillo c , Antonio Jaramillo-Morilla b a Departamento de Construcciones Arquitect´ onicas 1, Escuela T´ ecnica Superior de Arquitectura, Universidad de Sevilla, Avda. Reina Mercedes, 2, 41012, Seville, Spain b Departamento de Estructuras de Edificaci´ on e Ingeniería Del Terreno, Escuela T´ ecnica Superior de Arquitectura, Universidad de Sevilla, Avda. Reina Mercedes, 2, 41012, Seville, Spain c ´ Area de Estructuras y Construcciones Arquitect´ onicas, Escuela T´ ecnica Superior de Arquitectura, Universidad de M´ alaga, M´ alaga, Spain ARTICLE INFO Keywords: Building heritage Non-destructive testing (NDT) Infrared thermography (IRT) Laser levelling (LL) Accelerometer measures (AM) Ground-penetrating radar (GPR) Finite element method (FEM) ABSTRACT One of the major problems faced by historic cities today involves the conservation of heritage buildings. Damage suffered by these buildings can be irreversible and fast-acting, leading to their disappearance over a short period. The study and analysis of the origin of the damage suffered by these buildings have proved themselves to be key to their conservation. Non-destructive testing (NDT) can detect problems indiscernible to the naked eye, thereby preventing potential losses. In this paper, a non-invasive method for the diagnosis of building structures integrated with the Finite Element Method (FEM) was applied to the Tabernacle Chapel; a building included in the northwest wing of the Cathedral of Seville complex. Despite the many interventions carried out to date, the issue of the chapel’s deterioration has yet to be entirely solved. This research describes the results of a detailed constructive and structural diagnosis methodology for heritage buildings. The data provided from NDT methods, such as Digital Image Processing (DIP), Infrared Thermography (IRT), Laser Levelling (LL), Ambient Vibration Testing (AVT), and Ground-Penetrating Radar (GPR), has been verified and integrated as boundary conditions in a 3D Finite Element Method (FEM) in order to establish the critical points of the structure, including the failure mechanisms. The results led to the conclusion that the main causes of deterioration involved the settling of the grandstand built in the northwest sector of the building and the effects of the thrusts of the dome on the lateral façades. An integrated implementation methodology of NDT and FEM has enabled accurate knowledge to be ascertained of the principal damage affecting this heritage building. 1. Introduction Architectural heritage is exposed to a myriad of hazards that affect its state of conservation. Countless generations over the centuries have felt themselves responsible for the preservation of their inherited legacy, and have defined valid paradigms and operational procedures [1]. Preventive conservation is of major importance today, since it is considered one of the main disciplines in the preservation of architectural heritage [2]. Conceived from a transversal and inter-disciplinary perspective, this concept strives for the development of a set of systematised and periodical activities for the promotion of the correct visibility, understanding, and maintenance of the analysed heritage building [3]. All of this materialises into a set of preventive actions, based on monitoring and follow-up maintenance tasks, aimed at minimising future deterioration [4,5]. By bearing the impact on the materials of the building in mind, the methods applied in the analysis and diagnosis of buildings structures may be classified into three types: destructive, semi-destructive, and non-destructive [6]. The most useful Non-Destructive Testing (NDT) methods, based on the information they provide and their performance, are Digital Image Processing (DIP) [7], Photogrammetry (P) and Stereo photogrammetry (SP) [8,9], Laser levelling (LL), Ambient Vibration Testing (AVT) [10], Infrared Thermography (IRT) [11], and underground mapping analysis by Ground-Penetrating Radar (GPR) [12]. The validation of the techniques and the tests run in the laboratory through computer programs have enabled a huge leap in terms of conservation of * Corresponding author. E-mail address: [email protected] (C. Rivera-G´ omez). Contents lists available at ScienceDirect Journal of Building Engineering journal homepage: http://www.elsevier.com/locate/jobe https://doi.org/10.1016/j.jobe.2020.102134 Received 7 August 2020; Received in revised form 22 December 2020; Accepted 24 December 2020 Journal of Building Engineering 37 (2021) 102134 2 architectural heritage in recent decades [13]. These NDTs are, to a certain extent, controversial: they are considered very favourable techniques by many researchers, but unreliable by others [14], and have successfully been applied in ancient religious and heritage buildings with proven results [15]. Previous research shows how a detailed study of cultural heritage structures generally requires the application of various detection techniques, along with historical and technical knowledge [16]. The multidisciplinary synergy of NDT in recent decades has made it possible to identify damage that architects and engineers were previously unable to analyse [17]. The use of NDT to study the damage of the church of San Juan Bautista in Spain led to the detection of the humidity that was the underlying cause of the damage [18]. Chastre et al. [19] state that it is impossible to carry out destructive tests in most historical buildings due to the damage this would imply to the heritage asset. For this reason, it is preferable to choose NDT or other similar methodologies that enable the physical and mechanical characterisation of the structures and materials of heritage buildings. Consequently, the combined application of these techniques provides significant information on the geometry, materials, constructive stages and structural descriptions of historical buildings [20,21]. Previous research, such as the methodology developed by Lourenço et al. [22] in the Monastery of San Jeronimo in Lisbon, combines non-destructive inspection techniques with structural analysis tools. The combination of these two techniques is a major factor in the improvement of the conservation of cultural heritage. Other research, such as that conducted on the dome of the Cathedral of Pisa, carries out a methodological process based on laser scanning and photogrammetric tools to achieve concise and detailed structural models [23]. The strategies for the conservation of architectural heritage require the use of tools that lead to a deeper understanding of the complex behaviour of these structures. As a result, the correct diagnosis of their state of conservation can be achieved, thereby preventing the appearance of damage and providing new solutions [24]. In addition, previous research shows how the use of current tools, such as the Geographical Information System (GIS), has allowed georeferenced data previously collected in heritage buildings to facilitate a study of the dynamic process of damage in heritage buildings [25]. Previously, NDTs have been integrated with other software, such as Building Energy Modelling (BEM), to better characterise the model, and for a greater understanding of the thermodynamics of the building envelope. This integration, however, can also be carried out for the study of damage in heritage architecture [14]. In this respect, computer analysis using the Finite Element Method (FEM) [26,27] enables some of the results obtained with NDT to be verified, and is therefore helpful in the effective identification and structural diagnosis of typologically differentiated heritage case studies [28]. The information provided by the NDTs is employed to calibrate the models when both tools are combined [27, 29]. This paper focuses on the application of the aforementioned strategies on the study of a leading example of Spanish architectural heritage: the Tabernacle Chapel of Seville Cathedral. The case study has been chosen not only due to its extensive damage but also for being an example where the application of NDT has enabled full understanding of the origin of the existing pathologies. The data gathered has allowed for the evaluation of the current state of the building, and has increased the possibility of finding the origin of the existing damage. This research aims to provide a comprehensive approach to studying and understanding the structural and constructive deterioration of heritage buildings through the application of NDT and FEM in a methodological feedback process. Once all the procedures have been applied and the data gathered, the evaluation of the identified pathologies can be performed, and a methodology is provided that can be applied in future interventions on historic buildings. The NDTs employed can complement each other towards improving the volume of data collected in order to be able to compare and have a hypothesis of the damage [17]. Hitherto, there has been very little research that uses both techniques together, except for simply using non-integrated NDT and FEM to value the damage in certain heritage buildings [30]. The outcome of this paper illustrates the potential and validity of the combined and integrated use of NDT and FEM for a better understanding and diagnosis of historical buildings of great complexity and heritage value. 2. Case study The Cathedral of Santa Maria in Seville is a cultural heritage site built on top of the remains of Seville’s Old Great Mosque, and is considered the largest Gothic cathedral in the world. In 1987, its historical-artistic relevance was officially recognised through its incorporation into the UNESCO World Heritage List [31,32]. The current configuration of Seville Cathedral is the consequence of continuous extensions and modifications incurred throughout its history, which in many cases are the result of interventions triggered by natural phenomena, such as earthquakes, floods and thunderstorms [33,34] as well as anthropogenic actions, such as demolitions and pollution [35]. The Tabernacle Chapel was designed during the 17th century as an independent building, in the Baroque period [36,37]. The case study extends over a total area of 1121.12 m 2 , with a total length of 57.20 m (m), a width of 19.60 m, and a ceiling height of 16.00 m. The roof of the Fig. 1. Location of the tabernacle chapel in seville cathedral. E. Diz-Mellado et al. Journal of Building Engineering 37 (2021) 102134 3 church is almost flat built through sail vaults and is completed by a dome with a lantern over the transept, which reaches 27.00 m at its highest point. Located on the north-western side of the Cathedral (Fig. 1), the case study is perceived as a rectangular prism which has two corner façades adjoining Constitucion Avenue (western side) and Alemanes Street (northern façade), with independent entrances from the public space. 2.1. Chronological phases The construction process faced several setbacks, mainly due to its placement over the foundations of the ancient mosque, the weakness of the soil, and the weight of the new building. Regarding pre-existing conditions, the most widely accepted historiographical hypothesis concerning the construction of the building on top of the foundations of Seville’s Old Great Mosque is shown in Fig. 2. On redrawing the plan of the ancient mosque, the overlap of the plan of the Tabernacle Chapel over the old mosque is revealed [38,39]. A chronological study of the Tabernacle Chapel reveals the different stages of the construction of the building (Phase 1: 1617–1660) and the specific interventions that have been carried out over its more than three hundred years of existence (Phase 2: 1660–2020). All further interventions have resulted from the continuous presence of constructive and structural issues during the life of the building (Table 1) [40]. 2.2. Construction materials According to the chronological analysis, the architectural skeleton of the building is almost totally composed of stone masonry. Over the course of several centuries, stone blocks with similar mechanical properties were extracted from these locations to build remarkable buildings, such as the Andalusian cathedrals [41]. The working hypothesis of this research estimates that the foundation elements of the Tabernacle Chapel are made of a very low-resistance type of calcarenite stone [42]. Additionally, the load-bearing walls, pilasters, arches, vaults, and domes of the building are made of clastic Fig. 2. Relationship between the Tabernacle Chapel and the pre-existing structures of Seville’s Old Great Mosque based on Jim´ enez-Martín’s hypothesis. Perspective drawing of the old mosque and volume of the case study. Table 1 Chronological process of the Tabernacle Chapel’s construction phases. 1617- 1660 Phase 1: Construction of the building 1660–2020 Phase 2: Interventions 1617 Beginning of the construction work 1692 Arch reinforcement 1630 Completion of foundations 1730 Stained-glass substitution and roof repair 1640 Construction of all the stone masonry walls up to the first cornice 1755 Bracing reinforcements of the building subsequent to the Lisbon Earthquake 1649 Construction shutdown 1776 Replacement of ashlars and lightning of the roof and walls 1656 The dome over the transept and vaults are built. Underground crypt opening 1963 Overall consolidation work, structural reinforcement and lantern addition 1660 Completion of construction 2020 Reinforcement of the foundations Table 2 Main material properties of the Tabernacle Chapel. Based on the mechanical resistance and unit weight values, it is possible to provide operational values for the elastic characteristics of the materials. Elastic Module Poisson Coefficient Unit Weight (kN/m 3 ) Compressive strength (MPa) Dynamic E dyn (GPa) Elastic E st (GPa) Dynamic V dyn Elastic V st Stone masonry 2.46 1.81 0.25 0.38 23.50 2.70 Stone foundation 2.34 1.67 0.31 0.47 21.10 1.20 Concrete reinforcements 28.00 28.00 0.20 0.20 25.00 28.00 E. Diz-Mellado et al. Journal of Building Engineering 37 (2021) 102134 4 sedimentary rocks: mainly calcarenites and sandstones [43–45]. According to the consulted technical reports, these tests showed that the building material can be identified as a calcareous stone, which has an average unconfined compressive strength of 2.70 MPa and two subtypes of variations: simple calcareous sandstone and silt calcareous sandstone [46]. As a summary, Table 2 provides a list of the values of the main building materials that have been determined for this research. 2.3. Structural system approach Structurally, the Tabernacle Chapel works as a box of 57.20 m × 19.60 m x 24.50 m, emphasised along the longitudinal axis and supported by pilasters that transfer the weight of the sail vaults to the main walls of the building. A remarkable dome of 10.00 m in diameter and several sail vaults of various sizes and proportions configure the flat roof of the building. Table 3 provides the geometrical parameters for the evaluation of the structure to anticipate certain mechanical behaviours in a theoretical way, as a preliminary overview to further calculations and models. In this case, the coefficients are based on experimental and numerical studies that provide interesting reference values [47]. Additionally, it is considered that the load-bearing walls are supported by continuous footings of 1.50 m wide, which transmit their load to a layer of anthropic fill soil at an approximate depth of 4.50 m. 2.4. Soil properties The Tabernacle Chapel is located on an area with a stratigraphic configuration that is highly representative of subterranean Seville. Generally, it consists of a layer of anthropic fill that characterises the historical city, supported by alluvial soils with deposits of clay, sand, and gravel whose layers are of varying thicknesses, which are located on a bed of blue marlstones. Additionally, the phreatic level (PL) often appears in superficial levels as a consequence of the existence of numerous underground courses and the proximity to the Guadalquivir River [48]. From these factors, the geotechnical hypothesis indicated in Fig. 3 and Table 4 has been completed with geotechnical studies carried out in the surroundings of the case study [49]. 3. Methodology Given the main characteristics of the building, the need for a complete and rigorous diagnosis has been established for the evaluation of the origin of the damage suffered by the Chapel [50]. The number and complexity of the circumstances that must be considered in the pathological diagnosis of a structure increase considerably in the case of historical buildings, where there is a general lack of complete information regarding the original construction. It is therefore necessary to propose phases and tasks that enable the various dimensions and factors of the issue, which usually overlap, to be understood and studied separately, in order to be able to approach this issue with a comprehensive perspective. Consequently, a methodological approach is proposed that combines the use of NDT with the complementary development of FEM through a non-invasive characterisation protocol that integrates the two techniques. This procedure enables work to be organised in the following 4 thematic areas (Fig. 4). Documentary studies: general information on the building through an estimate of basic values from the study of documentary and bibliographic sources; NDT basic definition: confirmation of the basic properties of the building and their context; NDT Table 3 Geometric and structural parameters. According to the following nomenclature: Rat-L/W (Building Length/Width Ratio); Rat-H/W (Building Height/Width Ratio); St-D (Structural Element Density); W–Th (Wall Thickness); Op-% (Opening in Wall Percentage); Vt-Sl (Wall Vertical Slenderness. Height/Thickness Ratio); Fr-L (Wall Free Length. Length/Thickness Ratio). The different percentages have been calculated according to the respective elevation and plan surfaces of the elements analysed. Rat-L/ W Rat- H/W St-D W–Th Op-% Vt- Sl Fr- L Tabernacle Chapel 2.00 2.20 22.4% 1.00 m 10 8.7 3.3 Reference Values ≤2 ≤4 ≈20% >0.35 m <40% ≤9 ≤7 Fig. 3. Soil identifications: geological and geotechnical levels, depth in metres. P.L.: phreatic level. Table 4 Geotechnical ground data of the shallow layers. Fill Depth: 0.00 m–4.50 m Phreatic level: 5.00 m Unit weight (γ) =17 kN/m 3 Friction angle (Φ) =25◦ Unconfined compressive strength (q u ) =30 kN/m 2 Clay Depth: 4.50 m–11.00 m Unit weight (γ) =20 kN/m 3 Saturated unit weight (γ sat) =21 kN/m 3 Friction angle (Φ) =20◦ Unconfined compressive strength (q u ) =180 kN/m 2 Sand Depth: 11.00 m–13.20 m Unit weight (γ) =18 kN/m 3 Saturated unit weight (γ sat) =20 kN/m 3 Friction angle (Φ) =31◦ Unconfined compressive strength (q u ) =200 kN/m 2 Standard Penetration Test (N SPT ) =20 Gravel Depth: 11.00 m–23.00 m Unit weight (γ) =19 kN/m 3 Saturated unit weight (γ sat) =21 kN/m 3 Friction angle (Φ) =45◦ E. Diz-Mellado et al. Journal of Building Engineering 37 (2021) 102134 5 specific definition: determination of damaged elements and formulation and hypotheses relating to risk situations; FEM simulation: numerical testing of the hypotheses formulated. Therefore, it is considered that the results of the NDT tests can be used not only to establish a diagnosis of the detected damage, but also to verify the validity of the numerical data used in the development of a simplified calculation model that is capable of complementing the diagnosis made through the use of non-invasive tests, as well as to integrate some of the results into the FEM simulation model itself. 3.1. NDT implementation process Given the extensive overview of the variety of non-destructive techniques that can be applied in the current context, their combination allows for the coherent development of a protocol to evaluate the state of conservation of historic buildings. Additionally, the use of NDT must consider the study of the documentary information on the building which, in many cases, provides data from destructive tests performed in previous historical stages [51]. The application of several of the techniques employed has been carried out through the researchers’ methodologies, in an effort to obtain scientific results in the most rigorous, effective, and economical way possible, while still taking into account the needs of financial efficiency, that also require the diagnostic work of pre-existing buildings. In the sections corresponding to the referred cases, the advantages and particularities of the specific methodologies have been laid out and explained. A complete survey including NDT, such as Digital Image Processing (DIP), Infrared Thermography (IRT), laser levelling (LL), Ambient Vibration Testing (AVT), and geophysical techniques such as Ground- Penetrating Radar (GPR), has been carried out. The tests using NDT allow for the characterisation and diagnosis of the building, and at the same time enable the estimation of certain parameters to be taken into account in the simulation of structural aspects using FEM. Together these are employed to validate previous hypotheses and to carry out partial diagnoses. The use of all of them and the superposition of the results that they can contribute provide a comprehensive vision of the current state, by establishing comparative ranges that determine heterogeneities and constructive failures. 3.1.1. Digital Image Processing (DIP) Digital Image Processing is a technique that currently allows for the detailed geometric characterisation of heritage building models [52] and for the detection of material damage [53,54]. It plots a virtual mesh on the façade, to determine the pictures to be taken (Fig. 5a and b). This survey sets the main architectural patterns and spots the main pathologies (Fig. 5c). During this process, various graphic designs and assisted drawing programs have been used. For instance, the ashlars and damage have been drawn in AutoCAD 2019 version. Photogrammetry of the façades was used as a support to draw the damage of the chapel. Despite the restorations carried out within the last decade, the stone façades of the building display fissures and cracks involving pilasters, windows, and cornices. Vertical, tilted, and horizontal fissures are spread over the whole surface of each façade (Fig. 6). Ancient damage coexists alongside active issues: the different geometry and nature of the cracks highlight their different origins. Furthermore, inside the dome and vaults major cracks reveal its instability and potential to collapse due to movement. For this reason, a security net has been installed. Subsequent to this preliminary work, it can be concluded that the building presents undetected and unsolved issues that continue to be currently active. 3.1.2. Infrared thermography (IRT) Infrared Thermography is an NDT widely employed for quantitative and qualitative evaluations for building diagnostics [55]. In heritage architecture, it constitutes a highly valuable tool since it allows for the analysis of the state of conservation of construction materials without using invasive sampling methods. The infrared thermography technique is based on the measurement of the radiant thermal energy distribution that is emitted from a target, and translates this distribution into a visible image [56]. We have used a single-time passive thermal acquisition and measure the radiation intensity, in a qualitative study, to detect anomalies in the walls occurring under normal conditions, and emissivity of 1 has been considered in this case study. The thermal images of the Tabernacle Chapel, taken with a thermography camera model TROTEC AC080V (spectral range 8–14 μ m; Fig. 4. Integrated NDT and FEM global methodological process. E. Diz-Mellado et al. Journal of Building Engineering 37 (2021) 102134 6 LWIR, 160 ×120 px. resolution) have been used for building diagnosis, mainly as a qualitative test, since the objective is the identification of the location of the thermal anomalies, usually due to moisture issues, differences between materials, or wall cracks [57]. Although the measurements can be disturbed by environmental factors, thermal-imaging technology has become a valuable diagnostic tool when locating water filtrations and cracks (Fig. 7). IRT has also been utilised to confirm the non-existence of metallic reinforcements and connectors between the ashlar walls. Moreover, it has enabled the hypothesis to be verified since no abrupt changes in the materials nor transitions between them have been detected. Capillarity moisture stains have been detected in the north-western corner of the chapel (Fig. 7a). The northern façade displays the main issues with damp. This damage is visible inside the chapel with thermal images. It can be noted that the thermal image of the main vault shows several spots with lower temperatures. These points may be consistent with water leaks caused by cracks in the external masonry (Fig. 7b). Fig. 7c shows a spot with a high decrease in temperature, pointing out the existence of a crack that had been located through the visual inspection, which also happens to be a highly tensile spot in FEM. 3.1.3. Laser levelling (LL) Based on the knowledge of various laser-levelling techniques (LL) to determine building movements [58,59], a simplified method has been employed to detect the angular distortions of the structural elements from the measurement of their vertical deformations [60]. Consequently, an accurate levelling of the chapel floor has proved itself to be a very useful tool in assessing building damage. Vertical movements were obtained using a self-levelling laser model BOSCH GLL-80, placed at points near the pilasters and adjacent to the main loading areas. A detailed plan has been plotted with the numerous measurements, as shown in Fig. 8. The maximum variation of levels is located near the western façade wall, showing around 6 cm in the north-eastern sector. From this data, Fig. 5. Application of DIP to the eastern façade of the Tabernacle Chapel: (a) Photographic set-up of the area analysed (b) Photo-frame drawings using CAD (c) Detailed damage drawing. E. Diz-Mellado et al. Journal of Building Engineering 37 (2021) 102134 7 the angular distortions triggered by instances of differential settling between the measured points were calculated. The maximum distortion is 0.0039 (1/256), located between the points A2 and A3 in the façade (Fig. 8). These methods show the serious settling issues of the façade wall. The settling of the building is not homogeneous as a rigid solid: there are significant differential examples of settling between various areas of the walls. 3.1.4. Ambient Vibration Testing (AVT) Ambient Vibration Testing is employed to determine the rigidity of a structure in situ. This test is based on obtaining the measurement of the movement or vibration generated by the external sources of vibration. All systems undergo a series of environmental actions (wind, traffic, human activity) that generate a response in the form of oscillation or vibration, which, as the product of these external actions, is called environmental vibration. Knowledge regarding the way in which the structure responds allows its fundamental period or frequency to be estimated with sufficient precision: information from which it is possible to determine the rigidity and consequently the bracing degree of the structure studied [61]. The result of this test, the vibration fundamental period of the structure [62], means that an estimate of its overall structural rigidity can be made, thereby providing an empirical value with which to evaluate its state of conservation, because this fundamental period (T) is related to the rigidity (k) and total mass (m) of the structure (Equation (1)). T=2 π  m k √(1) Compared to the use of other methods, such as forced or induced vibration, environmental vibration presents significant advantages, such Fig. 6. Example of damage survey of the eastern façade of the Tabernacle Chapel. Identification of cracks up to 20 mm in width. Fig. 7. IRT images of the Tabernacle Chapel: (a) north-western corner; (b) main vault; (c) north-eastern corner. E. Diz-Mellado et al. Journal of Building Engineering 37 (2021) 102134 8 as efficiency, speed, and economy, in addition to not running any risk since no type of stress is exerted on a structure that could be in a poor condition, which would otherwise pose a risk to both the people performing the test and the structure itself. The results obtained in various experiments show that the use of environmental vibration to obtain the fundamental period of a structure and other dynamic characteristics is sufficiently precise [63]. The test is carried out by means of an accelerometer, which is a device capable of measuring these small oscillations imperceptible to humans. The data emitted by the accelerometer is filtered through an analogue-digital converter, which, through the appropriate software, enables this data to be collected by a laptop computer, thereby providing the natural frequency of vibration of the building through the analysis of the registered signal. Stiffness analysis of the structure is carried out using a high-sensitivity MMF uniaxial accelerometer (model KB12VD) to gauge the ambient vibration of the structure in each of the monitoring zones selected. This accelerometer has a bandwidth range of 0.08–4000 Hz, a dynamic range of ±0.5 to ±5 g, a sensitivity of 10 000 mV/g, a resolution of 8 mg and 210 g weight, connected by coaxial cables to a system of Front-end data acquisition with a 24-bit ADC. In order to facilitate contact of the accelerometers with the building surface, epoxy contact resin was placed on the base. The results obtained have been verified by taking several measures at different places of the walls. Two measurements were taken at all points: one parallel to the longitudinal direction of the church nave and the other perpendicular to it. The test was carried out at six points on the structure (Fig. 9) in order to obtain general information on the building, thereby ruling out any distortion of the measurement due to the Fig. 8. Plan showing levelling in centimetres (blue rectangles) and angular distortions (red ellipses). Fig. 9. Stiffness analysis of the building: (a) measuring device used, on point 2; (b) measuring points on the roof. Base orthophotography obtained from Google Earth. E. Diz-Mellado et al. Journal of Building Engineering 37 (2021) 102134 9 presence of injuries. Thus, the choice of measurement points 1 and 3 is due to the fact that these are points located at either end of the nave in a longitudinal direction, and they would therefore provide relevant information for the analysis of the overall behaviour of the whole building. If the results are very similar, then it can be stated that the building responds in a unique way as a rigid solid. Otherwise, there would be parts that move independently to those of the rest, which would indicate the existence of pathologies that affect the overall rigidity. For the purposes of comparison, point 2 is located in the upper part of one of the chapel’s vaults. This is a different construction element from the rest of the building and therefore the result of the measurement should indicate a different response. Point 4 is located on the vertical of the façade wall of the Constituci´ on Avenue, where it is suspected that there is settling in the foundation. In the same way, the choice of the location of points 5 and 6 is due to the existence of a notable vertical crack in the wall of the Tabernacle Chapel that reveals its resistance against the thrust it receives from one of the buttresses of the Cathedral. Table 5 shows the results obtained from the measurement points. It can be observed from the values shown at point 2 that the response values differ from those obtained in the other measurement areas. On the other hand, the comparison between points 1 and 3 indicates a major difference in rigidity between the longitudinal ends of the building, with the area where point 3 is located being much less rigid than the area of point 1 in the longitudinal direction (Fig. 10). This difference, albeit less pronounced, persists in the transversal direction. With regard to the remaining points analysed, the presence of vertical cracks in the walls is reflected in the increase in the fundamental longitudinal period at points 5 and 6, which is more than double that at point 1. Likewise, the increase in the fundamental longitudinal period at point 4 with respect to point 1, despite its spatial proximity, shows the incidence in rigidity of damage due to settling. In order to compare the results obtained empirically, a theoretical estimate of the fundamental periods and frequencies of the structure has been made. To this end, on the one hand, an empirical formulation proposed by certain regulations is used and, on the other hand, a modal analysis is carried out based on the Finite Element Model described in Section 3.2. Structural codes of certain countries include empirical formulas that allow the estimation of the fundamental period of load-bearing wall structures [64]. These are expressions that are obtained based on the most common construction systems used in each country. These expressions are useful to compare the theoretical value obtained with this formulation with respect to the empirical values of the measurements taken of the building. The following expression is proposed in the Spanish Seismic-Resistant Standard (NCSE-02) as well as in the Environmental French Code, where TF corresponds to the natural period, H is the height of the wall, and L is its length (Equation (2)): TF=0.06⋅H⋅ H/(2L+H) √/ L √(2) For the purposes of the analysis, two verifications are carried out. On the one hand, the longitudinal dimension (Lx) of the building is taken into account, while on the other hand, the transversal direction (Ly) is considered. The results obtained with the application of this empirical formula are indicated in Table 6. The results obtained clearly show the influence of the dimensions of the different panels on the fundamental period of the wall structures. On the other hand, based on the modal analysis carried out in the Finite Element Model of the Tabernacle Chapel, a fundamental frequency of 3.38 Hz (0.29 s) for the transversal direction (mode 1) and 6.10 Hz (0.16 s) for the longitudinal direction (mode 2) has been obtained. 3.1.5. Ground-Penetrating Radar (GPR) The application of geophysical methods, such as Ground-Penetrating Radar, provides highly relevant information regarding subsoil materials without the need for direct alteration of their properties [65]. This NDT has acquired a major standing in the analysis of historical buildings, since it allows a better characterisation of the ground layers and the assessment of foundations and archaeological elements [66–70]. The application of the GPR technique to the case study has been performed with Mala Geoscience equipment, in the form of the Easy Locator model. The use of the MID antenna, with a frequency of 300 MHz and a depth of 6 m, has confirmed the documentary hypotheses regarding subsoil stratigraphy. Additionally, a SHALLOW antenna, with a frequency of 500 MHz and a maximum depth of 2 m, has identified buried building remains. The existence of the crypt, which partially occupies the subsoil of the Tabernacle Chapel, has conditioned the development of this work. Hence, the longitudinal surveys have been carried out parallel to the façades of the building (Fig. 11b and e), while Table 5 Accelerometer measurement results. Measurement Point Longitudinal axis Transverse axis F (Hz) T (s) F (Hz) T (s) 1 Longitudinal end of the building 11.04 0.09 7.06 0.14 2 Upper part of the vault 9.18 0.11 5.27 0.19 3 Longitudinal end of the building 3.21 0.31 5.67 0.18 4 Possible foundation settling 6.99 0.14 7.88 0.13 5 Vertical crack 2.22 0.45 5.27 0.19 6 Vertical crack 4.61 0.22 3.12 0.32 Fig. 10. Result obtained for the longitudinal fundamental frequency at points 1 (a) and 3 (b). Table 6 Fundamental period and frequency of the building along its transverse and longitudinal axes. L x =57.20 m L y =19.60 m F F,x (Hz) T F,x (s) F F,y (Hz) T F,y (s) H tot ¼24.5 m 12.25 0.08 4.86 0.21 E. Diz-Mellado et al. Journal of Building Engineering 37 (2021) 102134 16 photogrammetry and ground-penetrating radar, Eng. Struct. 35 (2012) 296–306, https://doi.org/10.1016/j.engstruct.2011.11.004. [10] A. Saisi, C. Gentile, M. Guidobaldi, Post-earthquake continuous dynamic monitoring of the gabbia tower in Mantua, Italy, Constr Build Mater. 81 (2015) 101–112, https://doi.org/10.1016/j.conbuildmat.2015.02.010. [11] F. Cerdeira, M.E. V´ azquez, J. Collazo, E. Granada, Applicability of infrared thermography to the study of the behaviour of stone panels as building envelopes, Energy Build. 43 (8) (2011) 1845–1851, https://doi.org/10.1016/j. enbuild.2011.03.029. [12] V. P´ erez-Gracia, O. Caselles, J. Clapes, R. Osorio, G. Martínez, J.A. Canas, Integrated near-surface geophysical survey of the Cathedral of Mallorca, J. Archaeol. Sci. 36 (7) (2009) 1289–1299, https://doi.org/10.1016/j. jas.2009.03.001. [13] A. Moropoulou, K.C. Labropoulos, E.T. Delegou, M. Karoglou, A. Bakolas, Nondestructive techniques as a tool for the protection of built cultural heritage, Construct. Build. Mater. J 48 (2013) 1222–1239, https://doi.org/10.1016/j. conbuildmat.2013.03.044. [14] Y. El Masri, T. Rakha, A scoping review of non-destructive testing (NDT) techniques in building performance diagnostic inspections, Construct. Build. Mater. 265 (2020) 120542, https://doi.org/10.1016/j.conbuildmat.2020.120542. [15] E. Mesquita, R. Martini, A. Alves, P. Antunes, H. Varum, Non-destructive characterization of ancient clay brick walls by indirect ultrasonic measurements, J Build Eng 19 (May) (2018) 172–180, https://doi.org/10.1016/j. jobe.2018.05.011. [16] V. P´ erez-Gracia, O. Caselles, J. Clap´ es, G. Martinez, R. Osorio, Non-destructive analysis in cultural heritage buildings: evaluating the Mallorca cathedral supporting structures, NDT E Int. 59 (2013) 40–47, https://doi.org/10.1016/j. ndteint.2013.04.014. [17] G. Kilic, Using advanced NDT for historic buildings: towards an integrated multidisciplinary health assessment strategy, J. Cult. Herit. 16 (4) (2015) 526–535, https://doi.org/10.1016/j.culher.2014.09.010. [18] M.I. Martínez-Garrido, R. Fort, M. G´ omez-Heras, J. Valles-Iriso, M.J. Varas-Muriel, A comprehensive study for moisture control in cultural heritage using nondestructive techniques, J. Appl. Geophys. 155 (2018) 36–52, https://doi.org/ 10.1016/j.jappgeo.2018.03.008. [19] C. Chastre, M. Ludovico-Marques, Nondestructive Testing Methodology to Assess the Conservation of Historic Stone Buildings and Monuments, Elsevier Ltd, 2018, https://doi.org/10.1016/B978-0-08-101928-3.00013-6. [20] G. Faella, G. Frunzio, M. Guadagnuolo, A. Donadio, L. Ferri, The church of the nativity in Bethlehem: non-destructive tests for the structural knowledge, J. Cult. Herit. 13 (4) (2012) 27–41, https://doi.org/10.1016/j.culher.2012.10.014. [21] F. Gabellone, G. Leucci, N. Masini, R. Persico, G. Quarta, F. Grasso, Non-destructive prospecting and virtual reconstruction of the chapel of the Holy Spirit in Lecce, Italy, Near Surf. Geophys. 11 (2) (2013) 231–238, https://doi.org/10.3997/1873- 0604.2012030. [22] P.B. Lourenço, K.J. Krakowiak, F.M. Fernandes, L.F. Ramos, Failure analysis of Monastery of Jer´ onimos, Lisbon: how to learn from sophisticated numerical models, Eng. Fail. Anal. 14 (2) (2007) 280–300, https://doi.org/10.1016/j. engfailanal.2006.02.002. [23] S. Bennati, D. Aita, R. Barsotti, et al., Survey, experimental tests and mechanical modelling of the dome of Pisa Cathedral: a multidisciplinary study, Int J Mason Res Innov 5 (1) (2020) 142, https://doi.org/10.1504/IJMRI.2020.104850. [24] M.-G. Masciotta, J.C.A. Roque, L.F. Ramos, P.B. Lourenço, A multidisciplinary approach to assess the health state of heritage structures: the case study of the Church of Monastery of Jer´ onimos in Lisbon, Construct. Build. Mater. 116 (2016) 169–187, https://doi.org/10.1016/j.conbuildmat.2016.04.146. [25] L. Lopez-Gonzalez, R. Otero de Cosca, M. Gomez-Heras, S. Garcia-Morales, A 4D GIS methodology to study variations in evaporation points on a heritage building, Environ Earth Sci 75 (14) (2016), https://doi.org/10.1007/s12665-016-5907-8. [26] G. Kilic, Integrated health assessment strategy using NDT for reinforced concrete bridges, NDT E Int. 61 (2014) 80–94, https://doi.org/10.1016/j. ndteint.2013.10.001. [27] G. Bartoli, M. Betti, L. Facchini, M. Orlando, Non-destructive characterization of stone columns by dynamic test: application to the lower colonnade of the Dome of the Siena Cathedral, Eng. Struct. 45 (2012) 519–535, https://doi.org/10.1016/j. engstruct.2012.06.024. [28] P.B. Lourenço, Recommendations for restoration of ancient buildings and the survival of a masonry chimney, Construct. Build. Mater. 20 (4) (2006) 239–251, https://doi.org/10.1016/j.conbuildmat.2005.08.026. [29] H.S. Sousa, J.D. Sørensen, P.H. Kirkegaard, J.M. Branco, P.B. Lourenço, On the use of NDT data for reliability-based assessment of existing timber structures, Eng. Struct. 56 (2013) 298–311, https://doi.org/10.1016/j.engstruct.2013.05.014. [30] V. Bosiljkov, M. Uranjek, R.R. Rokoˇ zarní, V. Bokan-Bosiljkov, An integrated diagnostic approach for the assessment of historic masonry structures, J. Cult. Herit. 11 (2010) 239–249, https://doi.org/10.1016/j.culher.2009.11.007. [31] UNESCO World Heritage Committee, Convention Concerning the Protection of the World Cultural and Natural Heritage. Report of Eleventh Session, France, Paris, 1987. http://whc.unesco.org/en/list/383. [32] E.J. Mascort-Albea, J. Ruiz-Jaramillo, F. L´ opez Larrínaga, A de la Pe˜ na Bernal, Sevilla, Patrimonio Mundial: guía cultural interactiva para dispositivos m´ oviles, Rev PH 90 (2016) 152–168, https://doi.org/10.33349/2016.0.3778. [33] J. Ruiz-Jaramillo, A. Jaramillo-Morilla, E.J. Mascort-Albea, Seismic behavior of Mudejar structures, in: REHAB 2014. International Conference on Preservation, Maintenance and Rehabilitation of Historical Buildings and Structures, Green Lines Institute for Sustainable Development, Tomar, Portugal, 2014, pp. 983–992. http s://idus.us.es/xmlui/handle/11441/50811. [34] A.J. Prieto, A. Silva, J. de Brito, J.M. Macías-Bernal, F.J. Alejandre, The influence of pathological situations on churches’ functionality: an approach based on historical records, Int. J. Architect. Herit. (2017) 1–22, https://doi.org/10.1080/ 15583058.2016.1272011. [35] S.A. Ruffolo, V. Comite, M.F. La Russa, et al., An analysis of the black crusts from the Seville Cathedral: a challenge to deepen the understanding of the relationships among microstructure, microchemical features and pollution sources, Sci. Total Environ. 502 (2015) 157–166, https://doi.org/10.1016/j.scitotenv.2014.09.023. [36] A.M. Bravo Bernal, G. Ramallo Asensio, Ubicaci´ on de La Capilla Del Sagrario de La Catedral de Sevilla Pervivencia y Escenografía. Murcia, Universidad de Murcia. Consejería de Educaci´ on y cultura, Espa˜ na, 2003. [37] A.M. Bravo Bernal, A. Jim´ enez Martín, El Sagrario, Un Problema y Su Historia Estudio Arquitect´ onico y Documental de La Capilla Del Sagrario de La Catedral de Sevilla, Universidad de Sevilla, Sevilla, Espa˜ na, 2003. [38] A. Jim´ enez Martín, Cartografía de La Monta˜ na Hueca: Notas Sobre Los Planos Hist´ oricos de La Catedral de Sevilla, Cabildo Metropolitano de la Catedral de Sevilla, Sevilla, Espa˜ na, 1997. [39] A. Jim´ enez Martín, Anatomía de La Catedral de Sevilla, Diputaci´ on de Sevilla, Sevilla, Espa˜ na, 2013. [40] Jim´ enez Sancho ´ A, A. Jim´ enez Martín, La mezquita mayor almohade de Sevilla an´ alisis arqueol´ ogico de su construcci´ on, 2016. https://idus.us.es/xmlui /handle/11441/39118. [41] J.C. Rodríguez Est´ evez, Los Canteros de La Catedral de Sevilla: Del G´ otico Al Renacimiento, Diputaci´ on Provincial de Sevilla, Sevilla, Espa˜ na, 1998. [42] Barrios Padura ´ A, J. Barrios Sevilla, Estudio de Las Cimentaciones de Edificios Hist´ oricos En La Provincia de Sevilla Siglo XII Al XVI, Universidad de Sevilla, Sevilla, Espa˜ na, 2001. [43] A. Martín P´ erez, M. Alcalde Moreno, Morfología macrosc´ opica de alteraci´ on de la piedra de la Catedral de Sevilla/Espa˜ na, Mater. Construcci´ on 40 (219) (1990) 5–28. http://hdl.handle.net/11441/17707. [44] M.´ A. Bello L´ opez, Caracterizaci´ on y estado de alteraci´ on química de los materiales empleados en la construcci´ on de la Catedral de Sevilla, 1988. http://hdl.handle. net/11441/15517. [45] R.M. Esbert Alemany, J. Ordaz Gargallo, F.J. Alonso Rodríguez, et al., Caracterizaci´ on petrofísica y alterabilidad de las piedras de la Catedral de Sevilla, Mater. Construcci´ on 38 (210) (1988) 5–23, https://doi.org/10.3989/mc.1988.v38. i210.835. [46] Vorsevi Informe, T´ ecnico Relativo a Los Estudios Preliminares de Los Trabajos de Intervenci´ on En La Iglesia Colegial Del Divino Salvador (Sevilla, Espa˜ na), Espa˜ na, Sevilla, 2001. [47] N. Jorquera, J. Ruiz, C. Torres, Analysis of seismic design criteria of santo domingo church, a colonial heritage of santiago, Chile, Rev la Constr 16 (3) (2017) 388–402, https://doi.org/10.7764/RDLC.16.3.388. [48] E. Soler Arias, R. Huete Fuertes, C. Rodríguez-Li˜ n´ an, et al., Anejo I.2. Mapa geot´ ecnico B´ asico de la Ciudad de Sevilla, in: Protocolo de Inspecci´ on T´ ecnica de Edificaciones ITE. Sevilla, Espa˜ na: Colegio Oficial de Arquitectos de sevilla, Fundaci´ on Fidas, 2005. [49] C. Oteo Mazo, P. Arozamena, F. Menda˜ na, R. ´ Alvarez, Geotechnical problems during the soil boring in the Seville underground (Spain), in: Proceedings of the 17th International Conference on Soil Mechanics and Geotechnical Engineering: the Academia and Practice of Geotechnical Engineering, vol. 3, International Society for Soil Mechanics and Geotechnical Engineering (ISSMGE), London, UK, 2009, pp. 2461–2464. https://www.issmge.org/uploads/publications/1/21/ STAL9781607500315-2461.pdf. [50] X. Rom˜ ao, E. Paup´ erio, N. Pereira, A framework for the simplified risk analysis of cultural heritage assets, J. Cult. Herit. 20 (2016) 696–708, https://doi.org/ 10.1016/j.culher.2016.05.007. [51] D.M. McCann, M.C. Forde, Review of NDT methods in the assessment of concrete and masonry structures, NDT E Int. 34 (2) (2001) 71–84, https://doi.org/10.1016/ S0963-8695(00)00032-3. [52] P.V.V. De Paiva, C.K. Cogima, E. Dezen-Kempter, M.A.G. De Carvalho, L. R. Cerqueira, Intelligent digital built heritage models: an approach from image processing and building information modelling technology, in: VISIGRAPP 2018 - Proc 13th Int Jt Conf Comput Vision, Imaging Comput Graph Theory Appl, vol. 4, 2018, pp. 558–565, https://doi.org/10.5220/0006615005580565. Visigrapp. [53] R.A. Galantucci, F. Fatiguso, Advanced damage detection techniques in historical buildings using digital photogrammetry and 3D surface anlysis, J. Cult. Herit. 36 (2019) 51–62, https://doi.org/10.1016/j.culher.2018.09.014. [54] R. Perumal, S.B. Venkatachalam, Non invasive detection of moss and crack in monuments using image processing techniques, J Ambient Intell Humaniz Comput (2020), https://doi.org/10.1007/s12652-020-02006-x. Fitzner 2002. [55] L. Ruiz Valero, V. Flores Sasso, E. Prieto Vicioso, In situ assessment of superficial moisture condition in façades of historic building using non-destructive techniques, Case Stud Constr Mater 10 (2019), e00228, https://doi.org/10.1016/j.cscm.2019. e00228. [56] G. Leucci, R. Cataldo, G. De Nunzio, Assessment of fractures in some columns inside the crypt of the Cattedrale di Otranto using integrated geophysical methods, J. Archaeol. Sci. 34 (2) (2007) 222–232, https://doi.org/10.1016/j. jas.2006.04.012. [57] C. Rodríguez-Li˜ n´ an, M.J. Morales Conde, P. Rubio de Hita, F. P´ erez G´ alvez, Inspecci´ on mediante t´ ecnicas no destructivas de un edificio hist´ orico: oratorio San Felipe Neri (C´ adiz), Inf la Construcci´ on 63 (521) (2011) 13–22, https://doi.org/ 10.3989/ic.10.032. [58] O. Tsareva, N. Pshchelko, V. Glazunov, A. Yugov, Separation of relative deformations of buildings from a general displacement vector of deformation E. Diz-Mellado et al. Journal of Building Engineering 37 (2021) 102134 17 Marks, in: B. Anatolijs, V. Nikolai, S. Vitalii (Eds.), Proceedings of EECE 2019, Springer International Publishing, Cham, 2020, pp. 93–102. [59] M. Wr´ oblewska, Measurement methods of building structures deflections, E3S Web Conf. 36 (2018) 1–8, https://doi.org/10.1051/e3sconf/20183602010. [60] J. Ruiz-Jaramillo, E.J. Mascort-Albea, A. Jaramillo-Morilla, Proposed methodology for measurement, survey and assessment of vertical deformation of structures, Struct. Surv. 34 (3) (2016) 276–296, https://doi.org/10.1108/SS-02-2016-0006. [61] F. Espinoza, J.A. Canas, L.G. Pujades, O. Caselles, U. Mena, Utilizaci´ on de La Vibraci´ on Ambiental Como Fuente de Excitaci´ on Para El C´ alculo de Periodos Fundamentales de Edificios, first ed., Ministerio de Fomento; Direcci´ on General del Instituto Geogr´ afico Nacional, Madrid, 2000. [62] A.K. Chopra, Dynamics of Structures, fourth ed., M´ exico D.F.: Pearson, 2014. [63] L.F. Ramos, L. Marques, P.B. Lourenço, G. De Roeck, A. Campos-Costa, J. Roque, Monitoring historical masonry structures with operational modal analysis: two case studies, Mech. Syst. Signal Process. 24 (5) (2010) 1291–1305, https://doi.org/ 10.1016/j.ymssp.2010.01.011. [64] M.A. Najafgholipour, M.R. Maheri, H. Darvishi, S.M. Dehghan, A semi-analytical formulation for estimating the fundamental vibration frequency of historical masonry towers, Bull. Earthq. Eng. 17 (5) (2019) 2627–2645, https://doi.org/ 10.1007/s10518-018-00552-6. [65] H.M. Jol, Ground Penetrating Radar Theory and Applications, vol. 9, First Edit. Elsevier, 2009, https://doi.org/10.1016/B978-0-444-53348-7.00017-X. [66] N. Masini, R. Persico, E. Rizzo, Some examples of GPR prospecting for monitoring of the monumental heritage, J. Geophys. Eng. 7 (2) (2010) 190–199, https://doi. org/10.1088/1742-2132/7/2/S05. [67] D. Ranalli, M. Scozzafava, M. Tallini, Ground penetrating radar investigations for the restoration of historic buildings: the case study of the Collemaggio Basilica (L’Aquila, Italy), J. Cult. Herit. 5 (1) (2004) 91–99, https://doi.org/10.1016/j. culher.2003.05.001. [68] D. Barilaro, C. Branca, S. Gresta, S. Imposa, A. Leone, D. Majolino, Ground penetrating radar (G.P.R.) surveys applied to the research of crypts in San Sebastiano’s church in Catania (Sicily), J. Cult. Herit. 8 (1) (2007) 73–76, https:// doi.org/10.1016/j.culher.2006.10.003. [69] K.C. Lampropoulos, A. Moropoulou, M. Korres, Ground penetrating radar prospection of the construction phases of the Holy Aedicula of the Holy Sepulchre in correlation with architectural analysis, Construct. Build. Mater. 155 (2017) 307–322, https://doi.org/10.1016/j.conbuildmat.2017.08.044. [70] V. P´ erez-Gracia, J.A. Canas, L.G. Pujades, et al., GPR survey to confirm the location of ancient structures under the Valencian Cathedral (Spain), J. Appl. Geophys. 43 (2–4) (2000) 167–174, https://doi.org/10.1016/S0926-9851(99)00056-7. [71] G. Castori, M. Corradi, A. Borri, R. Sisti, A De Maria, Macro element and dynamic seismic analysis of the medieval government building of Perugia, Italy, Int J Mason Res Innov 4 (4) (2019) 297, https://doi.org/10.1504/IJMRI.2019.102529. [72] A. Tralli, A. Chiozzi, N. Grillanda, G. Milani, Masonry structures in the presence of foundation settlements and unilateral contact problems, Int. J. Solid Struct. 191–192 (2020) 187–201, https://doi.org/10.1016/j.ijsolstr.2019.12.005. [73] M. Valente, G. Brandonisio, G. Milani, A De Luca, Seismic response evaluation of ten tuff masonry churches with basilica plan through advanced numerical simulations, Int J Mason Res Innov 5 (1) (2020) 1, https://doi.org/10.1504/ IJMRI.2020.104849. [74] S. Galassi, G. Tempesta, The Matlab code of the method based on the Full Range Factor for assessing the safety of masonry arches, Methods 6 (June) (2019) 1521–1542, https://doi.org/10.1016/j.mex.2019.05.033. [75] G. Tempesta, S. Galassi, Safety evaluation of masonry arches. A numerical procedure based on the thrust line closest to the geometrical axis, Int. J. Mech. Sci. 155 (February) (2019) 206–221, https://doi.org/10.1016/j.ijmecsci.2019.02.036. [76] J. Heyman, The stone skeleton, Int. J. Solid Struct. 2 (2) (1966) 249–256, https:// doi.org/10.1016/0020-7683(66)90018-7. IN1-IN4, 257-264, IN5-IN12, 265-279. [77] G. Zuccaro, M. Angelillo, A. Gesualdo, A. Iannuzzo, A. Fortunato, Rigid block models for masonry structures, Int J Mason Res Innov 3 (4) (2018) 349, https:// doi.org/10.1504/IJMRI.2018.10016294. [78] A. Iannuzzo, F De Serio, A. Gesualdo, G. Zuccaro, A. Fortunato, M. Angelillo, Crack patterns identification in masonry structures with a C◦displacement energy method, Int J Mason Res Innov 3 (3) (2018) 295, https://doi.org/10.1504/ IJMRI.2018.093490. [79] P.B. Lourenço, Computations on historic masonry structures, Prog. Struct. Eng. Mater. 4 (3) (2002) 301–319, https://doi.org/10.1002/pse.120. [80] C. Rodríguez-Li˜ n´ an, R. Romero-Hern´ andez, E. V´ azquez-Vicente, et al., The materiality in the architecture of the Modern Movement: theoretical and constructive research: structural and foundation analysis, in: Consejería de Cultura y Patrimonio Hist´ orico, ed. Re-HABITAR El Carmen: Un Proyecto Sobre Patrimonio Contempor´ aneo, vol. I, Instituto. Sevilla, (Spain): Instituto Andaluz del Patrimonio Hist´ orico, 2019, pp. 178–195. [81] E.M. Diz-Mellado, Estudio de estructura y cimentaci´ on de la Capilla del Sagrario de la Catedral de Sevilla, June 2016. https://idus.us.es/xmlui/handle/11441/45741. (Accessed 1 October 2016). [82] Ministerio de Fomento, Documento B´ asico Seguridad Estructural vol. 2013, DB-SE, 2007. E. Diz-Mellado et al.