Integration of disciplines in the structural analysis of historical constructions. The Monastery of San Jer´onimo de Buenavista (Seville-Spain)

Integration of disciplines in the structural analysis of historical constructions. The Monastery of San Jer´onimo de Buenavista (Seville-Spain) Margarita C´amaraa,∗, Manuel Romeroa, Pablo Pach´ona, V´ıctor Compana, Paulo B. Louren¸cob aDept. of Continuum Mechanics, Universidad de Sevilla, Avenida Reina Mercedes, 41012 Sevilla, Spain bInstitute for Sustainability and Innovation in Structural Engineering, University of Minho, Guimaraes, Portugal Abstract The assessment of the structural health of historical constructions is needed to carry out correct diagnoses and implement proper decision making strategies in the preservation built cultural heritage. In order to provide information about the state of different structural elements of the Monastery of San Jer´onimo de Buenavista, in Seville (Spain), an extensive experimental campaign, mainly comprising non-destructive and in situ tests, was carried out. The present paper describes a structural analysis based on numerical models. The main goal of this research is to assess the improvement in the results of numerical model by integrating information from techniques which come from fields of knowledge that complement architecture and engineering, such as geophysics, archaeology or topography. A non-linear analysis under gravitational loads until reaching the ultimate load of the structure is developed. A model that is truer to the reality at a global level is obtained, highlighting significant improvements in the results at a local level. Keywords: multidisciplinary approach, historical constructions, experimental campaign, numerical model, non-linear analysis 1. Introduction1 All built heritage recovery processes require the prior assessment of the structural state of2 such constructions. This assessment can be carried out by means of different techniques involving3 varying degrees of complexity, ranging from mere visual analyses to the extraction of material4 samples to be tested in laboratories.5 Nowadays, the most valued techniques are those that are non-destructive or moderately de-6 structive and respectful of this heritage, while also providing both reliable and valuable informa-7 tion regarding the structural behavior of a building. Likewise, the structural analysis of historical8 constructions using mathematical models has experimented significant advances over these past9 years [1]. These models can provide a large amount of information. However, it is difficult to10 develop them, given the high degree of uncertainty that exists regarding relevant factors in struc-11 tural behavior [2]. Items such as the mechanical properties of constituting materials, which may12 ∗Corresponding author. Email address: [email protected] (Margarita C´amara) Preprint submitted to Construction and Building Materials October 3, 2022 have deteriorated with the passing of time, the ground-to-structure relationship or the influence of13 the construction process undergone by a building, are for the most part unknown and should be14 incorporated into a structural model in order for it to accurately show the behavior of the actual15 structure.16 The calibration of finite element models based on Ambient Vibration Testing (AVT) and Oper-17 ational Modal Analysis (OMA) have gained a foothold over the past years as a method to achieve18 structural models that show a dynamic behavior matching that of the actual structure, which is19 obtained experimentally from the actual structure. The mechanical properties of materials are the20 parameters of the model that are generally updated using this technique. In this way, values based21 on experimental tests are obtained for parameters that are initially uncertain [3–6].22 The dynamic identification of structures is a powerful tool which is able to provide reliable23 information regarding the behavior of the structure [7–9]. The main strengths of using techniques24 that apply this kind of information in the analysis of historical constructions reside in its non-25 destructive nature and in its capacity to also provide useful information to both determine and26 predict the damage state of the whole [6, 10].27 However, the results obtained from the calibrated finite element models mentioned above may28 not correspond to the actual behavior of the structure at a local level [10], especially in historical29 buildings which, over time, have been subjected to varying events, uses, extensions, demolitions,30 etc., that have affected their structure.31 In this sense, other non-destructive tests (NDT) or moderately destructive tests (MDT) are ca-32 pable of providing information regarding the different structural elements that constitute a building33 complex. These techniques allow to identify aspects such as the internal composition of elements or34 the deterioration of materials and they sometimes come from other disciplines beyond architecture35 and civil engineering. Thus, non-destructive techniques such as those based on waves propagation36 (seismic tomography, georadar,...) are able to provide information about the internal composition37 of different elements or the level of degradation of their constituting materials. Other techniques,38 such as photogrammetry, that also has a non-destructive character, is able to show the strain state39 of the building. On the other hand, other types of techniques entail a more aggressive approach to40 the monument in order to provide useful information, as they usually require partially breaking or41 removing material. For example, inspection openings allow both to observe construction elements42 and to analyze them if samples from them are also extracted, the extraction of samples allows to43 perform lab tests that are able to determine parameters such as compressive strength and Young44 and Poisson moduli, and continuous samplings of foundations and soil provides information about45 both foundation materials and soil layers on which the foundations rest.46 When the structural analysis process is based mainly on mathematical models, the results47 obtained from these tests are normally used as complementary information, that is, to validate48 or qualify those provided by the model itself. However, the information obtained can also be49 incorporated into the mathematical model in order for it to present results that are more in50 accordance with the actual behavior of the structure, not only at a global level, but also at a local51 level [11, 12]. During a structural analysis process, this would mean integrating other disciplines52 into the study, in addition to architecture and structural engineering.53 In this paper, the structural analysis of the Monastery of San Jer´onimo de Buenavista, in54 Seville, is presented. This analysis has been carried out based on a finite element model that was55 not only calibrated by using AVT and OMA, but also included information obtained from NDTs56 or MDTs performed by other fields of knowledge as a method to obtain a higher fidelity structural57 2 model of the building.58 The construction of the Monastery of San Jer´onimo began at the beginning of the fifteenth59 century. Nowadays, mainly the galleries of the main cloister and some parts of the church, like the60 tower, remain standing (Fig.1).61 Figure 1: Views of the current state of the Monastery of San Jer´onimo de Buenavista, Seville, Spain: (a) North and East wings and tower; (b) South and East wings; and (c) remains of the cloister church and the tower. As for the Monastery’s most recent history, it is important to emphasize two milestones. On62 one hand, the collapse of one of the columns of the northern wing of the cloister (rebuilt in 1973)63 as a result from the Portuguese earthquake of 1969 in the Gorringe bank between the Eurasian64 and African plates. On the other hand, the construction of a building attached to the remains of65 the southern and eastern wings of the cloister(2013) which currently houses a civic center (Fig.2).66 Figure 2: Views of the civic center (a) under construction (2012) and (b) in service (2013). After the construction of the new building, the existing damage in the cloister increased and it67 became urgent to assess the state of the entire complex. The Monastery is a building of significant68 size and it has a complex nature due to the numerous alterations it has suffered over the course of69 history, all of which have visibly affected its structure. However, this also enables the possibility of70 detecting localized deficiencies, making the Monastery a relevant case study to apply and validate71 the new approach of increasing the accuracy of a structural model by integrating information72 obtained from NDTs and MDTs.73 The aim of the analysis presented in this paper is twofold: (i) to assess the improvement74 that a structural model of a historical construction can attain by means of the incorporation of75 3 information obtained from techniques with a non-destructive or a moderately destructive character,76 and (ii) to analyze the structural capabilities of the whole through a non-linear analysis, in order77 to both understand the behavior of the structure and establish a framework for future remedial78 interventions on the monument.79 This paper is structured as follows. Section 2 contains a historical overview of the Monastery80 of San Jer´onimo and a description of its current architectural configuration. Section 3 describes81 a set of inspection techniques carried out in the Monastery. Section 4 includes the development82 of the structural analysis model, which incorporates the results obtained applying the techniques83 identified in Section 3. Section 5 discusses the results obtained after the structural analysis based84 on the mentioned model. Finally, the main conclusions of this research are presented.85 2. The Monastery of San Jer´onimo de Buenavista86 2.1. Historical aspects87 Construction on the Monastery of San Jer´onimo began in 1414 with the church. It was a gothic88 building with a main 45-meter-long nave, flanked by two wings with small chapels, an apse and a89 sacristy. During the first third of the sixteenth century, work on the church and the eastern cloister90 had finished, and the construction of the main cloister began, to the west, attached to the east91 cloister, over an ancient gothic cloister. This construction, built in renaissance style, was raised92 using calcarenite stone and was finished towards the end of that same century. The complex was93 completed by the middle of the seventeenth century, with the upper part of the tower and the94 printing house as the last additions [13] (Fig. 3.a).95 Figure 3: Historical evolution of the Monastery of San Jer´onimo: (a) Original configuration, 1650; (b) historical remains, 2000; and (c) current architectural configuration of the complex, 2019. The building was used as a monastery until the beginning of the nineteenth century. In 1809, its96 regular clergy became extinct and the monastery entered a period of decadence, until it was finally97 abandoned in 1835. In 1850, the building began to be used as a glass factory, which introduced98 changes in the architectural configuration of the church and the tower. The church was used to99 4 house the main oven and the inner floors of the tower were demolished in order to provide space100 for the drying of glassware. Over the course of the second half of the nineteenth century and101 the first half of the twentieth century, large areas of the building were demolished. This was102 probably due to the owners’ need for income, which they obtained by selling materials such as103 marble or stone ashlars. Thus, the eastern cloister, perimetral areas of the main cloister, as well104 as the sacristy, the apse and the central and the Gospel naves of the church were demolished. The105 complex reached its peak of decadence when it was used as a pig fattening farm, a situation that106 lasted well into the twentieth century. In 1964, the building was declared a National Historical and107 Artistic Monument. This led to consolidation works in 1966. However, the monastery once again108 suffered severe damages after the 1969 earthquake, involving the complete destruction of one of109 the columns of the northern wing of the main cloister [13].110 Ever since, the building has undergone constant archeological surveys and maintenance works.111 During the 1970s, the most important interventions regarding the structure of the cloister were112 carried out: the column that had collapsed after the earthquake was rebuilt using calcarenite stone113 and the infill over the upper gallery of the northern wing was replaced by a series of concrete beams114 with the goal of avoiding the collapse of the vaults beneath it. In the 1980s, more improvements115 were made, of which the introduction of a concrete slab above the infill of the entire first floor116 stands out [13].117 2.2. Current architectural configuration118 Presently, the eastern cloister and the printing house no longer exist. As for the church, only119 two chapels of the Epistle wing, the staircase and the wall attached to the main cloister remain120 standing. So does the tower, albeit with an internal configuration that differs from the original.121 After being used as part of the glass factory, its interior was almost completely emptied out.122 Regarding the main cloister (measuring 34.0 x 33.5 m in plan), its lower level has been completely123 preserved: a composition of semicircular arches that rest on half columns and coffered sail vaults124 (Fig. 4). Of the upper level, the only remaining elements are the vertical structures, three-centered125 arches in this case, and some of the vaults in the northern gallery.126 Figure 4: Geometric model of the module type. 5 Within the base of wings where some of the main spaces of the monastery once stood, along127 the southern and eastern side of the main cloister, a new building has recently been erected, used128 as a civic center (Fig. 3.c). In general, this building has a reinforced concrete structure that is129 not entirely freestanding, since it makes use of the original outer walls of the monastery’s galleries130 as part of its supporting elements (Fig. 5). The result is that, on the one hand, the eastern wing131 of the new construction is supported by both the existing wall and a line of reinforced concrete132 columns parallel to it. These columns rest on a linear foundation executed above the remains of133 the existing foundation. On the other, the southern wing is supported by a load-bearing clay block134 wall built over the remains of the outer wall of this former wing, and by the existing inner brick135 wall of the cloister [14].136 Figure 5: New building structure: (a) resting on the ancient one; (b) east wing; and (c) south wing. 2.3. Current state of the building137 Today, the historical part of the building presents severe damages, which have worsened with138 the construction of the new building. By comparing the inspections carried out in 2003 [13], that139 is, before the construction of the new civic centre, with others made since 2013, therefore after the140 attachment of the new building [15–17], changes in the damage state of the cloister were detected.141 Thus, por example, current damages such as the longitudinal cracks in the vaults of the north142 gallery (Fig. 6d), the cracks in the keys of the arches of the ground floor of the east wing (Fig. 6f)143 or the longitudinal cracks between vaults and eastern wall (Fig. 6e) were not mentioned as detected144 damages in the 2003 inspection report [13]. The current state shows that the most relevant damage145 is concentrated along the northern and eastern wings of the cloister. Damages includes cracks and146 material loss, as illustrated in Figure 6.147 6 Figure 6: Most significant damage: (a) vertical cracks in the north wing columns; (b) section loss in the north wing columns; (c) rebuilt column after the 1969 Portuguese earthquake (Fig. 9 - column 10); (d) longitudinal cracks in the vaults of the ground floor of the north gallery; (e) Longitudinal cracks at the intersection of the vaults with the historic wall of the east wing; and (f) cracks in the keys of the arches of the ground floor of the east wing. 3. Structural inspection of the monastery148 A series of techniques were applied to the building with the aim of inspecting the state of its149 structure, both at a global and at a local level. In this way, a set of mostly non-destructive tests150 were carried out in order to obtain information regarding the behavior of the structure and the151 condition of some of its elements.152 3.1. Inspection of the structure at a global level153 3.1.1. Ambient vibration tests (AVTs) and Operational Modal Analysis (OMA)154 With the aim of carrying out a dynamic identification test that could provide information155 regarding the global behavior of the structure, seven experimental ambient vibration campaigns156 were carried out on the object of study: four in the cloister of the monastery, one per each of its157 four wings, two on the wings of the new buildings and, lastly, a general one in order to compare158 and validate the results of the partial campaigns. Before these campaigns, a study was carried159 out based on a simplified preliminary model in order to be able to define the relevant measuring160 7 points. Figure 7 shows a diagram of the measuring points considered on a generic wing, a diagram161 that repeats itself on each of the studied wings, resulting in a total of 32 points per campaign.162 Four accelerometers were used as reference, and another four were placed on each column and163 walls, taking measurements at two heights: 6.80 m and 12.20 m, coinciding with the first floor level164 and at the springer line of the upper arches. Accelerations along the two orthogonal directions165 in plan were recorded with the objective of identifying the vibration modes that could develop166 longitudinally and transversally on each wing. In this way, a total of 16 measurements were taken167 in each experimental campaign.168 Figure 7: Plan showing the location of the accelerometers (reference accelerometers in blue). The measuring equipment used to carry out the different ambient vibration tests comprised169 force balance accelerometers with a bandwidth between 0.01 and 200 Hz, a dynamic range of 140170 dB, a sensitivity of 10 V/g and a mass of 0,35 kg (model ES-U2). These accelerometers were171 connected to a data gathering system with an ADC of 24 bits equipped with anti-alias filters172 (model GRANITE, by KINEMETRICS). The parameters established for the dynamic tests were173 a sampling frequency of 100Hz and a duration of 15 minutes per test. Similar temperature and174 humidity conditions were found during the tests.175 The data obtained was processed using the modal identification method known as Enhanced176 Frequency Domain Decomposition, a method in the frequency domain that is implemented in the177 ARTeMIS Modal software [18]. Table 1 summarizes the obteined results, including the frequencies178 associated with each vibration mode, the damping ratios and the standard deviations presented179 by these values, that is, both of the frequencies and of the damping ratios.180 Mode NoWing EFDD f(Hz) std(f)ξ(%) std(ξ) 1N 2.01 0.02 1.00 0.27 2W 2.33 0.02 0.86 0.12 3N, E, S 3.09 0.04 2.17 0.24 4N, E, S, W 3.35 0.03 0.62 0.31 5W 3.89 0.04 0.67 0.26 6N, E, S, W 4.31 0.05 1.56 0.80 Table 1: Modal parameters: natural frequencies (f), damping ratios (ξ) and standard deviation (std). 8 Likewise, Figure 8 shows the first six vibration modes that were identified, which fall within a181 frequency range of 0 to 5 Hz. The identified modes correspond for the most part with the bending182 modes of the different wings of the cloister. The first, second and fifth are local modes, in which183 only one of the wings undergoes excitation, while the rest of the modes are global modes, in which184 at least two of the wings undergo excitation under the same frequency value.185 Mode 1 (2.01 Hz) Mode 2 (2.33 Hz) Mode 3 (3.09 Hz) Mode 4 (3.35 Hz) Mode 5 (3.85 Hz) Mode 6 (4.31 Hz) N E S W Figure 8: First six experimental vibration modes of the experimental model. 3.1.2. Inspection of damage evolution186 Two inspection techniques were carried out in order to establish whether the damages were187 still active or if the building was mostly stable [19]. On one hand, changes after one year in the188 position of selected control points were topographically measured (from July 2015 until July 2016)189 . For this, 87 reflective targets were used. Most of them were placed along the eastern wing,190 on columns, arches and vaults keystones and the masonry wall. Likewise, other six targets were191 distributed among columns of the northern, western and southern wings. On the other hand, 11192 9 objetives. Therefore, and to allow an adequate adjustement to the geometry of the ancient cloister,362 Solid C3D4 elements were applied (first order reduced integration tetrahedral 4-node elements).363 The model has a total of 15.9M elements, 3.0M nodes and 9.6M degrees of freedom (Fig. 14).364 Figure 14: Three-dimensional FE model of the monastery (mesh with 15.M elements not shown). With respect to the boundary conditions, initially the movement of the nodes situated at365 the base of the supports was considered fixed. However, given the differential settlements detected366 during the surveys (section 3.2.3 and Fig. 13), a preliminary linear analysis of the model was carried367 out in order to assess the influence that considering these settlements would have on the results.368 This study revealed that taking into consideration these settlements in part of the supporting369 surface area of the columns was relevant to the analysis, since it entailed significant changes in370 their structural behavior. Figure 15 shows the results from this preliminary study from a qualitative371 point of view. In this study, only columns 1,9 and 11 were subjected to the mentioned settlement372 by an imposed downward displacement of 2cm, while the base of column 10 was completely fixed.373 As it can be observed, the consideration of the settlement along half the base of the column implies374 changes in the position of the more compressed areas on the column. Thus, in column 10, the375 highest compressive stresses are found in the lower areas of the outer face and in the upper areas376 of the inner face, while the highest compressive stresses of the rest of the columns are located377 along the inner face. In correspondence with results from archaeological inspections (section 3.2.3)378 and taking into consideration the results from the preliminary linear analysis mentioned above,379 differential settlements as those described were considered in the model at the base of columns of380 the northern wing. Thus, nodes at the half-base of each column that were next to the gallery were381 considered fixed, while those of the other half counted on imposed downward displacements. The382 boundary conditions of each column in the northern wing have been modeled as described with383 the exception of column 10 (rebuilt).384 16 Figure 15: Exterior (a) and interior (b) views from preliminary model with differential settlements only on columns bases 1, 9 and 11. A different structural behaviour of column 10 (without settlement) with respect to the other columns can be observed regarding compressive stresses. Materials and mechanical properties. In the part of the model that corresponds with the historical385 building, the different materials have been modeled in accordance to both the inspections carried386 out (Section 3.2) and the information extracted from previous visual inspections and archaelogical387 studies [13, 16, 17]. In this way, different layers have been adopted for the floor system and for388 the load bearing walls, with the exception of a rammed earth wall in the eastern wing, which has389 been considered as a single material. The main goal of this study refers to the improvement of390 the model results at a local level, so a more detailed model was developed in order to obtain more391 detailed results. The use of volumetric finite elements for multi-layer systems allowed both a better392 adjustement to the actual geometry of the structure and a higher degree of fidelity regarding the393 way load bearing works between structural elements. Thus, the floor system has been modeled394 with a curved lower layer of stone masonry (vaults), an upper horizontal slab and an infill which395 is set between them. On the other hand, bearing walls has been modeled with three layers, the396 outer ones as brick masonry and the inner one as an infill. The columns have been considered as397 solid stone masonry elements (Fig. 16).398 Figure 16: Materials used in the updated FE model. 17 On the one hand, density, Poisson’s ratio and compressive strength are obtained from biblio-399 graphical data [15, 20, 21, 28] and according to results from compressive tests assessed in section400 3.2.2., as shown in Table 2. The estimation of low compressive strength values of the stone masonry401 stand out, at 2.0 MPa. This value is coherent both with the most representative ones obtained402 from the compressive tests carried out, and with the reduction of the capabilities that this type403 of stone suffers with high humidity indexes, like those that have been detected (section 3.2.2.).404 On the other hand, the elastic modulus of the constituting materials is obtained by means of a405 process by which the model is calibrated. In this process, the aim is to reach the dynamic response406 of the model, obtained through a modal analysis, to adjust to the dynamic response of the real407 structure, which has been obtained experimentally with AVTs and OMA (section 3.1.1). In this408 way, the elastic modules are obtained from their consideration as updating parameters in this cal-409 ibration process. The aim is to have a calibration regarding two criteria: the modal shapes and410 the associated frequencies.411 Material Density (kg/m3) Young’s modulus (MPa) Poisson’s ratio Compressive strength (MPa) General Concrete 2500 23000 0.23 25.0 Steel 7850 210000 0.23 223.0 Infill (walls) 1500 500 0.23 0.9 Infill (vaults) 900 35 0.23 0.8 N. wing Stone masonry 1800 1200 0.23 2.0 (columns and vaults) Brickwork (wall) 1800 1000 0.23 1.8 Brickwork (tower) 1800 2200 0.23 2.4 S. wing Stone masonry 1800 1500 0.23 2.0 (columns and vaults) Brickwork (wall) 1800 1200 0.23 0.9 Mixed masonry (wall) 2200 4000 0.23 1.4 E. wing Stone masonry 1800 1000 0.23 1.8 (columns and vaults) Clay block masonry 2000 4000 0.23 3.2 Rammed earth 1400 700 0.20 0.9 W. wing Stone masonry 1800 1500 0.23 2.0 (columns and vaults) Brickwork (wall) 1800 1000 0.23 1.8 Table 2: Material properties used in the updated FE model. Model calibration process. The initial idea was to calibrate the model using just one value of412 the elastic modulus per material, regardless of the wing of the building it was in. However, the413 adjustment of the model was unsatisfactory according to the two calibration criteria that had414 been defined. To achieve an adequate calibration, different elastic modules had to be taken into415 consideration for the same material depending on the wing it was located in. This consideration416 was backed by supplementary data from two different sources. The first is the archaeological study417 18 of Monastery, which estimates that the construction of the different wings of the cloister took place418 in different periods up to 150 years apart [13]. The second are the experimental campaigns that419 were carried out: (i) the results provided by the high-resolution seismic tomography show different420 levels of deterioration depending on the wing; (ii) the sonic tests likewise show different values for421 the dynamic elastic modulus for the different wings. Table 3 relates the experimental and numerical422 values of the frequencies corresponding with the vibration modes identified. It confirms the high423 level of adjustment that occurs, with MAC values between 0.88 and 0.99, for all of the vibration424 modes. Here, fEF DD are the frequencies obtained from AVT, fN UM.M ODEL are the frequencies425 from the numerical model, the difference is measured with respect to the experimental frequency426 and MAC is the Modal Assurance Criterion, a statistical indicator that measures the difference427 between eigen-modes (usually accepted as coherent if it is higher than 0.70) [6].428 Experimental model vs. Numerical model Mode 1 Mode 2 Mode 3 Mode 4 Mode 5 Mode 6 fEF DD (Hz) 2.01 2.33 3.09 3.35 3.86 4.31 fNU M.M ODEL (Hz) 2.01 2.33 2.97 3.37 3.73 4.15 % Dif. 0.00 0.00 3.88 0.54 3.32 3.73 MAC 0.99 0.99 0.95 0.95 0.98 0.88 Table 3: Comparison between experimental and numerical eigen-frequencies. In addition to the model calibration based on eigen-frequencies, the adjustment of modal shapes429 was also achieved for the six first modes. As an example, Figure 17 relates the modal shape obtained430 numerically and experimentally for the fourth vibration mode. This figure shows bending modes431 along the four wings. The correlation between both numerical and experimental results can be432 observed even for inflexion points.433 On the other hand, and in addition to the adequate adjustment obtained, the values of the434 elastic modules acquired (Table 2) have been validated based on: (i) the range of the values of the435 material itself [28]; (ii) the dynamic elastic modules from the sonic testing, with the northern wing436 showing the lowest elastic modules, the southern wing the highest and the eastern and western437 wings intermediate and matching levels; (iii) the results of the high-resolution seismic tomography,438 which indicate a higher degree of deterioration in the columns of the norhern wing.439 19 Figure 17: Modal shape, fourth vibration mode. Numerical model (a) vs Experimental model (b). Constitutive model. Given the cracked state of the structure, and that one of the goals is to globally440 analyze the structural capacity of the building, a constitutive model available in ABAQUS software441 and known as Concrete Damage Plasticity (CDP) material model was adopted [27, 29]. Despite442 being a model conceived to model fragile isotropic materials such as concrete [29], its use has been443 extended to the modeling of masonry based on the consideration of an isotropic macro-model and444 since it allows the definition of materials with different compressive and tensile strengths as well445 as different failure mechanisms, that is, tensile cracking and compressive crushing. Some recent446 applications of this constitutive model to the structural analysis of historical masonry constructions447 can be found in [3, 30–34].448 In these kinds of models, beside the aforementioned defined values, those that correspond to449 the fracture energy and tensile strength must also be included. The values corresponding to both450 parameters have been taken from bibliographical references. Therefore, as fracture energy values451 we have used 0.02 KPa/m for the stone masonry and for the brickwork [35, 36]. As for tensile452 strength, the use of low values must be pointed out in order to generate a model that is weak to453 tensile forces. In general, 50 KPa has been considered, with values that are lower for the in-fill454 materials of walls and vaults, as well as for the rammed earth walls, in this case 40 KPa [37–39].455 456 Consideration of the construction phases in the analysis. In order to assess the need to consider457 the different construction phases of the building, a preliminary structural analysis was carried out458 that assumed an elastic and linear behavior of materials and which took into consideration the459 stiffness of the building as a whole, including the new civic center.460 The results showed concentrations of stresses and strains that did not correspond with reality.461 The main reason for this is that the low values identified for the elastic modulus cause great462 shortenings of the elements due to axial stresses [40]. These shortenings alter the stress and strain463 state of the areas closer to them. The elements that suffer this the most are those located between464 the tower and the northern gallery, as well as those between the cloister and the new civic center.465 Thus, for example, this previous model showed a very high level for tensile stresses at the base of466 the arches that belong to the cloister’s lower level and that are closer to the tower. The mentioned467 shortenings are different for the tower wall and for the columns, so it implies different displacements468 20 at the bases of the arches between them. This leads to aditional tensile stresses at the mentioned469 areas that do not correspond with reality.470 In addition, as mentioned, the monastery was built over the course of a drawn-out period and471 has been subjected, throughout its history, to unique milestones, such as the loss and reconstruction472 of one of its columns. Therefore, the results extracted from a model defined by construction phases473 with staggered increases of stiffness are of greater value. These phases have been defined according474 to the information provided by the archaeological studies of the monastery [28]. Figure 18 defines475 the 6 steps that have been taken into consideration as phased analysis.476 Figure 18: Construction phases taken into consideration in the analysis: STEP1, tower, staircase and chapels; STEP2, preserved elements of the cloister without the column lost during the earthquake; STEP3, differential settlements in the columns of the northern wing; STEP4, inclusion of the reconstructed column; STEP5, concrete beams and slabs introduced in consolidation works; STEP6, inclusion of the new building. Consideration of loads. As pointed out, the behavior of the building subjected to gravitational477 loads has been analyzed. In this model, the self-weight of the structure has been considered, which478 has been introduced in each of the numerical phases defined, gradually and in different steps, in479 such a way that the weight is fully introduced in one step of the analysis before proceeding onto the480 next step. Once the total load is introduced in the last step of the analysis, said load is increased481 until the system collapses, with the aim of analyzing its capabilities.482 4.2. Remarks483 The model created integrates specific data extracted from the results of the inspection cam-484 paigns that have been carried out. Based on previous structural analyses mentioned in section 4.1,485 those that assumed an elastic and linear behavior of materials, the influence that the incorporation486 of this information has on the results of the analysis at a local level has been demonstrated. In the487 case of the differential settlements, their consideration or not in the model involves an important488 variation in the results. The calibration of the model based on AVTs and OMA ensures that it489 maintains a global behavior in accordance with the actual structure despite the introduction of the490 aforementioned local singularities. Part of the data obtained from the inspection techniques has491 been incorporated directly into the model. Another set of data, however, is used as complementary492 information in the definition and/or validation of the intervening parameters.493 21 5. Results494 In a first step, the analysis of the results obtained for the historic building as a whole, before495 including the civic center, allows to verify that the model already shows that the northern wing496 presents a level of damage above that of the rest of the complex. Damage is located mainly on the497 keystones of the arches and the vaults, as well as at the base of the columns. The results provided498 by the model strengthen the hypothesis that the reason behind the collapse of column 10 during499 the 1969 earthquake was mainly due to the vibrations of the tower. This is so because the results500 show a tendency of the tower to bend towards the interior of the cloister and a higher level of501 damage on its northern facade in the vicinity of the existing large niche.502 Regarding the eastern and western wings, the model shows that they behave differently in spite503 of having the same geometric layout. The fact that the wall of the eastern wing is made out of504 rammed earth, in contrast with the corresponding wall on the western wing, which is brickwork,505 explains why the former is more affected, even before incorporating the civic center into the model.506 The model shows that the wall of the eastern wing tends to move towards the east, opening up the507 structure that supports the gallery. This is in line with the most pronounced damages presented508 by the arches of the upper floor of this wing. Likewise, and still within this tendency to open up, in509 this state, the structural model manages to identify damages compatible with the separation crack510 that exists in the eastern wing between the vaults of the first floor and the wall (Fig. 19). The511 southern wing, on its part, presents a continuity of material throughout its wall, along with less512 openings. The model shows that, in general, it holds up better, even though it also detects that the513 supporting structure of the gallery tends to open up, that is, a displacement of the aforementioned514 wall towards the south and of the columns towards the north.515 Figure 19: Section though West and East wings (a); Displacements along the X axis (b) and cracks between vaults and wall in the East wing. In order to obtain these results, specific for each wing and in line with the main damages present516 in the building, it has been important to identify the properties of the constituting materials for517 each of the wings. Therefore, for example, the consideration of the rammed earth in the eastern518 wall has been crucial in order for the model to show its distinct behavior with respect to the western519 wing, as mentioned. Likewise, in order to obtain the results for the northern wing, it has been520 equally important to include a building phase in which the column that collapsed was not present521 and to take into consideration the differential settlements at the base of the columns of this wing.522 The introduction of these settlements makes the model show incipient hinging of the arches of the523 22 northern wing, which becomes greater in the arches adjacent to the missing column. In addition,524 the introduction of the differential settlements at the base of the columns is the key for the model525 to show the damage that runs longitudinally along the vaults of the first floor (Fig. 20).526 Figure 20: North wing: Damage areas before (a) and after (b) considering differential settlements; (c) Cracks along vaults. Moreover, the results indicate that the construction of the civic center accentuates aspects of527 the structural behavior of the cloister that were already incipient before the construction of the528 new building. The most relevant are: (i) the development of hinges in the keystones of the arches529 of the first floor, and not only those of the northern wing (Fig. 21); (ii) the displacement towards530 the east both of the eastern wing wall and of the eastern side of the northern gallery; (iii) the531 opening up of the supporting structure of the southern wing, that is, the movement of the wall532 towards the south and of the columns towards the north.533 Figure 21: Increase of damage in the keystones of arches after introducing the new civic center: Views from below the historical construction, with past (a) and current architectural configuration (b), and example of cracks in an arch keystone (c). An analysis of the correspondence between the results obtained numerically and the damage534 that the actual structure presents demonstrates, on the one hand, that the model is capable of535 showing the most relevant damage once the step in which the civic center has been concluded (i.e.536 once the complex is fully introduced into the model with its corresponding self-weight). On the537 23 other hand, by increasing the load to determine the collapse, the model shows damage areas that538 coincide not only with those where the building presents cracks of importance, but even areas were539 minor cracks exist (Fig. 22). This occurs when a load that is 1.5 to 2.0 times that of the self-weight540 of the structure is introduced. Finally, if a load of 2.15 times the self-weight of the structure is541 applied, the same reaches a state of collapse due to the failure of the tower.542 Figure 22: Additional damages on the West wing: model results and current state of the building. 6. Conclusions543 This study carried out on the Monastery of San Jernimo in Seville has demonstrated that544 the incorporation of information from other disciplines other than architecture and structural545 engineering in numerical structural models helps to improve the results obtained from them. This546 improvement is based on the generation of a model that is truer to the reality of the building547 both at a global and at a local level.Therefore, disciplines such as geophysics, archaeology and548 topography have been crucial in the execution of the advanced structural analysis model.549 To achieve a high level of correspondence between the model and reality , the results of some550 of the experimental tests that were carried out have been incorporated directly into the model.551 These are: the composition of structural elements (from GPR and topography), values of the552 elastic modulus of materials (calibration of the model based on the results obtained by means553 of OMA), or construction phases and differential settlements (archaeology). On the other hand,554 results provided by other tests have been used to validate the model itself. These have been sonic555 testing, moisture content tests, photogrammetric surveys, archeological data or visual inspection.556 Destructive tests from a reduced number of samples to determine the resistance of stone masonry557 and brickwork have provided dispersed data. This led to the estimation of compressive strength558 values mainly based on bibliographical sources, to which the more representative values obtained559 by the compression tests carried out were added. Likewise, looking at the dynamic characteristics560 of the compound, it can be observed that the parameters introduced locally improved the results561 in the areas affected by them without significantly influencing the global behavior of the structure562 of the building.563 24 The structural model has been subjected to a non-linear analysis under gravitational loads until564 reaching the ultimate load of the structure. It is a detailed model that involves a high computational565 cost, taking, moreover, into account the need to consider the non-linearity of materials. However,566 the relatively fine detailing of the model was necessary to reach the goals set out in this study,567 which included the incorporation and comparison of the results with the information extracted568 from reality, and therefore, not simplified data.569 Regarding the structural behavior of the building, the numerical analysis shows damages in the570 historical building before the incorporation of the civic center, mainly in the arches, vaults and571 columns of the northern wing, which appears as the most deteriorated area. The results show that,572 when the new building was raised and the existing structure of the monastery was used to support573 it, the damages were accentuated in the form of a generalized hinging of the keystone of the arches574 or the opening of the supporting structures of the eastern and southern galleries of the cloister.575 Subjecting the entire complex to a gravitational load of 1.0g, damage areas are recognized576 in the model that correspond with the areas in which the historical building presents its main577 pathologies. For values between 1.5 and 2.0g, the model shows damages that are in line with578 the areas in which the building shows cracks of lesser importance. This indicates a high level of579 approximation between the results obtained in this calculation phase and the state that the actual580 structure presents. Finally, by analyzing the results when the ultimate load (2.15g) is reached,581 as observed, this collapse is caused by that this collapse is caused by the tower, with additional582 resistance remaining in the volume that constitutes the cloister.583 It is worth mentioning that other assessments will be carried out using the obtained numerical584 model once it has been validated. Thus, it will be important for this building to develope a safety585 assessment under seismic loading. Likewise, a continuous dynamic monitoring could be carried out.586 This would make it possible to detect changes in the damage state by taking into consideration587 changes in dynamic response of the structure. On the other hand, results from this monitoring588 could be used to validate a simulation of the environmental effects on the numerical model and589 further assess the importance of considering these environmental parameters in safety assessments590 of this structure.591 ACKNOWLEDGMENTS592 Thanks to the Town Planning Department of the Seville City Council and particularly to593 Architect Fernando S´anchez Navarrete. This work would not have been possible without their594 support.595 BIBLIOGRAPHY596 References597 [1] A. M. D’Altri, V. Sarhosis, G. Milani, J. Rots, S. Cattari, S. Lagomarsino, E. Sacco, A. Tralli, G. Castellazzi,598 S. de Miranda, Modeling strategies for the computational analysis of unreinforced masonry structures: Review599 and classification, Archives of Computational Methods in Engineering (aug 2019). doi:10.1007/s11831-019-600 09351-x.601 [2] S. Atamturktur, J. A. Laman, Finite element model correlation and calibration of historic masonry monuments:602 Review, The Structural Design of Tall and Special Buildings 21 (2) (2010) 96–113. doi:10.1002/tal.577.603 [3] V. Comp´an, P. Pach´on, M. C´amara, P. B. Louren¸co, A. S´aez, Structural safety assessment of geometrically604 complex masonry vaults by non-linear analysis. The Chapel of the W¨urzburg Residence (Germany), Engineering605 Structures 140 (2017) 1–13. doi:10.1016/j.engstruct.2017.03.002.606 25