Structural Assessment for Cultural Heritage: the Church of S

SCHOOL of ARCHITECTURE, URBAN PLANNING, and CONSTRUCTION ENGINEERING

Master of Science in “Building and Architectural Engineering” Course in “Building Engineering”

Structural assessment for Cultural Heritage: the church of S. Pietro in Casolate

Supervisor: Prof. M.A. Parisi

Co-Supervisors: Prof. L. Cantini

Ing. M. Locatelli

Francesca Gravante 905525

Anno Accademico 2019/2020

“Nei momenti bui e difficili della vita prendi esempio dal girasole. Alza la testa e cercalo tu, il tuo raggio di sole”

A mia mamma: il mio raggio di sole anche in piena notte.

Index

Index of figures ...... 7 Index of tables ...... 12 Index of graphs...... 13 Index of attached documents (technical drawings) ...... 14 Sommario ...... 15 Abstract ...... 16 1. Introduction ...... 17 2. Condition assessment on historical masonry buildings ...... 19 2.1. Italian National building Code and seismic design prescriptions ...... 19 2.1.1. Safety evaluation ...... 19 2.1.2. Definition of the model for the analysis...... 20 2.2. Guidelines of Cultural Heritage Ministry for the evaluation and reduction of the seismic risk ……………………………………………………………………………………………………21 2.2.1. Investigation techniques for the architectural heritage ...... 21 2.2.2. Confidence factor for a heritage masonry building ...... 22 2.2.3. Requirements for safety and conservation: the seismic safety index ...... 23 2.2.4. Levels for the evaluation of the seismic structural safety ...... 25 2.3. Masonry: code references, characteristics, possible forms of intervention and testing ...... 27 2.3.1. Historical masonry structures: mechanical behaviour and investigation techniques ... 27 2.4. Destructive and non-destructive tests for the characterization of masonry components .... 30 3. Description of the case study ...... 34 3.1. Identification of the site and overview of the building ...... 34 4. Historical analysis: modifications and interventions from the 18th to the 20th century ...... 42 4.1. Information related to “Catasto Teresiano” [XVIII century] ...... 42 4.2. Information related to “Catasto Lombardo Veneto” [XIX century] ...... 47 4.3. Information about the XX century ...... 51 4.4. General historical consideration and comments ...... 55 5. Geometrical survey and condition assessment of the church ...... 57 5.1. Fast geometrical details and plan definition ...... 57 5.2. Qualitative description of the volumes through photographic material ...... 60 5.3. Quantitative description of the volumes: sections ...... 68

5.4. Quantitative description of the volumes: elevations ...... 72 5.5. Qualitative summary of the volumes’ evolution: 3D representation ...... 76 6. Diagnostic approach to building characteristics and state of damage ...... 78 6.1. Basic principles on thermography ...... 78 6.2. Basic principles on the study of water content in a porous material ...... 80 6.3. Diagnostic approach for the façade analysis (thermography) ...... 82 6.4. Diagnostic approach for the analysis of masonry pattern on the East side of the fabrique (thermography)...... 84 6.5. Diagnostic approach to assess problems related to a tank for collecting rainwater ...... 85 6.6. Diagnostic approach to assess indoor condition of the fabrique considering temperature and thermographic results ...... 87 6.7. Diagnostic approach to define sacristy conditions (thermography) ...... 92 6.8. Diagnostic approach to define the apse characteristics (thermography) ...... 93 6.9. Diagnostic approach to define the belltower properties: thermography and relative humidity analysis ...... 95 6.10. Conclusions and main aspects after diagnostic approach ...... 104 7. Structural behaviour assessment ...... 105

7.1. Confidence factor FC, material properties and elastic response spectrum ...... 105 7.2. Vertical loads analysis and stresses definition ...... 110 7.3. Simplified assessment of the global capacity of the structure (LV1) ...... 112 7.3.1. Basic principles and main assumptions for LV1 assessment ...... 112 7.3.2. Shear capacity for longitudinal direction ...... 115 7.3.3. Shear capacity for transversal direction ...... 117

7.3.4. Assessment of the acceleration Se,SLV in both directions ...... 119

7.3.5. Assessment of the acceleration factor fa,SLV and seismic safety index IS,SLV in both directions ...... 121 7.4. Collapse mechanisms assessment through “scheda per il rilievo del danno e della vulnerabilità delle chiese” ...... 123 7.4.1. Definition of the mechanisms and vulnerability index assessment ...... 123 7.4.2. Linear kinematic analysis of the tympanum ...... 127 8. Conclusions ...... 132 Acknowledgements ...... 134 Bibliography and Sources ...... 135 Attached documents (technical drawings) ...... 137

Index of figures

Figure 1: description of the different levels of analysis for the knowledge path and associated partial confidence factors; Tab. 4.1., chapter 4.2; [Linee guida per la valutazione e la riduzione del rischio sismico del patrimonio culturale con riferimento alle Norme tecniche per le costruzioni di cui al decreto del Ministero delle Infrastrutture e dei trasporti del 14 gennaio 2008]...... 23 Figure 2: presence of multiple leaves, voids and cavities at different types of cross-section; Figure 2, chapter 3.3 [L. Binda, L.Zanzi, 2006]...... 28 Figure 3: position of Casolate respect to Milano and Lodi; [Google]...... 34 Figure 4: first document referring to Casolate church in 1554; historical analysis [Archivio diocesano di Lodi, 1554]...... 35 Figure 5: church’s elevations, a) South elevation, b) North elevation; [Google]...... 36 Figure 6: internal photo of the church describing the distribution of the volumes and structural elements; site inspection [Author]...... 36 Figure 7: Saint Andrea and Saint Peter painting in the centre of the nave; site inspection [Author].37 Figure 8: detail of the Baveno granite at the base of the in-built pillars; site inspection [Author]. ... 37 Figure 9: location of the old pulpit substituted by the statue and corresponding semi-filled cavity with bricks; site inspection [Author]...... 38 Figure 10: condition of the lateral walls to the entrance door; site inspection [Author]...... 38 Figure 11: condition of the exposed bricks of a pillar; site inspection [Author]...... 39 Figure 12: level of plaster decay possibly related to rising dump for the bases of in-built pillars; site inspection [Author]...... 39 Figure 13: condition of external walls of buildings nearby the church, the removal of plaster helps with the humidity problem; site inspection [Author]...... 40 Figure 14: crack at the base of sacristy vaults related to a roof beam collapse; site inspection [Author]...... 40 Figure 15: detail of the 1721 Casolate land registry map; Sheet number 2, Catasto Teresiano, historical analysis [Archivio di Stato di Milano,1721]...... 43 Figure 16: detail of the church’s plan in 1721; Sheet number 2, Catasto Teresiano, historical analysis [Archivio di Stato di Milano, 1721]...... 43 Figure 17: activities present nearby the church in Casolate in XVIII century; Fondo Catasto, Catasto Teresiano, historical analysis [Archivio di Stato di Milano, 1721]...... 44 Figure 18: description of the fields’ typology nearby the church in XVIII century; Fondo Catasto, Catasto Teresiano, historical analysis [Archivio di Stato di Milano, 1721]...... 44 Figure 19: 3D analysis of the volumes of the church in XVIII century (Catasto Teresiano); historical analysis [Author]...... 46 Figure 20: detail of the 1887 Casolate land registry map; Catasto Lombardo-Veneto, historical analysis [Archivio di Stato di Milano, XIX century]...... 47 Figure 21: green areas present nearby the church in XIX century; Catasto Lombardo-Veneto, historical analysis [Archivio di Stato di Milano, XIX century]...... 48 Figure 22: construction materials used for the church in XIX century; Fondo Catasto, Catasto Lombardo-Veneto, historical analysis [Archivio di Stato di Milano, 1866]...... 48

Figure 23: reference to interventions in 1887; Conto Consuntivo delle Rendite e delle Spese, Catasto Lombardo-Veneto, historical analysis [Archivio di Stato di Milano, 1887]...... 49 Figure 24: 3D analysis of the volumes of the church in XIX century (Catasto Lombardo-Veneto); historical analysis [Author]...... 50 Figure 25: plan distribution of church in Casolate in XX century; Nuovo Catasto Terreni, historical analysis [Archivio di Stato di Milano, XX century]...... 51 Figure 26: reference to interventions to the concrete roof and façade in XX century; Visita Pastorale, Nuovo Catasto Terreni, historical analysis [Archivio Diocesano di Lodi, 1929]...... 52 Figure 27: modifications needed in the church in 1930; Nuovo Catasto Terreni, historical analysis [Archivio Diocesano di Lodi, 1930]...... 52 Figure 28: today base of the in-built pillars not changed since 1947; Visita Pastorale, Nuovo Catasto Terreni, historical analysis [Archivio Diocesano di Lodi, 1947]...... 53 Figure 29: 3D analysis of the volumes of the church in XX century (Nuovo Catasto Terreni); historical analysis [Author]...... 54 Figure 30: timeline of the evolution of church with the main modifications [issued by the Author]; historical analysis, site inspection [Author]...... 56 Figure 31: timbering system of the roof renovated in XXI century. The previous concrete roof was substituted with a timber roof using the Lombard truss (“capriata alla lombarda”) technique; historical analysis [XXI century]...... 56 Figure 32: actual plan of the church considering Priest’s house, sacristy and belltower; historical analysis and site inspection [Author]...... 57 Figure 33: detail of the top part of the in-built pillars; site inspection [Author]...... 58 Figure 34: elliptical window over the arch of the lateral chapel; site inspection [Author]...... 59 Figure 35: church internal view from the nave to the apse; site inspection [Author]...... 59 Figure 36: photographic reportage through internal location of the views described in the photos; site inspection [Author]...... 60 Figure 37: photo number 1 and 2 showing the nave volume; site inspection [Author]...... 61 Figure 38: photo 3 describing the Baveno granite base of the in-built pillars; site inspection [Author]...... 61 Figure 39: photo 4 presenting the internal wood structure connected to the entrance door; site inspection [Author]...... 62 Figure 40: photo 5 describing the internal repartition of the apse in elevation; site inspection [Author]...... 62 Figure 41: photo 6 presenting the interaction of the two lateral chapels with the nave; site inspection [Author]...... 63 Figure 42: photo 7,8 and 9 describing the sacristy interaction with the rest of the volumes; historical analysis [Author]...... 63 Figure 43: photo 10 showing part of the volume of the belltower; site inspection [Author]...... 64 Figure 44: photographic reportage through external location of the views described in the photos; site inspection [Author]...... 64 Figure 45: photo A presenting South elevation; [Author]...... 65 Figure 46: photo B showing the external connection of the façade with the lateral walls; site inspection [Author]...... 65 Figure 47: photo C showing the relation between belltower and apse volumes; site inspection [Author]...... 66 Figure 48: photo D presenting the North elevation; [Author]...... 66 Figure 49: photo E presenting West elevation; [Author]...... 67

Figure 50: navigator locating the sections, graphic scale; [Author]...... 68 Figure 51: A-A section, graphic scale; [Author]...... 69 Figure 52: scheme of “capriata alla lombarda”; [Google]...... 70 Figure 53: B-B section, graphic scale; [Author]...... 70 Figure 54: C-C section, graphic scale; [Author]...... 71 Figure 55: D-D section, graphic scale; [Author]...... 72 Figure 56: 3D analysis of the volumes of the church in XXI century (present time); historical analysis [Author]...... 72 Figure 57: South elevation, graphic scale; [Author]...... 73 Figure 58: North elevation, graphic scale; [Author]...... 73 Figure 59: East elevation, graphic scale; [Author]...... 74 Figure 60: West elevation, graphic scale; [Author]...... 74 Figure 61: historical 3D summary of the volume’s variation during the year, North view; historical analysis [Author]...... 76 Figure 62: historical 3D summary of the volume’s variation during the year, West view; historical analysis [Author]...... 77 Figure 63: scheme of a thermocamera elements and principles; “Progetto di indagini per la diagnosi e metodi per il controllo dell’intervento”, Fig. 23, chapter 4.5.2 [Binda L. et al, 1999]...... 79 Figure 64: on site application of Moisture Encounter Plus by TRAMEX; diagnostic approach [Author]...... 80 Figure 65: positioning of the phials in the heater at 105 °C to reach constant mass MS; diagnostic approach [Author]...... 81 Figure 66: after being heated up, phials are cooled down in a drier at ambient temperature before weighings; diagnostic approach [Author]...... 81 Figure 67: facade of Saint Peter church; site inspection [Author]...... 82 Figure 68: lower part of the South elevation (façade). Real photo (left) and thermographic results with reference scale (right); diagnostic approach [Author]...... 82 Figure 69: top part of the South elevation (façade). Real photo (left) and thermographic results with reference scale (right); diagnostic approach [Author]...... 83 Figure 70: façade thermografic results with higher contrast. Reference scale associated; diagnostic approach [Author]...... 83 Figure 71: investigation of the East side to define masonry pattern (church and belltower recess). Real photo (left) and thermographic results with reference scale (right); diagnostic approach [Author].. 84 Figure 72: investigation of the East side to define masonry pattern (chapel and belltower). Real photo (left) and thermographic results with reference scale (right); diagnostic approach [Author]...... 84 Figure 73: individuation of the tank for collecting rainwater on East exposition. Real photo; diagnostic approach [Author]...... 85 Figure 74: thermografic analysis of the tank for collecting rainwater on East exposition. Thermographic image with reference scale; diagnostic approach [Author]...... 85 Figure 75: thermo-hygrometer used to study the temperature and humidity conditions of the church; diagnostic approach [Author]...... 87 Figure 76: investigation of the top internal part of the façade and nearby structural components to define construction materials. Real photo (left) and thermographic results with reference scale (right); diagnostic approach [Author]...... 88 Figure 77: investigation of the top internal part of the chapel and nearby structural components to define construction materials. Real photo (left) and thermographic results with reference scale (right); diagnostic approach [Author]...... 88

Figure 78: investigation of the internal part of the apse and nearby structural components to define construction materials. Real photo (left) and thermographic results with reference scale (right); diagnostic approach [Author]...... 88 Figure 79: exposed brick in the entrance structural elements of the church; site inspection [Author]...... 89 Figure 80: investigation of the internal part of the apse to define possible temperature variations. Real photo (left) and thermographic results with reference scale (right); diagnostic approach [Author].. 89 Figure 81: investigation of the lower internal part of the church to define problems of plaster decay. Real photo (left) and thermographic results with reference scale (right); diagnostic approach [Author]...... 90 Figure 82: investigation of the top internal part of the apse to detect possible humidity problems: thermographic images are blurred and so humidity is present in the indoor environment. Real photo (left) and thermographic results with reference scale (right); diagnostic approach [Author]...... 91 Figure 83: investigation of the lower internal part of the pillars to detect possible humidity problems: thermographic images are blurred and so humidity is present in the indoor environment. Real photo (left) and thermographic results with reference scale (right); diagnostic approach [Author]...... 91 Figure 84: investigation of the top internal part of the sacristy to define characteristics associated to the crack. Real photo (left) and thermographic results with reference scale (right); diagnostic approach [Author]...... 92 Figure 85: thermographic image with higher contrast of the sacristy conditions. Real photo (left) and thermographic results with reference scale (right); diagnostic approach [Author]...... 92 Figure 86: investigation of the lower external part of the apse to define temperature distribution and other details. Real photo (left) and thermographic results with reference scale (right); diagnostic approach [Author]...... 93 Figure 87: investigation of the top external part of the apse to define temperature distribution and other details. Real photo (left) and thermographic results with reference scale (right); diagnostic approach [Author]...... 94 Figure 88: location of the tests on the plan (left), annotation during the test performance (right); diagnostic approach [Author]...... 95 Figure 89: detection of the superficial humidity content during site inspection with Moisture Encounter Plus; diagnostic approach [Author]...... 96 Figure 90: drilling phase (left) and masonry dust collection (right) for the gravimetric definition of the humidity content of the masonry in belltower; diagnostic approach [Author]...... 96 Figure 91: phials containing the masonry powder to be analysed in laboratory; diagnostic approach [Author]...... 97 Figure 92: investigation of the lower internal part of the belltower to define temperature distribution and other details. Real photo (left) and thermographic results with reference scale (right); diagnostic approach [Author]...... 101 Figure 93: investigation of the lower internal part of the belltower, the area is in contact with the church and an evident discontinuity is present in the contact between the two walls. Real photo (left) and thermographic results with reference scale (right); diagnostic approach [Author]...... 102 Figure 94: investigation of the external part of the belltower to define temperature distribution and other details. Thermographic results with reference scale (right); diagnostic approach [Author]. . 103 Figure 95: photo of the internal part of the belltower to define inter-storey wood components location; diagnostic approach [Author]...... 103 Figure 96: description of the different levels of analysis for the knowledge path and associated partial confidence factors; Tab. 4.1., chapter 4.2; [Linee guida per la valutazione e la riduzione del rischio

sismico del patrimonio culturale con riferimento alle Norme tecniche per le costruzioni di cui al decreto del Ministero delle Infrastrutture e dei trasporti del 14 gennaio 2008]...... 105 Figure 97: description of the material’s characteristics according to the masonry typology; “Tab. C8.5.I.”, chapter C8.5.3; [Circolare 21 gennaio 2019 n.7]...... 106 Figure 98: minimum values for nominal life VN according to construction’s types; “Tab. 2.4.I.”, chapter 2.4.1; [NTC 2018]...... 107 Figure 99: values of “coefficient d’uso” CU according to the use class; “Tab. 2.4.II”, chapater 2.4.3; [NTC 2018]...... 107 Figure 100: response spectrum defined for the site considered (Casolate) using “Istituto Superiore dei Lavori Pubblici” device; “Fase 3” sheet; [Istituto Superiore dei Lavori Pubblici]...... 108 Figure 101: dependent and independent parameters at the base of Casolate response spectrum; “Fase 3” sheet; [Istituto Superiore dei Lavori Pubblici]...... 108 Figure 102: formula to calculate dependent parameters at the base of Casolate response spectrum; “Fase 3” sheet; [Istituto Superiore dei Lavori Pubblici]...... 109 Figure 103: vertical and horizontal response spectrum for Casolate defined with Excel device; “Fase 3” sheet; [Istituto Superiore dei Lavori Pubblici]...... 109 Figure 104: individuation of the masonry piers in the longitudinal direction (East and West elevation); [Author]...... 116 Figure 105: individuation of the masonry piers in the transversal direction (South and North elevation); [Author]...... 117 Figure 106: definition of values for indexes vki (vulnerability) and vkp (anti-seismic behaviour) according to effectiveness; “Tabella 5.1”, chapter 5.4.3; [Linee guida per la valutazione e la riduzione del rischio sismico del patrimonio culturale con riferimento alle Norme tecniche per le costruzioni di cui al decreto del Ministero delle Infrastrutture e dei trasporti del 14 gennaio 2008]...... 123 Figure 107: scheme of the tympanum volume for church in Casolate; [Author]...... 129

Index of tables

Table 1: summary of the main non-destructive tests (intrusive and not). [Author] ...... 31 Table 2: results obtained for indoor parameters: temperature and relative humidity; diagnostic approach [Author]...... 87 Table 3: Tramex measurements obtained for D1 area at different height; diagnostic approach [Author]...... 97 Table 4: Tramex measurements obtained for D2 area at different height; diagnostic approach [Author]...... 97 Table 5: gravimetric method results obtained for D1 area at different height and depth; diagnostic approach [Author]...... 98 Table 6: gravimetric method results obtained for D1 area at different height and depth; diagnostic approach [Author]...... 98 Table 7 : values of FCK assumed for the study case; [Author]...... 106 Table 8: material properties used for the study case considering the reduction coefficients and FC contribution; [Author]...... 107 Table 9: definition of the materials unitary mass later used in the calculation of the forces; [Author]...... 110 Table 10: definition of the resisting wall’s area for apse and church; [Author]...... 110 Table 11: definition of the total weight actin on the two areas (church and apse); [Author]...... 110 Table 12: definition of the compression stress acting on the two volumes (church and apse); [Author]...... 111 Table 13: check for the maximum compression stress accepted for the construction typology chosen; [Author]...... 111 Table 14: coordinates of the centre of gravity G; [Author]...... 115 Table 15: coordinates of the stiffness centre CR; [Author]...... 115 Table 16: summary of the parameters involved in the calculation of FSLV,LONG; [Author]...... 116 Table 17: summary of the parameters involved in the calculation of FSLV,TRASV; [Author]...... 118 Table 18: summary of the parameters involved in the calculation of Se,SLV; [Author]...... 119 Table 19: summary of the main parameters known for the tympanum volume and useful for the mechanism’s analysis; [Author]...... 129

Index of graphs

Graph 1: vertical temperature variation for external surface on tank for collecting rainwater on East exposition; [Author]...... 86 Graph 2: vertical temperature variation for internal apse elements; [Author]...... 90 Graph 3: vertical temperature variation for external lower surface of the apse; [Author]...... 93 Graph 4: vertical temperature variation for external top surface of the apse; [Author]...... 94 Graph 5: gravimetric method results obtained for D1 area at different height and depth; diagnostic approach [Author]...... 99 Graph 6: gravimetric method results obtained for D2 area at different height and depth; diagnostic approach [Author]...... 100 Graph 7: vertical temperature variation for interal surface of the belltower; [Author]...... 101

Index of attached documents (technical drawings)

Plans ...... 137 Sections ...... 141 Elevations ...... 146

Sommario

L’obiettivo della tesi è quello di caratterizzare le condizioni e il comportamento strutturale di un edificio in muratura classificato come bene culturale attraverso un numero limitato di prove in sito e di prove mirate. La chiesa di San Pietro a Casolate (LO), studiata nella presente tesi, è esemplificativa dei beni culturali e storici più diffusi in Italia. Ciò consente, quindi, di applicare i criteri suggeriti dalle norme tecniche NTC 2018 e dalle relative Linee Guida del Ministero dei Beni Culturali. La procedura prevede una ricostruzione storica del complesso attraverso piante, sezioni e prospetti grazie anche a quanto custodito negli archivi storici; un rilievo geometrico e fotografico dello stato attuale; studio dei materiali e delle tecniche costruttive attraverso approcci diagnostici (nello specifico termografia e studio del contenuto d’acqua con metodo ponderale); modellazione strutturale. La struttura è analizzata globalmente, secondo un approccio cosiddetto di primo livello (LV1) al fine di determinare qualitativamente non solo la vulnerabilità sismica in funzione dell’accelerazione e del periodo di ritorno, ma anche la presenza di meccanismi di collasso. Il complesso è analizzato anche localmente (LV2) computando l’attivazione del meccanismo di collasso del timpano confrontando la domanda al sito con la risposta della struttura. Lo studio ha messo in luce, per l’edificio analizzato, una muratura non solo uniforme per tutti gli elementi strutturali (anche per orditura e orientamento) ma anche secca (U.R. inferiore a 1%) e un basso livello di sforzo in esercizio. I parametri qualitativi evidenziano tuttavia una vulnerabilità strutturale di tipo sismico in tutte e due le principali direzioni. Ciò si ritiene dipendente dalla discontinuità causata da aperture evidenti (cappelle e simili) e da una limitata porzione di area resistente nella direzione trasversale (E-O) coincidente con la direzione più vulnerabile, a fronte tuttavia di una sismicità locale di basso livello. Lo studio ha permesso di verificare l’efficacia della procedura adottata.

Abstract

The goal of the thesis is to characterize the structural conditions and behaviour of cultural heritage masonry assets with limited diagnostics and well-focused simplified analyses. The church of St. Peter in Casolate (LO) is an example of the most frequent historical and cultural heritage buildings. This gives the possibility to apply the procedure suggested by Italian structural design code NTC 2018 and the Guidelines issued by the Cultural Heritage Ministry. The procedure is based on a historical analysis of the construction through plans based on the documental material preserved in the Archives; a geometrical and photographic relief of the present state; analysis of the materials and construction techniques also through NTD diagnostic approach (for this case thermography and water content analysis with gravimetric method); structural modelling. The structure is analysed globally, with reference to the so called first level approach LV1, to define qualitatively not only the seismic vulnerability through acceleration capacity and return period but also the possibility of collapse mechanisms. The elements are then studied locally (LV2) considering the activation of the tympanum collapse comparing demand on the site and response of the structure. It turns out that, the masonry is uniform for all the structural components (in terms of orientation and pattern) and dry (R.H. lower than 1%), and the work stress level moderate; yet the qualitative parameters highlight a seismic vulnerability in both the two principal directions. This can depend on the discontinuities present (e.g. due to lateral chapels and similar) and a limited portion of resisting area in the transversal direction (E-W) that makes this direction the weakest one asking for higher attention.

1. Introduction

The thesis work will focus on the definition of the historical evolution, structural vulnerability and material condition of Saint Peter church in Casolate realized with a masonry structure and dating back to the XVI century. The study case chosen may well represent a building typical of the Italian cultural and historical heritage. The purpose is to verify for such assets the possibility of characterizing the main structural features and sort out possible critical issues with a limited diagnostic plan and well- focused simplified analyses. Such first level of information could be useful for an initial assessment of the situation in view of pointing out possible needs to perform further investigations and plan interventions. It would be especially valuable to classify the needs of different buildings of a same group, like churches of a same diocese or the buildings of a same district. The procedures applied are derived not only by indications in the norm NTC 2018 (Italian national code) and its commentary (Circolare) but also by the Directive 9/02/11 (Linee Guida per la valutazione e riduzione del rischio sismico del patrimonio culturale con riferimento alle Norme Tecniche per le Costruzioni di cui al D.M. 14-01-2008) that presents the guidelines for the evaluation and reduction of the seismic risk for the cultural heritage. This document and the procedure applied in the following was originally intended for seismic safety, but it offers the opportunity of a general assessment of the asset. The vulnerability analysis of the cultural heritage buildings is based on the important milestone of the knowledge acquisition-path defined in the Guidelines. This milestone is reached through historical analysis, damage state and geometrical relief, definition of the transformation steps and of the construction materials with their properties. The collection of information during the knowledge path can be characterized by different levels of detail; the detail level will affect the mechanical model used to describe the structural behaviour. The model can be either global or local and will define the response of the fabrique under dynamic forces such as the one of seismic action at the site considered for a specific nominal life and return period defined according to NTC 2018 procedures. The church in Casolate has been studied according to two main approaches. The global approach (LV1) is used to define the global behaviour of the masonry structure for vertical loads and as shear resistance in view of possible seismic conditions. Once the shear resistance is defined in both the two main directions of the building, the acceleration that leads to the Life Safety limit State is defined as well as the associated return period. These parameters are useful in the definition of two safety indexes: acceleration factor (fa) and seismic safety index (ISLV). Then a local approach (LV2) is proposed after the definition of the possible collapse mechanisms from the first level analysis (LV1), performed according to the “Allegato C” of Directive 9/02/11 and seismic vulnerability index. For the most significant mechanism (tympanum one), the calculation on activation of the mechanism is proposed. The mechanical modelling comes as the last step of the so-called path of knowledge where useful information about the history of the fabrique, present condition and decay are defined. The study of the present condition has been developed considering also an experimental approach and the useful tool of non-destructive diagnostic techniques.

In fact, with the help of “Laboratorio Prove Materiali” of Politecnico di Milano, on-site and in- laboratory tests have been performed. Thermography has been used on site to obtain useful information about the structure uniformity and condition, the construction technique and materials and problems related to indoor relative humidity. Laboratory tests gave the possibility, on the other hand, to study the relative humidity of the structural components through the gravimetric method proposed by “UNI 11085 – Beni culturali – Materiali lapidei naturali ed artificiali – Determinazione del contenuto d’acqua: Metodo ponderale”. The steps followed for the analysis of the structural behaviour of Casolate church, without the aim of designing an intervention, are: - Definition of the characteristics of the site and soil; - Historical critical analysis to define the evolution of the church during time and possible effects of the modification on the present structural behaviour. The results of this stage are plans, elevations, sections and three-dimensional reconstructions of the different historical periods; - Photographic reportage of the present condition of the fabrique and comments on the principal details; - Geometrical information on the present state through plans, elevations and sections thanks to site inspection and photographic material (due to limitation imposed by the pandemic of COVID-19) with the goal of defining the most significant macro-elements and their structural correlation; - Material analysis through on-site inspections and diagnostic approach coincident with thermographic tests and relative humidity analysis using gravimetric method; - Definition of the decay state and crack pattern of the church. Fortunately, the church is not characterized by considerable crack problems; - Analysis of the present structural state of the building through a LV1 simplified global approach (compression and shear resistance definition, acceleration and return period definition, structural safety indexes and vulnerability indexes, definition of the possible collapse mechanisms) and LV2 local approach (after the definition of the possible collapse mechanisms, numerical analysis of the most evident mechanism of the tympanum). The following chapters describe such steps in this same order; observations and results are presented in the chapters and summarized in the conclusions.

2. Condition assessment on historical masonry buildings

Considering the recent seismic history all over the world and especially in Italy, after the many earthquakes occurred, the seismic protection of historic buildings and cultural heritage assets stands out as a task of major importance. The seismic vulnerability of such buildings is usually very high, due to their typological characteristics. In this perspective this thesis aims at analysing the effectiveness of a method that has been proposed for the study of the seismic safety of the masonry fabriques (main constructive technique for cultural heritage volumes) in its capability to produce a more general assessment of the building conditions, through experimental and qualitative approaches. In detail, the focus of the document is a church dating back to XVII century and fully developed in its present form in the XVIII century. This historic monument is assessed in terms of construction techniques, historical evolution during its lifetime and state of conservation and decay. The volumes composing the church are characterized by different levels of complexity in terms of investigation (geometrical analysis and reconstruction, material analysis and properties definition) giving the possibility to study and apply the different codes’ requirements and indications.

2.1. Italian National building Code and seismic design prescriptions

According to the Italian National Code, NTC 2018 and its previous version 2008, in particular to chapter 8 dedicated to seismic behaviour and design, an existing building is the one with the structure already built and usable at the moment of a safety check, survey and similar. The safety check and the consequent design for an intervention must take into account important features such as the history of the fabrique and the level of knowledge, the presence of defects not visible to human eye, the consequences (also not already appeared) of external forces, modifications and decay with respect to the original structure. So, depending on the availability of information, it is important to know for an existing building: - Geometry and constructive details; - Mechanical properties of materials and soil; - Acting loads on the structure.

2.1.1. Safety evaluation

With reference to chapter 8.3 of NTC 2018, the safety evaluation is a quantitative procedure able to define the level of forces that the analysed structure is able to withstand, ensuring the minimum level of safety required by the codes. In case this minimum level is not respected, the structural safety is provided by modifying the global behaviour of the structure also through local interventions. These checks are particularly problematic in the case of buildings part of the cultural heritage due to the limitations imposed by the need of preserving the integrity of the structure and the history hidden inside. For these reasons, checks must not be invasive and must come out after a detailed work of knowledge acquisition and a series of non-intrusive investigations in order to define the structural 19 behaviour and conditions of the existing building. The checks required by the Italian National Code are for SLU (Ultimate Limit State, Stato Limite Ultimo) and SLE (Serviceability Limit State, Stato Limite di Esercizio) with all the loads acting on the structure assumed equal between new and existing buildings. These checks have the aim at defining the structural behaviour of existing buildings and, for the scope of the paper, seismic action and consequent interventions in order to ensure safety for the occupants. After a first step of checking the condition of the structure also through structural models, according to chapter 8.4 of the NTC 2018, there are different possible intervention to be designed against seismic events for an existing structure. The categories for the intervention are: - Local intervention or restoration (intervento di riparazione o locale); - Seismic improvement intervention (intervento di miglioramento); - Retrofitting intervention (intervento di adeguamento).

2.1.2. Definition of the model for the analysis

According to chapter 8.5 of NTC 2018, there are specific steps in order to obtain a model able to be as close as possible to the real condition of the existing building. This path proposed by the national code is pretty similar and is the base for what proposed by the Cultural Heritage Ministry and that will be presented in the following chapters. In this model, moreover, the loads to be applied for the checks, even though dealing with existing buildings, are the one for new constructions and given by the code. According to NTC, first of all, it is important to have reliable information on the construction history of the investigated building, based on archives or on-site investigations, in order to understand the process of evolution of the structure and all the actions that can affect its behaviour. A geometric relief is needed in order to identify the resisting structure, its conditions and the quality of the materials. In particular, according to this procedure, the mechanical properties of the materials can be investigated through on-site tests (diagnostic tests and visual observation) and laboratory ones; the tests must be documented and limited to the necessary ones. After the collection of information, there is the possibility to define three levels of knowledge (livelli di conoscenza) according to the Italian National Code: LC1, LC2 and LC3. These levels are defined according to the quality of information about the geometry, constructive details, connection and mechanical properties of materials and elements that are the results of the previous path of knowledge.

2.2. Guidelines of Cultural Heritage Ministry for the evaluation and reduction of the seismic risk

The document presented by the Cultural Heritage Ministry (Ministero per i Beni e le Attività Culturali, MiBAC) in 2011 proposes a methodology for the evaluation and the reduction of the seismic risk for cultural heritage and artistic elements following also the principles given by the Italian National Code (in the version of D.M. 14 gennaio 2008, indicated as NTC 2008) and the associated commentary (Circolare contenente Istruzioni per l’applicazione delle Norme tecniche per le costruzioni di cui al D.M. 14 gennaio 2008). The Ministry Guidelines suggest a procedure based on key-points for assessing the structural safety of cultural heritage assets in seismic conditions. First of all, in order to obtain data necessary for the safety analysis, the structure must be investigated considering different sources of information (historical documentation, on-site investigation and so on). Different levels of knowledge may be reached, according to the detail to which the study has been carried out. As a consequence, a confidence factor FC quantifying the reliability of the obtained information will be defined, and subsequently applied in the safety analysis. After the investigations and collection of information, a model for the numerical analysis of the structure or its part is produced; finally the seismic response of the structure is evaluated and the seismic safety level is expressed, this in order to study the dynamic behaviour of the elements with different possible analysis method. Three possible levels of analysis are proposed in increasing detail and complexity, depending on the purpose for which the analysis of the safety conditions is performed, as described further in this text.

2.2.1. Investigation techniques for the architectural heritage

For historical buildings, it is important to know the characteristics at the moment they were built and all the time-changes due to damages because of human action, of weakening of the materials and of natural disasters. So, the fabrique (totally or just to limited areas) must be studied in detail and, according to the goal and the way in which it is reached, the reliability of the model that will describe the building may vary. To reach the goals previously mentioned, a knowledge acquisition-path (percorso di conoscenza) must be followed. The Ministry Guidelines have defined a series of steps for such a path with milestones to be respected. The path is defined as in the following list: A. Geological, geotechnical and seismic characterization of the soil; B. Historical critical analysis; C. Photographic documentation and reportage; D. Geometrical analysis and studies; E. Material analysis and characterization (diagnostic approach on site and in laboratory); F. Crack pattern and decay conditions; G. Definition of the impact of the technological solutions on the structural elements; H. Analysis of the current state of the structure and its structural behaviour (damage state definition);

V.S. Evaluation of the seismic structural safety. The “identification of the building and its location” is based on a first rough schematic survey with the aim also to define the presence of prestigious components. A first look at the building gives also the possibility to define possible areas for future investigations that can be either intrusive or not. Through this first approach, the hierarchy of the structure is defined. Then, a “geometrical survey of the construction at the present time” has the aim to highlight also possible cracks or other forms of damage and to understand the causes at their base. The relation of elements with the surrounding must be also defined. Section, elevations and plans of the building are realized for the scope. A possible problem that can be faced is related to the accessibility of some areas. In this case, some alternative tests can be useful: endoscopy, georadar or thermograpy. A study of the evolution of the fabrique during the years is required to understand which is the sequence of changes on the structural resisting part; this makes easier to discover inhomogeneities and discontinuities. This kind of information can be obtained not always easily due to the lack of precision and detail in early historical archives. The result of this analysis can be summed up in a series of elevations, plans and section showing the different steps of the building during the years. The study of the fabrique, also in terms of soil and foundations components, must highlight the construction materials, their mechanical properties and possible decay. This is possible thanks to investigation that can be either non-destructive (e.g. thermography or georadar) or minimally invasive (e.g. endoscopy). Non-destructive techniques give information about the homogeneity of the structure with a qualitative, not quantitative, result. To obtain quantitative information, intrusive tests are needed and can be performed or on site or in laboratory, but the condition of protected cultural heritage prevents extensive use of such tests. In conclusion, for assessing the masonry quality, it is important to know: o The presence of transversal elements and connecting ones between masonry leaves; o Which is the course of the masonry components and if it is regular or not; o Masonry pattern and position of the mortar joint; o Mortar and its composition; o Quality of the vertical components; o Quality of the connections between vertical and horizontal components; o Location of discontinuities such as air shafts; o Elements (also with no structural aim) with a high vulnerability.

2.2.2. Confidence factor for a heritage masonry building

Historical buildings are often made by masonry that has mechanical properties affected by a high level of uncertainty and a non-linear structural behaviour very difficult to be linearized and homogenized. As a result of the previous steps of knowledge and investigations, the engineer has to express a confidence factor (fattore di confidenza) FC that is a value between 1 and 1.35 that represents the uncertainties in the material as well as those related to the quality of knowledge that has been reached on structural components and the structure in general. This factor is the base for the reliability of the structural model and the results obtained. It is applied particularly in the definition of the values of the material’s mechanical properties for the calculations.

According to the Ministry Guidelines for cultural heritage, the confidence factor FC can be calculated as:

퐹 =1+ 퐹 Where k assumes a different value according to the type of investigation performed and with the variable FCk assuming the tabulated variants in Figure 1.

2.2.3. Requirements for safety and conservation: the seismic safety index

The problem of safety and conservation for cultural heritage is approached in the Guidelines considering three different levels of seismic safety: LV1, LV2 and LV3; this consideration is carried out by collecting data in a limited period of time and with simplified methods. For cultural heritage buildings, the only required checks are for SLV (Stato Limite di salvaguardia della Vita and part of the Ultimate Limit State checks) and SLD (Stato Limite di Danno and part of 23 the Serviceability Limit State checks). To these two limit states, it is important to add another limit state: Stato Limite di danno ai beni Aristici (SLA) that is similar for the approach to SLD one and proposes some limitations for crack dimensions and similar damages that can act on the quality and artistic entirety.

Considering the case of historical building, the parameter VN (nominal life), used for the structural design and that depends on the type of building, is quite high. According to NTC, it is possible to define another parameter depending on the use of the building itself; this parameter, which is an important factor depending on the expected use of the building, is called “Classe d’Uso”: CU. Knowing these two parameters, VR is defined and later used for the definition of the return period:

푉 = 푉 ∗ 퐶 The above mentioned parameters must take into account the effect of time passing and the impact of this on the structure that will lower the performance of the elements. This must be taken into account at the end of each VN defined.

Once VR is defined, there is an associated probability PVR of overcoming the seismic action in the reference period according to the limit state considered. According to this, the return period TR for seismic action is defined:

푉 푇 = − ln( 1 − 푃) In the case of:

- SLV (Stato Limite di salvaguardia della Vita), PVR is 10%; - SLD (Stato Limite di Danno), PVR is 63%.

An exception is represented by the SLA state in which the VRA parameter is calculated as:

푉 = 푛 ∗ 푉 where n represents the number of checking cycles during a monitoring period where direct inspections of the elements are performed. At the end, the seismic structural safety of the fabrique can be defined according to two parameters. It is possible to define the safety seismic index IS,X for a limit state x:

푇 퐼, = 푇, Where:

- Tx is the return period that leads to a certain limit state and associated to a specific acceleration; - TR,X is the reference return period for the considered limit state.

If IS,SLV is higher or equal than 1, the structural safety is ensured.

The definition of IS,SLV is valid for a level LV1 approach while for an LV2 and LV3 it is possible also to use another parameter that is the acceleration factor (fattore di accelerazione). In fact, the acceleration factor fa,x is calculated as:

푎 푓, = 푎, Where:

- aX is the acceleration defined for a specific condition and limit state of the building analysed; - ag,X is the peak ground acceleration for the site considered and for a specific return period. The calculation of the parameters will be presented in detail in Chapter 7.3.

2.2.4. Levels for the evaluation of the seismic structural safety

According to the Guidelines of the Cultural Heritage Ministry, the problem of estimating the seismic safety for historical building can be accessed through three levels of analysis: LV1, LV2 and LV3; each level has its own characteristic and approach and comes at the end of the knowledge path of the fabrique under analysis.

2.2.4.1. LV1: qualitative analysis and simplified mechanical models

The seismic structural safety can be studied in the case of LV1 through simplified models that may arrive to define a seismic safety index IS,K; as presented in the Guidelines, this index is based on the return periods of the capacity and the demand of the considered structure and so easily linked to the seismic vulnerability of the building itself.

In the definition of this simplified model, the confidence factor FC to be used is rather low due to the simple approach used. The qualitative assessment of the structural behaviour of churches is obtained through the analysis of macro-elements; this implies the definition of architectural parts that may be considered with an autonomous behaviour with respect to the rest of the structure. Each macro-element will be studied in order to define the vulnerability of the element based on the presence of initial signs of damage that may favour the development of collapse mechanisms and the presence of seismic protection devices (modern or old ones); possible transformations or interventions during the years must be considered. The result of this analysis is a vulnerability index value, and a report in which the seismic vulnerability is defined as low, medium or high. An alternative process that can be followed with the LV1 approach based on simplified models is the definition of a value of nominal life VN able to ensure a seismic safety index of 1. In this way, it is possible to obtain the return period in which the historical building has the same seismic safety of a new built fabrique.

2.2.4.2. LV2: study of specific macro-elements (local collapse mechanisms)

This analysis level is used when interventions of restoration are needed on limited areas of the construction. This approach is based on local models for independent macro-elements of the structure; the models are non-linear finite ones or based on the limit analysis as stated in the “ALLEGATO B”

25 of the Ministry Guidelines. The presence of previous irregularities and damages must be recognized and the possible evolution into a limit mechanism may be identified from the behaviour of similar components thanks to the availability of damage databases compiled and updated after each earthquake. If the local intervention is limited and will not affect strongly the totality of the structure and its structural behaviour, a deep and detailed knowledge of the whole structure is avoidable especially in the case in which it is really complex to obtain satisfactory material. In this case, the methods used for the LV1 approach are considered valid for the definition of the entire behaviour of the structure that in this case is described through a qualitative approach. The kinematic (linear or non-linear) analysis is the most used one at LV2. The results obtained in this case can be very precautionary due to the impossibility of considering the positive influence of the masonry pattern, trusses and horizontal strengthening components.

2.2.4.3. LV3: global evaluation of the seismic response of the building

The LV3 approach is used in the cases in which the interventions will modify the known behaviour of the structure or in the case of important buildings in which damage may be extensive and the safety of a huge number of occupants must be ensured. In the LV3 analysis, the building is considered in its totality and the acceleration of the ground that leads to ULS (for the totality of the system or of its most significant parts) is defined. Depending on the structural characteristics, a global model is not always needed to study the response of the fabrique. Global models are necessary for buildings, like palaces or villas, where there is collaboration of the vertical resisting elements and global failure patterns involving the majority of walls may occur; otherwise, where an extended damage or collapse is the result of individual behaviour of components by basically independent local mechanisms, like it is often for churches, it is possible to divide the structure into macro-elements considering the subdivision of the seismic action on the different parts based on their mutual connection and rigidity. This repartition can be also empirical and must ensure the equilibrium of horizontal seismic forces. The same approach of LV2 (non-linear finite analysis or based on the limit analysis; kinematic linear or non-linear analysis) must be used on each constructive element. In case of intervention design, comparing the results, it is possible to highlight: - A limited improvement in the seismic behaviour after the designed-intervention; - An excessive safety level given by certain component proposed in the intervention; - The absence of need for the proposed intervention.

2.3. Masonry: code references, characteristics, possible forms of intervention and testing

Masonry is a construction material which is the result of individual units laid in and bound together by mortar. The common materials of masonry in historical buildings are clay bricks or stones such as marble, granite, limestone, and in more recent buildings caststone, industrially produced clay and concrete bricks. The durability of the final element depends on the materials used and the quality of mortar and workmanship but also on the different possible configuration adopted during the realization phase. So, “masonry” is a term able to describe a series of alternatives associated to different materials and components but also is related to different construction techniques depending on the geographical area considered. Moreover, according to NTC 2018, masonry structures can be structurally classified as moderately dissipative ones and so at most under CD”B” medium ductility class for structural behaviour. This classification is obviously valid for the design of new structures and does not refer to old and even ancient ones. Nevertheless, it is mentioned here because it is a sign of the limited post-elastic behaviour that masonry of every type may develop before failure. In general, a satisfactory seismic behaviour may be developed by masonry buildings if some characteristics denoting good rule-of-art construction are present, such as a plan of the building that is as regular and symmetric as possible, with continuous walls (apart from openings) going from the foundation to the top without false and not-connected elements. Horizontal components can not apply a thrust on vertical components; if this thrust is present, structural auxiliary components must be used to retain the thrust. Slabs have the goal to distribute horizontal forces to the vertical components and must act as a constraint against out of plane actions. Geometric parameters, like wall thickness and dimensions, as well as good vertical and horizontal connections of walls resulting in a box-like behaviour are also strongly influencing the outcome. Seldom these favourable conditions are all present in old-masonry buildings, especially if subjected to modifications during their lifetime.

2.3.1. Historical masonry structures: mechanical behaviour and investigation techniques

In the case of historical buildings mainly realized with masonry structures (the main constructive technique of the time), the complexities previously mentioned are increased by the lack of a clear legislation about this specific typology of buildings not part of the common ones; for these buildings it is important to preserve as much as possible the original structure and characteristics but also to ensure safety for the occupants. So, there is nowadays a conflict between the need for conservation and the necessity for ensuring earthquake resistance and protection of this type of structure. [Binda, and Saisi; 2002] For what concerns masonry in historical buildings, there are different typologies of construction techniques depending on: - materials chosen often depending on the geographical area considered; - the way in which the elements are constructed depending on the characteristics of the stones or of the bricks;

- the typology of the section and so the number of the layers and the connection between the different elements; - the characteristics of the mortar and the interaction with the bricks and/or stones. Figure 2 shows few different typologies of historical masonry walls.

Figure 2: presence of multiple leaves, voids and cavities at different types of cross-section; Figure 2, chapter 3.3 [L. Binda, L.Zanzi, 2006]. In general, the thickness of the elements in historical masonry buildings is quite high with a more or less homogeneous distribution for the entire cross-section. Usually, just the outer layer is characterized by a regular distribution of the components; this outer layer will hide the internal part with stones and bricks connected by a thick layer of mortar that has a variable thickness. All these possible alternatives are associated to a wide variety of mechanical and structural behaviours defined, at time with difficulties, thanks also to non-destructive techniques. [Giusti, 2001] It is easy, then, to understand that the modelling of this type of behaviour is very difficult; so, in order to solve the problem, various simplifications were proposed during the years with a technique based on the homogenization of the material. In the same way, after the earthquakes of Friuli (1976) and of Irpinia (1981), the strengthening techniques and of interventions have been assumed similar for all the different types of buildings ignoring the variety of masonry constructive techniques and their characteristics. These two approaches have led to a passive solution with negative consequences for the structures such as the substitution of wood slabs and roof with concrete ones. These negative solutions are emblematic for the catastrophic consequences of the earthquake of 1997 in the Italian regions of Umbria and Marche as well as in those that followed in the current century. [Binda and Saisi;2002] In order to study the behaviour of historical buildings, it is possible to use non-destructive techniques. The application of this diagnostic approach has the aim to answer and clarify ideas already developed by the designer, giving information about the mechanical and physical parameters that are at the base of the structural model later produced. Generally non-destructive tests are preferred for historical buildings, but their application is also expensive and must be customized for the specific case. [Giusti, 2001] Two empirical models can be also used in the case of assessing the structural safety of historical buildings. The “ratios rule” is the simpler in order to define structural safety of an element. This definition is based on the determination of geometrical ratios that must be compared with given values postulated during history and based on experience. This method is used for structures like cathedrals

28 and bridges. To use the ratios rule, the required parameters are mainly referred to the geometry. [Binda, Zanzi et al., 2006] Another simple empirical method is the “graphic rule”. The technique is based on the graphic statics and was developed to explain the collapse of the arches. The main instruments used are the polygon of forces and the line of thrust concepts. The equilibrium of the structure is achieved when: - the line of thrust is inside of the geometry of the modelled structure; - the resultant of the forces in a possible sliding plane shows an angle between the sliding surfaces. In order to use the graphic rule, the geometry and loads must be known. [Binda, Zanzi et al., 2006]

2.4. Destructive and non-destructive tests for the characterization of masonry components

In order to study the behaviour of historical buildings, generally made up by masonry components, it is possible to use non-destructive techniques. There are different types of non-destructive tests among which non-intrusive tests and intrusive ones. Intrusive non-destructive tests are intended as minimally invasive procedures for the area investigated and that will not affect the integrity or stability of the component; on the other hand the non-intrusive non-destructive tests are represented by tests for which it is required, in the worst case, only to remove the element’s finishing and the test can be performed without affecting integrity or stability of the area. Non-intrusive non-destructive tests are generally performed on a surface either with contact (e.g. sonic/ultrasonic tests) or by distance (e.g. thermography). Thanks to this approach it is possible to define some of the characteristics of the masonry pattern such as: - Presence of damage and cracks patterns; - Presence and identification of hidden architectural elements; - Definition of the masonry pattern and of the thickness of the structural elements; - Evaluation of the bond between mortar and bricks or rocks; - Definition of the material characteristics; - Measurement of the stress level of the elements investigated; - Evaluation of the Elastic Modulus; - Thermo-hygrometric information; - Evaluation of the humidity level as a mean value on the environment considered. The application of this diagnostic approach has the aim to answer and clarify ideas already developed by the designer, giving information about the mechanical and physical parameters that are at the base of the structural model later produced. As anticipated, generally non-destructive tests are preferred for historical buildings but their application has to face a series of limitations such as the cost of the procedure and the required design for the specific case. [Giusti, 2001] The diagnostic phase can have different levels of knowledge depending on the building typology and the purpose of the investigation. For example, in the case of important monuments, where the structural safety is ensured, the survey can be focused on the state of conservation of the materials or on the presence and possible causes of decay or on the calibration of future mechanical models for the building under study. [Giusti, 2001] The Table 1 summarizes the main characteristics of non-destructive tests of both intrusive and non- intrusive type.

Table 1: summary of the main non-destructive tests (intrusive and not). [Author]

TEST CATEGORY TEST TYPE GOAL INSTRUMENTS MAIN ASPECTS It is needed to realize a pocket in a wall to insert the metal plate. The plate will increase its volume to reach Definition of Elastic metal the pocket’s the stress plate that will initial condition. Flat-jack partial level of an have a volume test investigated variation due to 푆 component. oil injection = 퐾 ∗ 퐾 ∗ 푃 through a pipe. With Sf the stress level, kj and ka constants < 1, Pf the hydraulic pressure in the plate. Definition of Two elastic metal the elastic plates connected Data collection to INTRUSIVE Flat- jack test modulus for a to a pump that show results in a masonry injects oil. The stress-strain NON- module of two plates will be graph. DESTRUCTIVE (40x50x25) inserted into two TESTS cm3. pockets in the wall. Possibility to Take samples perform to define compression and chemical, tensile tests; Laboratory tests physical and definition of the on bricks, stones mechanical / volume variation and mortar behaviour of in an interval of the time to define the investigated water content of material. the sample; study the chemical composition. In situ: Moisture In situ: definition Define water Encounter Plus. of the superficial Relative content in a water content. humidity study reference area In laboratory: or sample. driller to obtain In laboratory: the powder from definition of the masonry and water content phials to protect through drying 31

the powder up to process on a the test powder sample to performance. detect possible mass variations.

Information Thermocamera Possibility to on thermal with no contact define the energy on the surface. presence of emitted by a Thermocamera different body in the produces an elements, Thermography infrared field image later direction of to understand processed with a structural uniformity software. elements, and Possibility to thermal bridges composition artificially heat and humidity of the area. up the surface. problems. Knowing that Hammer to 푉 = , it is generate an Define overall elastic wave that possible to obtain NON condition and goes from 훿 (density of the INTRUSIVE Sonic tests state of sending to a material) and so NON- masonry or receiving point. the state of the mixed- Wave has a material DESTRUCTIVE material frequency around understanding TESTS elements. 3.5 kHz. An the presence of accelerometer discontinuities. registers the Different test velocity of wave configurations signal. are possible. Best solution for homogeneous and compact Define overall Hammer to materials (not for condition and generate a masonry). Higher Ultrasonic tests state of mechanic wave frequency gives a masonry or that goes from a higher resolution mixed- sending to a but lower material receiving point. penetration depth elements. Wave frequency of the wave. > 20000 Hz. Different test configurations are possible. Detect Radar antenna Discontinuities anomalies in with sender and or problems alter Georadar masonry and receiver. the path of the define Electromagnetic electromagnetic possible waves at high wave producing presence of frequency. echoes. Wave’s

relative results are plotted humidity. in a graph coincident with the planar section of the investigated element.

In the table above, the two tests highlighted are further discussed in Chapter 6.1. and 6.2. where they will be applied to the study case treated in the present document.

3. Description of the case study

According to the Ministry Guidelines, the process of knowledge acquisition corresponds to a series of analyses and steps that in the end give the possibility to the designer to understand the state of the fabrique and possibly to design and propose interventions to optimize its structural behaviour. The path followed here will focus on some of the aspects of the knowledge path outlined in the Guidelines. The aim is not to design an intervention but, rather, to outline a procedure for first level, simplified assessment of the building.

3.1. Identification of the site and overview of the building

The site is located in Casolate (Zelo Buon Persico, Lodi) in Lombardia (North of Italy) 26.5 km south- east of the metropolitan city of Milan. Zelo Buon Persico and so consequently Casolate are part of the province of Lodi.

Figure 3: position of Casolate respect to Milano and Lodi; [Google]. Casolate is located at an elevation of 90 m over the sea level. The first information about the small locality may be dated back to the XII century. From 1809 to 1816, Casolate was under the Napoleonic empire and became a hamlet of the nearby city of Zelo Buon Persico with the possibility of obtaining back the independence under the Regno Lombardo Veneto. This condition of independency did not last long because Casolate was finally aggregated to the municipality of Zelo Buon Persico in 1869. The soil characteristics are important to be defined because they have an impact on the structural behaviour of the building under analysis. In terms of seismic action, the definition of the response spectrum depends on the soil category. According to the lithological and hydrological maps, the area around Lodi is characterized by sandy gravel and sand, so by sediments with medium particle size. 34

Referring to “Tab. 3.2.II” of NTC 2018, the soil category is C that is at the base of the definition of the coefficient SS following the formula provided in “Tab. 3.2. IV”; then, referring to “Tab. 3.2.V” of NTC 2008, it is possible to define the topographic category for the site. The topographic category is T1, flat surface, with an associated topographic coefficient ST equal to 1. These two coefficients are important for the definition of S (= SS * ST) that defines the amplification in the response spectrum of the site. Besides the definition of the seismic action, but still in relation to soil, the region is rich in water and is characterized in general by cultivations that exploit the available high-water amounts, like rice. This situation may have an impact on moisture contents in walls due to rising damp, at least in some periods of the year, with consequent possible damage. Even though nowadays it is used only a few times per year, the church of Casolate is of high importance for its history. In fact, the first document referring to the church is dated back to 1554 as it can be seen in a document (Figure 4) preserved in Archivio Diocesano di Lodi.

Figure 4: first document referring to Casolate church in 1554; historical analysis [Archivio diocesano di Lodi, 1554]. The church of Casolate is dedicated to Saint Peter and has a very long and tormented story especially due to many changes to the shape and structure of the church during the years. The church rises at the entrance of the hamlet of Casolate and is characterized by a single central nave with two lateral chapels. The space distribution, so, is organized in three spans, subdivided by the contraction given by the giant built-in pillars along the lateral walls and the expansion provided by the two lateral chapels. The south façade was realized in Barocco style with the characteristic curvilinear profiles of the central window. The prospect is organized in two orders separated by plastic mouldings and crowned by a large tympanum (Figure 5).

Figure 5: church’s elevations, a) South elevation, b) North elevation; [Google]. As it can be seen from the picture on the right in Figure 5, the church has also a bell tower characterized by a high verticality. The verticality is anyway one of the most important characteristics of the church affecting also the structural behaviour of the construction. The photo on the right, shows also that the church is connected to a lower body that is coincident in part with the sacristy and in part with the Priest’s house. Nowadays the house is not used because since many years the church does not have its own Priest and is just used few times during the year in special occasions. The internal prospects present an ordered alternation of decorative elements. The balcony with the organ is placed between two giant built-in pillars with composite capitals supporting wide trabeations from which the triumphal arch rises to the barrel vault. Lateral niches and pilasters delimit the central arched openings introducing to the chapels. The altar is framed by other two giant built-in pillars supporting a triumphal arch (Figure 6).

Figure 6: internal photo of the church describing the distribution of the volumes and structural elements; site inspection [Author].

According to the archive’s documents, the first original nucleus was the one in which the altar is now located with the two fictious columns at the base of a vault. Vaults are repeated for the entire length of the central nave. In the middle of the nave’s ceiling, a painting dedicated to Saint Andrea and Saint Peter is present (Figure 7).

Figure 7: Saint Andrea and Saint Peter painting in the centre of the nave; site inspection [Author]. Under each vault, a system of tie-rods is present as highlighted in the Figure 7. There is a discontinuity in the type of pavement: the central part of the nave has a marble pavement unlike the two sides where a tiled floor is present. The internal surfaces were restored around 1980. The bases of the pillars are characterized by the use of Baveno granite to limit the possible rising dump but also to give prestige to the church (Figure 8).

Figure 8: detail of the Baveno granite at the base of the in-built pillars; site inspection [Author]. 37

There are two other important internal modifications that are evident just by visiting the church. First, the pulpit was removed and substituted by a statue (Figure 9).

Figure 9: location of the old pulpit substituted by the statue and corresponding semi-filled cavity with bricks; site inspection [Author]. This change had as consequence the closing of the corresponding opening in the sacristy. The hole, not totally closed generating a small recess, is filled with exposed bricks connected with mortar. Then, on the right part of the entrance, there are two voids in the wall, nowadays closed, used probably to insert the supports to sustain statues and have them cantilevering with respect to the wall (Figure 10).

Figure 10: condition of the lateral walls to the entrance door; site inspection [Author]. The entire structure is realized with bricks and mortar as it is confirmed during a first inspection on 22nd November 2019 (Figure 11).

Figure 11: condition of the exposed bricks of a pillar; site inspection [Author]. Figure 12 highlights also the high level of deterioration that is affecting the church in some areas. This problem is mainly caused by the humidity that is an issue affecting the geographical area of Lodi due to the close Po Valley and the high amount of rice fields nearby. The humidity decay for the church is quite important as it can be seen from the level of deterioration of the lower part of plaster in some columns (Figure 12).

Figure 12: level of plaster decay possibly related to rising dump for the bases of in-built pillars; site inspection [Author]. The problem of plaster decay is evident also for the nearby buildings where bricks are exposed to the outdoor environment (Figure 13).

Figure 13: condition of external walls of buildings nearby the church, the removal of plaster helps with the humidity problem; site inspection [Author]. The vaults, moreover, are made of bricks too, covered with wood trusses. The roof was also changed in the last years by using shingles that helped in reducing the problem of infiltrations especially on the right side of the building. Moreover thanks to the possibility of talking with people of interest and aware of the history of the church, it is possible to relate about a joist collapsed on the left part of the church with consequent necessary strong modifications of the roof. Then, some years ago a primary beam of the roof collapsed in the sacristy causing a crack in the left node as shown by the Figure 14.

Figure 14: crack at the base of sacristy vaults related to a roof beam collapse; site inspection [Author]. The study of this historical monument has followed the approach methodology contained in the previously mentioned Guidelines. As first step, the historical analysis about the building structural and architectural evolution must be carried out. It is important to know which are the characteristics of the volumes in their initial state, modifications due also to weathering agents, human activities and material deterioration that have produced the present conditions of the construction.

Thus after a first step of definition of the state of preservation of the church and its main problems with associated geometrical information, an historical analysis on its structural and geometrical modifications is required to understand the steps that lead to the present state of the construction and that could have generated instability or structural weaknesses and initiated collapse mechanisms.

4. Historical analysis: modifications and interventions from the 18th to the 20th century

This phase of the process has the aim to obtain historical information on the fabrique considered; this with the goal to define the different steps of transformations that a building may have undergone. These pieces of information are useful for a correct definition of the material’s condition, of the interaction between the different volumes, of the resistant structures and possible weak conditions developed after a series of actions on the fabrique. The information needed corresponds to the process of evolution of the fabrique during the years. This collection of information must be pertinent to the purpose and detailed as much as possible, in order to use what learnt for the study of the structural behaviour. In order to reach the previous goals, two main sources were consulted: - Archivio di Stato di Milano (State archive of Milano); - Archivio diocesano di Lodi (archive of Diocesis of Lodi). In the sources of the “Archivio di Stato di Milano”, two land registries were checked and corresponding to two main historical periods: “Catasto Teresiano”, that gives information up to XVIII century, and “Catasto Lombardo Veneto” that gives informations related to XIX century mainly. Moreover, thanks to site inspections, it was possible to talk with people aware of the history of the church in the last decades. This was very important because the information in the archives is available just until certain years because of privacy issues.

4.1. Information related to “Catasto Teresiano” [XVIII century]

Considering what is secured in the “Archivio di Stato di Milano”, it is possible first of all to locate the church and understand which were the hosted functions in the surrounding area at different times. The plan of the church in the year 1721 is available considering the second sheet of the land registry of the time (Figure 15).

Figure 15: detail of the 1721 Casolate land registry map; Sheet number 2, Catasto Teresiano, historical analysis [Archivio di Stato di Milano,1721]. The unit of measurement of the map is the trabucco milanese that is coincident with 2.6 m according to the modern units of measurement. The church is highlighted by the red rectangle and, unlike the common use of the time, is not associated to a specific letter that describes the function hosted in an attached table. This maybe since religious constructions were not obliged to pay fees at that time. From the plan above, it is not possible to recognize the bell tower. Then, it is possible to see a back- body connected to the church that nowadays is not present; maybe, this body was later added to the total volume of the church or removed. A zoom view of the red rectangle is presented in Figure 16.

Figure 16: detail of the church’s plan in 1721; Sheet number 2, Catasto Teresiano, historical analysis [Archivio di Stato di Milano, 1721]. Referring to the document of the archive called “Fondo Catasto”, it is possible to define which were the activities present near the church (Figure 17).

Figure 17: activities present nearby the church in Casolate in XVIII century; Fondo Catasto, Catasto Teresiano, historical analysis [Archivio di Stato di Milano, 1721]. As it can be seen from the above document, the Melzi family was the owner of the majority of the buildings near the church; the function of the buildings was “casa da massaro” meaning that the building was rented for agricultural aims. Figure 18 shows also that many fields, gardens and rice fields characterized the area with a considerable extension as may be understood from the associated profits expressed in ecus (ancient coin also called scudi).

Figure 18: description of the fields’ typology nearby the church in XVIII century; Fondo Catasto, Catasto Teresiano, historical analysis [Archivio di Stato di Milano, 1721]. This information is important because rice fields are full of salts that could be absorbed during the years by the structures of the fabrique generating deterioration or other similar problems. Considering then the documents stored in the “Archivio diocesano di Lodi”, it was possible to obtain details about the internal condition of the church through the register of “Visite Pastorali” (bishop of 44 the area visiting the church in an interval of time and describing the condition of the building, the interventions needed and other information important to understand the evolution of the construction). Since the “Visita Pastorale” of 1678 up to the one of 1711, the presence of two altars and one recess to host the wood statue of San Fermo is described. The two altars were the principal one and the one dedicated to the Virgin Mary on the opposite side to the statue of San Fermo. On the right side of the central nave there was the presence of a door to get into the church from the street; nowadays it is closed and it is not possible to understand its precise location due to the rudimental description of the document. The baptistery was located on the left side with respect to the entrance and there was also a specific position for the chorus. Three windows were present, even though no specific location is defined for them: indicatively one above the chorus, one above the main entrance and one above the altar dedicated to the Virgin Mary. The sacristy then had a wood roof and had also a window with two shutters. The bell tower on the other hand had two bells. In the document of “Visita Pastorale” of 1696, moreover, there is a reference to a problem of cracks in the sacristy, but no other details are given. The situation described in “Visita Pastorale” of 1744 is the same so no changes were performed in the church. In this document, there is also the additional description of the presence of two stairs used to get into the bell tower. They are nowadays not present anymore and it is not possible, so, to easily reach the top of the belltower. In the “Visita Pastorale” of 1786, due to a decree of the bishop, fences and balustrades were added to the two lateral altars. But, in 1786, there were three altars unlike in previous years: two lateral and the main one. This maybe coincided with an addition to the old volume or a possible reorganization of the internal space; no proper descriptions are present in this sense. In 1786 moreover, there was also a decree that asked to fix and adapt the stones under the main altar in order to close the openings nearby. These openings could have caused possible problems of rising humidity from the soil to the church. It is important to pay attention to all the possible causes of relative humidity increase because nowadays is one of the major issues affecting the construction as could be observed during the inspection of 22nd November 2019. It was possible to obtain some additional information also referring to the “Atti di governo” that is a document preserved in “Archivio di Stato di Milano”. In this document, the Priest of the time asked for a grant to the Curial Offices in order to end up the modifications and changes in the Priest house that his precursor already started. In one of the letters sent by the Priest, there is a reference to a possible reintegration of the cemetery that was previously sold by his precursor to obtain the money needed for the church restorations and reparation of 1766-1768. Then, it is important to highlight that the church was deeply changed in those years and this information should be searched in other documents. But in all the documents consulted, there is only a reference to this modification with no details on what was performed. Moreover, some documents refer to these years (1766-1768) as the years in which the church was really built so, for sure, the interventions were important and changed probably deeply the construction’s condition. It is important also to highlight that in 1793 the Priest wrote to ask for an increase of the church grant (up to 500 lire) because it was not possible for him to pay the debts of the church that may have been due to other possible modifications and restorations.

Starting from the plans of the land registry, it is possible to reproduce a rough three-dimensional volume of the church during these years. Two main North views are proposed in Figure 19 considering the possibility to see the evolution of the church in two significant years starting from the plan given in the land registry.

Figure 19: 3D analysis of the volumes of the church in XVIII century (Catasto Teresiano); historical analysis [Author].

4.2. Information related to “Catasto Lombardo Veneto” [XIX century]

Also in this case, the starting point is coincident with the planimetric information obtained in the “Archivio di Stato di Milano” (Figure 20).

Figure 20: detail of the 1887 Casolate land registry map; Catasto Lombardo-Veneto, historical analysis [Archivio di Stato di Milano, XIX century]. In comparison to the information present in “Catasto Teresiano”, the plan gives the possibility to better identify the boundaries of the Priest House (construction number 4) and the presence of the bell tower. Moreover, the body that was at the back of the Church in the “Catasto Teresiano” seems to have disappeared and maybe became part of the church itself. It is easy to recognize an additional opening on the right side of the church; this can create discontinuities in the resisting perimetral wall. The plan is anyhow still very irregular with many in-out volumes as for example the triangular element on the top-left part. Moreover, the top part with a semi-circular shape can be coincident with an additional part that increases the longitudinal trend of the church starting from the original nucleus previously described. Also, the nearby buildings changed during time, but they were still under the control of the Melzi family and were still rented. The presence of green areas (gardens and rice fields) is still dominant (Figure 21).

Figure 21: green areas present nearby the church in XIX century; Catasto Lombardo-Veneto, historical analysis [Archivio di Stato di Milano, XIX century]. Referring to “Fondo Catasto” of 1866, it is possible to obtain also important information about the construction materials that were typical of the area at the time (Figure 22).

Figure 22: construction materials used for the church in XIX century; Fondo Catasto, Catasto Lombardo-Veneto, historical analysis [Archivio di Stato di Milano, 1866]. In the subchapter “Circostanze Speciali”, there is a reference to the use of bricks for the walls and wood associated to tiles for the roofs that have generally a double slope to solve possible problems of rain and snow. This information is later used in order to define a possible solution for the roof referring to “capriata alla lombarda” technique and that will be later discussed in detail. Then, referring to the information of “Visite Pastorali” of “Archivio Diocesano di Lodi”, more details are available on the evolution path of the church during the years. In “Visite Pastorali” of 1873, there were still three altars and according to the bishop decree two important modifications were needed:

- First of all, angles should be removed and substituted with a buttress wall; this so for sure will introduce a strong modification in the wall behaviour as clearly seen in the plan of “Nuovo Catasto” that will be presented later; - The drainpipe of the Priest house should be removed: it is very near to the church wall and so this change may have affected the structural elements of the Priest house and sacristy; a proper alternative location to this building component had to be defined but no further details are given in this sense. Then, in “Visite Pastorali” of 1873, a modification to the pavement of the presbytery was needed too and the presence of cracks in the main entrance-door are highlighted. This is again an important information needed in order to understand possible weathering action on the structural elements of the church. Then, looking at “Conto Consuntivo delle Rendite e delle Spese” of 1887 that is the financial report of the church for the considered year, it is possible to understand that other small interventions and repairing were introduced (Figure 23).

Figure 23: reference to interventions in 1887; Conto Consuntivo delle Rendite e delle Spese, Catasto Lombardo-Veneto, historical analysis [Archivio di Stato di Milano, 1887]. The document above states that some payments were due to workers because of: - Lime application in the church; - Addition of tiles to the roof; - Some masonry-repairs in buildings connected to the church. It is not explained which is the effective activity performed; - Money anticipated by the Priest for some restorations in the church itself. For all the cases above, there was not detailed explanation on the causes of the intervention or on the areas interested by these modifications. In “Visite Pastorali” of 1892, there is an important information coincident with a reference to a deep change in the church volume in 1766 but, also in this document, no information is given about this intervention. In 1892, moreover, there were two problems related to relative humidity:

- One in the Priest house where a problem of humidity was evident both in South and West orientation; - The other in the roof of the church itself where also infiltrations were visible. This for sure affected the structural stability of the elements and speeded up the deterioration process of the materials. In “Visite Pastorali” of 1897, then, the need for new interventions in the building is underlined but no details are given on this possibility. In the same way, in “Visite Pastorali” of 1898, it is highlighted that the façade needs some restorations and intervention especially in the top part. In this case, starting from the plan given in the land registry of the years analysed, a three-dimensional representation of the church is proposed in Figure 24 to have a clearer idea of the impact on the fabrique considering two significant views.

Figure 24: 3D analysis of the volumes of the church in XIX century (Catasto Lombardo-Veneto); historical analysis [Author]. In the three-dimensional view, it is clearly seen that the old-back bodies disappeared respect to what seen in “Catasto Teresiano” [XVIII century]; then, the belltower is distinctly evident as a proper body.

4.3. Information about the XX century

For the XX century, the reference is mainly coincident with a plan of “Nuovo Catasto Terreni” preserved in the “Archivio di Stato di Milano”. The plan is represented in Figure 25.

Figure 25: plan distribution of church in Casolate in XX century; Nuovo Catasto Terreni, historical analysis [Archivio di Stato di Milano, XX century]. In the plan the solution of the angles, as stated in the previous paragraph, is realized and so the building assumed a more regular shape. The majority of the pieces of information for this period are obtained looking at the documents of “Archivio Diocesano di Lodi”. Referring to a first “Visita Pastorale” of 1903, there is the reference to a problem of humidity for some areas; so, the problem of presence of relative humidity is a constant, never solved, during the years. A bigger problem is highlighted in the “Visita Pastorale” of 1906, which underlines the absence of glasses to the windows; this for sure increased the exposition of the materials and occupants to weathering agents that made worse the condition of humidity already present in 1903. The absence of glasses to the windows is still recalled in 1909 so the direct exposition to weathering agents lasted long (at least 3 years). In “Visita Pastorale” of 1916 there was the request to use the electric power instead of the oil technology; so, changes in the wall structure were applied in order to realize the electric system. In 1919, the “Visita Pastorale” highlighted the grinding of the glasses of the window above the chorus and the consequent need for an intervention in order to solve the problem. Due to the impossibility to localize clearly the chorus, it is also difficult to define which is the window and so the area more affected by the weathering agents action. Even though no details are given, in 1922 the document “Taglio Piante” stated that 235 plants were cut in order to have money to pay for a part of the interventions needed in the church. It is important to highlight that these modifications could be also necessary for other buildings under the control of 51 the church of Casolate and not only for the church itself; no precise information was given for this activity. In the report written for “Visita Pastorale” of 1929, a fixing of the vault of the chapel and some changes to the roof, realized in concrete, became necessary. Moreover, also some interventions to the façade were performed: the priest provided to it and to the decoration of the internal environment. In April 1929, in the end, also the bell tower underwent some modifications such as the transformation of the roof into a concrete one. The document that stated this is shown in Figure 26.

Figure 26: reference to interventions to the concrete roof and façade in XX century; Visita Pastorale, Nuovo Catasto Terreni, historical analysis [Archivio Diocesano di Lodi, 1929]. Referring to a document dated back to 1930, other modifications were added to the church as it can be seen in Figure 27.

Figure 27: modifications needed in the church in 1930; Nuovo Catasto Terreni, historical analysis [Archivio Diocesano di Lodi, 1930]. Also in this case, it is possible to understand that some restorations were needed but no further details are available. In the report written for “Visita Pastorale” of 1931, the possibility to access to the bell tower from the church thanks to a door is described. This possibility was not present, or at least not nominated, in the previous documents. So possibly, an opening was added in the walls and this must be taken into account in order to define the continuity of the masonry pattern.

Another important information is given by the reports written for “Visita Pastorale” of 1935 and 1936. If on the one hand, in 1935 some repairs were needed for the Priest house, on the other hand the Visit of 1936 suggested to totally demolish it for absence of structural stability in the body. The document of 1936, moreover, highlighted good static conditions for the church itself and a need to substitute the roof of the building connected to the Priest house. A document of 1935 provides the construction materials used: earthenware material and lime bricks with a final neoclassic style. The last available document was the report of “Visita Pastorale” of 1947 in which there is a reference to the substitution of the pilasters in granite; this is maybe coincident with the modern aspect that is present in the church nowadays (Figure 28).

Figure 28: today base of the in-built pillars not changed since 1947; Visita Pastorale, Nuovo Catasto Terreni, historical analysis [Archivio Diocesano di Lodi, 1947]. The documents from 1947 on could not be accessed because of some limitations imposed by the archives and related to possible presence of personal data of people still alive or other privacy issues. In the end, it is possible to present a three-dimensional aspect of the church during the XX century starting from the plans available in the archives (Figure 29).

Figure 29: 3D analysis of the volumes of the church in XX century (Nuovo Catasto Terreni); historical analysis [Author]. Then, during the first site inspection of 22nd November 2019, it was possible to talk with people interested that gave important information (also photographic material) about the roof restoration in the XXI century. In fact, the concrete roof used for all the volumes (church, sacristy, Priest’s house and belltower) is substituted with a wood one using the technique of the Lombard truss (capriata alla lombarda) improving the structural box-behaviour.

4.4. General historical consideration and comments

The church under analysis is for sure characterized by a tormented history of modifications of different intensity affecting the global structure of the fabrique. In order to have a brief summary of the history of the church, considering only significant events, the following timeline (Figure 30) is proposed based on the details obtained thanks to archives and interviews to local people aware of the church’s history of last decades (remembering that this information was not available in the archives because of privacy issues).

Figure 30: timeline of the evolution of church with the main modifications [issued by the Author]; historical analysis, site inspection [Author]. As shown in the summary and previously presented in detail, it is understood that the structure is deeply rearranged during the years starting from an original nucleus to which all the other volumes were added to reach the final condition. The historical analysis gives the possibility to understand which are the construction materials used (bricks and mortar for all the components and wood structure for the roof) that is an important issue for the definition of the confidence factor FC, structural properties useful for the calculations and design of possible diagnostic tests to obtain details about the fabrique. An important detail is related to the transformation of the roof, it was realized in concrete around XX century but, as understood through the experience with earthquakes in other regions, this was not the best structural solution. In fact, the structural behaviour of the church is improved in the XXI century thanks to the realization of a wood roof with tiles able to ensure a better box behaviour for the structure without excessive load. Figure 31 shows the restoration of the roof.

Figure 31: timbering system of the roof renovated in XXI century. The previous concrete roof was substituted with a timber roof using the Lombard truss (“capriata alla lombarda”) technique; historical analysis [XXI century]. Figure 31 gives the possibility to define the structure of the roof: Lombard truss (capriata alla lombarda) is the most probable one and useful for further analysis.

5. Geometrical survey and condition assessment of the church

5.1. Fast geometrical details and plan definition

Due to the impossibility to obtain information from the archives and due to the limitations imposed by the COVID-19, the current plan is realized here starting from photos taken during the first inspection on 22nd November 2019 and base measurements of the main proportions of the interior spaces. From the photos and thanks to a first survey, it was possible to define a module considering as a first reference known dimensions such as human height to define the door’s dimensions, tiles and so on. These empirical pieces of information were then implemented thanks to some measurements available since the first site inspection. In the end, it was possible to obtain the plan of the present state of the church localizing also the arches and vaults (Figure 32).

Figure 32: actual plan of the church considering Priest’s house, sacristy and belltower; historical analysis and site inspection [Author]. The plan is characterized by a single nave with a longitudinal symmetry. On the top-right part the bell tower is located and is communicating with the rest of the church thanks to a door. On the left part, there is the location of the sacristy and of the Priest’s house.

As anticipated, the vaults and arches are repeated for the entire length of the single nave and at the base of these components a system of tie-rods is present. In the area with the painting dedicated to Saint Andrea and Saint Peter, two lateral chapels are present with the one on the left presenting an opening to connect to the sacristy area. The apse is preceded by a triumphal arch that is repeated with the same proportions at the entrance of the church. On top of the entrance door, a pipe organ is found; it may be reached thanks to a very narrow stair on the left part of the entrance. Each arch is sustained by columns on top of which a series of capitals and other cantilevering components are present as shown in Figure 33.

Figure 33: detail of the top part of the in-built pillars; site inspection [Author]. This organization of the columns leads so to a horizontal repartition of the internal space that is divided into three areas. Some of the arches, then, have on top recesses hosting the windows (Figure 34).

Figure 34: elliptical window over the arch of the lateral chapel; site inspection [Author]. The apse presents two window-openings and a back-painting reproducing wood components on the walls (Figure 35).

Figure 35: church internal view from the nave to the apse; site inspection [Author].

5.2. Qualitative description of the volumes through photographic material

The procedure suggested by the Cultural Heritage Ministry is based, not only on detailed measurements and representations, but also on the information obtained thanks to photographic reportages realized during the site inspections. Following this path, during the two inspections (22nd November 2019 and 18th September 2020), a photographic reportage is produced and summarized by the following schemes. The plans will show the grip point of the photos considering that: - numbers are used for indoor images while letters are used for outdoor ones; - the cones on the plan are wider in the direction in which the photo is taken. The photographic reportage helped, especially, in the reconstruction of the volumes and as sources to study details not evident on site (e.g. to fill the “scheda dei meccanismi di collasso delle chiese” proposed by the Guidelines). The indoor reportage is shown in Figure 36.

Figure 36: photographic reportage through internal location of the views described in the photos; site inspection [Author].

Figure 37: photo number 1 and 2 showing the nave volume; site inspection [Author]. Photo number 1 and 2 (Figure 37) show the development of the nave hosting the tie-rods below the arches and the repetition of the arches for the entire nave. Especially photo 2 shows also the location of the pipe organ above the entrance door. The photos give the possibility to understand the proportions of the built-in pillars and how the top of the capital is ornated with a series of cantilevering decorations (an important element to be highlighted due to the documented strong tendency to collapse during earthquakes). Then, referring to the pillars, a detail of their bases is given by photo 3 where the use of Baveno granite is clearly evident (Figure 38).

Figure 38: photo 3 describing the Baveno granite base of the in-built pillars; site inspection [Author].

The photo number 4 (Figure 39) is a detail of the entrance door on top of which a wood inner-door (controporta) is evident at a certain height.

Figure 39: photo 4 presenting the internal wood structure connected to the entrance door; site inspection [Author]. During the inspection, it has been understood that the apse was a volume added later to the original nucleus coincident with the present location of the altar. As photo 5 (Figure 40) shows, the apse is divided vertically into three parts: in the centre there is a painting with a bas-relief while two windows are located in the two lateral part.

Figure 40: photo 5 describing the internal repartition of the apse in elevation; site inspection [Author]. Photo 6 in Figure 41 gives the possibility to understand the interaction and the proportions of the two lateral chapels with respect to the nave. The arches at the entrance of the chapels are lower with respect to the height reached in the nave and are located at the base of an ornamental frame that is a direct continuation of the repartition of the capitals on top of the pillars. 62

Figure 41: photo 6 presenting the interaction of the two lateral chapels with the nave; site inspection [Author]. Photos 7, 8 and 9 in Figure 42 describes the interaction of the sacristy part with the rest of the volumes. As photo 8 shows, a lateral door in the West chapel’s wall connects to the sacristy that has a vaulted system for the roof as shown by photo 7. In the end, photo 9 shows a huge crack on the door (hidden by a curtain) connecting the sacristy with the Priest’s house that is not accessible.

Figure 42: photo 7,8 and 9 describing the sacristy interaction with the rest of the volumes; historical analysis [Author]. In the end, photo 10 in Figure 43 is able to describe the volume organization of the lower body connected to the belltower and maybe coincident in previous years with an outer small chapel.

Figure 43: photo 10 showing part of the volume of the belltower; site inspection [Author]. The photographic reportage is able to give also information on the outer aspect of the church and how the different bodies interact (Figure 44 for the picking points).

Figure 44: photographic reportage through external location of the views described in the photos; site inspection [Author]. Photo A (Figure 45) highlights the characteristics of South elevation giving the idea of the horizontal tripartition of the façade and the location of the window opening as well as the external height of the East lateral chapel.

Figure 45: photo A presenting South elevation; [Author]. It is important to zoom in with photo B (Figure 46) on the East side on the connection between the façade and the load bearing external wall.

Figure 46: photo B showing the external connection of the façade with the lateral walls; site inspection [Author]. As the photo highlights, the connection is realized through a recess that generates a discontinuity in the East wall. Photo C (Figure 47) then highlights the interaction between the belltower and the apse. The photo points out the main characteristic of the belltower: the verticality that generates so a slender component. The top part of the belltower is characterized by a belfry containing the bell.

Figure 47: photo C showing the relation between belltower and apse volumes; site inspection [Author]. Photo D (Figure 48), then, shows the North elevation highlighting deeply the verticality of the belltower and its proportions with respect to the apse.

Figure 48: photo D presenting the North elevation; [Author]. Photo E (Figure 49), in the end, describes West elevation and the interaction between the sacristy, the lateral chapel and the church. The three volumes, in fact, compenetrate and the sacristy and lateral chapel’s roofs are supported by the load bearing walls of the church generating a thrust on the masonry components. The belltower is clearly higher than the rest of the volumes and it is understood that also the façade is higher than the church’s volume due to the presence of the tympanum. In the end, the apse results to be lower than the nave.

Figure 49: photo E presenting West elevation; [Author].

5.3. Quantitative description of the volumes: sections

In order to understand better the organization of the volumes and their interactions and as required by the path of knowledge acquisition, some sections (both longitudinal and transversal) are proposed. Their location is indicated in Figure 50.

Figure 50: navigator locating the sections, graphic scale; [Author].

The section A-A (Figure 51) highlights some important aspects.

Figure 51: A-A section, graphic scale; [Author]. - The sacristy and Priest’s house part are not deeply analysed because of the lack of some information. The roof of this area is defined thanks to Google Maps view trying to reproduce its slope; - The tendency to verticality both in the church part and in the belltower is evident looking at the proportions in the section; - The triumphal arch and the tripartition of the space are evident thanks to the columns and the proportion used; - The roof is considered to be built using the technique of Lombard truss (capriata alla lombarda) so with a double-slope that is useful to solve the infiltration problems as also historical documents testified. The documents of the archives describe the substitution of the roof with a concrete one; this was true up to 1947. Then, talking with the present parish Priest, due to the impossibility of accessing the documents, it turned out that recently (less than 20 years ago) the roof was totally rebuilt due to some problems: it was realized with wood and covered with tiles. No detailed information is available for the construction technique and so, among all the possible options, the one of “capriata alla lombarda” is considered valid (Figure 52). In particular, the structure is realized with the chord (catena) supported by the perimetral-walls, false-struts (falsi puntoni) and post not reaching the chord.

Figure 52: scheme of “capriata alla lombarda”; [Google]. In terms of dimensions, the triumphal arch is 13m high while the one of the nave is nearly 15m. The external resisting walls have been supposed with a height of nearly 16 m.

Figure 53: B-B section, graphic scale; [Author]. The section B-B (Figure 53), then, shows the second triumphal arch at the entrance level, as well as, the location of the organ pipe. Particular importance in this sense is given to the height-proportions between the two lateral chapels and the church’s nave and to the section of the arches at the entrance of the two chapels; the chapels then have the roof sustained by the main perimetral-walls of the church. This section shows also the roof technique of capriata alla lombarda. The walls of the chapels have a height of 8m.

Figure 54: C-C section, graphic scale; [Author]. The section C-C (Figure 54) highlights better the horizontal tripartition of the height of the church. It gives also the opportunity to see that the lateral chapel is raising 13 cm above the pavement level of the church area. The section, then, shows the interaction between the recesses and the arches below. The interaction between the façade, the church and the apse is shown too. The façade is a little bit higher than the church’s body thanks to the tympanum; the church area then is higher than the apse area even though this difference is not easily perceived from the indoor. The height of the arch of the chapel is nearly 8m and the top of the horizontal tripartition given by the columns reaches a height of nearly 10m. The top of the vault’s system for the nave is located at 14m. The recess hosting the window above the columns has a height of nearly 5m. The vault’s system for the apse is located at 13m as well as the resisting wall structure for the apse.

Figure 55: D-D section, graphic scale; [Author]. The section D-D (Figure 55) is symmetric with respect to the section C-C and describes the height- proportion between the church and the belltower. The section shows also the door location to go from the church to the belltower area. Once, these main aspects are described, a three-dimensional representation (Figure 56) is capable to give a global idea of the interaction between the different parts of the building.

Figure 56: 3D analysis of the volumes of the church in XXI century (present time); historical analysis [Author].

5.4. Quantitative description of the volumes: elevations

The procedure, suggested by Ministero dei Beni Culturali, requires also the description of the building not only through sections but also through the elevations that are proposed below. The elevations are, in fact, important elements because in parallel with sections and plans are able to describe the building in the space and to generate the idea of the correlation among the volumes.

Figure 57: South elevation, graphic scale; [Author]. The South elevation (Figure 57) is coincident with the main entrance of the church. It is possible to define, in fact, the three areas of the façade (lower with the statue, central with the main window, tympanum) and the height-proportions of the three buildings: Priest’s house/sacristy, church and belltower. The elevations give the possibility to look at the verticality of the church and belltower recognizing so in this verticality one of the main characteristics of the church affecting also its structural behaviour. The façade of the church is also decorated with pilasters that with their height helped in the definition of the horizontal repartition of the indoor environment. The belltower reaches a height of 25m while the façade, considering also the tympanum, is 20m high. The lateral chapel, in the end, reaches an external height of 9m.

Figure 58: North elevation, graphic scale; [Author].

The North elevation (Figure 58), on the other hand, gives the possibility to look at the height- proportions between the façade, the nave and the apse; in fact, it is clear that, as anticipated in the sections’ description, the nave is higher than the apse and that the highest body is the one of the façade due to the tympanum. The apse reaches an external height of 15m while the nave has an external height of 18m.

Figure 59: East elevation, graphic scale; [Author]. The East elevation (Figure 59) shows the connection between the different bodies (church, belltower and lateral chapels). It is important to highlight that the façade is connected to the rest of the nave thanks to an in-out volume (vela) that is shown in the plan. This recess can affect the structural continuity of the façade with respect to the rest of the nave.

Figure 60: West elevation, graphic scale; [Author]. 74

The West elevation (Figure 60) is quite similar to the East one due to the symmetry of the plan itself. The peculiarity of this elevation is the demonstration of how the sacristy, Priest’s house and lateral chapel are connected. In fact, the roof of the sacristy is supported by both the lateral chapel’s walls and the nave’s perimetral ones.

5.5. Qualitative summary of the volumes’ evolution: 3D representation

It can be considered useful also to look at the three-dimensional layouts of the building evolution considering two main views (North and West) in order to observe the changes for the main components and possible features conservation along time (Figure 61 and Figure 62).

Figure 61: historical 3D summary of the volume’s variation during the year, North view; historical analysis [Author].

Figure 62: historical 3D summary of the volume’s variation during the year, West view; historical analysis [Author]. To conclude the historical evolution of the building, considering the three macro-historical periods, the main transformations can be summarized as follow: - First of all, the church has undergone a series of numerous changes during the years. Even though it is not possible to localize them in certain cases, changes were characterizing mainly the continuity of the walls inserting openings or closing them and also the roof that was subjected to a series of interventions; - The roof was originally with wood structure that was modified in the XX century with a concrete one both for church and belltower as it was common for the time. This was later discovered to have a negative impact on the earthquake resistance of the structure. Fortunately, the roof structure was then modified with a wood one in the XXI century, thus hopefully improving the structural behaviour; - Then, the problem of high presence of relative humidity (also capillary one) is a constant aspect during the history of the building; the high level of relative humidity is nowadays still present and strong in the area: in fact it is possible to see that many houses nearby removed part of the outer plaster in order to have bricks able to breathe and to prevent problems related to humidity too; - The construction technique used is with bricks and mortar for the walls and wood and joists for the roof (even though for a period it was changed into a concrete one). The arches and vaults, nowadays, are reinforced with tie-rods at their base to limit the horizontal thrusts and possible collapse mechanisms; - Starting from a limited original nucleus, a series of modifications by adding and subtracting volumes lead to the present state of the church. Sometimes, the volumes are not well linked with the other parts of the fabrique not ensuring a total continuous box behaviour. 77

6. Diagnostic approach to building characteristics and state of damage

Once the historical path of the church evolution is defined and all the interaction and changes are understood and located, the path for knowledge acquisition set by Ministero dei Beni Culturali proposes to use diagnostic tests to obtain more details about the present condition of the church and the effects on the structural behaviour. Non-intrusive (or slightly invasive) tests are performed in the considered building in order to study some parameters such as the level of humidity, materials used and state of conservation, masonry pattern and possible discontinuities or peculiarities of the resisting structure. The main tests used are the thermography and the definition of the water content in a powder sample according to UNI 11085 coupled with results obtained for surface measurements. The thermographic tests are performed without an artificial pre-heating and so by using the natural exposition of the surfaces to the sunlight; a thermo-camera is used too and the images are later processed with the appropriate software. The test to define the water content of a powder sample is minimally invasive because it requires the drilling of a masonry component to obtain the powder. The tests are performed on 22nd November 2019 and on 18th September 2020 to observe the behaviour of the materials under two different climatic conditions; only significative results are later proposed.

6.1. Basic principles on thermography

The radiant emissive power of an object depends on its temperature that is function of the thermal conductivity and of specific heat of the material itself. These two properties describe the tendency of the material to emit and to absorb heat. This non-intrusive non-destructive test uses a thermo-camera that is sensible to the infrared field of the radiation (part of the radiation that is not visible by the human eye but just perceived as heat) in order to have information on the different levels of the thermal energy emitted by a body. The emission in the infrared field will increase as the temperature of the body increases, considering that also cold bodies are able to emit in the infrared field of the radiation. This test does not need a contact with the investigated element. [Binda et al.; 2000] The modern thermo-cameras are based on the use of microbolometer detectors behind the lenses of the camera. The detectors are covered with a layer of vanadium oxide that has a different electric resistance according to the intensity of the infrared light that hits the surface of the detector. This will generate different signals in order to obtain the image of the investigated element. The images are in black and white colours and just after, using a specific software, it is possible to define a certain colour for a specific temperature range. [Binda et al.; 2000]

Figure 63 shows a scheme of the instrument and of the technique used.

Figure 63: scheme of a thermocamera elements and principles; “Progetto di indagini per la diagnosi e metodi per il controllo dell’intervento”, Fig. 23, chapter 4.5.2 [Binda L. et al, 1999]. Each material, so, has the possibility to emit in the infrared field in a different way and this gives the possibility to define the different layers of the considered element. This emission is linked to an energy transfer E registered by the thermocamera; this E-energy is given by the following formula: [Binda et al., 1999]

퐸 = 퐸 + 퐸 Where:

- Ec represents the energy emitted by the investigated surface; - Er is the emission coming from the surrounding surfaces. The thermographic test is influenced, in fact, by the surrounding physical and environmental conditions because this can modify the values of registered emissivity. In order to obtain valid information, a difference in temperature of 10 °C is needed between the surface and the surrounding environment; so, in certain cases, it is needed a thermal excitation of the surface before performing the tests. Thermographic test can be performed into two ways: - passive approach in which the influence of external natural thermal cycles is considered in the process of heating up the surface; - active approach where the surfaces are artificially heated up. In this case, layers at a depth of 10/20 cm can be investigated thanks to a long heating-up process, also lasting few hours. In this way, the heat transfer is able to reach the desired depth. Thermography gives the possibility to define the presence of different elements or layers in the framed portion of the element, the direction of the structural elements, the presence of thermal bridges or humidity levels above certain threshold. The limit of the thermography is coincident with the qualitative approach used and the sensitivity of the performer in reading and interpreting the results.

6.2. Basic principles on the study of water content in a porous material

For the case study in Casolate, two main approaches in the evaluation of the water content in masonry (the main porous material of the church) are considered. The first approach is non-intrusive and non-destructive, based on the use of an instrument: Moisture Encounter Plus by TRAMEX and shown in the Figure 64.

Figure 64: on site application of Moisture Encounter Plus by TRAMEX; diagnostic approach [Author]. This instrument defines the superficial relative humidity content. This is possible thanks to a potential difference between the two ends, one receiving and the other sending the input. The technique is based on the conductivity of a material that is a parameter influenced also by the presence of a water content in the material itself. Before the test, it is needed to set the typology of tested material (in this case Plaster-Brick) of which the humidity level is defined in function of the one expected for wood in the same conditions. The coloured scale gives back the value of humidity for wood while the lower one gives the result for the tested material. It is important to highlight that this is a surface measurement up to 3 cm depth. The results are deeply influenced by the contact of the instrument with the surface: the contact must be total and perfect otherwise the presence of air in-between can alter the results. The second approach is non-destructive and intrusive, proposed by “UNI 11085 – Beni culturali – Materiali lapidei naturali ed artificiali – Determinazione del contenuto d’acqua: Metodo ponderale”. This technique is slightly invasive because it requires to drill the masonry component in order to obtain a powder sample to be tested. The powder is obtained thanks to a drill playing on the wall; the drill bit is cooled down after each step thanks to an alcohol-based solution in order to not affect the composition of the powder. The technique is based on the gravimetric method for the definition of the water content in a powder sample with a mass between 2 g and 50 g. The goal of the test is to define the mass loss of the sample through a drying process by heating. The instruments needed for the test are: - A scale with an accuracy of 0.001g; - A laboratory heater with electric heating system and the possibility to maintain the drying- temperature uniform and stationary with a tolerance of ± 2 °C; - Drier containing silica gel. 80

The process starts with the definition of the initial mass of the powder sample (MU); the powders were brought to the laboratory thanks to hermetically closed phials. After the weighing of the samples, they were dried in a heater at 105 °C up to the reaching of a constant mass (MS) (Figure 65).

Figure 65: positioning of the phials in the heater at 105 °C to reach constant mass MS; diagnostic approach [Author]. The mass is considered constant if the difference between two consecutive weighings, at 4 hours of interval, is lower than 0.1%. Before each weighing, the sample must be cooled down up to the ambient temperature in a drier as shown in Figure 66.

Figure 66: after being heated up, phials are cooled down in a drier at ambient temperature before weighings; diagnostic approach [Author].

The water content Ca , rounded off to the first decimal place, is defined through the formula:

( 푀 − 푀) 퐶 = 푥 100 푀

Remembering that MU is the powder mass after the drilling and MS is the powder mass after the drying process.

6.3. Diagnostic approach for the façade analysis (thermography)

The façade is divided into three main areas (Figure 67): - In the lowest part, there is the entrance with on top the statue dedicated to Saint Peter; - In the central part, the main window is recognizable with on top of it a bas relief; - The upper part is coincident with the tympanum.

Figure 67: facade of Saint Peter church; site inspection [Author]. Some thermographies were carried out on the 18th September in order to define both the construction materials and the state of conservation of the façade itself (Figure 68 and Figure 69).

Figure 68: lower part of the South elevation (façade). Real photo (left) and thermographic results with reference scale (right); diagnostic approach [Author].

Figure 69: top part of the South elevation (façade). Real photo (left) and thermographic results with reference scale (right); diagnostic approach [Author]. These first thermographies are obtained considering a total natural exposition to sunlight of the investigated surface. It shows a uniform distribution of the temperatures testifying a uniform material in the realization of the façade. Considering also that the temperatures are pretty similar with the one of the bodies behind the façade on the right, the materials between the two entities are the same and are uniform for the entire height of the fabriques. Playing with the contrast of the two images and with the reference scale for the temperatures, it is possible to understand the construction material used for the façade (Figure 70).

Figure 70: façade thermografic results with higher contrast. Reference scale associated; diagnostic approach [Author]. The contrast shows, in fact, that the façade is realized with bricks and so can be considered a masonry component too. The bricks are oriented with the longest side parallel to the façade and are connected thanks to mortar joint that are a little bit more evident in the image on the right.

6.4. Diagnostic approach for the analysis of masonry pattern on the East side of the fabrique (thermography)

Defined that bricks and mortar are the materials used for the considered fabrique, it is useful to study their pattern and potential homogeneity. Also in this case, thermography can help (Figure 71).

Figure 71: investigation of the East side to define masonry pattern (church and belltower recess). Real photo (left) and thermographic results with reference scale (right); diagnostic approach [Author]. For the lower part of the eastern chapel, a black and white scale for the thermography gives the possibility to study the masonry pattern. The bricks are all oriented in the same direction for the investigated portion and so the components can be considered homogeneous and without any kind of discontinuities generating a good structural behaviour. As the thermography shows, the bricks are oriented with their heads parallel to the East elevation. Considering then a thermographic approach also for the lower part of the belltower on the East exposition, it is possible to observe the same masonry pattern of the rest of the fabrique (Figure 72).

Figure 72: investigation of the East side to define masonry pattern (chapel and belltower). Real photo (left) and thermographic results with reference scale (right); diagnostic approach [Author]. So, the resistant structure is uniformly oriented for the entire East exposition. The West part could not be analysed because of the impossibility to access to the garden on that side of the church.

6.5. Diagnostic approach to assess problems related to a tank for collecting rainwater

On the East side, there is a cistern dug into the soil for rainwater harvesting and it is highlighted by a red rectangle in the Figure 73.

Figure 73: individuation of the tank for collecting rainwater on East exposition. Real photo; diagnostic approach [Author]. The rainwater harvesting can generate possible problem of rising dump for the masonry components nearby and consequent decay. A thermography is used for this reason to define the condition of this portion of the fabrique (Figure 74).

Figure 74: thermografic analysis of the tank for collecting rainwater on East exposition. Thermographic image with reference scale; diagnostic approach [Author]. The temperature distribution is more or less constant for the considered area both considering horizontal and vertical distribution. No inhomogeneities are highlighted and so the masonry components are equally conserved. A vertical profile P1 of the temperatures is produced in order to detect possible problems of rising dump (Graph 1).

Graph 1: vertical temperature variation for external surface on tank for collecting rainwater on East exposition; [Author]. The temperature is constant all over the profile P1 and this means that the investigated area is emitting uniformly. If a surface emits uniformly, the material is uniform itself and so only masonry components are present there with no appreciable problems of water content.

6.6. Diagnostic approach to assess indoor condition of the fabrique considering temperature and thermographic results

First of all, the temperature condition of the indoor is studied on 18th September 2020 in order to detect possible inhomogeneities. In order to do this, a thermo-hygrometer is used to define the temperature and the level of relative humidity of the environment in which it is placed. This is possible thanks to an extractable probe that sends the measurements to a computer or phone through Bluetooth; the instrument used is shown in Figure 75.

Figure 75: thermo-hygrometer used to study the temperature and humidity conditions of the church; diagnostic approach [Author]. The measurements are realized for the apse area and for the centre of the nave; the instrument was left in position in the environment for an interval of time in order to detect possible variations. Table 2 summarizes the results.

Table 2: results obtained for indoor parameters: temperature and relative humidity; diagnostic approach [Author].

LOCATION PARAMETER VALUE Temperature 26 °C NAVE’S CENTRE Relative Humidity 61,3% Dry-bulb Temperature 18°C Wet-bulb Temperature 20.4 °C Temperature 25.5 °C APSE Relative Humidity 62.3 % Dry-bulb Temperature 17.9 °C Wet-bulb Temperature 20.3 °C

Temperatures’ distribution results to be uniform for the entire church area. Then, thermography is used to define the indoor condition of the church area without artificial pre- heating and with tests’ results related to 18th September 2020 and 22nd November 2019. The starting point is the consideration of the possibility to have different construction materials for distinct structural components such as walls and arches or vaults. A thermographic approach (Figure 76, Figure 77 and Figure 78) is able to give important information in this sense.

Figure 76: investigation of the top internal part of the façade and nearby structural components to define construction materials. Real photo (left) and thermographic results with reference scale (right); diagnostic approach [Author].

Figure 77: investigation of the top internal part of the chapel and nearby structural components to define construction materials. Real photo (left) and thermographic results with reference scale (right); diagnostic approach [Author].

Figure 78: investigation of the internal part of the apse and nearby structural components to define construction materials. Real photo (left) and thermographic results with reference scale (right); diagnostic approach [Author]. These three thermographies shows constant values of temperatures for all the components: walls, columns, arches and vaults. This means that they are all made up by the same material because they are emitting in the same way. Exposed bricks are present for the columns at the entrance door as shown in Figure 79.

Figure 79: exposed brick in the entrance structural elements of the church; site inspection [Author]. So, the thermography gives us the possibility to define that the entire structure of the considered church is realized with bricks and mortar without the use of lighter structures such as wood components. Another important aspect detected with thermography (Figure 80) is the small variation of temperatures between the lower and top part of both columns and walls.

Figure 80: investigation of the internal part of the apse to define possible temperature variations. Real photo (left) and thermographic results with reference scale (right); diagnostic approach [Author]. Considering for example the apse, temperatures have a very small variation between the top and lower part of each component. To make it clearer, a vertical profile P1 is used and the results of temperatures are plotted in Graph 2.

Graph 2: vertical temperature variation for internal apse elements; [Author]. The temperature variation is around 0.6 °C maximum; the lowest temperature values are associated to the part of the apse covered by the altar and so less exposed to direct sunlight. The material, so, is uniform for the entire height of the church body. An evident problem is the plaster decay and detachment in the lower part of the church. This problem is particularly affecting the columns and so thermography is used in this case to define possible associated problems of rising dump (Figure 81).

Figure 81: investigation of the lower internal part of the church to define problems of plaster decay. Real photo (left) and thermographic results with reference scale (right); diagnostic approach [Author]. The temperature is not constant for the wall’s height; especially, it changes more in the area with problem of plaster decay. So, considering that temperature and emissivity in thermography are 90 directly linked, it can be said that the material is not homogeneous in the considered area. This inhomogeneity can be associated to possible water content related to rising dump. Further analysis can confirm the hypothesis proposed. The problem of humidity, that is one of the major issues of the church, is also appreciable in the following thermographies (Figure 82 and Figure 83).

Figure 82: investigation of the top internal part of the apse to detect possible humidity problems: thermographic images are blurred and so humidity is present in the indoor environment. Real photo (left) and thermographic results with reference scale (right); diagnostic approach [Author].

Figure 83: investigation of the lower internal part of the pillars to detect possible humidity problems: thermographic images are blurred and so humidity is present in the indoor environment. Real photo (left) and thermographic results with reference scale (right); diagnostic approach [Author]. The thermographies above are clearly blurred. This problem is due to the water vapor present in the indoor environment as a consequence of the water evaporation from the walls; this water vapor was not able to reach outdoor generating then the perceived humid condition of the church area. This condition is registered into two different moments of the year: on the 22th November 2019 during a rainy and cold day and on the 18th September 2020 during a sunny and hot day. So, the problem is a constant for the fabrique affecting its structures and materials.

6.7. Diagnostic approach to define sacristy conditions (thermography)

The sacristy is on the left side of the church body and exposed to West. Few thermographies were performed on the18th September 2020 and two important aspects turned out.

Figure 84: investigation of the top internal part of the sacristy to define characteristics associated to the crack. Real photo (left) and thermographic results with reference scale (right); diagnostic approach [Author]. The sacristy turns out to be a colder space with respect to the church (Figure 84). This can be due to the Westward exposition receiving less sun, also due to shadows coming from other bodies of the fabrique. Then, an evident crack is present in the top part coming down from the vault (Figure 84). The same crack is present also on the opposite wall angle. Another temperature scale is used in order to have a clearer profile of the damage and to highlight possible smaller defects (Figure 85).

Figure 85: thermographic image with higher contrast of the sacristy conditions. Real photo (left) and thermographic results with reference scale (right); diagnostic approach [Author]. In this case, no additional information was obtained.

6.8. Diagnostic approach to define the apse characteristics (thermography)

The apse is analysed through thermography to detect possible problems. The lower part of the apse is presented in Figure 86.

Figure 86: investigation of the lower external part of the apse to define temperature distribution and other details. Real photo (left) and thermographic results with reference scale (right); diagnostic approach [Author]. The temperature distribution is more or less constant for the entire area. This means that no inhomogeneities are present. The lower part has lower temperatures due to a more limited exposition to sunlight at the moment of the test (around 11 a.m.). A temperature profile P1 is proposed in Graph 3.

Graph 3: vertical temperature variation for external lower surface of the apse; [Author]. Not considering the values of the lower shadowed part, the vertical variation of the temperature as expected is very limited (max. 0.8 °C) confirming that the masonry is uniform and is the only construction material for the apse too.

The thermography in Figure 87 will present the top part of the apse.

Figure 87: investigation of the top external part of the apse to define temperature distribution and other details. Real photo (left) and thermographic results with reference scale (right); diagnostic approach [Author]. Also in this case the temperature distribution is constant on the height of the body as Graph 4 of the profile temperature P1 shows.

Graph 4: vertical temperature variation for external top surface of the apse; [Author]. Also in this case, due to the circular shape of the apse, it is important to consider that the highest variations of the temperatures are present considering the shadowed areas. The window is characterized by a higher temperature because it has a metal grid in front of it generating a different emissivity with respect to the surrounding masonry.

6.9. Diagnostic approach to define the belltower properties: thermography and relative humidity analysis

The belltower area is studied both through thermographies and minimally invasive tests to define the water content (UNI 11085 and surface measurements). The tests according to UNI 11085 are performed there and not in the church due to limitations imposed in terms of prestigious plaster. A first set of tests has the aim to compare the results for two approaches, previously described, in the definition of water content in a material such masonry for the church considered. For the area under analysis, two points are chosen for this approaches’ comparison and they are shown in the following navigator in Figure 88 with also the moment of information registration on site.

Figure 88: location of the tests on the plan (left), annotation during the test performance (right); diagnostic approach [Author]. The area under analysis is the one of the belltower because in the rest of the church there was a limitation in the drilling possibilities in order not to damage the prestigious plaster. Two different walls are chosen, one in contact with indoor conditions and one with outdoor ones, to detect possible differences. Each investigated point is first analysed through the TRAMEX instrument to define the superficial humidity content (Figure 89); this test is performed at different heights to relate about possible rising damp problems.

Figure 89: detection of the superficial humidity content during site inspection with Moisture Encounter Plus; diagnostic approach [Author]. Then, at each height chosen, the gravimetric method is performed for three different depths: 4cm, 12 cm and 20 cm (Figure 90). The depth at 8cm is not considered because a low amount of powder was available for the test. In the end, the results obtained with the two approaches are compared.

Figure 90: drilling phase (left) and masonry dust collection (right) for the gravimetric definition of the humidity content of the masonry in belltower; diagnostic approach [Author]. For D1 case, the heights considered are 90 cm, 135 cm and 176 cm (this value is due to the presence of the mortar joint at 180cm); each of them is associated to the three depths before mentioned. For D2 case, the heights considered are 80 cm, 100 cm and 120 cm and are different respect to the D1 case because of the mortar joints’ locations. Each height is associated to the three depths before mentioned. In the end, so, the analysed samples are 19; some of them were later rejected in laboratory because of errors performed on site (Figure 91). 96

Figure 91: phials containing the masonry powder to be analysed in laboratory; diagnostic approach [Author]. Table 3 and Table 4 sum up the results obtained with the TRAMEX approach and so show the superficial humidity content for the two investigated areas at different height levels.

Table 3: Tramex measurements obtained for D1 area at different height; diagnostic approach [Author].

INVESTIGATED AREA HEIGHT (cm) TRAMEX MEASUREMENT 90 >100 D1 135 100 176 60

Table 4: Tramex measurements obtained for D2 area at different height; diagnostic approach [Author].

INVESTIGATED AREA HEIGHT (cm) TRAMEX MEASUREMENT 80 80 D2 100 20 120 0

The results obtained with TRAMEX shows how the value of superficial humidity content decreases as the height increases; the hypothesis of rising damp problems so seemed to be confirmed. This hypothesis was inspired by the condition of the plaster in the church itself; in fact, it shows a high level of damage in the lower part rather than in the top one especially in the case of pilasters. The damage and detachment of the plaster can be also related to the presence of salts that, in certain condition of temperature and humidity, become hygroscopic. The gravimetric method was performed on the 18th September 2020, so after the Summer period. This is an important information because, after a long period without rain such as the Summer one, the value of humidity in a material can be limited with respect to other conditions. The results of phial number 2 were considered not valid because of the low amount of powder obtained during the drilling phase; fortunately, phial number 3 was obtained in the same position and depth. Table 5 and Table 6 sum up the results in terms of mass (dried and not) and water content obtained for each sample in the two investigated areas with the gravimetric method approach.

Table 5: gravimetric method results obtained for D1 area at different height and depth; diagnostic approach [Author].

TESTED DRILLED WATER AREA HEIGHT DEPTH SAMPLE SAMPLE DRIED SAMPLE CONTENT (cm) (cm) NUMBER WEIGHT MU (g) WEIGHT MS (g) Ca (%) 4 1 13.3912 13.3449 0.3 90 12 3 12.7193 12.6832 0.3 20 4 13.9331 13.8791 0.4

4 5 13.3254 13.2682 0.4 D1 135 12 6 16.2148 16.152 0.4 20 7 16.8740 16.8034 0.4 4 8 16.0587 16.0332 0.2 176 12 9 17.3244 17.2931 0.2 20 10 14.4107 14.3876 0.2 N.B. The values of Ca are rounded off to the first decimal place as asked by the codes.

Table 6: gravimetric method results obtained for D1 area at different height and depth; diagnostic approach [Author].

TESTED DRILLED WATER AREA HEIGHT DEPTH SAMPLE SAMPLE DRIED SAMPLE CONTENT (cm) (cm) NUMBER WEIGHT MU (g) WEIGHT MS (g) Ca (%) 4 11 14.8637 14.8562 0.1 80 12 12 16.6069 16.5927 0.1 20 13 17.1198 17.106 0.1

4 14 14.3554 14.348 0.1 D2 100 12 15 18.1899 18.1724 0.1 20 16 17.3283 17.3074 0.1 4 17 13.7092 13.7012 0.1 120 12 18 17.5136 17.4969 0.1 20 19 15.8525 15.8384 0.1 N.B. The values of Ca are rounded off to the first decimal place as asked by the codes. Graph 5 and Graph 6 show for the two investigated areas the results obtained with the gravimetric method.

D1 test zone: water content (UNI 11085) 1,0 0,9 0,8 0,7 0,6 0,5 0,4 0,3

Watercontent (%) 0,2 0,1 0,0 0 2 4 6 8 10 12 14 16 18 20 22 Drilling depth (cm)

h:90cm h:135cm h:176cm

Graph 5: gravimetric method results obtained for D1 area at different height and depth; diagnostic approach [Author]. D1 area is without plaster so the comparison with the values read with TRAMEX is acceptable. This is because there is no plaster on this wall that can fake the TRAMEX measurement. The results show that the humidity content in the thickness of the masonry wall is approximately constant. The amount of powder obtained for a height of 90 cm is very limited (around 2.3g) and this can justify the apparent error in the graph comparing the results obtained for a height of 135 cm. Moreover, the limited amount of powder obtained can be influenced also by the drilling process. The limited available amount of powder can highlight either the presence of a near mortar joint or an irregular behaviour for the portion of the investigated masonry. In general, it appears that the water content is around 0.4% for a height between 90cm and 135cm. Considering that a brick is assumed to be wet when the humidity content is above 15%, the masonry components can be considered dried. This condition can be probably associated to a long period of drought and high temperatures of Summer season, remembering that the samples were obtained on the 18th September in a hot day.

D2 test zone: water content (UNI 11085) 1,0 0,9 0,8 0,7 0,6 0,5 0,4 0,3 Water content (%) 0,2 0,1 0,0 0 2 4 6 8 10 12 14 16 18 20 22 Drilling depth (cm)

h:80cm h:100cm h:120cm

Graph 6: gravimetric method results obtained for D2 area at different height and depth; diagnostic approach [Author]. D2 area is an area with plaster on the wall and this maybe can explain why the TRAMEX measurement are so different. TRAMEX in fact detects a high level of superficial humidity that is not evident through the gravimetric method approach. It is important to remember that TRAMEX measures the humidity content up to 3 cm depth that are more or less coincident with a reasonable thickness of the plaster. The humidity content is constant in the thickness of the wall. The values of water content are anyway very limited (around 0.1%) highlighting again a dry condition of the components. Some common considerations for the two investigated areas can be defined. First of all, the possible presence of superficial salts contents can influence the test acting on the conductivity of the material and so on the results of an instrument, such as TRAMEX, based mainly on this parameter. A possible further analysis, then, can be the definition of salts content in the powder samples following the principles given by UNI 11087-2003. Moreover, according to UNI 11086- 2003, it is important to remember that each salt is influenced in terms of solubility by the temperature and relative humidity of the surrounding environment. The presence of hygroscopic salts is also suggested by the conditions of the lower part of the plaster in the church area. Then, due to the results obtained in the same day and conditions through the gravimetric method, the high values of superficial humidity defined thanks to TRAMEX can be associated to superficial condensation and not to a global problem of humidity for the structure. For sure, this comparison highlights the limit of a contact measurement such as TRAMEX in the definition of the water content generating possible wrong considerations for the total behaviour of the component under analysis. The previous results can be read considering also another test such as thermography. The thermographic test was carried out the same day of the drilling tests and using a thermo-camera

100 without artificial pre-heating of the surface. Figure 92 will show a thermography of the D1 investigated area.

Figure 92: investigation of the lower internal part of the belltower to define temperature distribution and other details. Real photo (left) and thermographic results with reference scale (right); diagnostic approach [Author]. The image, processed with “IRsoft” of Testo, shows a more or less uniform distribution of the temperatures and so of the condition of the masonry under analysis. Discontinuities are highlighted in the lower part of the masonry-wall and associated to a high state of degradation of the exposed bricks without plaster. Then, a profile P1, as a straight-line intercepting temperature values and reproducing this information on a two-axis graph, is produced (Graph 7).

Graph 7: vertical temperature variation for interal surface of the belltower; [Author]. Graph 7 shows how the surface temperature is approximately constant all over the profile. Small variations of a magnitude of maximum 0.6 °C can be detected; this testifies how the conditions of the investigated area are constant in height in terms of humidity-temperature (two deeply linked parameters) and distribution of the materials, showing that the entire component is realized in masonry without other additional materials.

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Other areas of the belltower were investigated. In fact, particular stress is put on the West side of the belltower that is the side connected to the church body. In this area, an evident vertical crack is present and shown in the following image coupled with the thermographic one (Figure 93).

Figure 93: investigation of the lower internal part of the belltower, the area is in contact with the church and an evident discontinuity is present in the contact between the two walls. Real photo (left) and thermographic results with reference scale (right); diagnostic approach [Author]. The thermographic image gives the possibility to highlight two important aspects: - The crack between the North wall of the belltower and the church one is evident. This means that the wall of the belltower is just leaning against the church’s wall generating a structural discontinuity affecting the behaviour of the entire fabrique. Then, the box action between the members is not present. This information gives also the possibility to understand that the belltower was probably a later added component during the church’s history and not present since the first design; - The lower part of the masonry is totally exposed and not covered by plaster for the majority of the surface. A hole in the lower left part is present and associated to the lowest value of the temperature (around 22°C). This discontinuity has an effect both on the structural behaviour and on the exposition of the elements to the outdoor weathering agents. The belltower is investigated also on the external side thanks to thermography. No artificial pre- heating of the surface is used. Figure 94 shows the results.

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Figure 94: investigation of the external part of the belltower to define temperature distribution and other details. Thermographic results with reference scale (right); diagnostic approach [Author]. The distribution of the temperatures is uniform for the entire height of the belltower showing that the element is homogeneous and, for what seen from the inside, realized with bricks and mortar. So, also the belltower corresponds to a masonry component. Some stringcourses are evident from the outdoor and are coincident on the inner side with wood- beams used as a support to anchor a vertical element to reach the top of the bell tower (Figure 95).

Figure 95: photo of the internal part of the belltower to define inter-storey wood components location; diagnostic approach [Author].

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The horizontal wood components are embedded in the walls thanks to holes. This for sure generates discontinuities for the walls affecting their structural behaviour. These discontinuities were not detected by internal thermographies because this area is higher than the investigated one; they were not detected by external thermographies because maybe the holes are not present for the entire thickness of the wall. After all these tests for the belltower area, it is possible to understand that: - The masonry components are in a dry condition thanks to UNI 11085 test. On the other hand, the surface measurement shows a high level of humidity and this can be linked to problems of superficial condensation and salts’ content able to alter the conductivity of a material; - The masonry pattern is regular and uniform as thermographies show. Some bricks are exposed and with a high level of decay; - The North wall of the belltower is just leaning on the church resistant structure as an evident crack and holes show; then no box-behaviour is ensured in this part; - Horizontal wood connecting components are present and inserted into wall’s holes. These walls are, so, discontinuous and not uniform for their height affecting their structural attitude.

6.10. Conclusions and main aspects after diagnostic approach

Non-intrusive or minimally invasive tests give the possibility to define important structural parameters such as the construction materials, their patterns and uniformity and the state of decay related to problems such as water content or rising dump. For the church area, thermography gives the possibility to define a uniform construction technique for all the structural elements and to highlight problems of water vapor trapped in the indoor environment without an escape route. Applying thermography on the outer elements, the masonry pattern is defined and it is uniform for all the volumes: church, chapels, apse and belltower. So, even though the volumes are added during the years a uniformity in the masonry pattern is adopted giving a first structural continuity to the fabrique. For the belltower, thermography and relative humidity analysis is used. The relative humidity is studied through two approaches that are compared in terms of results showing the limits of each method. In fact, the problem of superficial water content detected with TRAMEX is not confirmed with gravimetric method for different depth. This can confirm the hypothesis proposed for the church area and so indoor relative humidity coming from the walls not able to be easily dissipated.

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7. Structural behaviour assessment

The structural behaviour of the fabrique must be defined considering both vertical and tangential stresses and possible collapse mechanisms that can be activated in the structure. These considerations will be the base for the realization of a structural model and modal analysis.

7.1. Confidence factor FC, material properties and elastic response spectrum

In order to study the structural behaviour and consequent considerations, it is useful to define the confidence factor and the material properties. The confidence factor is defined after the knowledge acquisition-path (percorso di conoscenza) proposed in the previous chapters. In order to obtain the FC value, the following formula is used as suggested in the Guidelines:

퐹 =1+ 퐹

Where the values of FCk are obtained starting from “Tabella 4.1” of “Linee guida per la valutazione e la riduzione del rischio sismico del patrimonio culturale con riferimento alle Norme tecniche per le costruzioni di cui al decreto del Ministero delle Infrastrutture e dei trasporti del 14 gennaio 2008” (Figure 96).

Figure 96: description of the different levels of analysis for the knowledge path and associated partial confidence factors; Tab. 4.1., chapter 4.2; [Linee guida per la valutazione e la riduzione del rischio sismico del patrimonio culturale con riferimento alle Norme tecniche per le costruzioni di cui al decreto del Ministero delle Infrastrutture e dei trasporti del 14 gennaio 2008].

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For the study case, the values may be assumed to be the ones of Table 7, considering that some additional details and tests would have been performed if the COVID emergency had not occurred, and considering that for cultural heritage assets the attainment of a value of maximum 1.2 for the confidence factor is usually required or advisable.

Table 7 : values of FCK assumed for the study case; [Author].

FC1 0 FC2 0.06 FC3 0.12 FC4 0

So, the value of FC is, for the considered process of knowledge and fabrique, equal to 1.18. This value is important because gives the possibility to modify the material’s properties read in “Tabella C8.5.I.” of “Circolare 21 gennaio 2019 n.7”. The material characteristics (Figure 97) are defined thanks to the investigation of the structure in the process of knowledge that gave the possibility to point out an ordinary masonry structure with bricks and mortar.

Figure 97: description of the material’s characteristics according to the masonry typology; “Tab. C8.5.I.”, chapter C8.5.3; [Circolare 21 gennaio 2019 n.7]. Where: - f is the medium compression resistance of chosen masonry type; - τ0 is the medium shear resistance of chosen masonry type; - fv0 is the medium shear resistance of chosen masonry type, see C8.7.1.3 of the document; - E is the elastic modulus of chosen masonry type; - G is the tangential modulus of elasticity of chosen masonry type; - w is the medium specific weight of chosen masonry type; For the masonry chosen, according to the codes suggestions, it is better to reduce the values of the elastic modulus of 0.8 and of the resisting values of 0.7 due to the lack of further analysis.

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So, considering also a FC equal to 1.18 and the reduction coefficients, the properties for the masonry structure of Casolate church are summarized in Table 8.

Table 8: material properties used for the study case considering the reduction coefficients and FC contribution; [Author].

f τ0d E G w 1.54 N/mm2 0.03 N/mm2 813.56 N/mm2 271.19 N/mm2 15.25 kN/m3

For each structure, a reference period VR can be defined according to the function hosted and the expected occupants. The definition of VR is useful to calculate the return period TR for the seismic action for the limit state considered.

So, according to “Tab. 2.4.I” of NTC 2018, it is possible to assess the nominal life VN for the considered fabrique (Figure 98).

Figure 98: minimum values for nominal life VN according to construction’s types; “Tab. 2.4.I.”, chapter 2.4.1; [NTC 2018]. Then, referring to “Tab. 2.4.II” of NTC 2018, it is needed to define a “classe d’uso” and the associated coefficient CU. For the study case, a class II is chosen (“Costruzioni il cui uso preveda normali affollamenti, senza contenuti pericolosi per l’ambiente e senza funzioni pubbliche e sociali essenziali. Industrie con attività non pericolose per l’ambiente. Ponti, opere infrastrutturali, reti viarie non ricadenti in Classe d’uso III o in Classe d’uso IV, reti ferroviarie la cui interruzione non provochi situazioni di emergenza. Dighe il cui collasso non provochi conseguenze rilevanti.”) (Figure 99).

Figure 99: values of “coefficient d’uso” CU according to the use class; “Tab. 2.4.II”, chapater 2.4.3; [NTC 2018].

VR is calculated as:

푉 = 푉 ∗ 퐶 =50∗1=50 푦푒푎푟푠

On the other hand, considering the SLV limit state, the return period TR is defined as:

푉 푇 = − ln(1 − 푃)

Where PVR is the probability to overcome the seismic action in the reference period and for the SLV limit state is equal to 10% (“Tab.3.2.I.”, NTC 2018), while VR is 50 years as calculated before. In the end, TR is 475 years. Once all these parameters are defined and remembering that the soil in Casolate (see Chapter 3.1.) is in category C with topographic class T1, it is possible to obtain the response spectrum for the considered site thanks to an Excel device provided by “Istituto Superiore dei Lavori Pubblici”. 107

The response spectrum proposed (Figure 100), the black one, is an elastic one considering a damping of 5%.

Figure 100: response spectrum defined for the site considered (Casolate) using “Istituto Superiore dei Lavori Pubblici” device; “Fase 3” sheet; [Istituto Superiore dei Lavori Pubblici]. Focusing on the area “Parametri e punti spettri di risposta”, it is possible to obtain the main parameters and values of the elastic response spectrum (Figure 101).

Figure 101: dependent and independent parameters at the base of Casolate response spectrum; “Fase 3” sheet; [Istituto Superiore dei Lavori Pubblici]. Where:

- ag is the maximum acceleration for the site considered and measured in g considering a certain limit state; - F0 is a factor describing the maximum amplification of the spectrum for horizontal acceleration; - TC* is a reference value used to define the position of the spectrum in which velocity of horizontal acceleration is constant. In fact, it is used with CC (“Tab. 3.2.IV”, NTC 2018) in the definition of TC; - TB, TC and TD are the characteristic values of the response spectrum. For all the “parametri dipendenti”, the Excel device gives the formula in order to assess them as in NTC 2008 (Figure 102). 108

Figure 102: formula to calculate dependent parameters at the base of Casolate response spectrum; “Fase 3” sheet; [Istituto Superiore dei Lavori Pubblici].

A value of period T (sec) is associated to a specific acceleration Se (g) in a table provided by the device. In the end, a more precise spectrum for the calculations can be obtained (Figure 103).

Figure 103: vertical and horizontal response spectrum for Casolate defined with Excel device; “Fase 3” sheet; [Istituto Superiore dei Lavori Pubblici].

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7.2. Vertical loads analysis and stresses definition

The vertical loads analysis starts with the definition of the specific weight per unit volume or per unit area of the materials used for the construction of Casolate Church. Three main materials can be considered as presented in Table 9.

Table 9: definition of the materials unitary mass later used in the calculation of the forces; [Author].

Material Weight Unit Details Structural Wood 290 kg/m3 Roof structure (rufter,chord and so on) 2 Brick tiles 45 kg/m Common bricks and lime mortar 15254.25 N/m3 Read from the table in Chapter 7.1

Some assumptions are taken into account during these calculations: - the loads taken into account are just related to the weight of the vertical components and the horizontal ones (arches, vaults, roofing), the variable and accidental loads are not considered; - the contribution of the belltower is not considered due to the independency of the volume and to the not good connection of the walls with the church volume. For the same reason, the sacristy and Priest’s house are not considered; - thanks to the diagnostic approach with thermography, it has been pointed out that the arches and vaults are realized with bricks and mortar as the rest of the structure of the church; - due to the circular geometry of the apse, the stress level of this area is considered independent respect to the church volume one; - the two lateral chapels are part of the church volume; - the height of the walls of the church volume is 16.3m while for the lateral chapel it is 8.5m. The resisting wall’s areas to compression are taken into account in Table 10.

Table 10: definition of the resisting wall’s area for apse and church; [Author].

Portion considered Value Unit Resisting wall’s area for the church 22.89 m2 Resisting wall’s area for the apse 19.92 m2

Then, once the mass is defined for each constructive element and multiplied by the gravity acceleration to have forces, the results obtained are shown in Table 11.

Table 11: definition of the total weight actin on the two areas (church and apse); [Author].

Portion considered Value of force Unit Church 11058.80 kN Apse 4115.13 kN

In the end, dividing the gravitational forces by the resisting areas of the two volumes (church and apse), Table 12 will present the vertical stresses acting on the reference areas.

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Table 12: definition of the compression stress acting on the two volumes (church and apse); [Author].

Value of Portion considered weight Unit Church 0.48 MPa Apse 0.20 MPa

The parameters obtained can be compared with the reference value of f (medium compression resistance of the considered masonry type), read in “Tabella C8.5.I.” of “Circolare 21 gennaio 2019 n.7”, in order to understand the compression capacity reached (Table 13).

Table 13: check for the maximum compression stress accepted for the construction typology chosen; [Author].

Limit Value of value Percentage of weight given by A < B ? compression Portion calculated the code resistance considered (A) (B) used Church 0.48 MPa 1.54 MPa YES 32% Apse 0.20 MPa 1.54 MPa YES 13%

The definition of these two values is important not only for the evaluation of the compression of the masonry components but also will be involved in the definition of the global shear capacity of the structure through FSLV value.

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7.3. Simplified assessment of the global capacity of the structure (LV1)

Once the vertical stresses on the main masonry components are defined, also the global shear capacity of the structure must be evaluated. According to the Ministry Guidelines, the box behaviour of the structure is assumed with a good link between the different components also ensured by the presence of tie-rods or similar elements. In this case, it is possible to define the seismic action leading to the limit state considered. The horizontal forces must be evaluated, for each floor, in both the directions of the plan in order to define a weak direction used in the calculations. This is the general approach that is proposed for buildings like palaces, but not for churches, because often they present damage from local behaviour rather than from a global one. Nevertheless, an appreciation of the total shear capacity, even if largely approximated, seems interesting to assess the level of possible lateral response that may be expected and to compare the two main directions of the church in this respect. In fact, for the church in Casolate, the shear capacity and all the associated parameters are evaluated in both the directions with the aim of describing the total structural behaviour of the fabrique.

7.3.1. Basic principles and main assumptions for LV1 assessment

Considering the courts and villas’ simplified approach for LV1 analysis valid also for churches, it is possible to define for SLV the ordinate of the elastic response spectrum and so the acceleration Se,SLV: 푞 ∗ 퐹 푆 = , 푒∗ ∗ 푀 Where: - q is the behaviour factor assumed, for the considered condition, between 2.25 and 2.8 and defined in this range because the fabrique is part of the existing historical buildings and it is not designed in modern engineering terms; - FSLV is the shear resistance of the building evaluated in the two principal directions for all the storeys; - e* is the percentage of the mass participating in the first modal shape; ( ∑ Ψ ∗ ) - M is the total seismic mass and calculated as 푀 = and so considering permanent and variable loads acting on the structure.

Focusing on the definition of the value of FSLV, the load bearing walls are considered for each direction and it is assumed that the collapse comes when a defined percentage of shear resistance of the structure is reached. Considering a generic x direction and a generic storey i, the shear resistance FSLV,xi is equal to:

μ ∗ ξ ∗ ζ ∗ 퐴 ∗ τ 퐹, = β ∗ κ Where:

- Axi represents the shear resisting area in the x-direction for the i-storey;

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- τ is the design shear resistance of the masonry component considered and calculated as σ τ = τ1+ . The value of τ is the shear resistance of the masonry components . ∗

read by the table “Tabella C8A.2.1.” and reduced by the confidence factor while σ is the mean compression value on the resisting area of the walls of the i-storey; - κ is the ratio between the seismic forces acting at the i-floor and the total seismic force of the building; - β takes into account the plan irregularities expressed in function of eyi (eccentricity of the stiffness center [centro delle rigidezze] and the centre of gravity [baricentro delle masse]) and of dyi (distance between the stiffness center [centro delle rigidezze] and the most external wall in the x-direction). In fact, it is calculated as β =1+2∗ and must be lower than 1.25; - μ is a coefficient considering the homogeneity of the stiffness and resistance of the masonry

,∗ ∑ , piers. It is calculated as μ = 1−0.2∗ −1 and must be higher or equal to

0.8. In detail, 푁, represents the number of masonry piers in the x-direction for the i-storey while Axi,j is the area of the generic masonry pier in the x-direction for the i-storey; - ξ is a coefficient considering the main collapse mechanisms for the masonry piers. It is assumed equal to 1 for a shear collapse while 0.8 for a bending failure (especially in case of slender masonry piers, not deeply vertically loaded); - ζ describes the resistance of masonry strips in direction x for the storey considered. It is equal to 1 for resisting strips while lower than 1 (up to 0.8) for strips not able to block the rotation on top of the walls.

It is necessary to suppose a modal shape to define e* and κ. In case, for example, of constant mass and heights in the fabrique, it can be defined through ϕ (displacement vector at the storeys considering the collapse hypothesis assumed):

∗ (∑ ) ∑ 푒 = κ = ∑ ∑ According to the ordinate obtained, the acceleration referred to soil category A for the site considered and leading to the SLV condition is:

⎧ 푆,(푇) ⎪ 푇 ≤ 푇 < 푇 푆 퐹 푎 = ⎨푆,(푇1) 푇 ⎪ 푇 ≤ 푇 < 푇 ⎩ 푆 퐹 푇 Remembering that:

- T1 is the fundamental period of vibration for the structure; - TB, TC and TD are the characteristic periods of the spectrum defined as suggested by NTC 2018; - S is the coefficient that considers the soil typology and topographic characteristics of the site. It is equal to: S = SS * ST. Then, the structural safety of a fabrique is defined for an LV1 simplified approach considering two variables as suggested by the Guidelines. 113

The first parameter is the acceleration factor (fattore di accelerazione) fa,SLV:

푎 푓, = 푎,

Where aSLV is the value of the acceleration calculated for the fabrique in a specific limit state (for the case considered Life Safety limit State) while ag,SLV is the peak ground acceleration for the considered site and for the assumed return period for the limit state considered. The second parameter to describe the structural safety is the seismic safety index (fattore di sicurezza sismica) IS,SLV:

푇, 퐼, = 푇

Where TR is the return period for a considered limit state (− ; for SLV is 475 years) while () TR,SLV is defined through an iterative process considering the 9 return periods and the associated values of the parameters (ag, F0 and TC*) given in “Allegato B” of NTC 2018. TR,SLV represents the return period by which the acceleration aSLV calculated for the fabrique will occur and so it is defined in function of aSLV:

푇, = 푇 ∗ 10 푇 log , 푇, 훼 = [log(푎) − log푎,]∗ 푎 log , 푎,

Considering TR1 coincident with the minimum period between the two individuated by the value of aSLV in the iterative procedure, while TR2 the maximum period obtained because of aSLV. ag,1 is associated to TR1 while ag,2 is associated to TR2 and the values are read in “Allegato B” of NTC 2018 for the considered site.

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7.3.2. Shear capacity for longitudinal direction

The calculations for the shear capacity of the structure must be carried out for the two main directions of the church considering that there is just a single storey. The calculations proposed are referred to the base of the building. The starting point is the longitudinal direction (N-S). First, the coordinates of both the centre of gravity and stiffness centre must be defined considering their position with respect to the origin of a reference system. For what concerns the centre of gravity G, the coordinates are shown in Table 14.

Table 14: coordinates of the centre of gravity G; [Author].

XG 7.09 m YG 11.00 m

Then, the plan of the fabrique has an evident symmetry with respect to the longitudinal axis and this helps in the definition of the coordinates of the stiffness centre CR. In fact, the x-coordinate of CR is 7.09m and so the same of the gravity centre. For the definition of the y-coordinate, due to the definition of all the characteristics of the walls (area, position and material thanks to site inspection and historical analysis), it is possible to calculate it as:

∑ 푌 ∗ 퐺 ∗ 퐴, 푌 = ∑ 퐺 ∗ 퐴,

Where YK is the position of the walls respect to the reference system, GMK is the shear resistance modulus of the masonry component and defined in Chapter 7.1., Axi,k is the area of the considered element. So, in the end, the coordinates of the stiffness centre CR are shown in Table 15.

Table 15: coordinates of the stiffness centre CR; [Author].

XCR 7.09 m YCR 11.25 m

The value of the shear resistance of the masonry components τd in the longitudinal direction (τ = σ τ1+ ) is calculated considering a mean compression stress σ0 of 0.26 MPa (the separation . ∗ between church and apse is not valid anymore). Referring to a value of τ0d (shear resistance of the masonry category read by tables and reduced by the confidence factor) equal to 0.029 MPa, the value of τd is 0.07 MPa. The shear resisting area in the longitudinal direction for the church is 29.04 m2 considering the contribution of the apse area through a linearization.

The coefficient κy, describing the ratio between the seismic forces at the floor considered and total seismic force of the fabrique, is calculated supposing a triangular modal shape. So, κy is equal to 1 for the considered case.

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The evaluation of the plan irregularity through the coefficient βy (β =1+2∗ ) shows that in this direction there is no eccentricity between the centre of gravity and stiffness centre (ex = 0). So, βy is 1.

The homogeneity of the resistance and stiffness of the masonry piers is evaluated through the

,∗ ∑ , coefficient μy ( μ = 1−0.2∗ −1 ). The masonry piers Nm,y are 8 and the components are considered as in Figure 104.

Figure 104: individuation of the masonry piers in the longitudinal direction (East and West elevation); [Author]. As shown, also part of the apse is considered in the shear resisting longitudinal area through a linearization. So, μy is 0.87 (≥ 0.8 ok). Considering an expected collapse for bending due to the slenderness of the piers and to the limited vertical loads playing on them analysed during the site inspection, the value of ξy is 0.8.

Then, assuming resisting masonry strips in the longitudinal direction, ζy is equal to 1.

So, Table 16 presents the values of the parameters involved in the calculation of FSLV,LONG (= ∗ ∗ ∗ ∗ ). ∗

Table 16: summary of the parameters involved in the calculation of FSLV,LONG; [Author].

2 Ay 29.04 m τd 0.07 MPa βy 1 μy 0.87 κy 1 ξy 0.80 ζy 1 FSLV, LONG 1565423.25 N

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7.3.3. Shear capacity for transversal direction

Also for the definition of the shear resistance of the masonry components τd in the transversal

σ direction (E-W) (τ = τ1+ ), a mean compression stress σ0 of 0.26 MPa is assumed. . ∗

Considering then a value of τ0d (shear resistance of the masonry category read by tables and reduced by the confidence factor) equal to 0.029 MPa, the value of τd is 0.07 MPa. The shear resisting area in the transversal direction for the church is 20.40 m2 considering not only the façade contribute but also the one of the apse area through a linearization.

The coefficient κx, describing the ratio between the seismic forces at the floor considered and total seismic force of the fabrique, is calculated supposing a triangular modal shape. So, κx is equal to 1 for the considered case.

The evaluation of the plan irregularity through the coefficient βx (β =1+2∗ ) shows that in this direction the eccentricity ey is 0.25 m while the distance dy between the stiffness centre and the most external wall in this direction is 10.17m. So, βx is 1.04. The homogeneity of the resistance and stiffness of the masonry piers is evaluated through the ,∗ ∑ , coefficient μx ( μ = 1−0.2∗ −1 ). The masonry piers Nm,x are 8 and the components are considered as shown in Figure 105.

Figure 105: individuation of the masonry piers in the transversal direction (South and North elevation); [Author]. As shown, also part of the apse is considered for the shear resisting transversal area through a linearization. Moreover, also the façade contributes to the shear resistance of the fabrique in this

117 direction considering also the presence of voids related to the rosette and the entrance door. So, μx is 0.88 (≥ 0.8 ok). Considering an expected collapse for bending due to the slenderness of the piers and to the limited vertical loads playing on them, the value of ξx is 0.8.

Then, assuming resisting masonry strips in the longitudinal direction, ζx is equal to 1.

So, Table 17 presents the values of the parameters involved in the calculation of FSLV,TRASV (= ∗ ∗ ∗ ∗ ). ∗

Table 17: summary of the parameters involved in the calculation of FSLV,TRASV; [Author].

2 Ax 20.40 m τd 0.07 MPa βx 1.04 μx 0.88 κx 1 ξx 0.80 ζx 1 FSLV,TRASV 1054573.74 N

The lowest value of the shear resistance, as expected due to the limited area, is in the transversal direction.

Generally, the acceleration Se,SLV is defined only for the direction in which the value of the shear force is lower (in this case the transversal direction). Instead, for the present document, the definition of the acceleration and the safety indexes is proposed for the two directions in order to understand better the total behaviour of the structure as a starting point for further analysis on local components.

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7.3.4. Assessment of the acceleration Se,SLV in both directions

The structural assessment of Se,SLV is based on the formula: 푞 ∗ 퐹 푆 = , 푒∗ ∗ 푀 For the considered case: - q is the behaviour factor. Not dealing with the design of the building but dealing with an already existing building with masonry structure, the NTC 2018 suggests to use a behaviour factor q between 2.25 and 2.8. Considering the information obtained during the site inspections, diagnostic approach and through the entire process of knowledge, the behaviour factor q is assumed equal to 2.3; - the participating seismic mass to the first modal shape e* is calculated considering a triangular modal shape through the simplified formula: 0.75+0.25N-0.75. N represents the number of storeys and in this case it is equal to 1. So, e* is 1; - The seismic mass M is then defined through the formula: ( 퐺 + ∑ Ψ ∗ 푄) 푀 = 푔 Considering by G all the permanent (structural and non-structural) loads while with Q all the variable ones defined with reference to Chapter 3 of NTC 2018. g is the gravity acceleration while Ψ is the combination coefficient for the variable actions and defined by NTC 2018 in “Tab.2.5.I”. In the considered case, the evaluation of the shear forces FSLV is at the base of the fabrique and so the value of the variable loads Qkj is not incident on the masonry walls considering also the presence of a single storey. The Table 18 summarizes the parameters involved in the calculation:

Table 18: summary of the parameters involved in the calculation of Se,SLV; [Author].

q 2.30 FSLV,LONG 1565423.25 N FSLV,TRASV 1054573.74 N e* 1 M 1491649.13 kg Se,SLV, LONG 0.241 g

Se,SLV, TRASV 0.162 g

Using the response spectrum calculated as shown in Chapter 7.1., it is possible to define the period TSLV associated to the acceleration Se,SLV,LONG and Se,SLV,TRASV calculated:

푇, = 0.495 푠

푇, = 0.737 푠

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It is important to highlight that both TSLV,LONG and TSLV,TRASV are coincident with points of the graph between TC and TD that are the characteristic values of the response spectrum. On the other hand, the value of T1 (fundamental period of the structure) is assessed through a simplified formula that is valid for regular structures both in elevation and plan. The church of Casolate can be considered, even though some irregularities in terms of elevation, as regular for the two conditions. So:

. 푇 = 0.05∗ 퐻 = 0.05∗ (20.10 푚) = 0.474 푠푒푐

The acceleration aSLV,LONG and aSLV,TRASV are so defined as:

푆,, 푇 0.241 0.474 푎, = = ∗ = 0.0645 푔 푆 퐹 푇 1.5 ∗ 2.6 0.454

푆,, 푇 0.162 0.474 푎, = = ∗ = 0.188 푔 푆 퐹 푇 1.5 ∗ 2.6 0.454

The values of S and F0 have been defined in Chapter 7.1..

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7.3.5. Assessment of the acceleration factor fa,SLV and seismic safety index IS,SLV in both directions

The first parameter used to describe the structural safety condition of Saint Peter church is the acceleration factor fa,SLV (defined in Chapter 2.2.3.) considering the two main directions of the fabrique: longitudinal and transversal one.

푎, 0.0645 푓,, = = = 0.96 푎, 0.067

푎, 0.0433 푓,, = = = 0.64 푎, 0.067 ag,SLV is the peak ground acceleration defined referring to the specific site and to a specific limit state, such Life Safety one that has a specific return period TR coincident with 475 years. This assessment is possible thanks to both the Excel file for the response spectrum definition of “Consiglio Superiore dei Lavori Pubblici” and “Allegato B” of NTC 2018. The second parameter for the definition of the structural safety of the church is the seismic safety index IS,SLV (fattore di sicurezza sismica). It is obtained as the ratio between the return period TR,SLV in which the calculated acceleration aSLV is luckily to occur and the return period for a specific limit state TR. TR is equal to 475 years (Chapter 7.1.) for the study case of the present document.

It is important to define TR,SLV,LONG and TR,SLV,TRASV that are the return period in which respectively the accelerations aSLV,LONG and aSLV,TRASV, defined in Chapter 7.3.4., are luckily to occur.

Considering aSLV,LONG and referring to “Allegato B” of NTC 2018, the two periods TR1 and TR2 are respectively 201 years and 475 years with ag1 equal to 0.0509 g and ag2 equal to 0.0672 g. So:

푇, 475 log 푇 log 훼 = [log푎 − log푎 ]∗ , = [log(0.0645) − log(0.0509)]∗ 201 = 0.320 , , 푎, 0.0672 log log 푎, 0.0509

. 푇,, = 푇 ∗ 10 = 201∗ 10 = 419.95 푦푒푎푟푠

Then considering aSLV,TRASV, the two periods TR1 and TR2 are respectively 101 years and 140 years with ag1 equal to 0.0393 g and ag2 equal to 0.0447 g. So:

푇, 140 log 푇 log 훼 = [log푎 − log푎 ]∗ , = [log(0.0433) − log(0.0393)]∗ 101 = 0.106 , , 푎, 0.0447 log log 푎, 0.0393

. 푇,, = 푇 ∗ 10 = 101∗ 10 = 128.92 푦푒푎푟푠

In the end, it is possible to define the seismic safety indexes:

푇,, 419.95 푦 퐼,, = = = 0.884 (<1) 푇 475 푦 121

푇,, 128.92 푦 퐼,, = = = 0.271 (<1) 푇 475 푦 The seismic safety index is a ratio describing the structural safety of the considered fabrique or investigated portion. If its value is higher or equal to 1 structural safety is ensured while if it is lower than 1 further analysis and attention must be paid. For the church under analysis, the seismic safety index is lower than 1 for both the two directions and so additional analysis and considerations must be performed, having a minimum that is rather low. The transversal direction is characterized by a limited shear resisting area at the base and so this can be considered a weak point of the structure in the seismic response. The calculations proposed consider as shear resisting area just the contribution of the church piers not considering the positive impact of the nearby bodies (belltower, sacristy and Priest’s house) of which no detailed information were obtained during the knowledge path. So, the seismic safety index IS,SLV,TRASV is evaluated considering a conservative approach and could be improved considering a more detailed analysis leading to the needed information.

On the other hand, the value of IS,SLV,LONG is near to 1 and maybe its reduction is due to the conservative approach previously described and to the discontinuities of the masonry piers in the church area generated by the presence of lateral openings (arches) for the chapels and the apse resisting contribution that is difficult to be linearized and expressed in such a simplified approach.

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7.4. Collapse mechanisms assessment through “scheda per il rilievo del danno e della vulnerabilità delle chiese”

Due to the complexity of the churches’ structure and to the continuous changes that can happen during their history, it is not useful to consider only a unitary behaviour for the entire volume. This coupled with the variety of constructive techniques for the churches makes less significant to refer to a simplified model for all the churches. In order to assess the seismic safety index for a simplified LV1 approach, a reference to “scheda per il rilievo del danno e della vulnerabilità delle chiese” can be used as suggested by the Guidelines. The document proposed as reference by the Ministry Guidelines is used in seismic emergencies since 1995 to assess the damage occurred during an earthquake, giving the possibility to define the relationship between the seismic action and the damage occurred. The same approach and assessment format may be used in a preventive modality to evaluate the seismic vulnerability of a church with respect to the different possible mechanisms of damage. The safety level at analysis level LV1 may be ascertained by such vulnerability analysis and computing the relevant vulnerability index. This approach is based on a statistic data collection and so the results obtained must be always read with a statistic attitude giving the possibility to understand if further analysis must be performed. The sheet proposed considers 28 collapse or damage mechanisms that can affect the different building components considering vulnerability indexes and indexes describing the contribution of anti-seismic elements.

7.4.1. Definition of the mechanisms and vulnerability index assessment

The vulnerability index iv is a value, statistically defined, ranging between 0 and 1 and calculated as:

1 ∑ 휌 ∗(푣 − 푣) 1 푖 = + 6 ∑ 휌 2 Where:

- vki is the vulnerability index and vkp is the anti-seismic components’ index evaluated according to “Tabella 5.1” of the Ministry Guidelines and shown in Figure 106.

Figure 106: definition of values for indexes vki (vulnerability) and vkp (anti-seismic behaviour) according to effectiveness; “Tabella 5.1”, chapter 5.4.3; [Linee guida per la valutazione e la riduzione del rischio sismico del patrimonio culturale con riferimento alle Norme tecniche per le costruzioni di cui al decreto del Ministero delle Infrastrutture e dei trasporti del 14 gennaio 2008].

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- ρk is a coefficient describing the impact of the possible collapse mechanisms. It is equal to 0 if the component of the mechanisms is not present in the church studied while, for all the other case, it ranges between 0.5 and 1. In particular, ρk must be equal to 0.5 for mechanisms 4 and 15; ranging between 0.5 and 1 for mechanisms 10, 11, 12, 18, 20, 22, 23, 24, 25, 26; equal to 1 for all the other cases. The list of the 28 collapse mechanisms is presented in “Allegato C” of the Guidelines. The approach of collapse mechanisms is based on the hypothesis of generation of kinematic chains leading to the detachment of solid blocks from the totality of the component and on the generation of plastic hinges in the contact points of the blocks. This approach is possible only if it is possible to consider that masonry components reach collapse without breaking up in several pieces. The mechanisms, moreover, are associated to the different macro elements part of the church (e.g. belltower, nave, apse, chapels, roof and so on). The attached document describes for each mechanism which can be the characteristics of an anti- seismic element or vulnerability detail. These elements and details can be implemented by the designer according to the level of knowledge and investigations performed for the case under analysis. In order to fill in this list, it is useful to have a deep knowledge of the church considering evolution during time, possible problems, crack pattern. So, the process of knowledge previously proposed is of great importance as well as the site inspections performed and the photographic reportage. In detail, the list of the possible mechanisms for the church is commented: - Mechanism 1: out of plane of the façade. This mechanism can be present for the considered church due to the way in which the façade is linked to main load-bearing walls. In fact, the connection is represented by a small masonry recess that is not considered by the guidelines as an index of vulnerability. But the freedom of the designer in this evaluation gives the possibility to consider this small connection as a vulnerable component possibly leading to the façade detachment. For this case, so, the value vki considered is equal to 1. In the end, no protective components or anti-seismic supports are evident against this mechanism; - Mechanism 2: mechanisms typical of the top of the façade (out of plane of the tympanum, masonry deterioration and so on). In this case, there are two big openings in the façade: the entrance door and the rosette. Then, the top part of the façade is characterized by a considerable dead load due to the dimensions of the tympanum. So, two indexes of vulnerability are highlighted with a consequent value of vki, according to the tables, equal to 2. No anti-seismic devices (connections with the roof, light components like curbs or metal reinforcing elements) or collaborative components are present so vkp is equal to 0; - Mechanism 5: transversal behaviour of the structure (cracks, rotation of the lateral walls, out of plane in the pillars). For Saint Peter’s church, none of the problems typical of this mechanism is evident but the slenderness and the presence of arches repeated for the entire nave give the possibility to this mechanism to develop. So, according to the description in “ALLEGATO C” of Ministry Guidelines, two vulnerability indexes are present with a consequent vki of 2. On the other hand, the transversal behaviour of the church is implemented by tie-rods at the base of the arches with a consequent vkp of 1; - Mechanism 6: shear problems for the lateral walls (cracks also at the discontinuities levels), this mechanism describes the longitudinal behaviour of the structure. No cracks are evident in this case but there is an index of vulnerability related to big openings (arches at the entrance of the lateral chapels and window openings) in masonry components with a limited

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thickness (compared to their height). So, vki is equal to 1. On the other hand, thanks to the diagnostic approach with thermography and part of the process of knowledge of the fabrique, it was possible to define a uniform constructive technique of the structural components (walls, arches, vaults) both in terms of orientation and materials used. So, this can be considered a positive aspect ensuring a better longitudinal response of the structure; for this reason, vkp is equal to 1; - Mechanism 13: triumphal arches (cracks, masonry components that slides from their original position or that are compressed and crushed). No indexes of vulnerability are evident for this mechanism because no concrete roofing is used or other kind of heavy solutions. A positive aspect is represented by tie-rods that are at the base of the two triumphal arches (at the entrance of the church and at the beginning of the apse area). So, for this mechanism, a value of vkp of 1 and of vki of 0 are assumed; - Mechanism 16: out of plane for the apse area (evident vertical cracks components or serious similar elements). The presence of two windows on the lateral parts of the circular apse generates discontinuities in the masonry components reducing their structural capacity; so, vki is 1. Even though this, a tie-rod system is present in the apse improving the connection of the components and reducing the thrust generated by the arches; then, vkp is 1; - Mechanism 19: roofing components and lateral walls’ behaviour (cracks for wood beams, shift of the roof components, not proper connection between the curbs and the masonry components). This mechanism is more related to the roof wood-structure and it is verified when seismic actions perpendicular to the main direction of the nave insist on the fabrique generating out-of-plane actions, coincident with the inertia forces of the roof structure, on the lateral walls with consequent out-of-plane of the walls and collapse of the roof. In certain cases, this mechanism generates a loss of constraints for the roof’s trusses with consequent cracks for the arches and vaults and out of plane for masonry piers or columns. This mechanism was a leading one in the seismic events of 2012 in Emilia-Romagna and a clear example of what happens in this case is given by Duomo di Santa Maria Maggiore in Mirandola (MO). Saint Peter church is characterized by this system of wood trusses and masonry walls giving the opportunity to the verification of this mechanism. No heavy solutions are applied for the roofing components but, due to the position of the roof of the lateral chapels leaning on the external walls of the church, possible thrusts can be introduced. So, vki is 1. On the other hand, supposing a good connection of the trusses to the masonry components and good connections for the roof-structure (due to the recent substitution of the roof in the last decades as understood during the historical analysis thanks to people of interest), two collaborating elements against this mechanism are present; then, vkp is 2; - Mechanism 22: overturning of the lateral chapels (detachment or disconnection of the walls of the chapels). No indexes of vulnerability are evident moreover an anti-seismic component helps the behaviour of the lateral chapels: the tie-rods system. In fact, a tie-rod is present under each entrance-arch of the two lateral chapels. So, vkp is 1; - Mechanism 24: chapels’ vaults (cracks or discontinuities). No vulnerable components are present (e.g. concentrated loads from the roof or segmental vaults) so vki is 0. On the other hand, as anticipated for other mechanisms and understood during the site inspection, the tie- rods improve the structural behaviour of the chapels limiting the thrust coming from the arches; then, vkp is 1; - Mechanism 25: interactions for discontinuous volumes both in elevation and plan (displacements where the interaction takes place, cracks for pounding). The indexes of vulnerability proposed by the guidelines are not present but an evident interaction of different 125

volumes (sacristy - lateral chapel - church) on the West side is present. The volumes are characterized by different heights and compenetrates one respect to the other generating discontinuities in the masonry components and possible additional external forces playing on the structural elements. This possible problem is not faced by any clear additional component. So, if vkp is 0, the value of vki is 1; - Mechanism 27: belltower (cracks nearby the connection with the church volume, shear cracks or vertical ones). No significative openings are present at the different levels of the belltower in Casolate but, thanks to the site inspection and the diagnostic approach important pieces of information are obtained for the belltower. First of all, it is evident a hole and a huge crack on the wall of the belltower connected to the church area; the discontinuity then of the load-bearing pier is evident as well as a not proper constraint at the base. Two elements are so highlighting possible problems of vulnerability with a consequent vki of 2. The diagnostic approach through thermography gave the possibility to define the masonry pattern of the belltower pointing out a uniform distribution of the bricks and mortar for the entire height of the volume. This has a positive impact on the structural behaviour giving continuity to the load-bearing components therefore vkp is 1. During the data listing, the process of knowledge (considering historical analysis that points out possible weak aspects and diagnostic approach and site inspection that gives information about actual conditions of the fabrique) turned out as a necessary and useful step.

This said, the seismic vulnerability index iv is equal to 0.56 for the considered church highlighting a condition of medium vulnerability.

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7.4.2. Linear kinematic analysis of the tympanum

The verifications proposed by NTC 2018 for the structural assessment of existing buildings are two: global verification (for the global behaviour of the building) and local verification (addressed to limited parts of the structure and macro-elements). Considering a limit state approach, it is possible to model the different parts of the structure using rigid masonry components that, due to the action of external horizontal forces such as the seismic ones, are able to generate a kinematic chain. The generation of the kinematic chain and the consequent mechanisms happens when a limit value of the acting force is reached; this value is the one to be defined with the checks. The limit state analysis can be linear or non-linear. In the case of a non-linear analysis, the goal is the description of the kinematic chain after the activation of the mechanism. The linear analysis, the one used for the tympanum of Saint Peter church in Casolate, has the aim to define the conditions that leads to a specific mechanism: so, this approach is intended to define the seismic action able to modify the equilibrium of a component up to its failure. The linear kinematic analysis defines a stress level that is coincident with the resistance of the component analysed. The resistance, function of material’s properties, must be compared with the response spectrum for the considered site assuming a nominal life VN and return period TR for the seismic action. In the end, the resistance of the material can be referred to as “capacity” while the seismic action to the site as “demand”. Both capacity and demand are expressed in terms of accelerations. The verification is satisfied (so the mechanism is not activated for the considered element) when: 퐶퐴푃퐴퐶퐼푇푌 ≥ 퐷퐸푀퐴푁퐷 According to NTC 2018, the activation of a mechanism is not necessarily coincident with the collapse of the structural element considered. So, the demand is divided by a q-factor, equal to 2, that considers the mechanism resistance to collapse: 퐷푒푚푎푛푑 푐푎푙푐푢푙푎푡푒푑 푤푖푡ℎ 푡ℎ푒 푟푒푠푝표푛푠푒 푠푝푒푐푡푟푢푚 퐷퐸푀퐴푁퐷 = 푞 (= 2) The kinematic linear analysis is developed in steps: - Definition and modelling of the mechanisms. In this step, the involved forces must be defined too (dead loads of the components, vertical loads coming from slabs, vaults and similar) as well as the position of the hinges for the mechanism and the position of the forces respect to the hinges line. At this stage, it is important to define also the external acting forces (seismic action, non-inertial thrusts and reactions due to constraints); - Definition of the horizontal forces multiplier α0. This value is the one by which the seismic forces are multiplied. The multiplier α0 can be assessed with two methods: either equilibrium method or virtual works principle. For the present case, the equilibrium method is chosen and defined in detail. The equilibrium method is based on the equilibrium between two bending moments:

푀 = 푀

Where MS is the overtopping moment while MR is the resisting bending moment. In detail: 127

훼푀 + 푀 = 푀 + 푀 + 푀

MS is the bending moment due to seismic action, Mext is the bending moment of external actions not considering seismic ones, MRC is the resisting bending moment depending on the cohesive forces, MRA is the resisting bending moment due to friction forces and MRF is the bending moment depending on the mechanism shape;

- Definition of the activation acceleration a0*. Once α0 is defined, it is possible to convert it into an acceleration a0* through the formulas given by “Circolare 21 gennaio 2019 n.7”: 훼 푔 푎∗ = 푒∗ 퐹퐶 Where g is the gravity acceleration (9.81 m/s2), FC is the confidence factor (defined in Chapter 7.1.) and e* is the fraction of participating mass to the mechanism. The lower is the e*-value, the lower will be the activation acceleration and so a stronger earthquake is needed to activate the mechanism. This fraction is calculated as: ∗ ∗ 푔푀 푒 = ∑ 푃

If Pi represents the gravitational forces applied, M* is the participating mass to the mechanism. The M* value is coincident with the total mass of the system only if it is considered to be applied in a single point; - Verification. The verification can be proposed for an element at ground level or for one that is located at certain height (case of the tympanum of Casolate). For the ground level component, it must be verified that: 푎 (푃)푆 푎∗ ≥ 푞 While for a component at a certain height from the ground: 푆 (푇1)Ψ(Z)γ 푎∗ ≥ 푞

Considering: Se(T1) the acceleration read in the response spectrum for the fundamental period of the structure considered, Ψ(Z) is the normalized first modal shape at a certain height Z and can be defined with a simplified assessment as with H the total height of the building from the foundation level, γ is the modal participation factor calculated as 3N(2N+1) with N number of storeys. The scheme proposed in Figure 107 will introduce the geometry of the tympanum, hinges line location, reference system location and points for forces application.

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Figure 107: scheme of the tympanum volume for church in Casolate; [Author]. The useful pieces of information are summarized in Table 19.

Table 19: summary of the main parameters known for the tympanum volume and useful for the mechanism’s analysis; [Author].

Parameter Valeue/Description Tympanum dimension in x 10 m Tympanum dimension in y 0.90 m Tympanum dimension in z 2.45 m Tympanum volume 13.40 m3 Masonry unitary weight (Chapter 7.1) 15254.20 N/m3 G Centre of gravity XG 5.30 m YG 0.45 m ZG 0.82 m (1/3 of the height) O Origin of the reference system FC (Chapter 7.1.) 1.18

The possibility to have an out-of-plane action in the tympanum can be compared with the possibility to have an overturning in the top part of a masonry wall. For the top part of a masonry wall and consequently for the tympanum case, the bending moments involved in the equilibrium are:

푆 푀 = 푊 + 퐹 푑 + 푃 푑 + 푇 ℎ 2

푀 = 훼 푊푍 + 퐹ℎ + 푃ℎ + 퐹ℎ + 푃ℎ

So, the force multiplier α0 is: 푆 ∑ ∑ ∑ ∑ ∑ 푊 2 + 퐹푑 + 푃푑 + 푇ℎ − 퐹ℎ − 푃ℎ 훼 = ∑ 푊푍 + ∑ 퐹ℎ + ∑ 푃ℎ Where:

- Wi is the own gravitational force of the i-component in the kinematic chain; - Si is the thickness of the i-component of the kinematic chain;

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- ZGi is coordinate of the gravity centre G respect to the hinges’ line; - FVi is vertical component of the i-force acting on the tympanum and equal to 0 for the considered case; - Fhi is horizontal component of the i-force acting on the tympanum and equal to 0 for the considered case; - dVi is the distance of the vertical i-force FVi respect to the hinges’ line; - hVi is the height at which the generic force Fi is applied; - PSi is the own gravitational force of the slab and equal to 0 for the considered case; - Ph is generic horizontal thrusts and equal to 0 for the considered case; - di is the distance between PSi and the hinges’ line; - Ti is the i-force generated by a tie-rod and equal to 0 for the considered case; - hi is the height at which Ti or PSi are applied respect to the hinges’ line.

So, the load multiplier α0 comes from the formula: 푆 ∑ 푊 2 훼 = ∑ 푊푍

Remembering that Wi for the tympanum is 204469,74 N, Si is 0.90 m and ZGi is 0.82m:

훼 = 0.55 Then, considering that the mass of the system is totally applied in a single point coincident with the centre of gravity G, the value of M* is coincident with the total mass of the tympanum. Consequently, ∗ ∗ e*(푒 = ) is equal to 1. ∑ Then: 훼 푔 0.55 ∗ 9.81 푚 푎∗ = = = 4.57 = 0.457 푔 푒∗ 퐹퐶 1 ∗1.18 푠

Due to the location of the tympanum (not at ground level), the verification must be performed considering the demand of the structure as:

푆 (푇 )Ψ(Z)γ 푞

- The fundamental period T1 for the structure is defined with the simplified formula suggested 0.75 by the codes: T1 = 0.05 * H considering H the height of the fabrique. For Casolate’s church the height H is 20.10 m from the ground level to the top part of the roof. So, T1 is 0.474 sec and the associated acceleration Se(T1) is 0.252g using the response spectrum for Casolate as calculated in Chapter 7.1; - Ψ(Z), normalized first modal shape at a certain height Z, is calculated as . Z is the height of the gravity centre of the hinges’ line respect to the foundation level while H is the total height of the building. In the case of the tympanum, Z is 17.70m while H is 20.10 m. So, Ψ(Z) is 0.88; - γ is the modal participation factor calculated as 3N(2N+1) with N equal to 1 for Saint Peter church. So, γ is 1; - q is a parameter to evaluate the mechanism resistance to collapse and is equal to 2. 130

In the end: 0.252 ∗ 0.88 ∗ 1 퐷퐸푀퐴푁퐷 = = 0.110 푔 2 The verification for the mechanism activation is proposed:

∗ 푎 ≡ 0.457 푔 > 0.110 푔 ≡ 퐷퐸푀퐴푁퐷 So, the mechanism will not be activated for the conditions considered and using a response spectrum with a return period TR of 475 years.

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8. Conclusions

The research developed in this thesis aimed at verifying the possibility to characterize the structural conditions and behaviour of the cultural heritage masonry assets recurring to a limited amount of diagnostic tests, a thorough historical analysis and well-focused simplified numerical approaches. The purpose of such assessment would be to define the main characteristics of the conditions of the asset, pointing out possible needs and critical issues and becoming a base for consideration of future maintenance or strengthening interventions. “Direttiva P.C.M 9 febbraio 2011 – “Linee Guida per la valutazione e riduzione del rischio sismico del patrimonio culturale con riferimento alle Norme Tecniche per le Costruzioni di cui al D.M. 14- 01-2008” are suitably formulated to consider the special needs of cultural heritage components. The procedure is based on a knowledge acquisition-path (percorso di conoscenza), that brings to collect all the necessary information for a correct analysis of the seismic response, on the subsequent evaluation of seismic safety and, if the case, the design of heritage-compatible interventions for the improvement of the safety level (this last step was not considered for the study case due to the first level, informative approach chosen). The specific case studied here is the church of Saint Peter in Casolate (LO). Following the path proposed, the building has been described in terms of historical evolution, present state and associated decay, materials used and construction technique as well as materials’ properties, definition of the macro-elements and their structural relationship. In the end, the seismic action for the site and consequent structural behaviour of the components is analysed. In order to acquire knowledge of the construction technique and the material properties, a diagnostic approach has been used coupled with a historical analysis. The thermographic approach on-site gives the possibility to highlight the use of bricks and mortar for all the structural components (walls, arches and vaults) as well as a uniform orientation of the bricks. The problem of high humidity levels inside the church was evident through the historical approach and on-site inspections. So, the humidity content has been studied through a superficial method using Moisture Encounter Plus and through the gravimetric approach suggested by UNI 11085. The area investigated has been that of the belltower due to limitations imposed by the prestigious finishing in the church area; the investigation was carried out in September, after the Summer period characterized by limited rain. If the superficial tests highlighted a high level of humidity, the gravimetric method gave back information of more or less dry components (R.H. < 1%). So, the possibility of superficial moisture problem without escape route from the indoor environment was considered. As a result, the humidity problem does not seem to affect negatively the structure of the fabrique. The problem of humidity, present also in the church area and causing decay of certain components (e.g. the plaster at the basis of the structural components such as walls and built-in pillars), can be related also to the presence of hygroscopic salts due to the near rice paddies of the Po valley. So, further analysis would be advisable to define salts’ content. A simplified global structural analysis has been performed for the entire fabrique through a first levele, LV1, approach. This analysis gives the possibility to evaluate the structural seismic safety index ISLV and the acceleration factor fa,SLV and, on this basis, to position the specific asset in a vulnerability ranking (graduatoria di vulnerabilità) for the cultural heritage buildings of a specific 132 area. This approach gives the opportunity to assess with simple approximation the structural safety for a specific seismic action. The church turned out to be vulnerable in both the two directions (longitudinal, that is along the nave, and transversal) with a higher criticality in the transversal direction where a limited amount of resisting structural masonry components are present. The transversal direction (E-W) turned out to be the weakest one. Subsequently, the collapse mechanisms typical of churches have been studied with reference to “Allegato C” of Direttiva P.C.M 9 febbraio 2011. The 28 possible collapse mechanisms are evaluated for the church considered defining vulnerable components and anti-seismic collaborating elements. In the end, a seismic vulnerability index iv has resulted (equal to 0.56, a medium vulnerability value); such value could be compared with the results obtained for similar structures of the area. The value of iv ranges between 0 and 1; so, for the church studied, the vulnerability condition is evident. In the end, it can be concluded that the procedure proposed shows that the analysis of the seismic vulnerability of an historical building part of the cultural heritage is deeply linked to the: - Historical analysis of the fabrique evolution. This information influences the definition of the material properties and construction technique used, the definition of the geometrical parameters, as well as the relation of the different macro-elements, the definition of the vulnerable elements and damage state, the definition of the possible collapse mechanisms of the main structural components; - Diagnostic approach, from which the hypotheses obtained during the historical analysis maybe confirmed, giving also additional information about the present state of the structure; - Use of different level of details in the structural and vulnerability analysis. The simplified global method of LV1 gives first useful information on the structural safety of the fabrique. The collapse mechanisms analysis highlights local vulnerability with a higher level of detail with the LV2 calculation on the most evident problems. Further analysis and steps would involve a more detailed structural analysis according to level LV3 for instance through finite element models and an accurate material modelling. In fact: - modal analysis can highlight the possible development of collapse mechanisms that are not evident; - elastic linear analysis can help in the definition of the possible causes of crack patterns; - non-linear analysis can analyse in detail the most vulnerable areas confirming the hypotheses proposed during the whole process. This level of analysis, however, needs to be performed, only after that a first approach has pointed out critical structural conditions and a plan for interventions has to be defined.

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Acknowledgements

La fine di questo percorso sembra essere finalmente arrivata e, nonostante le cose non siano andate sempre come speravo, sono comunque contenta e felice di aver raggiunto questo nuovo piccolo traguardo che mi ha fornito, non solo nuove conoscenze, ma anche degli importanti insegnamenti di vita. Tutto ciò non sarebbe sicuramente stato possibile senza l’aiuto delle persone che hanno condiviso con me questo percorso e alle quali porgo i miei più sinceri ringraziamenti. Un doveroso ringraziamento è dovuto alle tre persone che pazientemente mi hanno aiutato a portare a termine questo elaborato. Volevo ringraziare la Professoressa Parisi per aver messo a mia disposizione e senza limiti non solo la sua esperienza e le sue conoscenze, ma anche il suo tempo in questo difficile momento storico che tutti ci troviamo ad affrontare. Volevo ringraziare il Professore Cantini per aver condiviso con me un ulteriore parte delle sue conoscenze ed esperienze e per aver avuto sempre la pazienza di chiarire ogni mio dubbio. All’Ingegnere Locatelli non posso che dire grazie per aver avuto la volontà e la costanza di dedicarmi nelle diverse fasi di elaborazione dello studio parte del suo tempo e della sua esperienza. Ci tengo a ringraziare anche il Laboratorio Prove Materiali del Politecnico di Milano che si è reso disponibile ad aiutarmi nello sviluppo della parte diagnostica. Tra tutti, un ringraziamento in particolare va all’Architetto Tiraboschi che ha condiviso con me le sue conoscenze ed esperienza sul campo nell’approccio diagnostico; osservarla in azione è stato un momento importante per la mia crescita professionale. Tutto ciò non sarebbe sicuramente stato possibile se il Parroco Don Gianfranco Rossi non si fosse reso disponibile ad aprirmi le porte della sua Parrocchia, condividendo con me le informazioni a sua disposizione e dettagli che in altro modo non sarei riuscita ad ottenere. Il suo aiuto è stato senz’altro prezioso. Infine, ringrazio la mia famiglia e i miei amici che non mi hanno lasciato da sola nemmeno per un secondo credendo nel mio sogno anche quando a volte io non ne avevo più la forza.

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Attached documents (technical drawings)

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