A multidisciplinary approach for the structural assessment of historical constructions with tie-rods

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ULTIDISCIPLINARY

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Doctoral Dissertation of:

Mira Vasić

Supervisor:

Prof. Carlo Poggi

Prof. Dario Coronelli

The Chair of the Doctoral Program:

Prof. Roberto Paolucci

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Acknowledgments

The research work reported in this thesis has been possible thanks to the scholarship provided by the Politecnico di Milano, which is gratefully acknowledged by the author. The PhD school from the same University is acknowledged for providing the additional scholarship during the stage abroad.

I would like to express my biggest gratitude to my tutor and the thesis supervisor, Prof. Carlo Poggi for his continuous support and guidance during my PhD studies, so as for thrusting me to work on such a unique and a challenging topic.

I would like to give many thanks to Prof. Dario Coronelli for co-supervising my thesis in a dedicated way, for giving me an example to follow and encouraging during this “marathon”. I found our collaboration scientifically valuable and enjoyable experience and I will always remember our enthusiastic scientific discussions from which I learned a lot.

The present research is supported by the Fabbrica Veneranda del Duomo to which the author is grateful for the provided material, in particular Ing. Benigno Mörlin Visconti Castiglione, Geom. Francesco Aquilano, the technical and the archives team of the Fabbrica for information provided on Cathedral’s geometry and history.

I gratefully acknowledge Prof. Pere Roca for hosting me at the Universidad Politecnica di Cataluña and supervising my work during the 3 months research stay. It was a pleasure to collaborate with his research group in such enjoyable atmosphere. Also, I appreciated very much the collaboration and advices of Prof. Luca Pelà who co-supervised my work in Barcelona and contributed with his ideas and positive character. I would like to acknowledge the International Centre for Numerical Methods in Engineering (CIMNE, Barcelona) for providing me software GiD and COMET, which successfully contributed to my work. I would like to acknowledge Tech. Marco Cucchi and Arch. Claudia Tiraboschi for executing the on-site and laboratory testing in such dedicated and passionate way. Also I acknowledge Dr. Andrea Bonavita and Arch. Giulia Carozzi for making the historical research during the present work, which was of high relevance for the topic. Many thanks to master students Ilina Georgieva Stefanova, Antonello Ruccolo and Mariagrazia Bellanova who contributed to the present work during their thesis work.

I would like to thank to Prof. Carmelo Gentile and Ing. Marco Guidobaldi for their collaboration during the dynamic investigation of the tie-rods, so as for sharing their expertise on this topic with me.

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I am very grateful to Prof. Roberto Felicetti for believing in me and giving me the chance to assist in teaching his course during my PhD studies which was always a pleasant experience.

Sharing the PhD room and ideas with Savvas and spending time with him and Thasos in Barcelona made my stay in Spain even more pleasant and I will always remember it.

Special thanks goes to my office colleagues in the past three years - Juan, Giulia and Elisa for sharing the glory and the dust of our every-day PhD life, to Juan especially for his precious career advices and to the girls for their endless patient during the final phase of the thesis. I would like to thanks to Valter and to Giovanni for their positive character and pleasant talks in the past period.

I am very happy that I had the opportunity to meet and enjoy time with such intelligent, funny and positive character people during my stay at Poli as my Phd colleagues Ana, Bruno, Francesco F., Iva, Juan Antonio, Manuel, Marco, Milot, Srdjan, Valentina and Visar. I will always remember with a smile on my face our time in Milan.

Very special thanks go to my friends in Serbia – Damir, Ivan, Jelena and Vlada, so as to my sister Maria for not letting me go and keep on being precious support even from far away. My heartfelt thanks go to Mina, for being such a supporting friend, like a sister, sharing all the laugh and tears in the past three years.

I am very grateful to my family – my father, mother and brother for their unconditioned support, love and forgiveness for all the years that I am away. Thank you from the heart.

Finally, my wholehearted thanks go to my beloved Angelo who always makes me happy more than anything else. I am proud to have him by my side, giving me unique support and love every day in his ingenious, kind and funny way. This thesis I dedicate to him, who inspired me to start and motivated to reach the end of this journey.

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bstract

The present research studies the structural behaviour of historical constructions with tie-rods. Preservation and maintenance of buildings with heritage value include ensuring their sufficient bearing capacity against different loads. This is a challenging task when dealing with historical masonry structures that are characterized with a complex hyperstatic structural system. While currently there are extensive studies on masonry historical structures having no tie-rods as a permanent part of their structure, there is a limited number of studies on Gothic cathedrals with tie-rods where lateral thrusts are resisted by a combined action between tie-rods, spandrels and buttresses. Their analysis is therefore not straightforward because it is difficult to estimate what portion of the thrust is resisted by each of these elements. The thesis proposes how different approaches can be combined towards understanding the structural behaviour of masonry constructions with tie-rods. It also develops a methodology for estimating current state of the stress in such historical structures. In particular, a continuous process of data acquisition, analysis of structural behaviour, diagnosis and safety evaluation was employed for the case study of Milan’s cathedral (Duomo di Milano). This remarkable monument was chosen in the present research due to its multifaceted structural history, imposing dimensions and some structural issues observed at the present. The ancient builders used the tie-rods during the construction. Original tie-rods are still present in both longitudinal and transversal direction of the Duomo di Milano, which makes understanding its structural system challenging. Different techniques and fields of expertise were used for the data acquisition: historical investigation gave important information on the tie-rods origin, their structural purpose and the construction process of the Cathedral; the wide experimental campaign included visual inspection, material characterization, and dynamic tests on the original ties and contributed to the understanding of the structural system. Relevant aspects for the study of the Cathedral’s structural behaviour were addressed and various approaches were used, such as the limit analysis and Finite Element Modelling (FEM). The dynamic testing campaign confirmed that the tie-rods in the Duomo di Milano are active members, carrying part of the lateral thrust, as suggested by the historical research and structural analysis in the present work. Moreover, the axial tensile force was estimated for the largest portion of tie-rods in the Cathedral and was combined with graphic static analysis employing limit analysis for a representative

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bay of the Cathedral. Graphic static analysis gave one of the possible equilibrium solutions for the structure of the Duomo di Milano. Another solution was found using sophisticate FEM model, which took into account damage in masonry and simulated different construction stages of the Cathedral. Including structural history in the numerical analysis showed to be one of the essential aspects for understanding tie-rod’s behaviour in the past and present, so as for producing reliable results. In case of a cathedral with active tie-rods, as the Duomo di Milano, disregarding construction stages could underestimate current stress in the tie-rods for about 50%. The method for combining different approaches used in the present work resulted in understanding the structural system of a cathedral with tie-rods, but developed concepts can be applied to similar hyperstatic structures.

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ommario

La presente ricerca studia il comportamento strutturale delle costruzioni storiche con catene. La conservazione e manutenzione degli edifici con importanza storica includono la necessità di garantire una sufficiente capacità portante nei confronti di differenti azioni. Questo è un compito impegnativo quando si tratta di strutture murarie storiche che sono caratterizzati da un complesso sistema strutturale iperstatico. Anche se attualmente esistono studi approfonditi sulle strutture storiche in muratura che non presentano catene come parte permanente della loro struttura, vi è un numero limitato di studi su cattedrali gotiche con catene. In elli alle spinte laterali si oppone un’azione combinata tra questi elementi, pennacchi e contrafforti. La loro analisi non è quindi semplice perché è difficile stimare quale parte della spinta è contrastata da ciascuno di questi elementi. La tesi si propone di investigare come diversi approcci possono essere combinati verso la comprensione del comportamento strutturale delle costruzioni in muratura con catene. Si sviluppa, inoltre, un metodo per la stima dell’attuale stato tensionale presente in tali strutture storiche. In particolare, per il caso studio del Duomo di Milano (Duomo di Milano) è stato impiegato un continuo processo di acquisizione dei dati, l'analisi del comportamento strutturale, la diagnosi e la valutazione della sicurezza. Questo importante monumento è stato scelto nell’ambito della presente ricerca per la sua storia strutturale multiforme, per le sue dimensioni imponenti e per alcuni problemi strutturali osservati allo stato attuale. Inoltre, per la sua costruzione sono state utilizate catene, che sono ancora presenti in entrambe le direzioni (longitudinale e trasversale) del Duomo. Tecniche e campi di esperienza diversi sono stati utilizzati per l'acquisizione dei dati: l’indagine storica ha fornito importanti informazioni sull'origine delle catene, sul loro ruolo strutturale e sul processo di costruzione della Cattedrale; l'ampia campagna sperimentale ha compreso l'ispezione visiva, la caratterizzazione dei materiali e prove dinamiche sui legami originali e ha contribuito alla comprensione del sistema strutturale. In particolare, sono stati affrontati aspetti rilevanti per lo studio del comportamento strutturale del Duomo, impiegando vari approcci, come l'analisi limite ed il Metodo degli Elementi Finite (FEM). La campagna di prove dinamiche ha confermato che i tiranti nel Duomo di Milano sono elementi attivi, portando parte della spinta laterale, come suggerito dalla ricerca storica e dall’analisi strutturale nel presente lavoro. Inoltre, è stata stimata la forza di trazione assiale in catene della Cattedrale ed i risultati sono stati combinati con l'analisi statica grafica utilizzando l’analisi limite su una sezione rappresentativa della Cattedrale che ha dato una delle possibili soluzioni di equilibrio per la struttura del Duomo di

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Milano. Un'altra soluzione è stata trovata con un sofisticato modello FEM che ha preso in considerazione il danno nella muratura, attraverso il quale sono state simulate diverse fasi costruttive della Cattedrale. La considerazione della storia strutturale nell'analisi numerica ha mostrato di essere uno degli aspetti essenziali per la comprensione del comportamento delle catene in passato e nel presente, così come per la produzione di risultati affidabili. Nel caso di una cattedrale con tiranti attivi, come il Duomo di Milano, trascurare le fasi costruttive porta ad una sottostima del reale stato tensionale nei tiranti per circa di 50%. Il metodo per combinare diversi approcci utilizzato nel presente lavoro ha portato nella comprensione del sistema strutturale di una cattedrale con tiranti, ed ha permesso di sviluppare i concetti che possono essere applicati a strutture iperstatiche simili.

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ontent

Abstract

Sommario

1. Introduction

1.1 The Global Framework……….………...3

1.2 Historical Constructions with Tie-rods……….………...5

1.3 Research Scope and Aims………..……….………...9

1.4 Outline of the Thesis……….………...11

2. Symbiosis of Engineering Approach, Human Sciences and Art

2.2. Research Methodology……….……….………...19

2.3. Structural Assessment of the Duomo di Milano……….…………..…...21

3. Investigation and Survey of the Duomo di Milano

3.1.1. The structural history…….…….……...………….………...25

3.1.2. Important events….…….……….……….……….………...38

3.1.3. Previous structural intervention works….…….………….…….……...39

3.2. Monitoring Data….………..………….………...47

3.3. Survey….…….……….…….………...49

3.3.1. Geometry….………..………….………...49

3.3.2. Damage….……….………….………...58

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4.1. Tie-rods in Masonry Cathedrals………...69

4.1.1. Review of methods for the identification of axial load in tie-rods……...72

4.1.2. Calibration of the chosen method….………...82

4.1.3. Historic iron tie-rod: laboratory testing………...87

4.2. The On-site Experimental Campaign………...99

4.2.1. The test set-up………..………...99

4.2.2. Results of the campaign………...101

4.2.3. Frequency splitting phenomena………...105

4.2.4. Stress in the iron tie-rods………..………...109

4.3. Dynamic Testing as a Monitoring Tool………...117

4.4. Discussion……….………...121

5. The Structural Role of Tie-rods in the Duomo di Milano

5.2. Equilibrium Limit Analysis………...………...127

5.2.1. An overview of the theory development………..……...127

5.2.2. Leading hypothesis for the present analysis……….…...129

5.2.3. Main nave……….………...132

5.2.4. Lateral naves………..………....142

5.2.5. Graphic static analysis………..………...146

5.3. Finite Element Model (FEM) of the Cathedral’s Representative Bay………..……...149

5.3.1. The review of available models………...149

5.3.2. Adopted numerical modelling strategy………...151

5.3.3. Simulation of the construction process………...155

5.3.4. Presence of the temporary bell tower………...………...163

5.3.5. Soil settlement………..………...164

5.3.6. Removal of the tie-rod………..………...167

5.3.7. The push-over analysis……….………...169

IX 6.1. Method Proposed in the Thesis……….………...175 6.2. Results and Discussion………..………...177 6.3. Future developments……….………...185

Appendix A2

Appendix A3

Appendix A4

Appendix A5

Bibliography

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ntroduction

“Research is to see what everybody else has seen, and to think what nobody else has thought.”

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1.1 The Global Framework

Receiving, maintaining and leaving in legacy cultural heritage inherited from the past generations is a permanent task of the humankind, beneficial also for the future generations. Tangible cultural heritage includes historical areas, buildings, monuments and artefacts significant to the various scientific disciplines – archaeology, architecture, history, engineering and natural sciences. High interest in their preservation and maintenance shows human race awareness of their importance as witnesses of the human history and a basis for the future ideas and developments. Cultural heritage may also have a leading role in the improvement of education, access to information, social revitalization, economic development, and often as a city or national landmark (Figure 1.1).

From the structural restoration point of view, the main aim when dealing with historical constructions is to “ensure” its sufficient bearing capacity against the actions, including natural disasters, without changing its eventual heritage value. The first issue is determining what is a sufficient bearing capacity for a historical structure and according to which criteria it should be determined. Moreover, we are never able to predict accidental loading, such as future earthquakes, tsunamis, explosions or terroristic attacks. Finally, the most relevant from the conservation point of view is the part of non-impacting its heritage value, preserving unique architectonic and artistic character and keeping the intervention to its minimum. The adequate intervention should anyway address the causes of the problem and not its appearance and in this way ensure a compatible and durable solution. In order to explain the roots of the present damage or predict the future behaviour under a certain load conditions, the structural system of a building should be understood so as its current stage. This is typically done employing different qualitative and quantitative approaches, using as much as possible accurate geometry, material properties and constructive features, taking into account the construction history of the building, previous interventions, local failures and damage.

Opposite to the design of a new structure, where the engineer is defining the structural system himself, the structural system of a historical construction needs to be understood on the basis of its existence, past and the present performance. In many cases, the geometry, the morphology and structural features of historical buildings can be very complex or even unknown due to the lack of documentation or evidence. Evolution of the structural history, actions and damage during the time is also important parameter when it comes to historical structures and it has to be taken into account (Roca 2001), but this can be particularly challenging task. With the development of the theory of structures, constant efforts are made by the scientific community to develop the adequate theories for structural calculations of masonry

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cathedrals, but with the more common use of modern materials, such as steel and concrete due to an increased demand for the high-speed massive construction in the last two centuries, knowledge on the masonry structures has been partially lost.

Structural engineers and architects currently do not possess the adequate knowledge on the design of historical buildings, their performance and the methods for their assessment, so using a multidisciplinary approach has been recognized by several international documents (ICOMOS 2005, ISO 2010-annex H) as an effective tool. It enables to build an in-depth knowledge on the structural past and the present, with a final aim – predicting the future of the building under the certain circumstances. In this way, combining different fields of expertise and scientific disciplines, one could obtain reliable and relevant results. However, todays practice is still related to the individual work of experts and partial analysis, not combining different aspects that play role in the structural performance. Such practice may lead to poor and non-lasting interventions or interventions dealing with the appearance of the problem and not its causes.

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1.2 Historical Constructions with Tie-rods

In vaulted historical structures, particularly in masonry cathedrals, metallic or wooden ties were extensively used during the construction (Fitchen, 1961) or later on during interventions, such as seismic improvement. Understanding their structural behaviour and finding possible states of equilibrium which by the Safe Theorem (Heyman, 1995) would mean that the structure is safe and stable; is not a straightforward process. When the lateral thrust coming from the vaults and arches is balanced by a combined action of tie-rods, spandrels, buttresses and flying buttresses (if any), the amount of the thrust resisted by each of these elements is difficult to determine. Considering the life time of these structures, lasting several centuries, the issue of the durability of these structural elements is also a relevant issue. While currently there are extensive studies on structural behavior of masonry historical structures having no tie-rods as a permanent part of their structure (Alessandri and Mallardo 2012, Bacigalupo et al. 2013, Block and Lachauer 2014, Roca et al. 2014, Romera et al. 2008), there is a limited number of structural analysis studies on masonry cathedrals with tie-rods (Angelini et al. 2014).

The Cathedral of Milan (in further text “the Duomo di Milano”) is one of the most remarkable monuments designed partly in a Gothic style and constructed between 1396 and 1805. Its structural system is unique when compared to the other masonry cathedrals due to the use of tension wrought iron tie-rods under the arches in the whole building and the presence of a double vault system composed of barrel and cross vaults in all five naves of the Cathedral (Figure 1.2a). The preliminary analysis by Coronelli et al. (2014a) suggested that the tie-rods are active in resisting the lateral thrust from the vaults and arches, later confirmed by the preliminary dynamic test investigation done by the author of the present thesis (Vasic et al. 2015). These features make the structural system of the Duomo di Milano (Figure 1.2a) rather complex, with iron ties under and spandrels above the transversal arches which in combined action take the lateral thrust from the vaults.

One relevant question that the present thesis poses to the structural analysis is what portion of the lateral thrust from the vaults and arches (H’ in Figure 1.2a) is resisted by the ties (T in Figure 1.2a) and what by the spandrel and buttresses (B’ in Figure 1.2a). In the analogue way, the relevant question for the structural analysis of a cathedral with no tie-rods as a permanent part of the structure (e.g. Palma de Mallorca in Figure 1.2b) is what portion of the lateral thrust (H’’ in Figure 1.2b) is resisted by the flying arches and what by the buttresses (B’’ in Figure 1.2b). However, such masonry structures are hyperstatic (statically indeterminate) and can carry the load in many different ways. Other relevant information (e.g.

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the present deformation of the structure, monitoring of the deformation during the time, etc.) should be used to estimate the actual state of the stress in each element (Heyman 1995).

Research group from the Mechanical Department at Politecnico di Milano is in charge of the monitoring system in the Duomo di Milano for the control of deformations that each 6 months measures the variation of piers’ verticality and the floor level settlement inside and outside of the building for the last 50 years (Giussani A. 2011). These periodic measurements in May 2009 recorded an annual variation of the verticality of the pier 88 in the transversal direction of the Cathedral towards the outwards, which does not correspond to the previous year’s trend (e~1.12 mm, Figure 1.3). Subsequent examinations of the affected area by engineers from the institution in charge of the Cathedral (Veneranda Fabbrica del Duomo) have highlighted the failure of the tie-rod connecting the piers 58 and 88 (Figure 1.4a). This element was replaced with a new steel tie-rod (Figure 1.4b) during a structural intervention carried out in 2011 by the engineering team of Veneranda Fabbrica del Duomo. Consequently, the present thesis should understand why such a failure occurred and what the consequences to the rest of the structure were. The present state of all other tie-rods will be examined during the present thesis work by the author within the maintenance strategy. Taking into account the failure of the tie-rod discovered in 2011, fact that tie-rods are hand-made elements and that some of them are more than 600 years old, and that tie-rods are active in resisting the lateral thrust (as indicated by preliminary investigations, Coronelli et al. 2014a, Vasic et al. 2015), the health state of ties is of utmost interest for the structural stability of the building. Finally, this remarkable monument was chosen as a case study in the present thesis due to its multifaceted structural history, imposing dimensions and mentioned structural issues observed recently.

Figure 1.2 – Duomo di Milano (a) and Palma de Mallorca (b).

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Figure 1.3 – Periodic measurements - variation of the verticality of the pier 88, e~1.12 mm recorded in May 2009 (Giussani A. 2011).

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1.3 Research Scope and Aims

Previously described global framework showed that there is a permanent necessity for preserving the built heritage which in case of complex masonry structures can be a challenging task. Since the safety and the stability are one of the main concerns when dealing with such structures, the scope of the present thesis is the structural assessment of historical constructions. Main motivations for the present research are:

 Scientific community, practitioners and owners need better understanding of tie-rod’s structural

role in historical structures in order to improve current assessment practice and to fulfil the safety requirements.

 They also need better procedures to investigate the current state of these elements, damage or

alterations with regard to the development of mitigation and maintenance strategies.

Within the scope of the present research and taking into account the outlined motivation, this thesis aims: To understand the structural behaviour of cathedrals with tie-rods, to establish a procedure for tie-rods investigation which also estimates the current state of the stress in the tie-rods and to explain eventually observed damage in these elements.

To fulfil these aims, the thesis will propose how different experimental, numerical and analytical approaches can be combined. In particular, the author will employ a continuous process of data acquisition, analysis of structural behaviour, diagnosis and safety evaluation for the case study of the Duomo di Milano. On the bases of this case study, the thesis will present an overall methodology developed for estimating the current state of the stress in cathedrals with tie-rods that can be applied to

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1.4 Outline of the Thesis

The present thesis is composed of 6 chapters*.

Chapter 1 introduces the general framework for the present research contributions, scope and aims of the thesis. It presents the main issues related to historical structures having tie-rods as a permanent part of the structure.

Chapter 2 reviews previous research and current practice on the structural assessment of historical structures. It gives the basis for using a multidisciplinary approach and examples of approaches employed by different research groups. It develops the strategy how the present research will be conducted and introduces way of combining different approaches proposed in the thesis.

Chapter 3 firstly gathers the necessary information on the Cathedral’s past and present state from the relevant literature and survey results made on-site during the present work. Secondly, the author of the thesis derives the 3D geometry of the building, makes assumptions on construction features, proposes a more refined constructive map of the Cathedral and studies the material properties and morphology of structural elements.

Chapter 4 experimentally investigates the dynamic behaviour of 112 tie-rods. The author of the thesis estimates the actual state of the stress and gives the insight on the present overall structural behaviour of the Cathedral. A non-standard behaviour was observed in dynamic response of several tie-rods, as described in the present chapter.

Chapter 5 investigates the structural role of the wrought iron tie-rods in the Cathedral during the past, present and future. This is done using several structural models of the Cathedral's five nave "representative bay" developed by the thesis author on the basis of limit analysis and the nonlinear Finite Element Method (FEM) modelling. The thesis in this way demonstrates the significance of taking into account different construction stages during the structural analysis. It highlights the relevance of staged analysis for the identification of observed damage causes and understanding its progress during the time. Chapter 6 describes a method of combining different approaches proposed in the present thesis towards the investigation and understanding the structural behaviour of cathedrals with tie-rods. It also summarizes the main results, conclusion and proposes future developments of the work.

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ymbiosis of Engineering Approach, Human

Sciences and Art

“Scientific method refers to the body of techniques for investigating phenomena, acquiring new knowledge, or correcting and integrating previous knowledge. It is based on gathering observable, empirical and measurable evidence subject to specific principles of reasoning. “

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2.1 Multidisciplinary Approach for Heritage Structures

In general, there are two main aims when making the structural assessment of a historical building: to understand possible causes for the observed damage, relevant deformations or failures and to predict the response of the structure in the future due to the current and/or new loading. Although sometimes only the second task needs to be accomplished, it is difficult to predict the future structural behaviour without validating the model for the past and current load by comparing the results of structural analysis with the one from the on-site investigation or monitoring. In overall, the structural assessment is an approximation of the real building during the past, present and future using mathematical models based on the acquired data. This approximation may have different levels, corresponding to different accuracy level and the time devoted to the analysis (Figure 2.1). Structural assessment of historical structures can be a long and demanding process, requiring a high level of accuracy and time devoted to the analysis; which the present

thesis introduces as the 5th level in addition to the four levels already given by the fib MC 2010 (2012).

At the present, it is recognized by the scientific community that in case of a heritage structure, the multidisciplinary approach using many expertise fields, such as the history of the art, architecture, civil, geotechnical, chemical and mechanical engineering, should be exploited. Combining such different fields of expertise and investigation techniques, brings to the research the best of each field and contributes to the final diagnosis and safety evaluation. On one hand, the design rules for the construction of heritage structures used by the ancient builders were based on the “trial-error” practice during the centuries of previous positive and negative experience, while on the other hand nowadays engineering practice is based on the modern structural theory. In the last two centuries, focus of the scientific community was on the expansive use of modern materials for which the theories and engineering practice continuously grown. The knowledge on the historical masonry structures was partially lost and modern structural theories for masonry were not developed with the same trend as for the steel and concrete. Also, large scale stone and brick masonry structures, which are demanding from the engineering point of view, are rarely built in the contemporary architecture.

In the last three decades, many efforts were made by the scientific community working in the field of historical masonry to recover the lost knowledge. Significant advances in the methods to obtain the in-depth knowledge on the geometry, structural features, material's properties and present damage were made by Binda et al. (1997) and Vintzileou (2008). Formulation of the limit analysis theory by Heyman (1995) enabled foreseeing of ultimate condition state and fast insight into the structural stability. On the other hand, work by Block and Lachauer (2014), Lourenço (1996), Milani et al. (2006) and Roca et al.

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(2013) together with the rapid development of software for the structural analysis, nowadays enables more accurate numerical modelling of heritage structures’ reality. However, some of the basic input data for this kind of analysis is still difficult to determine, such as the compressive strength or the fracture energy of the masonry. In case of structures with the artistic value, it is preferred to use the non-destructive (NDT) methods (flat-jack test, digital image correlation, infrared tomography, etc.) to determine the unknown parameters, but their results might be difficult to interpret (Roca 2001).

Despite the efforts made by the International Scientific Committee for the Analysis and Restoration of Structures of Architectural Heritage (ISCARSAH) and the scientific community to prepare the Recommendations for the Analysis, Conservation and Structural Restoration of Architectural Heritage (ICOMOS-ISCARSACH, 2005), arbitrary decisions are still made and may lead to unsuitable interventions causing the heavy damage and collapses in historical structures, as during the recent L’Aquila (2009) and Emilia Romagna (2012) earthquakes (Candigliota et al. 2012, Gattulli et al. 2013, Lucibello et al. 2013). For example, the tie-rods were removed from the Spanish Fortress in L'Aquila. Removal of tie-rods resulted in extensive damage and activation of collapse mechanisms during the seismic excitation in 2009 (Binda et al. 2011). Therefore, the scientific community, practitioners and owners need better understanding of the tie-rod’s structural role in a historical structure in order to improve current assessment practice and to fulfil the safety requirements.

In most cases, due to a limited access to a historical building or limited funding, no NDT or laboratory testing is made on material properties of examined structure (Table 2.1). Moreover, combining structural analysis with results of monitoring data or comparison between different structural analysis methods is not widespread practise at the moment and most of the case studies analysis does not even take into account the ICOMOS recommendations (Table 2.1).

Figure 2.1 – Accuracy on the estimate of the actual behavior as a function of time devoted to the analysis for: I. Preliminary design, II. Classical design, III. Existing structure, IV. Critical structure, V. Historical structure (adapted to current study, starting from the Figure 3.1-1 in fib MC 2010, 2012).

17 T ab le 2 .1 – Mu ltid is cip lin ar y ap p ro ac h in d if fer en t c ase stu d ies . a - Ales san d ri (2 0 1 2 ), Aless an d ri an d Ma llar d o ( 2 0 1 2 ), Aless an d ri et al. ( 2 0 1 2 ), Faella et al. ( 2 0 1 2 ), B ac ci et al. ( 2 0 1 2 ); b B ay rak tar et al. ( 2 0 1 0 ); c - B ac ig alu p o et al. ( 2 0 1 3 ), B re n cich et al. ( 2 0 1 4 ); d B etti et al. ( 2 0 1 0 ); e - B o siljk o v et al. ( 2 0 1 0 ); f - L u b o wiec k a et al. ( 2 0 1 1 ); g R o ca et al. ( 2 0 1 3 ); h -R o m er a et al. ( 2 0 0 8 a, 2 0 0 8 b ); i - Salo u str o s et al. 2 0 1 4 . H is to ri c a l a n a ly s e s G e o m e tr ic a l s u rv e y L a b o ra to ry te s ti n g D a m a g e m a p p in g M o n it o ri n g O n -s it e NDT S tr u c tu ra l a n a ly s is M a te ri a l p a ra m e te rs b a s e d o n o n -s it e t e s ts V a ri o u s m e th o d s o f a n a ly s is R e a s o n in g o n t h e v e ri fi c a ti o n o f th e s tr u c tu ra l m o d e l a C h u rc h o f th e N a ti v it y B e th le h e m , P a le s ti n a X X X X X X X X b H a g h ia S o p h ia b e ll to w e r Tr a b zo n , Tu rk e y X X X c B a s il ic a o f S . M a ri a A s s u n ta G e n o a , It a ly X X X X X X d R e n a is s a n c e It a li a n p a la c e P ia n c a s ta g n a io , It a ly X X X X X X X e P is e c e C a s tl e S lo v e n ia X X X X X f Th e C e rn a d e la B ri d g e M o n d a ri z, S p a in X X X X g Th e M a ll o rc a C a th e d ra l P a lm a d e M a ll o rc a , S p a in X X X X X X X X h B a s il ic a o f P il a r Za ra g o za , S p a in X X X X X i C h u rc h o f th e P o b le t m o n a s te ry V im b o d í a n d P o b le t, S p a in X X X X X X X H is to ri c a l c o n s tr u c ti o n D a ta A c q u is it io n S tr u c tu ra l b e h a v io u r IC O M O S re c o m m e n d a ti o n s u s a g e L o c a ti o n

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2.2 Research Methodology

In general, the guidelines are aimed to assist studies, research and interventions on buildings with cultural and historical value and to give the recommendations on the process of the structural assessment. However, in some of the current guidelines for the historical buildings (ICOMOS 2005, ISO 2010 - annex I) there are no indications in which way the quantitative and the qualitative data should be combined and used for the diagnosis and safety evaluation.

Obtaining an in-depth knowledge about the past of the structure and its present stage in order to predict the future behaviour and response to different loading or excitations is a long process. It requires a very refined and large structural model to capture different phenomena throughout the structure and to produce reliable and realistic results, so that meaningful results are not omitted. Based on the findings during the inspection and testing of a structure, one should develop the structural analysis strategy, its aims and goals and choose among the variety of possibilities, such as the simple equilibrium analysis or advanced numerical simulations (Roca et al. 2010). Development of the modern computation tools nowadays presents a powerful resource for the reality simulation and in the case of a good diagnosis and pre-investigations of a heritage structure; the error in the behaviour prediction could be the minimal one. However, in the case of a complex structural system and a large amount of the unknown parameters – dimension of the elements, material characteristics or imposed displacements, it is difficult to estimate the state of the stress in the existing structures, both numerically and experimentally. Even in the case when the actual load is determined (for example experimentally using NDT), the stress values can change during the time and result in a different equilibrium state. In case when a disagreement is found between the behaviour predicted numerically and the one estimated in the current stage, the analysis can be refined or expanded to a bigger portion of the structure (even the whole structure) towards capturing the phenomena observed on-site.

The multidisciplinary approach used in the present research starts from the recommendations on structural assessment of heritage structures given by the ICOMOS (ICOMOS-ISCARSACH, 2005). It consists of the data acquisition, analysis of the structural behaviour, diagnosis and safety evaluation, concluding with the eventual intervention design (Figure 2.2). The thesis then proposes a way of combining above mentioned different fields of expertise and investigation techniques towards the better understanding of the structural system of a historical structure with tie-rods as a permanent part of their structure, so as for investigation of these elements. The first group of data will be acquired from the historical investigation, geometrical survey and laboratory testing and will be used as an input for the choice of different structural

20

schemes, material characteristics, decay process and actions. The second group of the acquired data - damage maps, field NDT testing and monitoring results will be later on used to verify the results of the structural analysis for the adopted input data. Once verified, the structural models will be used to predict future structural behaviour, explain the observed damage and large deformations. Together with historical, qualitative and experimental data, the results of the structural analysis are part of the quantitative analysis for the diagnosis and safety evaluation. Finally, further developments are proposed on the basis of the research outcomes.

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2.3 Structural Assessment of the Duomo di Milano

The particular feature of the Duomo di Milano is the fact that its iron tie-rods are active in balancing the lateral thrusts – as indicated by the static theory (Coronelli et al. 2014a) and the preliminary test measurements (Vasic et al. 2015). The Cathedral’s complexity - imposing dimensions, complicated structural system, big amount of the unknown characteristics, features of the used materials and structural elements; require various techniques of the data collection, processing and interpretation. Although a big archives collection exists regarding the Duomo di Milano and its life, there is a lack of data on the past maintenance or structural investigation work for the iron ties present in the Cathedral under the arches of all five naves, which makes the research even more challenging.

In order to study the structural behaviour of the Cathedral (and in particular of the iron tie-rods) in the past, future and at the present, a list of activities was performed by the author of the thesis, as described in the following. Historical investigation was done analyzing the relevant literature, testimonies and drawings, photos of the Cathedral during the time, past major events, their causes and possible consequences. Geometrical survey was combined with the results from the historical analysis and the on-site visual inspection, from which the geometrical origin of elements was derived (where possible). In this way a preliminary geometry for the five nave characteristic bay was formed. Results of the laser scanner survey were later on used to verify the assumptions made in the present thesis and update the geometry where necessary. Damage was mapped in zones of interest for the present study in terms of the damaged masonry and stone elements, materials replaced during the past and material deterioration. The laboratory campaign included two parts: mechanical and physical characterization of the original iron material and calibration of the chosen NDT dynamic method for estimating the tensile load. The dynamic investigation was made on 112 iron tie-rods trough the aerial platform. A database was formed with the geometrical characteristics of each tie, a photographical survey of the tie-rods and their clamping into the masonry, so as the main dynamic properties of tested elements – the natural frequencies and mode shapes. The tension in the ties was estimated on the basis of these results and employing a theory for vibration of an axially loaded beam. The structural behavior was studied using:

1. The body equilibrium - equilibrium of bodies was based on the limit analysis theory for the masonry

structures and assumptions on the construction stages within the each nave (different stages were individuated in the present research). This classical tool gave indications on the total thrust value, which should be later on resisted by a combined action of the tie-rods, spandrels and buttressing

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system. One of the equilibrium solutions is found by assuming that the portion resisted by the tie-rods is equal to the current one estimated experimentally using the dynamic NDT.

2. The linear FEM analysis - this advanced numerical tool took into account the material

non-linearity. It simulated different construction stages within the one characteristic bay and its results were compared to the results from the instantaneous FEM analysis and the experimental results for the current stress in the tie-rods. Several analyses were performed: taking into account the geometrical non-linearity, soil settlement effect, break of the tie-rods and horizontal loading effect. Each of them was compared to the data collected on-site and gave valuable contribution to the understanding of damage causes and its possible progress.

For the simplicity of notation trough the documents, tie-rods are noted with two numbers referring to the columns that they are connecting (Figure A2.1), while 5 bays are referred as given in Figure A2.1b.

CHAPTER

3

I

nvestigation and Survey of the Duomo di Milano

“The discovery of an important need is almost as important as the invention which satisfies this need.” Prof. Michael Pupin

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3.1 Historical Investigation

When dealing with an existing structure, and in particular a historical one such as the Duomo di Milano, it is essential to understand its original design, evolution of the construction and the damage during the time, so as to list major events in the past (seismic events, structural failures, previous restoration works, etc.). History of the structure can be considered as the most complete experimental laboratory (ICOMOS-ISCARSACH, 2005). Analysing the past behaviour of the structure can improve the understanding of its original features and their interaction with different actions, loads and alterations. It should be in any case underlined that the safety of a structure during a long-time period does not guarantee its safety also in the future. This is particularly important when the long-term effect cannot be disregarded (the collapse of the Civic tower in Pavia and of the Bell tower in Venice due to the creep in the masonry, Binda et al. 2008) or when the structure is working at the limit of its bearing capacity (tie-rods in the Duomo di Parma, Garziera and Collini 2010).

The historical investigation during the present work was done within this scope and included: review of the relevant literature, study of the historical “technical” drawings and comparison with the on-site inspection, analysis of the photos and drawings from the archive of the Cathedral. Data collected during the historical investigation was then used to study the structural history of the Cathedral and to list major structural events concerning the Cathedral. On the basis of historical investigation and visual inspection performed in the present work, several hypothesis were made in the present thesis on structural evolution of each bay and overall evolution of the building. This will be an important aspect of the study, since the structural history may have significant influence on the current state of the structure (Coronelli et al. 2014a, Roca et al. 2013, Romera 2008b). The effect of different construction stages will be taken into account during the structural analysis and will be based on the findings of this Chapter. Construction stages will also play an important role in understanding the overall structural behaviour of the building or justifying the variation in the structural performance of its elements. It will be used as a complementary tool to interpret the eventual damage in the structure.

3.1.1 The structural history

The construction of the Duomo di Milano started in 14th century; designed partly in a Gothic style and

compared with the other cathedrals from the same period (Table 3.1, Figure 3.1) had the highest main nave at that time. Moreover, cathedrals listed here have the system of massive buttressing walls and flying buttresses that together carry the lateral forces. The Duomo is among them the only one having metallic

26

ties as a permanent part of the structure after it has been completed. In other cathedrals these elements may have been used during their construction, but later on were removed (Fitchen, 1961).

Since the beginning of Duomo’s construction, European building masters were invited during the time to examine the quality of the design and give their opinion. Such was Mignot from Paris, who within a long list of remarks and issues expressed a concern regarding the stability of the structural scheme and the

members he observed at the end of the 14th century. In the response of Duomo’s engineers to his remarks

in year 1400 (Fabbrica del Duomo di Milano, 1877) it is said: “…and also the aforesaid masters want to put above the capitals the great iron ties, which connect a pillar with each other, and so should be done for the whole church …”*

. Present thesis considers such record as indication that the ancient builders used tie-rods during the Cathedral’s construction. Tie-rods are located under the arches in all five naves of the

Cathedral (both in the transversal and in the longitudinal direction), in the zone of the tiburio and the

apse (Figure A3.6, A3.8-9). Ties are clamped into the masonry through a fork connection that comes out of the masonry portion (Figure A3.5). Such clamping should enable the transfer of the axial force further to the masonry construction. Most of the-tis rods could be the original ones, since there is no historical evidence on their failure or replacement, apart for the four tie-rods under the tiburio. The tie-rods, which were connecting four piers under the tiburio (piers 74, 75, 84 and 85 in Figure A3.6), broke in 1470 when a series of hidden arches was built above them with the offset of 90cm relative to the axis of the piers (Ferrari da Passano 1988). This provided an eccentric loading, so the 2 tie-rods broke and felt to the ground of the Cathedral, while the other 2 were found broken close to their anchorage during the restoration works in 1980’s, when new steel ties were inserted at the same location (Ferrari da Passano 1988).

Part of the Duomo’s foundations was built on the remains of a previous church, Santa Maria Maggiore (Figure 3.2a), which was demolished contemporary with the construction evolution of the new Cathedral. Several historical drawings (Figure 3.2b, A3.1-4) are indicating that the Santa Maria Maggiore church or its parts have been present within the newly constructed cathedral. It is not clear if and which influence this had to the structural system of the Cathedral or its sequential erection. Present thesis proposes the hypotheses that the master builders used the remains of the old church as sort of a buttressing system in the longitudinal direction for evolving the structure (while new building is evolving, part of the old church is still partially present, Figure 3.2). Particular method of building Gothic cathedrals - each bay in

* “…et ulterius praedicti magistri volunt super capitellis ponere ferrous seu strictores ferri magnos qui inclavent unum pilonem cum altero et ita fiat ubique per totam ecclesiam…” – 11th

January 1400 (Fabbrica del Duomo di Milano, 1877, pg. 203)

27 its entire height, progressing in longitudinal direction, makes this direction vulnerable until the façade wall is completed (Figure 3.7).

A construction stages map (Figure 3.3a) was produced in the present work on the basis of information found in Dizionario storico artistico e religioso (Majo and Vigini, 1986), complemented with the relevant literature: the Annali of the Duomo (Fabbrica del Duomo di Milano 1877-1885), documentation on the past restorations (Archives of Veneranda Fabbrica del Duomo, Ferrari da Passano 1988, Ferrari da Passano 2005) and previous structural analysis (Coronelli et al. 2014a). A more refined map (Figure 3.3b) was later on derived by the author of the present thesis on the basis of the historical investigation and the visual inspection made during the present work, as described in the following. In particular, 112 tie-rods were examined visually throughout the on-site inspection in the present work, building up a photographic database and measuring their length and the average cross sectional dimensions. The average cross-section of each tie was then mapped on the floor plan (Figure 3.4a) and different groups of tie-rods were observed. Present thesis then assumes that tie-rods with similar cross sectional dimensions, belonging to different groups were probably used in different construction stages. Therefore, a new construction

transition between the 5th and the 6th bay was recognized as showed in the Figure 3.3b, with respect to the

construction stages map in the Figure 3.3a. This is based on the fact that dimensions of tie-rods in surrounding naves are characterized with different cross sectional dimensions (Figure 3.4a).

Further one, visual inspection in the present work distinguished four types of the typical tie anchorage (clamping fork and tie-end) into the masonry of the vaults (Figure 3.4b):

1. round-shaped both clamping fork and the tie-rod end - corresponding to the most recent anchorage type in the Cathedral (Figure 3.5: A)

2. tie strengthened during the past near the anchorage (Figure 3.5: B)

3. rectangular-shaped both clamping fork and the tie ending - corresponding to the “oldest” anchorage type in the Cathedral (Figure 3.5: C)

4. rectangular-shaped clamping fork and round-shaped tie ending - the “transition” anchorage, where the clamping was built in the masonry using the old rectangular shape, while the tie was shaped using the new rounded shape (Figure 3.5: D)

These differences in the shape of the anchorage also gave valuable indications regarding the construction period. They were appreciated after different clamping types were mapped on the floor plan of the Cathedral in the present thesis (Figure 3.4b) and accompanied with the dimensions of the ties, also mapped on the floor plan (Figure 3.4a). Comparing Figure 3.4a and Figure 3.4b, it can be seen that groups of tie-rods with similar dimensions correspond to the groups of tie-rods with similar anchorage. Present

28

thesis then attributes such groups of tie-rods with similar dimensions and similar type of anchorage to different construction periods. On the bases of this evidence, a more refined construction stages map (Figure 3.3b) was then proposed, introducing a new stage – the transition period around 1550. Such assumption is also in agreement with the construction stages map derived from the literature (Figure 3.3a). For example, there are the two groups of the tie-rods with different dimensions and different type of

clamping between the 1st and the 2nd bay in the south external lateral nave (Figure 3.4a and b). This can be

complemented with one of the historical photos provided by the archive of Veneranda Fabbrica del Duomo (Figure 3.6) where the two parts, possibly corresponding to different construction periods, can be distinguished in the zone of the main nave vaults.

The erection of the Cathedral started in 1386 from the east by constructing the apse and chapels next to it, further constructing the crossing towards the west (Figure 3.3, Figure 3.7). Zone of the bays, which is

characterized with a five nave structure, was finalised in 16th and the façade in 18th century (detailed

history of the structural evolution can be found in Coronelli et al. 2014a). The construction of each bay started from the extreme lateral naves, followed by the inner lateral naves, so the main nave was built at the end (Figure 3.3). Present thesis then assumes that each of these portions of the Cathedral (the apse, chapels, crossing, 5 parts of a bay), was built in its entire height, so that previously finished and roofed parts could be already used for the religious purposes and collection of donations for the work continuation. However, such way of constructing firstly the lateral vaults followed by the erection of the main nave vault might raise stability issues at the intermediate stages in the transversal direction (Roca et al. 2013), besides already mentioned instability in the longitudinal direction. This is probably another reason why the ancient builders decided to use the tie-rods during the construction of the Duomo di Milano and keep them as a permanent part of the structure. Placing tie-rods on top of the piers at corresponding construction stage certainly reduced the potential lateral deformation of the piers that could have occur if the transversal thrust in a bay was unbalanced at such intermediate stages. On the other hand, it might be relevant what amount of the thrust was resisted by the tie-rods at each of these intermediate stages. It is also benefit to understand if such state of the stress could have had a long-term effect on the defects that are today observable in some structural elements.

Present thesis assumes that the construction of the each nave started with the construction of stone masonry piers in their entire height, placing on them tas-de-charge, a single block of marble stone (similar to the one reported in Heyman 1995 pg. 107, originally from Viollet-le-Duc, Figure 3.8). Tas-de-charge provided the base for the erection of lateral and diagonal ribs, transversal arches and filling. Builders placed wrought iron ties on the top of these single blocks in each nave, so the ties gradually took the load from the structure evolving above. Approximately at that point the diagonal rib and Gothic arch

29 made of multiple voussoirs develop separately, built probably over a temporary wooden centring (as assumed in the present thesis). The space between the springing of the ribs and wall was filled with brick masonry parallel to the rib erection, providing the structure through which the thrust line from the vault can pass. Subsequently this backing cone was the solid base for the further construction of the vault over the arches and ribs starting from the top of the cone infill and, as the author believes, without the formwork for the masonry vault. Once the cross-vault was completely constructed, builders built spandrels over the transversal (Gothic) arches as the basis for the barrel vault and a longitudinal beam, all made of masonry, providing the support for the marble roof to be built on the top (Figure 3.7).

The final structure of the Duomo does not have a bell tower and the bells are situated above the main cupola over the crossing (Figure A3.9). However, several historical drawings and photos (Figure 3.6, 3.9-10) evidence that a provisional bell tower existed and was placed on the top of one of the main nave

vaults in the 6th bay going from the west to the east (Figure A3.5). It is not known when this temporary

structure was built, but the oldest evidence of its existence is a drawing from the early 17th century

(Figure 3.2b). However, the transcripts of major decisions by the engineers in charge of the Cathedral are

found during this research which indicate that the bell tower was demolished in 1866* (Fabbrica del

Duomo di Milano 1885, pg. 396): “…It is approved the immediate demolition of the bell tower, given the very serious and dangerous condition of damage in which it is…”. No evidence is found on how the bell tower was damaged and what caused the damage. According to the survey drawing from the same period

(Figure 3.9a), the bell tower was constructed directly on the main nave vault in the 6th bay. The influence

of such structure on the Cathedral at that time is not certain. Nevertheless, it is possible that this temporary construction had a significant role in the structural history of the Cathedral and will be investigated during the current research. It should be noted that the temporary bell tower was located in the same bay in which the tie 58_88 was found broken in 2011 (Figure 3.9b), so the effect of bell tower’s weight on the rest of the structure will be examined using the numerical modelling in the present thesis.

* _{“…É deliberata l’immediata demolizione della torre delle campane, stante il gravissimo e pericoloso stato di}

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Table 3.1 – Comparison of Gothic cathedrals.

Cathedral Date Free span of the main nave/choir [m]

Height of the main nave/choir [m]

Amiens 1220 14.60 42.30

Palma 1357 17.80 44.00

Milano 1386 16.65 45.22

Figure 3.1 – The overall dimensions of cathedrals: Palma de Mallorca (Roca et al. 2013) (a), Amiens cathedral (Monnier et al. 2010) (b) and the Duomo di Milano (c).

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Figure 3.2 – Position of the old church St. Maria Maggiore with respect to the nowadays Cathedral (courtesy of Veneranda Fabbrica del Duomo) (a) and Anonimo, “Scene carnevalesche in piazza del Duomo”, oil on canvas

1660 (Milan, Civiche raccolte storiche - Museo di Milano) (b). (a)

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(a)

(b)

33

(a)

(b)

Figure 3.4 – Average cross section (a) and different anchorages of the ties in the Duomo di Milano (b) (tie-rods in black were not accessible for examination).

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most recent types

A

B

C

D

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Figure 3.6 – The south façade, early 17th century (courtesy of Veneranda Fabbrica del Duomo).

Figure 3.7 – Assumption on the structural evolution of the Cathedral. Already built crossing

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Figure 3.8 – Detail of the tas-de-charge after Viollet-le-Duc (Heyman 1995 pg. 107) (a) and in the Duomo di Milano (b).

Figure 3.9 – Survey of the temporary bell tower in the Duomo di Milano on 26th August 1866 by Ing. Bianchi, city engineer and Ing. Vandoni (reported in Il duomo di Milano, Vol. I, 1973) (a) and its position with respect to

the current floor plan (b).

(a) (b)

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Figure 3.10 – Historical views of the old bell tower: Giovanni Migliara, Veduta di Piazza Duomo 1830 (a) and Excavations at Piazza Duomo during the erection of Galleria Vittorio Emmanuelle 1865 (b).

(b) (a)

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3.1.2 Important events

Several events in the structural life of the Duomo di Milano are to be taken into account due to their potential influence on the damage origination and propagation. The evidence of the ongoing phenomena will contribute in a qualitative way to the process of the diagnosis and safety evaluation. Although the focus of the current research is in the zone of bays, the damage occurred in other zones of the Cathedral might have had influence on the present stage in the zone of interest. For example, the damage of the four

piers under the tiburio originates from the 15th century when hidden arches were constructed to support

the structure above (the tiburio and the dome), which were eccentrically with respect to the piers under (Coronelli et al. 2014a). This caused the break of the ties connecting piers 74, 75, 84 and 85 (Figure A3.6) in 1470, which remained broken for 500 years until the restoration in the last century (1980-1984). Most columns of the tiburio and choir columns were restored and 4 piers under the tiburio were connected with a system of modern steel ties during the 1980’s restoration works. This caused severe damage during the time and significant deformation of columns in that zone, but also might have caused the load redistribution at that time on the rest of the built structure.

Another important historical phenomenon is the excessive water draining from the soil under the

Cathedral by the industrial companies in the 19th and 20th century. The groundwater level lowered for

about 20m in the last 200 years (Figure 3.11, Niccolai 1967), which caused differential settlement under the piers of the Cathedral. This could have influenced the high stress concentration in the transversal arches’ voussoirs that were replaced in the past and at the present are visible as new stones. Moreover, it accelerated the long-term damage present at that time in four piers under the tiburio and finally led to a

big structural intervention in the final decades of the 20th century (Ferrari da Passano 1988 and 2005).

Regarding the seismic loading of the Cathedral, the zone of Milano is a low-seismicity zone, and no major events have been recorded since the beginning of the construction, even if the vulnerability of the entire structure is unknown. Some studies have been performed on the seismic vulnerability of the main spire (Postoli and Giorgetti 2012). On the other hand, the underground train is running under the Duomo since 1964. Although the study by Bruschieri et al. (1987) committed that underground vibrations were not relevant for the heavy damage in the piers under the tiburio in 1980’s, modern scientific tools (numerical or monitoring) have not been used to assess the effect of the passing trains to the Cathedral and its effect nowadays, 30 years after the big intervention.

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Figure 3.11 – Lowering of the groundwater level in the urban area of Milan (Niccolai 1967).

3.1.3 Previous structural interventions

The maintenance of the Duomo di Milano is a continuous process, which includes both restoration and structural interventions. Most important works, relevant for this study, are listed and analysed in the following.

Historical interventions

The present research found evidence of the local historical strengthening of 5 tie-rods present in the Duomo di Milano (Figure 3.5 and 3.12). Present thesis assumes that such interventions were done probably in very diverse time periods giving the different shape of the bolts and the iron plates used for the strengthening. Necessity for this kind of intervention might have risen from the inherent problems, such as the material defects, which during the time could have developed and propagated into the damage in term of cracks. On the other hand, the eventual damage in these elements could have been originated from the overstressing or imposed deformation caused by the column settlement or deformation. In any case, this hypothesis will be accompanied with the results of experimental campaign and numerical simulations during the present research and give important information on the final diagnosis of the structure.