Dissertation RgN.60105112

SEISMIC RESPONSE AND REHABILITATION OF

HISTORIC MASONRY BUILDINGS

Dissertation submitted as part requirement

for the Degree of Master of Science in

Earthquake and Civil Engineering Dynamics

BY

FRANCISCO ROBERTO TRUJILLO LEON

Supervisor:

Prof. Kypros Pilakoutas

The University of Sheffield

Department of Civil and Structural Engineering

September 2007

ii

Declaration Statement

The author certifies that all the material within the thesis titled Seismic Response and

Rehabilitation of Historic Masonry Buildings is his work except where it its clearly

referenced to others.

Francisco Roberto Trujillo Leon

iii

Abstract

Historic masonry buildings in seismic areas are very vulnerable because they have

not been explicitly designed to withstand seismic forces. The assessment of their seismic

behaviour is very important to planning the correct rehabilitation strategies for the

improvement of their resistance during seismic events. This dissertation presents a procedure

for assessing the safety of historic masonry buildings under seismic vibrations based on

measurements of their natural frequencies, numerical simulations and failure mechanisms in

order to recommend the best rehabilitation technique.

As example a case study of the seismic behaviour of the Santo Domingo Church,

located in México, is included. For this purpose, a model of the historic masonry building

was created using the finite element basis.

The geometrical configuration of the church is as follows: the plan view inscribes a

cross (67.50m x 43.70m) with walls of 2.0m to 3.0m in depth, and vaulted roof; in the

connection a big cupola communicates with adjacent modules. In the first section of the

building two towers take part over the main facade, with 27.46m in high. The numerical

solutions obtained from the distinct element analysis are validated by comparing the results

with those obtained from the existing works (Mistler, Butenweg, & Meskouris, 2006; &

Meli, 1998) and by measurement of its natural frequencies and failure comparison with the

real structure.

The two seismic analyses performed on the structure reveals a brittle failure in wall

to wall connections of the main facade with the vaulted body, a possible cracking in middle

span of the vaulted roof and collapse of the towers by excessive tensional stresses. These

results are related to the elastic linear behaviour of the structure and should be considered

even more critical because nonlinear issues as crack, sliding and disconnections were no

measured in the structure. It is suggested the use of GFRP reinforcement in both intrados and

extrados faces of the vaulted area and the use of CFRP reinforcement bars as connections

between the towers and its base.

The conclusion of this assessment is that even when the finite element method

presents a revolutionary tool for the assessment of any structure, needs the application of

interdisciplinary tests to be confirmed as representative. Never must be considered as a

duplicate of the real behaviour and some engineering judgement is always necessary for the

correct interpretations of the results.

iv

Acknowledgements

I would like to thanks to my supervisor Prof. Kypros Pilakoutas for his guidance andsupportive analysis.

Particularly I really want to thank to my parents for all their support during all thistime without which I would not be able to study this degree.

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Table of Contents

Declaration Statement ........................................................................................... ii

Acknowledgements ............................................................................................... iii

Abstract .................................................................................................................. iv

1 INTRODUCTION ......................................................................................... 14

1.1 Foreword ............................................................................................................. 14

1.2 Aims and Objectives ............................................................................................ 15

1.3 Layout of the thesis .............................................................................................. 16

2 LITERATURE REVIEW ............................................................................. 17

2.1 Introduction ......................................................................................................... 17

2.2 Masonry components ........................................................................................... 18

2.2.1 Introduction ................................................................................................... 17

2.2.2 Stone ............................................................................................................. 19

2.2.3 Mud ............................................................................................................... 20

2.2.4 Mortar ........................................................................................................... 21

2.3 Masonry types ..................................................................................................... 22

2.4 Structural systems and elements ........................................................................... 23

2.4.1 Column .......................................................................................................... 23

2.4.2 Wall ............................................................................................................... 24

2.4.3 Arch .............................................................................................................. 25

2.4.4 Vault.............................................................................................................. 26

2.4.5 Dome ............................................................................................................. 27

2.4.6 Foundations ................................................................................................... 28

2.5 Typical failure mechanisms.................................................................................. 28

2.5.1 Historic masonry walls ................................................................................... 28

2.5.2 Historic masonry arches ................................................................................. 32

2.5.3 Historic masonry structures ............................................................................ 33

2.5.3.1 Problems due to new additions ............................................................... 34

2.5.3.2 Problems due to foundation movements.................................................. 35

2.5.3.3 Problems due to material deterioration .................................................... 36

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2.6 Assessment methods of historic masonry buildings .............................................. 36

2.6.1 Introduction ................................................................................................... 36

2.6.2 Scopes and limitations ................................................................................... 37

2.6.3 Linear static analyses ..................................................................................... 38

2.6.4 Nonlinear static analyses ................................................................................ 38

2.6.5 Dynamic analyses .......................................................................................... 39

2.6.6 Numerical modelling ..................................................................................... 39

2.6.6.1 Finite element method .............................................................................. 40

2.7 Seismic safety ...................................................................................................... 41

2.8 Rehabilitation methods ........................................................................................ 42

2.8.1 Repointing ..................................................................................................... 43

2.8.2 Grouting ........................................................................................................ 44

2.8.3 Pining ............................................................................................................ 44

2.8.4 Stitching ........................................................................................................ 45

2.8.5 Overall strengthening of old masonry buildings .............................................. 45

2.8.6 Fibre Reinforced Polymer (FRP) .................................................................... 45

2.8.6.1 FRP Strengthening of vaults and arches ................................................... 47

3 CASE STUDY ............................................................................................... 51

3.1 Historic background ............................................................................................. 51

3.2 Geometrical data of the structure .......................................................................... 52

3.3 Characteristics of the materials............................................................................. 53

3.4 Development of the Finite Element model............................................................ 54

3.5 Seismic assessment of the structure ...................................................................... 57

3.5.1 Static system configuration ............................................................................ 57

3.5.2 Previous repairs ............................................................................................. 58

3.5.3 Analysis of the model .................................................................................... 59

3.5.3.1 Static Analysis ....................................................................................... 60

3.5.3.1.1 Single arch model ............................................................................. 60

3.5.3.1.2 Global model .................................................................................... 61

3.5.3.1.3 Concluding remark ........................................................................... 61

3.5.3.2 Modal Analysis ...................................................................................... 62

3.5.3.3 Response spectrum analysis.................................................................... 64

3.5.3.3.1 Single arch model ............................................................................. 64

3.5.3.3.2 Global model .................................................................................... 65

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3.5.3.4 Time history analysis ................................................................................ 67

3.5.3.4.1 Global model .................................................................................... 67


3.5.4 Strengthening and repair recommendations .................................................... 71

4 CONCLUSIONS ........................................................................................... 72

4.1 General conclusions ............................................................................................. 72

4.2 Recommendations for future work ....................................................................... 73

5 REFERENCES .............................................................................................. 74

APPENDIX A: Letter of Venice, ICOMOS recommendations.

APPENDIX B: Drawings of the structure.

APPENDIX C: Seismic properties tables.

APPENDIX D: Time history analysis results.

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List of Figures

Figure 2- 1 Flowchart with the methodology for structural interventions proposed byICOMOS. ..........................................................................................................................16

Figure 2- 2 Stonehenge (Frédéric Vincent) .........................................................................17

Figure 2- 3 Massive columns of the Temple of Olympian Zeus (caribb.).............................18

Figure 2- 4 Adobe bricks drying in the sun (Isla del Sol, Titicaka Lake, Bolivia) ................19

Figure 2- 5 (a)Opus incertum (dressed stones), (b)Opus implectum (quarry-stones), (c)Multi-layer assembly. (M. Mistler & C. Butenweg & K. Meskouris, 2006) ...................................21

Figure 2- 6 Load condition in a column (Section of St. John's Chapel showing Vaults,Adapted from Bond, Gothic Architecture, p283).................................................................23

Figure 2- 7 (a)Schematic illustration of an arch. 1.Keystone, 2.Voussoir, 3.Back, 4.Impost,5.Intrados, 6.Rise, 7.Bay, 8.Abutment. (Messer Woland), (b)Arch supported by a leaningbuttress. (Block, Ciblac, & Ochsendorf, 2006) ....................................................................24

Figure 2- 8 View of a barrel vault from above showing forces developed by the static system. ..........................................................................................................................................25

Figure 2- 9 Dome on pendentive (Totya). ...........................................................................26

Figure 2- 10 Case 1. Contours of damage variables at failure. (a)Tensile damage.(b)Compressive damage. (Berto, 2005)...............................................................................28

Figure 2- 11 Case 2. Contours of damage variables at failure. (a)Tensile damage.(b)Compressive damage. (Berto, 2005)...............................................................................29

Figure 2- 12 Failure modes of masonry panels. (M. Mistler & C. Butenweg & K. Meskouris,2006) .................................................................................................................................30

Figure 2- 13 Four-hinge failure mechanism of a semi-circular masonry arch submitted to anasymmetrical loading (Oliveira, 2006) ................................................................................31

Figure 2- 14 (1)Failure of a building corner, (2)Out of plane collapse of a bearing wall,(3)Partial collapse due to the thrust of the roof and bad connection tie beam-wall,(4)Separation of the two leaves of a wall, (5)Shear failure of a wall. (Penazzi, 2001) ..........33

Figure 2- 15 Different FEM approaches for modelling masonry. (M. Mistler & C. Butenweg& K. Meskouris, 2006) .......................................................................................................40

Figure 2- 16 Impact on masonry of using (a)Repointing with soft mortar. (b)Repointing withhard mortar. (Pearson, 2007) ..............................................................................................42

Figure 2- 17 Masonry strengthening solutions with FRP composites (Oprisan at. al. 2004) .45

Figure 2- 18 (a)Reinforcement of vault with mortar. (b)Reinforcement with reinforcedconcrete. ............................................................................................................................47

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Figure 2- 19 Summary for the full length CFRP reinforcement at the intrados and extrados.(Basilio, Oliveira, & Lourenco, 2004). ...............................................................................48

Figure 2- 20 Strengthening arrangements adopted: (a)Localized strengthening;(b)Continuous intrados strengthening; (c)Continuous extrados strengthening. (Oliveira,Basilio, & Lourenco, 2006). ...............................................................................................48

Figure 3- 1 The front entry of the Church of Santo Domingo de Guzman in San Cristobal deLas Casas. (Agguizar) ........................................................................................................50

Figure 3- 2 Plan section of the Santo Domingo Cathedral ...................................................51

Figure 3- 3 Main facade of the Santo Domingo Church ......................................................52

Figure 3- 4 Historic materials distribution ..........................................................................53

Figure 3- 5 (a)Finite Element model of a single arch, (b)Discretization of the model...........55

Figure 3- 6 Santo Domingo church. ....................................................................................55

Figure 3- 7 Analytical model of the structure. .....................................................................56

Figure 3- 8 Grouting work .................................................................................................57

Figure 3- 9 Restitution works effectuated in the past ..........................................................58

Figure 3- 10 (a)Joints location into the numerical model. (b)Sections distribution. ..............59

Figure 3- 11 Principal maximum (a) and minimum (b) stresses under dead load. ................59

Figure 3- 12 (a)Principal compressive stresses under dead load. (b)Principal stresses of mainarches under dead load. ......................................................................................................60

Figure 3- 13 (a) First mode of vibration (T=0.28sec). (b) Second mode of vibration(T=0.23sec). .......................................................................................................................61

Figure 3- 14 Third mode of vibration (T=0.23sec) ..............................................................62

Figure 3- 15 Fourth mode of vibration (T=0.22sec). ...........................................................62

Figure 3- 16 Response Spectrum according to NTC. ...........................................................63

Figure 3- 17 (a)Shear stress diagram and deformed shape. (b)Stress diagram underearthquake loading in principal direction. ...........................................................................64

Figure 3- 18 (a)Principal stresses in Y-direction due to earthquake. (b)Principal stresses inX-direction due to earthquake.............................................................................................65

Figure 3- 19(a)Displacement contours originated by the design spectra in Y-direction.(b)Displacement contours originated by the design spectra in X-direction(Contours in cms). ..........................................................................................................................................65

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Figure 3- 20 (a) 1995 earthquake accelerograms in N-S direction (b) 1995 Earthquakeaccelerograms in E-W direction..........................................................................................66

Figure 3- 21 (a)Stresses diagram in Y-direction [95 Earthquake]. (b)Stresses diagram in X-direction [95 Earthquake]. ..................................................................................................67

Figure 3- 22 (a)Stresses diagram in X-direction [95 Earthquake]. (b)Maximum envelop ofstresses in X-direction [95 Earthquake]. .............................................................................67

Figure 3- 23 (a)Stresses diagram in Y-direction [95 Earthquake]. (b)Stresses diagram in Y-direction [95 Earthquake]. ..................................................................................................68

Figure 3- 24 Maximum envelop of principal stresses in X-direction [95 Earthquake]. .........68

Figure 3- 25 (a) Maximum envelop of principal stresses in Y-direction. (b) Deformed shapeunder recorded accelerations [95 Earthquake]. ....................................................................69

Figure 3- 26 (a)Displacement contours originated by the design spectra in X-direction.(b)Displacement contours originated by the design spectra in Y-direction(Contours in cms). ..........................................................................................................................................69

Figure B- 1 Longitudinal section A-A' ................................................................................84

Figure B- 2 Longitudinal section B-B' ................................................................................84

Figure B- 3 Transversal section C-C' ..................................................................................85

Figure B- 4 Transversal section D-D' ..................................................................................85

Figure D- 1 Displacement in X-direction of joint 588 (orange) and 579 (blue) VS time.......89

Figure D- 2 Displacement in X-direction of joint 591 (green) and 578 (blue) VS time. .......90

Figure D- 3 Displacement in Y-direction of joint 588 (orange) and 579 (blue) VS time.......91

Figure D- 4 Displacement in Y-direction of joint 591 (green) and 578 (blue) VS time. .......92

Figure D- 5 Response spectrum curve for joint 1365 matching with the third mode of thestructure at 0.23sec Period vs. Pseudo spectral acceleration in Y-direction. .........................93

Figure D- 6 Response spectrum curve for joint 591 matching with the first mode of thestructure at 0.3sec Period vs. Pseudo spectral acceleration in Y-direction. ...........................94

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List of Tables

Table 2- 1 Mechanical properties of Spanish historic masonry (Meli, 1998) ........................30

Table 2- 2 Technical specification of reinforced polymers. .................................................46

Table 3- 1 Historic Materials ..............................................................................................53

Table 3- 2 Modal Participating ratios for each mode. .........................................................61

Table C- 1 Modal participating ratios for each vibration mode. ...........................................87

Table C- 2 Modal periods and frequencies for each vibration mode. ...................................88

Without words,

without writing and without books there would be no history,

there could be no concept of humanity.

Hermann Hesse

S e i s m i c R e s p o n s e a n d R e h a b i l i t a t i o n o f H i s t o r i c M a s o n r y B u i l d i n g s | 1 3

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1 INTRODUCTION

1.1 Foreword

During the last decades, great advances in the application of numerical methods

relevant to the assessment of the structural behaviour of monuments and historic buildings

have been developed around the world; e.g. the finite element method (FEM). Recent facts

of two Peruvian churches collapsing by the 8.0 magnitude earthquake that hit the Peru coast

(BBC-NEWS, 2007); killing more than 500 people, confirm the idea that the applicability of

past seismic response calculation methods on historic masonry buildings and reliability of

existent retrofitting techniques need to be improved. As consequence advance analysis

simulation need to be implemented as additional tool that can lead us to increase the

confidence about the limits and capabilities of the strengthening work.

In order to do this, a good definition of the problems into the structure is required in

order to select the appropriate restoration and strengthening work. For the computational

evaluation of the structure, the development of a numerical model is needed. During this

process some difficulties need to be confronted including determining of material properties,

geometry, boundary conditions, loading characteristics and verification of the model.

Because masonry materials present a nonlinear behaviour and due to the lack of information

on their characteristics, a simplification by considering continuous material properties into

the elements can be suggested for the calculations.

In addition, any structural safety analysis and consequent rehabilitation proposal

against external agents, including seismic events, must be judged without forgetting that the

original construction must be preserved from an aesthetic and structural perspective,

according to the most recent international procedures, e.g. Letter of Venice, see Appendix A.

Another important issue to be accounted for is the correct assessment of the effects on the

structural behaviour of advanced strengthening materials and technologies as applied to

traditional elements (Christensen, Gilstrap, & Dolan, 1996).

Since this thesis intends to demonstrate the typical failure mechanisms and improved

repair techniques of masonry buildings under seismic actions, in particular historical

structures, a brief introduction to some materials, elements and historical facts is given first.

Following that, a numerical model for the a structure is developed, and at the end, a

computational analysis is used to determine the seismic behaviour of the Santo Domingo

Cathedral in Mexico and presented as a practical application of seismic assessment.


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1.2 Aims and objectives

The overall aim of this dissertation is the seismic assessment of historic masonry

buildings through finite element modelling with a commercial software (SAP2000®) and the

proposal of strengthening solutions by measuring the common failure mechanisms (local and

global cases). In this exercise, the engineer will be aided by the knowledge of the magnitude

of principal stresses, maximum displacements and deformed shapes, obtained by a linear

elastic finite element analysis under two sources of excitation: a response spectrum

according to the Mexican code (Mexican-Norms, 2007) and time history accelerations

recorded during the 21 of October of 1995 seismic event in the south of Mexico.

In order to achieve this, the following objectives will be intended:

· Understanding the mechanical behaviour and failure modes of historic masonry

buildings under external loading.

· Study of different calculation methods applied in the past to comprehend the

improvements and limitations of new techniques; in particular the FE method, to

reach a satisfactory representation of the structural system.

· Understanding of common types of seismic analysis, its differences, advantages and

limitations in historic masonry structures.

· Performing both static and dynamic linear analysis using CAE software

(SAP2000®) to determine potential stress concentrations and failure mechanisms.

Comparison with previous failures in the structure.

· Commenting on the advantages of the application of new retrofitting techniques.

· Developing of a retrofitting proposal and detailed description (mechanical

interpretation) of the damage or collapse process in the structure to be analysed.

· Depict conclusions on the seismic behaviour of historic masonry buildings.


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1.3 Layout of the thesis

This dissertation exposes means to determine typical failure mechanisms of historic

masonry buildings and general ways to strengthen the structure:

Chapter 2.2 The purpose of this chapter is to explain the structural characteristics of

composite materials employed in historic masonry buildings. The text centralizes in stone

and brick masonry, that were the most common materials employed during the last centuries.

Some mechanical properties of materials used in historic buildings are indicated in this

section, but according to experts in the matter, extreme provision should be taken in the

employment of these values.

Chapter 2.3 A short explanation is given in this chapter of masonry types used for

construction of monuments, cathedrals and other important buildings; mainly built with

composite masonry in different configurations.

Chapter 2.4 The purpose of this chapter is to describe the common elements in

historic masonry buildings that satisfied with the basic structural requirements of the epoch;

to explain its behaviour against external loads and failure modes as single components.

Chapter 2.5 The purpose of this chapter is to explain the typical failure mechanism

developed in masonry structures.

Chapter 2.6 This chapter discusses and present the new calculation techniques. The

improvement achieved by processors capable of compute thousands of calculations in

seconds and its impact on numerical methods is commented.

Chapter 2.8 Retrofitting methods are discussed in this chapter; its advantages and

limitations according to the type of failure presented in Chapter 2.5.

Chapter 3 Case study. The first part, contain a detailed description of the structure

and material properties chosen for structural analysis. The second part comments about the

way the structure is modelled, analytical results and strengthening recommendations.

Chapter 4 Present conclusions of the overall paper and gives recommendations for

future work.


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2 LITERATURE REVIEW

2.1 Introduction

Polemic has exited during the last two centuries in establishing criteria for

rehabilitation of historic buildings and monuments. Without coming to any general

consensus, the letter of Venice (see Appendix A) was written in May of 1964 as a result of

deliberations of many specialists and technicians in the restoration of historic monuments.

During the congress many issues for the preservation of historic structures were discussed.

The letter focuses on the maintenance of harmony between the structure and new

rehabilitation work. According to the paper such interventions must follow the next basic

principles: material compatibility, conservation of overall lay-out or decoration and mass

colour relationship, avoiding of removing any part, or additions to the building. At the end

the text precise documentation of all rehabilitation works by means of critical reports

(including drawings and photographs) and recommends its publication.

According to ICOMOS recommendations (see Appendix A), a full understanding of

the structural behaviour and material characteristics is essential for any project related to

architectural heritage. It is recommended that the work of analysis and evaluation should be

done with the cooperation of the specialists from different disciplines like earthquake

specialists, architects, engineers and art historians. Besides, it is necessary for these

specialists to have common knowledge on the subject of conserving and strengthening the

historical buildings. In the next figure a methodology is proposed for the assessment of

historic buildings.

Figure 2- 1 Flowchart with the methodology for structural interventions proposed by ICOMOS.


17

One indispensable requisite for the structural preservation of a historic masonry

building is the maintenance of stability in structure and robustness. We can think, for

example, in the setting of large standing stones of Stonehenge (Figure 2-1), where stone

lintels supported by upright stones surrounding an internal ditch have born the past of

centuries.

Figure 2- 2 Stonehenge (Frédéric Vincent)

For a historic building anyone that is the material, shape and construction method,

the structural behaviour is always dominated by the same basic principles of structural

mechanics applied to any present building; as a result it is common to guess that its stability

can be studied under the same principles. However, specialists in the matter consider, due to

different motifs derived from negative experiences in the past (Binda, Penazzi, & Saisi,

2003), to not limit the structural engineering only to calculus if not make use of different

implements as supervision, monitoring and constant evaluation of the general behaviour to

correct and establish the real conditions of the structure to be studied.

2.2 Masonry components

2.2.1 Introduction

Masonry is well known as the oldest material used for construction. The ease to

initial assembling, structural properties, strength against majority of external conditions;


18

made masonry the preferred construction method during ancient times. The Greek structures

and ancient cathedrals around the world are proving of the durability of this kind of

structures.

In terms of load behaviour the analysis of this structure is complicated in that

variations of shapes, materials and building techniques were used during construction.

In the following a short description of the must common masonry components is

presented.

2.2.2 Stone

The natural stone is the most common component in historic masonry buildings and

is considered as a structural material by its own. Many classical monuments are made of

stones which lie one on top of each other without any application of mortar. One clear

example is the Temple of Olympian Zeus (Figure 2-2).

In old times, the type of stone to be used during construction was selected based on

its durability and workability. The durability is considered as the most important property of

stone, even when both characteristics are connected by the density of the material. Another

important property is the strength, but in those times it wasn’t as important as the ability to

resist the local weather conditions (Meli, R., 1998).

Figure 2- 3 Massive columns of the Temple of Olympian Zeus (caribb.)


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2.2.2 Mud

The mud started to be used as rolled ground, or as covering or landfill. Its main

weakness is the degradation by environmental agents and cracking by drying of its

components. Few constructions of this kind are still remaining in America, were the use of

mud was relatively frequent in some Spanish constructions.

To reduce the problems of contraction by drying, the construction based on rolled

ground evolved to the preparation of small pieces; more manageable, that could be

previously dried in the sun to complete its contraction process before of being used in

construction (Figure 2-3). Blocks or bricks are locally known as adobes and are mainly

employed in the edification of walls embayed with mud as mortar.

Construction based on adobe data from about 3000 years ago, and is still being used

in rural areas of development countries (Meli & Sanchez-Ramirez, 1993).

The mechanical properties of adobe, has big variations and follows the

characteristics of the ground and elaboration. Its strength in compression varies from 5 to 20

kg /cm2 and between 0.25 and 1 kg /cm2 in tension (Meli, R., 1998).

Figure 2- 4 Adobe bricks drying in the sun (Isla del Sol, Titicaka Lake, Bolivia)


20

2.2.3 Mortar

The necessity of a new material that could fill the holes between stones and provide

with some adherence and continuity gave place to the appearing of mortars. The first element

used for this purposes was mud. In Mesopotamia was used since the third century B.C.;

adding asphalt as stabilizer of the mud for joints and landfills (Meli, R., 1998). Later, sand

and lime mortar will allow the construction of more resistant and durable elements until the

widespread and acceptance of Portland cement.

In our days, the historic masonries structures are generally made of lime mortar. It is

very important to not confuse the non-hydraulic with the hydraulic mortar; the last

demonstrate a different behaviour as construction material and is not valid to repair historic

monuments. Only the non-hydraulic lime mortar is capable of preserve its properties during

centuries; this because the lime requires many years to acquire certain strength during the

carbonization process, maintaining a constant porosity in the element and allowing lime to

have certain impermeability in the compound.

The lime and sand mortars have a typical strength around 50kg/cm2 and 200kg/cm2

(Meli, 1998). Even when there are more durable than the adobe mortars, are also affected by

external agents as humidity and salts.

In distinct eras and cultures, different additives where employed in mortars. Many of

these new mortars contained many types of different aggregates as chopped straw, reed,

manilla hemp, jute, sisal, and even sawdust (Bennett, 2002). These mortars were expensive

and employed only in very important monuments.

Decades later, Romans will achieve a significant advance when they added

puzzolana to lime mortars. The last caused lime to increase its carbonization process without

need of a long time period, giving place to a much faster hardening and important increase in

the strength and durability. This discovering will facilitate the development of the first

concrete.

The Portland cement was introduced in the XIX century. The cement mortar,

reached strengths a lot much superior to lime mortars (around 50-200 kg/cm2), had a very

fast hardening and high elasticity modulus (Meli, R., 1998).

The main characteristic of mortars such as concretes, bricks and stones is that have

a good capacity to absorb compression stresses, but its tensile strength is typically low,

generally around 10% of the compression strength.


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2.3 Masonry types

Masonry is without doubt the must important and developed building method of

early civilizations.

Masonry is the combination of stones or bricks with mortar, in which the mortar

plays multiple functions as to fill the holes between stones and bring better uniformity in the

transfer of loads into the element.

In the beginning the structures were erected without any grout, but with time soils

like clay and lime became to be widely used. For example, after the cyclopean masonry the

Greeks developed the dressed stone masonry, which became the standard way for

constructing monumental buildings in both Greek and Roman civilizations. Stones were

connected without mortar, formed of entire stone blocks one above other and with joints as

small as possible.

Brick masonry started to be employed in Greece since the 7th century A.D. as the

common construction form using opus caementitium (Roman concrete) (Mistler, Butenweg,

& Meskouris, 2006).

“The Romans have often combined the new technique of opus caementitium with

conventional masonry construction sacrificing some aesthetics along the line. To counteract

this, an outer layer from natural stones was used. Depending in the material used for the

outer layer of the wall, it was called opus incertum (dressed stones) (Figure 2-4(a)) or opus

implectum (quarry stones) (Figure 2-4(b)). Also, special shapes called opus mixtum were

developed (Figure 2-4(c))” (Mistler, Butenweg, & Meskouris, 2006).

Figure 2- 5 (a)Opus incertum (dressed stones), (b)Opus implectum (quarry-stones), (c)Multi-layerassembly. (M. Mistler & C. Butenweg & K. Meskouris, 2006)

The big variety of construction techniques found in historic masonry buildings

makes very hard any intent of classification. But, historic masonry can be roughly classified

into regular masonry and irregular masonry. Combinations of both types are very difficult to

identify and test and experiments are required to determine the internal composition of

masonry. There is also the multi layer form used for masonry walls over many centuries in


22

Europe (Mistler, Butenweg, & Meskouris, 2006). The outer layer consisted of quarry-stones,

dressed stones or brick and the inner part was formed of loose stonewall masonry.

All these layers were needed because in past centuries the thickness of the walls was

considered as the most important factor in the resistance of the structure as a whole; it is

clear in remaining structures that the dimensions often depended on the height of the

structure.

According to Williams (1986) a thicker mortar results into a weak masonry in terms

of strength. The old constructers having this in mind started to make use of a bigger

relationship of mortar in the final compound.

2.4 Structural systems and elements

2.4.1 Column

This element fulfils with the basic functions of supporting and transferring loads to

the ground and is considered as the simplest one according to its structural behaviour,

because is generally subjected to compression stresses and all loads are solved axially.

However, sometimes we must take into account the possible eccentricity in the load

application.

The more primitive columns were made of wood trunks buried into the ground until

reach some good support in the base. These forms evolved to columns formed by blocks and

in some cases masonry. Their localization into the structure caused that architects considered

columns as an opportunity to develop some aesthetics with the style of the epoch.

The load capacity of the column depends on the strength of the constitutive

materials, but is also affected by certain factors that considerably reduce its capacity. It is

argued (Meli, 1998) that added to axial loads, the arches sustaining the roof produces lateral

movements adding an extra load to the columns. Only if the loads at both sides of the

columns are well balanced, the horizontal components of the forces balance each other. As

result, in general, there is always some eccentricity in the resultant, and the columns are

constantly under flexion-compression (Figure 2-5).


23

Figure 2- 6 Load condition in a column (Section of St. John's Chapel showing Vaults, Adapted from Bond,Gothic Architecture, p283)

Columns only shows signs of damage when are close to collapse conditions, its type

of failure in historic structures is brittle. The main symptom of a column reaching its load

capacity is the developing of vertical cracks that indicates lateral expansion of the material

and result in the detachment of the constituents. There are some cases were columns clearly

indicate several damage but still under those situations have stand for a long time. Many

experts attribute it to load transmission between adjacent elements of support.

The main problematic with these elements is that they do not absorb lateral forces or

moments.

2.4.2 Wall

Walls are like columns, elements that usually support the weight of the building and

comply with different functions as absorbing lateral forces from wind, earthquakes and those

from static systems (arches, vaults).

The failure modes depend on the type of load is acting on the structure and to the

internal composition of the masonry. The cracking configuration is one of the best signs of

which phenomenon is affecting the structure, and is always merit of a careful evaluation

(Lourenco, 2004).


24

When a historic masonry structure suffers differential movements in different parts

of the foundation, distortions in the walls are produced giving place to stresses similar to

those produced by lateral forces suitable to earthquakes, with the only difference that the

deformation is only produced in the direction of the movement.

The typical failure modes of this element will be discussed later in Chapter 2.5.

2.4.3 Arch

The arch was first developed in the Indus Valley civilization close to 2500 BC and

subsequently in Mesopotamia, Egypt, Assyria, Etruria, and later refined in Ancient Rome

(Meli, 1998).

While for support elements the solution was direct and simple, for roofs and stories

the solutions became more difficult to formulate. Beams and wood were used at the

beginning to cover short spans. It is common to assume that these solutions evolved from

roofs with shapes of inverted V to arches.

The structural behaviour of an arch is significant. The vertical loads applied are

transmitted to the supports following a pat that depends on the distribution of the external

loads and geometry of the arch. This configuration eliminates tensile stresses in spanning an

open space and all forces are resolved into compressive stresses (Figure 2-6).

Figure 2- 7 (a)Schematic illustration of an arch. 1.Keystone, 2.Voussoir, 3.Back, 4.Impost, 5.Intrados, 6.Rise,7.Bay, 8.Abutment. (Messer Woland), (b)Arch supported by a leaning buttress. (Block, Ciblac, & Ochsendorf,2006)

By using the arch pattern significant spans could be achieved; looking in this way;

the design of the arches became more in a geometry problem than a stresses one. The

a) b)

http://en.wikipedia.org/wiki/Indus_Valley_Civilization

http://en.wikipedia.org/wiki/2500_BC

http://en.wikipedia.org/wiki/Mesopotamia

http://en.wikipedia.org/wiki/Egypt

http://en.wikipedia.org/wiki/Assyria

http://en.wikipedia.org/wiki/Etruria

http://en.wikipedia.org/wiki/Ancient_Rome

http://en.wikipedia.org/wiki/Tensile_stress

http://en.wikipedia.org/wiki/Compressive_stress


25

geometry is chosen based on two goals: to minimize the eccentricities between the pressure

line of the arch; and to minimize the lateral forces in the supports.

It is very difficult to find arches that collapsed only by effect of static loads, there is

always a movement in the supports due to external conditions as foundation settlements, or

seismic movements. The opening in these supports develops a cracking pat that begins in the

lower part of the middle span, and later cracking start to appear in the upper part of the

imposts. A very big crack is required into the structure to create a mechanism that fails by

collapse (Meli, 1998). This topic will be discussed more deeply later in the next.

2.4.4 Vault

The natural extension of the arch to form a complete roof is the barrel vault, which

can be considered as a series of arches. Its behaviour, failure modes and stress analyses can

be studied by considering a simple section of vault unity wide.

As in the arches, the critical aspect is in the rigidity of the supports. In this case is

needed to avoid any lateral movement in the whole vault or cracking that can induce sliding

in the supports (Figure 2-7).

Figure 2- 8 View of a barrel vault from above showing forces developed by the static system.


26

The typical failure mode by effect of an external load is when it develops a

mechanism with 4 hinges, same as arches. The position of the hinges depends on the

geometry of the arch and position of the load. Therefore, high concentration of loads can

represent local failures or shear failure.

The cracking observed in vaults is always influence by movement in the supports.

2.4.5 Dome

Same as arches, the development of the domes, passed through the false dome, in

which circular rings made of stone are built enclosing progressively the span, to double

domes with inner and outer shells (Meli & Sanchez-Ramirez, 1993).

Domes by its geometry sit directly on a circular base; however, when this is not

possible, vault sections are added in the corners providing the transition between dome and

the square base on which it is set. These structures that transfer the weight of the dome are

called pendentives (Figure 2-8).

Figure 2- 9 Dome on pendentive (Totya).

For its construction, the dome requires the use of stones of complex geometry. The

last triggered that most domes started to be built with mud bricks, lime mortars and

puzzolana additives. The structural performance of the domes is related to these elements

http://en.wikipedia.org/wiki/Pendentive


27

that act as shells: transferring all dead loads produced by its own weight, generating friction

and compression stresses in the two main directions and distributing the loads from the top to

the supports (Meli, 1998). Tangential stresses in compression are also produced in the top

and tensional in the bottom, where cracking and separation can be produced. The big

majority of damages are due to tangential stresses that are in compression in the top part but

that take some tension values when reach the base. Due to the low resistance in tension of

masonry, this stresses origin a cracking across the meridians virtually separating the dome

into a series of stripes.

The bulging problem is not critical in masonry domes, the minimum depth

commonly used for its construction is sufficient to avoid this mode of failure. As stated

before, the radial stresses of compression increase progressively from the top to the supports;

the preceding, guided engineers around the globe to solve it by decreasing the depth in the

crest part of the structure; in many historic constructions, nervures where used to reduce the

weight of the element.

A similar stress condition is produce by temperature changes; the tendency to

expansion generated by certain increase in the temperature, generates tangential stresses that

can cracks the dome in the same way as described before (Lourenco, 2004).

2.4.1 Foundations

The necessity for transmitting loads from support elements to the ground with

generally lower strength than the composite materials of the elements in the superstructure,

gave place to the requirement of a substructure (a transition structure between the ground

and the superstructure). This gave place to the appearing of foundations. This improved from

the employment of single support elements to form raft or strip foundations.

Foundations in historic masonry structures are one of the most important elements to

be considered for rehabilitation work. Many of the cracking in masonry walls of the structure

is due to consolidation of the ground. When this kind of problem is detected, one common

method to strengthening is by underpinning the entire foundation.

2.5 Typical failure mechanisms

2.5.1 Historic masonry walls

The mechanical properties of masonry vary from section to section and depend on

the quality of stones and mortar and the interaction between these materials, which lies in

general on its internal distribution.


28

To comprehend the mechanical behaviour of historic masonry buildings, a simple

model of stones and mortar can be analyzed; when masonry is under compression, the

structure develops a shortening in direction of the applied load and a widening in its

transversal direction. Assuming that the mortar is weaker than the units, a bigger

deformation is developed in the mortar during the application of any external load. In the

contact surface the transversal deformation of both materials must coincide, because of the

material interaction, producing a transversal contraction in the mortar and an expansion in

the stone. Due to the low strength of stones in tension, the transversal stresses generate a

cracking that increase with the load and governs the structural capacity to resist axial loads.

To verify the mechanical behaviour of a masonry wall, Berto, Saetta, Scotta, &

Vitaliani (2005) carried out a computational simulation by finite element model analysis

using an isotropic 3-dimensional micro-model based on the hypothesis of strain equivalence.

Two cases were considered and studied. Figure 2-9 shows the deformed mesh at failure of

the first case study; mortar weaker than units. Figure 2-10 represent the failure mode of a

masonry prism subjected to uniaxial compression load with mortar stronger than brick units.

Figure 2- 10 Case 1. Contours of damage variables at failure. (a)Tensile damage. (b)Compressive damage.(Berto, 2005)

To historic masonries with irregular distributions in stones, the failure mechanisms

are different than discussed; this doesn’t develop a transversal crack in the stones, instead of

this, a separation of the units is presented (Meli, 1998). The out of plane in one span leads to

bulging and collapse of the masonry as consequence. In this type of masonry the existence

of transversal stones that can tie in short direction the element becomes very important. As

result the resistance of the masonry has a low relationship with the strength of the stones, and

is more dependent to its distribution into the matrix and mortar quality.


29

Figure 2- 11 Case 2. Contours of damage variables at failure. (a)Tensile damage. (b)Compressive damage.(Berto, 2005)

The structural behaviour of historic masonry buildings against different stresses is

essentially brittle. This exhibits historic masonry buildings to suddenly collapse with few

signals or previous damage when its load capacity is reached.

The tensional strength in historic masonry is very low. To analysis purposes is

highly recommended to consider it as zero, but in many cases a value between 1 and 2

kg/cm2 can be used. The strength against shear is also dominated by stresses in tension, but

this time in diagonal direction, and the values are also low. This shear strength is very

important because the resistance of historic masonry buildings against lateral forces, such as

earthquakes, depends on this value (Meli & Sanchez-Ramirez, 1993).

The following table shows typical values of materials used for the construction of

Spanish historic masonry buildings.

MATERIAL Density

(t/m3)

Compression strength

(kg/cm2)

Shear Strength

(kg/cm2)

Elastic Modulus

(kg/cm2)

Adobe 1.8 2-5 0.5 3000

Tepetate block with cal

mortar

1.8 5-10 0.5 5000

Brick with mud mortar 1.6 5-10 1.0 5000

Brick with cal mortar 1.6 15-20 2.0 10000

Masonry of irregular stones

with cal mortar

2.0 10-15 0.5 5000

Masonry of good quality 2.0 30 2.0 20000


30

stones

Table 2- 1 Mechanical properties of Spanish historic masonry (Meli, 1998)

The main difficulty to determine the structure response and failure mechanisms

comes from the variability of the materials, mechanical properties and building techniques

applied during construction.

According to Mistler, Butenweg, & Meskouris, (2006) a masonry wall can fail in

different ways.

· Shear failure. Characterized by cracks in the mortar and where the case of a strong

mortar – low strength brick is presented, the cracks simply bisect the bricks (Figure

2-11(a)).

· Friction failure. This type of failure is presented when a strong lateral load is applied

to the structure in combination to the low vertical loads of the structure (Figure 2-

11(b)).

· Bending failure. This occurs when the sections are slender in relation with the

vertical loads (Figure 2-11(c)).

Figure 2- 12 Failure modes of masonry panels. (M. Mistler & C. Butenweg & K. Meskouris, 2006)

“The majority of these problems may occur due to decay of masonry materials and

subsequent weakening of the structures, the weak tensile and shear strength of unreinforced

masonry and the inadequate interconnection of the masonry elements” (Hassapis, 2000).


31

2.5.2 Historic masonry arches

For semicircular masonry arches without reinforcement under the application of a

concentrated load at the quarter span, four plastic hinges are expected to appear (Figure 2-

12) (Heyman, 1982).

Figure 2- 13 Four-hinge failure mechanism of a semi-circular masonry arch submitted to an asymmetricalloading (Oliveira, 2006)

An arched masonry structure maintains compression as long as the thrust line

(pressure line) is kept inside the central core. This line represents the compressive force at

each cross-section. When the pressure line moves outside the section, this sections becomes

in tension and the formation and consequent opening of a crack takes place, forming a plastic

hinge at the compressed edge of the arch.

By the using of a bonded FRP reinforcement, the formation of a fourth hinge

mechanism is prevented. Therefore, only three hinges are able to rise, transforming the arch

into an isostatic structure.

In this case four new failure mechanisms are likely to occur (Basilio, Oliveira, &

Lourenco, 2004).

· Shear failure due to sliding along a mortar joint.

· Failure due to masonry crushing.

· Failure due to detachment of the fibbers.

· Failure due to sliding along masonry joint.

Moreover, in addition to the usual stresses parallel to the fibbers, the curved shape of

arches originates stresses with a component normal to the fibbers, which may lead to the

detachment of the reinforcement from masonry (Oliveira, Basilio, & Lourenco, 2006).


32

Sliding between the fibbers and its support is usually neglected since shear stresses

at the FRP-masonry interface are of minor magnitude (Valluzzi & Modena, 2006). Also FRP

tensile failure is not likely to occur due to its high tensile strength.

2.5.3 Historic masonry structures

One big disadvantage of historic masonry structures consist in the very low tensile

strength of its constituents triggering in an absence of capacity to transfer tensional forces or

bending moments between adjacent elements. Moreover, the inertial forces are not correctly

transferred to the ideal elements to resist lateral forces.

The shear and tensile forces developed during earthquakes usually result in cracks at

the main body and disconnections of walls in the intersections.

Cracks can develop diagonally and run either partially or completely through the

masonry piers between window openings due to tensile stresses, or horizontally in masonry

piers between window openings due to alternating bending moments or diagonally above the

wall opening due to shearing (Hassapis, 2000).

In addition, for the case of isolated buildings four main mechanisms were identified

for non repaired structures (Penazzi, Valluzi, Saisi, Binda, & Modena, 2001):

1. Out of plane of loadbearing walls with local or total collapse of the facades or of

the corners, or large deformation of the walls. This mechanism is due to the lack of

connection between orthogonal walls (Fig. 2-13(1)) and between walls and floors or roofs

and to the presence of large openings (Fig. 2-13(2)).

2. Out of plane mechanisms with local or large failures of the upper part of the walls

and collapses of parapets, cornices and spandrels. This occurs due to the thrust of the roof

and absence of connection between the roof and the masonry (Fig. 2-13(3)).

3. Wall disconnection and leaf separation with local or global failures. The presence

of in-homogeneities in the wall, the lack of connection between the leaves of multiple leaf

walls (Fig. 2-7(4)), the filling of openings without good connection between the old and the

new parts or the use of different types of materials can be the causes of such mechanism.

4. In plane mechanisms due to shear stresses with diagonal cracks of piers and walls

at the different floors. They are mainly due to: bad positioned openings, differential stiffness

of the walls between openings, presence of weak lintels (Fig. 2-13(5)).


33

Figure 2- 14 (1)Failure of a building corner, (2)Out of plane collapse of a bearing wall, (3)Partial collapsedue to the thrust of the roof and bad connection tie beam-wall, (4)Separation of the two leaves of a wall,(5)Shear failure of a wall. (Penazzi, 2001)

The elements that present more risk to collapse in case of seismic events are: slender

towers, columns and isolated walls. According to Meli (1998), the failure mode in towers is

less critical than suspected. During the vibration of these elements a successive process of

opening and closing of cracks is presented by actions, bending and sliding of the joints and

horizontal cracking. Such process dissipates energy increasing the damping in the elements

and reducing any collapse threatens.

2.5.3.1 Problems due to new additions

The addition of new buildings to old ones represents another source of problems

under this category. In particular, (Bidwell, 1977) argues that the following considerations

should take place when new extensions are added to already existing buildings:

· Whether and how to tie the new structure to the old one.

· The effect that this may have on the sub-soil conditions and the foundations.

· Whether they will trigger any direct or indirect stresses to the old structure.


34

“Differential settlements are common (due to the addition of new buildings)” (Hassapis,

2000).

2.5.3.2 Problems due to foundation movements

Generally, many historic buildings do not present proper foundations; so, initial

settlements take place in the first years of its life (Cook & Pegram, 1993). However, such

building continues working firmly without compromising the safety of the structure;

normally such changes are likely to stop at an early stage, since structures usually adapt

themselves to their environment reaching to a new equilibrium of internal stresses, especially

when soft mortars were used during the construction of the structure (Feilden, 1994).

Two main sources of foundation movements can be clearly indentified; those

produced by earthquakes and settlements. Earthquake movements generally develop high

stresses into the structure in a short period of time, while for settlement these forces occur in

a long period and due to many causes.

According to Feilden, (1994) common causes responsible for subsidence are the

following:

· Mining nearby the structure;

· Existence of a wall near or underneath the structure;

· Other kinds of excavations near the foundations for purposes of drainage,

construction of basements, etc.;

· Problems caused by trees and creepers;

· Landslides caused by heavy rain, floods, etc.;

· Potholes or caves existing underneath a structure, which have been created by

underground streams;

· Abstraction of groundwater, causing lowering of the water table;

· Rise of the water table, caused by blocked underground water.

· Heavy structures built near old ones, which may change ground strains.

· Vibrations caused by heavy traffic passing from adjacent to an old structure road or

by pile driving operating near the structure.


35

· Gradual geological movements.

· Earthquakes

“When unequal settlement of masonry takes place, the appearance of cracks at the walls

is a common result of the in-plane deformations of the walls” (Hassapis, 2000).

2.5.3.3 Problems due to material deterioration

The durability of historic masonry structures is directly relative to its materials.

There are many cases encouraging the decay of materials. The presence of water is one of

the most common and hazardous ones both directly and indirectly, since it can trigger the

development of various other deterioration mechanisms. Water can help to dissolve mortar,

may reduce the strength of masonry units, may result in the decay of timber and iron, may

lead to frost and chemical crystallisation and may encourage chemical attack and organic

growth (Hassapis, 2000).

Cook & Hicks, (1992) argue that the allowed limit before a structure is deemed

unstable due to creep is dependent upon a variety of factors such as the flexibility of the

materials, their individual susceptibility to creep, the tolerance of the joints between the

different components and the interconnection of the structural elements, all of which are

usually more flexible in this type of structures.

There are many ways of crack to appear; due to moisture, thermal movements and

cracking.

2.6 Assessment methods of historic masonry buildings

2.6.1 Introduction

The study of historic masonry structures becomes complicated in that many

variations of materials and building techniques existed in the past without the guidance of

any established regulation. Most of the masonry structures were built on empirical data

based on experience acquire in previous constructions and following the basic interpretations

of nature, without use of any mathematical analysis.

According to Meli (1998), “The quantitative methods used to determine shape,

dimensions and material properties of the elements into a structure that is required to resist

external loads, are relatively recent. In the past, an important source for the development of

new aesthetic shapes was the observation of structures created by nature; the correct

lecture, interpretation and improvement were the base for new structural solutions”.


36

Even at present our knowledge about the mechanical behaviour of masonry is not

well known as for other materials and many calculation methods for capacity assessments

hardly ever consider the complex behaviour of masonry as a ‘composite’ material.

During the XX century numerical methods of analysis started to increase in

importance due to the employment of approaching methods that in a simple explanation

consisted in corroboration and adjustment by successive approximations until the error was

considered as despicable. This technique required a huge quantity of calculations, and this

method was not employed until the appearing of powerful computers capable of compute

calculations to unimaginable speeds (Meli & Sanchez-Ramirez, 1993).

Another element that increases the use of this method nowadays is the computed

aided engineering (CAE) packages, capable of solve different types of structures under many

different solicitations. The technique of general application for this purpose is widely known

as the Finite Element Method (FEM), it consists in the division of the structure into sub-

elements for which equilibrium and deformation equations are already assigned; boundary

conditions are established in the joints intersecting to two or more elements (Zienkiewicz &

Taylor, 1967).

2.6.2 Scopes and limitations

In the world there is still a preference for the intuitive a qualitative judgment of

historic monuments; however, for the engineer it is always important the support of

analytical models, as well as laboratory test of the material properties.

As discussed before, during the last decades there has been an important

improvement in the experimental and analytical methods for the studies of historic buildings,

also now we can count with powerful analytical tools that allow us to solve complex

structures with a reasonable computational cost. The weak point in these models is the

application of the procedures to determine the parameters and models that define the

response.

Since the preparation of an analytical model confronts many difficulties, starting

from the identification of the structure itself to the definition of its structural geometry. The

conditions of continuity between different elements are very difficult to establish. In historic

masonry buildings the elements sometimes are only one above the other, and exists a

possibility of rotations in the contact surface. There are some cases where the elements can

not be clearly established as a non-structural or structural component.


37

2.6.3 Linear static analyses

It is common to call static methods to those based on the hypothesis in which the

structural material has a linear behaviour, both in tension as compression; the interaction

between the internal deformations and applied stresses increase proportionally. This

hypothesis has allowed to obtain exact solutions for typical structural models, in which, the

equilibrium conditions are satisfied.

However, the behaviour of structural materials is not strictly a linear relationship of

stress-strain deformation; considered acceptable enough for new materials as steel and

concrete, for masonry, nevertheless, the differences are considerable; first, the material has

no strength in tension, by which is subjected to cracking that generates local deformations

and constantly changing in the stress state, this obviously corresponds to a high non-elastic

material. Moreover, masonry is affected by different external agents, as temperature changes,

the diverse deformations in mortar and movement effects in the supports. The big variability

of the material properties from section to section, also changes the stress distribution.

The main objection in the use of the elastic methods is that they don’t recognize the

non-linear behaviour of the masonry.

In summary, accurate results can not be obtained from a static analysis but can be

considered as representative of the structure and be used for the assessing.

2.6.4 Nonlinear static analyses

Nonlinear procedures generally provide a more realistic indication of the demands

on individual components of structures that are loaded significantly beyond their elastic

range of behaviour, than do linear procedures.

Most of the non linear models consider that the properties against tension stresses

are the same than those of compression and that both are invariable against any load. These

limitations are surpassed when in the models the materials are linear in compression, but

have zero strength in tension. The solution of these models requires a nonlinear analysis

method, because the level of load is increased, the size of area under tension increase,

becoming necessary to modify the characteristics of the model during time (Berto, Saetta,

Scotta, & Vitaliani, 2005).

They are particularly useful in that they provide for (Petkovski, 2007):

• More realistic estimates of force demands on potentially brittle components (force-

controlled actions), such as axial loads on columns and braces.


38

• More realistic estimates of deformation demands for elements that must deform

inelastically in order to dissipate energy imparted to the structure by ground motions.

• More realistic estimates of the effects of individual component strength and

stiffness degradation under large inelastic demands.

• More realistic estimates of inter-story drifts that account for strength and stiffness

discontinuities that may develop during inelastic response.

• Identification of critical regions in which large deformation demands may occur

and in which particular care should be taken in detailing for ductile behaviour.

• Identification of strength discontinuities in plan or elevation that can lead to

changes in dynamic characteristics in the inelastic range.

2.6.5 Dynamic analyses

The calculus of the effects over the structures produces external variations; it is

considered that the last has constant values in time (that proceed in static form). This is valid

for its own weight and for some solicitations as differential movements and contraction due

to changes in temperature.

Nevertheless, there are situations in which is important to do a dynamic analysis in

historic masonry, for example when there are high frequency vibrations, induced by traffic or

vibratory equipment, and the seismic response in situations in which the dynamic effect

results important at a local or global level.

Probably the must important tool for dynamic analyses can be the eigenfrequencies

and modal shapes. This allows evaluating the importance of the dynamic effects induced by

external agents.

To solve this, preference has been given to the employment of dynamic elastic

analyses, where the stiffness properties are modified manually. As a result, many

methodologies have been proposed, see (Ramos & Lourenco, 2005; Mistler, Butenweg, &

Meskouris, 2006 and Cardoso, Lopes, & Bento, 2005), where the modifications are guessed

from the result of the first analysis and results are compared according to the seismic

vulnerability of the structure.

2.6.6 Numerical modelling

For the structural modelling of masonry historic buildings the use of a three-

dimensional finite element model become necessary to obtain accurate results. This


39

numerical analysis is also found to be questionable due to many factors: the anisotropy and

decay of the constitutive materials, the fact that consists of two materials with different

properties and without any tensional strength. These factors trigger the developing of cracks

at any section affecting the global characteristics of the element. But, in spite of many

uncertainties, though, numerical models are considered as a very useful tool that used in

combination with experimental work can be very effective in the assessment of historic

masonry buildings.

The first attempt for the analytical treatment of monuments built of fitted stones

under dynamic excitation was presented by Housner (1963).

In actuality, to carry out a structural analysis for old masonry structures, many

engineers model the materials linked to linear behaviour without consider the whole complex

performance of masonry (as a composite material with anisotropic properties). This method

does not describe a realistic performance of the structure but, as stated before, gives an idea

about the main causes of failure and its more accessible and less cost-time consuming in

comparison with other methods, e.g. non-linear micro-models.

Lourenco (2005) point out that it is essential to verify the adequacy of the models

with the existing building; this can be carried out with different techniques, mainly flat-jack

testing or dynamic identification, but also a comparison with the damage survey (cracks,

displacements) is allowed.

According to (Syrmakezis, Asteris, & Mavrouli, 2006), the young’s modulus of

elasticity, E, is a parameter that determinatively influences the masonry’s response. For

micro-analysis purposes, materials are assigned with a value that can be determined from

experimental, destructive or non-destructive testing. For macro-analysis the value is selected

either using proper equations or as explained in chapter 2.5.1 by analytical evaluation of a

masonry block, for a model consisting of two blocks and a mortar joint.

2.6.6.1 Finite element method

The finite element method of analysis makes use of different finite elements: One-

dimensional (bar, frames), Two-dimensional (shell, plate, membrane) and Three-dimensional

(solid). For the simulation of the influence of composite materials in the structure, micro or

macro-analysis can be used, depending on the accuracy desired. During micro-analysis,

blocks, mortar and the interface are simulated separately simulating the contact nonlinearity,

while for macro-analysis, a homogeneous material represent the masonry behaviour. The


40

deformability in this type of models is considered by discretization of the mesh into finite

elements.

There are different approaching techniques to model a composite masonry structure

based on the finite element method (Figure 2-14). In the first one, each brick, mortar and

boundary are modelled by separated, so a large number of micro-models are produced to

simulate the nonlinear behaviour of each element. For the second, the bricks and the

boundaries are modelled together so the grout elements (mortar) are assumed of zero

thickness. This model is computationally less demanding and allows to be used on large

structures under dynamic loads. For this model the global behaviour has to be defined.

For the first previous mentioned approaching method, the accuracy found in the

results is very high, but is very expensive computationally speaking been suitable only for

small elements.

Figure 2- 15 Different FEM approaches for modelling masonry. (M. Mistler & C. Butenweg & K. Meskouris,2006)

2.7 Seismic safety

The historic masonry buildings are mainly very heavy and structurally stiff.

Therefore, high inertia forces that depend on the product of the mass and acceleration are

generated. As a result, the frequency of the vibration modes is typically between 1 and 4 Hz;

located in the interval where the dominant frequencies of dominant earthquakes are found

(Meli, 1998). Moreover, Cardoso, Lopes, & Bento, (2005) argued that a far distance

earthquake, with low frequency contents, is the one that induces higher accelerations to this

type of structures. This directs us to observe that the accelerations presented in this type of

buildings are very elevated and the damages are considerable.


41

As result, the masonry in historic buildings has a nonlinear anisotropic behaviour

and a post-peak load-carrying capacity, perhaps one of the keys to why buildings sometimes

withstand seismic load far beyond of its considered limits. So, the overall behaviour of

historic masonry structures is brittle and nonlinear.

The concept of redundancy is extremely important to the design of structures for

seismic resistance and a very important point to be taken into account for the assessment of

historic masonry buildings. In a redundant structure, multiple elements (or components) will

be available to resist forces induced. Individual components of the structure will be strained

beyond their elastic range. As this occurs, the structure starts to experience damage in the

form of cracking, spalling, buckling, and yielding of the various components. As

components become damaged, they degrade in stiffness, and some elements will begin to

lose their strength. All the brittle elements into the structure are not able to sustain inelastic

deformations and will fail suddenly (Petkovski, 2007).

Architectural walls and partitions can affect the stiffness of structural elements and

also introduce soft story and torsional conditions into otherwise regular buildings. Therefore,

many engineers having this in mind add extra lumped masses to simulate the effect of non-

structural elements in the total behaviour.

Obviously an analytical refinement does not eliminates the considerations previously

commented and must be taken into account for this type of structures, in particular in historic

masonry buildings; where the elegance and apparent perfection of the finite element method

can make to loose contact with the real structure.

2.8 Rehabilitation methods

According to Pearson (2007), rehabilitation interventions in historic masonry

structures can be classified into two concepts. First, the repair concept; carried out for

structures in which the deficiencies are related to isolated structures with typical modes of

failure, known to cause a poor earthquake performance in the past. This is based on the

insertion of new materials into parts of the existing historic masonry. Second, the

strengthening concept; a process in which a complete analysis of the structure is performed,

here the objectives are checked for adequacy to resist strength and deformation demands

against different solicitations; mainly those derived from earthquakes.

During any rehabilitation work special care most be taken for discontinuity in the

flow of forces, alterations in the existing structural systems and local differences in rigidity

could lead to shifts in load transfer that inevitably become into cracks.


42

There are numerous techniques aiming to the consolidation of decayed masonry

structures and materials.

When working on historic and, in particular, listed structures, repairs should ideally

be carried out using similar materials to the original. Not only are more appropriate to the

historic character of the architecture, but they usually work better than modern alternatives,

especially when used in conjunction with other traditional materials and construction

techniques (Bennett, 2002).

2.8.1 Repointing

According to (Ashurst, 1988c) pointing is the process of filling the outer part of the

joints between masonry units, where the bedding mortar has been deliberately left or raked

back from the surface or where the original mortar has weathered.

Repointing represents an important repair method in historic buildings, because it

can radically change the character and appearance of the structures and protect them from

various causes of decay.

The selection of the appropriate mortar becomes a very important issue in the

effectiveness of this technique. A soft mortar than the units can absorb stresses developed

through movements of the adjacent masonry, while a hard mortar will produce cracks

between mortar and bricks or will cause spalling (Figure 2-15).

Figure 2- 16 Impact on masonry of using (a)Repointing with soft mortar. (b)Repointing with hard mortar.(Pearson, 2007)

“Repairs using inappropriate materials can also trigger a variety of masonry

problems. In particular, stiffer mortars have been seen to lead to extensive problems when

used on masonry walls, due to their excessive strength and impermeable matrix compared to

original masonry materials” (Hassapis, 2000).


43

2.8.2 Grouting

“Is a term used for the introduction into a structure or into the ground of a material

in liquid form, which subsequently cures or sets into a durable solid or gel form” (Hassapis,

2000).

The evaluation of repair documents, the computational analysis of stress conditions

in repaired masonry and the knowledge obtained from interference into the substance by

experimental test, prove that there is an increase in load-bearing capacity after injection. This

is obviously caused by the reduction of cavities and faulty areas in the old masonry. Loads

can then be transferred directly and peaks of strain can be reduced.

The degree of injection depends on the specific components of the old masonry

being repaired or strengthened and on its structure and moisture content, on the composition

of the suspension as well as on the procedure selected to prepare and carry out the injection,

including the applied pressure.

In contrast to the apprehension on the part of monument preservation, it has been

discovered that hardly any new injection material intrudes into the old mortar. The grout fills

the cracks, voids and cavities, basically remains in the damaged and faulty areas of the

masonry, and does not penetrate the old mortar in the sense of a mixture. With this

exception, areas of contact between both materials are limited to the surfaces of cracks,

cavities and drill-holes resulting in more or less abrupt and plane marginal zones (Pearson,

2007).

There are various methods of grouting, the most important of which are presented

next: hand grouting, pressed injection or pumped system, vacuum system and gravity

grouting.

2.8.3 Pinning

Pinning is more repair technique than a strengthening one. The process involves the

insertion of pins into holes left by missing stones and drilled holes. During the process it is

important to replace any missing pinnings or loose stones back into their original position

and to ensure that all the replaced stones make physical contact each other. It is also used for

replacing old masonry units or for redressing the faces of old units. Small fractures and voids

can be also repaired with this method. The insertion of the pins removes the resins or grouts,

which, consequently, flow into internal cracks and fissures (Coonie, 1992).


44

In doing so, this gives the wall back its full structural strength and original

appearance. Any missing pinning stones will generally be revealed by the remaining wide

joints.

2.8.4 Stitching

In general, stitching as subsequent reinforcement happens where tension or thrust

occurs which the masonry cannot withstand. Stitching is always connected with grout

injection to form the bond between steel and masonry as well as to provide corrosion

protection. In multi-leaf masonry the reinforcement bars connect the two outer leaves

through the inner filling which was strengthened by injection. As the outer leaves are usually

only one stone thick, special attention must be paid to the anchorage of the bars (Pearson,

2007).

In particular, the diameter of the drilled holes is approximately 20-40mm wide,

while the diameter of the reinforcement is usually the 12-15mm. The amount of holes drilled

per unit area is dependent on the conditions and nature of the structure, its weakness etc., but

many times there are 3-4 hoes per square meter of wall surface. The length of the holes is

usually about three times the wall´s thickness (Souden, 1990)

2.8.5 Overall strengthening of old masonry

For seismic strengthening of historic masonry buildings, the solutions usually consist

in corrections that guide us to a better behaviour against any movement in the base.

When inadequate seismic structural response is detected, actions can be directed to

different objectives: reduction in the overall weight (directed to top stories); elimination of

any asymmetric configuration in plan; continuity between the elements that transmit the

seismic forces.

2.8.6 Fibre Reinforced Polymer (FRP)

Among the innovating techniques to rehabilitate deteriorated structures, there is a

new method that has been gaining acceptation in the market due to its several advantages;

commonly know as FRP.

According to Pilakoutas (2007), some of its advantages are:

· Strength/Specify gravity (10-15 times than steel)

· Corrosion immunity


45

· Fatigue characteristics

· Electromagnetic Neutrality

· Effective solution in aggressive environments

· Temperature resistance

· Low density

As a result, all this advantages makes FRR highly attractive and cost effective to be

used as a common material in strengthening works. Moreover, the use of FRP in special

applications in construction becomes cost-effective due to durability improvement, reduced

life-cycle maintenance cost and also savings from easier transportation and enhancement on

site-productivity (Triantafillou & Fardis, 1997).

Schwegler (1994) was the first person to propose and study the use of carbon

laminates as strengthening elements for masonry structures (Figure 2-16).

Figure 2- 17 Masonry strengthening solutions with FRP composites (Oprisan at. al. 2004)

Carbon, glass and aramid fibres exhibit a linear elastic behaviour under tensile

loading up to failure. Due to the absence of plastic flow at yield, FRP composites are

incapable of relieving stress concentrations.


46

Components Specific

weight

(Ton/m3)

Tensile

elastic

modulus

(kg/cm2)

Compression

elastic

modulus

(kg/cm2)

Direct tensile

strength

(kg/cm2)

Tensile

strength per

unit width

(N/cm)

Heat

expansion

coefficient

[10-6(1/˚C)]

Ultimate

strain (%)

Carbon fibre1 1,820 2,300,000 - 35,000 5,660 - 1.5

Epoxy matrix2 1,020 30,000 - 500 - 60 2.5

Glass fibre2 2,490 870,000 - - - 5 5.5

Glass net - - - - 900 - -

Cement

matrix3

2,000 - 150,000 33 - 6 0-01

Table 2- 2 Technical specification of reinforced polymers.

Carbon fibres show high specific strength and stiffness, as the elastic modulus

increases, ultimate tensile strength and failure elongation decrease. Compressive strengths of

FRPs are much lower than the tensile strengths (Table 2-2).

“Composites are materials consisting of two or more chemically distinct

constituents on a macro-scale, having a distinct interface separating them, and with

properties which cannot be obtained by any constituent working individually” (Pilakoutas,

2007).

One of the main conclusions from studies is that, for the sake of both economy and

effective mechanical response, unidirectional FRP reinforcement in the form of strips (that is

100 - 300 mm wide bands) is preferable than two-dimensional fabrics that cover the whole

surface.

2.8.6.1 Strengthening of vaults and arches

These elements work by gravity transferring all the loads to walls and buttresses.

The instability is presented when there is an opening in the supports, modifying the centre of

pressure. In the Figure 2-17 is illustrated a typical repair of these elements. Basically consists

in the consolidation of masonry and reinforcement with layers of mortars and reinforcement

bars.

1 MAC S.p.a., Treviso, Italy.2 GAVAZZI S.p.a., Lecco, Italy.3 Produced in laboratory.


47

Figure 2- 18 (a)Reinforcement of vault with mortar. (b)Reinforcement with reinforced concrete.

Numerous experimental works were carried out showing that FRP technique is

effectively valid as an option to strengthen or repair masonry structures, in particular arches

ones, see (Valluzzi, Valdemarca, & Modena, 2001), (Lissel & Gayevoy, 2003) and

(Foraboshi, 2004) for further details. On the other hand, available experimental results show

that the strengthening of masonry arches with glass fibbers, which exhibit lower mechanical

properties than carbon ones, allow a better control of the collapse mechanisms and provide

higher strength and better global ductility characteristics (Valluzzi, Valdemarca, & Modena,

2001).

According to numerical model experiments realized by Basilio, Oliveira, & Lourenco

(2004), an unreinforced arch shows that the interface opening produces separation between

the bricks causing the developing of plastic hinge rotation and collapse due to sliding at the

abutments. Arches with full length CFRP reinforcement placed at the intrados present higher

peak load values when they are compared with full length CFRP reinforcement placed at the

extrados (Figure 2-18).

For both full length and partial length reinforcements, the optimal width is

approximately 14cms. Beyond this value only marginal increase in the load values is

observed.

Basilio, Oliveira, & Lourenco (2004) argued that the adoption of full length CFRP

reinforcement instead of partial length reinforcement at the intrados originates an important

increase in the peak loads. Consideration must be taken when simultaneous partial length

reinforcement option is used, since the location of plastic hinges might change causing

openin of the joints.

a) b)

Strengthening with mortar

Longitudinal wall

Landfill

Reinforcement withconcrete beams in theperimeter

Buttresses

Landfill

Reinforcement with aconcrete& steel layer

Arches

Longitudinalwall

Column

Vault


48

Figure 2- 19 Summary for the full length CFRP reinforcement at the intrados and extrados. (Basilio, Oliveira, &Lourenco, 2004).

Figure 2- 20 Strengthening arrangements adopted: (a)Localized strengthening; (b)Continuous intradosstrengthening; (c)Continuous extrados strengthening. (Oliveira, Basilio, & Lourenco, 2006).


49

Many issues are relevant with respect to the strengthening of masonry arches with

composite materials. It is argued (Basilio, Oliveira, & Lourenco, 2004) that when the CFRP

reinforcement is placed at the intrados, it contributes to holding the bricks together. Also,

experimental research (Figure 2-19) has showed that for arches strengthened at the extrados,

sliding along the joints is the prevalent failure mechanism. A solution can be resolved by

increasing the amount of material near the abutments.

If we follow these experimentations, the fibres are able to maintain equilibrium until

total collapse of the specimens by adding continuous reinforcement at intrados. Another

important feature is the large deformation capacity exhibited prior to failure, providing to the

arches with important ductility behaviour.


50

3 CASE STUDY

3.1 Historic background

The selected structure (Figure 3-1) is an old temple located in San Cristobal de las

Casas, Chiapas. In order of importance, the Santo Domingo Church was second after

Guatemala, but the first Dominican settlement in south of Mexico. The first stone was placed

by Francisco Marroquín, a Franciscan bishop of Guatemala, the 19 of January of 1547 and

the entire construction was completed in the year of 1551 (Sidney, 1984).

Figure 3- 1 The front entry of the Church of Santo Domingo de Guzman in San Cristobal de Las Casas.(Agguizar)


51

Both Convent and Church have been under repair, modifications and even total

reconstruction during more than 400 years. Though the temple was built in the second half of

XVI century, very little from the first edification actually remains. The main body and the

adjacent modules probably come from the last third of XVII century, while the monumental

facade was built in the beginnings of the XVIII century (Sidney, 1984).

Taking advantage of the location of the Church (into a seismic active region) an

assessment of its seismic behaviour is carried out and presented in the following chapters.

3.3 Geometrical data of the structure

The Temple of Santo Domingo is a clear construction of Spanish inspiration. The

plan view inscribes a cross (67.50m x 43.70m); in the connection a big cupola communicates

with the adjacent modules. In the first section of the building two towers take part over the

main facade followed by the chorus allocated above a mezzanine. The mezzanine is formed

by a vault in which a landfill was applied in the top to reach a horizontal surface. The roof is

vaulted, spanning over masonry walls (Figure 3-2).

8

7

6

5

4

3

2

1

a B C D E F G H

Figure 3- 2 Plan section of the Santo Domingo Cathedral

There is a certain variation in the depth of the walls due to the constantly repairs

carried out in the past. This works led to enhance the reinforcement, such as increasing the


52

dimensions of the masonry walls and addition of buttresses. The depth of the walls is as

follows: in the front wall, is around 3.10m, from which 90cms can be counted as

architectural detailing; the towers in the front are solid buttresses made of masonry with

1.30m in depth and 2.30 in width; the choir walls are 2.30m in depth; the walls supporting

the vault are thinner, approximately 2.00m; the longitudinal walls in the cross are 2.30m at

floor level, but reduced in the niches formed by arches, giving us a dimension of 1.55m to

1.60m in depth.

The height of the structure from the base to the towers is of 27.46m; from the base to

the vaulted roof, 16.31m. The main facade is clearly of baroque inspiration (Figure 3-3).

Figure 3- 3 Main facade of the Santo Domingo Church

Complete drawings of the Church are included in Annexe 2.

3.3 Characteristics of the materials

Masonry walls are conformed by a combination of local quarry stones and lime

mortar mixed with agave sap added as additive to increase the viscosity and gluing

properties of the mixture. The roof in the beginning was build with wood; after its collapse,

adobe bricks with lime mortar were used to form the vaulted roof.


53

The Material distribution of the Temple is shown in Figure 3-4 and Table 3-1; this

includes all the material values used in the numerical model. These values were based on

values proposed by (Meli, 1998).

Figure 3- 4 Historic materials distribution

Number Name Ρ (Ton/m3) E(kg/cm2) f’c(kg/cm2)

1 Brick masonry with lime

mortar

1.6 10000 15

2 Irregular stone masonry

with thick lime mortar

2.0 10000 15

Table 3- 1 Historic Materials

3.4 Development of the Finite Element model

Even when in the last decades important improvements have been achieved in

analysis techniques, the preparation of any analytical model confronts some difficulties. The

geometry is a lot more elaborated than for modern buildings and in many cases is very

difficult to distinguish between structural and non-structural (decorative) elements. There is

also an uncertainty about the materials employed for its construction; in consequence some

information related to the mechanical properties of the materials is not accurate.

The developing of the numerical model first started with the generation of a 3D

geometry model based on the drawings and information taken by previous data.


54

Due to the complexity of the structure geometry, it was divided into sub-models.

Each one was built using isoparametric three and four-node shell elements. The adjacent

temple surrounding the Church in one of the sides, which has positive influence on the

dynamic behaviour, was not considered leading to conservative results.

The basement conditions were found satisfactory and no failure in the foundations

has been reported during the life of the structure. Therefore, the boundary conditions of the

numerical model were modelled rigidly fixed at the bottom and did not include any soil

structure interaction effects.

Many experienced engineers in the area agree that for the use of a homogenized

model, the nonlinear behaviour of the material properties needs to be calibrated with the

modal characteristics of the structure and some testing must be done to obtain some

parameters (Binda, Penazzi, & Saisi, 2003; Lourenco, 2006; Meli, 1998), but in accordance

with Mistler, Butenweg, & Meskouris (2006) and due to absence of information, the

characteristic values of the constituents (which are known for a wide variety of brick and

mortar types) were used as input variables of the numerical model. In addition, different

depths were used in the vault, taken into account the recurrent variation from thin to thick as

the arch approach to the supports.

Masonry walls were modelled as isotropic elastic homogeneous material using a

uniaxial failure criterion. Most of the finite elements employed are shell type, allowing all

kind of actions.

Shall be considered that the walls are in reality composed by rocks of different sizes

and in some areas the density of these varies in relationship with the mortar.

The adopted model validation technique was executed by means of deformed shapes

evaluation, comparison with the damage exhibited by the church in the reality and

correlation of resulting fundamental frequencies with similar works.

After completion of all sub-models, the overall structure was assembled and

exported to SAP2000® to execute multimodal, response spectrum and time history linear

analyses.

It must be clarified that even when this model is useful for a seismic assessment,

must not be considered as an exact representation of the structure. It is common that a

precise estimation of the stresses in this type of structures is difficult to obtain. Many issues,

as nonlinear material properties and ground conditions were not integrated into the numerical

simulation. In some cases, there were some uncertainties about the correct size of the


55

materials depth into each wall. So, results obtained with linear behaviour modelling can not

be supposed as exact, but instead can be considered qualitatively correct.

In the next the characteristics of the main models are described.

Single Arch model

A model (Figure 3-5) built with 711 frame elements and 515 shell elements was

employed to study the stress distribution and failure mechanisms in the arches. Due to the

simplicity of the structure and for more confidence in the results; a refined mesh employing a

discretization of 0.5mx0.5m per element was produced.

Figure 3- 5 (a)Finite Element model of a single arch, (b)Discretization of the model.

Global Model of the Church

Figure 3- 6 Santo Domingo church.

a) b)


56

Due to the computational cost of analyze a 3D model on solid elements, a simplified

model (Figure 3-6) was employed; it is based on shell elements with homogenized material

properties. The model includes 6714 frame elements and 1568 shell elements (Figure 3-7).

Figure 3- 7 Analytical model of the structure.

This model was employed to observe the stress distribution due to seismic actions; to

visualize the deformations in the towers and arch elements and the overall capacity to resist

lateral movements.

3.5 Seismic assessment of the structure

3.5.1 Static System configuration

As it has been explained in the first part of this document, it is normal to expect a

good static behaviour from arches and vaulted structures. The best prove of its good load-

carrying behaviour is that are still there remaining with the time.

Another important aspect of the static system in terms of horizontal loads is the way

the forces are distributed in the connexion of the main copula with the perimeter walls and

pendentives.

The most typical failure in vaulted areas is due to load concentration at any point in

the spanning section. This can be minimized by adding landfill at the extremes in the

extrados face of the vault. This increases the amount area to be in compression in sections


57

near to the supports. In this way the pressure line is maintained in compression in this

section.

3.5.2 Previous repairs

Many repairs were carried out through its existence. A new wall had to be rebuilt

due to its partial collapse during a seismic event in XIX; years later, the whole roof was

substituted by a masonry vault (Figure 3-9). In addition, minimal repair works have been

carried out during the last years. Restitution was made in the mezzanine and roof floors and

the rear facade was repaired by grouting the cracks (Figure 3-8).

An extra section was added to the building in module C during the XX century. This

section has helped to the structure to withstand several earthquakes through the years.

The last repair works carried out on the structure includes: Changing in the

fulfilment of the vault, by cement:sand:lime aggregate. Cleaning and painting of decorative

elements. Any structural interventions have being taken place in actuality.

The next figures show the areas that have been repaired during the existence of the

structure.

20.98

13.63

18.15

9.11

87654321

8.29 5.40 6.06 2.50 6.85 3.95 8.28

41.32

GROUTING OF CRACKS

Figure 3- 8 Grouting work


58

PROYECCION

a B C D E F G H

7.50 5.35 9.10 8.80 9.80 2.45 10.62

2.44

CASA CURAL

1.55

1.68

1.81

1.39

1.72

5.32

1.59

1.59

1.66

15.09

3.02 3.55 1.50 3.32 1.53

2.994.012.125.501.319.063.96 3.63 8.17

40.74

12.93

15.671.030.882.01

63.44

4.73

2.70 2.43

4.063.652.78

8

7

6

5

4

3

2

1

8.29

5.40

6.06

2.50

6.85

3.95

8.28

RESTITUTION OF ROOF

MASONRY WALL SUBSTITUTION

Figure 3- 9 Restitution works effectuated in the past

3.5.3 Analysis of the model

Analysis comprises: Model creation, stress calculation and failure evaluation.

As stated before, to calibrate the computations that define the capacity degradation

of the numerical model; the results obtained from the analytical calculations where compared

with the damage presented into the original structure. With this, an attempt was made to

model dynamic response in a simple way suitable for computational analyses, but with

satisfying final results on the behaviour at individual levels (Gavrilovic, Ginell, & Sendova,

2001).

The process to establish a final model was: geometry definition, drawing creation,

boundary definition, material definition, load cases definition, dynamic properties definition,

analysis process, connection checking, behaviour checking, result comparison, fixing of

tentative problems in the numerical model.

After the analytical model is established, the structure is divided into 3 modules in

order to simplify the interpretations of the results. The following figure illustrates such

distribution as well as joint locations later used in time history analysis.


59

Figure 3- 10 (a)Joints location into the numerical model. (b)Sections distribution.

3.5.3.1 Static analysis

In the following, pictures with different stress contours of the structure are shown.

Negative values are treated as compressive stresses and positive values as tensile stresses.

All values in the figures are indicated in kg/cm2.

3.5.3.1.1 Single arch model

For assessing the stress distribution in a typical single arch, a four-node shell

element based model was employed.

Figure 3- 11 Principal maximum (a) and minimum (b) stresses under dead load.

The Figure 3-11 shows the principal stress distribution in the structure. It can be

notice from the drawings that 4 plastic hinges are likely to develop. This stresses are not

a) b)

Joint 591

Joint 578

Joint 588

Joint 591

Module C

Module A

Module B

X

Y

a) b)


60

bigger than 5kg/cm2 for compressive stresses but increases near to 13kg/cm2 in some small

individual areas. Very low tensile stresses are observed to take place.

In spite of having a heavy structure, the stresses due to vertical load are slightly

important comparing with the compression strength of masonry. The strength considered for

masonry is in the range of 15 kg/cm2. Probably for the masonry ordered in the core the

strength is even greater than considered.

3.5.3.1.2 Global model

For the gravity load case, the own weight of the structure produces compressive

stresses in most part of the vaulted area, whit low tensions in some zones. This tensional

stresses are known to be prompted to develop a failure mechanism in elements with the arch

configuration. The common zone were tensional stresses appear is in the bottom at middle

span of the arches; see (Figure 3-12).

It can be notice that the maximum compressions in most cases are lower than

3kg/cm2.

Figure 3- 12 (a)Principal compressive stresses under dead load. (b)Principal stresses of main arches underdead load.

3.5.3.1.3 Concluding remark

This analysis demonstrates that under the assumption of a homogeneous material,

the structure should not present any damage due to vertical loading. The maximum

compression stresses produced by gravitational loads, are between the admissible limits. It is

clear that the resultant force in arches and vaults in any section is inside of its core.

a) b)


61

The localized damage of the structure, the stability of the structure without any

differential movements detected, and the excellent conditions of the foundations, indicate

that must of the observed past damage is due to seismic events.

3.5.3.2 Modal analysis

For the modal analysis, the resulted fundamental modes are lower than expected;

such difference can be attributed to the developing of cracks and foundation flexibility in the

real structure, which were not taken into account for this study case.

The Table 3-2 shows the natural periods and modes of vibration for the first 10

modes. Complete tables of modal participating mass ratios and modal periods and

frequencies can be found in Annexe 3.

Modal Participating Mass RatiosOutputCase StepType StepNum Period UX UY UZ SumUX SumUY SumUZ

Text Text Unitless Sec Unitless Unitless Unitless Unitless Unitless Unitless

MODAL Mode 1 0.282433 0.02015 0.001882 0.000002322 0.02015 0.001882 0.000002322

MODAL Mode 2 0.235932 0.008672 0.01779 0.000002503 0.02882 0.01967 0.000004826

MODAL Mode 3 0.231895 0.12 0.04748 0.000001625 0.15 0.06715 0.000006451

MODAL Mode 4 0.219753 0.01437 0.44 0.0001192 0.16 0.51 0.0001257

MODAL Mode 5 0.17981 0.03507 0.02161 0.000003126 0.2 0.53 0.0001288

MODAL Mode 6 0.157572 0.0762 0.00004178 0.00003837 0.27 0.53 0.0001671

MODAL Mode 7 0.140973 0.008581 0.03486 0.0008166 0.28 0.57 0.0009837

Table 3- 2 Modal Participating ratios for each mode.

Figure 3- 13 (a) First mode of vibration (T=0.28sec). (b) Second mode of vibration (T=0.23sec).

In the first two modes of vibration (Figures 3-13) both towers are excited in X-direction. This mode has an effective mass of 2%, confirming that is a particular vibrationmode of the towers.

The third mode (figure 3-14) acts along X-direction exciting one side of thestructure, affecting both tower and the module C. This mode has an effective participatingmass of 12%, becoming an important mode for the structure.

a) b)


62

Figure 3- 14 Third mode of vibration (T=0.23sec)

Figure 3- 15 Fourth mode of vibration (T=0.22sec).

The fourth mode (Figure 3-15) is related to the excitation of the structure in Y-direction having a torsional effect on the structure. In addition a sagging effect can belocalized in the walls of the main vault. The constant lateral movement of the structure originthe development of compressive and tensile stresses in the adjacent buildings, which act asbuttresses of the main body. The differences in height between the two buildings cause anegative interaction in the walls and cupola. This mode is the most important for theresponse of the structure against seismic actions because it affects 44% of the total mass.

The following modes are less important, and basically excite the structure in atorsional mode.


63

3.5.3.3 Response spectrum analysis

The seismic area under which the Church is stand was found B, corresponding to a

C=0.3g. The predominant type of soils corresponds to a very high load capacity soil formed

mostly by rocks.

The response spectrum was defined according to the Mexican code (Mexican-

Norms, 2007), which is the one used in the local area (Figure 3-16). The response spectrum

analyses were carried out in both longitudinal and transversal directions. The internal forces

were computed according to the SRSS rule and superposed with 30% in each direction in

accordance to the NTC (Mexican-Norms, 2007).

Figure 3- 16 Response Spectrum according to NTC.

The code requires that the effective mass of the considered modes to be greater than

90% of the overall mass of the structure and that every mode with an effective mass greater

than 5% must be taken into account. These requirements were satisfied by using the first 50

modes.

Damping estimation in historic masonry structures is a critical issue. Due to lack of

experimental measurements that can establish a proper damping value and moreover due to

the unique of this type of structures, a damping value of 5% was chosen for the numerical

analyses; considering the appearing of cracks and sliding in the joints. The software used for

the earthquake simulation was SAP2000®.

3.5.3.3.1 Single arch model

For the study of seismic actions, the displacement of the structure was restrained in

its perpendicular direction.

00.02520.05040.07560.1008

0.1260.15120.17640.20160.2268

0.2520.27720.30240.3276

0 0.5 1 1.5 2 2.5 3 3.5 4

Sd(g

)

T(s)

ERS type 1


64

Figure 3- 17 (a)Shear stress diagram and deformed shape. (b)Stress diagram under earthquake loading inprincipal direction.

It was observed tensional stresses lower than 1kg/cm2 in most of the structure, but

surpassed in the bottom of supports and arch connections (Figure 3-17).


The finite element model previously discussed and shown in (Figure 3-6) and

(Figure 3-7) was presented for the study of the seismic structural behaviour of the Santo

Domingo church. All the dimensions where obtained from drawings of previous repair

works.

As concluded before, the structure of the church is clearly conceived to sustain

gravity loads. Sometimes the characteristics of the materials impede an adequate seismic

behaviour; a very heavy structure with very low carrying capacity and low ductility. In this

case a response spectra analysis is carried out to corroborate the seismic safety of the

structure.

Seismic actions are frequently variable. For earthquakes of low intensity it can be

expected that all sections present a minimum displacement, maintaining the section under

compression or perhaps with tolerable tensions. Nevertheless, in strong events, the structure

can develop high tensile stresses. In the actual condition, these tensions could origin the

collapse of the towers.

The linear response spectrum analysis of the global structure shows that the design

spectrum would produce maximum tensile stresses of around 3 kg/cm2 at the towers and

walls of module C (Figure 3-18). This clarify that with the addition of an extra section in the

Module C, the structure gained more arguments to withstand lateral forces and avoid the

collapse of one of the cupolas.

a) b)a) b)


65

Figure 3- 18 (a)Principal stresses in Y-direction due to earthquake. (b)Principal stresses in X-direction dueto earthquake.

The Figure 3-19 shows in a magnified scale, the maximum displacements originated

by the design earthquake acting in X and Y directions. The maximum displacement is

presented in the top part of the towers, and it’s about 2cms in X-direction. It can be notice

that in the main structure the maximum horizontal displacement is of 0.5cms. For the

displacements along Y-direction it shows that the vaulted body displaces around 2cms, this

behaviour can lead to the detachment between the vault and its supports.

Figure 3- 19(a)Displacement contours originated by the design spectra in Y-direction. (b)Displacement contoursoriginated by the design spectra in X-direction(Contours in cms).


Estimating that all the components will remain intact, the structural system shows a

good behaviour against its own weight and low intensity earthquakes. The forces are

transmitted axially with low stresses due to the big size of the elements. This allows masonry

a) b)

a) b)


66

to resist moderate compressive and shear stresses. Otherwise, a large earthquake will cause

local damage causing arches and vaults to separate from its connection with the walls.

I would like to mention that the real structure shows a cracking in the middle span of

the vault. According to these findings it should be considered that the geometry of the vault

is suitable enough to avoid a separation between the vault and walls, but instead of this, a

plastic hinge is developed at the middle span.

As result, the computations with the response spectrum method show a good

structural behaviour of the church against low seismic events, but for the case of high

intensity earthquakes, local failures leading to local collapse in the vault are substantially to

take place and must be studied by refined methods.

3.5.3.4 Time history analysis

Time History analyses were carried out to verify the results from the response

spectrum analysis and to compute the internal forces and displacements as a function of time.

For this purpose, recordings of the 21 of October of 1995 earthquake on hard ground at a

distance of about 100 km from the epicentre and with a magnitude of Ms=6.2 were used.

The record samples the near field strong motions that triggered damage to some buildings in

the city. The duration of the recording of the motion is about 165 sec. and the maximum

accelerations are 348.61cm/s2 in the N-S direction and 441.95cm/s2 in the E-W direction

(Figure 3-20). For the computation the accelerograms are applied in two horizontal

directions as in the response spectrum analysis.

Figure 3- 20 (a) 1995 earthquake accelerograms in N-S direction (b) 1995 Earthquake accelerograms in E-W direction


Tensile stresses of 2kg/cm2 above the limit of the proposed material strength are

observed in the two towers (Figure 3-21). Tensile stresses are observed in the connection

between the main body and the adjacent module that can lead in the disconnection in some

areas.

a) b)


67

Figure 3- 21 (a)Stresses diagram in Y-direction [95 Earthquake]. (b)Stresses diagram in X-direction [95Earthquake].

The next figure shows the development of relative low tensional stresses in the

intrados of the main arches. To reduce the detachment of units at the extrados face, the

addition of a GFRP plate is proposed to increase the tensile capacity of the structure and to

add an extra bonding between the constitutive elements.

The Figure 3-22(b) shows the stresses contours of the main facade, having

significant tensional stresses in the towers, from about 1kg/cm2.

Figure 3- 22 (a)Stresses diagram in X-direction [95 Earthquake]. (b)Maximum envelop of stresses in X-direction [95 Earthquake].

A typical mode of failure of horizontal cracking between windows due to tensile

forces clearly appears in the numerical model (Figure 3-23(a)). Maximum stresses contours

in adjacent module (Figure3-23(b)). Such stresses can lead to a large deformation in the wall

and cupola-wall connections.

a) b)

a) b)


68

Figure 3- 23 (a)Stresses diagram in Y-direction [95 Earthquake]. (b)Stresses diagram in Y-direction [95Earthquake].

The Figure 3-24 shows the safety of the arches in the mezzanine and vault section.

No high tensile stresses were found to occur during the applied accelerations, it means that

the landfill above the mezzanine and the big size of the sections establish a good system

against this type of excitations. Again, this analysis was carried out without considering any

sliding in the joints.

Figure 3- 24 Maximum envelop of principal stresses in X-direction [95 Earthquake].

The time history analysis shows relative displacements in the central arches of

building-A (vaulted body); the stresses are not significant, around 0.4 kg/cm2. The local

displacement is about 0.2cms and can not lead to any sliding in the supports and activate a

typical mode of failure (Figure 3-25(a)). At difference with the response spectra, this

earthquake actives a typical torsional effect in the structure and towers, where the central

arches suffer from lateral displacements (Figure 3-25(b)). This zigzag movement can cause

an out of plane mechanisms in the top part of the longitudinal walls affecting the connection

with the vaulted roof.

a) b)

a) b)


69

Figure 3- 25 (a) Maximum envelop of principal stresses in Y-direction. (b) Deformed shape under recordedaccelerations [95 Earthquake].

The maximum displacement found occurs at the arches of the vaulted body

(0.22cms) (Figure 3-26). The difference in displacements between the top and bottom part

indicates why this section of the structure presents higher concentration of tensional stresses.

Figure 3- 26 (a)Displacement contours originated by the design spectra in X-direction. (b)Displacementcontours originated by the design spectra in Y-direction(Contours in cms).

The complete results of the displacement distribution in the 4 selected joints over the

time can be found in Appendix D.


Therefore, the results obtained by the time history analysis prove to develop similar

tensional stresses to those found with the response spectrum case, but with the only

difference that the torsional vibration mode is more obvious in the time history case.

Joint 1426

Joint 1339

Joint 1344

Joint 1365

a) b)

a) b)


70

The principal stresses where slightly lower and it was found that the shear stresses

do not have a significant effect in the structure

3.5.4 Strengthening and repair recommendations

Prior to board a rehabilitation design, it is always necessary to understand whether

the building, in its existing condition, is capable of withstand the intended seismic levels.

The process used for this purpose is one of examining the deficiencies in the existing

structure to determine the principal requirements for additional strength, stiffness, or

deformation capacity.

According to the findings, the actual condition of the church is safe against gravity

loads, settlements and low intensity earthquakes. But the seismic analyses demonstrate that

one common failure mechanism in this type of structure is the tendency of the tower to

separate from its base triggering in failure at the connections between the main facade and

the vault; causing towers to continue working as isolated structures and as consequence a

collapse.

A proper solution for strengthening the towers should be the addition of

reinforcement bars in lateral and vertical directions, to function as an extra connection

between the main facade and the structure. The bars must be made of CFRP to avoid any

future affectation in the historic masonry due to material incompatibility.

For the arches a strengthening based on layers of GFRP fibres in both extrados and

extrados faces, is proposed, to give the sections more capacity to resist moments, ductility

and lateral movements.

The remedial measures were considered taking into account the modern principles of

architectural heritage protection, specifically, minimal repair, unobtrusiveness, removability,

stability, durability and compatibility.


71

4 CONCLUSIONS

4.1 General conclusions and recommendations

Historical buildings and monuments are an important link between our time and

history. Unfortunately, most historical buildings have already disappeared; damaged or

collapsed because of several external factors. For this reason, it is very important to protect

them immediately, taking into account the importance of choosing the best rehabilitation

technique based on analytical and numerical assessments, so action can be taken ascertaining

that any work will lead to a better behaviour of the structure.

The thesis try to demonstrate by analytical tools and failure comparisons, how to

predict and prevent an eventual failure or collapse of the structure and corroborate that the

basic principles and criteria of structural engineering are valid for any type of construction

and that the methods applied on modern buildings, with clever modifications, can be used in

historic masonry buildings.

For the investigation of the seismic performance of the Santo Domingo church, a

three dimensional numerical model was created and analysed using an advanced earthquake

simulation software (SAP2000®). The model then was corroborated by the measurement of

its natural frequencies. The first mode period is considered a local mode of the towers

(T=0.28sec) and the third (T=0.23sec) and fourth (T=0.22 sec) modes were considered as the

fundamental modes of the structure shaking it in X and Y directions respectively. Such

modes were not expected for a heavy and medium high structure; it means that the structure

oscillate around 4.5 times per seconds. But these findings were correlated with other works

in the field (Meli, 1998) and reviewed by its deformed shapes and then by correct

interpretation of the stress concentrations taken from the numerical results.

From the static analysis was found that the structure of the church is conceived to

support gravitational loads. The geometric form of arches, cupolas and vault is enough to

distribute the forces in a good manner, allowing it to resist actions with the employed

materials. But, in contrast, individual elements as the towers in the front of the building are

flexible against lateral loads. In general is a slender structure which its relationship between

base and height induces a heavy change in the stiffness.

Two main types of analyses were carried out. A linear static response spectrum

analysis (based on (Mexican-Norms, 2007)) and a time history linear analysis (based on

accelerograms from the 21 of October of 1995 seismic event). The results of the static and

dynamic analysis cases demonstrate differences in the deformed shapes. For the response


72

spectrum case the modules A & B basically moves in the Y-direction and the towers and

module C in X-direction. While for the time history analysis, the module A becomes in

torsion, a zigzag effect is developed in the middle section of the vaulted body due to the high

stiffness in Y-direction of the mezzanine and facade in relationship with this part.

These analyses provided us with very useful information related to the vibration

modes and stress diagrams. The response spectrum analysis shows stresses of around

3kg/cm2 in the towers and in one wall of the adjacent section, stresses that will lead to

cracking. The maximum displacements were found to take place in X-direction (2cms) while

for the whole structure does not surpass the 5 mm. These are considered conservative results.

For the Time history case tensional stresses are developed in the intrados of the arches of

less than 1kg/cm2. Again high tensile stresses around the walls of the adjacent section are

taking place.

Additionally it was found that general elastic behaviour of the structure is relatively

safe against gravity and minor lateral loads. This is attributed to precedent repair works, in

which the addition of buttresses and resizing of walls was correctly decided.

It is agreed the use of FRP for the strengthening works in the towers as additional

reinforcement bars and for the arches based on layers of GFRP fibres in both extrados and

extrados faces.

Recommendations for future work

As commented due to the lack of time and information, the numerical model and

parameters were not fully studied.

The previous work and strengthening recommendations only must be realized under

an extended investigation, in which is recommended:

· The most accurate determination of dimensions and material properties by

testing in situ with non-destructive methods and destructive for representative

samples, this to allow us to obtain more confidence in the results.

· The developing of analytical models that allow us to accurately describe the

nonlinear behaviour of the materials in the structure, and also to appreciate in a

better way the benefits of reinforcement.

· A dynamic testing comprising: signal acquisition, sensor choice (e.g.

accelerometers) and location (if where permanent). To calibrate the natural

frequencies and damping values of the real structure.


73

· The developing of a numerical model avoiding any averaging of elements,

taking into account all nonlinear issues related to: material properties,

foundation conditions, cracking development, sliding of the joints, different

layers of the masonry walls (if exist).

· Corroboration and calibration of the FE model based on testing measurements.

· A detailed failure investigation of the building. In where all the previous repair

and strengthening works, as well as present problems, where stated and

indicated by drawings and photographs.


74

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Appendix A

Letter of Venice

Preamble

Imbued with a message from the past, the historic monuments of generations of people

remain to the present day as living witnesses of their age-old traditions. People are becoming

more and more conscious of the unity of human values and regard ancient monuments as a

common heritage. The common responsibility to safeguard them for future generations is

recognized. It is our duty to hand them on in the full richness of their authenticity.

It is essential that the principles guiding the preservation and restoration of ancient buildings

should be agreed and be laid down on an international basis, with each country being

responsible for applying the plan within the framework of its own culture and traditions.

By defining these basic principles for the first time, the Athens Charter of 1931 contributed

towards the development of an extensive international movement which has assumed

concrete form in national documents, in the work of ICOM and UNESCO and in the

establishment by the latter of the International Centre for the Study of the Preservation and

the Restoration of Cultural Property. Increasing awareness and critical study have been

brought to bear on problems which have continually become more complex and varied; now

the time has come to examine the Charter afresh in order to make a thorough study of the

principles involved and to enlarge its scope in a new document.

Accordingly, the 2nd International Congress of Architects and Technicians of Historic

Monuments, which met in Venice from May 25th to 31st 1964, approved the following text:

Definitions

ARTICLE 1. The concept of an historic monument embraces not only the single

architectural work but also the urban or rural setting in which is found the evidence of a

particular civilization, a significant development or an historic event. This applies not only to

great works of art but also to more modest works of the past which have acquired cultural

significance with the passing of time.

ARTICLE 2. The conservation and restoration of monuments must have recourse to all

the sciences and techniques which can contribute to the study and safeguarding of the

architectural heritage.


79

Aim

ARTICLE 3. The intention in conserving and restoring monuments is to safeguard them

no less as works of art than as historical evidence.

Conservation

ARTICLE 4. It is essential to the conservation of monuments that they be maintained on a

permanent basis.

ARTICLE 5. The conservation of monuments is always facilitated by making use of them

for some socially useful purpose. Such use is therefore desirable but it must not change the

lay-out or decoration of the building. It is within these limits only that modifications

demanded by a change of function should be envisaged and may be permitted.

ARTICLE 6. The conservation of a monument implies preserving a setting which is not

out of scale. Wherever the traditional setting exists, it must be kept. No new construction,

demolition or modification which would alter the relations of mass and colour must be

allowed.

ARTICLE 7. A monument is inseparable from the history to which it bears witness and

from the setting in which it occurs. The moving of all or part of a monument cannot be

allowed except where the safeguarding of that monument demands it or where it is justified

by national or international interest of paramount importance.

ARTICLE 8. Items of sculpture, painting or decoration which form an integral part of a

monument may only be removed from it if this is the sole means of ensuring their

preservation.

Restoration

ARTICLE 9. The process of restoration is a highly specialized operation. Its aim is to

preserve and reveal the aesthetic and historic value of the monument and is based on respect

for original material and authentic documents. It must stop at the point where conjecture

begins, and in this case moreover any extra work which is indispensable must be distinct

from the architectural composition and must bear a contemporary stamp. The restoration in

any case must be preceded and followed by an archaeological and historical study of

the monument.

ARTICLE 10. Where traditional techniques prove inadequate, the consolidation of a

monument can be achieved by the use of any modem technique for conservation and


80

construction, the efficacy of which has been shown by scientific data and proved by

experience.

ARTICLE 11. The valid contributions of all periods to the building of a monument must

be respected, since unity of style is not the aim of a restoration. When a building includes

the superimposed work of different periods, the revealing of the underlying state can only be

justified in exceptional circumstances and when what is removed is of little interest and the

material which is brought to light is of great historical, archaeological or aesthetic value, and

its state of preservation good enough to justify the action. Evaluation of the importance of

the elements involved and the decision as to what may be destroyed cannot rest solely on the

individual in charge of the work.

ARTICLE 12. Replacements of missing parts must integrate harmoniously with the

whole, but at the same time must be distinguishable from the original so that restoration

does not falsify the artistic or historic evidence.

ARTICLE 13. Additions cannot be allowed except in so far as they do not detract from

the interesting parts of the building, its traditional setting, the balance of its composition

and its relation with its surroundings.

Historic Sites

ARTICLE 14. The sites of monuments must be the object of special care in order to

safeguard their integrity and ensure that they are cleared and presented in a seemly manner.

The work of conservation and restoration carried out in such places should be inspired by the

principles set forth in the foregoing articles.

Excavations

ARTICLE 15. Excavations should be carried out in accordance with scientific standards

and the recommendation defining international principles to be applied in the case of

archaeological excavation adopted by UNESCO in 1956. Ruins must be maintained and

measures necessary for the permanent conservation and protection of architectural features

and of objects discovered must be taken. Furthermore, every means must be taken to

facilitate the understanding of the monument and to reveal it without ever distorting its

meaning. All reconstruction work should however be ruled out "a priori." Only anastylosis,

that is to say, the reassembling of existing but dismembered parts can be permitted. The

material used for integration should always be recognizable and its use should be the least

that will ensure the conservation of a monument and the reinstatement of its form.

Publication


81

ARTICLE 16. In all works of preservation, restoration or excavation, there should

always be precise documentation in the form of analytical and critical reports,

illustrated with drawings and photographs. Every stage of the work of clearing,

consolidation, rearrangement and integration, as well as technical and formal features

identified during the course of the work, should be included. This record should be placed

in the archives of a public institution and made available to research workers. It is

recommended that the report should be published.


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ICOMOS recommendations

Structures of architectural heritage, by their very nature and history (material and

assembly), present a number of challenges in conservation, diagnosis, analysis, monitoring

and strengthening that limit the application of modern legal codes and building standards.

Recommendations are desirable and necessary to ensure rational methods of analysis and

repair methods appropriate to the cultural context.

Principles

A multi-disciplinary approach is obviously required in any restoration project and

the peculiarity of heritage structures, with their complex history, requires the organisation of

studies and analysis in steps that are similar to those used in medicine. Anamnesis, diagnosis,

therapy and controls, corresponding respectively to the condition survey, identification of the

causes of damage and decay, choice of the remedial measures and control of the efficiency

of the interventions. Thus, no action should be undertaken without ascertaining the likely

benefit and harm to the architectural heritage.

Therapy should address root causes rather than symptoms. Each intervention should

be in proportion to the safety objectives, keeping intervention to the minimum necessary to

guarantee safety and durability and with the least damage to heritage values. The choice

between “traditional” and “innovative” techniques should be determined on a case-by-case

basis with preference given to those that are least invasive and most compatible with heritage

values, consistent with the need for safety and durability. At times the difficulty of

evaluating both the safety levels and the possible benefits of interventions may suggest “an

observational method”, i.e., an incremental approach, beginning with a minimum level of

intervention, with the possible adoption of subsequent supplementary or corrective measures.

The characteristics of materials used in restoration work (in particular new materials)

and their compatibility with existing materials should be fully established. This must include

long-term effects, so that undesirable side effects are avoided.

Finally, a most relevant aspect is that the value and authenticity of architectural

heritage cannot be assessed by fixed criteria because of the diversity of cultural backgrounds

and acceptable practices.


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Guidelines

A combination of both scientific and cultural knowledge and experience is

indispensable for the study of all architectural heritages. The purpose of all studies, research

and interventions is to safeguard the cultural and historical value of the building as a whole

and structural engineering is the scientific support necessary to obtain this result. The

evaluation of a building frequently requires a holistic approach considering the building as a

whole, rather than just the assessment of individual elements.

The investigation of the structure requires an interdisciplinary approach that goes

beyond simple technical considerations because historical research can discover phenomena

involving structural issues while historical questions may be answered from the process of

understanding the structural behaviour. Knowledge of the structure requires information on

its conception, on its constructional techniques, on the processes of decay and damage, on

changes that have been made and finally on its present state.

The methodology stresses the importance of an “Explanatory Report”, where all the

acquired information, the diagnosis, including the safety evaluation, and any decision to

intervene should be fully detailed. This is essential for future analysis of continuous

processes (such as decay processes or slow soil settlements), phenomena of cyclical nature

(such as variation in temperature or moisture content) and even phenomena that can

suddenly occur (such as earthquakes or hurricanes), and for future evaluation and

understanding of the remedial measures adopted in the present.


84

Appendix B

a B C D E F G H

Figure B- 1 Longitudinal section A-A'

aBCDEFGH

Figure B- 2 Longitudinal section B-B'


85

Figure B- 3 Transversal section C-C'

Figure B- 4 Transversal section D-D'


86

Appendix C

Modal Participating Mass RatiosOutputCase StepType StepNum Period UX UY UZ SumUX SumUY SumUZ

Text Text Unitless Sec Unitless Unitless Unitless Unitless Unitless Unitless

MODAL Mode 1 0.282433 0.02015 0.001882 0.000002322 0.02015 0.001882 0.000002322

MODAL Mode 2 0.235932 0.008672 0.01779 0.000002503 0.02882 0.01967 0.000004826

MODAL Mode 3 0.231895 0.12 0.04748 0.000001625 0.15 0.06715 0.000006451

MODAL Mode 4 0.219753 0.01437 0.44 0.0001192 0.16 0.51 0.0001257

MODAL Mode 5 0.17981 0.03507 0.02161 0.000003126 0.2 0.53 0.0001288

MODAL Mode 6 0.157572 0.0762 0.00004178 0.00003837 0.27 0.53 0.0001671

MODAL Mode 7 0.140973 0.008581 0.03486 0.0008166 0.28 0.57 0.0009837

MODAL Mode 8 0.134707 0.007274 0.001003 0.01767 0.29 0.57 0.01865

MODAL Mode 9 0.1339 0.06161 0.00001964 0.0009161 0.35 0.57 0.01957

MODAL Mode 10 0.128017 0.01515 0.0004043 0.11 0.36 0.57 0.13

MODAL Mode 11 0.119477 0.002405 0.001288 0.0007224 0.37 0.57 0.13

MODAL Mode 12 0.113768 0.006004 0.01508 0.001262 0.37 0.58 0.13

MODAL Mode 13 0.113242 0.0002788 0.01176 0.001715 0.37 0.6 0.13

MODAL Mode 14 0.109395 0.0002262 0.01069 0.03015 0.37 0.61 0.16

MODAL Mode 15 0.107326 0.004575 0.0003702 0.0294 0.38 0.61 0.19

MODAL Mode 16 0.103307 0.01488 0.000639 0.17 0.39 0.61 0.36

MODAL Mode 17 0.102862 0.0004251 0.001029 0.005568 0.39 0.61 0.37

MODAL Mode 18 0.098475 0.0006796 0.07831 0.0343 0.39 0.69 0.4

MODAL Mode 19 0.096762 0.001132 0.0002064 0.07547 0.4 0.69 0.48

MODAL Mode 20 0.095192 0.06637 0.001108 0.13 0.46 0.69 0.61

MODAL Mode 21 0.092777 0.000009486 0.00009639 0.01057 0.46 0.69 0.62

MODAL Mode 22 0.089349 0.01243 0.006649 0.0007609 0.47 0.69 0.62

MODAL Mode 23 0.088045 0.002833 0.001307 0.11 0.48 0.7 0.73

MODAL Mode 24 0.085685 0.02072 0.0004754 0.001957 0.5 0.7 0.73

MODAL Mode 25 0.083668 0.0006661 0.006511 0.01641 0.5 0.7 0.74

MODAL Mode 26 0.081569 0.001158 0.0001143 0.002666 0.5 0.7 0.75

MODAL Mode 27 0.077992 0.006571 0.00003985 0.007988 0.51 0.7 0.76

MODAL Mode 28 0.073775 0.04142 0.0002779 0.008046 0.55 0.7 0.76

MODAL Mode 29 0.073515 0.0000689 0.007154 0.01812 0.55 0.71 0.78

MODAL Mode 30 0.071112 0.01377 0.01051 0.02524 0.56 0.72 0.81

MODAL Mode 31 0.06835 0.01744 0.004694 0.01245 0.58 0.73 0.82

MODAL Mode 32 0.067235 0.0004709 0.01117 0.009937 0.58 0.74 0.83

MODAL Mode 33 0.062312 0.0003333 0.04206 0.001013 0.58 0.78 0.83

MODAL Mode 34 0.059716 0.0105 0.0002094 0.007469 0.59 0.78 0.84

MODAL Mode 35 0.058999 0.0001711 0.004449 0.01543 0.59 0.78 0.85

MODAL Mode 36 0.054038 0.001839 0.03074 0.0006776 0.59 0.81 0.85

MODAL Mode 37 0.050795 0.03833 0.0004317 0.00006366 0.63 0.81 0.85

MODAL Mode 38 0.048573 0.003121 0.003067 0.01044 0.63 0.82 0.86

MODAL Mode 39 0.044196 0.0132 0.01774 0.000572 0.65 0.84 0.86

MODAL Mode 40 0.041969 0.01816 0.00602 0.000609 0.66 0.84 0.87

MODAL Mode 41 0.039007 0.002688 0.001242 0.01284 0.67 0.84 0.88

MODAL Mode 42 0.034282 0.00007933 0.03339 0.0004543 0.67 0.88 0.88

MODAL Mode 43 0.029091 0.03537 0.00004729 0.00006603 0.7 0.88 0.88

MODAL Mode 44 0.027612 0.0001698 0.0002448 0.01725 0.7 0.88 0.9

MODAL Mode 45 0.022914 0.0003263 0.0326 0.0002176 0.7 0.91 0.9

MODAL Mode 46 0.020045 0.01441 0.0001587 0.0105 0.72 0.91 0.91


87

MODAL Mode 47 0.019169 0.04911 0.00008844 0.002057 0.77 0.91 0.91

MODAL Mode 48 0.010953 0.0002948 0.04912 0.0002109 0.77 0.96 0.91

MODAL Mode 49 0.008544 0.13 0.0002192 0.0000256 0.9 0.96 0.91

MODAL Mode 50 0.007364 0.00001748 0.001432 0.03585 0.9 0.96 0.95

Table C- 1 Modal participating ratios for each vibration mode.

Modal Periods And FrequenciesOutputCase StepType StepNum Period Frequency CircFreq Eigen value

Text Text Unitless Sec Cyc/sec rad/sec rad2/sec2

MODAL Mode 1 0.282433 3.5407 22.247 494.91

MODAL Mode 2 0.235932 4.2385 26.631 709.23

MODAL Mode 3 0.231895 4.3123 27.095 734.14

MODAL Mode 4 0.219753 4.5506 28.592 817.51

MODAL Mode 5 0.17981 5.5614 34.943 1221

MODAL Mode 6 0.157572 6.3463 39.875 1590

MODAL Mode 7 0.140973 7.0935 44.57 1986.5

MODAL Mode 8 0.134707 7.4235 46.643 2175.6

MODAL Mode 9 0.1339 7.4683 46.925 2201.9

MODAL Mode 10 0.128017 7.8115 49.081 2408.9

MODAL Mode 11 0.119477 8.3698 52.589 2765.6

MODAL Mode 12 0.113768 8.7898 55.228 3050.2

MODAL Mode 13 0.113242 8.8307 55.485 3078.6

MODAL Mode 14 0.109395 9.1412 57.436 3298.9

MODAL Mode 15 0.107326 9.3174 58.543 3427.3

MODAL Mode 16 0.103307 9.6799 60.821 3699.2

MODAL Mode 17 0.102862 9.7218 61.084 3731.2

MODAL Mode 18 0.098475 10.155 63.805 4071.1

MODAL Mode 19 0.096762 10.335 64.934 4216.4

MODAL Mode 20 0.095192 10.505 66.005 4356.7

MODAL Mode 21 0.092777 10.779 67.724 4586.5

MODAL Mode 22 0.089349 11.192 70.322 4945.2

MODAL Mode 23 0.088045 11.358 71.364 5092.8

MODAL Mode 24 0.085685 11.671 73.329 5377.2

MODAL Mode 25 0.083668 11.952 75.097 5639.5

MODAL Mode 26 0.081569 12.26 77.029 5933.5

MODAL Mode 27 0.077992 12.822 80.562 6490.2

MODAL Mode 28 0.073775 13.555 85.167 7253.5

MODAL Mode 29 0.073515 13.603 85.468 7304.8

MODAL Mode 30 0.071112 14.062 88.356 7806.8

MODAL Mode 31 0.06835 14.63 91.926 8450.4

MODAL Mode 32 0.067235 14.873 93.452 8733.2

MODAL Mode 33 0.062312 16.048 100.83 10167

MODAL Mode 34 0.059716 16.746 105.22 11071

MODAL Mode 35 0.058999 16.95 106.5 11342

MODAL Mode 36 0.054038 18.506 116.27 13520

MODAL Mode 37 0.050795 19.687 123.7 15301

MODAL Mode 38 0.048573 20.588 129.36 16733


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MODAL Mode 39 0.044196 22.626 142.17 20211

MODAL Mode 40 0.041969 23.827 149.71 22413

MODAL Mode 41 0.039007 25.637 161.08 25947

MODAL Mode 42 0.034282 29.17 183.28 33591

MODAL Mode 43 0.029091 34.375 215.98 46648

MODAL Mode 44 0.027612 36.216 227.55 51780

MODAL Mode 45 0.022914 43.641 274.2 75188

MODAL Mode 46 0.020045 49.887 313.45 98251

MODAL Mode 47 0.019169 52.166 327.77 107430

MODAL Mode 48 0.010953 91.303 573.67 329100

MODAL Mode 49 0.008544 117.05 735.43 540860

MODAL Mode 50 0.007364 135.8 853.26 728050

Table C- 2 Modal periods and frequencies for each vibration mode.


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Appendix D

Figure D- 1 Displacement in X-direction of joint 588 (orange) and 579 (blue) VS time.


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Figure D- 2 Displacement in X-direction of joint 591 (green) and 578 (blue) VS time.


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Figure D- 3 Displacement in Y-direction of joint 588 (orange) and 579 (blue) VS time.


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Figure D- 4 Displacement in Y-direction of joint 591 (green) and 578 (blue) VS time.


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Figure D- 5 Response spectrum curve for joint 1365 matching with the third mode of the structure at 0.23secPeriod vs. Pseudo spectral acceleration in Y-direction.


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Figure D- 6 Response spectrum curve for joint 591 matching with the first mode of the structure at 0.3secPeriod vs. Pseudo spectral acceleration in Y-direction.

Dissertation RgN.60105112

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