An-Najah National University 

Faculty of Graduate Studies   

 
Seismic Assessment of Historical 

Buildings in Palestine 

Nativity Church as a Case-Study 

 
 

By  

Ali Abdellatif Ali Abu Safiyeh 

 
Supervisors  

Dr. Munther Ibrahim 

 

This Thesis is submitted in a Partial Fulfillment of the Requirements 

for the Degree of Master of Structural Engineering, Faculty of 

Graduate Studies, An-Najah National University, Nablus, Palestine. 

2019 



II 



III 

Dedication 

 

 

This Thesis is dedicated to my Dear Parents First of all, 

To my Beloved Wife Fidaa, 

To my Sisters and Brothers, 

To my Daughter Amal, and Son Abdellatif, 

To my Great Family and my Loyal Friends. 

 

 

May Allah (SWT) Grant You Endless Happiness and Peace. 
 



IV 

 

 
 

 

 

 



V 

 

 

 إلقزار

 :أَا انًٕقغ أدَاِ، يقذو انشعانت انخٙ ححًم انؼُٕاٌ

Seismic Assessment of Historical Buildings in Palestine 

Nativity Church as a Case-Study 

ٌ   أقش    إنّٛ اإلشاسة، باعخزُاء يا حًج صٓذ٘ انخاص   ًا ْٙ َخاسإَعانت يا اشخًهج ػهّٛ ْزِ انش   بأ

، أٔ أ٘ صضء يُٓا نى ٚقذو يٍ قبم نُٛم أ٘ دسصت ػهًٛت أٔ بحذ تهايحٛزًا ٔسد، ٔأٌ ْزِ انشعانت ك

 ػهًٙ أٔ بحزٙ نذٖ أ٘ يؤعغت حؼهًٛٛت أٔ بحزٛت أخشٖ.

Declaration 

The work provided in this thesis, unless otherwise referenced, is the 

researcher's own work, and has not been submitted elsewhere for any other 

degree or qualification. 

 

 :Student's name                            اسم الطالب: 

 :Signature                                                      التىقيع: 

 :Date                                             التاريخ: 



VI 

Table of content 

 Dedication  III 

 Acknowledgment  IV 

 Declaration  V 

 Table of Contents  VI 

 List of Tables XI 

 List of Figures X 

 Abstract  XIV 
 

CHAPTER ONE :  INTRODUCTION 
 

    

 1.1 General 2 

 1.2 Thesis Need 3 

 1.3 Thesis Objectives 4 

 1.4 Problem Statement  5 

 1.5 Organization of Thesis 7 

  1.5.1 Chapter 1 7 

  1.5.2 Chapter 2 7 

  1.5.3 Chapter 3 7 

  1.5.4 Chapter 4 7 

  1.5.5 Chapter 5 8 

  1.5.6 Chapter 6 8 

  1.5.7 Chapter 7 8 
 

CHAPTER TWO :  LITERATURE REVIEW 
 

 2.1 Masonry Structure 10 

  2.1 .1  General Characteristics  11 

  2.1.2 Failure Behavior   12 

  2.1.3 Possible Failure Mechanisms  13 

 2.2 Analysis of Seismic Behavior 17 

  2.2.1 Analysis Methods 18 

        2.2.1.1 Pushover Analysis 19 

        2.2.1.2 Time History Analysis  21 

 2.3 Seismic Hazard 23 

 2.4 Seismic Risk 26 

 2.5 Seismicity of Palestine 26 

  2.5.1 General 26 



VII 

  2.5.2 Fault of Dead Sea  28 

  2.5.3 Seismicity of the Site 29 

 2.6 Recent Studies  30 

  2.6.1 Over The World 26 

  2.6.2 Relevant Studies for Palestine 46 

 2.7 Progressive Collapse of Masonry 49 

  2.7.1 Introduction 49 

  2.7.2 Researches of Progressive Collapse 49 

  2.7.3 Relevant Codes and Standards  54 

       2.7.3.1 IBC 2012 54 

       2.7.3.2 ASCE 7-10 55 

       2.7.3.3 MSJC-13 56 

       2.7.3.4 GSA 2013 56 

       2.7.3.5 UFC 04-023-03 57 

       2.7.3.6 ASCE 41-13  57 

       2.7.3.7 EUROCODE 58 
 

CHAPTER THREE : MODELING of CASE STUDY 
 

 3.1 Introduction 62 

 3.2 Case Study: The Church of Nativity 62 

 3.3 Finite Element Method 63 

  3.3.1 Software‟s used in the Study 65 

  3.3.2 Mechanical Properties for Models 68 

  3.3.3 Verifications of Models 69 

       3.3.3.1 Modal Shapes 69 

       3.3.3.2 Modal Analysis 73 
 

CHAPTER FOUR NON-LINEAR STATIC ANALYSIS 
 

 4.1 Introduction 77 

 4.2 Constitutive Model 77 

 4.3 Cracks Propagation 81 

  4.3.1 Cracks Pattern in X – Direction 81 

  4.3.2 Cracks Pattern in Y – Direction 85 
 

CHAPTER FIVE : NON-LINEAR DYNAMIC ANALYSIS 
 

 5.1 Introduction 91 

 5.2 Used earthquakes 91 

 5.3 Relative Displacement 95 



VIII 

  5.3.1 X – Direction 96 

  5.3.2 Y – Direction 109 
 

CHAPTER SIX : PROGRESSIVE COLLAPSE 
 

 6.1 Introduction 124 

 6.2 Analysis Procedures 124 

 6.3 Failure Criterion 127 

 6.4 Principle Stresses 129 

  6.4.1 X - Direction 129 

  6.4.2 Y - Direction 131 

 6.5 Critical Region Identification 134 

  7.5.1 Evaluation Results : X-Direction 135 

  7.5.2 Evaluation Results: Y-Direction 137 
 

CHAPTER SEVEN : DISCUSSION AND CONCLUSION 
 

 7.1 Discussion of Results 140 

  7.1.1 Discussion of Pushover analysis Results 141 

  7.1.2 Discussion of Time History Analysis Results 143 

  7.1.3 Discussion of Progressive Collapse Results 148 

 7.2 Conclusion 149 

 7.3 Recommendations and Future Studies  152 
  

References  154 

Appendices 160 

 ب انًهخض

 

 

 

 

 

 

 

 

 

 

 

 

  



IX 

List of tables 

Table (3.1) Properties OF Nativity Church 69 

Table (3.2) corresponding modal periods for the first 8 modes 74 

Table (7.1) Max Crack Width In X Vs. Y Directions 143 

Table (7.2) Effect of Relative Displacement Analysis 144 

Table (7.3) Effect of Progressive Collapse Analysis 149 

 

 

 

 

 

 

 

 

 

 



X 

List of Figures 

Figure (1.1) 
Some of Historical Religious Buildings for Muslims in 

Palestine. 
2 

Figure (1.2) 
Some of Historical Religious Buildings for Christians in 

Palestine. 
3 

Figure (2.1) Modeling Strategies of Masonry Structures.  11 

Figure (2.2) 
Yield Criterion and a Typical Stress-Strain Model for Brick 

Unit.  
13 

Figure (2.3) In-Plane Failure Mechanisms. 14 

Figure (2.4) Out of Plane Failure Mechanisms.  15 

Figure (2.5) 
Force-Displacement Curve Corresponding to Out of Plane 

Failure. 
16 

Figure (2.6) Earth Disturbances Recorded by Seismograph. 18 

Figure (2.7) Load Displacement Curve. 20 

Figure (2.8) 
Mass and Stiffness Proportional Damping - Rayleigh 

Damping 
22 

Figure (2.9) Seismic Hazard Map for Palestine. 24 

Figure (2.10) 
Hazard Response Spectra for 2% & 10 %, POE in 50 

Years. 
25 

Figure (2.11) Dead Sea Fault. 27 

Figure (2.12) Fault Line Between the African and Arabian Plates. 29 

Figure (2.13) 
General View of St. James Church and the Numerical 

model.  
31 

Figure (2.14) Virtual Collapse Mechanisms. 32 

Figure (2.15) Camponeschi Palace - L’Aquila, Italy.  33 

Figure (2.16) Photograph of Madre Santa Maria del Borgo church, Italy. 34 

Figure (2.17) Armenian Church in Famagusta. 36 

Figure (2.18) Sonic Test Applied to the Armenian Church. 36 

Figure (2.19) Views of the Temple of San Antonio. 37 

Figure (2.20) 
Plan and Cross-Section of the Church of the Poblet 

Monastery. 
38 

Figure (2.21) Principal Tensile and Shear Stresses for Jama. 40 

Figure (2.22) Elti Hatun Mosque with its Outside and Inside View 41 

Figure (2.23) General and 3D view of Cathedral of the Blessed Sacrament 41 

Figure (2.24) General and 3D view of Kaisariani Monastery in Athens. 43 

Figure (2.25) General and 3D view of Civic Museum. 44 

Figure (2.26) 3D model of Fresco. 45 

Figure (2.27) Location and 3D of St. Salvatore church.  46 



XI 

Figure (2.28) 3D Finite Element Model for the Nativity church.  47 

Figure (2.29) Aerial View of the South Wall.  48 

Figure (2.30) 
Masonry Barrel Vault with Possible Loads Paths in the 

Arches. 
51 

Figure (2.31) 
Picture for the Bund 18 Building, and its  Plan View of First 

Floor  
52 

Figure (2.32) 
The 3D Model with Collapse Due to Removal of Some 

Columns 
53 

Figure (3.1) Perspective Picture for Church of the Nativity 63 

Figure (3.2) Different Approaches for Modeling of Masonry Walls 66 

Figure (3.3) Eight Node Solid Element in SAP2000 66 

Figure (3.4) 3D Numerical Model Built in  DIANA FEA Software 67 

Figure (3.5) 3D Solids Used in Modeling According to DIANA Manual 70 

Figure (3.6) 
Periods and Modal Shapes Concerning the 3D model – 

SAP2000 
72 

Figure (3.7) 
Periods and Modal Shapes Concerning the 3D model – 

DIANA FEA 
75 

Figure (3.8) Comparison Between Frequencies of Two Models 75 

Figure (4.1) Material Models Used for the Behavior of Masonry. 78 

Figure (4.2) Force Control Versus Displacement Control. 79 

Figure (4.3) 
Load Increment Methods Characteristics and Arc-Length 

Control. 
80 

Figure (4.4) 
Crack Widths Generated by Gravity Loads Analysis in X – 

Direction. 
82 

Figure (4.5) 
Crack Widths Generated by Pushover Analysis in X – 

Direction. 
84 

Figure (4.6) 
Crack Widths Generated by Gravity Loads Analysis in Y – 

Direction. 
86 

Figure (4.7) 
Crack Widths Generated by Pushover Analysis In Y – 

Direction. 
88 

Figure (5.1): Elastic and Design Spectra Concerning the Site Seismicity. 92 

Figure (5.2) Accelerograms Used for Dynamic Analysis. 93 

Figure (5.3) Rayleigh Damping Model. 94 

Figure (5.4) Locations of Reference Nodes for Dynamic Analysis. 95 

Figure (5.5) 
Points of Masonry Block where the Displacements 

Measured. 
96 

Figure (5.6) Relative Displacement for Node (1) - X direction 97 

Figure (5.7) Relative Displacement for Node (2) - X direction 97 

Figure (5.8) Relative Displacement for Node (3) - X direction 98 

Figure (5.9) Relative Displacement for Node (4) - X direction 99 

Figure (5.10) Relative Displacement for Node (6) - X direction 99 



XII 

Figure (5.11) Relative Displacement for Node (7) - X direction 100 

Figure (5.12) Clear Separation in the Longitudinal Wall. 100 

Figure (5.13) Relative Displacement for Node (8) - X direction 101 

Figure (5.14) Relative Displacement for Node (9) - X direction 102 

Figure (5.15) Ties of Masonry Buildings 102 

Figure (5.16) Relative Displacement for Node (10) - X direction 103 

Figure (5.17) Relative Displacement for Node (11) - X direction 103 

Figure (5.18) Relative Displacement for Node (12) - X direction 104 

Figure (5.19) Relative Displacement for Node (13) - X direction 104 

Figure (5.20) Relative Displacement for Node (14) - X direction 105 

Figure (5.21) Relative Displacement for Node (15) - X direction 105 

Figure (5.22) Relative Displacement for Node (16) - X direction 106 

Figure (5.23) Relative Displacement for Node (17) - X direction 106 

Figure (5.24) Relative Displacement for Node (18) - X direction 107 

Figure (5.25) Relative Displacement for Node (19) - X direction 107 

Figure (5.26) Relative Displacement for Node (20) - X direction 108 

Figure (5.27) Maximum Relative Displacement for all Nodes - X direction 108 

Figure (5.28) Relative Displacement for Node (1) - Y direction 109 

Figure (5.29) Relative Displacement for Node (2) - Y direction 110 

Figure (5.30) Relative Displacement for Node (3) - Y direction 110 

Figure (5.31) Relative Displacement for Node (4) - Y direction 111 

Figure (5.32) Relative Displacement for Node (5) - Y direction 111 

Figure (5.33) Relative Displacement for Node (6) - Y direction 112 

Figure (5.34) Relative Displacement for Node (7) - Y direction 112 

Figure (5.35) Relative Displacement for Node (8) - Y direction 113 

Figure (5.36) Relative Displacement for Node (9) - Y direction 114 

Figure (5.37) Relative Displacement for Node (10) - Y direction 115 

Figure (5.38) Relative Displacement for Node (11) - Y direction 115 

Figure (5.39) Relative Displacement for Node (12) - Y direction 116 

Figure (5.40) Relative Displacement for Node (13) - Y direction 117 

Figure (5.41) Relative Displacement for Node (14) - Y direction 117 

Figure (5.42) Relative Displacement for Node (15) - Y direction 118 

Figure (5.43) Relative Displacement for Node (16) - Y direction 118 

Figure (5.44) Relative Displacement for Node (17) - Y direction 119 



XIII 

Figure (5.45) Relative Displacement for Node (18) - Y direction 120 

Figure (5.46) Relative Displacement for Node (19) - Y direction 120 

Figure (5.47) Relative Displacement for Node (20) - Y direction 121 

Figure (5.48) Maximum Relative Displacement for all Nodes - Y direction 122 

Figure (6.1) Accelerogram of El Centro Earthquake. 126 

Figure (6.2) 
Modified Von-Mises failure Criterion for Masonry 

Structures  
127 

Figure (6.3) Locations of the Reference Nodes for Progressive Analysis 128 

Figure (6.4) Connections Between Transverse Walls and Façade 129 

Figure (6.5) Principle Stresses for X – Direction 130 

Figure (6.6) 
The Church’s Plan, Showing locations of South and North 

Walls. 
131 

Figure (6.7) 
South Masonry Wall Location with Geometric Section 

Height. 
132 

Figure (6.8) Principle Stresses for Y – Direction 133 

Figure (6.9) 
Von Misses Function for Church Components, X – 

Direction. 
135 

Figure (6.10) Lateral Walls Failure After 7.53 sec 136 

Figure (6.11) Lateral Walls Failure after as a Second Stage. 136 

Figure (6.12) 
Von Misses Function for Church Components, Y – 

Direction. 
137 

Figure (6.13) External and Internal lateral Walls Failure 138 

Figure (7.1) 
Maximum Crack Propagation in Each Direction With 

Respect to Load Step 
141 

Figure (7.2) Maximum Crack Propagation, X- Direction. 144 

Figure (7.3) Inadequate Connection Between Wythes 145 

Figure (7.3) Maximum Crack Propagation, Y- Direction. 146 

 

 



XIV 

Seismic Assessment of Historical Buildings in Palestine 

Nativity Church as a Case-Study 

By 

Ali Abdellatif Ali Abu Safiyeh 

Supervisors 

Dr. Munther Ibrahim 

Abstract 

This thesis addresses the study of the seismic assessment of 

historical structures in Palestine, by focusing on general condition and 

structural stability of The Church of Nativity in Bethlehem, which is the 

most valuable structure over the world, because it is earliest Christian 

structures, and the birth place of Jesus. 

The work of this thesis can be divided into the following main 

phases: a focus on the one case study with its properties, review of the state 

of art, preparation and calibration of a 3D finite element models, and the 

structural analysis to assess the seismic behavior of the Church. The 

assessment was done by using the static pushover and dynamic time history 

methods and the results of these analyses are studied in terms of the 

generated cracks propagation in each direction, effects of relative 

displacement of masonry blocks and progressive collapse analysis for the 

structures elements. 

In particular, the results of the pushover analysis carried out, 

conclude that the transversal direction is the most vulnerable and the 

damage concentrates at the main lateral (longitudinal) walls, mainly at the 

south and north alignment walls, also at the vaults and at the connections of 



XV 

the vaults to the apses. On the other hand, the dynamic analysis presented 

similar conclusions in terms of structural performance. Furthermore, it 

allowed conclude that for the considered earthquake, the relative 

displacement of adjacent masonry blocks (RDAMB) indicates the locations 

of failure, and the prediction of reasons. Furthermore, the progressive 

collapse technique is able to predict the critical regions, and effect of rock 

falls in masonry walls of the structure. 



1 

  

 

 

 

 

 

Chapter One 

Introduction 

 

 

 

 

 

 

 

 



2 

Chapter One 

Introduction 

 

1. Introduction  

1.1 General 

Buildings may be classified as historical for two main reasons 

summarized as; long time has passed upon its construction, and they are 

irreplaceable with associated acts of historical importance. It is well known 

from past and recent earthquakes that traditional masonry buildings, do not 

respond well to strong dynamic demands, so due to these causes (damage 

and loss of cultural heritage) more and more attention given for need of 

safety evaluation of old buildings in the seismic zones. Figure (1.1) show 

some historical structures in Palestine which are considered very special 

religious landmarks for Muslims, for example, the Dome of Rock, with Al-

Aqsa Mosque in Jerusalem, also Cave of the Patriarchs in Hebron. 

  

The Dome of Rock with Al-Aqsa Mosque Cave of the Patriarchs 

Figure (1.1); Some of Historical Religious Buildings for Muslims in Palestine 



3 

Also for Christians, Church of Holy Sepulcher in Jerusalem, and 

Church of Nativity in Bethlehem are considered very holy structures in 

Palestine, figure (1.2). 

  

Church of Holy Sepulcher Church of Nativity 

Figure (1.2); Some of Historical Religious Buildings for Christians in Palestine 

1.2 Thesis Need 

Palestine is vulnerable to earthquake events, and until now there is 

no seismic code for designing buildings for the Palestinian Authority, 

although engineers design their buildings depending on national and 

international building codes, which they are not subordinate under certain 

regulation for Palestinian authority,  however in the last years, a strong 

earthquake event took place in this area, averagely, every hundreds of years 

i.e. 1837 earthquake that took place in the northern part of Palestine, also 

the 1927 earthquake resulted in hundreds of victims and a lot of damage. 

The need of this thesis was generated due to the architectural 

complex of historical structures in Palestine, most of the existing historical 

monumental structures are made of masonry, using stone or brick blocks, 

these unreinforced blocky masonry structures cannot be considered 



4 

continuum, but rather an assemblage of compact stone or brick elements 

linked by means of mortar joints, so the mortar replacement, stabilization, 

and repair interventions are often insufficient to prevent cultural losses 

caused by poor structural performance of these buildings during 

earthquakes. 

In this case, the upgrading of a historical buildings require deliberation of 

such building, which is based on the following aspects  

1- The life safety judgment, 

2- Prevention of damage to building elements and components, 

3- Cultural significance. 

1.3 Thesis Objectives 

The main objective of this thesis is the assessment of the seismic 

performance of an existing unreinforced masonry building subjected to 

seismic loading, the area under consideration is Bethlehem, locating in 

Palestine, and has the historical building; The Church of Nativity, which is 

the case study of this thesis. 

In additional to the main objective, this thesis aims to predict the 

materials‟ properties and expected damage in these materials, for the used 

building of the case study. 



5 

This work intends also to contribute for the discussion of using static 

and dynamic analysis to evaluate the seismic performance, thus, in order to 

satisfy these objectives, the following tasks were carried out: 

1. Review of the methods used to examine masonry structures. 

2. Review of the state of art of seismic analysis methods commonly 

used for the assessment of the response of structures. 

3. Preparation and calibration of two models based on the finite element 

method. 

4. Comparing the 3D finite element models of the Case Study “The 

Church of Nativity” considering the main geometrical features of the 

building. 

5. To perform a non-linear finite element analysis of the church for 

gravity and lateral loading, employing two different methods: non-

linear static pushover analysis and non-linear time-history analysis. 

6. To perform progressive collapse of the church based on non-linear 

time-history analysis to evaluate the performance against collapse. 

7. To assess the current safety of the church. 

1.4 Problem Statement  

Regrettably, most of restoration projects for historical buildings in 

Palestine have been done with concentration on architectural features of 



6 

historical buildings, not on the response of such buildings to the 

earthquakes excitations. For example, between years 2015-2017, the 

restoration of Nativity Church has been done, and concentrated on 

rehabilitation works for scaffolding and temporary roof, wall mosaics, 

external stone surfaces, paintings of columns, repairing floor mosaics, 

modification of lighting system, adding new fire alarm etc...  With now 

adequate structural and seismic rehabilitation for the church, knowing that 

this church inscribed on the world heritage list in 2012, also it is classified 

on the list of world heritage in danger due to the lack of repair of the roof 

structure. 

So the main scope of the present work consists of the 

characterization of the seismic performance of historical buildings in 

Palestine as general, and will study in details the case study of The Church 

of Nativity by a non-linear static and dynamic analysis, to generate a 

pattern for cracks propagation in masonry and their relative displacement in 

elements, in order to predict the failure mechanisms of this type of 

buildings.  

Also, buildings like that may be prone to rock falls caused by lateral 

forces, this direct the analyst to assess the building against progressive 

collapse, which is an approach  based on progressive analysis and used 

recently to check the sudden and unexpected loads that leading to the 

collapse of the entire building or substantial part.  



7 

1.5 Organization of Thesis 

This thesis is organized into seven chapters, including the present 

introduction. Also the appendices and references are stated in the last. The 

following subsections summarize each chapter with its content: 

1.5.1 Chapter 1 

It is an introduction to the research; define the research‟s need, 

objectives, problem statement, and the scope of the work. 

1.5.2 Chapter 2 

Address the historical development of seismic analysis of masonry 

structures, discussing the present limitations and inherent uncertainties of 

the various approaches, with mention of similar researches done over the 

world, and in the Palestine. 

1.5.3 Chapter 3 

Show brief about the used case study, with how the finite element 

continuum macro-models are prepared to study the response of the 

structure, also this chapter discuss the model analyses and compare them 

between different methods used. 

1.5.4 Chapter 4 

Focus on the non-linear static analysis for the structure, and show the 

results of pushover analysis. 



8 

1.5.5 Chapter 5  

Present the non-linear dynamic analysis for the same structure used, 

and show the results of time history analysis, based on using three different 

accelerograms each of them for a different earthquake. 

1.5.6 Chapter 6 

Make the progressive analysis, use the data of El Centro earthquake, 

in order to define the critical regions and load paths. 

1.5.7 Chapter 7 

This final chapter, discusses the results of approaches used, and 

includes the conclusions, and future research topics to extend the current 

work. 



9 

 

 

 

 

 

 

 

CHAPTER TWO 

LITERATURE REVIEW 



10 

2. Literature Review  

2.1 Masonry Structures 

Masonry structures have been separated widely all over the world. 

They are a much types of constructions which can be built rapidly, cheaply 

and often without particular technical competence. Thus, historical 

materials such as stone‟s masonry are characterized by very complex 

mechanical and strength phenomena, which still challenging the modeling 

abilities. In particular, masonry is characterized by its high rigidity, low 

shear and tensile strength, low capacity of bearing reverse loading, and low 

ductility. These are the main reasons for the frequent collapse of masonry 

buildings during earthquakes excitations, as a result, masonry  

properties can vary depending on the type of stone units and mortar  

used, in additions; other factors influencing the behavior of masonry  

are the dimensions of the units, the mortar width and the arrangement of 

units, (Mosalam, Glascoe, & Bernier, 2009).  

Masonry can be classified into three main categories depending on 

the construction method used, the first one is the confined masonry, which 

consists of horizontal and vertical RC members, the second, reinforced 

masonry where steel bars are usually used for the reinforcement, and the 

third, is unreinforced masonry which refers to stand alone masonry units.  



11 

2.1.1 General Characteristics  

Masonry is a composite material showing an anisotropic behavior; it 

is characterized by distinct directional properties due to the existence of 

mortar joints, which act as planes of weakness. The numerical 

representation of masonry structures can vary based on the level of 

accuracy needed; the following modeling strategies, figure (2.1), can be 

used:  

A. Detailed Micro Modeling: continuum elements represent units and 

mortar in the joints, whereas their interface is represented by 

discontinuous elements, as figure (2.1a&b) show. 

B. Simplified Micro Modeling: expanded units are represented by 

continuum elements, while their interface is lumped in discontinuous 

elements, as figure (2.1c) show. 

C. Macro Modeling: units, mortar and interface are smeared out in the 

continuum, as figure (2.1d) show. 

 
Figure (2.1): Modeling Strategies of Masonry Structures. [Lourenço , 2013] 



12 

The mechanical properties of masonry depend on many parameters, 

such as the material properties of units and mortar, the arrangement of bed 

and head joints, anisotropy of units, dimensions of units, joint width, 

quality of workmanship, degree of curing, age of construction and 

environment. 

2.1.2 Failure Behavior   

Masonry usually characterized by a quasi-brittle behavior, which 

refers to the way the force is transferred through the material. In details, 

after the peak load is reached the force gradually decreases to zero, which 

is called softening procedure, which is defined as the gradual decrease of 

resistance under a continuous increase in force caused deformation upon a 

material‟s structure. It is a notable feature of quasi-brittle materials like 

concrete, ceramics, clay brick, mortar, and rock, which fail due to a process 

of progressive internal crack growth. The phenomenon of softening has 

been well identified in parallel in tensile and shear failures of masonry, 

(Lawrence Livermore National Laboratory, 2009). Otherwise, in 

compression, softening behavior depends on the boundary conditions in the 

experiments and sizes of the specimen, figure (2.2) below, present the 

stress-strain relationship of unreinforced brick masonry and the yield 

criterion. 



13 

 

Figure (2.2): Yield Criterion and a Typical Stress-strain Model for Brick Unit. 

[Lawrence Livermore National Laboratory, 2009]. 

2.1.3 Possible Failure Mechanisms  

Unreinforced masonry structures should be examined considering its 

horizontal and vertical effects, because the types of failure may be 

occurring in plane and out of plane mechanisms. Observed failure in 

unreinforced masonry structures from past earthquakes expose that the two 

types of failure are independent, so they should be examined in parallel. 

The general modes of failure related to unreinforced masonry structures 

buildings include; 

A. In-plane failure. 

B. Out-of plane failure. 

C. Lack of anchorage or anchors failure. 

D. Diaphragm related failures. 



14 

When the in plane behavior is examined, the actual behavior of 

masonry walls looks like the shear walls behavior, Anthoine and 

Magonette, and Kikuchi et al. (2015) have been thoroughly examined, and 

generate the following two types of failure:  

a. Flexural Failure: The compression and tension failures are 

combined, because the exceedance of tensile bond strength which 

results in a crack in the interface of mortar and brick, is followed by 

loss of the resisting section in compressive crushing, and these also 

known as toe crushing.  

b. Diagonal Failure: The Cracks which developed through the unit 

mortar interface and the units itself as a case of biaxial tension 

compression state. Unfortunately there are low aspect ratios and 

lower axial load characterize this failure.  

Also, Elgawady, Badoux, & Lestuzzi, 2006; Magenes & Penna, 

2009, can show the types of failure but separated in three main forms, 

figure (2.3), summarized as flexural failure, shear failure, and sliding 

failure. These are also defined as global response mechanisms. 

  

Shear  Sliding  Flexural 

 

Global response  

Figure (2.3): In-plane Failure Mechanisms. [Elgawady, Badoux, & Lestuzzi, 

2006; Magenes & Penna, 2009] 



15 

On the other hand, the out of plane failure mechanisms are important 

for the overall structural behavior of the masonry structures. Some types of 

failures are associated to the spandrels of walls, which are not well 

restrained by structural elements, which might generate rocking falling 

when earthquake loads are present, (Calvi, Pinho, Magenes, Bommer, 

Restrepo-Vélez, & Crowley, 2006). Possible out of plane collapse 

mechanisms are presented in figure (2.4).  

 

Figure (2.4): Out of Plane Failure Mechanisms. [Calvi, Pinho, Magenes, Bommer, 

Restrepo-Vélez, & Crowley, 2006] 

Figure (2.5) can show the main line connecting the point of force 

corresponding to rocking mechanism (λW) and the point of displacement 

where instability happened under static loads (Δ), assumes that the system 

is cracked before the movements of parts considering to wall panels 

participating to rocking behave as rigid bodies. Also the dashed line, 

however, is a more accurate representation of the real behavior, it assumes, 

the wall can be initially avert cracks, and the point around which the 



16 

rocking is activated has finite dimensions. A more detailed description of 

the phenomena is given in Doherty et al. (2002). 

When the failure is associated to the connections of diaphragms to 

the masonry walls, three of the failure modes are identified; (1) parapet 

failure, (2) wall diaphragm shear failure, and (3) wall diaphragm tension tie 

failure.  

 

 

Figure (2.5): Force-Displacement Curve Corresponding to Out of Plane Failure 

[Doherty et al. 2002]. 

Also for the roof and floor diaphragms, they can be considered as: 

(1) Flexible, (2) Semi rigid and (3) Rigid. Diaphragms are considered 

flexible when the maximum lateral displacement along its length is greater 

than twice the average inter story drift of the vertical lateral load resisting 

elements, (Doherty et al. 2002). Otherwise the diaphragms range from semi 



17 

rigid to rigid. According to FEMA 356, unreinforced masonry buildings 

with timber floors can be considered flexible; the connections between 

masonry walls are defined as weak points and are expected to separate 

during cyclic loading.  

2.2   Analysis of Seismic Behavior 

An earthquake is defined as ground shaking caused by the sudden 

release of energy in the Earth‟s crust, caused by tectonic movements. The 

main cause is that when tectonic plates collide, one ride over the other, and 

this create relative motion between the plates leads to increasing the 

stresses. 

The tectonic movements originate from different sources, for 

instance, volcanic activities, releasing of locations of the crust, folding and 

faulting, or even by human made explosions (USGS, 2005). Thus, while 

earthquakes are defined as natural disturbances, Richter has provided a list 

of major earth disturbances recorded by seismographs as shown in figure 

(2.6). 

https://simple.wikipedia.org/wiki/Plate_tectonics


18 

 

Figure (2.6): Earth Disturbances Recorded by Seismograph, [Dowrick, 2009] 

2.2.1 Analysis Methods 

The impact of the excitations to the structure can be caught by 

different methods;  

A. Lateral force analysis: which is static analysis where the seismic 

action is applied as a concentrated force to the center of mass for 

each floor,  

B. Response spectrum analysis: this method cicatrized by linear 

dynamic analysis where the seismic action is given as a spectrum,  

C. Nonlinear pushover analysis: the load is applied statically but in 

nonlinear influence, and the material nonlinearity is taken into 

account,  



19 

D. Nonlinear time history analysis: the load is applied as an 

accelerogram and the nonlinearity of the material is also considered.   

The following sections, show in details the two methods of analysis 

used in this work. This thesis set up on static and dynamic analysis both. 

2.2.1.1 Pushover Analysis 

It is a simple method, used to predict the nonlinear behavior of the 

structure, under seismic loads. The pushover analysis process employs the 

lateral forces with increasing loads used to push the structure until the 

ultimate displacement is reached. This method provides useful data about 

the peak response in terms of floor‟s displacement, story‟s drift, and other 

deformations quantities. (Chopra, 2012), also it can help demonstrate how 

progressive failures in structure can really occur, and differentiate the mode 

of final failure. 

Capacity curve is a characteristic curve to be defined by a pushover 

analysis, where the displacements are plotted versus the base shear, i.e. 

capacity curve where the difference between experimental and numerical 

results is emphasized is illustrated in the following figure (2.7). However, 

pushover analysis can also estimate the strength capacity of a structure 

beyond its elastic limit up to its ultimate strength in the post elastic range. 

In the process, the method also predicts potential weak areas in the 

structure, by keeping track of the sequence of damages of each and every 

member in the structure by use of what are called hinges. 



20 

Different ways for the application of the load can be performed, for 

defining different types of pushover analysis. A monotonic pushover 

analysis considers a monotonic lateral load pattern which pushes the 

structure until the lateral capacity is reached; therefore the capacity of the 

structure is dependent mainly on the loading pattern. 

 

Figure (2.7): Load Displacement Curve. [Facconi, Plizzari, & Vecchio, 2013] 

In Euro code the pushover analysis is defined as a nonlinear static 

analysis with constant gravity loads and monotonically increasing 

horizontal loads, for masonry buildings capacity is defined in terms of roof 

displacement (EN 1998-1, 2004). The ultimate displacement capacity is 

taken at the point of roof displacement where total lateral resistance has 



21 

dropped below 80% of peak resistance, (EN 1998-3 , 2005) due to failure 

of lateral load resisting elements and progressive damage.  

2.2.1.2 Time History Analysis  

The Nonlinear dynamic analysis utilizes the combination of ground 

motion records with a detailed structural model, which is the most 

advanced method so far, therefore it is capable of giving results with 

relatively low uncertainty. Theoretically time histories have complete 

information about the seismic event in a certain location and record three 

traces which are two in horizontal, and one in vertical, (Chen & Lui, 2005). 

The nonlinear properties of the structure are considered as part of 

a time domain analysis and this approach is the most rigorous, required by 

some building codes for buildings of unusual configuration or of special 

importance. However, the calculated response can be very sensitively to the 

characteristics of the individual ground motion used as seismic input; 

therefore, several analyses are required using different ground motion 

records to achieve a reliable estimation of the nearly realistic distribution of 

structural response. Correia, Almeida, and Pinho, 2013, can show the 

damping models available to represent, categorized as:  

a. Mass-proportional. 

b. Initial stiffness-proportional. 

c. Tangent proportional. 

https://en.wikipedia.org/wiki/Time_domain
https://en.wikipedia.org/wiki/Building_code
https://en.wikipedia.org/wiki/Probability_distribution


22 

d. Rayleigh damping. 

Rayleigh damping, figure (2.8), is the most type of damping, used in 

time history analysis, which can be expressed by the following equation as 

shown by (Chopra, 2012):  

c = a0.m+a1.k (2.1) 

Where; 

- c; damping matrix, 

- m; mass matrix, 

- k; stiffness matrix, 

- a0; mass proportional coefficients; 

- a1; stiffness proportional coefficients; 

 

Figure (2.8): Mass and Stiffness Proportional Damping - Rayleigh Damping. 

[Chopra, 2012] 



23 

2.3 Seismic Hazard 

The seismic hazard, defined as the probability that an earthquake will 

occur in a given geographic area, within a given range of time, and ground 

motion intensity exceeding a given threshold. It is used as the first step in a 

process used to assess risk. In details, the process of quantitatively 

estimating the ground motion at region of interest based on the 

characteristics of seismic sources. 

The seismic hazard is either analyzed in a probabilistic or 

deterministic way. In the deterministic analysis, a particular earthquake 

scenario is assumed, while the probabilistic explicitly considers 

uncertainties, while the probabilistic analysis the earthquake source needs 

to be identified. The source is identified using all possible sources such as 

fault maps giving geological, tectonic and historic information as well as 

instrumental records of seismicity of the past. 

The outputs of the hazard‟s analysis is either a curve showing the 

exceedance probabilities for various ground motions, or a graphical map 

shows the estimated magnitude distribution of ground motion that has a 

specific exceedance probability over a specified time period at a region. 

The output maps developed for Palestine is shown in figure (2.9). 

https://en.wikipedia.org/wiki/Earthquake
https://en.wikipedia.org/wiki/Risk


24 

 

Figure (2.9): Seismic Hazard Map for Palestine,  

[ESSEC, USAID-MERC (M18-057)] 

For seismic risk analysis, Poisson model can be used, which is the 

standard model considered  the best model for large earthquake occurrence, 

in which the tectonic stress is released when a fault breaks, however, 

according to the Poisson model, the probability of at least one earthquake 

equal to or greater than a specific magnitude (M) occurring within t years 

is,  

 (2.2) 

Where τ is the average recurrence interval. For 2% and 10% 

probability of exceedance in 50 years that are commonly considered in 



25 

earthquake engineering, gives τ of 2500 and 475 years, respectively, figure 

(2.10) 

  

A. San Francisco B. South Carolina 

Figure (2.10): Hazard Response Spectra for 2% & 10 %, POE in 50 years. 

In IBC, the maximum considered earthquake spectral response 

accelerations for short periods, SMS, and at 1 second period, SM1 adjusted 

for site class effect is determined from the following equations: 

SMS = FaSS (2.3) 

SM1 = FvS1 (2.4) 

Where Fa and Fv are site coefficients and SS and S1 are mapped 

parameters that indicate the 5% damped spectral acceleration of the 

Maximum Considered Earthquake, in short and long periods (0.2 s and 1.0 

s), respectively. The design spectral acceleration parameters in IBC are SDS 

and SD1 rather than seismic zone factor used in UBC and can be found by:  

SDS = (2/3)Sms (2.5) 

SD1 = (2/3)SM1 (2.6) 



26 

2.4   Seismic Risk 

Many seismologists have said that “the earthquakes don't kill people, 

their structures do”, this is because most deaths from earthquakes are 

caused by main damage of structures or other human construction falling 

down during an earthquake. So before any assessments start, a good 

practice to study two fundamentally different concept of the hazards and 

risk. In general terms, Risk, in its simple manner, is the probability of harm 

if someone or something that is vulnerable to expose the hazard, the hazard 

can be defined as a phenomenon that has potential to cause harm. 

Phenomena are both natural and man-made. For example, earthquakes, 

hurricanes, fires, and floods are natural hazards; whereas car crashes, and 

terror attacks are man-made hazards.  

Seismic risk = (Seismic hazard) × (Vulnerability) × (Value) 

Where Vulnerability is the amount of damage induced by a given 

degree of hazard, and expressed as a fraction of the Value of the damaged 

item under consideration. 

2.5  Seismicity of Palestine  

2.5.1 General 

The area of Palestine is affected mainly by seismic activities along 

the Syrian - African fault, which is included; the Jordan Valley, Dead Sea, 

Gulf of Aqqaba and Near Sharm-El Sheikh in Sinai. Also Palestine may be 

affected by earthquakes in the Mediterranean, or in Turkey. Almost the 



27 

earthquakes which have occurred in the Mediterranean area during this 

century have not left any significant effects.  

In recent years, there were much seismic studies have improved, due 

to the installation of more sophisticated equipment‟s, i.e. accelerometers 

and seismographs; the measurement of accelerations indicates that the 

geological structure of Palestine generates faster attenuation than assumed 

earlier. 

However, other evidence, concerning the activity of secondary faults, 

besides the one in the Jordan Valley that may indicate a higher activity than 

previously thought. Palestine is located between the Arabian and African 

plates (Klinger, Avouac, Dorbath, Abou Karaki, and  Tisnerat, 2000), as 

the figure (2.11) present.  

 
Figure (2.11): Dead Sea Fault, [Klinger,  Avouac ,Dorbath,  Abou Karaki, and  

Tisnerat , 2000] 

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28 

2.5.2  Fault of Dead Sea  

The Dead Sea fault defined as separating the Sinai sub-plate and 

Arabian plate. It is about 1.200 km long, and connects the Taurus Zagros 

compressional front in the north, to the extensional zone of the Red Sea in 

the south (Yankelevsky, 2008). 

Over the past million years tectonic movements have shaped the 

Dead Sea Fault system. It is one of the most seismically active regions in 

the Middle East. The region has a remarkable historical and geological 

record of seismicity, and several historical earthquakes have caused 

extensive damage in the area. Places such as Jericho, the oldest city in the 

world one of the largest cities in the region in Roman time, were greatly 

affected by seismic activity. 

The recent studies of crustal structure, shown the crust directly under 

the fault valley is somewhat different from that on the sides, so as a result, 

these differences in crustal structure may have controlled the evolution of 

physiography in the region (Ben-Avraham, Lazar, Schattner, Marco 2001). 

Moreover, the physiography of the Dead Sea fault is also affected by the 

vertical motion, which caused settlements of the floor of the rift and uplift 

of its shoulders. The Dead Sea fault characteristics can be arranged into 

into four main segments; S1: Ghab Valley segment, S2: Missyf Graben 

segment, S3: Lebanon Bend segment, and S4: Jordan & Araba Valley 

segment. 



29 

2.5.3 Seismicity of The Site 

Bethlehem is located between two areas of low to medium 

seismicity, one to the east and one to the west side. It is situated close to the 

fault line separating the African and Arabian tectonic plates, figure (2.12), 

and has been affected by several minor and major earthquakes with 

epicenters in the surrounding areas, such as the 1927 Palestine earthquake, 

also called Jericho Earthquake. Many Palestinian cities were heavily 

damaged, thousands of people were left homeless and at least 500 were 

estimated to be killed. (Touqan, and Salawdeh, (2016)), 

District of Bethlehem, where the Church of Nativity is located, is 

similar in seismicity to the eastern parts of the states, so 10% probability of 

exceedance in 50 years used in this dissertation with no limitations, 

therefore, IBC 2015 can be used without using previous equitation‟s (2.5 

and 2.6) with no need for concerning the factor of safety 1.5 (factor times 

the design earthquake features). 

 

Figure (2.12): Fault Line Between the African and Arabian plates. 



30 

2.6  Recent Studies  

2.6.1 Over The World 

The purpose of investigating the seismic behavior concerning the 

monuments, such as masonry structures is divided for two paths, the first is 

to identify the mechanisms to be used for the protection of monuments for 

the purpose to help it avoiding structural collapse and destructions during 

earthquakes excitations, and the second is to select the most effective and 

suitable rehabilitation aspects. 

Most of historical and monumental structures consist of masonry 

material, as mentioned before, which is considered to be the historically 

oldest structural material, and they may be located in geographically 

regions subjected to a higher risk of earthquakes, i.e. around the 

Mediterranean Sea, also the investigation of an old masonry structure is 

often combined with several difficulties, such as, the difficulty to find the 

original designs and architectural plans. Over the time, changes may have 

occurred to the structure, these might be structural modifications due to 

changes of use or renovations. Another reason may be any new technical 

installations such as a heating system that fixed during the life of the 

structure, epically these modifications often concern the structural system, 

and if modifications took place, they should be notified in the building 

chronology.  



31 

Over the years, and especially in last twenty years, researchers have 

studied the seismic assessment and performance of historical buildings, 

including their details, difficulties, mechanisms, regions, and rehabilitation 

process. One of the important studies was done by, Araújo, Lourenço, 

Oliveira and Leite, in 2012, for the St James Church, which was studied 

and assessed by means of pushover analysis  (Before and After the New 

Zealand Earthquake), and presents a numerical study in details for the 

seismic assessment of the St James Church in Christchurch- South Island, 

The structural behavior of the Church has been evaluated using the finite 

element modeling technique, by using it; the nonlinear behavior of the 

structure has been taken into account by proper constitutive assumptions, 

figure (2.13). 

  

Figure (2.13): General View of St. James Church and the Numerical Model. 

[Araújo, B. Lourenço, Oliveira, Leite, 2012] 

After the nonlinear pushover analyses are carried out on both 

principal directions, the Church can no longer be considered safe. The 

analysis results of the model show moderate agreement with the visual 

inspection performed in the site, which further validates the model used, 



32 

and finally, the limit analysis using macro block analysis was also carried 

out to validate the main local collapse mechanisms of the Church. 

Paulo Lourenço, with cooperation with another team consisted of 

João Roque, and Daniel Oliveira, in the same year (2012), investigates the 

seismic safety of Monastery Church in Geronimo – Portugal. The work was 

done with a full data about the seismic behavior of the Church of 

Monastery of Geronimo, which is discussed with a numerical simulation, 

figure (2.14). Using artificial seismic acceleration time histories in 

agreement with three seismic hazard scenarios for 475, 975 and 5000 years 

return periods, allowing assessing its seismic safety. The detailed analysis 

for vertical loading and seismic loading results is indicating that the safety 

level of the structure is adequate for vertical and horizontal loadings. Also, 

the monitoring system installed allows the structural health of the church to 

be monitored, particularly in case of future earthquakes, providing 

excellent feedback for future analysis of damage. 

  

Figure (2.14): Virtual Collapse Mechanisms. [P. Lourenço, J. Roque, D. Oliveira, 2012] 



33 

In similar manner, F. Bucchi, S. Arangio and F. Bontempi, in 2013, 

work on the seismic assessment of an historical masonry structures, using 

the nonlinear static analysis. They give the attention for the nonlinear static 

analysis of equivalent frames models, and under the propose of giving a 

measure of the response of the structure with simple implement.  

In particular, its application with SAP2000 is presented; this 

approach is applied to a façade of an historical building that was damaged 

by the 2009 L‟Aquila earthquake central Italy. The considered building is 

the Camponeschi Palace which is shown in figure (2.15), located in 

L‟Aquila city center. The damage mechanisms obtained are compared with 

the observed damage and with those obtained from other approaches. 

 
 

Figure (2.15): Camponeschi Palace - L‟Aquila, Italy. [ F. Bucchi, S. Arangio and 

F. Bontempi , 2013] 

In the same topic, G. Castellazzi, C. Gentilini, and L. Nobile, in 

2013, study the seismic vulnerability of the Basilica of church which is 

located in Italy, by means of limit analysis and nonlinear finite element 

analysis, figure (2.16). The attention here is posed similarly to the failure 

mechanisms of the façade of the church and its interaction with the lateral 



34 

walls. For more details, the limit analysis and the nonlinear finite element 

analysis provide an estimate of the load collapse multiplier of the failure 

mechanisms. 

Investigations based on results obtained from limit analysis and 

nonlinear finite element analysis have been conducted on some macro 

elements with special attention to those that interact with the façade, and 

the results obtained from both approaches are in agreement and can support 

the selection of possible rehabilitation process and scenarios in order to 

decrease the vulnerability under seismic loads. 

  

Figure (2.16): Photograph of Madre Santa Maria del Borgo Church, Italy. [G. 

Castellazzi, C. Gentilini, and L. Nobile , 2013] 

P.G. Asteris , M.P. Chronopoulos , C.Z. Chrysostomou , H. Varum , 

V. Plevris , N. Kyriakides , and V. Silva,  in 2014, presents a methodology 

for earthquake resistant assessment of the masonry structures. The entire 

process is established using case studies of historical masonry structures 



35 

located in the area of Europe; In particular, the reliability of the proposed 

method is checked using analysis of existing masonry buildings in three 

different countries, i.e. Cyprus, Greece and Portugal, for different 

seismicity levels that influencing the risk impacting the masonry structures. 

They conclude according to the analysis of results for the strengthened 

structures. The methodology followed, has been proved helpful to the 

analysis of existing masonry historical buildings.  

Andrés Braga, and Paulo B. Lourenço, published their thesis under a 

title of Study the Armenian Church in Famagusta. The detailed study of the 

medieval Armenian Church in Famagusta was done in three main research 

steps. The first step concerning the historical analysis and restoration works 

of the edifice. This work phase included the characterization of the current 

condition of the structure based on an in-situ visual inspection, figure 

(2.17). The second step corresponded to the application of nondestructive 

tests (namely dynamic analysis, using ambient vibration techniques, and 

sonic tests) to the Armenian Church members as figure (2.18) shows. The 

results of these investigation techniques allowed identifying important 

dynamic properties of the structure, such as frequencies and modes of 

vibration, and the dynamic modulus of elasticity of the church masonry. 

And the final research step regarded the construction of a tridimensional 

finite element model of the Armenian Church.  



36 

 

 

Figure (2.17): Armenian Church in Famagusta [Paulo B. Lourenço, Andrés Braga, 

2013] 

 

 
 

Figure (2.18): Sonic Test Applied to the Armenian Church [Paulo B. Lourenço, 

Andrés Braga, 2013] 



37 

After the aforementioned work, the results indicate that the building 

presents a considerable safety level in terms of seismic performance, as 

well as a good overall vertical loading; these characteristics can be 

attributed to the regularity of the masonry structure and to the high stiffness 

and almost moderate height of the masonry walls. 

Another adapted methodology was followed by H. Animas, M. 

Navarro, J. Pacheco Martínez, J. L. García, T. Cordero, C. J. Esparza, and 

J. A. Ortiz-Lozano, in the year of 2014, with purpose of perform an 

structural analysis of the temple of San Antonio in Aguascalientes, México, 

figure (2.19) According to this work, three-dimensional analytical macro 

models are evaluated using the finite element method, the analysis was 

performed taking into account the linear and non-linear behavior of the 

masonry. 

 

Figure (2.19): Views of The Temple of San Antonio, [H. Animas, M. Navarro, J. Pacheco 

Martínez, J. L. García, T. Cordero, C. J. Esparza, and J. A. Ortiz-Lozano, , 2014] 



38 

The safety level of the structure was evaluated, and the higher 

probability zones to be damaged were located, also the seismic 

vulnerability calculated using a pushover approach. The dynamic response 

of the structure was determine for different values of the material 

properties, after that a comparative assessment between all of the results 

was performed, in order to determine how the change of the properties can 

affect the results of the modal analysis. 

Turning to Spain, the assessment of the structural damage and 

stability of the church of the Royal Monastery of Santa Maria de Poblet, 

was done by Savvas Saloustros, Luca Pelà, Pere Roca, and Jorge Portal, in 

the year of 2015, figure (2.20). This case study is one of the UNESCO 

World Heritage sites. 

 

Figure (2.20): Plan and Cross-Section of The Church of the Poblet Monastery, 

[Savvas Saloustros, Luca Pelà, Pere Roca, and Jorge Portal, 2015] 

The analysis presents damage affecting the lateral aisles and main 

nave, including existence of the cracking in the vaults and deformation in 

the clerestory walls. Based on the historical survey and site visiting, a 



39 

sophisticated finite element model was used for the structural analysis. The 

3D model was developed on the basis of the results of the terrestrial laser 

scanning survey, in order to take into consideration the current deformed 

state of the structure. The continuum damage model allowed a realistic 

representation of the masonry behavior under tension and compression, and 

simulation of past reported or possible actions i.e. structural alterations and 

settlements and earthquakes, provided valuable information on the causes 

of the present deformation and damage of the church.  

Also in India, M. Shariqa, S. Haseebb and M. Arifc, 2016, 

investigate the analysis of existing masonry heritage building subjected to 

earthquake loading. The work was done on an existing masonry heritage 

building situated in Aligarh city based on the time history method using El-

Centro earthquake data which has been employed for seismic performance 

of the chosen building.  The maximum principal tensile stress and 

maximum shear stress has been observed and compared with permissible 

stresses as figure (2.21) presents. It has been found that these stresses 

exceed the permissible limit at few locations such as dome-wall junction, 

wall-roof junctions and the minarets. It has also been found that these 

locations are the most critical portion of the building under earthquake 

forces. 



40 

  

Figure (2.21): Principal Tensile and Shear Stresses for Jama Masjid [M. Shariqa, 

S. Haseebb and M. Arifc, 2016] 

For the Turkey historical moments, again P. B. Lourenço with L. 

Mangia, B. Ghisaasi, E. Sayın, O. Onat, show the pushover analysis of a 

historical masonry structure Elti Hatun Mosque, figure (2.22), which is 

located in Tunceli, Turkey. It is located in the seismic zone 2 according to 

seismic zone map of Turkey. The modeling and analyzing with Diana finite 

element software based on real dimensions measured by site visiting, and 

by adapting macro modeling strategy to model masonry elements. 

The results show that the structure is two times weaker in the 

transversal direction than longitudinal direction, for the main reason 

referred to existence of the main gate of the structure which works as a 

rigid support system in the longitudinal direction. On the other hand, the 

vertical pushover analysis also was done in the same manner, to investigate 

the safety factor of the mosque under its self-weight, the results is 

acceptable in all directions. However, the presented results are only a 

prediction of the behavior due to several uncertainties about the material 

properties.  



41 

  

Fig.(2.22): Elti Hatun Mosque with its Outside and Inside View. [P. B. Lourenço 

with L. Mangia, B. Ghisaasi, E. Sayın, O. Onat, 2016] 

K. Ip, J. Lester and A. Brown, in 2016, investigate the Cathedral of 

the Blessed Sacrament, Christchurch – New Zealand, and focusing on the 

seismic nonlinear analysis of these damaged historic buildings, because as 

they said, there is no existence for any established guidelines and the only 

methods of prediction of the structural behavior of historic buildings is 

empirical. Their used approach is to combine the advantages of the 

continuum method i.e. Finite elements, with the discrete method, by using 

constitutive models and contact surface algorithms, which are available in 

the numerical simulation software LS-DYNA, figure (2.23) 

  

Figure (2.23) : General and 3D View of Cathedral of the Blessed Sacrament. [K. Ip, J. 

Lester and A. Brown, 2016] 



42 

In details, the discrete element and finite element can simulate the 

complex nonlinear dynamic behavior, and the macro and micro damage 

modeling in the initial analysis can provide a reasonable estimation of 

stiffness and strength degradation for the existing cathedral. Also, a good 

correlation with observed damage on site, can be obvious by the crack 

patterns, such the estimated stiffness reduction gives a physical measure of 

the level of damage. The crack, stiffness and strength degradation can be 

carried over to the pushover analysis or the nonlinear time history analysis 

as an initial stage situation.  

The results of pushover analysis show the existing cathedral as a 

brittle structure with no ductility, with assumption of damping 5% and the 

structure is elastic for base shear demand (i.e. μ=1) without considering the 

strength reduction factor (i.e. ф=1), the ultimate residual base shear 

capacity could be up to 53%.By the way, the actual capacity is limited by 

the local instability of structural components; this performance was further 

confirmed by dynamic analysis, which verified the dynamic response and 

identifies the local instability considering the structure. The results show 

also, there is no global collapse occurred, but the arch and portico mega 

columns completely lost stability under the strong ground shaking. 

Panagiotis G. Asteris , Maria G. Douvika, Maria Apostolopoulou, 

and Antonia Moropoulou, 2017, present a new stochastic computational 

framework for earthquake-resistant design of masonry structural systems. 

The proposed framework is based on the probabilistic behavior of crucial 



43 

parameters, such as seismic characteristics, material strength, and utilizes 

fragility analysis based on different failure criteria. The application of the 

entire methodology is illustrated in the case of a historical and monumental 

masonry structure, namely the assessment of the seismic vulnerability of 

the Kaisariani Monastery in Athens, Greece, figure (2.24). 

  

Figure (2.24): General and 3D view of Kaisariani Monastery in Athens, [Asteris , 

Douvika, Apostolopoulou, and Moropoulou, 2017] 

Based on the 3d analysis, the new stochastic computational 

framework for earthquake-resistant design of masonry structural systems 

has been established, namely, the fragility analysis has been applied based 

on the probabilistic behavior of crucial parameters involved in the 

modeling of the structure, such as the values of materials‟ strength and the 

peak ground acceleration.  According to the analysis, it has been shown 

that the proposed approach offers a ranking method that supports civil 

authorities in optimizing decisions for choosing, among a plethora of 

structures, which ones present the highest levels of vulnerability and are in 

need of immediate strengthening. It also plays an important role for the 



44 

engineers, in choosing the optimal repairing scenario among a number of 

competing scenarios.  

Giulio Castori , Antonio Borri , Alessandro De Maria , Marco 

Corradi , and Romina Sisti, 2017, presents the results of analysis carried 

out on a the monumental masonry building, known as the Civic Museum of 

the small city of Sansepolcro in Tuscany – Italy, figure (2.25). The building 

characterized as one of the most important and renowned civic structures, 

and by presence of one of the masterpieces of late 15th-Century 

Renaissance art. A full three-dimensional non-linear static analysis based 

on the limit analysis theorems are used for understand the macro scale 

structural behavior.  

 

  

Figure (2.25): General and 3D View of Civic Museum,  [Castori , Borri , Maria , 

Corradi , and Sisti, 2017] 

Afterwards, the results of the finite element method analyses 

performed on a detailed 3D model of the wall panel containing the fresco, 

which are used for investigating the causes of the cracks patterns. The 



45 

results 3D pushover analysis show, on the one hand, the results of the limit 

analysis and, on the other one, the calibration of the use of a refined 3D 

finite element model for catching the response of the wall containing the 

fresco. The results highlight some problems related to the ability of the 

construction to withstand and offer a good performance levels for both the 

conservation of the fresco and safety of people who use the Museum. The 

simplified scheme of limit analysis and the results obtained from the non-

linear static analysis presents that the structural behavior in the transversal 

direction is poor and inadequate, due to the out of plane mechanism, figure 

(2.26). Also, the application of 3D pushover analysis confirmed some 

structural deficiencies also in the in plane behavior of the wall panel 

supporting the fresco, however the observed damage is mainly associated 

for the presence of shear failure mechanisms. 

  

Figure (2.26): 3D Model of Fresco. [Castori , Borri , Maria , Corradi , and Sisti, 2017] 

Stay in Italy, in 2018, Gessica Papa, and Benedetta Silva, propose an 

approach for the assessment of seismic vulnerability from the perspective 

of prevention and conservation. A comparison of the state of damage has 

been carried out based on using the case study, St. Salvatore church, figure 



46 

(2.27), which underwent two important seismic events in the Central Italy 

area, the 1997 and the 2016 earthquakes. 

  

Figure (2.27): Location and 3D of St. Salvatore Church. [Papa, and Silva, 2018] 

The multidisciplinary procedure for the assessment of seismic 

damage demonstrates the advantages in terms of a more exhaustive vision 

of the damage. This methodology could be applied to other churches in 

similar manner in Italy and to other similar situations.  

2.6.2   Relevant Studies for Palestine 

Gabriele Milani, Marco Valente, and Claudio Alessandri, in 2016, 

present some results of investigations of advanced numerical model carried 

out on the church of Nativity in Bethlehem. They studied the seismic 

response of the church and identify possible causes of failure. In details, 

three dimensional finite element models of the church are developed with 

the damage plasticity of the material figure (2.28). Nonlinear bidirectional 

dynamic analysis is first performed on the model in the actual configuration 

and resulting in observe the damage in the semi-domes, vault system, and 

near the interlocking of the walls. In second step, the narthex is separated 

from the church and analyzed under seismic excitation only in the 

longitudinal direction.  



47 

The narthex is considerably affected by presence of vaults which act 

as connecting element between the façade of the Church and the façade of 

the narthex. The vault system is subjected to severe damage due to 

significant stresses. The second critical element of the narthex is the 

western façade, which tends to show a local overturning mechanism due to 

the gradual accumulation of damage near the base of the vault system. 

Also, the façade of the narthex can reach displacements under seismic 

actions with ag=0.25g. The results seem to indicate that the rotation of the 

narthex façade, with a consequent maximum out-of-plane displacement of 

40 cm approximately, is probably due to a seismic event of great intensity 

or to several seismic events occurred in sequence over time. Certainly, 

results closer to the measured data can be obtained by introducing proper 

unilateral contact conditions at the interface between vaults and façade 

walls or between longitudinal walls and façade walls. 

 
Figure (2.28) : 3D Finite Element Model for The Nativity Church. [Milani, 

Valente, Alessandri, 2016] 



48 

In another side, Claudio Alessandri, with cooperation with Jessica 

Turrionim in 2017, propose an innovative technique for reinforcing the 

wall of the Church of the Nativity against earthquakes. Local seismicity 

data and the parameters of an equivalent Italian site provided the input data 

for a design earthquake, and 3D modal analysis of the entire Church 

revealed that the structure is characterized by clear local modes of 

vibration. As per the most recent studies on masonry structures, local 

assessment based on limit analysis procedures was performed. This showed 

that in the event of an earthquake, a Crusade era wall addition is at risk of 

collapse via simple overturning around its own base, due to the lack of firm 

connections with the orthogonal walls of the façade and the transept. 

Hence, a novel double system of horizontal steel tension structures was 

designed to consolidate the wall, conforming to the main restoration 

Charter requirements, i.e. lightness, non-invasiveness and reversibility, and 

being hidden from the sight of visitors. In the absence of reliable local 

regulations, all analyses, computations and checks on the proposed 

intervention were carried out with reference to the Italian technical 

regulations. 

  

Figure (2.29): Aerial View of the South Wall. [Claudio Alessandri, Jessica 

Turrionim, 2017] 



49 

2.7  Progressive Collapse of Masonry 

2.7.1 Introduction 

ASCE, which is known as the American Society of Civil Engineers, 

makes a definition for the progressive collapse, summarizes as the process, 

by which the failure can spread among the parts of the structure, and by the 

end, total or partial collapse of a structure occurred. 

Seismic excitation, and the need for heightened security of life 

safety, has created an increased concern for structural design and analysis 

against progressive collapse for new and existing buildings. Many of the 

existing structures that are in need of strengthening for those considerations 

are the masonry structures and monuments. In particular, due to the load 

bearing wall system and material characteristics of masonry, a loss of load 

bearing members can lead to multi locational failures, without much 

warning or time for evacuation of the building. Furthermore, progressive 

collapse assessment and rehabilitation of the masonry structures can be 

difficult due to the heterogeneous and anisotropic characteristics of the 

material, also the brittle nature considering the material, and lack of 

redundancy in the structural system. 

2.7.2   Researches of Progressive Collapse 

McGuire and Leyendesker, in 1974, studied five different existing 

unreinforced masonry buildings and their response to the explosions loads, 

also if the building would be critical to the progressive collapse. The results 



50 

summarized as, two of the buildings are considered to be critical to the 

progressive collapse, one building has no conclusive results, and the final 

two buildings are found not critical. Surly at that time, no adequate 

information for masonry structures, and this led to make the analysis and 

assumptions different than what they may be today, as an example, the 

cracking or tensile stress limits of masonry was ambiguous at that time. But 

today, the Masonry Standard Joint Committee (MSJC) code 2013 provides 

information and guidelines for dealing with masonry. In details some of the 

assumptions and outcomes generated from McGuire and Leyendecker in 

1974 will be different if done today.  

Alternative path examples vary due to the different situations 

possible with masonry buildings. Providing alternative load paths in 

masonry structures is dependent upon the connection between load bearing 

elements and the floor system. The arch behavior, and large openings, with 

other unique capabilities of masonry are important aspects to consider 

when looking into progressive. Joint and ties continuity help to resist 

progressive collapse, and add some integrity to the building. After 

strenuous efforts, the researcher concluded that there are slight researches 

in the topic of progressive collapse in masonry structures. Due to this 

inadequate researching work of directly relevant literature,  and to attempt 

finding information related to progressive collapse analysis of masonry 

structures, the following approaching topics will be showed: 



51 

F. Palmisano, A. Vitone, & C. Vitone, 2005, published their research 

of the title, “Load path method in the interpretation of masonry vault 

behavior”, which deals with the performance of application of load path 

method, figure (2.30). This method offers an interpretation of masonry 

vaults behavior which is immediately exhibits the correlation between 

geometry, and distribution of loads, it can be very useful to understand the 

link between structure and form to diagnose the pathologies of the masonry 

structures. 

  

 

Figure (2.30): Masonry Barrel Vault With Possible Loads Paths in the Arch‟s. [F. 

Palmisano, A. Vitone, & C. Vitone, 2005] 

In similar manner, LIN Feng, WANG Ying, GU Xianglin and 

ZHAO Xinyuan, in 2010, evaluate historical building structures against 

progressive collapse. They state, for historical buildings, two aspects make 

them different from the modern buildings, its properties are usually 

deteriorated to some extent, and the structural constructions may not meet 

the requirements of current codes. Therefore, a method for evaluations the 



52 

performance of the historical buildings to resist progressive collapse is 

shown here started from evaluate the building layout to protect the 

inhabitants from the possible collapses, investigate the geometrical 

information considering the structural constructions and the material 

properties, and finally analyze the structure with means of alternative path 

method and tie force method, to establish the resistance capacity for 

progressive collapse. The proposed method is illustrated by means of a case 

study of a steel frame historic building in Shanghai, China, namely the 

Bund 18 building, shown in figure (2.31). 

 
 

Figure (2.31): The Bund 18 Building, and its  Plan View of First Floor.  

[LIN Feng, WANG Ying, GU Xianglin and ZHAO Xinyuan, 2010] 

The case study (Bund 18 building) was built in 1923, having a total 

floor area of 10,450 m
2
, with height reaches 53.10 m. the current situation 

of the Historic Building in Shanghai is excellent. In the original design the 

building was mainly used for as offices, but its function now transformed 

into a commercial building.  



53 

The evaluation of building layout shows that the roads around the 

building are straightforward with no obstructions, also, the distance 

between building and the roadside is about 5m, which is less than 

requirements 25m in the relative criterion (DoD 2003). In addition, there is 

no explosion proof wall around the sides of the building according to the 

retrofitting plan, and no any protective measures taken for the structural 

elements. For the investigation of geometrical information and material 

properties, an in situ inspection technique used to determine it. And finally, 

the analysis of the structure with means of alternative path method and tie 

force method, gives the results proved that the constructions of the building 

meet the requirements of DoD (2005), for all types of tie forces. Also for 

alternative path method, a computational model, using finite element 

method and based on computer program SAP2000, shown in figure (2.33), 

used for removal of some columns, and analyze the building with the 

nonlinear static analysis, to evaluate the performance of this structure to 

resist progressive collapse, which is relatively concluded well. 

  

Figure (2.32): The 3D Model With Collapse Due to Removal of Some Columns. 

[LIN Feng, WANG Ying, GU Xianglin and ZHAO Xinyuan, 2010] 



54 

On the other hand, Xu, Zhen, Lu, Xinzhrng, Guan, Hong, Lu, Xiao, 

Ren, and Aizhu, in 2013, Published a paper of “Progressive Collapse 

Simulation and Critical Region Identification of a Stone Arch Bridge” In 

Journal of Performance of Constructed Facilities. The need for this paper 

was generated due to occurring of progressive collapses of arch bridges in 

recent years, which is resulting in many damages and significant losses. 

2.7.3 Relevant Codes and Standards  

In this part, the reader will see the codes and standards which are 

studied to resist progressive collapse, and to determine deficiencies that 

may exist in the analysis for existing masonry buildings. The researcher 

focuses on current codes and standards starting from American standards to 

Europe codes, in order to find differences that may exist. 

2.7.3.1 IBC 2012 

The International building code (IBC) 2012, establish the foundation 

for minimum requirements considering buildings and public safety. In 

particular, for high rise buildings, or high risk regions, IBC, lays out, the 

requirements to ensure the structural integrity, also for load bearing 

structures, the vertical ties are required in all walls, in addition to 

transversal, longitudinal ties at each floor. IBC goes on, to provide design 

methods and equations in order to meet these design requirements. 



55 

2.7.3.2 ASCE 7-10 

The American Society of Civil Engineers (ASCE) 2010, in similar 

manner, provides minimum design requirements for buildings through the 

United States. ASCE provides a minimum requirement for structural 

integrity for all buildings, in particular, the section 1.4 of ASCE 7-10 states 

that “all structures must have a continuous load path for the structure and a 

lateral force resisting system capable of resisting the appropriate notional 

loads for each level derived from the structure‟s weight”.  

The commentary of section 1.4 indicates that these requirements are 

intended for “normal service and minor unanticipated events”.  

ASCE 7-10 also, provides load combinations for design, in two 

general approaches, known as direct and indirect, and provides guidelines 

for the provision of general structural integrity, as shown below: Indirect 

Design: defined in ASCE 7-10 as “implicit consideration of resistance to 

progressive collapse, during the design process through the provision of 

minimum levels of strength, continuity, and ductility”. The indirect design 

method will be difficult to use for existing masonry buildings, due to the 

addition of ties. Direct Design: defined in ASCE 7-10 as “explicit 

consideration of the resistance to progressive collapse during the design 

process”. Two procedures, known as alternate path method and specific 

local resistance method, are presented to accomplish this consideration. 

These procedures allows local failure to occur, but seeks to provide 

alternate load paths so that the damage is absorbed and major collapse is 



56 

averted” while the local resistance method “seeks to provide sufficient 

strength to resist failure from accidents or misuse” (ASCE, 2009). 

Guidelines for the Provision of General Structural Integrity: ASCE 

7-10 shows several concepts that would achieve the required structural 

integrity of buildings, i.e. adding load bearing members or partitions, 

adding reinforcement in slabs, and changing the direction of span of floor 

slabs. 

2.7.3.3 MSJC-13 

The Building Code Requirements and Specification for Masonry 

Structures (Masonry Standards Joint Committee, 2013), states that, the 

masonry structures are load bearing systems, so it is important to review 

the guidelines that may be presented within masonry code requirements, 

with regard to progressive collapse. Also, states that masonry structures 

may be required to have enhanced structural integrity as part of a 

comprehensive design against progressive collapse due to accident, misuse, 

sabotage or other causes” (MSJC, 2013). So, it goes on to reference the 

commentary section 1.4 of ASCE 7-10, as general design guidance.  

2.7.3.4 GSA 2013 

The General Service Administration (Alternate Path Analysis and 

Design Guidelines for Progressive Collapse Resistance) which is known 

shortly as General Services Administration, (GSA, 2013), publish the latest 

previsions in October 2013 and replaced the document “GSA Progressive 



57 

Collapse Analysis and Design Guidelines for New Federal Office Buildings 

and Major Modernization Projects” which was published in June 2003. The 

new provisions have good modifications which can be summarized as 

elimination of the tie force method and the local resistance method, which 

presented in Unified Facilities Criteria (UFC) 04-023-03: Design of 

Buildings to Resist Progressive Collapse for all materials, which leave only 

the alternative path method for design and analysis. 

2.7.3.5 UFC 04-023-03 

Design of Buildings to Resist Progressive Collapse, (Department of 

Defense, 2009), shows the guidelines for progressive collapse were updated 

in 2009. These guidelines are written by the United States Department of 

Defense, and state three different design procedures that can be used with 

masonry, such that, tie force, alternate path , and Enhanced Local 

Resistance. Occupancy category ensures for applying the tie force and 

enhanced local resistance procedures, but when tie force requirements 

cannot be met, the alternate path method must be used. It is noted within 

the UFC that the alternate path method is “often the most practical choice” 

for load bearing wall structures (DoD, 2009).  

2.7.3.6 ASCE 41-13  

American Society of Civil Engineers, 2014, (ASCE 41-13) is 

referenced by UFC 04-023-03 for analysis procedures with respect to the 

building material of the structure. All details and material sections in ASCE 



58 

41-13 provide analysis guidelines such as modeling criteria, acceptance 

criteria, and strength calculations. For the strength calculations as an 

example, it lacks in some areas when compared to the steel and concrete 

sections of the standard. These areas include information about 

recommendations for retrofit strategies, and connections in masonry 

structures. The masonry section of ASCE 41- 13 addresses the condition 

assessment for existing buildings, and the strength requirements of 

reinforced masonry, unreinforced masonry, infill panels, and foundation 

elements.  

2.7.3.7 EUROCODE 

This national standard for European countries lays out guidelines and 

requirements for designing buildings to resist progressive collapse. Euro 

code: Basis of Structural Design (EN 1990) sets out the general 

requirements for structural design by stating “A structure shall be designed 

and executed in such a way that it will not be aged by events such as: (1) 

explosion, (2) impact, and (3) the consequences of human errors, to an 

extent disproportionate to the original cause” (European Committee for 

Standardization, 2001). It continues on to state that this shall be avoided or 

limited by selecting and designing a structural system such that it can 

survive adequately from the accidental removal of an individual member 

(aka: progressive collapse) Euro code 1 – “Actions on structures – Part 1-7 

(EN 1991-1-7): General Actions – Accidental Actions” (European 

Committee for Standardization, 2006): This section gives more specific 



59 

requirements for progressive collapse actions on structures and the 

strategies that should be used to prevent progressive collapse depending on 

the risk category of the structure. Along with taking measures to reduce the 

probability of an event that would cause progressive collapse, the design 

strategies mentioned include the use of horizontal and vertical ties, and/or 

ensuring that upon the removal of an element, the building remains stable 

and damage does not extend past a certain limit. The limit stated in this 

national standard is 100 m2 or 15% of the floor area, whichever is smaller. 

For load-bearing structures, the length of wall to be removed for analysis is 

2.25 times the story height for internal masonry walls and for exterior 

masonry, the length between other vertical lateral supports. In the event of 

using notional removal of a section of wall for design, these sections are 

referred to as key elements and should be designed to withstand the 

recommended load of 34 kN/m2. Similarly to UFC, Eurocode states that 

for load-bearing wall structures, the notional removal of a section of wall is 

most likely the most practical approach for design compared to using ties. 

Eurocode 6 – “Design of Masonry Structures – Part 1-1 (EN 1996-1-1): 

General Rules for Reinforced and Unreinforced Masonry Structures” 

(European Committee for Standardization, 2005): This section for masonry 

design demands that masonry structures are to be designed so there is a 

“reasonable probability” the structure will not be damaged to an extent that 

causes progressive collapse due to accidental situations. The section also 

lists the design methods discussed in EN 1991-1-7 in order to ensure 

progressive collapse does not occur. Like the masonry standard, other Euro 



60 

codes for steel and concrete also reference EN 1991-1-7 for design against 

progressive collapse. Unlike the UFC 04-023-03 and the GSA provisions 

referencing ASCE 41, the Euro code does not reference the seismic 

analysis procedures that exist in the Euro code to be used for analysis of 

progressive collapse. 



61 

 

 

 

 

 

 

CHAPTER THREE 

MODELING of CASE STUDY 



62 

3. Modeling of Case Study 

3.1 Introduction 

The seismic assessment for any structure needs to study fundamental 

dynamic properties. In this thesis, the needed dynamic properties are 

obtained by using the finite element method. 3D linear and nonlinear 

analyses are done for the case study which is the church of nativity. The 

model built using two software‟s, the first by SAP2000, and the another by 

DIANA FEA, this work done after the survey of archeological existing 

building, and making the data acquisition to produce a clear geometrical 

Image. 

3.2 Case Study: The Church of Nativity 

This Church is one of the earliest Christian structures, which is the 

birth place of Jesus. The original Basilica, created in the 4th century by 

Emperor Constantine, which was completely damaged in the Samaritan 

Revolt, (Qustandi Shomali (2015)). It was replaced later on the same site, 

by another Basilica; it was different in its plan and had at that time, 

modified parts of the original building, figure (3.1) present this basilica. 

The location of church is Bethlehem, separated as a 10 km south of 

Jerusalem, which was built over fertile limestone hills. The district center 

developed moderately two hills and the extent of the settlement that existed 

at the end of the 19th century has been delineated as the „historic center‟ 

for management and conservation processes. Appendix (A), show the 

general drawings of the case study 



63 

 

Figure (3.1): Perspective Picture for Church of the Nativity 

The church mainly constructed of masonry walls, which are 

composite material consisting of an assemblage of stones and mortar joints, 

each of them has different properties, and due to the low tensile and shear 

bond strength, mortar joints act as a plane of weakness.  

3.3  Finite Element Method 

The Finite Element Method FEM is a numerical technique used to 

perform analysis for any given physical phenomenon, its solution is the 

most spread one among researchers because it offers accurate 

representation of complex geometry, permit researchers to work with 

inclusion of dissimilar material properties, capture of local effects, and also 

support variety of possibilities for the description of the structures made of 

masonry. In more details, when creating a Finite Element model it is usual 



64 

make some assumptions to simplify the work, such as, boundary conditions 

and connections between different structural parts which are not modeled 

with complete certainty. In addition, this method is based upon the material 

properties (Young's modulus, mass density, etc.). The shape function of the 

chosen elements determines the distribution of the mass and stiffness 

properties, so that the terms in the mass and stiffness matrices can be 

understood physically. However, alternative elements are available with 

different shape functions and for that reason the Finite Element models are 

meaningful but non-unique.  Consequently, the researcher will need to 

examine the sensitivity of the created model, and its results to changes in 

the mesh configuration and/or boundary constraints.  

For the case study of church, there are two main approaches to model 

masonry walls, the first one can be by studying walls as each component 

like solid elements, mortar, and backfill which is summarized by micro 

level, and the other one can be by studying it as composite material which 

is summarized as macro level. 

The aforementioned approaches refer to different fields of 

application; micro 3D models are applicable when the object of the study is 

specified in local behavior of masonry itself, while macro 3D models are 

used when there must be a compromise between accuracy and efficiency. 

When using macro modeling, every component of wall such as unit, mortar 

and their contact is represented as a homogeneous anisotropic block, and 

meshes are very simple, since the internal structure of the masonry is not 



65 

described, and may not reproduce the masonry pattern which is make this 

approach is less mathematical and computations demanding, as a result 

most researchers prefer! On the other side macro models are used when the 

purpose of research is scrutiny seismic behavior of historical, 

archaeological, and complex structures (i.e. cathedrals, bridges).  

3.3.1 Software’s used in the Study 

Through the study of SAP2000 and DIANA FEA software‟s which 

are used, in the analysis, important highlights can be shown, in the first 

hand; SAP2000 is a finite element package used mainly by civil engineers, 

can analyses general structures, i.e. buildings, bridges, dams, and solids etc. 

but, in the second hand, DIANA FEA is advanced finite element software 

usually used for advanced works and simulations, also mainly in academic 

purposes. In details; the physical problems concerning fluids flow, heating, 

contact analysis, also, static and dynamic analysis can be simulated by 

DIANA FEA easily. 

The solid element used by SAP2000 is an eight node; each solid 

element has six quadrilateral faces, with a joint located at each of the eight 

corners as shown in Figure (3.2), in addition, the solid elements of 

SAP2000 have three translational degrees of freedom at each joint, and the 

rotational degrees of freedom are not active. The stresses are evaluated by 

using the standard Gauss integration points of the elements and 

extrapolated to the joints. 



66 

 
Figure (3.2): Eight Node Solid Element in SAP2000 

After investigating the SAP2000, the DIANA FEA takes the place, 

and gives numerous kinds of solid elements. The type of regular solid 

elements used for the numerical model, figure (3.3), according to the 

DIANA FEA manual, are; firstly, HX24L element, which is brick 

geometric element with eight nodes, figure (3.4a), and establish about 

17280 unit in the model.  

 
 

Figure (3.3): 3D Numerical Model Built in  DIANA FEA Software. 



67 

Secondly, PY15L element which is pyramid geometric element with 

5 nodes, 4 sides, and found in 238 location in the model, figure (3.4b), 

thirdly, there are a 624 units of TE12L element, figure (3.4c),  which is 

characterized as tetrahedron geometric element with 4 nodes and 3 sides, 

and in the final, the trusses elements in model, are modeled as bars which 

meet the condition that the dimension D perpendicular to the bar axis are 

small in relation to the bar‟s length L, as figure (3.4d), and exist in 47 

location as 484 units. 

  

a. HX24L elements b. PY15L elements 

  

c. TE12L elements t. Trusses elements 

Figure (3.4): 3D Solids Used in Modeling According to DIANA Manual 

 



68 

3.3.2 Mechanical Properties for Models 

It‟s important to show that, a finite element model of the Nativity 

church is created by using both software‟s SAP2000 and DIANA FEA, 

with the same material characteristics. In details, the Nativity Church has 

different materials which are can noticed through a visual inspection. 

The use of in situ inspection techniques such as coring, flat jack 

tests, thermo vision, sonic tomography, etc. is not applicable in some cases 

for obtaining all the desirable information, sometime these  limitations due 

to saintliness, privacy, and no permissible demolitions in the structure. As a 

result, and due to lack of laboratory information for materials of the church, 

the mechanical properties of the material observed will be used based on a 

number of onsite tests have been carried out by Claudio Alessandri and 

Jessica Turrioni in 2017, and published in their paper under the title of 

“The Church of the Nativity in Bethlehem: Analysis of a Local Structural 

Consolidation”. These tests focusing on the structural components of the 

Church, and generating the material properties of masonry walls like 

compressive strength (Fm), shear strength (td), Young‟s modulus (E), shear 

modulus (G), Poisson coefficient υ, and own weight (w). The constitutive 

model is a macro model with the given elastic material properties 

summarized in table (3.1) reports the selected values needed for the 

definition of the model parameters with respect to some principal elements.  

Another important two points must be discussed; the first which is 

the most predominant characteristic of masonry is that it has a very low 



69 

tensile strength. So in the analysis work, the tensile strength will be 

assumed 5% of the compression strength of the macro model elements. In 

more details, for narthex and the church walls, the tensile strength is 0.233 

MPa, for some specific narthex components it is 0.175 MPa, and finally it 

is 0.05 MPa for the vaults. The second point, considering the shear transfer 

coefficients which are taken 0.1 for open cracks and 0.9 for closed cracks. 

This means that 90% of the force is redistributed to the adjacent nodes 

when the crack opens and 10% of the force are redistributed when a crack 

closes.  

Table (3.1) ; Properties OF Nativity Church 

Properties for Perimeter walls of the narthex and the Church itself 

Fm (MPa) td (MPa) E (MPa) G (MPa) 

4.66 0.089 1429 460.75 

Properties for some specific narthex components 

Fm (MPa) td (MPa) E (MPa) G (MPa) 

3.49 0.067 868.38 147.25 

Properties for vaults 

Fm (MPa) td (MPa) E (MPa) G (MPa) 

1.01 0.02 456.75 147.25 

3.3.3 Verifications of Models 

3.3.3.1 Modal Shapes 

The modal shapes concerning the deformations established using 

SAP2000 and DIANA FEA, are summarized and compared in this section. 

The following figures show the deformed shapes for the first 8 modes, for 

the model built using SAP2000, figure (3.5) show the arrangement start 

from mode (1) to mode (8). Similarly, for the model built using DIANA 



70 

FEA, figure (3.6) arranges them also from mode (1) to mode (8). It is 

manifest that both models give analogical modal shapes. 

  
Mode (1): T = 0.53 sec, f = 1.89 Hz Mode (2): T = 0.45 sec, f = 2.22 Hz 

  

Mode (3): T = 0.35 sec, f = 2.86 Hz Mode (4): T = 0.29 sec, f = 3.45 Hz 

Figure (3.5): Periods and modal shapes concerning the 3D model – SAP2000 

 



71 

  

Mode (5): T = 0.25 sec, f = 4.00 Hz Mode (6): T = 0.24 sec. f = 4.17 Hz 

 
 

Mode (7): T = 0.20 sec, f = 5.00 Hz Mode (9): T = 0.18 sec, f = 5.56 Hz 

Figure (3.5): Periods and Modal Shapes Concerning the 3D Model – SAP2000 – Cont‟d 

 

 



72 

  

Mode (1): T = 0.55 Sec, f = 1.83 Hz Mode (2): T = 0.41 Sec, f = 2.47 Hz 

  

Mode (3): T = 4.31 Sec, f = 3.24 Hz Mode (4): T = 4.27 Sec, f = 3.69 Hz 

Figure (3.6): Periods and Modal Shapes Concerning the 3D Model – DIANA FEA 

 

  



73 

Mode (5): T = 4.23 Sec, f = 4.32 Hz Mode (6): T = 0.23 Sec, f = 4.40 Hz 

  

Mode (7): T = 0.21 sec, f = 4.74 Hz Mode (8): T = 0.19 sec, f = 5.27 Hz 

Figure (3.6): Periods and Modal Shapes Concerning the 3D Model – DIANA FEA  – 

Cont‟d 

3.3.3.2 Modal Analysis 

Although, the real structure has infinite number of modes, not the all 

modes in practice for application, or can be concerned. In this section, 

investigation of figures (3.5) and Figure (3.5) represents the modal analysis 

which shows the vulnerability and possibility for out of plane mechanisms, 

in details the first, forth, and sixth modes show the applicability of interior 

walls to overturn and move in harmonically motion. In addition, out of 

plane mechanisms are possible also for the southern and northern walls, 

whose safety assessment would be necessary with a local analysis, and can 

be confirmed in the second and third modes. As similar, the five and eight 

modes of the “as is”  model involves the translation motion in the two 

principal directions of churches shoulders, these shoulders which have the 

properties of perimeter walls, plays an important role in connections 

between semi-circular apses, and finally the seventh mode shows the 



74 

overturning mechanism of the façade, which undergoes larger 

displacement.  

Table (3.2) 

No. Mode SAP2000 DIANA FEA 

1 Mode (1) 0.55 Sec 0.53 Sec 

2 Mode (2) 0.41 Sec 0.45 Sec 

3 Mode (3) 0.31 Sec 0.35 Sec 

4 Mode (4) 0.27 Sec 0.29 Sec 

5 Mode (5) 0.23 Sec 0.25 Sec 

6 Mode (6) 0.23 Sec 0.24 Sec 

7 Mode (7) 0.21 Sec 0.20 Sec 

8 Mode (8) 0.19 Sec 0.18 Sec 

Table (3.2) shows the corresponding modal periods for the first 8 

modes, and followed by a comparison between them. One of the expected 

behaviors of this kind of a masonry structure is low modal periods. The 

results verify this anticipation as shown. Also, the Figure (3.7) and Figure 

(3.8) show the modal frequencies and the error corresponding to the modal 

periods assuming DIANA FEA results as more accurate. It‟s obvious that 

modal periods are very close to each other and the maximum percentage 

error is 11.23%. 



75 

 

Figure (3.7): Comparison Between Frequencies of Two Models 

 

Figure (3.8): Errors Between Frequencies of Two Models 

 



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CHAPTER FOUR 

NON-LINEAR STATIC ANALYSIS 



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4. Non – Linear Static Analysis 

4.1 Introduction 

The non-linear static analysis with horizontal forces, also known as 

pushover analysis, is carried out with the finite element program DIANA 

FEA after modeling the structure of The Church of Nativity. The model is 

close to the real condition and used to simulate the historical masonry 

components, and it is provide reliable results.  

In the first stage, the seismic analysis are performed and concerning 

the first unidirectional mass proportional load pattern, in both directions, X 

direction, as a longitudinal direction, and Y direction, which is refer to the 

transversal direction, and uses an incremental iterative procedure with 

monotonically increasing horizontal loads, with constant gravity loads.  

The purposes that direct the researcher to apply this method start 

from the goal of estimation the distribution of damage, expected failure 

mechanisms, and ends with the assessment of structural performance of the 

existing building, i.e. the static loads applied in horizontal direction and a 

selected control displacement caused by these loads (EN 1998-1, 2004).   

4.2  Constitutive Model 

The material model used for the behavior of masonry combines the 

plasticity model for compression (Drucker-Prager failure criterion), and the 

smeared cracking model for tension (Rankine failure criterion), figure 



78 

(4.1). In details, the Smeared cracking is specified as a combination of 

shear retention, tension softening and tension cutoff, with constant stress 

cut off is chosen. The linear tension softening based on the energy of 

fracture was selected, and used the crack bandwidth, where the cracks are 

not described one by one but are continuously spread within the element 

and reduce the stiffness, and finally, constant shear retention is chosen due 

to the cracking of the material, results of shear stiffness to be usually 

reduced. 

   

Rankine & Drucker-Prager  Tension cut-off Tension softening. 

Figure (4.1): Material Models Used for The Behavior of Masonry. 

Also, in the modeling procedure, the overestimation of the stiffening 

effect given by the flexible roof is avoided, so in other words, only the 

weight of the new roof was estimated, and lower values of the mechanical 

properties are applied to the connections. These values are used in 

connections between facade and upper wall of the nave, transept and nave, 

transept and apses. The buttresses supporting the chapel vaults are assumed 

totally connected with the wall of the narthex. 



79 

Note that all the other linear and non-linear material parameters 

stated before are used with no modifications, and finally, for the entire 

aforementioned pushover analyses, uses the regular Newton-Raphson 

method for the iteration process, an energy convergence control with a 

tolerance of 10e6, the line search algorithm and arc length control.  

In Force control method, and for models experiencing the softening, 

this method cannot lead to a solution when the load applied is higher than 

the capacity, on another hand, in a displacement control analysis the 

displacement of a reference point is incrementally applied. Figure (4.2) 

show the way of two procedures. 

 
 

Figure (4.2): Force Control Versus Displacement Control. [Palacio, 2013] 

 

After that, the details of arch length should be present, when the 

curve of load-displacement is almost horizontal, the prediction of the 

displacements increment are very large, also when the loads increment is 

fixed, this mean the result of predictions the displacements will be large. 

This overcome this behavior, the analyst use an arc-length control, where 



80 

the increment is adjusted. This method works is illustrated in the figure 

(4.3).  

  

Figure (4.3): Load Increment Methods Characteristics and Arc-Length Control. 

[Palacio, 201