Assessment of the seismic out-of-plane behavior of unreinforced masonry walls

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Assessment of the seismic out-of-plane behavior of unreinforced masonry walls

by

M. Veenstra (Marijke)

0950364

prof. ir. S.N.M. Wijte (TU/e) dr. P. Poorsolhjouy (TU/e) ir. H.G. Krijgsman RO (ABT)

7K45M0

Graduation Project Structural Engineering and Design Eindhoven University of Technology

3 December 2021

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Preface

For as long as I remember, the built environment got my attention. During the secondary school, I also discovered my interest in the technical disciplines. Hence, it has been no surprise that

‘bouwkunde’, in particular the structural design track, was the right choice for me. I like to dive into technical problems, which I often compare to puzzles that first need to be decomposed and under- stood, before being able to solve them in an adequate and creative manner. The combination of my analytical drive, together with my eager to learn new things, led to the choice for the current theme of my graduation project: the assessment of the out-of-plane behavior of unreinforced masonry walls in residential buildings in the Groningen area as a result of earthquake loading. Within the chosen graduation research, I was able to dive into the, for me yet unknown, field of dynamics. The rather complex nature of dynamic nonlinear problems gave me many opportunities to explore and to learn.

Together with the fact that the topic of earthquakes in the Groningen area is (unfortunately) very relevant at the moment, I think I made the right choice. Although the graduation process was quite challenging and tough at some times, I am very happy to eventually present my research.

The master thesis in front of you is written as a partial fulfilment of the requirements for the Master of Science degree in Architecture, Building and Planning, with a specialization in Structural Engineering and Design at the Eindhoven University of Technology. As stated before, the subject of the thesis concerns the assessment of the out-of-plane behavior of unreinforced masonry walls in residential buildings in the Groningen area as a result of earthquake loading.

The research is carried out under supervision of the graduation committee, consisting of prof. ir.

Simon Wijte (TU/e), dr. Payam Poorsolhjouy (TU/e) and ir. Han Krijgsman RO (ABT). I would like to thank my supervisors for sharing their enthusiasm and knowledge on the actual content of the research, as well as for their guidance throughout the process. Besides the regular and irregular meetings with my graduation committee, there were several moments at which I discussed diverse aspects with others, among others people who work for ABT, BORG, TU Delft and Eucentre. I am very grateful for the support I received from this group of people. Lastly, I want to express my special thanks to my family, friends and fellow students, who always supported me and helped me throughout this challenging period.

Marijke Veenstra Eindhoven, November 2021

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Summary

In the province of Groningen, gas drilling takes place since the sixties. As a consequence, the region experiences so-called induced earthquakes. Due to the fact that the region originally did not suffer from seismic activities, the corresponding seismic loading conditions have not been considered during the design phase of the building stock from that time. The majority of the buildings in Groningen is composed of unreinforced masonry (URM) buildings, in which URM walls with high slenderness are applied. The walls are therefore highly sensitive to out-of-plane (OOP) loading conditions. Hence, a genuine risk of damage applies for part of the building stock in Groningen: approximately 26,000 buildings must be assessed to find out whether strengthening is needed. Of course, it is preferred to evaluate these buildings in a short period of time, thus in an efficient manner. At the same time, a sufficiently accurate assessment must be ensured in order to minimize unnecessary strengthening.

The current research aims to improve the knowledge on and the insight into the assessment of the OOP behavior of URM walls. Herein, the balance between the efficiency of the overall assessment process and the accuracy of the assessment outcomes is of particular interest.

For the assessment of the OOP behavior of URM walls in buildings in Groningen, Annex H of the Nederlandse Praktijk Richtlijn (NPR) must be applied. In this standard, three levels of assessment methods are proposed: Tier 1, Tier 2 and Tier 3. The first two methods compare the OOP demand, which is defined as the wall’s response due to the analyzed earthquake load, against the OOP capacity, which is defined as the maximum force or displacement that the wall can withstand before failure occurs. For the determination of the OOP demand, a nonlinear pushover (NLPO) analysis is applied for the structure in which the wall is located. Afterwards, the wall’s OOP demand can be calculated in a relatively simple manner. The Tier 2 method is more complex, as well as more accurate, than the Tier 1 method. The Tier 3 method corresponds to an even higher complexity, as well as a higher accuracy. The method utilizes a nonlinear time history (NLTH) analysis, in which both the OOP demand and the OOP capacity of the wall are included. In this transient analysis, the analyzed structure is subjected to an earthquake load that varies over time. The dynamic response of both the structure and the wall are taken into account. A Tier 3 method can have varying complexities as a result of the usage of NLTH analyses with different levels of detail. Often, an extensive 3D micro-NLTH model is applied, however, less complex macro-NLTH models can also be used to represent the structure.

In order to investigate the assessment process of the OOP behavior of URM walls in terms of the balance in efficiency and accuracy, the research includes the basic Tier 1 and Tier 2 method, as well as three different Tier 3 methods that utilize relatively simple macro-NLTH analyses: Tier 3a, 3b and 3c. In the Tier 3 methods, the analyzed structure and wall are idealized as systems with lumped masses and massless supporting structures with a certain stiffness and a certain damping level. These mass-spring-damper systems differ for the Tier 3a, 3b and 3c method. In this way, the influence of simplifications in the considered idealized systems on the eventual accuracy of the assessment of the OOP behavior of URM walls can be examined. The proposed Tier 3 methods are more complex than the Tier 1 and the Tier 2 method, however, require much less time and effort

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than more complex Tier 3 methods that make use of micro-NLTH analyses.

With the aim of evaluating and comparing the different assessment methods, the OOP behavior of two walls in a two-story terraced house that typifies the building stock in Groningen is assessed.

The structure is constructed to be similar to a structure that has been tested on a shaking table in full-scale. The corresponding experimental data are used to set up the hysteretic material models that are assigned to the springs in the idealized systems that represent the lateral behavior of the building layers. The bilinear springs that represent the OOP behavior of the URM walls, on the other hand, are constructed in a theoretical manner, assuming that the walls behave according to the perfect rigid body mechanism. The eventual idealized systems are subjected to earthquake loads of varying magnitude. In the conducted research, the OOP behavior of the walls in the two-story structure is assessed in accordance to the Tier 1, the Tier 2 and the Tier 3 methods. Besides the assessment of the two URM walls in the analyzed structure, a sensitivity study is included in the research in order to investigate the influence of several aspects on the assessment process.

Several statements can be made from the results of the research. First of all, the Tier 3a method appears unsuitable for assessing the OOP behavior of URM walls. The incorporated simplification of subjecting the system that represents the wall to the average displacement time history of the two floors that enclose the analyzed wall is incorrect. The system, instead, must be subjected to two input loads in order to account for the difference in movements of the two floors.

Furthermore, from the comparison of the Tier 3b and the Tier 3c method, it can be stated that the Tier 3b method yields less accurate and less certain results than the Tier 3c method. At the same time, the complexity of the Tier 3b method, in which the cascade approach is applied, is not considerably reduced compared to the Tier 3c method. Hence, from the three Tier 3 methods, the Tier 3c method shows the best balance in terms of efficiency and accuracy. In this assessment method, the dynamic interaction between the wall and the structure is taken into account.

In contrast to the expectation that the more complex Tier 3 methods, utilizing NLTH analyses, yield more accurate assessment outcomes than the Tier 2 method, utilizing an NLPO analysis, the opposite is observed. The differences in results can be attributed to the substantial difference in the utilized analysis methods. The NLTH analyses, as applied in the Tier 3 methods, appear to be highly sensitive to the nonlinear wall behavior. For walls that have a relatively high flexibility, or a high tendency to show nonlinear behavior, the dynamic response often escalates. Furthermore, in some cases, the NLTH analyses get aborted due to an excessive dynamic wall response, which is considered as OOP failure of the analyzed wall.

From the results of the research, it cannot be stated whether the Tier 3c method yields more accurate or less accurate assessment outcomes than the Tier 2 method. Further research is needed to find the actual accuracy of the Tier 3c method. In the first place, the assessment method must be verified by comparing the numerical results against experimental data. For the numerical analyses, it is important to optimize (the construction of) the idealized systems. In addition, the inclusion of a more accurate, yet more complex, assessment method is recommended in order to conclude on the actual functioning of the proposed Tier 3 methods, rather than the relative functioning. By following up on these recommendations, in continuation of the conducted research, a statement can be made on the ability of the proposed Tier 3 methods to assess the OOP behavior of URM walls in an efficient, yet sufficiently accurate manner.

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List of Figures

2.1 Modelling of one-story structure [15]. . . 7

2.2 Modelling of two-story structure [15]. . . 8

2.3 Force-deformation relationship laterally IP loaded URM shear wall [16]. . . 9

2.4 Free vibration of critically damped, overdamped and underdamped system [15]. . . . 10

2.5 Dynamic amplification factor for different frequency ratios and damping ratios [15]. . 11

2.6 Compressive stress-strain relationship of both brick units and mortar [23]. . . 12

2.7 Compressive stress-strain relationship of units, mortar and masonry [23]. . . 13

2.8 Failure envelope of masonry, subjected to a shear force and an axial load [24]. . . 14

2.9 Failure mechanisms of masonry, subjected to a shear force and an axial load [26]. . . 14

2.10 Planes of failure of masonry in bending [27]. . . 15

2.11 In-plane failures of URM walls. . . 16

2.12 Out-of-plane failure of parapet [35]. . . 17

2.13 Qualitative force-deformation loops for different IP failure mechanisms URM walls [36]. 19 2.14 Force-deformation loops for OOP behavior URM wall [37]. . . 19

2.15 Representative normalized accelerograms (Overschild, Groningen). . . 20

2.16 Elastic response spectrum and design spectrum (Overschild, Groningen). . . 21

2.17 Illustration of LFM. . . 22

2.18 Illustration of MRS analysis. . . 23

2.19 Illustration of NLPO analysis. . . 24

2.20 Illustration of NLTH analysis. . . 25

2.21 Numerical modelling approaches [41]. . . 25

2.22 Secondary spectrum corresponding to Tier 1 method. . . 27

2.23 Rigid body mechanism of one-way vertically spanning URM walls [43]. . . 28

2.24 Force-displacement relationship of OOP loaded URM wall [42]. . . 28

2.25 Types of vertical crack lines [21]. . . 29

2.26 Building specific secondary spectrum corresponding to Tier 2 method [21]. . . 31

3.1 Illustration of ‘accuracy vs. efficiency’-spectrum. . . 33

3.2 Assessment outcomes Tier 1, Tier 2 and Tier 3 (= macro-NLTH) method [48]. . . . 34

3.3 Comparison of NLPO- and ADRS-curve [48]. . . 36

3.4 Parameters NLKA method for determination OOP capacity of URM walls [21]. . . . 39

3.5 Nonlinear floor spectrum [21]. . . 41

3.6 2DOF mass-spring-damper system. . . 44

3.7 SDOF mass-spring-damper system that represents wall in Tier 3a method. . . 44

3.8 SDOF mass-spring-damper system that represents wall in Tier 3b method. . . 45

3.9 3DOF mass-spring-damper system with wall on BL1. . . 45

3.10 3DOF mass-spring-damper system with wall on BL2. . . 46

3.11 Modified Takeda models [55]. . . 47

3.12 NL lateral behavior of building layers. . . 48

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3.13 NL OOP behavior of walls. . . 50

3.14 Validation of construction method bilinear capacity curve of OOP wall behavior [37]. 52 3.15 Two types of SDOF mass-spring-damper systems for representation of wall. . . 54

3.16 Eigenmode of the two types of SDOF mass-spring-damper systems. . . 54

3.17 Rayleigh damping [15]. . . 56

3.18 Linear substitute structure [64]. . . 58

4.1 EUC-BUILD-1 structure and corresponding structure A. . . 60

4.2 Lumped masses m1 and m2. . . 61

4.3 Construction of BBC for BL1 of structure A using experimental data. . . 62

4.4 BBCs of BL1 and BL2 of structure A. . . 62

4.5 Positive displacement range of OOP capacity curves of analyzed URM walls. . . 63

4.6 Elastic response spectrum (Overschild, Groningen). . . 64

4.7 Flowchart representing conducted research. . . 65

5.1 Unity check values for structure A per PGA value. . . 67

5.2 Hysteresis of wall spring Tier 3a (GM1). . . 68

5.3 Hysteresis of wall springs Tier 3b (GM1). . . 69

5.4 Deformation of wall springs over time (GM1). . . 69

5.5 Relative deformation of wall over time (GM1). . . 69

5.6 Comparison Tier 3b and 3c (PGA = 0.25 g). . . 71

5.7 Unity check values for structure A for PGA value that causes UC value of ca. 1 for Tier 2 method. . . 72

6.1 Unity check values for wall on BL1 (PGA = 0.15 g). . . 75

6.5 Unity check values for wall on BL1 of structure A for different BCs (PGA = 0.15 g). 79 6.6 Positive displacement range of OOP capacity curves of analyzed URM walls. . . 80

6.7 Unity check values for wall on BL1 of structure A for different BL behavior (PGA = 0.25 g). . . 81

A.1 Mass-spring-damper system SDOF system. . . 96

A.2 Mass-spring-damper system 2DOF system. . . 97

A.3 Average acceleration versus linear acceleration [15]. . . 99

A.4 Two types of iterative procedures [15]. . . 100

B.1 Generation of response spectra. . . 102

C.1 Construction of BBC of hysteretic material for BL1 of structure A. . . 104

C.2 Validation of β-value equal to 0.9 for BL1 of structure A. . . 106

C.3 Validation of construction method bilinear capacity curve of OOP wall behavior [37]. 108 D.1 Two types of SDOF mass-spring-damper systems for representation of wall. . . 111

D.2 Material models that are assigned to wall spring(s). . . 112

D.3 Absolute displacement time history of wall for two SDOF systems. . . 113

D.4 RWA pulse load. . . 114

D.5 Theoretical damping decay curve [83]. . . 115

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D.6 Validation of assignment of Rayleigh damping to overall structure. . . 115

D.7 Validation of assignment of Rayleigh damping to SDOF system. . . 116

E.1 Accelerograms for ground motion records 1-6 of cluster E (Overschild, Groningen). . 117

E.2 Accelerograms for ground motion records 7-11 of cluster E (Overschild, Groningen). 118 F.1 Unity check values for different PGA values per wall within structure A. . . 119

F.2 Unity check values for wall on BL1 of structure A per PGA value. . . 120

F.3 Unity check values for wall on BL2 of structure A per PGA value. . . 121

G.1 Illustration of structure A, B and C. . . 122

G.2 Construction of BBC for BL1 of structure B using experimental data. . . 125

G.3 Overview of BBCs of BL1 and BL2 for structure A, B and C. . . 126

G.4 Positive displacement range of OOP capacity curves of analyzed URM walls. . . 127

H.1 Deformation BL1 (Tier 3c, GM1, PGA = 0.15 g). . . 128

H.2 Hysteresis wall springs of wall on BL1 (Tier 3c, GM1, PGA = 0.15 g). . . 128

H.3 Relative deformation wall on BL1 (Tier 3c, GM1, PGA = 0.15 g). . . 129

H.14 Relative deformation wall on BL2 (Tier 3c, GM10, ascending PGA values). . . 134

H.16 Hysteresis wall springs (Tier 3c, GM1, PGA = 0.15 g). . . 135

H.17 Relative deformation wall (Tier 3c, GM1, PGA = 0.15 g). . . 135

H.18 Force BL1 (Tier 3c, GM1, PGA = 0.25 g). . . 136

H.19 Yielding BL1 (Tier 3c, GM1, PGA = 0.25 g). . . 136

H.21 Deformation wall springs (Tier 3c, GM1, PGA = 0.25 g). . . 137

H.22 Hysteresis wall springs (Tier 3c, GM1, PGA = 0.25 g). . . 137

H.23 Relative deformation wall (Tier 3c, GM1, PGA = 0.25 g). . . 137

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List of Tables

3.1 Investigated percentages and corresponding optimal situations [47]. . . 34

3.2 Explanation OpenSees material model Hysteretic [62]. . . 48

3.3 Explanation OpenSees material model ElasticBilin [62]. . . 50

3.4 Formulas for determination F_max and d_maxof URM walls for BCs of interest [63]. . 51

3.5 Characteristics of the two types of SDOF mass-spring-damper systems. . . 54

3.6 Explanation OpenSees material model Viscous [62]. . . 58

4.1 Summary of structural masses of structure A, equal to EUC-BUILD-1 structure [69]. 60 4.2 Summary of lumped masses of idealized system of structure A; units of t. . . 60

4.3 Parameters OOP capacity of analyzed URM walls. . . 63

C.1 Standard beam equations for derivation F_y and d_y [80]. . . 107

C.2 Properties corresponding to OOP loaded URM wall [37]. . . 108

D.1 Parameters SDOF systems that represent wall. . . 112

G.1 Summary of lumped masses of idealized systems of structure A, B and C; units of t. 124 G.2 Summary of structural masses of structure A, B and C; units of t. . . 124

G.3 Parameters OOP capacity of analyzed URM walls. . . 127

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Acronyms

ADRS Acceleration Displacement Response Spectrum BBC Backbone curve

BC Boundary condition BL Building layer BL1 Building layer 1 BL2 Building layer 2

CL Clay

CQC Complete quadratic combination CS Calcium silicate

DAF Dynamic amplification factor DDC Damping decay curve DOF Degree of freedom

EC6 Eurocode 6

EC8 Eurocode 8

EOM Equation of motion

EUC Eucentre

GM Ground motion record

IP In-plane

LFM Lateral force method MDOF Multiple degrees of freedom MRS Modal response spectrum MVA Method of virtual work

NAM Nederlandse Aardolie Maatschappij (Dutch Petroleum Company)

NC Near collapse

NCG Nationaal Coordinator Groningen (National Coordinator Groningen)

NEN Stichting Koninklijk Nederlands Normalisatie Instituut (Royal Netherlands Standardiza- tion Institute)

NL Nonlinear

NLKA Nonlinear kinematic analysis NLPO Nonlinear pushover

NLTH Nonlinear time history

NPR Nederlandse praktijkrichtlijn 9998 (Dutch code of practice)

NZ New Zealand

OOP Out-of-plane

OpenSees Open System for Earthquake Engineering Simulation PFA Peak floor acceleration

PGA Peak ground acceleration

RB Rigid body

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RC Reinforced concrete RWA Ricker wavelet acceleration SDOF Single degree of freedom SF Scale factor

So.ph.i SOftware for PHenomenological Implementations SRSS Square root of the sum of the squares

TL Top load acting on building layer

UC Unity check

URM Unreinforced masonry

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Symbols

ag;d Design value of the peak ground acceleration A Instability rotation of wall

b Width of wall

c Damping matrix

ccr,i Critical damping coefficient of damper i c_i Damping coefficient of damper i

cw Damping coefficient of single damper in SDOF wall system c_wi Damping coefficient of damper i in SDOF wall system Cm Seismic coefficient corresponding to onset RB mechanism

di Deformation of building layer corresponding to BBC envelope point i dmax Instability displacement of wall

dy Displacement of wall at transition point of continuous model to RB mechanism DAF Dynamic amplification factor

e0 Eccentricity of Wb relative to mid-hinge of wall eb Eccentricity of Wb relative to bottom hinge of wall eP Eccentricity of Wt relative to top hinge of wall e_t Eccentricity of W_t relative to mid-hinge of wall E Modulus of elasticity

E_s Secant modulus of elasticity

EI Bending stiffness of wall according to continuous model f_d Natural cyclic frequency of damped system

fD Damping force f_I Inertia force

fm Compressive strength of masonry

f_n Natural cyclic frequency of undamped system fS Spring force

F_b Seismic base shear force on structure

F_b^∗ Seismic base shear force on equivalent SDOF system of structure F_bi Seismic shear force on floor i

Fbi,j Seismic shear force on floor i in mode j

F_i Shear force in building layer corresponding to BBC envelope point i Fmax Maximum lateral force on wall at onset of perfect RB mechanism

F_y Lateral force on wall at transition point of continuous model to RB mechanism g Acceleration of gravity, set equal to 9.81 m/s²

h Height of wall

hn Height of structure

J Rotational moment of inertia of wall

Janc Rotational moment of inertia of elements that are connected to wall xiii

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Jb0 Rotational moment of inertia of bottom half of wall J_t0 Rotational moment of inertia of top half of wall k Stiffness matrix

k₀ Initial stiffness of wall

kef f Effective stiffness of linear substitute structure of wall k_i Stiffness of spring that represents building layer i kt Tangent stiffness of spring

k_w Stiffness of single spring in SDOF wall system kwi Stiffness of spring i in SDOF wall system

K Stiffness of continuous model that represents wall K0 Initial stiffness of building layer

K_t Unloading stiffness of building layer

m Mass matrix

m^∗ Mass of equivalent SDOF system of structure mi Mass of lumped mass i

m_w Mass of wall

p External force

P Overburden load on top of wall P F Ai Peak floor acceleration of floor i

q Behavior factor

qa Element behavior factor

qn Time variation of displacement of free vibrating undamped system Rd OOP capacity of wall

Sa(T ) Spectral acceleration S_d(T ) Spectral displacement

SEa;d Spectral OOP acceleration of a wall

t Time

tef f Effective thickness of wall t_nom Nominal thickness of wall

T1,i Natural period of building layer i T_a Natural period of wall

Td Natural period of damped system T_{ef f} Effective vibration period of structure Tef f,i Effective vibration period of building layer i

T_i Vibration period of structure corresponding to mode i Tn Natural period of undamped system

u Displacement

˙

u Velocity

¨

u Acceleration

uduct,sys Lateral NC displacement capacity of equivalent SDOF system of structure

u_w OOP mid-height displacement of wall relative to average displacement of floor level at top and bottom side of wall

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uy,sys Yield displacement of equivalent SDOF system of structure W Self-weight of wall

W^∗ Equivalent self-weight of wall W_b Self-weight of bottom half of wall Wt Self-weight of top half of wall

y_b Distance from center of W_b to bottom side of wall yt Distance from center of Wtto top side of wall z Height of center of mass of wall within structure

α Mass-proportional damping factor

β - Degradation of unloading stiffness of building layer based on ductility

- Parameter to define variation of acceleration for Newmark’s integration method - Stiffness-proportional damping factor

β₀ Foundation radiation damping effect

γ - Parameter to define variation of acceleration for Newmark’s integration method - Mass participation factor

Γ Modal participation factor

∆_i Instability displacement of wall

∆m Maximum usable displacement of wall

∆t Time step

ζ Damping ratio

ζ₀ Inherent viscous damping ζh Hysteretic damping ζ_i Damping ratio of mode i ζsys Equivalent viscous damping ηζ Spectral reduction factor

θv OOP rotation of wall due to initial interstory drift

µ Ductility

µsys Global structural ductility ρCS Density of CS masonry

φi,j Normalized displacements of mass i in mode j ωd Natural circular frequency of damped system ω_i Natural circular frequency of mode i

ωn Natural circular frequency of undamped system

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Chapter

1

Introduction

1.1 General

In 1959, the NAM (Nederlandse Aardolie Maatschappij ) discovered the natural gas field in Slochteren [1], which is located in the province of Groningen. Four years later, in 1963, the first gas drilling took place. In the subsequent years, The Netherlands switched from using coal to using natural gas. Besides the fact that gas was a more environmentally friendly alternative, the Dutch economy significantly benefited from the gas field in the Groningen area. The downside of the gas drilling came to light in the beginning of the nineties, in which the province of Groningen had to deal with the first earthquakes. Nowadays, the region still experiences seismic activities due to the gas drilling, despite of the reduced amount of gas that gets extracted the last couple of years.

The earthquakes in the Groningen area are categorized as induced earthquakes. Such earthquakes are the result of human activity [2]. The extraction of gas, at a depth of circa 3 kilometers, results in compaction of the specific earth layer. Differences in compaction between adjacent layers lead to stresses in the faults, i.e. in the fractures in the ground formations [3]. At a certain moment, the stresses become too high and the layers suddenly start sliding over the faults, resulting in ground motions. This phenomenon is called an induced earthquake. Tectonic earthquakes, on the other hand, are caused by the release of built-up stresses on tectonic plate boundaries and faults of the earth’s crust [3].

In order to provide a common approach to the structural design and assessment of buildings and civil engineering works across European countries, the so-called Eurocodes are set up [4]. Corresponding national annexes contain information on parameters that are undefined in the Eurocodes, so that the overall guideline matches the national safety level and the specific circumstances in a country.

Eurocode 8 describes the design and assessment of structures for earthquake resistance. The NEN (Stichting Koninklijk Nederlands Normalisatie Instituut ) decided not to write a national annex that is directly linked to Eurocode 8, due to the fact that Eurocode 8 is based on tectonic earthquakes [5] and the fact that the guideline is meant to be applied to structures with masonry walls with a minimum thickness of 240 mm [6]. The characteristics of the induced earthquakes in Groningen differ from the characteristics of tectonic earthquakes and the common thickness of masonry walls in Groningen of around 100 mm is significantly smaller than the required thickness of 240 mm, as implemented in Eurocode 8 [7]. Therefore, the NPR (Nederlandse Praktijk Richtlijn) 9998 was launched in 2015, which is based on induced earthquakes and which corresponds to the building methods that are typically applied in Groningen. Using the NPR 9998, it can be checked whether an existing building meets the so-called Meijdam-norm. This norm prescribes the maximum acceptable chance of a Dutch citizen dying as a result of an earthquake [8].

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The evaluation of a structure, according to NPR 9998, consists of seven steps [9]:

1. Determination of the soil properties of the specific location;

2. Determination of the material properties of the structure (structural and non-structural components);

3. Choosing the seismic analysis method for evaluating the structure;

4. Choosing the calculation method (analytically or numerically, using macro models or finite element models) for performing the seismic analysis;

5. Determination of the normative earthquake load at the specific location;

6. Determination of the seismic demand of the structure as a result of the normative earthquake load;

7. Evaluation of the structure by comparing the seismic demand against the capacity of the structure.

The first five steps provide the input for the seismic analysis that is performed in step 6. Executing the analysis results in the seismic demand of the structure due to the normative earthquake load, expressed in e.g. forces or displacements imposed on the structure. The seismic demand thus can be described as the way the structure behaves under the normative earthquake load.

In step 7, it is verified whether the structure is able to resist the derived seismic demand of the structure. A simple check is performed, in which the seismic capacity must be equal to, or greater than the seismic demand. The seismic capacity can be described as the structure’s force resistance or its displacement capacity.

When designing a new building, the capacity of the structure should be designed based on the expected demand. However, for many existing buildings in the province of Groningen, the structure is designed before the region started suffering from earthquakes. Therefore, the seismic activities in the region have not been taken into account during the design phase of these buildings. This explains the fact that the common thickness of masonry walls in Groningen is significantly smaller than the thickness of masonry walls in regions that have always suffered from earthquakes. As a result, many structures in the Groningen area have experienced a certain amount of damage.

The NPR 9998 can be used in order to determine whether an existing structure needs any strengthening. First, data are collected regarding the specific building. Then, the building is evaluated according to the previously mentioned steps. Structures for which the seismic capacity appears to be smaller than the seismic demand, need to be strengthened. In that case, strengthening measures are set up by an engineer in an advisory report.

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1.2 Problem statement

According to figures provided by NCG (Nationaal Co¨ordinator Groningen), the procedure of check- ing whether a construction needs strengthening must be carried out for approximately 26,000 buildings in the Groningen region [10]. Of course, it is preferred to evaluate this large amount of buildings in a short period of time, so that both the safety risks and the emotional impact on the citizens get minimized. Therefore, it is desirable to optimize the procedure, so that it can be performed in an efficient manner.

There is, among other things, a lot to gain by optimizing the evaluation procedure of buildings, for which both the seismic demand and the seismic capacity of a structure need to be determined.

A difficult step in this procedure is the determination of the structure’s seismic demand, since this requires accurate modelling and seismic analysis [11]. Without a reliable quantification of the seismic demand, the performance of a structure cannot be accurately assessed [12]. Optimizing the accuracy of the seismic demand reduces the uncertainty and, therefore, reduces the needed conservatism in the evaluation procedure. This eventually reduces the number of buildings that need to be strengthened.

The majority of the buildings in the Groningen area is composed out of unreinforced masonry, which is only designed for relatively moderate wind loads. Due to the slenderness of the unreinforced masonry (URM) walls, their lateral load bearing capacity is rather critical [13]. Therefore, an accurate quantification of the out-of-plane (OOP) demand of the URM walls is of great importance.

A wall’s out-of-plane behavior depends on the dynamic behavior of the building as a whole in which the wall is situated. However, it does not only depend on the movements of the floor levels that enclose the specific URM wall. Also the floor-wall-interaction and the normal force that is present within the wall have a certain influence on the OOP demand of a URM wall within a structure [14].

A lot of research on both the out-of-plane demand and the out-of-plane capacity of URM walls has been performed at component-level, yet, very few full-scale building tests have been performed.

Considerable differences in results are obtained between the full-scale building tests and the component tests. This suggests that the OOP demand of URM walls is significantly influenced by the interaction between the wall and the structure in which the wall is located. Uncertainties still exist concerning this interaction.

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1.3 Research objective

In this research, the assessment process of the OOP behavior of one-way vertically-spanning URM walls, in which the OOP capacity and the OOP demand are compared to each other, is investigated for walls in typical terraced houses in the Groningen area. The research mainly aims for a better and more clear view on the determination process of the OOP demand, in which the interaction between the URM wall and the structure as a whole is taken into account in a realistic manner. A more precise determination of the demand will make sure that the eventual assessment of a URM wall describes the actual OOP behavior in a more accurate manner. A balance between the efficiency of the overall assessment process and the accuracy of the results is searched for, so that the 26,000 buildings in Groningen can be correctly evaluated within a relatively short period of time. This leads to the following main research question:

How can the out-of-plane (OOP) behavior of unreinforced masonry (URM) walls, as a result of earthquake loading, be assessed in an efficient, but sufficiently accurate manner?

Different methods with different levels of detail do exist in order to assess the OOP behavior of URM walls, yielding variations within the assessment results. Furthermore, the complexity of the model that represents the analyzed building has a certain influence on the derived OOP demand, and thus also influences the outcome of the assessment. In order to find a balance between efficiency and accuracy, the influence of the type and the level of detail of the assessment process on the accuracy of the assessment outcome is examined. The following sub-questions are formulated:

1. What different assessment methods do exist and how is the OOP demand and the OOP capacity of URM walls determined within these different assessment methods?

2. To what different results will the assessment methods yield when they are applied to an identical structure?

3. To what extent do simplifications in the considered models reduce the accuracy of the assessment of the OOP behavior and how can this reduction be minimized?

1.3 Research objective page 4

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1.4 Methodology

A specific methodology will be followed in order to answer the main research question. The methodology is divided in several tasks, which are elaborated in the following chapters:

• Chapter 2: A literature review is conducted on several relevant subjects. In section 2.1, the basis of performing dynamic analyses on structures is described. Afterwards, section 2.2 introduces the material properties, mechanical properties and failure mechanisms of unreinforced masonry (URM). Also, the hysteretic behavior of URM structures is presented. In section 2.3, two different ways to represent earthquake loading for design and analysis purposes is described. The dynamic behavior of structures under earthquake loading can be analyzed using different methods. In section 2.4, the main seismic analysis methods are presented. The obtained dynamic behavior of a structure as a whole results in a certain dynamic behavior of the URM walls within the structure. In section 2.5, several methods that are prescribed in Annex H of the NPR are introduced that can be used for the assessment of the out-of-plane behavior of URM walls under earthquake loading;

• Chapter 3: The assessment methods that are prescribed in Annex H are evaluated. Based on this evaluation, the assessment methods to be included and compared in the current research are chosen. These methods are introduced. The first two methods that are prescribed in Annex H of the NPR, the Tier 1 and the Tier 2 method, will be included. These methods make use of an NLPO analysis in order to determine the effective vibration period of the overall structure. This effective vibration period is then used to determine the OOP demand of the analyzed wall. For the determination of the wall’s OOP capacity, the displacement- based NLKA method is applied. The third method that is prescribed in Annex H, the Tier 3 method, makes use of an NLTH analysis. In order to investigate the influence of performing such a transient analysis, as well as the influence of considering the interaction between the URM wall and the structure as a whole in the dynamic analyses, three assessment methods are constructed that can be categorized as a Tier 3 method. Tier 3 methods do exist in different levels of detail and complexity. The three assessment methods that are included in the current research utilize a simplified NLTH analysis for the assessment of the OOP behavior of URM walls. Besides an overview of the included assessment methods, the chapter explains how the models are numerically modeled;

• Chapter 4: A two-story structure that is representative for terraced houses in the province of Groningen is introduced. This Groningen typology will be used in the research of assessing the OOP behavior of URM walls. Also, the earthquake loads that will be used in the research are introduced. The last section presents an overview of all different assessment methods that are included within the scope of the current research.

• Chapter 5: The results are discussed. The differences in assessment outcomes when applying different assessment methods to an identical structure, referred to as structure A, are evaluated.

• Chapter 6: A sensitivity study is presented. In this study, several adaptations are made to the original research in order to increase the insight into the topic of investigation. First, the

1.4 Methodology page 5

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influence of assessing the OOP behavior of URM walls in two Groningen typologies that differ from the original structure A, referred to as structure B and C, is evaluated. Afterwards, the effect of the boundary conditions of the analyzed wall is examined. The last part of the sensitivity study investigates the influence of nonlinear behavior of the building layers of the overall structure on the wall’s OOP behavior;

• Chapter 7: Overall conclusions are drawn and answers to the research questions are formulated.

Furthermore, limitations of the current research, as well as recommendations for future research are given;

1.4 Methodology page 6

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Chapter

2

Literature review

2.1 Dynamic analysis of structures

The inertial (mass), elastic (stiffness) and energy dissipation (damping) properties of an actual structure result from the properties of all structural members in the structure and the interaction between the members [15]. For analysis purposes, however, a structure can be idealized as a system with a specific number of lumped masses and a massless supporting structure with a certain stiffness and a certain damping level. Relatively simple structures can be schematized with a single lumped mass, whereas multiple lumped masses are used in order to idealize more complex structures. Such systems are called single degree of freedom (SDOF) and multiple degrees of freedom (MDOF) systems, respectively.

2.1.1 Equation of motion

Figure 2.1 shows the idealization of a simple, one-story structure, that is subjected to an external force p(t) in the lateral direction. Three separate components must be assigned to this SDOF system:

the mass component m1, the stiffness component k1 and the damping component c1.

a) idealized SDOF structure b) mass-spring-damper system Figure 2.1: Modelling of one-story structure [15].

In order to find the lateral displacement u(t) of the mass over time due to the external force p(t), the dynamic equilibrium equation, Eq. 1, must be solved. This differential equation, which is based on D’Alembert’s principle of dynamic equilibrium, is also called the equation of motion (EOM). The EOM equates the external force p(t) on a system to the resulting reaction forces within the system:

the inertia force f_I, the damping force f_D and the spring force f_S.

f_I+ f_D+ f_S = p(t) → m₁u(t) + c¨ ₁u(t) + k˙ ₁u(t) = p(t) (1) where ¨u(t) is the acceleration, ˙u(t) is the velocity and u(t) is the displacement of the mass over time due to external force p(t).

Literature review page 7

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Many structures, however, cannot be accurately idealized using a single lumped mass. Such structures get schematized as systems with multiple lumped masses and, hence, multiple degrees of freedom. For MDOF systems, a mass matrix m, stiffness matrix k and damping matrix c must be determined which contain the masses, stiffnesses and damping coefficients corresponding to all degrees of freedom for all eigenmodes of deformation. Figure 2.2 shows the idealization of a two-story structure, that is subjected to an external force p(t) in the lateral direction.

a) idealized 2DOF structure b) mass-spring-damper system Figure 2.2: Modelling of two-story structure [15].

In order to find the lateral displacement u(t) of the masses for all eigenmodes due to the external force p(t), the dynamic equilibrium equation, Eq. 2, must be solved. The EOM for MDOF systems is similar to the EOM of SDOF systems, despite of the fact that scalars are replaced by matrices and vectors, due to the higher number of degrees of freedom and eigenmodes.

m¨u + c ˙u + ku = p(t) (2)

For the 2DOF system that is shown in Figure 2.2, the EOM can be described as follows:

"

m₁ 0 0 m2

# (u¨₁

¨ u2

) +

"

c₁+ c₂ −c₂

−c2 c2

# (u˙₁

˙ u2

) +

"

k₁+ k₂ −k₂

−k2 k2

# (u₁ u2

)

= (p₁(t)

p2(t) )

(3)

In order to solve the EOM of a SDOF system, the scalars m1, k1 and c1 must be determined, whereas the matrices m, k and c must be determined for solving the EOM of a MDOF system. The determination of the three components is described in section 2.1.2. Using the derived scalars or matrices, the vibration properties of the idealized structure can be derived as described in section 2.1.3. Several methods can be used to solve the EOM. Some of these methods can only be used for analyzing linear structures, whereas others can also be applied for analyzing nonlinear structures. In the current research, Newmark’s integration method is applied to solve the EOMs. This method, which can be applied to analyze both linear and nonlinear structures, is briefly introduced in Appendix A.3.

2.1 Dynamic analysis of structures page 8

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2.1.2 Mass, stiffness and damping

The mass m1 can be determined by estimating which part of the structure will (most significantly) contribute to the inertia force of the system that arises as a result of earthquake loading. In case a structure contains a heavy roof and relatively light columns, it may be assumed that the corresponding mass m₁is equal to the mass of the roof, while the mass of the columns is neglected due to their low inertial impact.

The spring stiffness k₁represents the lateral stiffness of the structure. This value therefore depends on the material, the dimensions and the boundary conditions of the structural elements. In case both spring stiffness k₁ and damping coefficient c₁ do not change over time, independent of the load’s magnitude, the SDOF system can be categorized as a linear system. In reality, however, the stiffness k1generally changes due to a fluctuating and/or increasing load. Figure 2.3 shows the force- deformation relationship of a laterally in-plane (IP) loaded URM shear wall over several load cycles.

As can be seen, the unloading and reloading curves differ from the initial loading curve. Therefore, the value of the stiffness k1 is not a constant factor: its value depends on the past deformations u of the element and on whether the deformation is increasing or decreasing. Hence, for nonlinear systems, the component k1u(t) in the EOM is replaced by k1(u(t), ˙u(t))u(t).

Figure 2.3: Force-deformation relationship laterally IP loaded URM shear wall [16].

The damping coefficient c₁ cannot be determined using the damping properties of the individual structural elements, since such properties are not well established [15]. Also, several factors would then not be included, such as energy that is dissipated in friction at connections in steel structures, in friction between structural and non-structural elements, and in the opening and closing of micro- cracks in concrete structures. Instead, the damping coefficient c₁ is determined using the damping ratio ζ and the critical damping coefficient ccr,1 of the structure. The damping ratio ζ must be based on available data on similar structures, whereas the latter coefficient ccr,1 often is determined using the values of the mass m1and the spring stiffness k1of the structure. This regularly applied type of damping, depending on the mass and the stiffness of a system, is called Rayleigh damping.

Usually, the damping ratio ζ of a structure is assumed to be 0.05 (i.e. 5%), resulting in the following damping coefficient c1:

c1= ccr,1ζ = ccr,10.05 = (2p

k1m1)0.05 (4)

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In case the damping ratio ζ equals one (i.e. 100%), the damping coefficient c1 equals the critical damping coefficient ccr,1. In this situation, the mass m1 loses all its restoring force, that is the force in the spring, by the time it reaches its equilibrium state. Therefore, the mass m1 does not overshoot this state and oscillation is completely inhibited. A corresponding system is called a critically damped system. Systems with a damping ratio ζ smaller than 1 are called underdamped systems, as are all existing structures [15]. For such systems, the mass m₁overshoots its equilibrium state due to its non-zero restoring force and then oscillates around this state. However, damping causes a decrease in the amplitude of the oscillation over time. Systems with a damping ratio ζ greater than 1 are called overdamped systems. Due to high damping strengths, such systems absorb most of the restoring force even before the mass m₁reaches its equilibrium state. As a result of this early omittance of the restoring force, it takes longer for the system to reach the equilibrium state than for the critically damped systems [17]. The dynamic behavior of the three types of damped systems is illustrated in Figure 2.4.

Figure 2.4: Free vibration of critically damped, overdamped and underdamped system [15].

2.1.3 Vibration properties

The dynamic behavior of an undamped (c1= 0) idealized system can be described by its vibration properties: the natural circular frequency ω_n[rad/s], the natural period T_n[s] and the natural cyclic frequency fn [Hz]. For a damped (c1 > 0) idealized system, the vibration properties do not only depend on the mass and stiffness components, but also on the damping ratio ζ of the examined system. The subscript n of the undamped properties is then replaced by subscript d for the damped properties. For both damped and undamped SDOF systems, the equations for the determination of the vibration properties are described in Eq. 5. These equations are the resulting equations of an eigenvalue analysis on the analyzed system. The basis of deriving vibration properties using eigenvalue analyses is introduced in Appendix A.2.

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ωn=r k1

m₁ T_n= 2π ω_n f_n= 1

Tn

= ω_n 2π

↔

ωd = ωn

p1 − ζ² T_d= 2π

ωd

= T_n p1 − ζ² fd= 1

Td

= ωn

p1 − ζ² 2π

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The dynamic response of a system as a result of specific dynamic loading depends on the system’s vibration properties. In case a system is subjected to a sinusoidal load with a vibration period that is similar to the natural period Tn of the system, the system will show a high amplified dynamic response. This phenomenon is called resonance. In static analysis methods, resonance is taken into account by means of dynamic amplification factors (DAFs), which are defined as the ratio between the system’s response as a result of a dynamic load and the system’s response as a result of a static application of the maximum amplitude of the same load [18]. Figure 2.5 shows the DAF that applies to the acceleration of a SDOF system with different damping ratios ζ. Indeed, the highest DAFs are obtained for the scenario in which the ratio between the excitation frequency and the natural circular frequency is equal to 1.

Figure 2.5: Dynamic amplification factor for different frequency ratios and damping ratios [15].

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2.2 Unreinforced masonry

A significant part of the buildings in the province of Groningen is constructed of unreinforced masonry (URM). URM is a composite material, consisting of brick units that are interconnected by mortar. The basic material properties of both individual elements are presented in section 2.2.1.

Then, section 2.2.2 introduces several mechanical properties of the composite material. Afterwards, section 2.2.3 describes common failure mechanisms of URM walls. Eventually, in section 2.2.4, the hysteretic behavior of URM structures is described.

2.2.1 Material properties of individual elements

Brick units can be made out of different materials. The majority of the building stock in Groningen comprises structures that contain either clay (CL) units or calcium silicate (CS) units [19]. The units generally show brittle behavior in compression, as can be seen in Figure 2.6a. Their tensile strength is relatively small compared to the compressive strength, which is common for brittle materials.

Nevertheless, the tensile strength generally still exceeds the bond strength between the units and the mortar [20]. Due to the fact that the tensile strength of the units will not be normative when applied in a masonry structure, the compressive strength of the units is of main interest. In order to connect the brick units, mortar is applied. In the majority of the masonry structures in Groningen that are constructed using CL brick units, general purpose mortar is applied [21]. For masonry structures that are constructed using CS brick units, the type of applied mortar generally depends on the construction year of the structure [22]. Mortars are classified by their compressive strength, although they show significantly more ductility than brick units, as shown in Figure 2.6b.

a) CL units b) mortar

Figure 2.6: Compressive stress-strain relationship of both brick units and mortar [23].

The individual material properties of both the brick units and the mortar have quite a significant influence on the eventual behavior of the composite material. However, also the adhesion between both components is of great importance, because the level of adhesion determines the initial shear strength and the flexural bond strength of the masonry [24].

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2.2.2 Mechanical properties Compressive strength

Figure 2.7 shows compressive stress-strain relationships for three types of masonry, that are constructed using one type of clay brick units and three different types of mortar: (a) weak, (b) strong;

and (c) intermediate mortar. The masonry prisms show a response that can be categorized in between the brittle response of the brick units and the more ductile response of the mortar. Furthermore, the significant influence of the applied type of mortar can be seen.

Figure 2.7: Compressive stress-strain relationship of units, mortar and masonry [23].

Shear strength

The shear strength of masonry is influenced by the normal stress that is present in a masonry wall, which depends on the weight and the loading conditions of the structure that is surrounding the masonry wall of interest. Therefore, no single value can be derived that describes the shear strength of a masonry wall on itself.

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Figure 2.8 shows the failure envelope of masonry, subjected to a shear force and an axial load, for different ratios between the shear stress and the normal stress in the wall. Three different failure mechanisms, as illustrated in Figure 2.9, can be distinguished from the failure envelope [24]:

a. Sliding shear failure

The maximum shear stress increases for an increasing normal stress, until the bed joints fail in shear. This type of failure is shown in Figure 2.9a;

b. Diagonal tension cracks

For a further increase of normal stress, the maximum principle tensile stress exceeds the diagonal tensile stress of the masonry, which results in a diagonal crack [25]. This crack can either run via the joints or in a straight diagonal line through the brick units. The type of diagonal tension crack that will occur depends on the relative material properties of the brick units and the mortar. This type of failure is shown in Figure 2.9b;

c. Failure in compression

For an even further increase of normal stress, the masonry wall will fail in compression at the toe, i.e. the masonry in the bottom right corner will crush. This type of failure is shown in Figure 2.9c.

Figure 2.8: Failure envelope of masonry, subjected to a shear force and an axial load [24].

a) sliding shear failure b) diagonal tension cracks c) failure in compression Figure 2.9: Failure mechanisms of masonry, subjected to a shear force and an axial load [26].

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Flexural strength

The flexural strength having a plane of failure parallel to the bed joints (bending around horizontal axis) differs from the flexural strength having a plane of failure perpendicular to the bed joints (bending around vertical axis). Both planes of failure are shown in Figure 2.10.

a) bending around horizontal axis b) bending around vertical axis Figure 2.10: Planes of failure of masonry in bending [27].

For the flexural strength around the horizontal axis, the adhesion between the brick units and the mortar is normative. For the flexural strength around the vertical axis, the eventual failure mechanism will depend on several factors, such as the relative strengths of the mortar and the brick units, the adhesion between both elements and the applied masonry bond [24].

2.2.3 Failure mechanisms

URM structures often suffer damage due to earthquake loading. The observed damages can be categorized in the following common failure modes [28]:

• lack of anchorage;

• anchor failures;

• in-plane failures;

• out-of-plane failures;

• combined in-plane and out-of-plane effects;

• diaphragm-related failures.

These failure modes are shortly described in the following sections [28,29].

Lack of anchorage

In URM structures, beams and floor slabs often simply rest on walls. In such a structure, there is an absence of positive anchorage of floors and roofs to the URM walls. In case ground motions do occur, the exterior URM walls therefore can behave as cantilevers over the total height of the building. This behavior results in high flexural stresses at the base of the walls, which increases the risk of out-of-plane failure. In case the beams slip from their supports, this can even yield global failure of the URM structure.

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Anchor failures

In case any anchorage of beams and floors to walls is present in URM structures, these anchors are often not designed for seismic reasons. Therefore, anchor failure is likely to occur as a result of earthquake loading. The type of failure naturally depends on the type of anchors that is used:

failure of the anchor itself can occur, as well as rupture at the connection points between the anchor and its base.

In-plane failures

In-plane (IP) failures can occur due to shear or bending. The first type of IP failure, due to shear, is most common for URM structures. The failure mechanisms sliding shear failure and diagonal tension cracks, as illustrated in Figure 2.9a and b, concern IP failures due to shear. Due to the nature of earthquakes, the direction of the corresponding lateral loading fluctuates over time. Therefore, double-diagonal (X) cracks are regularly observed in seismic zones, as shown on the left side in Figure 2.11.

The latter type of IP failure, due to bending, mainly occurs to slender piers. Due to bending, flexural tensile cracks arise at the base of the pier. For an increasing lateral load, the pier starts to rotate around the compression zone. This relatively ductile phenomenon is called rocking. In case the compressive stresses in the compression zone exceed the compressive strength of the masonry, so-called toe-crushing of the masonry occurs at the pier’s toe. This is illustrated in Figure 2.9c.

Failure of the ends of a specific URM pier causes the pier to behave as a loose rigid body that is isolated from the adjacent structural elements. Therefore, the pier does not provide any lateral resistance anymore to the rest of the structure. This type of failure is shown on the right side in Figure 2.11. Generally, IP failures do not directly endanger the load-bearing capacity of the wall.

a) In-plane shear failure [30] b) In-plane bending failure [31]

Figure 2.11: In-plane failures of URM walls.

The IP failure behavior of a URM wall is influenced by several factors, among others by the aspect ratio. The aspect ratio is defined as the ratio between the height and the length of a (part of a) URM wall. A slender pier tends to fail in bending, whereas a stocky pier tends to fail in shear [32].

The residual lateral resistance of a URM wall is relatively high in case an IP shear failure is present, compared to a situation in which an IP bending failure is present [33]. Due to the fact that the

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aspect ratio of a URM wall has a significant influence on the type of IP failure that will most likely occur, the aspect ratio also influences the lateral resistance of a URM wall.

Generally, numerous openings are present in URM facades. The positioning of the openings determines the geometry and the corresponding aspect ratios of the URM wall and, therefore, influences the type of failure that will tend to occur. Adapting the configuration of openings in URM walls can change the ductility and the seismic capacity of walls significantly [34].

Out-of-plane failures

URM structures are most vulnerable to flexural out-of-plane (OOP) failure. Due to the unstable nature of this type of failure, the load-bearing capacity of a URM wall will be endangered in case an OOP failure occurs. The vulnerability of a wall to an OOP failure depends, among other things, on the level of anchorage between the floors in a structure and the wall.

In case there is no or insufficient anchorage between floors and walls, no OOP support is provided to the walls over their height. This results in cantilever behavior over the total height of the building instead of over the individual story heights.

The same principle applies to parapets, which are non-structural URM elements, at the top of the building, that vertically extend beyond the roof line [28]. Such a URM part often is supported at the bottom side only and, therefore, behaves as a cantilever. In combination with the fact that parapets are subjected to the greatest amplification of the ground motions, due to their high position in a structure, OOP failures of parapets are commonly observed. Figure 2.12 shows a parapet failure due to the Christchurch earthquake in 2011.

Figure 2.12: Out-of-plane failure of parapet [35].

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In case a sufficient number of anchors is present between floors and a specific URM wall, the total wall can be schematized as several individual walls that span in between the floors of the structure.

In this situation, the URM walls are supported at both ends by the floors at the bottom and the top of the wall. In case of an earthquake, the movements of the structure will be introduced to the URM walls via the floors, so at the two supports of the URM walls. This configuration will be evaluated in this research.

Combined in-plane and out-of-plane effects

URM walls are loaded in both their in-plane and their out-of-plane direction, due to the bidirectional nature of earthquakes. Therefore, combined IP and OOP effects do occur. For example, an IP failure, resulting in diagonal cracks, can change the configuration and the supporting conditions of a URM wall, making the wall more vulnerable to OOP failure. Identification of this combined failure mode, however, is complex. Generally, such failures will therefore be wrongly attributed to OOP loading only.

Diaphragm-related failures

The flexibility of floor diaphragms within a URM structure can have a substantial impact on walls that are surrounding the diaphragms. IP rotation of the ends of a diaphragm can induce damage to the adjacent walls. Also, a lack of shear anchors between floors and adjacent walls can yield diaphragm-related failures. For example, a lack of shear anchors between a floor diaphragm and a wall that is positioned parallel to a ground motion can yield damage in an adjacent wall that is positioned perpendicular to the ground motion. The shortage of anchors prevents a full transmission of IP shear forces in the floor diaphragm to the shear wall, resulting in a transfer of the residual forces perpendicular to the other wall. This type of failure mainly occurs in long, narrow buildings.

2.2.4 Hysteresis

At larger deformations, URM structures dissipate energy due to their nonlinear behavior. In case of cyclic forces or deformations, which is the case for earthquake loading, this behavior results in a force-deformation hysteresis loop. The area within a singe hysteresis loop indicates the amount of damping energy that has been dissipated within the corresponding deformation cycle [15]. In order to account for the energy dissipation due to nonlinear behavior, the nonlinear relationship between force and deformation must be implemented in the stiffness component in the EOM.

Due to the complexity of predicting the exact behavior of URM structures, it is desirable to obtain the correct nonlinear relationship between force and deformation through experiments. Therefore, many experiments have been performed in which URM components are subjected to cyclic loading conditions. The obtained nonlinear behavior depends on the type of failure, and thus on related influencing factors such as the applied materials, the aspect ratio and the normal stress that is present [29]. Figure 2.13 shows qualitative force-deformation loops that correspond to the aforementioned IP failure mechanisms, as illustrated in Figures 2.8 and 2.9. Differences in the areas of the hysteresis loops can be obtained, indicating the significant influence of the factors on the eventual energy dissipation in the system.

Assessment of the seismic out-of-plane behavior of unreinforced masonry walls