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UNIVERSITÀ DEGLI STUDI DI FERRARA Dipartimento di Ingegneria Corso di Laurea Magistrale in Ingegneria Civile

EXPERIMENTAL CHARACTERIZATION OF THE COMPRESSIVE BEHAVIOUR OF BRICK/LIME-MORTAR MASONRY

Laureanda: ELISA CANELLA Relatore: Prof.ssa ALESSANDRA APRILE

Correlatore: Prof. LUCA PELÀ

Anno Accademico 2013-2014


Acknowledgments The present work was developed at the Universitat Politècnica de Catalunya. This research was carried out under the supervision of Prof. Luca Pelà . I would like to thank him to have supported me throughout my thesis with his knowledge and his constant encouragement and incitement along all the research. I would like to thank Prof. Pere Roca for his carefully and patient advice. I am grateful to Prof. Alessandra Aprile for having given me useful suggestions, especially for having given me the opportunity and the support to do this special experience. I thank all the laboratory staff who have helped me with my experimental campaign, especially Tomås Garcia, Camilo Bernard, Robert Michael, and Jordi Cabrerizo who have support me during all the laboratory phases. I am grateful to the colleagues and friends who worked with me at the realization of the investigation and helped me in many occasion, especially Savvas Saloustrous, Lucia Garijo, Diego Marastoni and the students of SAHC 2014, Chandand Gowda, Amir Farmanara and Francesco Vanin. I thank all the new friends that I have met in Barcelona, especially Rossella Siano, Fabiola Meignen and Ane Ruiz de Gordoa, thanks for your sincere friendship. A very special thanks goes to my Italian friends, in particular, Chiara, Jessica, Cristina, Francesco C., Francesco Q., and Stefano. I would like to express my sincere gratitude to my mother Sandra, my father Federico, my aunt Susanna, my uncle Andrea, my cousins Roberto and Riccardo and my grandparents for the continuous support, for their patience and motivation. I am this person thanks to them teaching and love. My all gratitude to Mattia, my boyfriend, in every moment I knew I was not alone. His effort, his support, his help, his encouragement, his love cannot be describes in few words, I will never forget.


Abstract The thesis is focused on the study and the characterization of existing masonry in compression. The main objective is to evaluate a method to assess the mechanical parameters of the masonry and its constituents. The experimental techniques used in this investigation are innovative and based on improvement of moderate destructive methods that are applicable to existing structures of the built cultural heritage. In particular, compression test on masonry cylinders extracted from existing masonry were carried out in laboratory. In order to have a comparison with the test proposed by the present standard, masonry wallets and stack prisms were also tested under compression. The materials used to build the specimens were terracotta handmade bricks and hydraulic lime mortar, without cement content, to reproduce an historical existing masonry. Each material was tested and characterized, in order to determine the elastic parameters, the compressive strength and the tensile strength. Finally, the FE simulation of the compression tests on masonry cylinders was carried out, using the materials’ parameters found during the experimental campaign. The results from the tests and the numerical model were compared with the aim of validating the proposed moderate destructive test technique. A general purpose of this thesis is to promote future works on these innovative minor destructive test techniques and to encourage the improvement of the existing standards.


Sommario Titolo: “CARATTERIZZAZIONE SPERIMENTALE DEL COMPORTAMENTO A COMPRESSIONE DELLA MURATURA DI MATTONI E MALTA DI CALCE” La tesi si focalizza sullo studio e la caratterizzazione del comportamento a compressione della muratura esistente. L’obiettivo principale è quello di valutare un metodo di misurazione dei parametri meccanici della muratura e dei suoi componenti. Le tecniche sperimentali usate in questa ricerca sono innovative e si basano sullo sviluppo di metodi moderatamente distruttivi, i quali sono applicabili a strutture esistenti di edifici di valenza culturale. In particolare, test a compressione su cilindri di muratura estratti da muratura esistente sono stati eseguiti in laboratorio. Per avere un confronto normativo sono stati testati muretti e prismi di muratura a compressione, seguendo le normative attuali. I provini sono costruiti utilizzando mattoni fatti a mano in terracotta e malta di calca idraulica, senza contenuto di cemento, per riprodurre la muratura storica esistente. Ogni materiale è stato testato e caratterizzato, con lo scopo di determinarne i parametri elastici, la resistenza a compressione e la resistenza a trazione. Infine è stata effettuata la modellazione agli elementi finiti del test a compressione su cilindri di muratura, utilizzando come parametri dei materiali, quelli ottenuti durante la campagna sperimentale. Il risultato dei test sperimentali e del modello numerico sono stati confrontati con l’obiettivo di valutare e validare la tecnica di prova moderatamente distruttiva proposta. L’obiettivo generale della presente tesi è di promuovere lavori futuri su queste tecniche innovative debolmente distruttive e di incoraggiare lo sviluppo degli standard esistenti.


Resumen Titulo:

“CARACTERIZACIÓN

EXPERIMENTAL

DEL

COMPORTAMIENTO

A

COMPRESIÓN DE LA ALBAÑILERÍA DE LADRILLOS Y MORTERO DE CAL” La tesina se enfoca en el estudio y descripción del comportamiento a compresión de la obra de fábrica existente. El objetivo principal es evaluar un método para analizar los parámetros mecánicos de la obra de fábricay sus componentes. Las técnicas experimentales usadas en la investigación son novedosas y están basadas en la mejora de métodos moderadamente destructivos, aplicables a estructuras existentes del patrimonio cultural arquitectónico. En particular, en el laboratorio han sido realizados ensayos de compresión en cilindros de obra de fábrica extraídos de paredes. Para obtener una comparación con los análisis propuestos por la normativa vigente, también han sido ensayados en compresión muretes y prismas de albañilería. Los materiales usados para construir las muestras han sido ladrillos cerámicos hechos a mano y cal hidráulica de mortero, sin usar cemento, para reproducir una obra de fábrica histórica existente. Cada material ha sido analizado y descrito para poder determinar sus parámetros elásticos, la resistencia a compresión y la resistencia a tracción. Finalmente, se ha llevado a cabo la simulación de los ensayos de compresión mediante el método de los Elementos Finitos, usando los parámetros de los materiales obtenidos de la campaña experimental. Los resultados de los ensayos y del modelo numérico han sido comparados con el objetivo de validar la técnica moderadamente destructiva propuesta.


Table of Contents

LIST OF FIGURES ............................................................................................................... VI LIST OF TABLES ..............................................................................................................XIII CHAPTER 1

INTRODUCTION........................................................................................ 1

1.1

Motivation for the present research ....................................................................... 1

1.2

Aim and Objectives.................................................................................................. 2

1.3

Outline of the Thesis ................................................................................................ 3

CHAPTER 2 2.1

STATE OF THE ART ................................................................................. 5

Overview on masonry .............................................................................................. 5 2.1.1 Bricks ............................................................................................................. 7 2.1.2 Mortar ............................................................................................................ 8

2.2

Uniaxial behaviour of the masonry ........................................................................ 9

2.3

Biaxial behaviour ................................................................................................... 12

2.4

Estimation of the compressive strength of the masonry .................................... 13

2.5

Methods of investigation ....................................................................................... 14 2.5.1 Destructive Tests (DT) ................................................................................. 14 I


Table of Contents

2.5.2 Non-destructive tests (NDT) ........................................................................ 15 2.5.3 Minor destructive tests (MDT) .................................................................... 17 2.5.3.1 Punching test on mortar joints ............................................................ 19 2.5.3.2 Compression test on masonry cylinders extracted ............................. 20 CHAPTER 3 3.1

EXPERIMENTAL CAMPAIGN ............................................................. 23

Introduction............................................................................................................ 23 3.1.1 MICROPAR research project ...................................................................... 23

3.2

Experimental program of compression tests ....................................................... 27

3.3

Materials used ........................................................................................................ 27 3.3.1 Bricks ........................................................................................................... 28 3.3.1.1 Compressive strength ......................................................................... 28 3.3.1.1.1 Whole brick ................................................................................. 28 3.3.1.1.2 Brick cubes .................................................................................. 29 3.3.1.2 Tensile strength .................................................................................. 30 3.3.1.3 Young’s modulus................................................................................ 32 3.3.2 Mortar .......................................................................................................... 35 3.3.2.1 Preparing and storing of samples ....................................................... 36 3.3.2.2 Flexural strength ................................................................................. 37 3.3.2.3 Compressive strength ......................................................................... 39 3.3.2.4 Tensile strength .................................................................................. 40 3.3.3 Mortar high strength .................................................................................... 42 3.3.3.1 Compressive strength and Young’s modulus ..................................... 43

3.4

Compression campaign: testing procedure ......................................................... 45 3.4.1 Specimens’ construction .............................................................................. 45 3.4.2 Extraction of cylindrical specimens ............................................................. 46 3.4.3 Punching test ................................................................................................ 52 3.4.4 Compression test on wallets......................................................................... 54 3.4.5 Compression test on stack prisms ................................................................ 57 3.4.6 Compression tests on cylinders extracted .................................................... 59 3.4.6.1 Mortar regularization .......................................................................... 59 3.4.6.2 Test setup ............................................................................................ 60

II


Table of Contents

CHAPTER 4

RESULTS AND DISCUSSION ................................................................ 63

4.1

Introduction............................................................................................................ 63

4.2

Results of the punching tests ................................................................................. 64 4.2.1 Introduction .................................................................................................. 64 4.2.2 Analysis of the results .................................................................................. 64

4.3

Results of the test on Wallets ................................................................................ 71 4.3.1 Introduction .................................................................................................. 71 4.3.2 Elastic cyclic loading ................................................................................... 71 4.3.2.1 Young’s modulus................................................................................ 71 4.3.3 Loading test to failure .................................................................................. 73 4.3.3.1 Compressive strength and Young’s modulus ..................................... 73 4.3.3.2 Poisson’s ratio .................................................................................... 75 4.3.4 Failure mode ................................................................................................ 76

4.4

Results of the tests on stack prisms ...................................................................... 80 4.4.1 Introduction .................................................................................................. 80 4.4.2 Elastic cyclic loading ................................................................................... 81 4.4.2.1 Young’s modulus................................................................................ 81 4.4.2.2 Poisson’s ratio .................................................................................... 83 4.4.3 Loading test failure ...................................................................................... 85 4.4.3.1 Compressive strength and Young’s modulus ..................................... 85 4.4.3.2 Poisson’s ratio .................................................................................... 86 4.4.3.3 Failure mode ....................................................................................... 87

4.5

Results of the tests on the two joints cylinders .................................................... 90 4.5.1 Introduction .................................................................................................. 90 4.5.2 Elastic cyclic loading ................................................................................... 92 4.5.2.1 Young’s modulus................................................................................ 92 4.5.2.2 Poisson’s ratio .................................................................................... 96 4.5.3 Loading test to failure .................................................................................. 99 4.5.3.1 Young’s modulus and compressive strength ...................................... 99 4.5.3.2 Analysis of LVDT4 behaviour ......................................................... 102 III


Table of Contents

4.5.3.3 Poisson’s ratio .................................................................................. 103 4.5.4 Failure mode .............................................................................................. 106 4.6

Comparison between the experimental E modulus and the spring model ..... 110

4.7

Comparison of the results obtained ................................................................... 112 4.7.1 Compressive strength ................................................................................. 113 4.7.2 Young’s modulus ....................................................................................... 113 4.7.3 Poisson’s ratio ............................................................................................ 114

4.8

Comparison between the results and the Standards and theoretical formulas 116 4.8.1 Compressive strength ................................................................................. 116 4.8.1.1 Decreto Ministeriale, 14 gennaio 2008 ............................................ 116 4.8.1.2 Eurocode 6 1-1:2005 ........................................................................ 116 4.8.1.3 Documento Básico SE-F, abril 2009 ................................................ 117 4.8.1.4 NTC 2008 – Circolare applicativa – D.M. 14/01/2008 .................... 117 4.8.1.5 Analytical formula by Como (2009) ................................................ 117 4.8.1.6 Comparison between experimental and theoretical formulas .......... 119 4.8.2 Young’s modulus comparison ................................................................... 121

CHAPTER 5

NUMERICAL ANALYSIS ..................................................................... 123

5.1

Introduction.......................................................................................................... 123

5.2

Constitutive law ................................................................................................... 124

5.3

Failure surface ..................................................................................................... 126

5.4

Modelling of cylindrical specimens .................................................................... 127 5.4.1 Non-Linear Analysis: Three-Joint Cylinders ............................................. 129 5.4.2 Non-Linear Analysis: Two-Joint Cylinders ............................................... 134

5.5

Comparison between the analyses ...................................................................... 139

5.6

Comparison between numerical and experimental test ................................... 140

CHAPTER 6

IV

CONCLUSIONS ...................................................................................... 143

6.1

Summary .............................................................................................................. 143

6.2

Conclusions ........................................................................................................... 144


Table of Contents

6.3

Suggestions for future work ................................................................................ 145

REFERENCES 147

V


List of Figures

List of Figures Figure 2.1.1 – a) American (or common) bond; b) English (or cross) bond; c) Flemish bond; d) Stack bond; e) Stretcher bond. (Lourenço, 1998) .................................................................. 6 Figure 2.1.2 – Different types of bricks; a) solid bricks; b) perforated bricks ........................... 7 Figure 2.1.3 – Nomenclature of the faces of the brick ............................................................... 8 Figure 2.2.1 –Triaxial state of stress at the interface of brick and mortar in masonry prism (Singhal, 2014) ......................................................................................................................... 10 Figure 2.2.2 – Failure mode under uniaxial compression (Page, 1981, 1983)......................... 11 Figure 2.2.3 - Possible bond strength tests: (a direct tensile bond strength test; (b flexural bond strength test (Oliveira, 2003) ........................................................................................... 11 Figure 2.2.4 – Failure mode under uniaxial tension (Page 1981, 1983). ................................. 11 Figure 2.2.5 - Test set- ups for shear-compression loading: a) couplet test; b) triplet test (Oliveira, 2003) ........................................................................................................................ 12 Figure 2.3.1 – Failure mode in solid clay unit under biaxial compression (Page, 1981, 1983)12 Figure 2.3.2 – Failure modes of solid clay units under biaxial tension-compression (Page, 1981, 1983)............................................................................................................................... 13 Figure 2.5.1 – In situ compression test setup (Corradi et al. 2002). ........................................ 15 Figure 2.5.2 – Diagonal test setup (Corradi et al. 2002). ......................................................... 15 Figure 2.5.3 – Sonic method a)Hammer generating the impulse; b)receiving accelerometer (Dalla Benetta, 2012). .............................................................................................................. 16 Figure 2.5.4 – Inspections: a)Coring (Binda et al., 2001); b)Endoscopy (Binda et al., 2001). 17 Figure 2.5.5 – Equipment and setup for flat jack test. ............................................................. 18 Figure 2.5.6 - View (a and results (b of the double punch test as a function of the thickness (Benedetti, 2008) ...................................................................................................................... 19 Figure 2.5.7 – Testing setup by Brenchic (2006) ..................................................................... 20 Figure 3.1.1 - Penetrometer tests; a) Helix pull-out; b) Windsor Pin; c) .PNT-G ................... 24 Figure 3.1.2 – Specimens: a) Wallet; b) Stack Prism............................................................... 24 Figure 3.1.3 - Shear test on masonry triplets............................................................................ 25 Figure 3.1.4 - Specimens for punching test: a) before cutting; b) after cutting ....................... 25 Figure 3.1.5 - Cylindrical specimens extracted from masonry ................................................ 26 Figure 3.1.6 – Compressive test on masonry cylinders of 150mm diameter ........................... 26 Figure 3.1.7 – Brazilian test on 90 mm diameter masonry cylinders....................................... 26 VI


List of Figures

Figure 3.2.1 - Mortar specimens; a) Mortar prepared in moulds; b) Mortar joints prepared in bricks ........................................................................................................................................ 27 Figure 3.3.1 - “Terra Cuita Piñol Pallarés S.L” Bricks ............................................................ 28 Figure 3.3.2 - Bricks cut to be tested........................................................................................ 29 Figure 3.3.3 – Cube specimens for compression test ............................................................... 29 Figure 3.3.4 - Prisms for flexure test ........................................................................................ 30 Figure 3.3.5 – Extraction of cylinders from bricks .................................................................. 32 Figure 3.3.6 - Regularization of the specimens; a) Regularized Cap of X60 glue; b) Specimen for Young’s modulus test ......................................................................................................... 33 Figure 3.3.7 - Compression test; a) Specimen; b) Failure mode .............................................. 33 Figure 3.3.8 - Young’s modulus on bricks; a) Extensometer used; b) Young’s modulus test . 34 Figure 3.3.9 – Sand grain size, cumulative curve; x-axis showed the size in [mm], y-axis shoed the percentage of pass .................................................................................................... 35 Figure 3.3.10 - Natural hydraulic mortar by the company "Cemento Tigre" .......................... 36 Figure 3.3.11 - Preparing of mortar samples (Peverini, 2014); a) Compacting of mortar inside the mould; b) Mortar inside the steel moulds ........................................................................... 37 Figure 3.3.12 - Flexure test EN 1015:11; a) Setup of the test; b) Correct position of the sample; c) Failure mode of the sample..................................................................................... 37 Figure 3.3.13 - Flexural strength of mortar prisms. ................................................................. 38 Figure 3.3.14 - Compression test EN 1052:11:2007 a) Specimens obtained from the flexure tests; b) Setup of the test .......................................................................................................... 39 Figure 3.3.15 - Compressive test a) Failure; b) Typical hourglass failure mode ..................... 39 Figure 3.3.16 - Compressive strength of mortar prisms. .......................................................... 40 Figure 3.3.17 - Brazilian test; a) Setup of the test; b) Failure in the whole prisms.................. 41 Figure 3.3.18 - Brazilian test; a) Setup of the test in the halves; b) Failure mode in the halves .................................................................................................................................................. 41 Figure 3.3.19 - High strength mortar; a) Cylindrical specimens (D=10cm); b) Compression test setup ................................................................................................................................... 43 Figure 3.3.20 - Young’s modulus test setup............................................................................. 43 Figure 3.3.21 - Failure modes of the high strength mortar cylinders ....................................... 44 Figure 3.4.1 - Construction of the walls; a) Bricks and handmade mortar; b) Firsts layer of masonry at one leaf .................................................................................................................. 45 Figure 3.4.2 - Construction of the walls; a) Particular of the vertical joint construction; b) Wall completed ........................................................................................................................ 45 VII


List of Figures

Figure 3.4.3 - Built specimens; a) Stack prisms; b) Wallet...................................................... 46 Figure 3.4.4 - The walls before the extraction; a) The first wall; b) The second wall ............. 47 Figure 3.4.5 - Layout of extractions from the first wall ........................................................... 47 Figure 3.4.6 - Layout of extractions from the second wall ...................................................... 47 Figure 3.4.7 - Dynamometer key and application point. .......................................................... 48 Figure 3.4.8 – Equipment for extraction; a) Extraction apparatus fixed at the forklift; b) Drill cylinders used ........................................................................................................................... 49 Figure 3.4.9 - Dry and vertical extraction of cylinders from the masonry walls ..................... 49 Figure 3.4.10 – Extraction phases; a) Cleaning by compressed air; b) Dust inside the core drill; c) Hole after extraction .................................................................................................... 50 Figure 3.4.11 - Phases of the extraction; a) from the lateral part; b) from the centre .............. 50 Figure 3.4.12 - End of the extraction; a) First wall; b) Second wall ........................................ 50 Figure 3.4.13 - Specimens extracted; a) One joint cylinders; b) Two joint cylinders ............. 51 Figure 3.4.14 - Three joint cylinders extracted ........................................................................ 51 Figure 3.4.15 - Extraction of mortar specimens for punching test; a) Extraction with chisel; b) Specimens obtained .................................................................................................................. 52 Figure 3.4.16 - Mortar joints prepared following DIN 8555-9:19999; a) Mortar placed between two units; b) Mortar joint extracted from the wall ..................................................... 52 Figure 3.4.17 - Specimens for the punching test; a) Some specimens; b) Gypsum; c) Specimen regularized ................................................................................................................................ 53 Figure 3.4.18 - Specimens prepared for testing ....................................................................... 53 Figure 3.4.19 - Test setup (DIN 8555-9:1999)......................................................................... 54 Figure 3.4.20 - Punching test; a) Starting of the test; b) Test ended ........................................ 54 Figure 3.4.21 - Testing setup; a) Two load cells of 500 kN; b) Data acquisition .................... 55 Figure 3.4.22 - Compression machine; a) Frame used for the first two tests; b) Instron machine used for the last test ................................................................................................... 55 Figure 3.4.23 – Wallets: Instrumentation ................................................................................. 56 Figure 3.4.24 - Loading setup, load control. ............................................................................ 57 Figure 3.4.25 - Ibertest machine, load cell 3000 kN ................................................................ 58 Figure 3.4.26 - Setup of the test; a) Positioning of the stack prisms in the centre of the machine; b) Positioning f the LVDTs ...................................................................................... 58 Figure 3.4.27 - Stack prisms: Instrumentation ......................................................................... 58 Figure 3.4.28 - Mould preparing; a) Wooden mould; b) Specimen regularized; c) All specimens regularized. ............................................................................................................. 60 VIII


List of Figures

Figure 3.4.29 - Cylinders: Instrumentation .............................................................................. 61 Figure 3.4.30 - Cylinder during a test; a) Front part of the specimen; b) Back part of the specimen. .................................................................................................................................. 61 Figure 4.2.1 – Punching tests – 120 days ................................................................................. 64 Figure 4.2.2 – Punching tests – 190 days ................................................................................. 65 Figure 4.2.3 - Punching tests – 260 days.................................................................................. 65 Figure 4.2.4 – Punching tests- Age comparison....................................................................... 66 Figure 4.2.5 - Punching test – Specimens extracted. ............................................................... 66 Figure 4.2.6 – Punching test – Specimens extracted regularized. ............................................ 67 Figure 4.2.7 – Punching test – Standard specimens. ................................................................ 67 Figure 4.2.8 – Punching test – Standard regularized specimens. ............................................. 68 Figure 4.2.9 – Punching test –Typology comparison............................................................... 68 Figure 4.2.10 – Punching test vs. half prisms comparison. ...................................................... 69 Figure 4.2.11 - Punching tests divided in typologies and ages ................................................ 70 Figure 4.2.12 – Results of punching tests ................................................................................ 70 Figure 4.3.1 - Specimens tested; a) Wallet 1; b) Wallet 2; c) Wallet 3.................................... 71 Figure 4.3.2 – Elastic cycles: wallet 2 ...................................................................................... 72 Figure 4.3.3 – Elastic cycles: wallet 3 ...................................................................................... 72 Figure 4.3.4 - Comparison of the two wallets .......................................................................... 73 Figure 4.3.5 – Wallets stress strain, obtained using the LVDTs .............................................. 74 Figure 4.3.6 - Wallets stress strain, obtained using the horizontal LVDTs ............................. 75 Figure 4.3.7 – Wallet 1 – Peak time, back side ........................................................................ 76 Figure 4.3.8 - Wallet 1 - End of the test; a) Front side; b) Back side ...................................... 77 Figure 4.3.9 - Wallet2 – Failure mode – Peack time; a) Front side; b) Left side; c) Back side. .................................................................................................................................................. 77 Figure 4.3.10 – Wallet 2 – End of the test; a) Front side; b) Left side; c) Back side, left part; d) Back side and right part. ........................................................................................................... 78 Figure 4.3.11 - Wallet 3 – Failure mode – Peak time; a) Front side; b) Left side; c) Back side; d) right side............................................................................................................................... 79 Figure 4.3.12 - Wallet 3 – End of the test; a) Front side; b) Left side; c) Back side; d) Right side. .......................................................................................................................................... 79 Figure 4.4.1 – Specimens tested; a) Stack prisms 1; b) Stack prism 2; c) Stack prism 3; d) Stack prisms 4; e) Stack prism 5; f) Stack prism 6; g) Stack prism 7. ..................................... 80 Figure 4.4.2 – Stack prisms – Elastic cycles: vertical strain comparison ................................ 81 IX


List of Figures

Figure 4.4.3 - Stack prisms – Elastic cycles: vertical strain (shifted) comparison - ................ 82 Figure 4.4.4 – Stack prisms – Elastic cycles: horizontal strain comparison ............................ 83 Figure 4.4.5 - Stack prisms – Elastic cycles: horizontal strain (shifted) comparison .............. 84 Figure 4.4.6 - Stack prisms: Stress – strain under displacement control ................................. 85 Figure 4.4.7 – Peak load; a) Stack prism 1 (back) ; b) Stack prism 2 (front). ......................... 87 Figure 4.4.8 - Peak load; a) Stack prism 2 (back); b) Stack prism 5 (right); c) Stack prism 6 (left). ......................................................................................................................................... 88 Figure 4.4.9 - Peak load; a) Stack prism 6 (back); Stack prism 7 (right-front)........................ 88 Figure 4.4.10 - End of the test; a) Stack prism 2 (back-right); b) Stack prism2 (front-right). . 88 Figure 4.4.11 - End of the test; a) Stack prism 3 (left); b) Stack Prism 4 (left); c)Stack prism 4 (back-left). ................................................................................................................................ 89 Figure 4.4.12 - End of the test; a) Stack prism 5 (back-right); b) Stack Prism 5 (front-left). .. 89 Figure 4.4.13 - End of the test; a) Stack prism 6 (front-left); b) Stack Prism 7 (left). ............. 89 Figure 4.5.1 - Three joint cylinders; a) 3JC4; b) 3JC7; c) 3JC8; d) 3JC11; e) 3JC14; f)3JC15. .................................................................................................................................................. 90 Figure 4.5.2 - Two joint cylinders; a) 2JC2; b) 2JC4; c) 2JC5; d) 2JC6; e) 2JC7; f)2JC10. ... 91 Figure 4.5.3 - Dimensions name of cylinder specimen. ........................................................... 92 Figure 4.5.4 - Three joint cylinders – Elastic cycles: vertical strain (measure of the displacement with LVDT3);..................................................................................................... 93 Figure 4.5.5 - Three joint cylinders – Elastic cycles: vertical strain (measure of the displacement with LVDT4);..................................................................................................... 93 Figure 4.5.6 - Two joint cylinders – Elastic cycles: vertical strain (measure of the displacement with LVDT3);..................................................................................................... 94 Figure 4.5.7 -Two joint cylinders – Elastic cycles: vertical strain (measure of the displacement with LVDT4); ........................................................................................................................... 94 Figure 4.5.8 - Three joint cylinders – Elastic cycles: horizontal strain (displacements average LVDT1-2)................................................................................................................................. 96 Figure 4.5.9- Three joint cylinders – Elastic cycles: horizontal strain (displacement sum LVDT5-6)................................................................................................................................. 96 Figure 4.5.10 - Two joint cylinders – Elastic cycles: horizontal strain (displacements average LVDT1-2)................................................................................................................................. 97 Figure 4.5.11 - Two joint cylinders – Elastic cycles: horizontal strain (displacements sum LVDT5-6)................................................................................................................................. 97

X


List of Figures

Figure 4.5.12 - Three joint cylinders –Vertical strain (measure of the displacement with LVDT3). ................................................................................................................................... 99 Figure 4.5.13 - Three joint cylinders –Vertical strain (measure of the displacement with LVDT4). ................................................................................................................................... 99 Figure 4.5.14 - Two joint cylinders –Vertical strain (measure of the displacement with LVDT3). ................................................................................................................................. 100 Figure 4.5.15 - Two joint cylinders –Vertical strain (measure of the displacement with LVDT4). ................................................................................................................................. 100 Figure 4.5.16 – LVDT4 movement during the 3JC15 tests. .................................................. 103 Figure 4.5.17 - Three joint cylinders – Horizontal strain (displacement average LVDT1-2). ................................................................................................................................................ 103 Figure 4.5.18 - Three joint cylinders – Horizontal strain (displacement sum LVDT5-6). .... 104 Figure 4.5.19 - Two joint cylinders –Horizontal strain (displacement average LVDT1-2)... 104 Figure 4.5.20 - Two joint cylinders –Horizontal strain (displacement sum LVDT5-6). ....... 105 Figure 4.5.21 - Three joint cylinders failure modes – Peak time; a) 3JC4; b) 3JC7; c) 3JC11; d) 3JC14; e) 3JC15. ................................................................................................................ 106 Figure 4.5.22 - Two joint cylinders failure modes – Peak time; a) 2JC2; b) 2JC4; c) 2JC5; d) 2JC6; e) JC7; f) 2JC10. .......................................................................................................... 107 Figure 4.5.23 – Three joint cylinders failure modes – End of the tests; ; a) 3JC4; b) 3JC7; c) 3JC8; d) 3JC11; e) 3JC14.; f) 3JC15...................................................................................... 108 Figure 4.5.24 - Two joint cylinders failure modes – End of the tests; a) 2JC2; b) 2JC4; c) 2JC5; d) 2JC6; e) 2JC7; f)2JC10............................................................................................ 108 Figure 4.6.1 – Spring models used ......................................................................................... 110 Figure 4.7.1 – Comparison between the compression strength.............................................. 113 Figure 4.7.2 - Young's modulus from elastic cycles comparison........................................... 114 Figure 4.7.3 - Young's modulus comparison – elastic part from loading test to failure ........ 114 Figure 4.7.4 - Poisson’s ratio comparison – Elastic cycles; a) Two joint cylinders and stack prisms; b) Three joint cylinders and wallets. ......................................................................... 115 Figure 4.7.5 - Poisson’s ratio comparison; a) Two joint cylinders and stack prisms; b) Three joint cylinders and wallets. ..................................................................................................... 115 Figure 4.8.1 – Standard compressive strength comparison .................................................... 119 Figure 4.8.2 - Theoretic compressive strength comparison ................................................... 120 Figure 5.4.1 – FE mesh of cylindrical specimens ; a) Three-joint cylinder; b) Two-joint cylinder ................................................................................................................................... 128 XI


List of Figures

Figure 5.4.2 – Force displacement graph of three joint cylinder ........................................... 129 Figure 5.4.3 – Three-joint cylinder - Point 1; a) Compressive damage; b) Tensile damage . 131 Figure 5.4.4 – Three-joint cylinder - Point 2; a) Compressive damage; b) Tensile damage . 131 Figure 5.4.5 – Three-joint cylinder - Point 3; a) Compressive damage; b) Tensile damage . 131 Figure 5.4.6 – Three-joint cylinder - Point 4; a)Compressive damage; b) Tensile damage .. 132 Figure 5.4.7 – Three-joint cylinder - Point 1; a) Principle tensile stress; c) Principle compressive stress .................................................................................................................. 133 Figure 5.4.8 – Three-joint cylinder - Point 2; a) Principle tensile stress; c) Principle compressive stress .................................................................................................................. 133 Figure 5.4.9 – Three-joint cylinder - Point 3; a) Principle tensile stress; c) Principle compressive stress .................................................................................................................. 133 Figure 5.4.10 – Three-joint cylinder - Point 4; a) Principle tensile stress; c) Principle compressive stress .................................................................................................................. 134 Figure 5.4.11 - Force displacement graph of two joint cylinders .......................................... 134 Figure 5.4.12 – Two-joint cylinder - Point 1; a) Compressive damage; b) Tensile damage . 135 Figure 5.4.13 – Two-joint cylinder - Point 2; a) Compressive damage; b) Tensile damage . 136 Figure 5.4.14 – Two-joint cylinder - Point 3; a) Compressive damage; b) Tensile damage . 136 Figure 5.4.15 – Two-joint cylinder - Point 4; a) Compressive damage; b) Tensile damage . 136 Figure 5.4.16 – Two-joint cylinder - Point 1; a) Principle tensile stress; b) Principle compressive stress .................................................................................................................. 137 Figure 5.4.17 – Two-joint cylinder - Point 2; a) Principle tensile stress; b) Principle compressive stress .................................................................................................................. 138 Figure 5.4.18 – Two-joint cylinder - Point 3; a) Principle tensile stress; b) Principle compressive stress .................................................................................................................. 138 Figure 5.4.19 – Two-joint cylinder - Point 4; a) Principle tensile stress; b) Principle compressive stress .................................................................................................................. 138 Figure 5.5.1 – Cylinders comparison – graphs obtained with COMET ................................. 139 Figure 5.6.1 – Three joint cylinders – Comparison between experimental and numerical graphs ..................................................................................................................................... 140 Figure 5.6.2 – Two joint cylinders – Comparison between experimental and numerical graphs ................................................................................................................................................ 140

XII


List of Tables

List of Tables Table 2.1.1 – Traditional mortar classification .......................................................................... 9 Table 3.3.1 – Whole bricks – Compressive strength................................................................ 28 Table 3.3.2 – Cubic brick specimens – direction z .................................................................. 29 Table 3.3.3 - Bricks - Flexural test in x direction .................................................................... 31 Table 3.3.4 - Bricks - Flexural test in y direction .................................................................... 31 Table 3.3.5 - Compressive strength of the two lateral faces of the bricks ............................... 33 Table 3.3.6 - Young’s modulus of the two lateral faces of the bricks. .................................... 34 Table 3.3.7 – Sand granulometry ............................................................................................. 35 Table 3.3.8 - Results obtained from the flexure test. ............................................................... 38 Table 3.3.9 – Mortar - Indirect tensile strength........................................................................ 39 Table 3.3.10 - Results obtained from the compression test. .................................................... 40 Table 3.3.11 - Results obtained from the Brazilian test on whole prisms. ............................... 42 Table 3.3.12 - Results obtained from the Brazilian test on half prisms. .................................. 42 Table 3.3.13 - Results for the high strength mortar. ................................................................ 44 Table 4.3.1 – Wallets: Young’s modulus in the elastic cycles ................................................. 73 Table 4.3.2 - Wallets results – Displacement control .............................................................. 74 Table 4.3.3 - Wallet Poisson’s ratio ......................................................................................... 76 Table 4.4.1 - Stack prisms Young’s modulus – Elastic cycles ................................................ 82 Table 4.4.2 - Stack prisms – Elastic cycles: Poisson’s ratio .................................................... 84 Table 4.4.3 - Stack prisms: Compressive strength and E modulus, displacement control phase .................................................................................................................................................. 85 Table 4.4.4 Stack prisms – Compressive strength considered. ................................................ 86 Table 4.4.5 - Stack prisms: Poisson’s ratio, displacement control phase................................. 87 Table 4.5.1 - Three joint cylinders – Elastic cycles - Young’s modulus ................................. 95 Table 4.5.2 - Two joint cylinders – Elastic cycles - Young’s modulus ................................... 95 Table 4.5.3 - Three joint cylinder – Elastic cycles – Young’s modulus .................................. 98 Table 4.5.4 - Two joint cylinder – Elastic cycles – Young’s modulus .................................... 98 Table 4.5.5 - Three joint cylinder – Young’s modulus .......................................................... 101 Table 4.5.6 - Two joint cylinder – Young’s modulus ............................................................ 101 Table 4.5.7 - Three joint cylinders compressive strength. ..................................................... 102 Table 4.5.8 - Two joint cylinders compressive strength ........................................................ 102 XIII


List of Tables

Table 4.5.9 – Three joint cylinders - Poisson’s ratio ............................................................. 105 Table 4.5.10 – Two joint cylinders – Poisson’s ratio ............................................................. 105 Table 4.6.1 – Materials Young’s modulus ............................................................................. 111 Table 4.6.2 – Three joint cylinders , Young’s modulus comparison ..................................... 111 Table 4.6.3 – Two joint cylinders, Young’s modulus comparison ........................................ 111 Table 4.6.4 – Stack prisms, Young’s modulus comparison ................................................... 112 Table 4.6.5 – Wallet, Young’s modulus comparison ............................................................. 112 Table 4.8.1 –Compressive strength by Como, 2009 .............................................................. 118 Table 4.8.2 – Compressive strength – Characteristic values.................................................. 119 Table 4.8.3 – Compressive strength – Theoretic values ........................................................ 120 Table 4.8.4 – Young’s modulus comparison.......................................................................... 121 Table 5.4.1 - Mechanical properties of cylindrical joint specimens ...................................... 128 Table 5.4.2 – Points description – Three joint cylinder ......................................................... 129 Table 5.4.3 - Points description – Two joint cylinders .......................................................... 135 Table 5.5.1 – Cylinders strength values obtained with COMET ........................................... 139 Table 5.5.2 – Cylinders elastic values obtained with COMET .............................................. 139 Table 5.6.1 – Three joint cylinders – Results obtained by experimental and numerical analyses .................................................................................................................................. 141 Table 5.6.2 – Two joint cylinders – Results obtained by experimental and numerical analyses ................................................................................................................................................ 141

XIV


Chapter 1

Introduction 1.1 Motivation for the present research Since ancient times to the present, the masonry has been a material widely used worldwide in buildings, and it is an important part of the existing heritage. This is due to the properties that can deliver the materials as low cost and the facility in their application. As a traditional material, the analysis of masonry structures has been based on empirical rules and design criteria. Although historically there is a lot of experience in construction with this material, some specific features of the material have not been understood completely. The inherent complexity depends on many variables of its composts, process executions and performance under multiple actions. The number of these buildings typologies is huge, thus, these structures may require intervention for the purpose of repair or reinforcement. This is because, throughout its life a structure may be subjected to direct or indirect actions, environmental effects or deficiencies related to construction phases. Such factors can trigger problems of stability or durability of heritage structures. For such situations, historical structures must be analyzed and properly evaluated to determine their status, getting more information about their materials. Under this requirement,

1


Chapter 1 - Introduction

it is necessary to conduct onsite non-destructive tests or controlled destructive laboratory tests. The destructive tests are not applyed directly on ancient structures or part of them, and nondestructive tests can give only a part of the information about the materials. An important aspect is standardized minor destructive test to obtain mechanical parameters from the masonry. These tests may substitute invasive destructive tests, providing all data necessary to improve the knowledge of the material, and they may be combine with the non-destructive ones. The research project “MICROPAR� (Identification of mechanical strength parameter of structural masonry by experimental methods on numerical micro-modelling), realized by the Department of Construction Engineering of the Polytechnic University of Catalonia (UPCBarcelonaTech), is aimed to obtain and validate general criteria that enable the characterization of the mechanical properties of the structural masonry elements. In particular, it is expected that the research will make available a practical methodology allowing a realistic and accurate definition of the material parameters. These parameters are the ones necessary for the preparation of the numerical models used in the analysis and verification of this type of masonry. The present work has been developed within this project, with the aim of evaluating the compressive behaviour of the masonry by the calibration of minor destructive tests. These tests have been verified by numerical meso-models.

1.2 Aim and Objectives The main objective of the thesis is the evaluation of Minor Destructive Tests (MDT) for the investigation of existing masonry. These new techniques have the great advantage to be applied on existing buildings and offer the chance to achieve information about strengths and elastic parameters of the materials used. Providing the validity of these tests, another objective is to provide suggestions for the current standards, which lack in guidelines for the analysis of existing historical buildings. The materials reproduce those used in old buildings, since it aims to calibrate the innovative tests for historical masonry. The new promising technique mainly investigated is the compression test on extracted masonry cylinders, according to the guidelines of UIC 778-3R formed by international Union Railways. This test is also compared with the standard tests. In addition to that, in order to 2


Chapter 1 - Introduction

investigate the properties of the materials, some tests are carried out, using standard and not standard methods. The most investigated of them is the punching test on mortar joints. The standard and non-standard tests performed on masonry are analyzed in order to obtain elastic parameters, compressive and tensile strengths. The results are compared with analytical and standard formulas. Finally, the test on masonry cylinder is modelled to verify the validity of the proposed experimental techniques. The purpose is to assess the correspondence between the obtained materials’ parameters and the behaviour of the masonry subjected to uniaxial compression. The models are modelled using a pre-post processor called GID and a finite element software called COMET (Cervera et al., 2002), both developed at the International centre of Numerical Methods in Engineering (CIMNE, Barcelona, Spain). The research is organized on the basis of followings steps: -

To gather information on the existing masonry about the behaviour of units and mortar masonry.

-

To determine the parameters and the strength of masonry using different approaches.

-

To compare the results obtained with analytical and standard formulas.

-

To assess and validate the reliability of the experimental technique by comparing the results with the experimental tests, the standard tests and the subsequent numerical model.

1.3 Outline of the Thesis The present thesis is divided into six chapters. The first chapter deals with the objectives and focus of the thesis. The second chapter deals with the state of the art, where an introduction is given on masonry, brick and mortar, along with the behaviour of masonry in compression and different test approaches. The third chapter deals with the experimental campaign, along with the research results on bricks, mortar, masonry wallets, masonry prisms, three-joint masonry cylinders and two-joint masonry cylinders. In chapter four, the results obtained in chapter 3 are analysed. A discussion of results is also proposed as well as a comparison between the results obtained experimentally and those calculated applying the relations suggested by the standards.

3


Chapter 1 - Introduction

Chapter 5 present the FE modelling, the results and the comparison with experimental tests on cylindrical specimens of masonry. Firstly, the non-linear analysis of three-joint and two-joint specimens are shown. Then, the comparison of numerical results with experimental ones is discussed. Chapter six concludes the thesis with the summary and main outcomes of the present research and suggestions for the future work.

4


Chapter 2

State of the art 2.1 Overview on masonry Masonry is the oldest building material that still finds wide use in today’s building industries. The most important characteristic of masonry construction is its simplicity. Laying pieces of stone, bricks or blocks on top of each other, either with or without cohesion via mortar, is a simple, though adequate, technique that has been successfully used ever since remote ages. Naturally, innumerable variations of masonry materials, techniques and applications occurred during the course of time. The influence factors were mainly the local culture and wealth, the knowledge of materials and tools, the availability of material and architectural reasons. According to P. Lourenço (1998) the huge number of possible combinations generated by the geometry, nature and arrangement of units as well as the characteristics of mortars raises doubts about the accuracy of the term “masonry”. Just for brick masonry, some usual combinations are shown in Figure 2.1.1. Nevertheless, the mechanical behaviour of the different types of masonry has generally a common feature: a very low tensile strength. This property is so important that it has determined the shape of ancient constructions.

5


Chapter 2 – State of the art

(a)

(b)

(d)

(c)

(e)

Figure 2.1.1 – a) American (or common) bond; b) English (or cross) bond; c) Flemish bond; d) Stack bond;

e) Stretcher bond. (Lourenço, 1998)

In the above arrangements, the bricks are named according to their placement in the wall. A stretcher is a brick laid horizontally flat, with its long side exposed on the outer face of the wall. A header is a brick laid flat across the wall’s width with its short end exposed. Bricks may be laid in a variety of patterns, or bonds, of alternating headers and stretchers. Masonry can be regarded as a discontinuous material. Bed and head joints are responsible for its discontinuous nature. This features becomes evident when considering dry joint masonry. By acting as planes of weakness, the joints induce an anisotropic behaviour in both elastic and plastic domain. As a result, the strength of masonry, highly depends on the geometrical arrangement of units and mortar There are many other factors which influence the behaviour of masonry. According to Hendry (1990), in general the stress strain behaviour is dependent on: -

Units: compressive and tensile strength, type and geometry (solid, perforated, hollow etc.) and absorption capacity;

-

Mortar: strength, thickness, Poisson’s ratio;

-

Unit-mortar interface: bond between the two, direction of stress and local strain.

The features of units are possible to determine during the manufacturing process but in case of mortar it is subjected to variations, since it depends on the constituent materials. A brief introduction on the behaviour of brick and mortar in masonry is given below.

6


Chapter 2 – State of the art

2.1.1 Bricks Masonry units form the main part of masonry. Units are produced from clay, shale, soft slate, and calcium silicate. All units have broadly similar uses although their properties differ depending on the raw materials and the method of manufacture. The selection of a particular type of unit for any given structure is also dependent on strength, durability, adhesion, fire resistance, thermal properties, acoustic properties and aesthetics. Bricks and blocks are produced in many formats: solid, perforated, and hollow (Figure 2.1.2). Clay bricks are obtainable in strength up to

but much lower strength

are generally sufficient for domestic building and for cladding for taller building. Where no recent test certificates are available, tests may be carried out to demonstrate that the units satisfy the engineering requirements.

(a)

(b)

Figure 2.1.2 – Different types of bricks; a) solid bricks; b) perforated bricks

The characterization of old clay bricks is an hard task due to the difficulties in collecting samples, the scatter in the properties, and the lack of standard procedures for testing (Elert et al. 2003). Still, characterization is relevant to understand damage, to assess safety, to define conservation measures, and even to make a decision on reusing or replacing existing materials, as modern materials can be unsuitable from a chemical, physical or mechanical perspective. According to Lourenço et al, (2010), ancient materials have low characteristics in comparison with the modern ones, such as high porosity and absorption, low and compressive strength and elastic modulus. For this reason, many researches have been carried out to assess the aging process, durability, and physical and chemical deterioration process of clay bricks (Binda et al., 1997). As regards the mechanical parameters, they may vary within the same bath of bricks. It depends on the duration of burning, the temperature, and manufacturing process. All these contribute to the variation of their properties. 7


Chapter 2 – State of the art

This study analyzes handmade terracotta solid brick, since this is the typology most used in historic buildings, because it was easy to produce, lighter than stone and formed a wall that was fire resistant and durable. The nomenclature used in the present research to call the different faces of the brick is shown in Figure 2.1.3.

Figure 2.1.3 – Nomenclature of the faces of the brick

2.1.2 Mortar Mortar is a workable paste used to bind masonry blocks together and fill the gaps between them (M. Como, 2013). It becomes hard when it sets and it gains stiffness and resistance over the time, resulting in a rigid aggregate structure. The functions carried out by mortar in the masonry, are mainly three (Martinez et al., 2001): to fill the joints, avoiding the passage of water; to regularize the disposition of bricks and to distribute uniformly the load; cooperate to lead horizontal stresses until foundations. Hydraulic lime was the principal binder for mortar up to the mid 1800’s when Portland cement was developed as a product. Although relatively weak and slow in setting and developing strength, when compared to cement based mortars, mortars produced with hydraulic lime were suitable for the relatively thick walls and lower stresses that generally characterized the more massive masonry construction of former times. According to the European standard BS EN 459-1 lime with hydraulic properties can be classified into three sub families: -

natural hydraulic lime (NHL): this is produced by burning more or less argillaceous or siliceous limestone and then reducing it to a powder by slaking with or without grinding;

-

formulated lime (FL): it consists of air lime and/or natural hydraulic lime with added hydraulic or pozzolanic material;

8


Chapter 2 – State of the art

-

hydraulic lime (HL): this is a binder consisting of lime and other materials such as cement, blast furnace slag, limestone filler and other suitable materials.

For all three categories there are three compressive strength grades in accordance with BS EN 459-2. Concerning natural hydraulic lime, it is traditionally classified as shown in Table 2.1.1 , where the number that follows the acronym NHL, is related to the compressive strength of lime at 28 days Table 2.1.1 – Traditional mortar classification

Type of lime

Traditional name

NHL 2

Feebly hydraulic lime

NHL 3.5

Moderately hydraulic lime

NHL 5

Eminently hydraulic lime

As in the case of bricks, the main properties of mortar, that affect its behaviour inside the masonry are: the compressive strength, the modulus of elasticity and the Poisson’s ratio. The mechanical characterization of mortars sampled from historical masonry constructions is usually very difficult. Joints are generally very thin, so it is impossible to apply the traditional codified tests, used to study new mortars produced in laboratory. Nevertheless innovative laboratory testing of small and irregular samples of mortars have been studied (Binda et al.,2002, Valek and Veiga, 2005, Drdacky et al., 2008, Drdacky, 2011, Benedetti and Pela, 2012, Pela el al., 2012).

2.2 Uniaxial behaviour of the masonry A large amount of studies has been realized in order to understand and describe the behaviour of the masonry under uniaxial compressive load, among which: Hildsorf (1969), Samarashinge et al. (1982), McNary and Abrams (1985), Binda et al. (1988), Anthoine (1992), Brencich (2002), Vermeltfoort (2005), et. In particular, the study of Hidlsdorf (1969) demonstrated that the failure of masonry is due to the difference elastic properties of the units and the mortar. The masonry units can be of two combinations. The first possibility when the brick is more strength than the mortar, the second possibility when the mortar is more strength than the brick. Type one is the most common type of construction found in old and also carried out in modern construction. The behaviour of brick and mortar in masonry is shown in Figure 2.2.1. The mortar is subjected to triaxial compression and the brick is subjected to uniaxial compression and biaxial tension. The triaxial compression on mortar is due to load in one direction and the 9


Chapter 2 – State of the art

confinement of brick in the other two direction making the mortar to be in triaxial compression state. The brick is subjected to uniaxial compression in the loading direction and this makes the other two directions of the brick to expand subjecting it to biaxial tension.

Figure 2.2.1 –Triaxial state of stress at the interface of brick and mortar in masonry prism (Singhal, 2014)

In order to better understand the behaviour of the masonry under uniaxial load, some different typologies of tests are presented below:

-

Compressive testing

Compressive strength experiment on masonry wallet and masonry stack prisms are rather easy to carry out. These test, such as the RILEM (RILEM, 1994b) and the EN 1052:1 test specimens, are frequently used to assess the uniaxial compressive strength of masonry. In a stacked bond prism loaded in uniaxial compression, the mortar tends to expand laterally more than the brick, due to their different elastic properties (softer mortar behaviour). The continuity between bricks and mortar, assured by cohesion and friction, creates a lateral confinement to the mortar. As a result, shear stresses develop at the mortar-brick interface, producing a triaxial compressive stress state in the mortar and bilateral tension coupled with uniaxial compression in the brick. Consequently, failure generally occurs by the development of cracks in the bricks, parallel to the loading direction. The failure mode under uniaxial compression for different orientation of mortar joints is as shown in Figure 2.2.2.

10


Chapter 2 – State of the art

Figure 2.2.2 – Failure mode under uniaxial compression (Page, 1981, 1983)

-

Tensile testing

The tensile bond strength of the unit-mortar interface is a very important mechanical property of masonry constructions, in both historical and new structures, since most of the times nonlinear behaviour is originated by cracking in the mortar joints. It should be noted that the nonlinear behaviour of the joints is controlled by the unit-mortar interface. The tensile strength is evaluated between two different types of tests, tensile bond strength tests and flexural bond strength tests, see Figure 2.2.3.

Figure 2.2.3 - Possible bond strength tests: (a direct tensile bond strength test; (b flexural bond strength test (Oliveira, 2003)

The failure mode under tensile uniaxial tension of masonry for different orientation of mortar joints is as shown in Figure 2.2.4.

Figure 2.2.4 – Failure mode under uniaxial tension (Page 1981, 1983).

11


Chapter 2 – State of the art

-

Shear testing

Shear has been identified as the governing mode of failure in masonry constructions subjected to lateral loads like wind and earthquakes (Mann and Müller,1982). A certain degree of confinement present in the masonry walls is associated to these shear actions. Thus, pure shear mode is altered to shear-compression mode. This issue must be considered in testing where direct shear loading applied to joints has to be accompanied by normal loading, see Figure 2.2.5

Figure 2.2.5 - Test set- ups for shear-compression loading: a) couplet test; b) triplet test (Oliveira, 2003)

2.3 Biaxial behaviour In case of biaxial compression-compression the splitting failure occurs in the plane parallel to free surface near the mid span thickness without the influence of the orientation angle. The failure is brittle and starts at one of the edges and propagates to the centre, shown in Figure 2.3.1

Figure 2.3.1 – Failure mode in solid clay unit under biaxial compression (Page, 1981, 1983)

In order to understand the other types of biaxial behaviour, a series of tests were carried out by Page (1983), under tension-tension, tension-compression and under compressioncompression. The failure modes of biaxial tension compression of solid clay units (with different orientations of the bed joints) are shown in Figure 2.3.2

12


Chapter 2 – State of the art

Figure 2.3.2 – Failure modes of solid clay units under biaxial tension-compression (Page, 1981, 1983)

2.4 Estimation of the compressive strength of the masonry In order to estimate the compressive strength of the masonry, by knowing unit and the joint parameters, some equation by the standard and theory are reported. Eurocode 6 for design of masonry structures suggest the equation Where

to be used.

is the compressive strength of masonry, K is a constant which depends on type of

masonry,

is compressive strength of brick and

is compressive strength of mortar. Finally

are constants. But as seen above the equation does not take into consideration the tensile strength of brick which causes the failure, as explained in Section 2.2. There are many estimations that try to provide the masonry compressive strength. One of them is proposed by Hilsdorf (1969). According to Hilsdorf the ccompressive strength of masonry can be obtained by using equation

.

is the compressive strength of brick, compressive strength of mortar, brick and

is the tensile strength of brick,

is the

is the ratio of thickness of mortar joint to thickness of the

is coefficient of non uniformity which Hilsdorf established according to his

experimental investigation. Finally another interpretation, similar to Hilsdorf, but most recent, is the one by Como (2009) in equation

.

is the brick compressive strength,

is the brick tensile strength,

the mortar thickness and the brick thickness, modulus and the mortar Young’s modulus.

is the ratio between

is the ratio between the brick Young’s

take in consideration the elastic parameters of

the masonry materials, Poisson’s ratio and Young’s modulus.

is obtained in equation

). 13


Chapter 2 – State of the art

Where

and

are respectively the Poisson’s ratio of the mortar and the brick, and is the

ratio between brick Young’s modulus and mortar Young’s modulus. The Como’s formula take into consideration all parameters of the materials that composed masonry.

2.5 Methods of investigation Achieving good characterization of ancient structures and materials, detailed enough in order to be used by advanced numerical models, is, most of the times, a very demanding task, both in time and cost. The methods available to investigate existing structures can be split basing on the intrusiveness which the structures is undergone. Basing on this aspect, three main test categories can be defined: non-destructive, minor destructive, destructive tests. The obtained information are both qualitative and quantitative, and aim to study and know the structure subjected to enhancement. 2.5.1 Destructive Tests (DT) The analysis of an historical masonry construction can rarely be based on destructive tests on the original material. This kind of test allow direct measurement of the mechanical characteristics of the walls, in particular the compression and shear strength and elastic moduli. They can be carried out in laboratory and in situ on new specimens or existing ones. The in situ tests are carried out isolating the sample with vertical cuts to eliminate the lateral confinement and applying the load through a contrast structure. Usually the test may be performed only on masonry parts destined to demolition. It is allowed the extension of the results to the remaining parts of the buildings which present similar masonry properties in terms of morphology and conservation (Circolare n.617, 2009) The in situ compression test consists in loading a panel with monotonic or cyclic compression load in order to distribute the vertical stresses as uniform as possible and the compressions resultant is centred on the specimen section. Once the load increases, the strain are recorded by means of displacement transducer. The test mechanism is composed of two metallic plates positioned over the panel and two hydraulic jacks, interposed in parallel between the plates, in order to permit that the panel be subjected to uniformly distributed compressive stress (see Figure 2.5.1). During the loading, the two jacks compress the two plates: the first one is 14


Chapter 2 – State of the art

impeded to translate and it acts as a base for the two jacks, which compress the panel through the second plate.

Figure 2.5.1 – In situ compression test setup (Corradi et al. 2002).

The diagonal compression test, as well as the shear compression test, was designed in order to evaluate the shear strength, the shear elastic modulus and the ductility of the masonry. The test mechanism is composed of a set of metallic elements fixed at the two corners of a diagonal of the panel. A jack, placed at one corner, is interposed between two metallic elements which permit it, on the one hand, to act directly on a corner of the panel, while at the same time resulting in a rigid connection to an analogous metal element located at the opposite corner. A closed system is obtained in which the jack compresses the panel along one of two diagonals (Figure 2.5.2).

Figure 2.5.2 – Diagonal test setup (Corradi et al. 2002).

2.5.2 Non-destructive tests (NDT) Non-destructive tests can be distinguished from minor destructive tests because they do not exert a direct action on the masonry. Many times, diagnostic investigations on a given 15


Chapter 2 – State of the art

structure are performed using non-destructive testing techniques, such as sonic methods or radar techniques. Sonic methods consist in the generation of sonic or ultrasonic impulses at a point on the structure (see Figure 2.5.3). The referential standards of this test are: ASTM C597-83 and RILEM TC 127-MS (1996). As regards the test: the time the impulse takes to cover the section of material between the generator and the receiver is then qualitatively correlated with some masonry characteristics, such as its homogeneity.

(a)

(b)

Figure 2.5.3 – Sonic method a)Hammer generating the impulse; b)receiving accelerometer (Dalla Benetta, 2012).

The radar technique consists in the emission and reception of electromagnetic pulses broadband, short sequences of electromagnetic waves at high frequency. The reception takes place by means of an antenna positioned on the examined point of the structure. Non-destructive testing equipment is, in general, not very expensive and testing is relatively simple to perform (Rossi, 1997). However, the results concerning non-destructive tests have a qualitative nature and only give a preliminary evaluation of the mechanical characteristics of masonry. An important and promising technique of the non-destructive kind is dynamic identification (Fanelli and Pavese, 1993; Doebling et al., 1996). This method is based on the measurement of the vibration response, in terms of amplitude and frequency content, of the structure to a given excitation and can be used to monitor the structure both locally (identification of properties of a single part) and globally (characterization of its overall properties). This method is based on the fact that the dynamic response of the structure to natural excitations of the environment (e.g. wind) or to artificial excitations (e.g. railroad traffic, vibrodyne), characterized by its dynamic parameters (natural frequencies, modal shapes and damping ratios), is a function of the stiffness, the mass, the damping and the boundary conditions.

16


Chapter 2 – State of the art

The knowledge of these parameters allows the numerical computation of the structural response to any known dynamic action as well as the localization of possible damaged zones in the structure. On the other hand, dynamic identification tests repeated over a length of time allow the assessment of damage evolution, since changes in the physical properties of the structure will cause detectable changes in the modal parameters. 2.5.3 Minor destructive tests (MDT) For some materials, as masonry, it is possible to obtain experimental data about their mechanical properties by using techniques that only slightly and damage temporarily the structure, which is easily repaired after testing. Usually, these techniques are denoted as minor destructive tests (Rossi, 1997). This class of tests allows a quantitative determination of the parameters that influence the mechanical behaviour of masonry, e.g. Young’s modulus. Due to the minor damage induced onto the structures, slightly destructive testing techniques are especially convenient when testing valuable historical buildings. The MDT can be split into four main categories: inspections, coring, endoscopies and flat jack. For a comprehensive introduction the reader is referred to Bøving (1989) and Suprenant and Shuller (1994). In the case of masonry composed of multi-layers, the coring technique is often used (see Figure 2.5.4 a)). This method consists in the coring of small diameter boreholes and taking samples in the most representative sections, which can be mechanically tested. The boreholes can be used later for endoscopies (see Figure 2.5.5 b)), which can provide valuable information about the existence of internal cavities and cracks.

(a)

(b)

Figure 2.5.4 – Inspections: a)Coring (Binda et al., 2001); b)Endoscopy (Binda et al., 2001).

17


Chapter 2 – State of the art

Another common minor destructive technique is the flat-jack test. First used in the field of rock mechanics, flat-jack testing was later adapted by Rossi (1982) to be used on masonry structures. Nowadays, the flat-jack technique is used in the following tests: -

Evaluation of the compressive stress state of masonry;

-

Evaluation of the compressive deformability properties of masonry;

-

Evaluation of the shear strength along the mortar joints.

The compressive stress state is evaluated using a single flat-jack placed inside a cut mortar bed joint. To evaluate the deformability characteristics of masonry, a cut parallel to the first one is made and a second flat-jack is inserted in this second cut. Therefore, the uniaxial compressive deformability properties of the masonry sample between the two parallel horizontal cuts can be assessed, including loading-unloading behaviour.

Figure 2.5.5 – Equipment and setup for flat jack test.

The flat-jack method also allows the measurement of the shear strength along a mortar joint, although this technique is seldom used. This test implies the removal of a brick from the centre of the masonry sample delimited by the two flat-jacks. A hydraulic jack is then put in the place of the removed brick and shear load is applied. This test allows one to obtain the peak and residual shear strength of the mortar joints. By performing this test on other places on the structure with different compressive stress states, it is possible to compute the friction angle and the cohesion of the mortar joints. All these evaluations can be done with minimum disruption to the masonry, since flat-jack testing requires only the removal of a portion of mortar joints and some individual bricks, which can be easily repaired to its original condition. The masonry coring is usual used also with the aim of extracted cylinders for testing. Tests on cylindrical cores are basically of two types: axis wise compression tests on specimens, and splitting tests along a symmetry plane (Benedetti et al. 2008). The cylinders extracted for splitting tests were investigated by many authors (Filardi, 1996, PelĂ et al 2012, Benedetti et 18


Chapter 2 – State of the art

al 2008), the evaluation of the splitting tests using different inclinations of the mortar joint can give interesting information about the shear masonry behaviour. In the following, two of the most interesting and promising minor destructive technique are presented. The first is the punching test in mortar joint, the second is the compression test on extracted masonry cylinder. 2.5.3.1 Punching test on mortar joints The determination of masonry mortar characteristics is a fundamental task for cultural heritage conservation, however, when historic masonries belonging to cultural heritage are analyzed, only small and irregular mortar samples are usually available for testing. Whereas such samples can be suitable for performing micro-structural characterization (Sandrolini and Franzoni, 2010). Some methods have been proposed in the literature for estimating mortar mechanical propertyes, by making use of small, non-standard sample (Drdacky et al., 2008, Drdacky, 2011). In particular, one of the most used method is the double punch test. This test was proposed by Henzel and Karl, 1987. In the same investigation the authors found the optimal diameter for the two punches, equal to

.

Investigation on the influence of mortar quality, mortar porosity, mortar curing and confining effect of mortar surrounding the loaded are were reported in the literature (Henzel and Karl, 1987; PelĂ et al., 2012; Sassoni and Mazzotti, 2013). The importance in this tests is due to the fact that the mortar joints specimens for punching are more representative of the real behaviour inside the masonry.

Figure 2.5.6 - View (a and results (b of the double punch test as a function of the thickness (Benedetti, 2008)

The test and the typical curve obtained are shown in Figure 2.5.6. Exponentially decreasing strength is obtained for increasing ratios. McNary and Abrams (1985) had highlight, that the compressive strength increment with the confining effect. Therefore the behaviour shown in

Figure 2.5.6 b) have a possible explanation in the effect of confinement. 19


Chapter 2 – State of the art

In the present research, a parallel campaign of punching test on mortar joint extracted by masonry and built in laboratory is carried out.

2.5.3.2 Compression test on masonry cylinders extracted It is difficult to estimate the compressive strength and the elastic parameters of existing masonry, since only non-destructive and minor destructive tests need to be carried out. One of most innovative minor destructive test proposed by UIC 778-3R (International Union Railways, 1995) is the compression test on extracted masonry cylinders. The diameter of the cylindrical specimens is recommended to be

by UIC and

Brencich et al (2004, 2006), this dimension allow the brickwork bond to be represented.

Figure 2.5.7 – Testing setup by Brencich (2006)

The specimen and the testing setup are shown in Figure 2.5.7. The load is apply in the same direction as in the real wall. In order to apply the load, it is used a steel cap, with the dimension of the specimen. To compare and understand the results obtained with experimental tests, the authors had also carried out a numerical modelling. The failure of the cylindrical specimens in experiments and the numerical model were almost the same viz. the failure of brick in tension and the vertical mortar joint resulting in the detachment of the lateral parts of the brick. The failure of the specimen in the numerical model is at lower load, resulting in lower compressive strength in comparison to the experimental results. Following UIC 778-3R guidelines, only the compressive strength is obtained by this test, on the contrary Brencich (2004) supported that it is possible to evaluate from this test also the elastic parameters. The values are calibrated on his tests and reported in Brencich, 2004.

20


Chapter 2 – State of the art

The compressive strength is given by the equation

. The area off consideration is the full

diametric area of the specimen, which is assumed to resist the applied force.

21


Chapter 2 – State of the art

22


Chapter 3

Experimental Campaign 3.1 Introduction The present experimental campaign was carried out within the research project “MICROPAR” (Identification of mechanical and strength parameter of structural masonry by experimental methods and numerical micro-modelling), developed at the Department of Construction Engineering of the Polytechnic University of Catalonia (UPC-BarcelonaTech). The project is currently funded by the Ministerio de Educación y Ciencia of the Spanish Government and the ERDF (European Regional Development Fund). The aim of the project is to obtain and evaluate general criteria able to characterize the mechanical and structural properties of the masonry. The present research aims at providing a practical methodology that gives realistic and accurate mechanical parameters for masonry and its components. These values will be validated during the numerical modelling performed in the last part of this work. 3.1.1 MICROPAR research project The MICROPAR project is carried out developing different steps. Firstly, the choice of the most appropriate materials, secondly the construction of the masonry specimens and finally the tests execution. Some of the main tests are listed below: 23


Chapter 3 – Experimental Campaign

- Penetrometer tests with different types of devices and equipment, e.g. Windsor Pin, PNT-G, X-drill, screw helix pull-out (Figure 3.1.1);

a)

c)

b)

Figure 3.1.1 - Penetrometer tests; a) Helix pull-out; b) Windsor Pin; c) .PNT-G

- Standard tests according to the European Standard EN 1052-1:1999 and to the LUM B1, RILEM (1994b) for the determination of the compressive strength of masonry (Figure 3.1.2);

a)

b) Figure 3.1.2 – Specimens: a) Wallet; b) Stack Prism

- Standard tests, according to the current standards EN 1052-3:2002, for the determination of the shear strength on masonry triplets, varying the level of the confinement (Figure 3.1.3);

24


Chapter 3 – Experimental Campaign

Figure 3.1.3 - Shear test on masonry triplets

- Punching test on mortar joints built or extracted from the masonry, according to the DIN 18555-9:1999 (Figure 3.1.4);

a)

b)

Figure 3.1.4 - Specimens for punching test: a) before cutting; b) after cutting

-

Extraction of cylindrical specimens from existing masonry wall to be subjected to either compression or splitting test. These masonry specimens are characterized respectively by: 1) two bricks and a diametrical mortar joint and a diameter of

;

2) four bricks, a vertical mortar joint and two horizontal mortar joints and a diameter of

; 3) three bricks and two horizontal mortar joints and a diameter of (Figure 3.1.5);

25


Chapter 3 – Experimental Campaign

Figure 3.1.5 - Cylindrical specimens extracted from masonry

- Compressive test on masonry cylinders of

diameter, according to the

guidelines of the UIC 778-3R (UIC 1995) (Figure 3.1.6);

Figure 3.1.6 – Compressive test on masonry cylinders of 150mm diameter

- Brazilian

test

on

diameter

masonry

cylinders

according

to

the

recommendation of ASTM C496:1996, performed varying the inclination of the diametrical mortar joint (45°, 50°, 55°, 60°) to assess the shear behaviour of mortar joints (Figure 3.1.7);

Figure 3.1.7 – Brazilian test on 90 mm diameter masonry cylinders

26


Chapter 3 – Experimental Campaign

The research that has been developed during this thesis focuses only on the tests related to the evaluation of the compression behaviour of masonry and its components (bricks and mortar joints).

3.2 Experimental program of compression tests The present experimental campaign aims to investigate the masonry mechanical response when subjected to uniaxial compression, in addition it is intended to evaluate the parameters of the single masonry components, namely bricks and mortar. The parameters that are investigated are the compressive strength and Young's modulus. Concerning the components, the Poisson's ratio and the tensile strength are also assessed during the research. The specimens have been constructed in laboratory. They were made up of handmade terracotta bricks and hydraulic lime mortar with ratio of 1:3. The overall campaign consists of two walls (

), seven Stack Prisms of five bricks and four mortar

joints and three Wallets ( previous specimens, mortar prisms (

). At the same time of construction of the ) and joints

)

were prepared using metallic moulds or bricks, in order to characterize the properties of the mortar at the time of the tests (see Figure 3.2.1).

a)

b)

Figure 3.2.1 - Mortar specimens; a) Mortar prepared in moulds; b) Mortar joints prepared in bricks

3.3 Materials used A key part of this research was the choice of the materials. In order to simulate the historical materials constituting the existing structures of the built cultural heritage, natural lime mortar (without cement) and handmade bricks, cooked following ancient procedures, were used.

27


Chapter 3 – Experimental Campaign

These particular materials may arguably be considered also for modern structural intervention projects. 3.3.1 Bricks The units used in this research are handmade terracotta bricks, coming from the company “Terra Cuita Piñol Pallarés S.L.”, Spain (see Figure 3.3.1). The nominal dimensions of the units are

. It is important to point out that there is a large variability of

the brick dimensions due to its peculiar construction procedure.

Figure 3.3.1 - “Terra Cuita Piñol Pallarés S.L” Bricks

3.3.1.1 Compressive strength 3.3.1.1.1 Whole brick The compression test of the whole brick is the only procedure proposed by the current codes and it allows to obtain the uniaxial compressive strength along the larger base direction of the brick. The test was performed by the Terracuita company, according to the UNE EN772:2011. The compressive strength values obtained are shown in Table 3.3.1. Table 3.3.1 – Whole bricks – Compressive strength

Whole Bricks σ [MPa] 31.2 Polished_1 29.4 Polished_2 30.4 Polished_3 30.3 Polished_4 34.2 Polished_5 28.9 Polished_6 28


Chapter 3 – Experimental Campaign

Average St. Dev. CV

30.7 1.88 6%

3.3.1.1.2 Brick cubes The bricks were cut in cubes, with dimensions of

. These cubes were

tested in compression, under force control. The aim of this test was to obtain the compressive strength, in the three different directions. This evaluation is important to assess the material behaviour and the values obtained are necessary in the modelling calculation. The variability of this material is high, for this reason it was decided to cut some bricks in different part, and to test the different direction in different part of the bricks specimens were selected in order to test cubes with parallel and clean faces. As seen in Figure 3.3.2 and in Figure 3.3.3, the bricks were cut to obtain cube for compression test and prisms for direct tensile and Young’s modulus tests. These last two tests were not perform in the present research.

Figure 3.3.2 - Bricks cut to be tested

Figure 3.3.3 – Cube specimens for compression test

The values obtained are shown in Table 3.3.2. Table 3.3.2 – Cubic brick specimens – direction z

Compression test on cubic specimens - z Area Fmax fc Specimen [mm2] [kN] [MPa] 1351 26.44 19.57 T1Z1 29


Chapter 3 – Experimental Campaign

T1Z2 T1Z3 T2Z1 T2Z2 T3Z1

1296 1368 1369 1417 1378

25.24 26.08 25.04 23.55 24.10 Average St. Dev. CV

19.47 19.06 18.29 16.62 17.48 18.42 1.18 6%

In the present research are shown only the results in direction z, since the evaluation in the other two directions is in phase of completing for other works. 3.3.1.2 Tensile strength The characterization of the tensile strength was performed using the three point bending test on cut brick. Due to the lack of a reference standard for this kind of test, it was decided to follow the EN 1015-11:2007 used for the mortar. Three bricks were cut, in order to obtain specimen with dimension of

. The tests were performed in

direction. It was not possible to perform the test in

and

direction, that is the vertical direction,

because the thickness not permit to have a sufficient length of the specimen (see Figure 3.3.4).

Figure 3.3.4 - Prisms for flexure test

The flexural strength is changed in tensile strength using three standards, each one for concrete, since the lack of standard for brick. The standards compared are: -

Where

30

Eurocode 2 1-1:2005, in Section 3.1.8:

is the element high in

, and

is the flexural strength.


Chapter 3 – Experimental Campaign

-

Where

CEB-FIP Model Code 1990:

is the depth of the beam (in this case is a brick prism),

base support and is equal to -

Where

and

is the distance of the two

is the flexural strength.

D.M 14/01/2008 (Italian standard):

is the flexural strength.

The results are in Table 3.3.3 and in Table 3.3.4. Table 3.3.3 - Bricks - Flexural test in x direction

Flexural test – x direction Specimen T1X1 T1X2 T1X3 T2X1 T2X2 T2X3 T3X1 T3X2 T3X3

Dimensions [mm] b 34.6 34.3 34.2 39 38.5 37.7 37 37 37

h 32.8 32.5 32.9 31.2 32.3 32.3 32.8 31.5 32.4 Average St. Dev. CV

fflex

fctm (EC2)

fctm (D.M)

fctm (CEBFIP)

[Mpa] 3.81 3.67 3.60 3.52 3.51 3.59 3.88 3.48 3.63 0.14 4%

[Mpa] 2.43 2.34 2.31 2.26 2.25 2.30 2.48 2.23 2.32 0.09 4%

[Mpa] 3.17 3.06 3.00 2.93 2.92 2.99 3.23 2.90 3.03 0.12 4%

[Mpa] 1.61 1.54 1.68 1.61 1.58 1.59 1.74 1.55 1.61 0.07 4%

Table 3.3.4 - Bricks - Flexural test in y direction

Flexural test – y direction Specimen T1Y1 T2Y1 T1Y2 T1Y3 T2Y2 T3Y1 T4Y1 T4Y2

Dimensions [mm] b 36 40 36 35.5 39.5 39 40 40

h 32.5 31 32.5 32.5 32 32.7 32.5 33

fflex

fctm (EC2)

fctm (D.M)

fctm (CEBFIP)

[Mpa] 3.81 3.53 3.57 3.74 3.19 3.32 4.40 4.73

[Mpa] 2.43 2.26 2.29 2.39 2.04 2.12 2.82 3.04

[Mpa] 3.17 2.94 2.98 3.11 2.65 2.76 3.67 3.95

[Mpa] 1.66 1.65 1.58 1.62 1.48 1.53 2.08 2.22 31


Chapter 3 – Experimental Campaign

Average St. Dev. CV

3.79 0.53 14%

2.42 0.34 14%

3.15 0.44 14%

1.73 0.27 16%

3.3.1.3 Young’s modulus The Young’s modulus is a value necessary to define the response of the material in the elastic range. The assessment of this parameter is also important for the following numerical modelling. However, there is still no reference standard, given the difficulty in obtaining this value. Therefore it was decided to attempt a new technique based on the evaluation of the concrete Young’s modulus, following the EN 12390-13:2013. Cylinders were extruded by the two lateral sides of the brick (header and stretcher) with a diameter of around

and a height of

, trying to maintain the diameter-high ratio of

(Figure 3.3.5). Subsequently, it was applied a regularization layer of glue X60

over the top of the sample (Figure 3.3.6). It is important, in fact, that the top and the bottom faces are absolutely parallel to achieve a uniform distribution of the compressive force in the whole volume. According to the code, the compressive strength in the two considered directions of the brick were determined (see Figure 3.3.7, with the typical fragile failure). An additional test to evaluate the Young’s modulus consisted in applying three cycles of loading and unloading, remaining in the elastic range, keeping a maximum load value equal to one third of the ultimate strength found.

Figure 3.3.5 – Extraction of cylinders from bricks

Concerning the test setup, two extensometers (Extensoemter “Epsilon” gage length range

32

, full scale

, linearity

of F.S.) were installed at

and

, on the


Chapter 3 – Experimental Campaign

specimen lateral surface, in order to evaluate the vertical deformation. The extensometer were placed

a)

b)

Figure 3.3.6 - Regularization of the specimens; a) Regularized Cap of X60 glue; b) Specimen for Young’s modulus test

a)

b)

Figure 3.3.7 - Compression test; a) Specimen; b) Failure mode

The tests were performed in the Instron machine with a load cell of

, load control.

In Table 3.3.5 the results of the compression tests are shown: Table 3.3.5 - Compressive strength of the two lateral faces of the bricks

Name Ca1T Ca2T Ca3T

Stretcher face F max [kN] 12.12 12.23 8.88 Average St. Dev CV

σ [MPa] 12.67 12.88 9.29 11.61 2.01 17.35%

Name Te1T Te2T Te3T

Header face F max σ [kN] [MPa] 17.48 18.28 8.07 8.44 14.13 14.77 Average 13.83 St. Dev 4.99 CV 36.06%

33


Chapter 3 – Experimental Campaign

The scattering in the compressive strength is quite high because of the heterogeneity of the handmade bricks. However, it is possible to consider a compressive strength of about for this type of specimen.

a)

b)

Figure 3.3.8 - Young’s modulus on bricks; a) Extensometer used; b) Young’s modulus test

According to the recommendations reported in the EN 12390-13:2013 standard and in some researches (i.e. Egermann, 1990; Binda, 1996; Binda, 1997) the load cycles were performed with two different load and unload phase, the first from 10% to 30% of the estimated maximum force, whereas the second from the 30% to 60% of the estimated maximum force, both for three times. The results of the tests are presented in Table 3.3.6. Table 3.3.6 - Young’s modulus of the two lateral faces of the bricks.

Cn2tc Cn2'tc Cn2''tc3 Average St. dev. CV

Header face E10-30% [MPa] E30-60% [MPa] 7572 7697 11470 9103 10335 7518 9792 8106 2005 868 20% 11%

Tte4'tc6 Te4tc5 Average St. dev. CV

Stretcher face E10-30% [MPa] E30-60% [MPa] 5129 6127 5073 6222 5101 39 0.8%

6175 67 1.1%

The heterogeneity of the material tested is clearly evident: in some tests it was enough to reach the

of the maximum load to have a good evaluation of the Young’s modulus, in

others it was necessary to reach the

. As a matter of fact, these tests and the previous

ones about the determination of the strength are affected by the anisotropy of the material. Unfortunately it was not possible to have an evaluation of the Young’s modulus in the vertical direction of the bricks, since the thickness of the brick is too much thin.

34


Chapter 3 – Experimental Campaign

3.3.2 Mortar The choice of the most appropriate mortar has been a critical issue of the present work since it was fundamental to find the correct mix that can reproduce the mortar of the old structures. According to previous experimental programs developed at UPC in the framework of the MICROPAR project (Peverini 2014, Witt 2014), the hydraulic lime mortar (without cement) was used with a constituents dosage of of the sand was considered (

. In the present campaign a smaller granulometry ), in order to represent as better as possible a

typical washed river sand for historical masonry. In Figure 3.3.9 and Table 3.3.7 the granulometry made by the material laboratory which supplied the sand is shown.

Figure 3.3.9 – Sand grain size, cumulative curve; x-axis showed the size in [mm], y-axis shoed the percentage of pass Table 3.3.7 – Sand granulometry

Sieve size [mm]

Pass %

4 2.5 2 1 0.5 0.25 0.125 0.063

100 100 100 97 79 26 4 0.9

The mortar was produced in laboratory and it was hand mixed using a trowel. Its workability and cohesion were evaluated through the capability to obtain a smooth surface in the mixed paste using a trowel and creating a spherical lump by hand without losing integrity. Concerning the lime used in the mortar mix, it was used a natural hydraulic lime (NHL 3.5) in

35


Chapter 3 – Experimental Campaign

powder, provided by the Spanish company “Cemento Tigre” (Figure 3.3.10), with chemical composition according to EN 459-1:2010.

Figure 3.3.10 - Natural hydraulic mortar by the company "Cemento Tigre"

For the mortar characterization, the European standard for mortar testing EN 1015:11 (CEN, 2007) was followed. This standard includes the instructions to prepare and store the samples. It is mostly oriented to mortars with higher strength than lime mortars, although it may still be used as a guideline. Due to the low strength of the mortar samples, the Ibertest machine with load cell of

was needed in order to ensure the proper control during testing.

Regarding the characterization of the flexural strength and the compressive strength, different ages were considered

in order to evaluate the development

of strength over the time and to allow a comparison with the other tests performed. The Young’s modulus was evaluated following the same approach applied to the bricks, using the extensometer to measure the deformation, and following as a guideline the experimental tests performed in the Deliverable 5.3 of NIKER project (2011). Finally the evaluation of the tensile strength was tried with the Brazilian test following the ASTM C496:1996. 3.3.2.1 Preparing and storing of samples At the same time of the walls construction, the mortar was poured and appropriately compacted in lubricated steel moulds to prevent adhesion of the mortar to the mould walls, according to the European standard for mortar testing EN 1015-11 (CEN, 2007). Mortar was casted in two layers, each of which was compacted with 25 strokes of a tamper (Figure 3.3.11).

36


Chapter 3 – Experimental Campaign

a)

b)

Figure 3.3.11 - Preparing of mortar samples (Peverini, 2014); a) Compacting of mortar inside the mould; b) Mortar inside the steel moulds

Each mould was divided in three compartments, in order to obtain three standardized prismatic samples measuring

. The overall campaign consists of 30 moulds

prepared and successively stored in a climatic camera with conditions of 22.5° C and 70% humidity. Each sample was extracted after 2 days from the casting, as required for hydraulic lime samples, and were subsequently stored in the same conditions. Finally, they were tested at the ages reported above. 3.3.2.2 Flexural strength The tensile strength was evaluated indirectly by the flexure test of the prismatic samples according to the EN 1015-11:2007. Three prisms for each age studied were tested. The tests were performed in the Ibertest machine with a load cell of

, in load control. The load

rate was kept constant during the test with a value of

that is the lower bound

prescribed by the code. In Figure 3.3.12 the testing procedure is shown.

a)

b)

c)

Figure 3.3.12 - Flexure test EN 1015:11; a) Setup of the test; b) Correct position of the sample; c) Failure mode of the sample

37


Chapter 3 – Experimental Campaign

The results obtained over the time are shown in the Table 3.3.8: Table 3.3.8 - Results obtained from the flexure test.

Flexural strength [MPa] 7 Days 14 Days 28 Days 42 Days 66 Days 90 Days 190 Days 260 Days 0.572 0.598 0.563 0.537 0.518 0.750 0.396 0.401 NHL 0.593 0.551 0.539 0.502 0.656 0.388 0.354 (W/L=0,9) 0.563 0.539 0.488 0.516 0.385 0.357 0.797 Average 0.572 0.595 0.559 0.538 0.502 0.680 0.390 0.371 St. Dev 0.0033 0.0068 0.0014 0.0152 0.118 0.006 0.03 CV 1% 1% 0% 3% 18% 2% 7%

Flexural strength Flexural strength [MPa]

0,9

Flexural strength average Flexural strength

0,8 0,7 0,6 0,5 0,4 0,3 0,2 0,1 0

0

50

100

150

Days

200

250

300

Figure 3.3.13 - Flexural strength of mortar prisms.

As reported in Figure 3.3.13, the behaviour of the flexural strength presents a small increase up to 14 days and a subsequent decrease until the stabilization of the strength at 190 days, except for the values obtained at 90 days. At that time some problems occurred as demonstrated by the high dispersion of the values obtained. Due to this high variation of the flexural strength value at 90 days, it was decided to consider the average that entailed an evident increase of the curve over the time. A similar trend of decrease after the peak was observed also in the same test with a different mortar mix, by (Baronio, 1999; Witt, 2014), in the framework of the MICROPAR project. Witt obtained a strength peak at 75 days and a subsequent sudden fall of the strength at 110 days. The reason of such a decrease of strength is still not clear at all and might be related to ageing of mortar, deserving to be better investigated in further research. 38


Chapter 3 – Experimental Campaign

In order to have an evaluation of the tensile strength , the flexure strength was changed in tensile strength using the CEB-FIP Model Code 1990 (see equation (3.2)), as the same as in flexural test of the brick, the results are shown in Table 3.3.9. Table 3.3.9 – Mortar - Indirect tensile strength

Indirect tensile strength [MPa] 7 Days 14 Days 28 Days 42 Days 66 Days 90 Days 190 Days 260 Days 0.247 0.238 0.222 0.300 0.172 0.164 NHL(W/L=0,9) 0.252 0.263

3.3.2.3 Compressive strength The compression test was made following the EN 1015-11:2007, once again the Ibertest machine with the load cell of

was used. The load rate was kept equal to

that is

the lower bound prescribed by the code. The compression tests were made on the two halves produced by the flexure test, since all flexure tests produced solid cubes with dimensions of at least

. The tests

provided the compressive strength of the mortar. In Figure 3.3.14 and Figure 3.3.15 the testing procedure and a typical failure are shown.

a)

b)

Figure 3.3.14 - Compression test EN 1052:11:2007 a) Specimens obtained from the flexure tests; b) Setup of the test

a)

b)

Figure 3.3.15 - Compressive test a) Failure; b) Typical hourglass failure mode

39


Chapter 3 – Experimental Campaign

The results obtained over the time are shown in the Table 3.3.10: Table 3.3.10 - Results obtained from the compression test.

Compressive strength [MPa] 7 Days 14 Days 28 Days 42 Days 66 Days 90 Days 190 Days 260 Days 0.76 0.91 1.52 1.76 1.82 1.64 2.63 2.40 0.58 0.93 1.63 1.67 1.87 1.56 2.33 2.50 0.64 0.93 1.54 1.75 1.77 2.09 2.93 2.40 NHL 0.49 0.87 1.60 1.81 1.86 2.91 2.14 (W/L=0,9) 0.92 1.59 2.07 2.79 2.69 1.76 2.69 2.81 2.59 2.54 2.60 Average 0.62 0.91 1.61 1.75 1.82 2.13 2.73 2.45 St. Dev 0.113 0.024 0.085 0.056 0.050 0.438 0.224 0.191 CV 18% 3% 5% 3% 3% 21% 8% 8%

Compresive strength [MPa]

Compressive strength 3,5

Compressive average

3

Compressive Strength

2,5 2 1,5 1 0,5 0

0

20

40

60

80

100

120

140

160

180

200

220

240

260

280

Days Figure 3.3.16 - Compressive strength of mortar prisms.

Considering Figure 3.3.16, as expected, the compressive strength behaviour increases with time. After 190 days it comes to stabilize. The graph shows a first peak at 28 days, then the strength is stable up to 66 days, where it starts to increase and it is finally stabilized at 190 days. Also in this test at 90 days the dispersion of the data is quite large. 3.3.2.4 Tensile strength The assessment of the direct tensile strength is an important issue when the material is very brittle. Therefore, it was decided to perform the Brazilian test following the ASTM C496:1996, designed for concrete, and some available researches (Rocco et al. 1999). 40


Chapter 3 – Experimental Campaign

The Brazilian test was performed at 190 days on the prismatic mortar samples with dimension of

. After testing, the two halves obtained were tested another time with the

Brazilian test, since the dimensions exclude different results due to the size effect. The tests were made using a test frame expressly prepared for the Brazilian test. The machine used was the Ibertest with a load cell of

, and the load rate was

. An

important characteristic of this test is the dimension of the strip of wood used to distribute the point load over the specimen. In this test the dimension of the strips was correspond at the

, that

of the base of the specimen. The setup details are reported in Figure

3.3.17 a) and Figure 3.3.18 a).

a)

b)

Figure 3.3.17 - Brazilian test; a) Setup of the test; b) Failure in the whole prisms

a)

b)

Figure 3.3.18 - Brazilian test; a) Setup of the test in the halves; b) Failure mode in the halves

The failure mode showed a clear diametric fracture through the centre of the specimen (Figure 3.3.17 b) and Figure 3.3.18 b)). The formula used to calculate the tensile strength, knowing the maximum force obtained, is:

Where F,

are respectively the force, the base and the length of the loading area. 41


Chapter 3 – Experimental Campaign

The results obtained have little scattering but the strength values are rather low. Table 3.3.11 - Results obtained from the Brazilian test on whole prisms.

Prisms

Fmax [kN]

σmax [MPa]

NHL_1_B_muro_int NHL_2_B_muro_int NHL_3_B_muro_int

0.195 0.201 0.184 Average St. Dev. CV

0.078 0.080 0.073 0.077 0.003 4%

Table 3.3.12 - Results obtained from the Brazilian test on half prisms.

Half prisms

Fmax [kN]

σmax [MPa]

NHL_1A_B_muro_int NHL_1B_B_muro_int NHL_2A_B_muro_int NHL_2B_B_muro_int NHL_3A_B_muro_int NHL_3B_B_muro_int

0.168

0.067

0.185 0.188 0.200 0.190 Average St. Dev. CV

0.073 0.075 0.080 0.075 0.074 0.005 6%

As reported in the Table 3.3.11 and Table 3.3.12, the results obtained with the Brazilian test are hardly acceptable. The values are too low and if compared with the flexure test they are five times lower. Such discrepancy might be due to the very low friction angle of the material, insufficient to develop the typical complete splitting mechanism characterized by two wedge regions under the punches and a vertical connection crack connecting them. The very low experimental values might be related to a local failure mechanism. Further investigation is necessary to gain a better understanding of this phenomenon. 3.3.3 Mortar high strength High strength mortar was used to regularize the surfaces of the cylindrical specimens to be subjected to the UIC 778-3R (UIC 1995) test (see Section 3.4.5). Further details about casting and application of this mortar are explained in the following. The mix used for the regularization was the Sika® FastFix-130 TP. The content of water used in this experimental program was slightly higher than that suggested by the provider, in order to have a mix more liquid. 42


Chapter 3 – Experimental Campaign

3.3.3.1 Compressive strength and Young’s modulus The assessment of the mechanical properties was carried out according to the EN 1239013:2013, because this type of mortar is considerably similar to the concrete. Four cylinders of high strength mortar were made (

), with a water ratio of 5:1 (Figure 3.3.19 a)).

One cylinder was used to have the maximum compressive strength once known this value (Figure 3.3.19 b)), it was possible to create three cycles of load and unload from the

to

of the maximum load expected. The other three cylinders where tested first to obtain

the Young’s modulus, then to evaluate the compressive strength, the failure modes are shown in Figure 3.3.21.

. a)

b)

Figure 3.3.19 - High strength mortar; a) Cylindrical specimens (D=10cm); b) Compression test setup

a)

b) Figure 3.3.20 - Young’s modulus test setup

The setup used for the Young’s modulus test is reported in the Figure 3.3.20. Three LVDTs (with a range of

and a precision of

) are fixed to a metallic frame conceived

especially for this type of set. The value of the vertical deformation is the average of the three values obtained by the LVDTs.

43


Chapter 3 – Experimental Campaign

Figure 3.3.21 - Failure modes of the high strength mortar cylinders

The results are shown in Table 3.3.13. Table 3.3.13 - Results for the high strength mortar.

Mortar High Strength σ [MPa] E [MPa] MS_1 31.0 MS_2 26.3 21219 MS_3 32.0 23399 MS_4 26.6 20547 Average 29.0 21722 dev. St 2.95 1491 CV 10.17% 6.86%

The variations of the results obtained are acceptable. The Young’s modulus is one order of magnitude greater than the brick, therefore the material can be used as the regularization of the specimens.

44


Chapter 3 – Experimental Campaign

3.4 Compression campaign: testing procedure Once selected and characterized the materials, the experimental campaign was programmed. First of all, it was decided which and how many specimens to build. Secondly, a careful planning of tests was carried out in order to test the specimens at the same age. The tests were carried out when the specimens were seven months old. The hydraulic lime mortar was characterized at the beginning and at the end of the program. 3.4.1 Specimens’ construction In the present experimental campaign, two single-leaf walls were built, with dimensions , in order to allow the extraction of masonry cylinders of different size and with the presence of different numbers of mortar joints (see Figure 3.4.1 and Figure 3.4.2). Both walls were built on steel beams to permit their displacement after construction.

a)

b)

Figure 3.4.1 - Construction of the walls; a) Bricks and handmade mortar; b) Firsts layer of masonry at one leaf

The mortar used was mixed by hand and poured so that the joints are parallel and constant, also with the aid of a level.

a)

b)

Figure 3.4.2 - Construction of the walls; a) Particular of the vertical joint construction; b) Wall completed

45


Chapter 3 – Experimental Campaign

Over the last layer of bricks a steel beam was positioned. Once built the two walls, seven stack prisms with five bricks and three wallets with dimensions

were built (Figure 3.4.3). All specimens were built

following the recommendations of the EN 1052-1:1999. The stack prisms and the wallets were built over a hard flat surface. The faces of the units did not receive any treatment prior to construction of the masonry. The layers, however, were sufficiently flat and parallel one to another, which is desirable during the construction and for the proper load distribution during compressive testing. The wallets were built over a steel beam to make displacement easier after the construction. The dimensions were decided following the prescription of the EN 1052-1:1999.

a)

b)

Figure 3.4.3 - Built specimens; a) Stack prisms; b) Wallet

3.4.2 Extraction of cylindrical specimens When the walls were two months old, the masonry cylinders were extracted. At that time it was supposed that the hydraulic mortar was hardened enough to support the coring operations. In order to obtain the maximum number of different specimens and to avoid the disjointing of the wall, the locations of extractions were carefully planned. The specimens required were: -

1JC: cylinder with one bed joint and

;

-

2JC: cylinder with two bed joints and

-

3JC: cylinder with two bed joints and one vertical joint and

; .

The project of core extraction is shown in Figure 3.4.4, in Figure 3.4.5 and in Figure 3.4.6.

46


Chapter 3 – Experimental Campaign

a)

b)

Figure 3.4.4 - The walls before the extraction; a) The first wall; b) The second wall

Figure 3.4.5 - Layout of extractions from the first wall

Figure 3.4.6 - Layout of extractions from the second wall

Four steel bars were welded to the two steel profiles and were subjected to tensile force in order to apply a low compression load to the wall. The precompression was set to confine properly the material during coring and to avoid a collapse during the extraction. The dynamometer key was used to apply a moment of

to each bar. The bars were tensioned 47


Chapter 3 – Experimental Campaign

gradually to prevent the inclination of the beam. The arm of the dynamometer key is (Figure 3.4.7).

a)

b) Figure 3.4.7 - Dynamometer key and application point.

The extraction of cylindrical specimens is a delicate stage. In the previous experimental campaign, by Peverini (2014) and Witt (2014), the samples were extracted after turning the wall over. The extraction procedure was made using the wet procedure, i.e. water was employed during drilling to prevent drill overheating and the accumulation of dust inside them. This methodology led to the early disaggregation of several specimens, due to low strength of mortar. The first problem was the extraction from the horizontal laying of the wall, which induced a transversal point load to the wall affecting his integrity. The second problem was the presence of water washing away the weak mortar and detaching the bricks from the specimens. In the present work, the cylinders extraction was made following a new procedure (equipment in Figure 3.4.8). The first big difference is the vertical position of the wall during the extraction of specimens (Figure 3.4.9). This is more representative of the real procedure of extraction from a wall of an existing building. In order to prevent the overturning of the wall during the extractions, the wall was set against a laboratory wall.

48


Chapter 3 – Experimental Campaign

a)

b)

Figure 3.4.8 – Equipment for extraction; a) Extraction apparatus fixed at the forklift; b) Drill cylinders used

The second novelty was the dry procedure of extraction of specimens. The core drilling machine was connected to an aspirator that was intended to eliminate part of the dust. Every specimen was extracted in three stages to prevent core drill overheating and to remove the excess of dust. Firstly, the machine drilled the core until half thickness of the wall. Secondly, the drilling machine was stopped to take the dust out of the core(see Figure 3.4.10). Finally, the extraction was completed by drilling until all the thickness of the wall. Making use of this careful procedure, the specimens were extracted without problems or unexpected failures.

Figure 3.4.9 - Dry and vertical extraction of cylinders from the masonry walls

49


Chapter 3 – Experimental Campaign

a)

b)

c)

Figure 3.4.10 – Extraction phases; a) Cleaning by compressed air; b) Dust inside the core drill; c) Hole after extraction

The cylinders were firstly extracted from the lateral parts of the wall and then from the central part, as shown in Figure 3.4.10.

a)

b)

Figure 3.4.11 - Phases of the extraction; a) from the lateral part; b) from the centre

a)

b)

Figure 3.4.12 - End of the extraction; a) First wall; b) Second wall

After the extraction, the following specimens were obtained:

50

-

22 one joint cylinders (1JC);

-

15 two joint cylinders (2JC);


Chapter 3 – Experimental Campaign

-

15 three joint cylinders (3JC).

All the specimens expected before the extraction were then obtained without undesired failures (see Figure 3.4.12, Figure 3.4.13, Figure 3.4.14).

a)

b)

Figure 3.4.13 - Specimens extracted; a) One joint cylinders; b) Two joint cylinders

Figure 3.4.14 - Three joint cylinders extracted

After the extraction procedure, the two drilled walls were reused for other testing purposes. A wall was completely dismantled to extract mortar joints for the Punching test (Figure 3.4.15), according to the DIN 18555-9:1999. The other wall was used for another experimental program, not presented in this thesis, focused on the calibration of penetrometer tests.

51


Chapter 3 – Experimental Campaign

a)

b)

Figure 3.4.15 - Extraction of mortar specimens for punching test; a) Extraction with chisel; b) Specimens obtained

3.4.3 Punching test The punching test was performed on the specimens obtained from the single-leaf wall that was dismantled after the extraction of cylindrical cores (the specimens obtained are shown in Figure 3.4.15 b) and in Figure 3.4.16 b)). In addition, some new specimens were built, following the code DIN 8555-9:1999 method III. These samples were prepared simply by placing mortar between two masonry units (see Figure 3.4.16 a)). The two types of specimens were tested at the same time of the mortar prisms in order to make a comparison between different testing methods.

Figure 3.4.16 - Mortar joints prepared following DIN 8555-9:19999; a) Mortar placed between two units; b) Mortar joint extracted from the wall

The specimens for the punching test were cut in squares of constant due to the wall construction procedure, with a range of

side. The thickness is not .

The DIN standard suggests to use specimens with parallel faces and whenever this is not possible it recommends to put a layer of gypsum with a thickness lower than

52

(Figure


Chapter 3 – Experimental Campaign

3.4.17). In order to have a complete investigation of the test, it was decided to regularize a half of specimens, choosing the most irregular ones. In conclusion, the different types of specimens were: -

Standard: specimens built according to the DIN 18555-9:1999;

-

Standard Regularized: specimens built following the DIN 18555-9:1999 and regularized with a layer of gypsum;

-

Extracted: specimens extracted from the wall after coring;

-

Extracted Regularized: specimens extracted from the wall after coring and regularized with a layer of gypsum.

a)

b)

c

Figure 3.4.17 - Specimens for the punching test; a) Some specimens; b) Gypsum; c) Specimen regularized

a)

b)

Figure 3.4.18 - Specimens prepared for testing

The tests were performed with the Ibertest machine with a load cell of was

to have the end of the test in a range of

The specimens were placed centrally between the loading platens (

. The load rate

. ) of the testing

machine, with a full contact between specimen and platens over the area of load transmission. In Figure 3.4.18 is shown the drawing made to permit the alignment. The setup is shown in Figure 3.4.19 and Figure 3.4.20. 53


Chapter 3 – Experimental Campaign

Figure 3.4.19 - Test setup (DIN 8555-9:1999)

a)

b)

Figure 3.4.20 - Punching test; a) Starting of the test; b) Test ended

3.4.4 Compression test on wallets The wallets were tested at the age of seven months, as well as the other masonry specimens. Before testing, a cement layer was placed on the top of the specimens, after that a steel IPE beam was arranged on the top of the wallet. The steel beam was necessary to spread the load on the total area of the specimens during test. A steel frame was built especially for testing the wallets. The test setup consisted of two load cell of

controlled by the Ibertest machine (Figure 3.4.21 a), Figure 3.4.22 a)). In

addition, it was necessary to use two external data acquisition “Canhead direct”, HBM España (Figure 3.4.21 b)). 54


Chapter 3 – Experimental Campaign

The test was divided in two phases: the first phase was performed under load control whereas the second phase was performed under displacement control. After the first and second tests, it was clear that the Ibertest machine had some problems to control the two cells under displacement control, for this reason the last test were performed in the Instron machine with a single load cell of

(Figure 3.4.22 b)). Despite the change of the control machine,

the setup of the tests was the same for the three specimens.

a)

b)

Figure 3.4.21 - Testing setup; a) Two load cells of 500 kN; b) Data acquisition

a)

b)

Figure 3.4.22 - Compression machine; a) Frame used for the first two tests; b) Instron machine used for the last test

The main purpose of the test was to evaluate the compressive strength of the wallet. Additional parameters that were obtained by the test are the Young’s modulus, the Poisson’s ratio and the compressive fracture energy. With this test it was also possible to make a comparison with the innovative compressive test on cylinders extracted from the masonry walls. 55


Chapter 3 – Experimental Campaign

The specimen geometry and the test setup are reported in the Figure 3.4.23.

Figure 3.4.23 – Wallets: Instrumentation

As can be seen above the four LVDTs were put in the same configuration of the LVDTs used for the compression test on the masonry cylinders. In addition, two potentiometers were positioned to evaluate the behaviour of the whole specimen. The potentiometers had also the important function of evaluating if the wallets bent during the tests.. The characteristics of the instruments used are: -

LVDT3, LVDT4: placed in vertical position (range

; precision

-

LVDT1, LVDT2: placed in horizontal position (range

-

V1, V2, V3, V4: Potentiometers placed in vertical position (range

; precision

); ); ; precision

); -

H1, H2: Potentiometers placed in horizontal position (range

; precision

); -

D1, D2: Potentiometers placed in vertical position, in the lateral part of the Wallets (range

56

; precision

);


Chapter 3 – Experimental Campaign

As mentioned above, the loading was divided in two different parts. The first part is under loading control and composed of three loading-unloading cycles, from maximum load expected (

to

of the

), with the aim of evaluating the elastic behaviour of

masonry (Figure 3.4.24). The second part is under displacement control, with a ratio of , in order to evaluate the post peak behaviour. The results are discussed in Chapter 4.

Figure 3.4.24 - Loading setup, load control.

3.4.5

Compression test on stack prisms

The Stack Prisms were tested at the age of seven months, as well as the others masonry specimens. Before testing, a layer of high strength mortar was placed on the top of the specimen. Each sample was tested in the Ibertest machine, using a load cell of

. A hinge

configuration was employed for the loading plate in order to facilitate the uniform load distribution over the specimen. The “MCGPlus” (by HBM España company) was used as external data acquisition. The test was divided in two parts: the first part was performed under load control whereas the second part under displacement control with a ratio of 0.008 mm/s. Concerning the first part, three cycles of loading and unloading were carried out, with the aim of evaluating the elastic behaviour of masonry. In particular, the load changed cyclically from maximum load expected, that corresponds to a variation between

to

of the (see Figure

3.4.24). The second part of the test was performed directly after the last cycles of loading and unloading. The adopted machine and the test setup are reported in Figure 3.4.25 and in Figure 3.4.26.

57


Chapter 3 – Experimental Campaign

Figure 3.4.25 - Ibertest machine, load cell 3000 kN

a)

b)

Figure 3.4.26 - Setup of the test; a) Positioning of the stack prisms in the centre of the machine; b) Positioning f the LVDTs

Six LVDTs were placed in order to assess the vertical and horizontal displacements of the specimen. The configuration was designed with the aim of being able to compare the displacements obtained in the compression test on the two joint cylinders. The main parameters that this test provided were the compressive strength, the Young’s modulus, the Poisson’s ratio and the compressive fracture energy. It is important to point out that the assessment of these parameters were obtained with the LVDTs positioned in the part of masonry without vertical joints (see Figure 3.4.27).

Figure 3.4.27 - Stack prisms: Instrumentation

58


Chapter 3 – Experimental Campaign

Referring to the Figure 3.4.27, the LVDTs . The LVDTs precision of

have a ratio of

and a precision of

, placed in horizontal position, have a ratio of

and a

.

3.4.6 Compression tests on cylinders extracted As stated in Section 3.4.2, the cylinders used to perform the compression tests were extracted from the single-leaf walls and they were successively regularized with cement mortar caps. The specimens were 30 divided into

two joint cylinders and

three joint cylinders. In

order to reduce the scattering of the results, the specimens in best conditions were selected and tested. Before starting the tests, two specimens were tested to find the correct parameters of the test setup. The tests carried out and analysed in this research are 6 for both three joint and two joint specimens. The cylindrical specimens were used to perform a non-standard compressive test with the aim of determining the compressive strength, the Young’s modulus and the Poisson’s ratio of the brickwork. To perform the test, the standards guidelines UIC 778-3R (UIC 1995) and previous studies have been taken into consideration (Gambarotta et al. 2001, Brencich and Sterpi 2006, Bilello et al. 2007, Brencich and Sabia 2008, Peverini 2014). The testing procedure consists in applying a compressive load on the lateral surface of the specimen, in the same way as in the original structure, recording both the vertical and the horizontal displacements. The diameter of the specimens was

, as recommended by the UIC

778-3E:2011 guidelines. 3.4.6.1 Mortar regularization The regularization of the cylinders was made with the high strength mortar whose characterization has been presented in Chapter

. The moulds prepared specifically for

the cylinders were made of wood and filled with high strength mortar (see Figure 3.4.28). The parallelism between the sides of the mould was checked and adjusted before the regularization of each specimens. The purpose of this particular kind of regularization is to ensure an optimum adherence between the specimen and the regularization during the test. This approach is new and completely different from that proposed by UIC 778-3R (UIC 1995) guidelines and Brencich and co-workers, in which rounded metal loading plates were recommended. 59


Chapter 3 – Experimental Campaign

a)

b)

c)

Figure 3.4.28 - Mould preparing; a) Wooden mould; b) Specimen regularized; c) All specimens regularized.

After the pouring of mortar into the mould, the specimens were kept in laboratory conditions until the mortar achieved the adequate strength. After that, the specimens were extracted from the regularization moulds, ready to be tested. 3.4.6.2 Test setup The cylinders were tested at the age of seven months, as the other specimens. The two joints cylinders were tested in the Ibertest machine with a load cell of

, and it was

necessary to use the MG-Plus as external acquisition, since the number of instrument used was more than four. At the end of the tests on the three joint cylinders the data acquisition had a problem and it was necessary to change the testing machine. Therefore the two joint cylinders were tested in the Instron machine with the load cell of

. Despite the change

in machine the testing setup was equal for the two types of specimens. The test was divided in two parts, like the other tests on masonry. The first part was performed under load control, carrying out three cycles of loading and unloading with the aim of evaluating the elastic behaviour of the masonry. The second part was performed under displacement control with a ratio of changing cyclically the force from

. In this test the cycles were performed to

correspond to an interval of force of

of the maximum force expected, that . The maximum value considered for the

cycles of loading and unloading is lower than the

of the maximum force expected.

The specimens’ geometry and the layout of the instruments are reported in Figure 3.4.29. In Figure 3.4.30 is shown one test performed in Ibertest.

60


Chapter 3 – Experimental Campaign

Figure 3.4.29 - Cylinders: Instrumentation

a)

b)

Figure 3.4.30 - Cylinder during a test; a) Front part of the specimen; b) Back part of the specimen.

The test setup consists in six LVDTs placed in order to assess vertical and horizontal displacements of the specimen: -

two LVDTs were positioned vertically (LVDT 3 and LVDT 4 with a range of and a precision of

-

);

four LVDTs were arranged horizontally (LVDT 1 and LVDT2 with a range of and a precision of

-

);

two LVDTs were placed on the lateral part of the specimen (LVDT5 and LVDT6 with a range of

and a precision of

).

In particular, the two vertical LVDTs were placed in different position with the aim of evaluating if the regularization could actually be considered infinitely rigid compared to masonry. As regards the horizontal LVDTs, the two external ones were placed to check the appearance of cracks and possible splitting of the specimen. The two internal LVDTs have been introduced with the aim of evaluating the Poisson’s ratio in the first part of the loading cycles, when the load is very low.

61


Chapter 3 – Experimental Campaign

62


Chapter 4

Results and discussion

4.1 Introduction The experimental campaign has provided many experimental results. In this Chapter, the results from the different tests are interpreted, in order to obtain the mechanical parameters of the materials. The typologies of tests are analysed to evaluate if are suitable for assessing the parameters requested. The first test investigated is the punching test on mortar. The following tests that are analyzed are those on masonry. All the tests are shown and discussed, and critically compared each other. The validity of results is proved in the last Sections. The Young’s modulus is compared with an analytical evaluation. Finally the compressive strengths and the Young’s moduli are compared with the standards.

63


Chapter 4 – Results and discussion

4.2 Results of the punching tests 4.2.1 Introduction The punching tests on the mortar joints were performed using different types of specimens at different ages (120, 190, 260 days). Considering that the area is the same for each specimen, the most important characteristic is the relation between the thickness and the compressive stress obtained. The trend expected is that the strength is higher when the thickness is smaller. This is due to the confinement effect (Mc Nary, 1985). 4.2.2 Analysis of the results The first analysis was carried out dividing the specimens only by the different ages and not by the different typologies. In Figure 4.2.1, Figure 4.2.2 and Figure 4.2.11 the stress-thickness graphs are showed at the different ages. Pnching tests - 120 days 8

120 days

Stress [MPa]

7 6 5 4 3 2 1

10

15

20 Thickness [mm]

Figure 4.2.1 – Punching tests – 120 days

64

25

30


Chapter 4 – Results and discussion

Punching tests -190 days 8,00

190 days

Stress [MPa]

7,00 6,00 5,00 4,00 3,00 2,00 1,00

10

15

20 Thickness [mm]

25

30

Figure 4.2.2 – Punching tests – 190 days

Punching test - 260 days 8,00

260 days

Stress [MPa]

7,00 6,00 5,00 4,00 3,00 2,00 1,00

10

15

20 Thickness [mm]

25

30

Figure 4.2.3 - Punching tests – 260 days

The thickness considered is the real one for the specimens without regularization, and the sum of gypsum and real thickness for the specimens regularized. At the age

and

the trend is similar, the increment of the strength is

indirect proportional to the thickness. Meanwhile this trend is not so much evident at . It is pointed out that the specimens’ thickness at that age presents higher values than the younger specimens. In order to better understand the obtained results it was considered a central range of thicknesses: between

and

. In Figure 4.2.4

the comparison is illustrated, with the respective tendency lines.

65


Chapter 4 – Results and discussion

Punching test - Age comparison

8

120 days

7

190 days

Stress [MPa]

6

260 days

5

120 days

4

190 days 260 days

3 2 1

10

15

20 Thickness [mm]

25

30

Figure 4.2.4 – Punching tests- Age comparison

Considering the same range of values, the tendency is quite similar at the different ages. In fact seeing Figure 3.3.15, the compressive strength evaluated following EN 1015-11:2007 is stabile from the age of

. The strength does not presents highly increments in the

later tests. The tendency lines at

and

are almost parallel, whereas the line at

presents a lower inclination but the trend is quite similar to the younger specimens. The second evaluation was to consider the different typology of the specimens (Figure 4.2.5, Figure 4.2.6, Figure 4.2.7 and Figure 4.2.8). Punching test - Extracted 8

Extracted

Stress [MPa]

7 6 5 4 3 2 1

10

15

20 Thickness [mm]

25

Figure 4.2.5 - Punching test – Specimens extracted.

66

30


Chapter 4 – Results and discussion

Extracted regularized 8

Extracted regularized

Titolo asse

7 6 5 4 3 2 1

10

15

20 Titolo asse

25

30

Figure 4.2.6 – Punching test – Specimens extracted regularized.

Punching test - Standard 8

Standard

Stress [MPa]

7 6 5 4 3 2 1

10

15

20 Thickness [mm]

25

30

Figure 4.2.7 – Punching test – Standard specimens.

67


Chapter 4 – Results and discussion

Standard regularized 8

Standard regularized

Stress [MPa]

7 6 5 4 3 2 1

10

15

20 Thickness [mm]

25

30

Figure 4.2.8 – Punching test – Standard regularized specimens.

The specimens extracted are the most irregular in thickness since during the construction of the walls it is important to obtain the parallelism of the lines and this means that the irregularity of the bricks lead to the consequent joints thickness irregularity. The regularization was preferred in many cases. The extracted specimens were thicker than the standard specimens and the regularization increased more the thickness. The standard specimens are more regular in dimensions and it is evident seeing Figure 4.2.7 and Figure 4.2.8, where the specimens not regularized are all less than

.

The trend is clearer if the different joint specimens are in the same graph (see Figure 4.2.9). Punching test - Typology comparison 8 7

P_2_ER

Stress [MPa]

6 5 4 3 2 1

10

15 Extracted Standard regularized Stand

20 Thickness [mm] Extracted regularized Extra Stand Reg

25

Figure 4.2.9 – Punching test –Typology comparison

68

30 Standard Extra Reg


Chapter 4 – Results and discussion

The trend of the different specimens is quite different. The point that moved the extracted regularized lines is the specimen

with a thickness more than

. It was decided

to exclude this point because in order to be tested it was necessary to smooth it, since the testing machine configuration does not permit thickness higher than

. The mechanical

smoothing might have compacted more the specimen. Figure 4.2.10 shows the previous graph without the specimen excluded, and now the updated tendency line presents a negative slope similar to the others. Punching test vs. Half prisms

8 7 Stress [MPa]

6 5 4 3 2 1

10

15

20

Extracted Standard regularized Extra Reg

25 30 Thickness [mm] Extracted regularized Prisms Stand

35

40

45

Standard Extra Stand Reg

Figure 4.2.10 – Punching test vs. half prisms comparison.

It is pointed out that the tests with a different behaviour are the specimens with the bigger thickness. The reason why they present a big stress despite the bigger thickness it is explained in Figure 4.2.10. In fact, comparing the punching test with the results obtained with the half prisms in the standard compression test, at almost (

and

days, it is evident that after a value of

the confinement effect is negligible for the cross sections considered ).

The Figure 4.2.11 showed the different specimens’ typologies at the different ages, gathered all together. Note that a total of 60 punching tests were carried out in the experimental program.

69


Chapter 4 – Results and discussion

Punching test 8 120d stand

7

120d stand reg

σ [MPa]

6

120d extra 120d extra reg

5

190d stand

4

190d stand reg

3

190d extra

2

190d extra reg 260d stand

1 0

260d stand reg 10

15

20 t [mm]

25

30

260d extra 260d extra reg

Figure 4.2.11 - Punching tests divided in typologies and ages

The specimens can be evaluated in the same graph (Figure 4.2.11), since the mortar after has matured. The trend of the cloud of point is exponential, and in Figure there is a preliminary equation that represent the trend. As shown in Figure 4.2.12, the apparent strength is inversely proportional to the layer thickness. The results are in according with Benedetti, Pelà (2012). Punching tests 8

Specimens

7

Potenza (Specimens)

Stress [MPa]

6 5 4 3 2 1

y = 82,784x-1,116 R² = 0,3786 10

12

14

16

18 20 Thickness [mm]

22

Figure 4.2.12 – Results of punching tests

70

24

26

28


Chapter 4 – Results and discussion

4.3 Results of the test on Wallets 4.3.1 Introduction As mentioned before, three wallets were tested under compression load, in order to evaluate the compressive strength and the Young’s modulus of masonry. The first two specimens were tested in the Ibertest machine (with two load cell of

), however the displacement

control system was not working well. For this reason the third specimen was tested in the Instron machine (with only one load cell of

).

The results obtained from all specimens are satisfactory to the evaluation of the compressive strength and the masonry elastic parameters, except for the first specimen. In fact, in the first test, the only value obtained was the compressive strength, since being the first test the setup was not calibrated. The Figure 4.3.1 represent the three specimens before testing.

a)

b)

c)

Figure 4.3.1 - Specimens tested; a) Wallet 1; b) Wallet 2; c) Wallet 3.

4.3.2 Elastic cyclic loading 4.3.2.1 Young’s modulus In the initial stage of cyclic loading, the results obtained, in terms of stress-strain, showed that the equipment well recorded the walls’ behavior. However, it is necessary to point out, that the test on wallet 2 showed an anomalous behavior of the potentiometers that in some points presented a big scatter. As for the wallet 3, the LVDTs and the Potentiometers showed a regular behavior. The results obtained in the first part of the loading setup, the three load cycles, are shown in Figure 4.3.2 and in Figure 4.3.3.

71


Chapter 4 – Results and discussion

1,6

Wallet 2 - Elastic Cycles

1,4

Stress [MPa]

1,2 1

0,8 0,6 0,4 0,2

0 0,0000 -0,2

0,0005

0,0010

LVDTs - vertical average

0,0015

0,0020

0,0025

Strain Potentiometers - vertical average

Figure 4.3.2 – Elastic cycles: wallet 2

1,6

Wallet 3 -Elastic cycles

1,4

Stress [MPa]

1,2 1 0,8 0,6 0,4 0,2 0 0,0000

0,0005

LVDTs - vertical average

Strain

0,0010

0,0015

Potentiometers - vertical average

Figure 4.3.3 – Elastic cycles: wallet 3

The comparison between the two tests is difficult, since they are performed with different machines. The Instron, used for wallet 3, is more precise than the Ibertest. However, the two tests were compared showing the LVDTs vertical average.

72


Chapter 4 – Results and discussion

σ - εvertical

1,6 1,4

Stress [MPa]

1,2 1 0,8 0,6 0,4 0,2 0 0,0000

0,0005

0,0010 0,0015 Strain Wallet 3 - Vertical LVDT Wallet 2 - Vertical LVDT Figure 4.3.4 - Comparison of the two wallets

The behavior of the two wallets is similar and with the aim of verifying numerically this similarity the calculation of Young’s modulus has been made, taking as a reference the last load cycle, in which it is assumed that all the adjustment of the specimen had already occurred. Table 4.3.1 – Wallets: Young’s modulus in the elastic cycles

Wallets - E modulus - Elastic cycles ELVDT [MPa]

EPOT [MPa]

wallet_1

-

-

wallet_2

2364

2106

wallet_3

1847

2187

Average

2106

2147

St. Dev.

366

57

CV

17.36%

2.67%

The values obtained are in good agreement and the estimation of Young’s modulus is considered valid with both types of instrumentation. 4.3.3 Loading test to failure 4.3.3.1 Compressive strength and Young’s modulus As mentioned before, the wallet 2 had problems during the displacement control phase. The graphs obtained are still comparable with those obtained in the wallet 3 test. As for the wallet

73


Chapter 4 – Results and discussion

1, the graph obtained is not comparable, because of many variations of the load, however the compressive strength was recorded anyway. Figure 4.3.5 shows the comparison of the results. σ - εLVDTvertical

3,5 3

Sress [MPa]

2,5 2 1,5 1 0,5 0 0,000

0,005

0,010 Strain

Wallet 2

0,015

0,020

Wallet 3

Figure 4.3.5 – Wallets stress strain, obtained using the LVDTs

It was decided to present only the results obtained with the LVDTs average, since they are more accurate. The graphs show clearly that the test control on wallet 3 was much better than in the wallet 2. The compressive strength is calculated, and also the value of the Young’s modulus by evaluating the first linear part of the stress - strain curve. Table 4.3.2 - Wallets results – Displacement control

Wallets σ [MPa]

ELVDT [MPa] EPOT [MPa]

wallet_1

6.20

-

-

wallet_2

3.11

2023

1867

wallet_3

3.63

1876

2203

Average

4.31

1950

2035

St. Dev.

1.7

104

238

CV

38.36%

5.33%

11.68%

As seen in Table 4.3.2, the compressive strength obtained has a remarkable high coefficient of variation. This is due to the higher strength value in the first test than in the others. The difference is due to the large variability of the dimensions and characteristics of the materials 74


Chapter 4 – Results and discussion

used to build the wallets and also to the considerable thickness of the horizontal joints (sometimes greater than 20 mm). The Young’s moduli obtained are similar to the values of the elastic cycles. The coefficients of variation are quite low, despite the problems during the tests. 4.3.3.2 Poisson’s ratio The evaluation of the Poisson’s ratio is made considering the relation between the horizontal and the vertical strain. Two horizontal LVDTs were placed in the central part of the wallet through a vertical joint. The Poisson’s ratio is evaluated only in displacement control part, since the results obtained in the initial part of the tests were unacceptable. The load range chosen is the same one of that used for the evaluation of the Young’s modulus. The evaluation of this parameter is difficult, since the masonry give a high range of values. Furthermore, great accuracy in the instrumentation is required to record the horizontal displacement, largely smaller than the vertical ones. σ - εLVDT horizontal

3,5 3

Stress [MPa]

2,5 2 1,5 1 0,5 0 0,000 -0,5

-0,001 Wallet 2

-0,002 Strain

-0,003

-0,004

Wallet 3

Figure 4.3.6 - Wallets stress strain, obtained using the horizontal LVDTs

As shown in Figure 4.3.6, the first part of the stress-strain curve of wallet 3 presents an higher slope than in the wallet 2, since the horizontal displacement was an half of that of the wallet 2. In fact, the Poisson’s ratio is lower for the wallet 3.

75


Chapter 4 – Results and discussion

Table 4.3.3 shows the calculations made by taking the average of the two horizontal LVDT, because of the higher accuracy of the instrument than the Potentiometer. Table 4.3.3 - Wallet Poisson’s ratio

ν wallet_1

-

wallet_2

0.33

wallet_3

0.15

Average

0.24

Dev.st

0.1

CV

53.03%

The range of the values obtained is acceptable for masonry, but the scatter is higher, due to the high difference of the vertical joints dimensions, with a range of

. The higher

value is more appropriate to describe the masonry strain behavior. 4.3.4 Failure mode This Section presents the failure modes at the peak and at the end of the compression tests on wallets. At the load peak time, the wallet 1 presented thin and diffuse fractures that started from the top of the specimen. With the continuation of the test, the fractures increased their thickness and propagated along the specimen, while other new ones appeared.

Figure 4.3.7 – Wallet 1 – Peak time, back side

76


Chapter 4 – Results and discussion

a)

b)

Figure 4.3.8 - Wallet 1 - End of the test; a) Front side; b) Back side

As shown in Figure 4.3.7 and in Figure 4.3.8, the right side of the wallet 1 was weaker than the other side, in fact a greater number of fractures was present. At the end of the test, the load beam placed above the specimen showed a clear inclination. At the peak load time (see Figure 4.3.9), on the wallet 2 some diffused cracks appeared starting from the top of the specimen. On the right side the fractures were not extremely marked. On the other hand, on the left side a big fracture appeared. It was observed that the horizontal mortar joints were quite large (some of them more or equal to

).

a)

b)

c)

Figure 4.3.9 - Wallet2 – Failure mode – Peack time; a) Front side; b) Left side; c) Back side.

The components’ imperfection and the remarkable joints dimensions may have led the specimen to a premature collapse.

77


Chapter 4 – Results and discussion

a)

b)

c)

d)

Figure 4.3.10 – Wallet 2 – End of the test; a) Front side; b) Left side; c) Back side, left part; d) Back side and right part.

At the end of the test, as shown in the Figure 4.3.10, the left side was splitted into two, whereas the front side showed a swelling of the bricks. As in the previous test, the wall showed an inclination towards the right part. As for regard the wallet 3, at the load peak time, some cracks spread from the top of the specimen to the central joints. This behavior was homogeneous throughout the specimen.

78


Chapter 4 – Results and discussion

a)

b)

c)

d)

Figure 4.3.11 - Wallet 3 – Failure mode – Peak time; a) Front side; b) Left side; c) Back side; d) right side.

As can be seen in the Figure 4.3.11, the cracks are diffused in all sides of the specimen.

a)

b)

c)

d)

Figure 4.3.12 - Wallet 3 – End of the test; a) Front side; b) Left side; c) Back side; d) Right side.

At the end of the test on the wallet 3, as shown in Figure 4.3.12, the failure behavior is characterized by further opening of the cracks observed at peak load. As in the other two tests, one side presented more fractures than the other one. The top right angle fell off. Despite the failure occurred in a sufficiently homogeneous mode, the resistance obtained (see Table 4.3.2) is less than the expected value. In conclusion, the failure modes of the three wallets had a similar behavior. As shown in Table 4.3.2, the great variability of the strength obtained is probably due to the variability of the joints dimensions. In fact, all three walls are affected by a failure greater at one side. This cannot be attributed at the testing machines, because the Ibertest used two load cells instead the Instron used one cell. Moreover the specimen were centered before testing.

79


Chapter 4 – Results and discussion

4.4 Results of the tests on stack prisms 4.4.1 Introduction Seven stack prisms were tested under compression load, in order to evaluate the compressive strength, the Young’s modulus and the Poisson’s ratio of masonry. All the specimens were tested in the Ibertest machine with a load cell of

, and the MG-Plus was used as

external data acquisition to record the specimens’ displacement. The results obtained from all specimens are suitable to the evaluation of the compressive strength and the masonry elastic parameters. The Figure 4.4.1 shows the specimens before testing.

a)

b)

c)

d)

e)

f)

g)

Figure 4.4.1 – Specimens tested; a) Stack prisms 1; b) Stack prism 2; c) Stack prism 3; d) Stack prisms 4; e) Stack prism 5; f) Stack prism 6; g) Stack prism 7.

80


Chapter 4 – Results and discussion

4.4.2 Elastic cyclic loading 4.4.2.1 Young’s modulus The results obtained in the first part of the test, under loading and unloading cycles, were the vertical and the horizontal displacement. The E modulus were calculated considering the third last cycle. In Figure 4.4.2, the behaviour of the average vertical displacement is shown. The first part of the graph, for all specimens, represents the preliminary settlement of the specimen that is different for all the specimens, as expected.

σ - εvertical

1,8 1,6 1,4 Stress [MPa]

1,2 1

0,8 0,6 0,4 0,2 0

-0,2 0

0,0005

0,001

0,0015

0,002

0,0025

0,003

0,0035

0,004

Stack Prism 1

Strain Stack Prism 2

Stack Prism 3

Stack Prism 4

Stack Prism 5

Stack Prism 6

0,0045

Stack Prism 7 Figure 4.4.2 – Stack prisms – Elastic cycles: vertical strain comparison

In order to have a clear comparison among the vertical displacements, Figure 4.4.3 shows the last cyclic part avoiding the preliminary settlement stage of each specimen

81


Chapter 4 – Results and discussion

σ - εvertical (Shifted) 1,8 1,6 1,4 Stress [MPa]

1,2 1 0,8 0,6 0,4 0,2

-0,00065

0 -0,00025 -5E-05 Strain Stack Prism 1 Stack Prism 2 Stack Prism 4 Stack Prism 5 Stack Prism 7

-0,00045

0,00015 Stack Prism 3 Stack Prism 6

Figure 4.4.3 - Stack prisms – Elastic cycles: vertical strain (shifted) comparison -

It is important to point out that the general trend is quite similar for all specimens. The Young’s modulus obtained, considering the third cycle, is shown in the Table 4.4.1. Table 4.4.1 - Stack prisms Young’s modulus – Elastic cycles

Stack prisms E modulus E Elastic cycle [MPa] SP_1

2220

SP_2

2541

SP_3

2022

SP_4

2169

SP_5

2628

SP_6

4053

SP_7

3519

Average

2736

Dev.st

763

CV

27.89%

The coefficient of variation is acceptable for this type of evaluation and the Young’s modulus is representative of the masonry.

82


Chapter 4 – Results and discussion

4.4.2.2 Poisson’s ratio The evaluation of the Poisson’s ratio is made considering the relation between the horizontal and the vertical strain. Two horizontal LVDTs were placed on the central brick and no vertical joints were considered. In this test, in the elastic cyclic part, the Poisson’s ratio evaluation was difficult but some significant values were obtained anyway. The stress-horizontal strain graphs of the cycles are shown in Figure 4.4.4.

σ - εhorizontal

1,8 1,6 1,4

Stress [MPa]

1,2 1 0,8 0,6 0,4 0,2

-0,0003

-0,00025

-0,0002

-0,00015

-0,0001 Strain

0 -5E-05 -0,2 -5,5E-18

Stack Prism 1

Stack Prism 2

Stack Prism 3

Stack Prism 4

Stack Prism 5

Stack Prism 6

5E-05

Stack Prism 7 Figure 4.4.4 – Stack prisms – Elastic cycles: horizontal strain comparison

The adjustment part of the curves, the first part, is different for every specimen and very irregular. After observing the curves shifted, it is interesting to point out that the behavior of the specimens present a quite different trend (see Figure 4.4.5).

83


Chapter 4 – Results and discussion

σ - εhorizontal (Shifted) 1,8 1,6 1,4 1,2 Titolo

1 0,8 0,6 0,4 0,2

-0,00011

0 -1E-05 -0,2 Titolo

-6E-05

4E-05

Stack Prism 1

Stack Prism 2

Stack Prism 3

Stack Prism 4

Stack Prism 5

Stack Prism 6

9E-05

Stack Prism 7 Figure 4.4.5 - Stack prisms – Elastic cycles: horizontal strain (shifted) comparison

The Poisson’s ratio obtained, considering the third cycle as the same as the Young’s modulus, are shown in Table 4.4.2. Table 4.4.2 - Stack prisms – Elastic cycles: Poisson’s ratio

Stack prisms: Elastic cycles ν SP_1

0.12

SP_2

0.18

SP_3

0.19

SP_4

0.14

SP_5

0.08

SP_6

0.23

SP_7

0.15

Average

0.16

St. Dev.

0.05

CV

31.65%

The Poisson’s ratio obtained could be representative for a brick (Nichols, 2014), but this value is less than the typical masonry Poisson’s ratio. However the value obtained could be characteristic for this type of specimen, since the assessment is made between a vertical strain, which considers also two mortar joints, and the horizontal strain, which considers no joint. 84


Chapter 4 – Results and discussion

4.4.3 Loading test failure 4.4.3.1 Compressive strength and Young’s modulus The evaluation of the compressive strength and the Young’s modulus was possible for all specimens. The stress-strain graphs, after the first cracks, presented change of slope in the curves. The specimen presented more cracks then the wallets. The diffused cracks in some case interested the instrumentation. This is the reason why after the elastic part of the curves, when the cracks appeared, the curves were more instable. The stress-strain graphs, considering the average vertical strain, are reported in the Figure 4.4.6.

σ - εvertical

7

Stress [MPa]

6 5 4 3 2 1 0 0,000

0,002

0,005

Stack Prism 1 Stack Prism 4 Stack Prism 7

0,007 0,010 Strain Stack Prism 2 Stack Prism 5

0,012

0,015

Stack Prism 3 Stack Prism 6

Figure 4.4.6 - Stack prisms: Stress – strain under displacement control

The graphs presents the specimens’ behaviour until the failure. The elastic behaviour is identifiable in the first linear branch of the curve, until reaches

. When the vertical strain

, the stack prisms started to fracture. Table 4.4.3 - Stack prisms: Compressive strength and E modulus, displacement control phase

Stack prisms σ [MPa]

E [MPa]

SP_1

5.00

2323

SP_2

5.43

2618

SP_3

4.16

2411

SP_4

6.08

2202

85


Chapter 4 – Results and discussion

SP_5

6.41

2948

SP_6

6.54

3613

SP_7

5.43

3580

Average

5.58

2814

St. Dev.

0.84

586

CV

15.10%

20.82%

As shown in Table 4.4.3, the stack prism 3 presented a compressive strength lower than the others. This value can be due to a not perfectly parallel regularization on the top of the specimen. In fact, there was a little swelling on the upper face. Subsequently, the load was more concentrated in the center and the specimen arrived to failure before reaching the real compressive strength. However, the obtained Young’s modulus is acceptable. The Young’s modulus is similar to that obtained in the third elastic cycle. In fact, after the specimen’s settling phase, the elastic behavior remains constant. In order to give a correct evaluation of the compressive strength, the average of the specimens is assessed without the stack prism 3 (Table 4.4.4). Table 4.4.4 Stack prisms – Compressive strength considered.

Stack prisms σ [MPa] SP_1

5.00

SP_2

5.43

SP_3

-

SP_4

6.08

SP_5

6.41

SP_6

6.54

SP_7

5.43

Average

5.82

St. Dev.

0.62

CV

10.63%

4.4.3.2 Poisson’s ratio The Poisson’s ratio is calculated considering the same branch of the curves considered for the E modulus. The values obtained are presented in Table 4.4.5: 86


Chapter 4 – Results and discussion Table 4.4.5 - Stack prisms: Poisson’s ratio, displacement control phase

Stack Prisms ν SP_1

0.13

SP_2

0.19

SP_3

0.23

SP_4

0.14

SP_5

0.10

SP_6

0.22

SP_7

0.16

Average

0.17

Dev.st

0.05

CV

28.84%

The obtained values are similar to those of the elastic cycles phase. The same observations can be done, as reported in Section 4.4.2.2. 4.4.3.3 Failure mode The specimens tested had a common failure mode. Each specimen presented, firstly, some cracks in the upper part and in the central bricks. Secondly, new cracks appeared also on the bottom bricks. The cracks were vertical, starting from the upper brick and propagating throughout all the height of the specimens. The lateral faces of the stack prisms had one or more big cracks as shown in Figure 4.4.8 b) and Figure 4.4.9 b). The failure modes presented by the specimens are shown in Figure 4.4.7, Figure 4.4.8, Figure 4.4.9.

a)

b)

Figure 4.4.7 – Peak load; a) Stack prism 1 (back) ; b) Stack prism 2 (front).

87


Chapter 4 – Results and discussion

a)

b)

c)

Figure 4.4.8 - Peak load; a) Stack prism 2 (back); b) Stack prism 5 (right); c) Stack prism 6 (left).

a)

b)

Figure 4.4.9 - Peak load; a) Stack prism 6 (back); Stack prism 7 (right-front).

At the end of the test the cracks appeared also in the bottom brick. When the tests finished, the specimens were totally dismantled to check if the cracks have interested the internal part. Figure 4.3.10, Figure 4.3.11, Figure 4.3.12 show the finals cracks and the inner part of the specimens.

a)

b)

c)

Figure 4.4.10 - End of the test; a) Stack prism 2 (back-right); b) Stack prism2 (front-right).

88


Chapter 4 – Results and discussion

a)

b)

c)

Figure 4.4.11 - End of the test; a) Stack prism 3 (left); b) Stack Prism 4 (left); c)Stack prism 4 (back-left).

a)

b)

Figure 4.4.12 - End of the test; a) Stack prism 5 (back-right); b) Stack Prism 5 (front-left).

a)

b)

Figure 4.4.13 - End of the test; a) Stack prism 6 (front-left); b) Stack Prism 7 (left).

As seen in Figure 4.4.13 a), the cracks propagated also through the centre of the specimens.

89


Chapter 4 – Results and discussion

4.5 Results of the tests on the two joints cylinders 4.5.1 Introduction Six two joint cylinders and six three joint cylinders were tested at the age of six months. The three joint cylinders were tested in the Ibertest using a load cell of cylinders were tested in the Instron machine using a load cell of

. The two joint . The machine change

was required because of the external data acquisition, used for the Ibertest machine, had some problems after the tests. The results obtained from all specimens are suitable to the evaluation of the compressive strength and the masonry elastic parameters. In order to obtain the correct setup, one specimen was used as trial. The cylinders testes are reported in Figure 4.5.1 and in Figure 4.5.2.

a)

d)

b)

e)

c)

f)

Figure 4.5.1 - Three joint cylinders; a) 3JC4; b) 3JC7; c) 3JC8; d) 3JC11; e) 3JC14; f)3JC15.

90


Chapter 4 – Results and discussion

a)

d)

b)

e)

c)

f)

Figure 4.5.2 - Two joint cylinders; a) 2JC2; b) 2JC4; c) 2JC5; d) 2JC6; e) 2JC7; f)2JC10.

Before presenting the results, it is important to highlight how the compressive strength is calculated for this type of specimen. The compressive strength of cylindrical specimens was assessed by considering to values. These values represent the maximum and minimum limit that the strength assume. The higher value ( ) is obtained considering the force recorded during the test divided by the area of the regularization mortar. The lower value ( ) is assessed dividing the force by the area obtained multiplying the diameter of the cylinder by the length of the cylinder. The formulas used are and

and the sizes scheme is shown in Figure 4.5.3.

91


Chapter 4 – Results and discussion

(4.1)

(4.2)

Figure 4.5.3 - Dimensions name of cylinder specimen.

In the next Sections, the graphs and the Young’s modulus values are referred to the higher strength

.

The ratio of the two different strength is a constant value. The relation is shown in the equation (4.3).

In the present work the

value is obtained dividing

and

by

, providing

, since

.

The same formula is used in the UIC 778-3R (UIC 1995), but the the geometry of the test and is assumed as

value does not depend on

.

4.5.2 Elastic cyclic loading The elastic cycles shown in this Section refers all to

. The behavior considering

exactly the same, the unique difference is that, if we consider

or

is

the stress is lower according

to the ratio (Equation 4.3). 4.5.2.1 Young’s modulus The Young’s modulus is calculated considering the displacement recorded by the two vertical LVDTs. The graphs, in Figure 4.5.4 and Figure 4.5.5, show the loading and unloading cycles performed on the three joint specimens. The Figure 4.5.6 and the Figure 4.5.7 show the cycles for the two joint cylinders.

92


Chapter 4 – Results and discussion

The LVDT3 and the LVDT4 are shown into different Figures, because the LVDT3 was placed on the high mortar regularization, whereas the LVDT4 was placed directly on the bricks of the specimens. The cycles of all specimens have been overlapped, disregarding the first cycle of specimen’s settlement. In fact, this type of specimens presented different initial cycles, whereas the following ones showed similar trend. Three joint cylinders: σ2 - εv3

1,4 1,2

Stress [MPa]

1 0,8 0,6 0,4 0,2

-0,0005

-0,0004

-0,0003 3JC4 3JC11

0

-0,0002 -0,0001 Strain

0

3JC7 3JC14

0,0001

0,0002

3JC8 3JC15

Figure 4.5.4 - Three joint cylinders – Elastic cycles: vertical strain (measure of the displacement with LVDT3);

Three joint cylinders: σ2 - εv4 1,4

Stress [MPa]

1,2 1 0,8 0,6 0,4 0,2 -0,0006 -0,0005 -0,0004 -0,0003 -0,0002 -0,0001 Strain 3JC4 3JC7 3JC11 3JC14

0

0

0,0001

0,0002

0,0003

3JC8 3JC15

Figure 4.5.5 - Three joint cylinders – Elastic cycles: vertical strain (measure of the displacement with LVDT4);

The strains presented in Figure 4.5.4 and in Figure 4.5.6, are obtained dividing the LVDT3 measure by the diameter of the masonry cylinders (

), since, as confirmed in

Section 3.3.3, the high strength mortar regularization placed on the cylinders is infinitely rigid compared to the masonry. 93


Chapter 4 – Results and discussion

The strains presented in Figure 4.5.5 and in Figure 4.5.7, are obtained dividing the displacement measured with LVDT4 by the distance between the two LVDT 4 supports. The length was different for every specimen, for that reason it was recorded before each test. The difference in sign from the three joint cylinders test and the two cylinders is due to the change of the testing machine and corresponding setting. Two joint cylinders: σ2 - εv3

1,4 1,2 Stress [MPa]

1 0,8 0,6 0,4 0,2 0,0006

0,0005

0,0004

0,0003

2JC2 2JC6

0,0002 Strain

0,0001

2JC4 2JC7

0

0

-0,0001

-0,0002

2JC5 2JC10

Figure 4.5.6 - Two joint cylinders – Elastic cycles: vertical strain (measure of the displacement with LVDT3);

Two joint cylinders: σ2 - εv4

1,4 1,2

Stress [MPa]

1 0,8 0,6 0,4 0,2 0,00035

0,00025 2JC2

0,00015 Strain 2JC4

2JC6

2JC7

5E-05

0

-5E-05

-0,00015

2JC5 2JC10

Figure 4.5.7 -Two joint cylinders – Elastic cycles: vertical strain (measure of the displacement with LVDT4);

The graphs shows that the LVDT4 reading is more unstable compared to the LVDT3 reading. This is due to the fact that the LVDT4 was placed in contact with the two bricks directly loaded.

94


Chapter 4 – Results and discussion

The Table 4.5.1 and the Table 4.5.2 show the Young’s modulus values assessed considering the third loading and unloading cycle, in which is expected that the adjustment of the specimens had already occurred. Table 4.5.1 - Three joint cylinders – Elastic cycles - Young’s modulus

3JC - Elastic Cycles E3 [MPa] E4[MPa] 3JC4

2726

-

3JC7

1930

1541

3JC8

2483

3432

3JC11

3560

4447

3JC14

2036

2465

3JC15

2686

4538

Average

2570

3285

St. Dev.

587

1290

CV

22.82%

39.27%

Table 4.5.2 - Two joint cylinders – Elastic cycles - Young’s modulus

2JC -Elastic Cycles E3 [MPa]

E4[MPa]

2JC2

2027

4339

2JC4

2749

2439

2JC5

2262

4020

2JC6

2241

3039

2JC7

3857

6440

2JC10

2105

3964

Average

2540

4040

St. Dev.

692

1373

CV

27.26%

33.97%

The Young’s modulus values obtained with the LVDT4 are highly different, as was expected seeing the graphs in Figure 4.5.5 and in Figure 4.5.7. The measure of LVDT4 is different for each specimen, since it is affected by any swelling or cracks, being directly located on the loaded bricks. Therefore, the only LVDT3 measure is considered as a realistic reading. The movements that created problems on the LVDT4 reading are shown in Figure 4.5.16.

95


Chapter 4 – Results and discussion

4.5.2.2 Poisson’s ratio The Poisson’s ratio is assessed using two couples of horizontal LVDTs. The first couple is placed on the two faces of central bricks (LVDT1 and LVDT2), whereas the second couple is located externally (LVDT5 and LVDT6), as shown in Figure 3.4.29. The displacement calculated for the LVDT1 and 2, is the average of the two ones. As for LVDT5 and LVDT6, the sum of the displacements is considered. Figure 4.5.8, Figure 4.5.9, Figure 4.5.10 and Figure 4.5.11 show the stress cycles and the horizontal strain for both specimens type. Three joint cylinders: σ2 - εh12 1,4 1,2 Stress [MPa]

1 0,8 0,6 0,4 0,2

-0,00012

0 -2E-05

-7E-05 3JC4 3JC11

3E-05 Strain 3JC7 3JC14

8E-05

0,00013

3JC8 3JC15

Figure 4.5.8 - Three joint cylinders – Elastic cycles: horizontal strain (displacements average LVDT1-2).

1,4

Three joint cylinders: σ2 - εh56

1,2 Stress [MPa]

1 0,8 0,6 0,4 0,2 -5E-05

-3E-05

0 -1E-05 3JC4 3JC11

1E-05

3E-05 5E-05 Strain 3JC7 3JC14

7E-05

9E-05

0,00011

3JC8 3JC15

Figure 4.5.9- Three joint cylinders – Elastic cycles: horizontal strain (displacement sum LVDT5-6).

96


Chapter 4 – Results and discussion

Two joint cylinders: σ2 - εh12 1,4 1,2 Stress [MPa]

1 0,8 0,6 0,4 0,2 5E-06

0

-5E-06

-1,5E-05

2JC2 2JC6

-2,5E-05 Strain 2JC4 2JC7

-3,5E-05

-4,5E-05

2JC5 2JC10

Figure 4.5.10 - Two joint cylinders – Elastic cycles: horizontal strain (displacements average LVDT1-2).

1,4

Two joint cylinders: σ2 - εh56

1,2 Stress [MPa]

1 0,8 0,6 0,4 0,2 0,00004

0,00002

0

0

-0,00002 -0,00004 -0,00006 -0,00008 -0,0001 -0,00012 Strain 2JC2 2JC4 2JC5 2JC6

2JC7

2JC10

Figure 4.5.11 - Two joint cylinders – Elastic cycles: horizontal strain (displacements sum LVDT5-6).

The specimens similar behavior, except the three joint cylinder 4 in both readings and the two joint cylinder 5 in LVDT5 and 6 reading. The evaluation of the Poisson’s ratio was quite complex because the horizontal displacements are much lower than the vertical. As for the three joint cylinders, the difficulty in evaluating the horizontal displacement is due to the big variability of the vertical joints dimensions. As for the two joint cylinders, the difficulty is due to a displacement of one order of magnitude lower than in the three joints cylinders, due to lack of vertical joint. Another important aspect is that the LVDT1 and 2 presented higher precision than the LVDT5 and 6. This difference is more evident in the Figure 4.5.10 and the Figure 4.5.11. 97


Chapter 4 – Results and discussion

The Poisson’s ratio is calculated considering the vertical and the horizontal strains obtained in the third load cycle, and is shown in Table 4.5.3 and in Table 4.5.4. Table 4.5.3 - Three joint cylinder – Elastic cycles – Young’s modulus

3JC - Elastic cycles ν12

ν56

3JC4

0.37

0.17

3JC7

0.27

0.21

3JC8

0.39

0.18

3JC11

0.55

0.34

3JC14

0.44

0.26

3JC15

0.41

0.27

Average

0.41

0.24

St. Dev.

0.09

0.06

CV

22.62%

26.99%

Table 4.5.4 - Two joint cylinder – Elastic cycles – Young’s modulus

2JC - Elastic cycles ν12

ν56

2JC2

0.06

0.03

2JC4

0.07

0.09

2JC5

0.07

0.19

2JC6

0.06

0.04

2JC7

0.14

0.09

2JC10

0.06

0.09

Average

0.08

0.09

St. Dev.

0.03

0.06

CV

40.97%

64.21%

The Poisson’s ratio obtained for both types of specimens presents a big variation. The three joint cylinders were influenced by the big variability of the vertical joint dimension. As for the two joint cylinder, the precision of the LVDTs used, especially for LVDT5 and 6, is similar to the horizontal movement of the brick. It was difficult to have a good evaluation of this parameter.

98


Chapter 4 – Results and discussion

4.5.3 Loading test to failure 4.5.3.1 Young’s modulus and compressive strength The last part of test is performed under displacement control. The specimens reaches the maximum force, and the evaluation of the compressive strength is possible. As in the previous tests, the first part of the curves were considered to find the elastic parameters. The Figure 4.5.12, Figure 4.5.13, Figure 4.5.14 and Figure 4.5.15 show the vertical strains

Stress [MPa]

evaluated considering the LVDT3 and LVDT4 displacements. 10 9 8 7 6 5 4 3 2 1 0

Three joint cylinders: σ2 - εv3

0

0,005

0,01 3JC4 3JC11

0,015 Strain

0,02

3JC7 3JC14

0,025

0,03

3JC8 3JC15

Stress [MPa]

Figure 4.5.12 - Three joint cylinders –Vertical strain (measure of the displacement with LVDT3).

10 9 8 7 6 5 4 3 2 1 0

Three joint cylinders: σ2 - εv4

0

0,005 3JC4 3JC11

0,01

0,015 Strain 3JC7 3JC14

0,02

0,025

3JC8 3JC15

Figure 4.5.13 - Three joint cylinders –Vertical strain (measure of the displacement with LVDT4).

99


Chapter 4 – Results and discussion

Also in this part of the test, it is clear that the LVDT4, placed directly on the specimens, presents an unusual behavior. Until the beginning of the test, the cracks and the brick swelling interested the faces of the two bricks, where the LVDT4 is placed (see Figure 4.5.16). The test on 3JC14 was performed in two stages. The first step was composed by the three loading and unloading cycles and the displacement control part until 90 kN. After that, the machine had a problem and the test were stopped. The second part was only in displacement control to find the compressive strength. The Figure 4.5.12 and the Figure 4.5.13 present the second step. It is observed that the elastic part in the first step was exceeded, indeed the second step presented a nonlinear part from the beginning of the test. The elastic values were calculated considering the first step. Two joint cylinders: σ2 - εv3

12 10

Stress [MPa]

8 6 4 2 0

-0,002

-0,007 2JC2 2JC6

-0,012 Strain -0,017 2JC4 2JC7

-0,022 2JC5 2JC10

-0,027

Figure 4.5.14 - Two joint cylinders –Vertical strain (measure of the displacement with LVDT3).

Two joint cylinders: σ2 - εv4

12 10

Stress [MPa]

8 6 4 2 0

-0,008

-0,018 2JC2 2JC6

Strain -0,028 2JC4 2JC7

-0,038 2JC5 2JC10

-0,048

Figure 4.5.15 - Two joint cylinders –Vertical strain (measure of the displacement with LVDT4).

100


Chapter 4 – Results and discussion

During the test on 2JC10, the LVDT3 had a problem, it is clear seeing Figure 4.5.14. However, the elastic behaviour was obtained, since the first part of the curve is realistic. The Young’s modulus assessment is shown in Table 4.5.5 and in Table 4.5.6. Table 4.5.5 - Three joint cylinder – Young’s modulus

Three joint cylinders E3

E4

3JC4

2398

-

3JC7

1982

1681

3JC8

2476

3924

3JC11

2643

3397

3JC14

2042

2506

3JC15

2331

4399

Average

2312

3181

St. Dev.

255

1094

CV

11.04%

34.39%

Table 4.5.6 - Two joint cylinder – Young’s modulus

Two joint cylinders E3

E4

2JC2

2055

3283

2JC4

2317

1843

2JC5

2006

3222

2JC6

2152

3124

2JC7

2775

3964

2JC10

2120

4268

Average

2238

3284

St. Dev.

284

841

CV

12.69%

25.61%

The Young’s modulus obtained are more stable than the t obtained by the cycles. The coefficient of variation is low, since after the three loading and unloading cycles, the specimens were sufficient stable A different initial linear segment was considered for each specimen depending on the shape of the curve, thus making a more accurate assessment. The compressive strength assessed is shown in Table 4.5.7 and in Table 4.5.8.

101


Chapter 4 – Results and discussion Table 4.5.7 - Three joint cylinders compressive strength.

3JC Compressive strength [MPa] σ1 σ2 5.95 8.47 3JC4 6.04 8.52 3JC7 5.84 8.24 3JC8 6.46 9.12 3JC11 5.97 8.42 3JC14 5.51 7.64 3JC15 5.96 8.40 Average 0.31 0.48 St. Dev. 5.16% 5.69% CV Table 4.5.8 - Two joint cylinders compressive strength

2JC Compressive strength [MPa] σ1 σ2 7.06 9.97 2JC2 6.54 9.14 2JC4 6.50 9.09 2JC5 6.41 8.97 2JC6 8.10 11.33 2JC7 7.44 10.41 2JC10 7.01 9.82 Average 0.67 0.93 St. Dev. 9.50% 9.52% CV

As mentioned before, the ratio between

and

is

. The values obtained show a

small coefficient of variation. 4.5.3.2 Analysis of LVDT4 behaviour In order to give an explanation about the strange behaviour of LVDT4, it was made a check to understand the reason why it presented a high ratio of Young’s modulus. For each specimen a video was recorded. The Figure 4.5.16 shows four frames of the LVDT4 behaviour during the test on the 3JC15 specimen. The different LVDT4 angles were qualitatively calculated. It is clear that the instrument presented an important movement. The big variation of Young’s moduli obtained with this LVDTs is clearer seeing the movements to which is submitted.

102


Chapter 4 – Results and discussion

Figure 4.5.16 – LVDT4 movement during the 3JC15 tests.

4.5.3.3 Poisson’s ratio The curves obtained for the couples of LVDTs, and for the two typology of specimens are

Stress [MPa]

shown in Figure 4.5.17, Figure 4.5.18, Figure 4.5.19, Figure 4.5.20. 10 9 8 7 6 5 4 3 2 1 0 -0,002

Three joint cylinders: σ2 - εh12

-0,007

-0,012 3JC4 3JC11

-0,017 -0,022 Strain 3JC7 3JC14

-0,027

-0,032

-0,037

3JC8 3JC15

Figure 4.5.17 - Three joint cylinders – Horizontal strain (displacement average LVDT1-2).

103


Stress [MPa]

Chapter 4 – Results and discussion

10 9 8 7 6 5 4 3 2 1 0

Three joint cylinders: σ2 - εh56

-0,01

-0,03

-0,05 Strain

3JC4 3JC11

-0,07

3JC7 3JC14

-0,09

-0,11

3JC8 3JC15

Figure 4.5.18 - Three joint cylinders – Horizontal strain (displacement sum LVDT5-6).

The horizontal strain for the three joint cylinders showed an homogeneous behaviour. As regard the two cylinders, the movements in the first part of the curves are quite small. In fact the LVDT measured the horizontal movement of the brick. The Poisson’s ratio is assessed consider the same part of the curves both for vertical strain and

Stress [MPa]

horizontal strain. The values are shown in Table 4.5.7 and in Table 4.5.8.

0

10 9 8 7 6 5 4 3 2 1 0

Two joint cylinders: σ2 - εh12

-0,005

-0,01

-0,015

2JC2

-0,02 Strain 2JC4

2JC6

2JC7

-0,025

-0,03

-0,035

-0,04

2JC5 2JC10

Figure 4.5.19 - Two joint cylinders –Horizontal strain (displacement average LVDT1-2).

104


Chapter 4 – Results and discussion

Two joint cylinders: σ2 - εh12

12 10 Stress [MPa]

8 6 4 2 0 -2E-17

-0,02

-0,04 2JC2 2JC6

-0,06 Strain 2JC4 2JC7

-0,08

-0,1

-0,12

2JC5 2JC10

Figure 4.5.20 - Two joint cylinders –Horizontal strain (displacement sum LVDT5-6). Table 4.5.9 – Three joint cylinders - Poisson’s ratio

Three joint cylinders ν12

ν56

3JC4

0.46

0.24

3JC7

0.27

0.22

3JC8

0.4

0.2

3JC11

0.8

0.5

3JC14

0.44

0.27

3JC15

0.51

0.36

Average

0.48

0.30

Dev.st

0.18

0.11

CV

36.78%

38.07%

Table 4.5.10 – Two joint cylinders – Poisson’s ratio

Two joint cylinders ν12

ν56

2JC2

0.07

-

2JC4

0.07

0.02

2JC5

0.07

0.14

2JC6

0.06

0.06

2JC7

0.12

0.06

2JC10

0.07

0.09

Average

0.08

0.07 105


Chapter 4 – Results and discussion

St. Dev.

0.02

0.04

CV

28.18%

60.13%

The Poisson’s ratio values obtained presented also in this case a big instability, as regard the two joint cylinders, using the LVDT5 and 6. The values obtained are a little higher than the values obtained during the elastic cycles., except in the case of the two joint cylinder using the LVDT1 and 2, where the value obtained is the same. 4.5.4 Failure mode In Figure 4.5.21 and in Figure 4.5.22, the different failure modes are shown at the peak time.

a)

b)

d)

c)

e)

Figure 4.5.21 - Three joint cylinders failure modes – Peak time; a) 3JC4; b) 3JC7; c) 3JC11; d) 3JC14; e) 3JC15.

At the peak time, the three joint cylinders showed cracks on the two central half bricks, and in the upper and the lower brick in correspondence of the high mortar regularization. In many tests, the crack appeared in the vertical central joint. The cracks were in correspondence of the interface vertical joint-lateral brick, for this reason it was difficult to identify them. The vertical joint had a slightly detectable separation from the brick. Moreover the Ibertest

106


Chapter 4 – Results and discussion

machine used for three joint cylinders give a less visibility than the Instron machine used for two joint cylinder. The appearance of a central crack was noticed also in Brencich, 2006.

a)

b)

c)

d)

e)

f)

Figure 4.5.22 - Two joint cylinders failure modes – Peak time; a) 2JC2; b) 2JC4; c) 2JC5; d) 2JC6; e) JC7; f) 2JC10.

In two joint cylinders at peak time, the first cracks appeared mainly in the central brick and in the other two bricks in correspondence of the high mortar regularization. In Figure 4.5.23, and in Figure 4.5.24 the specimens are shown at the end of the tests.

a)

b)

c)

107


Chapter 4 – Results and discussion

d)

e)

f)

Figure 4.5.23 – Three joint cylinders failure modes – End of the tests; ; a) 3JC4; b) 3JC7; c) 3JC8; d) 3JC11; e) 3JC14.; f) 3JC15

a)

d)

b)

c)

e)

f)

Figure 4.5.24 - Two joint cylinders failure modes – End of the tests; a) 2JC2; b) 2JC4; c) 2JC5; d) 2JC6; e) 2JC7; f)2JC10.

Increasing the displacement, the same cracks that both specimens typology showed at the peak time, opened more and expanded along the specimens. In all the specimens, after the peak time, the cracks in correspondence of the regularization created two wings, which fall off from the specimens. In the previous campaign by Peverini (2014), the behaviour of the wings was similar, but in many cases arrived before the time of the peak. In the present 108


Chapter 4 – Results and discussion

research, the cracks appeared before or during the time of the peak, but the fall off was later. This different behaviour might be due to the different type of bricks used for the two researches. The bricks showed a different grip and a consequently different interaction with the mortar joints.

109


Chapter 4 – Results and discussion

4.6 Comparison between the experimental E modulus and the spring model In order to have an evaluation of the Young’s modulus with an analytical method, the experimental values were compared with a spring model. The spring model considers the different materials as a system of springs, in parallel or in series. The formulas are different if the spring are in series (4.4) or in parallel (4.5).

In the Figure 4.6.1, the schemes used are shown for each specimen.

Figure 4.6.1 – Spring models used

The model A was used for three joints cylinders and wallets, the model B for two joints cylinders and stack prisms. Before testing, the units stiffness was measured, and for each specimen it was possible to have an assessment of the Young’s modulus with the spring model.

110


Chapter 4 – Results and discussion

The Young’s modulus considered for the two materials are shown in Table 4.6.1.

Table 4.6.1 – Materials Young’s modulus

Young’s modulus [MPa] Brick

10000

Mortar

600

Tthe calibration and the average considered for the dimension are all approximated to respect perfectly the experimental evaluations. The results and the comparison are shown in Table 4.6.2, Table 4.6.3, Table 4.6.4 and Table 4.6.5.

Table 4.6.2 – Three joint cylinders , Young’s modulus comparison

Three joints cylinders Cycles [MPa]

Disp. control [MPa]

E3cyc

Model A

%

E3

Model A

%

3JC4

2726

2104

-30%

2398

2104

-14%

3JC7

1930

2329

17%

1982

2329

15%

3JC8

2483

2025

-23%

2476

2025

-22%

3JC11

3560

2081

-71%

2643

2081

-27%

3JC14

2036

2246

9%

2042

2246

9%

3JC15

2686

1972

-36%

2331

1972

-18%

Average

2570

2126

-21%

2312

2126

-9%

St. Dev.

587

136

255

136

CV

22.82%

6.38%

11.04%

6.38%

Table 4.6.3 – Two joint cylinders, Young’s modulus comparison

Two joint cylinders Cycles [MPa]

Disp. control[MPa]

E3cyc

Model B

%

E3

Model B

%

2JC2

2027

2189

7%

2055

2189

6%

2JC4

2749

2163

-27%

2317

2163

-7%

2JC5

2262

1977

-14%

2006

1977

-1%

2JC6

2241

2347

5%

2152

2347

8%

2JC7

3857

2152

-79%

2775

2152

-29%

2JC10

2105

2105

0%

2120

2105

-1%

Average

2540

2156

-18 %

2238

2156

-4%

111


Chapter 4 – Results and discussion

Dev.st

692

120

284

120

CV

27.26%

5.58%

12.69%

5.58%

Table 4.6.4 – Stack prisms, Young’s modulus comparison

Stack prisms Cycles [MPa]

Disp. Control [MPa]

E cyc

Model B

%

E

Model B

%

SP_1

2220

2692

18%

2323

2692

14%

SP_2

2541

2422

-5%

2618

2422

-8%

SP_3

2022

2833

29%

2411

2833

15%

SP_4

2169

2499

13%

2202

2499

12%

SP_5

2628

3517

25%

2948

3517

16%

SP_6

4053

3310

-22%

3613

3310

-9%

SP_7

3519

2972

-18%

3580

2972

-20%

Average

2736

2892

5%

2814

2892

3%

St. Dev.

763

406

586

406

CV

27.89% 14.05%

20.82% 14.05%

Table 4.6.5 – Wallet, Young’s modulus comparison

Wallets Cycles [MPa] Elvdt cyc Wall_1

Disp. Control [MPa]

Model A

%

Elvdt

Model A

%

2270

-

-

2270

-

Wall_2

2364

2151

-10%

2023

2151

-6%

Wall_3

1847

2200

16%

1876

2200

-17%

Average

2106

2207

5%

1950

2207

-13%

Dev.st

366

60

104

60

CV

17.36%

3%

5%

3%

The model and the experimental values showed a good agreement considering the average of the Young’s modulus. The values obtained are good both for the Young’s modulus assessed with the loading-unloading cycles and during the second phase of the load.

4.7 Comparison of the results obtained The tests performed had the objective to give information about the mechanical characteristics of the masonry. The intention was also to give a standardization of the innovative test on masonry cylinders extracted from existent masonry. 112


Chapter 4 – Results and discussion

4.7.1 Compressive strength In the Figure 4.7.1, the compressive strength comparison is shown. The most important evidence is the size effect of the specimens, also observed in other researches (like Mohammed, 2011). The smaller specimen has the bigger strength. Compressive strength - σ [MPa] 12,00 10,00 8,00 6,00 4,00 2,00 0,00 2JCs σ2

3JCs σ2

2JCs σ1

3JCs σ1

SPs

Wallets

Figure 4.7.1 – Comparison between the compression strength

As regard the cylinders specimens, the elastic parameter are evaluated considering

. As

shown in the following Sections, the elastic parameter obtained are acceptable, for this reason the referred maximum strength is

. By knowing the two strength values it is possible to

obtain the stack prisms strength, and knowing the three cylinders strength is possible to obtain the wallet strength, rewriting the formula (4.3). (4.6) (4.7) Where :

The cylinders’ strengths have to be reduced by the

factors in order to obtain the strength of

the standard tests. 4.7.2 Young’s modulus The comparison of Young’s modulus is shown in Figure 4.7.2 and in Figure 4.7.3.

113


Chapter 4 – Results and discussion

E modulus - Elastic cycles - σ [MPa] 3000 2500 2000 1500 1000 500 0 2JCs

3JCs

SPs

Wallets

Figure 4.7.2 - Young's modulus from elastic cycles comparison

The order of magnitude of Young’s modulus for the different specimens is almost the same. The values calculated at the third cycles of loading-unloading are almost the same, as in the research performed by Mohammed, 2011. This result was expected, since the size effect affect the strength, but the material considered is the same, therefore the elastic parameters are the same, evaluating the same number of bricks and mortar joint, with the same instrumentation. E modulus - σ [MPa] 3000 2500 2000 1500 1000 500 0 2JCs

3JCs

SPs

Wallets

Figure 4.7.3 - Young's modulus comparison – elastic part from loading test to failure

4.7.3 Poisson’s ratio Finally, Figure 4.7.4 and Figure 4.7.5 show the Poisson’s ratio comparison. The difficulties in obtaining this parameter were explained in the previous Sections and the comparison shows a big variability.

114


Chapter 4 – Results and discussion

ν - Elastic cycles - 3JCs and Ws

ν - Elastic cycles - 2JCs and SPs 0,2

0,5 0,4

0,15

0,3

0,1

0,2

0,05

0,1

0

0 2JCs 1-2

2JCs 5-6

SPs

3JCs 1-2

a)

3JCs 5-6 b)

Figure 4.7.4 - Poisson’s ratio comparison – Elastic cycles; a) Two joint cylinders and stack prisms; b) Three joint cylinders and wallets.

The Poisson’s ratio for the specimens without vertical joints presents results similar during the loading and unloading cycles. However, the values presented less variations in the displacement control part of tests. In that part the stress ratio considered was higher than those considered for the elastic cycles. Consequently the horizontal displacement is higher and it is easier to evaluate. As for the specimens that presented a vertical joint, the variability is due to the different dimensions of the joints. The Poisson’s ratio comparison in Fig b) shows that the measurement of the horizontal displacement in the three joint cylinders, using two external LVDTs (LVD5 and 6), gives values more similar to the expected masonry parameter. Moreover, the values obtained with LVDT5 and 6 are similar to those obtained on wallets tests. ν - 2JCs and SPs

ν - 3JCs and Ws

0,2

0,6 0,5

0,15

0,4

0,1

0,3 0,2

0,05

0,1

0

0 2JCs 1-2

2JCs 5-6

SPs

3JCs 1-2

a)

3JCs 5-6

Wallets

b)

Figure 4.7.5 - Poisson’s ratio comparison; a) Two joint cylinders and stack prisms; b) Three joint cylinders and wallets.

115


Chapter 4 – Results and discussion

4.8 Comparison between the results and the Standards and theoretical formulas The European standards and the literature give different formulas to obtain the compressive strength and the Young’s modulus. In this Section the results obtained in the present research are compared with the Italian, the Spanish and the European masonry standards, thus respectively: “Decreto Ministeriale, 14 gennaio 2008”, “Circolare applicativa – D.M. 14/01/2008”, “Documento Básico SE-F, abril 2009”, “Eurocode 6, 2005”. 4.8.1 Compressive strength The standard formulas referred to a type of masonry with a modern bricks and mortar, and the mortar joints thickness have to be regular and with a dimension of

. In the present

research the mortar joints thicknesses were irregular and sometimes of about

.

4.8.1.1 Decreto Ministeriale, 14 gennaio 2008 The Italian standard considered the characteristic average compressive strength values of the masonry units, doing a conversion of the experimental value obtain with a

factor that

depends on the number of specimens tested. Even if the minimum number of the tests required is

, the conversion is made the same considering as coefficient

corresponding to the minimum value for 6 tests (

the value

).

The masonry units compressive strength value is obtained using the formula (4.8). Where

is the average strength of the bricks and

characteristic strength is

is the standard deviation. The brick

and with a mortar type of

the masonry

compressive strength provided by the Table 11.10.V, D.M. 14/01/2008 is :

4.8.1.2 Eurocode 6 1-1:2005 The Eurocode 6 recommends the formula (4.9) for the determination of the compressive strength of masonry. Considering as mortar compressive strength,

, the strength calculated at 260 days equal to

(EN 1015-11:2007). The coefficient 116

, corresponding to the type of


Chapter 4 – Results and discussion

masonry used. The units normalized compressive strength,

, is the value of the average

compressive strength calculated in polished bricks multiplied by the shape factor. In the present research the shape factor is

, considering the dimensions of the bricks (EN 772-1).

The units compressive strength is shown in equation (4.10). The masonry compressive strength is:

4.8.1.3 Documento Básico SE-F, abril 2009 The Spanish standard provide a formula for the determination of the characteristic compressive strength of a brickwork composed by ordinary mortar (4.11). The units normalized compressive strength,

, is the value of the average compressive

strength calculated in polished bricks multiplied by the shape factor (see equation (4.10)). The compressive strength of mortar,

at

days is equal to

. The

coefficient

corresponding to a wall made of solid bricks and with the thickness of one brick, equal to . The compressive strength of the wall studied results:

4.8.1.4

NTC 2008 – Circolare applicativa – D.M. 14/01/2008

In “Tabella C8A.2.1” of the Circolare applicativa – D.M. 14/01/2008, that consider the existing masonry, the compressive strength of a masonry made with solid clay bricks and lime mortar has a ratio of

.

4.8.1.5 Analytical formula by Como (2009) In order to have a comparison with an analytical formula, the one used by Como, 2009, is used to make a comparison. This formula take into consideration the mortar joint thickness, the compressive and tensile strength of the bricks, and the Poisson’s ratio of the materials that composed the masonry. The formula (4.12) is the one used by Como, 2009, where

is the masonry compressive

strength.

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Chapter 4 – Results and discussion

-

is the brick compressive strength, it is used the one assessed with the cubic specimens of the bricks, in Section 3.3.1.1.2 (

), since it represent the

material characteristic strength; -

is the brick tensile strength, evaluated from the flexural strength applying the CEB-FIP MC,1990 standard, explained in Section 3.3.1.1.3. The standard chosen is the CEB-FIP because is the lower value of brick strength;

-

is the ratio between the mortar thickness and the brick thickness;

-

is the ratio between the brick Young’s modulus and the mortar Young’s modulus;

-

take in consideration the elastic parameters of the masonry materials, Poisson’s ratio and Young’s modulus.

Where

and

are respectively the Poisson’s ratio of the mortar and the brick, and is the

ratio between brick Young’s modulus and mortar Young’s modulus. The formula (4.12) give different values that depend on thickness and elastic parameters of the materials. In order two understand the big variability of the results due to the thickness of the mortar, two solutions are chosen, considering as elastic parameters the values obtain in Chapter 3. The solutions are shown in Table 4.8.1, the underlined values are the values that changes in the two solutions. Table 4.8.1 –Compressive strength by Como, 2009

Como, 2009 Materials parameters Calculations 10000 16.67 Eb [MPa] ø 600 0.58 Em [MPa] β_1 0.35 43 hb [mm] β_2 25 0.31 hm_1 [mm] χ 15 hm_2 [mm] 0.18 νb 0.25 νm 18 brc [MPa] 1.5 brt [MPa] Lower bound – Como 1 Upper bound – Como 2 5.07 7.91 frc1 [MPa] frc2 [MPa]

118


Chapter 4 – Results and discussion

4.8.1.6 Comparison between experimental and theoretical formulas The values obtained are resumed in Table 4.8.2, in order to compare the experimental strength with the standard values, it is necessary to change the strengths in characteristics strengths, with the formula (4.8). The characteristic wallets compressive strength is not possible to assess, since the standard deviation is too high, and using the formula (4.28) the value is not realistic. Table 4.8.2 – Compressive strength – Characteristic values

Compressive strength characteristic σ [MPa] D.M. 14/01/2008 6.8 D.B. SE-F (2009) 5.51 EC 6 (2005) 6.16 3JC σ2 7.28 2JC σ2 7.65 SP 4.38 WALLET -

The comparison is shown in Figure 4.8.1. The graphs show the correspondence line. If the experimental results are the same as the standard values, the points will be located on the line. As mentioned in the previous Sections, the cylindrical specimens have an higher compressive strength due to the smaller dimensions.

Compressive strength comparison Experimental and standard

Experimental tests [MPa]

9 2JC_σ2 8 3JC_σ2 7

Correspondence line

6 5

Stack prisms

4 3 2 1 0

0

2

4

Circolare

6

D.B. EC6 D.M .

8

Standards and theoretical strength [MPa] Figure 4.8.1 – Standard compressive strength comparison

119


Chapter 4 – Results and discussion

The stack prisms have a lower compressive strength then the standards values. The standards give values for new buildings, with materials with higher strength. Another lack presents in the standard is that they do not take into consideration the joint dimensions. On the contrary, the Italian standard (NTC 08 Circolare), that gives an evaluation of the strength for existing masonry, shows a value very similar to the tests performed. In Figure 4.8.2 is shown the comparison between the theoretic Como’s formula and the average of the compressive strength obtained by the experimental values. The graph shows also the correspondence line. The line helps to understand how many higher or lower are the experimental values than the results evaluated with Como’s formula. In Table 4.8.3 the compressive strengths are shown. Table 4.8.3 – Compressive strength – Theoretic values

Theoretic compressive strength σ [MPa] Como 1 5.73 Como 2 7.87 3JC σ2 9.82 2JC σ2 8.4 SP 5.82 WALL 4.31

Theoretic compressive strength comparison

Experimental tests [MPa]

2JC_σ2

10

3JC_σ2

Correspondence line

8

Stack prisms 6 Wallets

4 2 0

0

2

4

6 Como1

8 Como2

Standards and theoretical strength [MPa] Figure 4.8.2 - Theoretic compressive strength comparison

120

10


Chapter 4 – Results and discussion

The Como1 results is more representative of the experimental tests carried out in this research. This evaluation take into consideration the real thickness of the mortar joints. Comparing stack prisms and wallets with Como1 it is clear that the experimental values are more similar to the Como1 strength. In conclusion the lower compressive strength in the experimental tests is due to the characteristic of the weak materials and to the big variability of the mortar joints dimensions. 4.8.2 Young’s modulus comparison The EC6, D.M. 14/01/2008, D.B.SE-F 04/2009 give all the same formula (4.14) to obtain the Young’s modulus and the Poisson’s ratio. In order to carry out a comparison between this value and the ones obtained in the present study, the ratio between

is calculated for the results of the tests and shown in Table

4.8.4. Table 4.8.4 – Young’s modulus comparison

The

2JC 3JC SP Peverini, 2014

fk 7.28 7.65 4.38 7.65

E 2540 2570 2736 3765

E/fk 349 336 625 492

NTC08 Circolare DM DB EC6

4 6.8 5.51 6.16

1800 6800 5510 6160

450 1000 1000 1000

ratio is lower in the cylindrical specimen, and higher in the stack prisms, that is due

to the size effect. A similar relationship is obtained in Mohammed, 2011, where smaller specimens have smaller ratio than the bigger ones. The standards for new buildings give higher ratio that are not adequate for lime-mortar masonry. On the other hand, the NTC08 Circolare provides more representative values.

121


Chapter 4 – Results and discussion

122


Chapter 5

Numerical analysis 5.1 Introduction Finite element models (FEM) are able to provide us an in-depth understanding of the experimental tests. It can also provide a validation of the experimentally assessed materials’ parameters. The parameters necessary to perform a nonlinear numerical analysis are the compressive strength, tensile strength, Young’s modulus, Poisson’s ratio, compressive fracture energy and tensile fracture energy. The model can describe the behaviour of the masonry and the interaction of its elements. To get this objective, it is possible to use three different models. The first type is micromodelling where the brick, mortar and the interface are studied individually to access the whole behaviour. The brick–mortar interfaces are modelled by means of non-linear interface elements. The second type is the meso-scale modelling, where both the blocks and mortar joints are modelled using continuous elements. The third type is the macro-modelling where the whole material is homogenised as a continuum. The numerical modelling can show accurately, in a masonry compressed member, the triaxial compressive state in mortar and the uniaxal compression and the biaxial tension state in brick. In order to model masonry using finite element technique, three parts need to be carefully

123


Chapter 5 – Numerical Analysis

examined: behaviour of clay bricks, behaviour of mortar joints and mechanisms of joint failure (Page, 1978).

5.2 Constitutive law The damage model proposed by Faria et al. (1998) is used in this research. In this model, the split of stress tensor into tension and compression is considered. It is performed to capture the unilateral behaviour of the material when it passes from tension to compression. The split of effective stress tensor presented in equations

Where

into tension and compression, in according to Ortiz (1985), is and

denotes the th principle stress extracted from tensor

unit vector for the associated principle direction.

and

corresponds to the

are the Macaulay brackets, which return

the value if positive or zero if negative. The constitutive law is shown in equation

.

The split of the stress is defined according to equation

and

, where the first

equation represents the tensile stress and the second represents the compressive stresses.

This derivation is based on Helmholtz free energy potential of the form: Where

and

are the elastic free energies, which are defined according to

and 5.8.

The internal variables consist of plastic strain tensor ,

and

the scalar damage variables

linked directly to the tensile and compressive deteriorations assumed as independent variables. Strain tensor is the only single variable admitted. During any loading process the dissipation of energy is always positive, which states the entropy increases leading to an irreversible process, according to second principle of 124


Chapter 5 – Numerical Analysis

thermodynamic. The dissipation for an isothermic elasto–damageable process is the form as shown in equation

, which is according to Clausius-Duhem inequality.

To guarantee the positive dissipation, Coleman’s method is applied and the constitutive law is obtained

Since

.

and

are to be positive terms, it can be inferred that the dissipation is

according to equation

.

Which results to satisfy the Clausius-Dhuem inequality Considering the equations stress split in equation

and

, the linear independency between

and the fact that

functions of , we obtain equation

and

Substituting equation

in equation

equation is obtain

and

.

and

and , the

are first degree homogeneous

according to Euler’s theorem.

, the final form of the constitutive

. For further information regarding the derivation of the constitutive

law the reader is advised to refer Faria et al., (1998). In equation

is clear the assumption of the distinction between tension and compression.

A tensile equivalent stress

and a compressive equivalent stress

are postulated according

to the forms

Where

are non-dimensional fourth-order metric tension that define the shape of the

damage bounding surfaces. Calling for the effective stress norms defined in

and

, two damage criteria

in

terms of effective stress tensors are introduced

125


Chapter 5 – Numerical Analysis

The damage variables are computed in accordance to (Oliver et al., 1990)

Where the positive hardening/softening functions

are related to internal variables

,

which in turn obey the kinematics With

being damage multipliers which participate in the Kuhn Tucker conditions

If

, the damage criterion is not satisfied and by condition

further damage takes place. If condition

, hence no

, that is, further damage (“loading�) is taking place,

now implies that

. In this event the value of

is determined by the

damage consistency condition, i.e. Integrating for a generic instant , in view of this equation the following conclusion arises

Where

are the threshold that bound the initial linear elastic domains.

5.3 Failure surface The failure surface most often used for frictional materials are the Mohr-Coulomb and Drucker-Prager criteria, both of which may be written in the form where

is the cohesion, and

:

is a function that is homogenous in the first degree in the

stress components. However, both these yield criteria have notoriously poor correlation with experimental data. A new yield criterion, which can fit better the experimental data, is presented here below, as proposed by Lubliner (1989). Excluding the high-pressure region, all available failure data can be fitted well into equation , in which

where ,

and

has the form

:

are dimensionless constants. This form will be adopted in the present work

for the failure surface in compression. It should be noted that when

, i.e., in biaxial

compression, this is just the Drucker-Prager criterion, the only parameter then being , which

126


Chapter 5 – Numerical Analysis

can be obtained by comparing the initial equibiaxial and uniaxial yield stresses

and

:

in the present research, this ratio is equal to The parameter (

.

appears only in triaxial compression, that is, in stress states with

in this research). This parameter takes into consideration the important rule of the

triaxial compression. In fact, in uniaxial compression test on masonry, the horizontal mortar joints are subjected to triaxial compression. Another main value to define is

.

that is a constant, and in the present research is equal to The

.

equation is the Lubliner criteria and in the present research is used for the

compression behaviour, that is linked to Rankine criteria for the tensile part of the yield surface. The equation

represents Rankine behaviour in tension and shear.

The Rankine formula means that, in the multiaxial stress state, the collapse arrived when

,

the maximum principal material stress, becomes equal or greater than the maximum normal stress, 5.4

.

Modelling of cylindrical specimens

A three-dimensional model for each type of masonry cylinder tested was modelled in the final element software COMET (Cervera et al. 2002), developed at the International Center for Numerical Methods in Engineering (CIMNE, Barcelona). Pre and post-processing is done with GiD (2002), also developed at CIMNE. The dimensions considered are the same as in the real cylinders. The diameter is regularization mortar is the specimen is average of

thick in the centre and

, the

wide, the overall thickness of

. Since the width of the joints is variable for each specimen, an has been chosen.

Because of the symmetry of the specimen, only one quarter of the geometry was modelled, with the purpose of having a lower computational cost.

127


Chapter 5 – Numerical Analysis

Axis of symmetry is assigned to XY plane and XZ plane representing the continuity of the model. Eight-node hexahedron mesh elements are used, with average size of each hexahedron being

. The model consists of

elements and 9800 nodes and is shown

in Figure 5.4.1

a)

b)

Figure 5.4.1 – FE mesh of cylindrical specimens ; a) Three-joint cylinder; b) Two-joint cylinder

The mechanical materials parameters assumed are shown in Table 5.4.1. Most of them were found in experimental tests, and shown in Chapter 3. Table 5.4.1 - Mechanical properties of cylindrical joint specimens

Lubliner Young's modulus - E [MPa] Poisson's ratio - ν Uniaxial tensile strength [MPa] Uniaxial compressive strength [MPa] Compressive fracture energy [N/m] Tensile fracture energy [N/m]

Brick 8500 0.18 1.50 18 10.00 0.50

Cylindrical specimen Mortar Mortar Cap 550 23000 0.25 0.20 0.17 3.57 2.00 0.15 -

The brick Young’s modulus was chosen considering the tests made in Section 3.3.1.3. The mortar Young’s modulus was chosen considering the research by Peverini, (2014), being the hydraulic mortar similar as the one used in the present research. The Poisson’s ratio of the brick has the same the order of magnitude found in Nichols, (2014), evaluating clay brick. The compressive strength of brick and mortar are respectively the values obtained in cubic compressive test in Section 3.3.1.1.2 and from the punching test considering a thickness of (Section 4.2). The tensile strengths used were found using CEB-FIP MC:1990 formula, that gives a lower value of strength respect the other formulas (Section 3.3.1.2 for 128


Chapter 5 – Numerical Analysis

brick and Section 3.3.2.2 for mortar). Finally the remaining values were calibrated considering the typical material values and the present model. 5.4.1 Non-Linear Analysis: Three-Joint Cylinders The force displacement curve of the FE analysis is shown in Figure 5.4.2. The displacement measured, is the relative displacement of the whole specimen, from the topmost point to the bottom most point. That displacement is more similar to the LVDT3 measure made during the experimental test. The high regularization mortar is considered infinitely rigid respect to the masonry and the displacement of that are negligible (Section 3.3.3). 3JC - Comet 160,00 140,00

Point 3 Point 2

Force [kN]

120,00

Point 4

100,00 80,00 60,00

Point 1

40,00 20,00 0,00

0,0

0,4

0,8

1,2

1,6 2,0 2,4 Displacement [mm]

2,8

3,2

3,6

Figure 5.4.2 – Force displacement graph of three joint cylinder

Four points are chosen in the graph to explain the behaviour of the specimen. The points are listed in Table 5.4.2. Table 5.4.2 – Points description – Three joint cylinder

Point Number 1 - Step 7 2 - Step 19 3 - Step 32 4 - Step 49

3JC Force [kN] 57.34 109.71 138.93 125.69

Displacement [mm] 0.25 0.56 1.12 1.72

The tensile damage, compression damage, tensile stresses and compression stresses are illustrated in the following Figures, where the four steps most representative are shown, in order to understand the evolution of the specimen’s behaviour during the test.. In

a)

b) 129


Chapter 5 – Numerical Analysis

Figure 5.4.3, Figure 5.4.4, Figure 5.4.5,

a)

b)

a)

b)

Figure 5.4.6 the tensile and compressive damage comparison is made step by step. Observing step 7 (point 1), where the elastic field finishes, it is noticeable that the locations affected by the damage are mainly in the mortar. The two horizontal joints present compression damage, while the vertical is affected by tensile damage. In fact, horizontal joints are subjected to triaxial compression, whereas the vertical joint presents horizontal traction due to transversal dilation of the specimen during the test. The damage is greater in the vertical one, where already in step 7, reaches 0.

. The result is coherent with the parameters considered for the

materials, in fact the tensile strength of the mortar is far low compared to that of the brick. Also bricks are affected by the damage, close to the mortar regularization. The same behaviour was observed in experimental tests, where the damage was noted initially in the central joint and in some cracks on the bricks, near to the edge of the mortar regularization. In the subsequent steps, the damage spreads evenly. It is pointed out, that the compression damage appears in the horizontal joint (visible in part a) of the Figures) spreading even in the vertical joint around the tensile damage (visible in part b) of the Figures). At the peak time,

a)

b)

Figure 5.4.5, the tensile damage reaches 0.99 in mortar joints and

in bricks, in

correspondence of the mortar regularization. Even some areas of the bricks are interested to damage. The brick, near to vertical mortar joint, get to

of tensile damage and

he

compressive damage. Finally at the last step, the damage reaches high values, even in compression where the damage is about

130

.


Chapter 5 – Numerical Analysis

a)

b)

Figure 5.4.3 – Three-joint cylinder - Point 1; a) Compressive damage; b) Tensile damage

a)

b)

Figure 5.4.4 – Three-joint cylinder - Point 2; a) Compressive damage; b) Tensile damage

a)

b)

Figure 5.4.5 – Three-joint cylinder - Point 3; a) Compressive damage; b) Tensile damage

131


Chapter 5 – Numerical Analysis

a)

b)

Figure 5.4.6 – Three-joint cylinder - Point 4; a)Compressive damage; b) Tensile damage

In the following Figures (Figure 5.4.7, Figure 5.4.8, Figure 5.4.9, and Figure 5.4.10) the principle tensile and compressive stresses distribution are shown for each step considered. The Figures show the redistribution of stresses in the specimen before failure and how stresses evolves after damage appears. The first point (step 7) presents already tensile peaks in the bricks in correspondence of the mortar regularization. These peaks of stress reach almost the maximum strength of the brick. The bricks are horizontally tensioned due to interaction with compressed horizontal joints. It can be observed from the compression stress distribution results the sand glass central core, bearing the applied load. The rest of the cylinder, in particular the external part of brick outside the capped area, receives lower compressive stress. As a result the failure occurs along the sand glass shape, due to different confinement conditions in the specimen, resulting in separation of the external part, as in the experimental tests. The cracks occurs in the bricks and permit the wings to fall off as observed in the experimental test before the peak load.

132


Chapter 5 – Numerical Analysis

a)

b)

Figure 5.4.7 – Three-joint cylinder - Point 1; a) Principle tensile stress; c) Principle compressive stress

a)

b)

Figure 5.4.8 – Three-joint cylinder - Point 2; a) Principle tensile stress; c) Principle compressive stress

a)

b)

Figure 5.4.9 – Three-joint cylinder - Point 3; a) Principle tensile stress; c) Principle compressive stress

133


Chapter 5 – Numerical Analysis

a)

b)

Figure 5.4.10 – Three-joint cylinder - Point 4; a) Principle tensile stress; c) Principle compressive stress

5.4.2 Non-Linear Analysis: Two-Joint Cylinders The force vs. displacement curve of the FE analysis is shown in Figure 5.4.11. The displacement measured, is the relative displacement of the whole specimen, from the topmost point to the bottom most point. That displacement is more similar to the LVDT3 measure made during the experimental test. The high regularization mortar is considered infinitely rigid respect to the masonry and the displacement of that are negligible (Section 3.3.3). These consideration are the same as three joint cylinders. 2JC - Comet 180,00 160,00

Point 3

Force [kN]

140,00

Point 4

Point 2

120,00 100,00 80,00 60,00

Point 1

40,00 20,00 0,00

0,0

0,4

0,8

1,2

1,6 2,0 2,4 Displacement [mm]

2,8

3,2

3,6

Figure 5.4.11 - Force displacement graph of two joint cylinders

Four points are chosen in the graph to explain the behaviour of the specimen. The points are listed in Table 5.4.3. 134


Chapter 5 – Numerical Analysis Table 5.4.3 - Points description – Two joint cylinders

Point Number 1 - Step 7 2 - Step 16 3 - Step 36 4 - Step 63

2JC Force [kN] 60.07 133.44 155.44 140.93

Displacement [mm] 0.25 0.67 1.26 2.21

The evolution of tensile and compressive damage is shown in Figure 5.4.12, Figure 5.4.13, Figure 5.4.14, Figure 5.4.15, step by step. The compressive damage starts in the two horizontal joints, and in the same step the compressive damage is presented only in the brick in correspondence of the high mortar regularization. From the second step is clear the beginning of tensile damage in central brick, that became

at the peak. The maximum of

tensile damage is in the typical position of the crack found during the experimental tests. The compressive damage increases during the analysis in mortar joints and the tensile damage increases in central brick. Jointing the damages at the last step is clear the sand glass shape in the cylinder.

a)

b)

Figure 5.4.12 – Two-joint cylinder - Point 1; a) Compressive damage; b) Tensile damage

135


Chapter 5 – Numerical Analysis

a)

b)

Figure 5.4.13 – Two-joint cylinder - Point 2; a) Compressive damage; b) Tensile damage

a)

b)

Figure 5.4.14 – Two-joint cylinder - Point 3; a) Compressive damage; b) Tensile damage

a)

b)

Figure 5.4.15 – Two-joint cylinder - Point 4; a) Compressive damage; b) Tensile damage

136


Chapter 5 – Numerical Analysis

The principal stresses distribution are shown in Figure 5.4.16, Figure 5.4.17, Figure 5.4.18, Figure 5.4.19. Each Figure represents one step, on the left the tensile stress contour is shown, whereas on the right the compressive stress. Observing the tensile stress is understandable that the brick is affected by high transversal tension stress from the first step. The stress arrives to reach the maximum strength

in the second step. That behaviour explained the

appearance of the cracks in the central brick, before the peak, during experimental tests. After the peak the tensile stress spreads along the brick. It is evident that the mortar joints are not subjected to high tensile strength being triaxially compressed. The compressive stress is highly diffuse in the whole specimen. In the second point (step the stress reaches the maximum strength in mortar joint, more than

)

. At the peak it is

clear that in the middle of the specimen the compressive stress is higher than in the external part. At the end of the test the compressive stress increase and reaches the brick compressive strength.

a)

b)

Figure 5.4.16 – Two-joint cylinder - Point 1; a) Principle tensile stress; b) Principle compressive stress

137


Chapter 5 – Numerical Analysis

a)

b)

Figure 5.4.17 – Two-joint cylinder - Point 2; a) Principle tensile stress; b) Principle compressive stress

a)

b)

Figure 5.4.18 – Two-joint cylinder - Point 3; a) Principle tensile stress; b) Principle compressive stress

a)

b)

Figure 5.4.19 – Two-joint cylinder - Point 4; a) Principle tensile stress; b) Principle compressive stress

138


Chapter 5 – Numerical Analysis

5.5 Comparison between the analyses The comparison in force-displacement, between three-joint cylinders and two-joint cylinder analysis in shown in Figure 5.5.1. The comparison of force, displacement and stresses are shown in Table 5.5.1. The results show that three joint specimen has

lower strength

than two joint specimen. Cylinders comparison - Comet 180,00

3CJ

160,00

2CJ

Force [kN]

140,00 120,00 100,00 80,00 60,00 40,00 20,00 0,00

0,0

0,4

0,8

1,2

1,6 2,0 2,4 Displacement [mm]

2,8

3,2

3,6

Figure 5.5.1 – Cylinders comparison – graphs obtained with COMET Table 5.5.1 – Cylinders strength values obtained with COMET

Type 3JC 2JC

Max Force

Δ at max F

σ1 (Diametric area)

σ2 (Area below loaded cap)

Variation

[kN] 138.93 155.44

[mm] 1.12 1.19

[MPa] 6.30 7.05

[MPa] 8.71 9.75

-10.6% -

The Young’s modulus evaluation is presented in Table 5.5.2. The variation is low, as the expected one. Table 5.5.2 – Cylinders elastic values obtained with COMET

Type 3JC 2JC

E (Diamteric area) [MPa] 1614 1691

E (Area below loaded cap) [MPa] 2230 2336

Variation -5%

139


Chapter 5 – Numerical Analysis

5.6 Comparison between numerical and experimental test The comparison between numerical an modelling analysis is shown by the graphs forcedisplacement in Figure 5.6.1 and Figure 5.6.2. Young’s modulus and the compressive strength of both cylinders well approximate the real curves. Also the fracture energy of the specimens are quite representative of the real ones. The difference between the model and the experimental tests is the displacement reached at the peak time. The FE model provides slightly lower displacement than in the experimental tests. 3JC - Experimental/numerical comparison 160 140 Stress [Mpa]

120 100 80 60 40 20 0

0,0

0,5

1,0 3JC4

1,5

2,0 3JC7

2,5 3,0 3,5 Strain 3JC11 3JC15

4,0

4,5

5,0

5,5

3JC COMET

Figure 5.6.1 – Three joint cylinders – Comparison between experimental and numerical graphs

2JC - Experimental/numerical comparison

200 180 160 Stress [MPa]

140 120 100 80 60 40 20 0,0

0

-0,5

-1,0 2JC2

-1,5 2JC5

-2,0

-2,5 -3,0 Strain 2JC6 2JC7

-3,5

-4,0

-4,5

2JC COMET

Figure 5.6.2 – Two joint cylinders – Comparison between experimental and numerical graphs

140


Chapter 5 – Numerical Analysis

In Table 5.6.1 and Table 5.6.2 the comparison of the results is shown. With subscript indicated the values obtained with the diametric area, with subscript

are

are indicated the values

obtained with the area below the regularization cap. Table 5.6.1 – Three joint cylinders – Results obtained by experimental and numerical analyses

Three joint cylinders Elastic cycles Max Force Experimental Numerical Variation

[kN] 131.36 138.93 5.76%

Δ at max F [mm] 1.45 1.12 -22.76%

σ1

σ2

E1

E2

[MPa] [MPa] [MPa] [MPa] 5.96 8.4 1823 2570 6.30 8.71 1582 2230 5.70% 3.69% -13.23% -13.23%

Displacement control E1

E2

[MPa] 1640 1582 -3.52%

2312 2230 -3.55%

Table 5.6.2 – Two joint cylinders – Results obtained by experimental and numerical analyses

Two joint cylinders Elastic cycles Max Force Experimental Numerical Variation

[kN] 154.50 155.44 0.61%

Δ at σ1 σ2 E1 max F [mm] [MPa] [MPa] [MPa] 1.84 7.01 9.82 1801 1.19 7.05 9.75 1657 -35.33% 0.57% -0.76% -8.03%

Displacement control

E2

E1

E2

[MPa] 2540 2336 -8.03%

[MPa] 1587 1657 4.40%

2238 2336 4.38%

In conclusion, the numerical model gives a good evaluation of the tests. The values and the graphs obtained are similar to the experimental ones. The unique parameter that presents a scatter is the displacement at the maximum force. However, the displacements at the end of the tests, as well as the maximum force, show the same order of magnitude both in the experimental and numerical analysis. A better agreement between peak displacements

could be obtained by improving the

evolution laws of the damage variables in the numerical model. However, it is possible that the experimental tests presented a bigger displacement at the peak due to rather low force adopted in the elastic cycles. For that reason it could be possible to increase the settling force of the elastic cycles, as a suggestion for future work.

141


Chapter 5 – Numerical Analysis

142


Chapter 6

Conclusions 6.1 Summary The present research deals with the evaluation of non-standard minor destructive tests on masonry. The aim is to obtain a characterization of the mechanical behaviour of masonry, without resorting to destructive tests suggested by standards on new constructions. Firstly, the components of masonry (units, mortar) are analysed to assess the mechanical properties such as compressive strength, tensile strength, Young’s modulus and Poisson’s ratio. The values obtained are necessary for the numerical models and for analytical evaluations of the masonry characteristics. Secondly, laboratory tests on masonry are performed following the EN standard. These are compared with non-standard moderate destructive tests carried out in according to UIC 7723R-1995 guidelines and previous researches, such as Brencich (2006) and Peverini (2014). Such studies investigated the capability of compression tests on cylindrical specimens of masonry. This thesis provides a further contribution along the same line of research. The values of Young’s moduli obtained by the standard and non-standard tests are compared with the spring model of stiffness. The values of compressive strength are compared with an analytical formula by Como (2009). In both cases, quite well correlations are found. Another 143


Chapter 6 - Conclusions

correlation is made between the current standards for new masonry and the results obtained by the present experimental program. Finally, a FE numerical model is implemented, following the previous work by Gowda, (2014). The materials’ parameters found during the experimental campaign are used as input data for FE model. The comparison between experimental and numerical results shows a good agreement and helps to understand better the experimental behaviour of the masonry specimen.

6.2 Conclusions In view of the results obtained and observations made during the present investigation, it is possible to draw the following conclusions: -

The obtained materials’ parameters with standard and non-standard tests provide a good evaluation of the mechanical parameters.

-

The punching tests highlight the importance of the thickness and the confinement in the compressive behaviour of the mortar. These are characteristics affecting remarkably the compressive strength of masonry.

-

The extraction of masonry cylinders using the dry technique has been improved to ensure the successful completion of the extraction and without damaging any specimen.

-

The compressive strength of masonry can be obtained by the compression test on cylindrical masonry. It is necessary a more accurate evaluation of the reduction factor . This parameter takes into account the size effect. This work has proposed some suggestions for the determination of this parameter, for the specific type of masonry considered.

-

The elastic parameters of the masonry may be well evaluated with the non-standard tests on masonry cylinders extracted. The load area to consider is that of the regularization. The values obtained are very realistic.

-

The elastic modulus assessed in all standard and non-standard tests is in good agreement with the expected one, being verified by analytical models.

-

The numerical model of the cylinders correlates well the curves and the behaviours of the experimental samples.

-

The numerical model confirms the correctness of the mechanical parameters of mortar and bricks that have been found in the characterization tests.

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Chapter 6 - Conclusions

6.3 Suggestions for future work Based on the results obtained from the experimental work and the numerical analysis, the following suggestions can be carried out to deepen the research topic. -

The first suggestion is to try to build more regular joints in the specimens Even if in historical masonry the joints are usually irregular and the present campaign reproduce fairly well the reality, uniform thickness joint would decrease the experimental variable and help the post-processing of experimental results.

-

Continuing to investigate the potential of punching testing techniques since it seems accurate to get a more realistic characterization of the mortar, considering the actual size of the joints and the confinement.

-

Continuing to investigate and improve the tests on masonry cylinders, as they are very promising and minimally invasive.

-

The evaluation of the Poisson’s ratio could be enhanced using more precise instrumentation.

-

Calibrating better the size-effect parameter

the by developing more experimental

tests on difficult types of masonry. -

Improving the numerical model with a better calibration of the failure criteria and constitutive model by sensitivity analysis.

-

Looking for a better matching to the first branch of the response of the specimen to compression, in order to obtain the same displacement at the maximum force for both the experimental and numerical analysis. This would require an improvement of the constitutive model, especially in the definition of the evolution law of the compression damage variable.

-

Increase the database of experimental results in order to propose possible improvements to current standards, especially those referring to the analysis of existing historical constructions.

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146


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Elisa Canella - Ingegnere Civile - A.A. 2013-2014  

Experimental characterization of the compressive behaviour of brick/lime-mortar masonry.

Elisa Canella - Ingegnere Civile - A.A. 2013-2014  

Experimental characterization of the compressive behaviour of brick/lime-mortar masonry.

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