UNIVERSITA’ DEGLI STUDI DI FERRARA Facoltà di Ingegneria Corso di Laurea Magistrale in Ingegneria Civile
STRENGTHENING OF SCHIST WALLS ELEMENTS: EXPERIMENTAL AND NUMERICAL RESEARCH
Laureando: MATTIA COLOMBO Relatore: Prof. ALESSANDRA APRILE
Correlatore: Prof. JOAQUIM ANTONIO OLIVEIRA DE BARROS
Anno Accademico 2013-2014
Acknowledgments First and foremost I offer my sincere gratitude to Prof. Alessandra Aprile who has supported me throughout my thesis with her patient and knowledge and also gave me the precious opportunity to do this memorable international experience. I would like to thank Prof. Joaquin A. O. Barros for his valuable advice he gave me during my all stay in Portugal. I gratefully acknowledge all the staff of CiviTest: Tiago, Delfina and Ines for their helpful suggestions and support; Inaldo and Antonio for their technical support during my experimental campaign. Thanks to all of them for their friendship. Finally, I thank my family, Daniele, Patrizia, Anna, Andrea for their support and encouragement throughout in all possible ways. A sincere and profound thanks to Elisa, my girlfriend, her love, her cares and support have been for me a source of incommensurable energy, and I will be forever grateful for that.
Abstract The traditional schist masonry constructions are part of the vast universal architectural heritage. Their resistance under seismic actions is particularly reduced and for this reason their maintenance is a primary need for the community. However the studies on this issues are still scarce, therefore the development of effective procedures, able to increase the load carrying capacity towards the seismic actions is of primary interest. Among the strengthening techniques available to improve the seismic responses of masonry elements, one recently developed is considered of great potential and consists in the application, via spray, of Fiber-Reinforced Mortar. The assessment of this innovative technique towards the seismic actions, namely in-plane and out-of-plane behavior, is capital to evaluate its effectiveness. The aim of this project is twofold: to investigate the applicability of the reinforcement system adopted and to assess its effectiveness in terms of load-displacement when subjected to outof-plane behavior. With this purpose, strengthened schist masonry elements were made and then subjected to three point bending test performed with a non-standard configuration. In order to validate the results obtained from the experimental tests and to provide a preliminary assessment of the material parameters adopted, a numerical simulation have been carried out. In conclusion, the importance of this project is to highlight the improvement given and to promote future works on this promising technique.
Riassunto Le costruzioni di scisto fanno parte del vasto patrimonio culturale ed architettonico europeo. La loro resistenza alle azioni sismiche è particolarmente ridotta ed è per questo che la loro salvaguardia è una necessità primaria per la comunità. Tuttavia gli studi su questo tema sono ancora pochi, pertanto, lo sviluppo di procedure efficaci in grado di aumentare la capacità di carico nei confronti delle azioni sismiche è di primario interesse. Tra le tecniche di rinforzo, atte a migliorare la risposta sismica di elementi in muratura, una di recente sviluppo è considerata dalle grandi potenzialità e consiste nell’applicazione via spray di malta fibro-rinforzata. La caratterizzazione di questa tecnica innovativa nei confronti delle componenti nel piano e fuori dal piano delle azioni sismiche è di fondamentale importanza per valutarne l’efficacia. Lo scopo del presente progetto è duplice, da un lato si vuole indagare l’applicabilità del sistema di rinforzo adottato, dall’altro ne viene studiata l’efficacia in termini di carico e spostamento che fornisce alla muratura di scisto quando soggetta a carichi fuori dal piano. Con questo obiettivo sono stati realizzati alcuni elementi verticali di muratura di scisto, rinforzati tramite tecnica spray e sottoposti a test di flessione a tre punti con configurazione verticale. I risultati ottenuti, sono stati poi confrontati con una preliminare simulazione numerica, il cui scopo è quello di dare una prima valutazione dei parametri del materiale di rinforzo studiato. In conclusione l’importanza di questa ricerca è quella di evidenziare il miglioramento apportato e di promuovere futuri approfondimenti su questa tecnica che già dai primi studi ha mostrato ottime qualità.
Table of Contents
LIST OF FIGURES ................................................................................................................ V LIST OF TABLES ................................................................................................................. XI CHAPTER 1
INTRODUCTION........................................................................................ 1
1.1
Aim and objectives ................................................................................................... 1
1.2
Outline of the thesis ................................................................................................. 2
CHAPTER 2
STATE OF ART .......................................................................................... 3
2.1
The Masonry of historic buildings ......................................................................... 3
2.2
Traditional schist constructions ............................................................................. 6 2.2.1 Typological characterization .......................................................................... 6 2.2.2 Foundation system ......................................................................................... 7 2.2.3 Masonry walls ................................................................................................ 7 2.2.4 Common damages in Schist masonry ............................................................ 9 2.2.4.1 Damages relating to the schist elements ............................................... 9 2.2.4.2 Posting or deterioration of the plaster ................................................ 11 2.2.4.3 Alteration or absence of bedding mortar ............................................ 11 2.2.4.4 Splitting and deformation of elements in openings ............................ 12 I
Table of Contents
2.2.4.5 Cracking walls .................................................................................... 12 2.3
Necessity of strengthening ..................................................................................... 14 2.3.1 Conventional Strengthening Techniques ..................................................... 14 2.3.1.1 Restoration using masonry replacement ............................................. 15 2.3.1.2 Techniques concerning crack treatment ............................................. 16 2.3.1.3 Technique regarding surface external treatments ............................... 17
2.4
Fiber Reinforced Polymers in Masonry .............................................................. 19 2.4.1 Characteristics of composites and their constituents ................................... 19 2.4.2 Structural Strengthening of Masonry Walls ................................................ 21 2.4.2.1 Surface Coatings ................................................................................. 21 2.4.2.2 Application of FRP Strips .................................................................. 21 2.4.2.3 Encasement of Masonry Buildings in Fiber-Reinforced Polymers .... 22 2.4.2.4 Use of Polymer Grids ......................................................................... 23 2.4.3 Structural Repointing of Masonry Walls ..................................................... 23 2.4.3.1 Epoxy Injections ................................................................................. 23 2.4.3.2 Joints Reinforcement .......................................................................... 24
2.5
Experimental characterization of stone masonry ............................................... 25 2.5.1 Out-of-Plane Behavior ................................................................................. 25 2.5.2 Out of-Plane investigations .......................................................................... 27
CHAPTER 3
EXPERIMENTAL PROGRAM ............................................................... 31
3.1
Introduction............................................................................................................ 31
3.2
Materials properties .............................................................................................. 32 3.2.1 Schist Stones ................................................................................................ 32 3.2.1.1 Physical properties.............................................................................. 32 3.2.1.2 Mechanical properties ........................................................................ 34 3.2.2 Natural Hydraulic Lime (NHL) Mortar ....................................................... 37 3.2.2.1 Composition ....................................................................................... 37 3.2.2.2 Granulometric analysis ....................................................................... 38 3.2.2.3 Mechanical properties ........................................................................ 40 3.2.2.3.1 Flexural Strength ......................................................................... 40
II
Table of Contents
3.2.2.3.2 Compressive Strength.................................................................. 42 3.2.3 Fiber Reinforced Mortar (FRM) .................................................................. 45 3.2.3.1 Composition ....................................................................................... 45 3.2.3.2 Adhesive strength: Pull off test .......................................................... 46 3.2.3.3 Projection technology of FRM ........................................................... 50 3.2.3.3.1 Casting ......................................................................................... 50 3.2.3.3.2 Flexural Strength ......................................................................... 53 3.2.3.3.3 Compressive strength .................................................................. 60 3.2.3.4 Normal casting.................................................................................... 63 3.2.3.5 Vertical and normal casting comparison ............................................ 68 3.3
Flexural Strengthening efficiency ........................................................................ 72 3.3.1 Specimen construction ................................................................................. 72 3.3.2 Test Setup..................................................................................................... 75
CHAPTER 4
EXPRIMENTAL RESULTS .................................................................... 79
4.1
Introduction............................................................................................................ 79
4.2
Results and analysis of the Flexural strengthening ............................................ 80 4.2.1 Introduction .................................................................................................. 80 4.2.2 Unreinforced specimen (1 SC_UR) ............................................................. 80 4.2.2.1 Load – Displacement response ........................................................... 81 4.2.2.2 Failure mode ....................................................................................... 82 4.2.3 Reinforced specimen (1 SC_FRM) .............................................................. 85 4.2.3.1 Load – Displacement response ........................................................... 86 4.2.3.2 Failure mode ....................................................................................... 87 4.2.4 Reinforced specimen (2 SC_FRM) .............................................................. 91 4.2.4.1 Load – Displacement response ........................................................... 92 4.2.4.2 Failure mode ....................................................................................... 93
4.3
Discussion of results ............................................................................................... 97 4.3.1 Introduction .................................................................................................. 97 4.3.2 Comparison of results of Flexural strengthening ......................................... 97
CHAPTER 5
NUMERICAL ANALYSIS ..................................................................... 101 III
Table of Contents
5.1
Introduction.......................................................................................................... 101
5.2
Nonlinear finite element analysis ....................................................................... 102 5.2.1 Software used for nonlinear material analysis. .......................................... 102 5.2.2 Iterative techniques for the solution of nonlinear problems ...................... 103 5.2.3 Arc-length method ..................................................................................... 105 5.2.3.1 Arc-length technique in FEMIX 4.0 ................................................. 108 5.2.4 Elasto-plastic multi fixed smeared crack model ........................................ 109 5.2.4.1 Yield surface ..................................................................................... 109 5.2.4.2 Constitutive equation ........................................................................ 110 5.2.4.3 Crack status ...................................................................................... 111
5.3
Modelling of the unreinforced schist masonry prototype ................................ 114 5.3.1 Modelling ................................................................................................... 114 5.3.2 Material properties ..................................................................................... 116 5.3.3 Numerical results ....................................................................................... 118 5.3.4 Comparison between experimental and numerical results......................... 123
5.4
Modelling of the reinforced schist masonry prototype .................................... 126 5.4.1 Modelling ................................................................................................... 126 5.4.2 Material properties ..................................................................................... 127 5.4.3 Numerical results ....................................................................................... 128 5.4.4 Comparison between experimental and numerical results......................... 131
CHAPTER 6
CONCLUSIONS ...................................................................................... 135
6.1
Summary .............................................................................................................. 135
6.2
Conclusions........................................................................................................... 136
6.3
Suggestions for future work ................................................................................ 137
ANNEX A
FLEXURAL STRENGTH – VERTICAL CASTING .......................... 139
ANNEX B
FLEXURAL STRENGTHENING COMPARISON ............................ 145
REFERENCES .................................................................................................................... 147
IV
List of Figures
List of Figures Figure 2.1.1 - Regular brickwork (Como M., 2013). ................................................................. 4 Figure 2.1.2 - Masonry built with tuff blocks (Como M., 2013). .............................................. 4 Figure 2.1.3 - Examples of masonry with a mix of stones and bricks. a) edged masonry; b) mixed masonry with bricks. ....................................................................................................... 5 Figure 2.1.4 – Masonry built with huddled stones and mortar. ................................................. 5 Figure 2.2.1 - Examples of building typologies: a) Carrazedo de Montenegro (PT); b) Vila Nova de Foz Coa (PT); (Ribeiro et al. 2008). ............................................................................ 6 Figure 2.2.2 – Schist wall arrangement: a) simple wall; b) two leaves wall; c) three leaves wall; (Barros R.S., 2013). ........................................................................................................... 7 Figure 2.2.3 - Joint in schist masonry: a) with earth mortar; b) without mortar; (Barros R.S., 2013)........................................................................................................................................... 8 Figure 2.2.4 - Interior partition walls: a) schist with granite; b) wall with timber frame; (Barros R.S., 2013). .................................................................................................................... 8 Figure 2.2.5 - Building corners: a) schist; b) granite; (Ribeiro et al. 2008). .............................. 9 Figure 2.2.6 – Typical schist erosion (Bell F., 2007). .............................................................. 10 Figure 2.2.7 – Deterioration of the plaster – Vilar de Mouros, Portugal. ................................ 11 Figure 2.2.8 – Deformation of elements in openings: a) wood lintels; b) granite lintels; (Barros R. S., 2013). ................................................................................................................. 12 Figure 2.2.9 – Diagonal cracks – Carazedo de Montenegro, Portugal (Barruchello L., 2004). .................................................................................................................................................. 13 Figure 2.2.10 - Several cracks in the walls caused by the change of surrounding environment construction – Bragança, Portugal (Tubi, 2006). ..................................................................... 13 Figure 2.3.1 – Steps in replacement techniques (EU-India Cross Program, 2006).................. 15 Figure 2.3.2 - Strengthening an existing wall with buttresses (Bothara & Brzev, 2011). ....... 15 Figure 2.3.3 - Steps for repointing strengthening intervention (Mach & Speweik, 1998; Hassapis, 2000; Secondin, 2003). ............................................................................................ 16 Figure 2.3.4 - Steps for reinforced repointing strengthening intervention (Valluzzi, Blinda, Modena, 2004). ........................................................................................................................ 17 Figure 2.3.5 - Reinforced concrete jacketing (EU-India Cross Program, 2006). ..................... 18 Figure 2.4.1 - Reinforcing masonry by textile embedded in cementitious mortar (Papanicolau et al.., 2008).............................................................................................................................. 21 V
List of Figures
Figure 2.4.2 - Reinforcing masonry by FRP strips with/without connectors (Candeias et al. 2005)......................................................................................................................................... 21 Figure 2.4.3 - Reinforcing masonry with unidirectional carbon/glass fibers sheets (Borri et al., 2003)......................................................................................................................................... 22 Figure 2.4.4 - Fiber wrapping/encasement of masonry buildings in FRP shells (Borri et al. 2003)......................................................................................................................................... 22 Figure 2.4.5 - Polymer grids used to confine masonry and wrapping around the masonry building, as presented by R. Sofronie, 2004. ........................................................................... 23 Figure 2.5.1 - Flexure in two directions of a wall subject to out-of-plane loading. ................. 26 Figure 2.5.2 – Crack pattern at failure for walls supported on three and four edges. .............. 26 Figure 2.5.3 – Arching mechanism of masonry behaving under out-of-plane loading. .......... 27 Figure 2.5.4 – Test setup scheme of out of plane action: a) schematic representation; b) acting forces during the test (Costa A., Arede A., Costa A. & Oliveira C. S., 2011). ........................ 28 Figure 2.5.5 - In-situ test out-of-plane using airbags: a) Initial phase of displacement; b) Final phase of displacement (Costa A., Arede A., Costa A. & Oliveira C. S., 2012). ...................... 28 Figure 2.5.6 – Out of plane testing: a) location of the wall; b) test scheme (Dizhur et al., 2010)......................................................................................................................................... 29 Figure 3.2.1 - Schist stones used. ............................................................................................. 32 Figure 3.2.2 – Axial compressive strength machine. ............................................................... 34 Figure 3.2.3 - Point load test machine. ..................................................................................... 35 Figure 3.2.4 – Test directions: a) normal to the anisotropy plane; b) parallel to the anisotropy plane. ........................................................................................................................................ 36 Figure 3.2.5 – Components of NHLM. a) Aggregate; b) Binder; c) Final aspect. ................... 37 Figure 3.2.6 - Granulometric analysis. a)particles retained on the sieve n°200; b)adopted sieves; c)sieves contents after sieving operation. ..................................................................... 38 Figure 3.2.7 - Granulometric Curve. ........................................................................................ 39 Figure 3.2.8 – Molds casted. .................................................................................................... 40 Figure 3.2.9 – Flexural strength test setup. .............................................................................. 41 Figure 3.2.10 - Evolution of the flexural strength of NHLM over time ................................... 42 Figure 3.2.11 - Compressive strength test setup. ..................................................................... 42 Figure 3.2.12 - Evolution of the compressive strength of NHLM over time............................ 44 Figure 3.2.13 – FRM composition. a) components; b) glass fibers; c) final aspect. ................ 46 Figure 3.2.14 – Sample preparation: a) Stone cleaned; b)Creation of the mold; c)FRM layer thickness. .................................................................................................................................. 46 VI
List of Figures
Figure 3.2.15 – Sample preparation. ........................................................................................ 47 Figure 3.2.16 – Pull-heads glued to the FRM layer. ................................................................ 47 Figure 3.2.17 – Proceq Dyna 216 test machine........................................................................ 48 Figure 3.2.18 – Fracture patterns. 1-Pull-head plate; 2 – adhesive layer; 3 – mortar; 4 – substrate. ................................................................................................................................... 48 Figure 3.2.19 – Different samples fracture. ............................................................................. 49 Figure 3.2.20 - Spray equipment: a)IMER 120 plus mixer; b)TURBOSOL T7 spraying machine; c) RUBETE R24 compressor. .................................................................................. 50 Figure 3.2.21 – First attempt: a)Steel molds in vertical position; b)Spraying operation. ........ 51 Figure 3.2.22 - Slipping of the mortar ...................................................................................... 51 Figure 3.2.23 - Second attempt: a)Plywood panels; b)Spraying operation. ............................. 52 Figure 3.2.24 - Third attempt: a) Plywood panel; b) Spraying operation. ............................... 52 Figure 3.2.25 – Surface treated with the roller. ........................................................................ 53 Figure 3.2.26 - Final panel – dimensions 0.7 x 1.4 m2............................................................. 53 Figure 3.2.27 – Samples preparation: a) Available surface; b) layout of the strips. ................ 54 Figure 3.2.28 - 4 point bending setup (dimensions in cm). ...................................................... 54 Figure 3.2.29 – Stress – Displacement behavior at 28 days. .................................................... 56 Figure 3.2.30 - Presence of voids in the 50 days samples. ....................................................... 58 Figure 3.2.31 – 3 point bending test: a) samples; b) test setup. ............................................... 59 Figure 3.2.32 - Evolution of the flexural strength of FRM over time. ..................................... 60 Figure 3.2.33 - Evolution of the compressive strength of FRM over time. ............................. 62 Figure 3.2.34 - Normal casting: a) Steel molds; b) samples orientation; c) samples cut. ........ 63 Figure 3.2.35 - Stress - displacement behavior at 28 days. ...................................................... 65 Figure 3.2.36 - Stress - displacement behavior at 50 days. ...................................................... 66 Figure 3.2.37 – Normal casting - Samples crack pattern. ........................................................ 71 Figure 3.2.38 – Vertical casting - Samples crack pattern......................................................... 71 Figure 3.2.39 - Diagonal fracture in the sample 2_FRM_90° tested at 50 days. ..................... 71 Figure 3.3.1 - Wooden support................................................................................................. 72 Figure 3.3.2 – Positioning of the steel plates in the bottom of each specimen. ....................... 73 Figure 3.3.3 – Steps of the specimens construction. ................................................................ 74 Figure 3.3.4 – Application of the reinforcement system: a)Spray operation; b) Levelling with spatula; c)Final result. .............................................................................................................. 75 Figure 3.3.5 – Test setup: a) & b)Testing frame; c) & d)Point load application; e) & f)Support................................................................................................................................... 76 VII
List of Figures
Figure 3.3.6 – Test setup (dimensions in cm). ......................................................................... 77 Figure 3.3.7 – LVDT’s disposition. ......................................................................................... 78 Figure 4.2.1 – Unreinforced Sample: a) General view; b) Intrados beam-top; c) Intrados beam-bottom; d) Extrados beam-top; e) Extrados beam-bottom. ............................................ 81 Figure 4.2.2 - Load vs displacement responses. ....................................................................... 82 Figure 4.2.3 – Crack pattern at the peak load: a) lateral side - front; b) lateral side - back. .... 83 Figure 4.2.4 – Additional crack in the bottom part of the sample: a) lateral side - front; b) lateral side – back. .................................................................................................................... 83 Figure 4.2.5 - Crack pattern at the end of the test: a) lateral side front; b) Opening of the crack in the middle of the lateral side back........................................................................................ 84 Figure 4.2.6 – First reinforced sample: a) General view; b) Intrados beam-top; c) Intrados beam-bottom; d) Extrados beam; e) Extrados beam-point load detail. .................................... 85 Figure 4.2.7 - Load vs displacement responses – LVDTs. ...................................................... 86 Figure 4.2.8 - Load vs displacement responses – Actuator. ..................................................... 86 Figure 4.2.9 – Crack pattern at the peak load in the lateral side –front: a) General view; b) Detail of the middle of the column........................................................................................... 88 Figure 4.2.10 – Crack pattern at the end of the test in the lateral side – front: a) Bottom part; b) Top part. ............................................................................................................................... 89 Figure 4.2.11 - Crack in the reinforced layer - intrados of the Column. .................................. 90 Figure 4.2.12 - Second reinforced sample: a) General view; b) Intrados beam-top; c) Intrados beam-bottom; d) Extrados beam-middle; e) Extrados beam-point load detail. ....................... 91 Figure 4.2.13 – Load – displacement responses....................................................................... 92 Figure 4.2.14 – Crack pattern at the peak load: a) lateral side – front; b) lateral side – back (middle of the sample).............................................................................................................. 93 Figure 4.2.15 – Crack pattern at the end of the test (lateral side – front): a) Detail (cracks in blue); b) General view. ............................................................................................................. 94 Figure 4.2.16 – Crack details at the end of the test: a) lateral side – front; b) lateral side – back. ......................................................................................................................................... 95 Figure 4.2.17 – Cracks in the FRM layers: a) extrados of the beam; b) intrados of the beam. 95 Figure 5.2.1 – Newton-Raphson method. .............................................................................. 104 Figure 5.2.2 – Arc-length technique – system with one degree of freedom (b=1.0). ............ 105 Figure 5.2.3 – Arc-length iterative procedure for a system with one degree of freedom (b=1.0). ................................................................................................................................... 107 Figure 5.2.4 – Newton-Raphson method with and without arc-length technique.................. 108 VIII
List of Figures
Figure 5.2.5 – Load increment correction through the η factor. ............................................ 109 Figure 5.2.6 – Yield surface adopted in the elasto-plastic multi-fixed smeared crack model. ................................................................................................................................................ 110 Figure 5.2.7 – Tensile softening diagram: a)Tri-linear; b)Exponential (Cornelissen et al., 1986)....................................................................................................................................... 112 Figure 5.2.8 – Crack status. .................................................................................................... 113 Figure 5.3.1 – Unreinforced numerical model (supports in blue): a) Complete mesh; b) Top part; c) Bottom part. ............................................................................................................... 115 Figure 5.3.2 - Quadri-linear tensile softening diagrams......................................................... 117 Figure 5.3.3 - Load-Displacement behavior (LVDT 1): experimental and numerical curves. ................................................................................................................................................ 119 Figure 5.3.4 - Load-Displacement behavior (Actuator): experimental and numerical curves. ................................................................................................................................................ 119 Figure 5.3.5 – Quadri-linear tensile-softening diagram – adopted material. ......................... 120 Figure 5.3.6 – Quadri-linear tensile softening diagram - 2nd analysis. ................................. 121 Figure 5.3.7 - Load-Displacement behavior (LVDT 1): experimental and numerical curves. ................................................................................................................................................ 121 Figure 5.3.8 - Load-Displacement behavior (Actuator): experimental and numerical curves. ................................................................................................................................................ 122 Figure 5.3.9 – Deformed mesh: a) Peak load; b) End of the analysis. ................................... 123 Figure 5.3.10 – Opening crack status at the peak load: a) Numerical model; b) Experimental test. ......................................................................................................................................... 124 Figure 5.3.11 – Crack patterns at the end of the analysis: a) Opening status; b) Fully open status; c) Experimental test. ................................................................................................... 125 Figure 5.4.1 - Reinforced numerical model (supports in blue): a) Complete mesh; b) Top part; c) Bottom part......................................................................................................................... 127 Figure 5.4.2 - Load-Displacement behavior (LVDT 1): experimental and numerical curves. ................................................................................................................................................ 129 Figure 5.4.3 - Load-Displacement behavior (Actuator): experimental and numerical curves. ................................................................................................................................................ 130 Figure 5.4.4 – FRM Quadri-linear tensile softening diagram. ............................................... 131 Figure 5.4.5 - Deformed mesh: a) Peak load; b) End of the analysis. .................................... 132 Figure 5.4.6 – Opening crack status at the peak load: a) Numerical model ;b) Experimental test. ......................................................................................................................................... 133 IX
List of Figures
Figure 5.4.7 - Crack patterns at the end of the analysis: a) Opening; b) Fully open; c) & d) Experimental test. ................................................................................................................... 133
X
List of Tables
List of Tables Table 2.4.1 – Characteristic of composites and their constituents (CNR-DT 200/2004 Tab.2.1). ................................................................................................................................... 20 Table 3.2.1 – Water absorption at atmospheric pressure of diverse rocks. 1Noronha et al. (2011), 2Reis(2010). ................................................................................................................. 33 Table 3.2.2 – Density and porosity of diverse rocks. 1Noronha et al. (2011), 2Manuale di Progettazione Edilizia (2007), 3Kobranova (1989). ................................................................. 33 Table 3.2.3 – Results from test of: water absorption at atmospheric pressure, density and porosity. .................................................................................................................................... 33 Table 3.2.4 – Compressive strength of diverse rocks. 1Noronha et al. (2011) and Burcio (2004), 2 Vasconcelos et al. (2005), 3 Bell (2007), 4Mogi (2007). ........................................... 34 Table 3.2.5 - Point load strength of diverse rocks. 1Pinho (2003), 2Bell (2007). ..................... 35 Table 3.2.6 – Results from tests of mechanical characterization. ............................................ 36 Table 3.2.7 – Mortar quantity proportions. .............................................................................. 37 Table 3.2.8 - Summary table of the granulometric analysis..................................................... 39 Table 3.2.9 – Flexural strength results. .................................................................................... 41 Table 3.2.10 – Results variation over the time. ........................................................................ 41 Table 3.2.11 – Compression test results. .................................................................................. 43 Table 3.2.12 - Young's Modulus Evaluation. ........................................................................... 44 Table 3.2.13 - Results variation over the time. ........................................................................ 44 Table 3.2.14 – Adopted composition (per m3 of FRM). .......................................................... 45 Table 3.2.15 - Loading rate. ..................................................................................................... 48 Table 3.2.16 - Pull off test results. ........................................................................................... 49 Table 3.2.17 – Vertical casting - Geometrical properties at 28 days. ...................................... 55 Table 3.2.18 - Results vertical casting at 28 days .................................................................... 55 Table 3.2.19 - Vertical casting - density comparison. .............................................................. 57 Table 3.2.20 – Results comparison. ......................................................................................... 57 Table 3.2.21 - Flexural strength test results ............................................................................. 59 Table 3.2.22 – Results variation over the time ......................................................................... 60 Table 3.2.23 - Compression strength results. ........................................................................... 61 Table 3.2.24 - Young's Modulus evaluation. ........................................................................... 61 Table 3.2.25 – Results variation over time............................................................................... 62 XI
List of Tables
Table 3.2.26 - Normal casting - geometrical analysis at 28 days ............................................. 64 Table 3.2.27 - Results normal casting at 28 days ..................................................................... 64 Table 3.2.28 - Normal casting - geometrical analysis at 50 days ............................................. 65 Table 3.2.29 - Results normal casting at 50 days ..................................................................... 66 Table 3.2.30 - Results comparison. .......................................................................................... 67 Table 3.2.31 - Density comparison at 28 days. ........................................................................ 68 Table 3.2.32 - Density comparison at 50 days. ........................................................................ 69 Table 3.2.33 – Normal vs Vertical casting at 28 days. ............................................................. 69 Table 3.2.34 - Normal vs Vertical casting at 50 days. ............................................................. 70 Table 4.3.1 - Comparison of the peak load data....................................................................... 97 Table 4.3.2 - Displacements at the Peak load. ......................................................................... 97 Table 4.3.3 - Increment of the displacement at the peak load. ................................................. 98 Table 4.3.4 - Displacements variation in the strengthened samples. ....................................... 99 Table 5.3.1 – Schist masonry mechanical properties. 1Luso E. C., (2012). 2Barros R. S., (2013). .................................................................................................................................... 116 Table 5.3.2 – Quadri-linear tensile softening parameters range. ........................................... 117 Table 5.3.3 – Adopted parameters for schist masonry. .......................................................... 120 Table 5.3.4 - Adopted parameters for schist masonry – 2nd analysis. .................................... 120 Table 5.3.5 – Final ranges for schist masonry mechanical properties. .................................. 123 Table 5.4.1 – FRM mechanical properties adopted. .............................................................. 130
XII
Chapter 1
INTRODUCTION
1.1 Aim and objectives The aim of the present project is to assess the effectiveness of an innovative strengthening system used for the rehabilitation of buildings deficiently prepared for seismic events. In particular, it is intended to characterize and quantify the increase of the load carrying capacity and deformation of strengthened schist masonry elements by applying via spray a high performance fiber reinforced mortar. In order to give a contribution to the development of this pioneering strengthening technique, its application methodology as well as its effectiveness towards the out-of-plane behavior of schist walls elements has been investigated. However, the aforementioned assessment does not involve only the experimental observations, in fact a preliminary finite element modelling has been carried out on the schist masonry elements, using FEMIX 4.0 computer code (Azevedo et al., 2003). The main purpose of this primary numerical analysis has been to validate the experimental results as well as to understand the failure mechanism of the strengthened samples under flexural loading configuration.
1
Chapter 1 - INTRODUCTION
In conclusion the research aims to provide reasonable parameters for the mechanical properties of both schist masonry and reinforcement system.
1.2 Outline of the thesis The present thesis is divided into six chapter. The first chapter provides an overall introduction to the project, presenting the aims and the objectives that the author wanted to achieve. The second chapter deals with the state of art whose main purpose is to provide an overview on the historical natural stone masonry, addressing some main aspects such as: the common damages, the strengthening techniques and the structural issues under seismic loads. In chapter three, the experimental campaign carried out is presented in detail. All the materials used are carefully analyzed according to the current guidelines and the results are then shown. Particular attention is given to the characterization of the material constituting the reinforcement system, being the reference material of this project. Finally the construction of the schist walls elements and test setup are illustrated in all their phases. The fourth chapter provides a detailed discussion of the results obtained from the schist masonry prototypes. The load-deflection curves and the crack patterns observed in both the reinforced and the unreinforced samples are analyzed and then compared. Chapter five deals with the numerical analysis carried out. Firstly an introduction on the constitutive model and the computer code used is presented. Next, modelling and results of both prototypes typologies carried out are shown and discussed comparing with the experimental results. Finally, chapter six concludes the thesis with the summary and outcome of the present research and suggestions for the future works.
2
Chapter 2
STATE OF ART
2.1 The Masonry of historic buildings Masonry constructions, whose oldest examples date back to about eight thousand years ago, developed during the beginning of the earliest urban civilizations, when more ancient techniques employing building materials such as wood, straw, and hides were gradually replaced by more advanced technologies, enabling the construction of stronger and longer lasting structures. Masonry is an heterogeneous material composed of natural or artificial units that are jointed together with dry or mortar joints. Irregular stones, ashlars, adobes and blocks are used as units. The units can be jointed together using mortar (such as: clay, lime, chalk or cement based mortar) or just by simple superposition. Thanks to the different combination of these two components (units and joints), a huge number of arrangements can be accomplished. A possible classification of this wide variety of masonry types, used in historic buildings, is given by Mario Como (2013) who, according to the elements used, subdivided masonry into: - Regular brickwork: constructed with brick elements laid with mortar in horizontal courses with staggered vertical joints.
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Figure 2.1.1 - Regular brickwork (Como M., 2013).
In this arrangement 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. Thinner walls are made using a stretcher bond, also known as a running bond, with stretchers forming the entire thickness of the wall. Others kind of walls are constructed with a single row of stretchers, so that the wall is as thick as the brick head, 12đ?‘?đ?‘š. There are many other types of bonds that use two or three headers in different alternating configurations with stretchers. - Regular brickwork with squared stone blocks: they are built with tuff blocks bound by horizontal mortar and vertically staggered joints, as in regular brickwork (Figure 2.1.2). Thick walls may present an internal rubble core.
Figure 2.1.2 - Masonry built with tuff blocks (Como M., 2013).
- Brickwork with mixed stone and brick: they come in two different types. In the first, called edged masonry, the bricks are arranged in horizontal courses along the entire thickness of the wall at varying distance (80 − 160 đ?‘?đ?‘š) between the stone masonry. In the second,
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mixed masonry with bricks, single bricks are laid in various places to level the stone planes (Figure 2.1.3).
a)
b)
Figure 2.1.3 - Examples of masonry with a mix of stones and bricks. a) edged masonry; b) mixed masonry with bricks.
- Ordinary brickwork with huddled stones: it is obtained by mortaring irregularly shaped elements, such as chunks of bricks or stones, along roughly horizontal planes in such a way as to reduce the space between them (Figure 2.1.4). Such masonry, frequently used frequently to build homes in small historical communities in southern Italy, is particularly vulnerable to earthquake.
Figure 2.1.4 – Masonry built with huddled stones and mortar.
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2.2 Traditional schist constructions Schist constructions represent a very important cultural, architectural and historical legacy in Europe, that needs to be preserved. Among the wide European architectural heritage, there are many traditional buildings in schist masonry. They are distributed throughout Europe, from the North to the South and for this reason: the buildings, the constructive methodologies and even the material (depending on the area where schist is extracted it may have different properties and characteristics) can be different. The constructive techniques and solutions of these traditional structures have been developed in direct relation with various factors that influence them, including economic, environmental and social ones, adapting to different environments and requirements over the time, originating a wide diversity of constructions typologies. 2.2.1 Typological characterization According to Ricardo S. Barros (2013), usually the traditional schist houses have slightly square or rectangular in-plan geometry, with two or three floors at most. As these buildings are traditionally built in mountain areas, it is common that the ground-floor contains spaces for animals, cellar and storage, while the rooms and halls are located upstairs. Some details such as the access made by a stone stairway, the lack or the existence of a rudimentary chimney and a wooden roof structures are typical of this type of houses (see Figure 2.2.1). Thus, it is clear that the different typologies of schist constructions are closely related to the material available, the population itself, its culture, traditions and knowledge, as well as its economic power.
a)
b)
Figure 2.2.1 - Examples of building typologies: a) Carrazedo de Montenegro (PT); b) Vila Nova de Foz Coa (PT); (Ribeiro et al. 2008).
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2.2.2 Foundation system The foundations of the schist rural constructions are normally made of schist, except for some buildings where they are made of granite. These constructive elements are practically an extension of the walls to the foundation soil, with a current depth of 60 đ?‘?đ?‘š, but it may vary depending on the soil type implantation and the dimension of the building. 2.2.3 Masonry walls In the schist masonry walls construction, larger stones were used at the corners, where the concentration of larger stresses tends to occur, so appropriate connection between the wall panels should be provided. Stones of smaller dimensions are used in the remaining part of the wall, facilitating their handling during the walls construction process. The walls stiffness and strength, as well as the connections, not only depends on the quality and size of the stones used in their construction, but also on their arrangement and constructive method. An adequate arrangement of the schist stones in the construction of the walls is extremely important, and it largely affect their mechanical properties and structural performance. In relation to the typology, where it is possible to extract larger schist stones and combine them with granite stones, the walls construction, is usually simple (Figure 2.2.2 a)). When it is not possible to extract larger schist stones, the walls can present two or three leaves, see Figure 2.2.2 b) and c). In these cases, the schist stones are neatly arranged and the bonding mortar is usually made of earth. In this type of schist fabric, wood or stone connectors can be found. They play a fundamental role for the monolithic behavior of the masonry walls.
a)
b)
c)
Figure 2.2.2 – Schist wall arrangement: a) simple wall; b) two leaves wall; c) three leaves wall; (Barros R.S., 2013).
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In existing walls, different types of mortar connecting the schist stones can be found, such as lime or simple earth mortar. But, it can be also found masonry schist walls without mortar, for which the meticulous settlement of the schist provides imbrications which ensures the adequate mechanical behavior of the walls.
a)
b)
Figure 2.2.3 - Joint in schist masonry: a) with earth mortar; b) without mortar; (Barros R.S., 2013).
The partition interior walls, when they are structural as in larger buildings, are usually constructed also in schist. In some particular cases there is the combination of schist with granite, see Figure 2.2.4 a). However, the partitions walls are most commonly made with a timber frame with a cover made of lime, see Figure 2.2.4 b).
a)
b)
Figure 2.2.4 - Interior partition walls: a) schist with granite; b) wall with timber frame; (Barros R.S., 2013).
Masonry corners play an important role in the building structural performance: on one hand they ensure the connection between perpendicular walls, however, on the other hand, these elements in the masonry structures tend to concentrate larger stresses, due to the horizontal loadings induced by wind and earthquakes, as well as the resulting thrust from the roof structure. The quality of the materials and its arrangements in the corners is even more important for building with multi-leaf walls, considering that for these cases the quality of the
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masonry is lower, as stated before, due to the smaller dimensions and the poor mechanical properties of the stone units.
a)
b)
Figure 2.2.5 - Building corners: a) schist; b) granite; (Ribeiro et al. 2008).
2.2.4 Common damages in Schist masonry Historical masonry constructions inevitably suffer damages with time. These damages can be intrinsically linked to the materials or to the structural elements. Regardless of the nature of the damages, in certain circumstances they may affect the overall behavior of the building, and even compromise the performance and the structural safety. Therefore Daniel Vitorino de Castro Oliveira (2003) states that careful periodic inspections to the structural elements are necessary in order to evaluate their actual structural safety levels and acquire information on the agents of degradation and its most common manifestations in each region. In particular, there are three types of damages related to stone masonry: deformation, cracking and displacement. According to Baruchello L. and Assenza (2004), the deformations arise when registering a change of the geometrical shape of the structural element without the presence of non-linear material behavior. Cracking occurs when it exceeds the elastic limit of the material. Displacement may be recorded in various forms: vertical displacement, rotational or the combination of both. 2.2.4.1 Damages relating to the schist elements Basically, the damages of stony elements may have chemical, physical or biological sources. The main chemical actions can be defined by reduction, hydrolysis, oxidation and dissolution. Moreover, the physical actions can be defined by thermal expansion, expansion by freezing/thawing cycles, expansion caused by decompression or mechanical actions such as water and wind. 9
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As previously mentioned, most of the schist buildings do not have plaster or any other type of coating, therefore structures remain exposed to the environment actions during the entire useful life of the building. This exposure to environment is a major cause for the appearance of several non-structural damages related to the deterioration of the material, which over time can lead to structural damages or at least create a greater susceptibility to the occurrence of thereof. One of the most severe damage in traditional schist structures is the erosion of the stone. Schist erosion usually appears in the ground floors of buildings, on the outer compartments walls, where were animals. Thus, this damage has chemical origin related to animal waste, combined with temperature differences existing between the inner and the outer part of the building (see Figure 2.2.6).
Figure 2.2.6 – Typical schist erosion (Bell F., 2007).
Another main event in the deterioration of the rocks used in the constructions is the ice. The porosity, the pore size and the degree of saturation are the main factors to take into consideration regarding the susceptibility of rocks to freezing/thawing cycles. According to Bell F. (2007), as the water freezes, it swells giving rise to an increase in pore pressure. When ice is formed, the pressure rapidly increases with decreasing temperature, at temperature of about −22°đ??ś, the ice can exert a pressure of 200 đ?‘€đ?‘ƒđ?‘Ž. Moreover, the exposure to heat allows for expansion of the various constituent of the schist may cause exfoliation of the surfaces. Being made of a large schist variety of minerals, this is a phenomenon that can cause many damages. In fact, such as regards Bell F., quartz is one of the most expansive minerals, expanding about 3.7% between room temperature and 570°đ??ś.
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2.2.4.2 Posting or deterioration of the plaster As previously stated, it is not very common to find plaster in schist buildings. However, plaster may be found in buildings of greater importance or value such as religious buildings or stately constructions. The deterioration of the plaster, is an injury commonly detected in these buildings, and it is mainly caused by the lack of maintenance. This damage, that can lead to a more severe situation that is the detachment of the plaster and the exposure of the structure to surrounding environment. Thus, the plaster has the grout function, as a protection coat of the masonry structure. When it is weak or even absent, this can lead to the emergence of structural damages associated with the exposure to the environment, such as the appearance of vegetation and microorganisms or even the erosion of the binder and the degradation of schist (see Figure 2.2.7).
Figure 2.2.7 – Deterioration of the plaster – Vilar de Mouros, Portugal.
2.2.4.3 Alteration or absence of bedding mortar Usually, in traditional schist masonry constructions, the most common binder was mortar made of land, however, in certain cases such as in small buildings, the masonry walls were constructed with dry joints. Less frequently a lime-based binder was applied, or in cases of new or recent recovery interventions or rehabilitation is possible to find cement mortars. The most common injury observed in bonding mortar is related to the alteration of the initial characteristics of the mortar. However, this situation when it occurs comes to traditional mortars made of land, is not particularly onerous, as these mortars already have a low mechanical strength. Furthermore a change in the properties of the mortar may not have a significant impact on the mechanical properties of the schist walls. A typical damage associated to the newest constructions, is the occurrence of salts originating from the application of cement mortars which by chemical reaction with water it creates white spots, especially on not plastered walls. 11
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2.2.4.4 Splitting and deformation of elements in openings In schist masonry, openings are one of the most sensitive areas of the building, taking into account the small size of the schist elements and the necessity of an adequate distribution of the efforts that constitute the walls. For correct operation of the schist walls in the areas of the openings are typically used other materials for the construction of the lintels, such as wood or granite. These elements, when made in wood, may undergo deformations caused by excessive overloads (see Figure 2.2.8 a)), or by the degradation of the wood itself. When the lintels are built in granite, cracking (see Figure 2.2.8 b)) or breakdown caused by high demands mostly derived from deformations of the support structure are common.
a)
b)
Figure 2.2.8 – Deformation of elements in openings: a) wood lintels; b) granite lintels; (Barros R. S., 2013).
2.2.4.5 Cracking walls According to Tubi N. (2006), the cracks are the result of the deformation of wall parts. The main causes of cracks in schist walls are: damage caused by vertical shear, horizontal drift or crushing. The first two lesions can easily be confused, since both can be caused by problems in the foundations. However, the former can also be caused by differences in the structure of the wall decrease, while it may originate rotation of the building (Barruchello L., 2004). With regard to the damages caused by crushing, according to Baruchello L., these strains can be derived from excessive compression. The main causes are: insufficient dimensioning, degradation, poor quality of the original binder mortar from excessive overloads, increasing loads by change of use or super-elevation of the structure. The presence of diagonal cracks in schist walls usually originates from the malfunction of foundations (e.g. settlements or other similar events). This is a common situation in some of these buildings implanted on slopes (see Figure 2.2.9). 12
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Figure 2.2.9 – Diagonal cracks – Carazedo de Montenegro, Portugal (Barruchello L., 2004).
Malfunction or settlements of foundations in stone masonry buildings are the most common problems. It can be considered that in the case of schist masonry this damage becomes more onerous, especially in constructions performed with three leaves, where smaller materials are applied. According to Tubi N. (2006), the settlements may be caused by insufficient dimensioning of the foundations or terrain instability. In the case of popular constructions sizing was not formally considered and, in general, there was a lack of knowledge on the foundation soils and their properties. Changes in the surrounding area of traditional buildings such as the implantation of new constructions (more rigid), that confines with the old, may severely affects the structure of traditional buildings, causing damages, such as cracks or even the partial or total collapse of the wall leaves. The increase of the concentrated loads from the support of a structural element, such as a beam floor covering or walls, can cause cracking in the lower restraints areas.
Figure 2.2.10 - Several cracks in the walls caused by the change of surrounding environment construction – Bragança, Portugal (Tubi, 2006).
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2.3 Necessity of strengthening Masonry structures were built on ancient times when no appropriate theory and good knowledge were available. People usually built their houses according to the available knowledge and experience. For this reason many buildings which still exist do not satisfy the present guidelines. Also the recent worldwide earthquakes make people more conscious about the safety of life and property. Some of the famous building which becomes valuable in terms of culture and history demand life. It is also a common issue that places where there were residential area some years ago, now has become industrial area, and people usually want to change the usage of their previous building. Furthermore, sometimes during the construction mistakes could have been made. Taking all this into account, there are a lot of reasons for strengthening existing buildings, that can be summarized as follows: - To eliminate structural problems or distress which result from unusual loading or exposure conditions, inadequate design, or poor construction practices. Distress may be caused by overloads, fire, flood, foundation settlement, deterioration resulting from abrasion, fatigue effects, chemical attacks, weathering, inadequate maintenance, etc.; - To be conform to current codes and standards; - To allow the feasibility of changing the use of a structure accommodating a different use from the present one; - Durability problems due to poor or inappropriate construction materials; - Design or construction errors; - Aggressive environments not properly understood during the design stages; - Increased life-span demands made on ageing infrastructure; - Exceptional or accidental loading; - Varying life span of different structural or non-structural components. 2.3.1 Conventional Strengthening Techniques The repairing and retrofitting of existing masonry structures are traditionally accomplished by using conventional materials and constructions techniques. There are two kind to rehabilitation methods: the repairing technique, when the purpose is to restore the load bearing capacity of the masonry elements, and the strengthening techniques, when the purpose is to increase the load bearing capacity.
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2.3.1.1 Restoration using masonry replacement a) Masonry replacement technique using similar materials. This strengthening solution is commonly applied on walls with severe but localized cracks or highly deteriorated parts. The existing masonry pattern is locally removed where major deterioration has occurred and it is replaced with new masonry reproducing closely the mechanical properties of the original one (Figure 2.3.1). It is one of the first techniques applied to restoration. The main objectives of this method are: preserving of the mechanical efficiency and improving of the continuity of the masonry structures (Budescu et al., 2001).
Figure 2.3.1 – Steps in replacement techniques (EU-India Cross Program, 2006).
b) Strengthening masonry using wall buttresses. This strengthening technique consists in adding additional supports (buttress) in vertical plane vulnerable walls to out-of-plane loads (Figure 2.3.2). The main advantages of this solution are: preventing the failure mechanism related to the lateral deformations and a good behavior in case of horizontal forces (Bothara & Brzev, 2011).
Figure 2.3.2 - Strengthening an existing wall with buttresses (Bothara & Brzev, 2011).
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2.3.1.2 Techniques concerning crack treatment a) Repointing. This strengthening solution is based on improving and reinforcing the damaged mortar joints due to leaking roofs or gutters, capillarity actions causing rising damp, extreme weather (freeze/thaw cycles), cracks along the joints due to differential settlements. The technique consists in removing, cleaning, washing, filling the mortar joints with a new mortar. This mortar should be compatible with the properties of the masonry units, resistant to agents of deterioration and it should have almost the same mechanical properties and durability as the original one. The main targets are: increasing the compressive and the shear strength, improving the appearance and reduction of deformation.
Figure 2.3.3 - Steps for repointing strengthening intervention (Mach & Speweik, 1998; Hassapis, 2000; Secondin, 2003).
b) Structural repointing. This strengthening actions consists in using steel reinforcement which involves the application of short steel rods across cracks caused of the masonry assemblage under long-term high level dead loads. This technique offers some advantages as reduced surface preparation and preservation of aesthetic. The main targets are: restoring the integrity and/or upgrading the shear and/or flexural capacity of walls, confining effect on the walls and improvement of the tensile behavior of masonry due to steel anchorages in masonry.
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Figure 2.3.4 - Steps for reinforced repointing strengthening intervention (Valluzzi, Blinda, Modena, 2004).
c) Covering and injecting the cracks. This strengthening method consists in covering, injecting the mortar into the walls for anchoring, bonding the missing parts and, increasing the strength and stiffness of the wall by solid filling of hollows in masonry with cement mortar, fluid cement mortar or grout (depending on the size and the density of the cracks). The effectiveness of the strengthening technique depends on the mechanical properties (high tensile strength, high bond to mortar units) of the new injected material, and its chemical and physical compatibility with the original masonry. The main targets are: restoring the initial stiffness and improving lateral resistance of the retrofitted walls to in plane loads, filing exiting cavities and internal voids to make the masonry more homogeneous, to prevent displacement during earthquake actions and sealing possible cracks (Budescu et. Al., 2001; ElGawady et al., 2004; Jeffs P.A., 2000) The morphology of the walls has suggested that in some case reinforcement by injection is not appropriate due to the fact that inside the masonry there was effectively loose material and no voids were present. 2.3.1.3 Technique regarding surface external treatments a) Walls reinforcing overlays, jacketing. This strengthening actions consist in the application of a self-supporting reinforced concrete cover or a cement mortar matrix reinforced with independent bars, that surrounds the structural elements. It is applied to elements subjected to high compression stresses and lateral deformations. Jacketing wall surfaces must be interconnected by means of through-wall anchors. The overlay starts from the foundations through a belt of reinforced concrete in order to ensure an effective transmission of loads to the soil. Overlays are not conceived to work independently, but they are designed to undertake the loads from the reinforced structure. With this view, the reinforcement is fixed to the masonry wall with steel connectors and staples, and the overlays are connected through the mortar ribs which are formed in the mortar joints. It is known that 17
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the effectiveness of the intervention is better when jacketing is applied on both sides of the wall, with diffuse connections. The main targets are: improving
strength and stiffness,
providing additional strength to seismic loads, obtaining a continuous confinement, a monolithic behavior of the element.
Figure 2.3.5 - Reinforced concrete jacketing (EU-India Cross Program, 2006).
b)
The shotcrete technique. This strengthening action consists in spraying overlays made
of a mixture of a mineral matrix onto the surface of a masonry wall over a mesh of reinforcing bars. The thickness of the shotcrete can be adapted according to the requirements for the projection to seismic actions. The shotcrete overlay is usually reinforced with welded wire fabric to the approximately minimum ratio for crack control. In order to transfer the shear stress on the entire surface of the shotcrete, shear dowels are fixed using epoxy resins or cement grout in holes drilled into masonry wall. However, there is no consensus regarding the bonding between the bricks and the shotcrete material or the need of using the anchor system. Moreover, it is recommended wetting the masonry surface before applying the shotcrete. This treatment does not affect the cracking or ultimate load, it only limits extended the inelastic deformations. The main targets are: increasing the ultimate load of the retrofitted walls, increasing of the capacity to axial loads and also to lateral ones, significant development of the energy dissipation mechanism, improving stability (El Gawady et al., 2004) c) The ferrocement technique. This method is applicable to most types of masonry walls and consists of applying orthotropic composite material matrix based on cement mortar of high resistance and multiple layers of steel meshes. The tensile strength of the ferrocement depends on the nature of the mesh, on the orientation and the thickness of the reinforcement. The main targets are: improving the behavior to in plane inelastic deformation capacity, ferrocement improves out-of-plane stability and arching action.
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2.4 Fiber Reinforced Polymers in Masonry Because of the low tensile strength of the masonry material, structural engineers have coupled masonry with several kinds of reinforcements to overcome such intrinsic weakness. The most used materials for the reinforcements of masonry are concrete and iron, but nowadays new materials, such as composites, begin to be used. Conventional retrofitting techniques (e.g. steel jacketing, grout injection, shotcrete etc.) have several disadvantages such as the reduction of available space, architectural impact, heavy mass addition, potential corrosion etc. During the last decade or so on, fiber reinforced polymers (FRPs) offered a promising alternative solution for retrofitting of masonry structures. FRPs present several well-known advantages over existing conventional techniques, such as high strength to weight ratio, ease of application, and high resistance to corrosion. 2.4.1 Characteristics of composites and their constituents Composite materials exhibit the following characteristics: - they are made of two or more materials (phases) of different nature and “macroscopically” distinguishable; - at least two phases have physical and mechanical properties quite different from each other, such to provide FRP material with different properties than those of its constituents. Fiber-reinforced composites with polymeric matrix satisfy both of the above mentioned characteristics. In fact, they are made out of both organic polymeric matrix and reinforcing fibers. Carbon fibers may exhibit values of Young’s modulus of elasticity much larger than those of typical construction materials. Therefore, they are more effective from a structural point of view. The matrix may be considered as an isotropic material, while the reinforcing phase, with the exception of glass fiber, is an anisotropic material. The defining characteristics of FRP materials are as follows: - geometry: shape and dimensions; - fiber orientation: the orientation with respect to the symmetry axes of the material; when random, the composite characteristics are similar to an isotropic material (“quasi-isotropic”). In all other cases the composites can be considered as an anisotropic material; - fiber concentration: volume fraction, distribution (dispersion). 19
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Therefore, composites are in most cases a non-homogeneous and anisotropic material.
Table 2.4.1 – Characteristic of composites and their constituents (CNR-DT 200/2004 Tab.2.1).
To summarize FRP properties, it is convenient to divide fiber-reinforced composites in two categories, regardless of their production technology: single-layer (lamina); multi-layer (laminates). Laminates are materials composed of stacked layers (the lamina) whose thickness is usually of some tenths of a millimeter. In the simplest case, fibers are embedded only in the lamina’s plane (there are no fibers arranged orthogonally to that plane). The size of laminates is intermediate between those of the fibers and those of engineering structures. There is also a special class of multi-layer composites, so called hybrid laminates, where each single lamina is made out of both different fibers (e.g. epoxy matrix composites with carbon and aramid fibers to get a stiff and tough composite) or different materials (e.g., composites with alternate layers of epoxy resin with aramid and aluminum fibers). The main advantage of laminates is represented by the greater freedom of fiber arrangement. Due to the anisotropic characteristics of FRP material, their mechanical properties depend on the choice of the reference system. The main axes are usually chosen to be concurring with the symmetry axes of the material. Composite materials can be stronger and stiffer (carbon FRP) than traditional construction materials. As a result, composites may become very attractive when the weight of the structure becomes an issue. FRP tensile strength and Young’s modulus of elasticity can be up to four and two times that of traditional materials, respectively. This means that a composites material structure may weigh nearly half of a traditional construction material structure of equal stiffness or less.
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2.4.2 Structural Strengthening of Masonry Walls 2.4.2.1 Surface Coatings The technology consists of cleaning both faces of the wall, removing the dust and any loose particles by high air pressure and following by a standard wet laying-up procedure to bond textile sheets on both sides of the wall and cover the entire surface by using a bonding agent. For specimens receiving mortars, the wall surface is previously dampened. Then, the bonding of the textile is made by hand and roller pressure. The bonding agent is applied in 2 đ?‘šđ?‘š thick layers with a smooth metal towel and the textile is pressed slightly into mortar which protrude through all the perforations between fiber rovings (Figure 2.4.1).
Figure 2.4.1 - Reinforcing masonry by textile embedded in cementitious mortar (Papanicolau et al.., 2008).
2.4.2.2 Application of FRP Strips The system consists of using strips of composite material, glass fibers and epoxy resin matrix, with/without connectors to stick together the strips from both sides of the wall (Candeias et al.,2005), applied in two layers with the composite strips oriented after the principal directions of tensile stresses (Figure 2.4.2).
Figure 2.4.2 - Reinforcing masonry by FRP strips with/without connectors (Candeias et al. 2005).
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Another system used to strengthen masonry consists of using sheets of unidirectional carbon fiber or glass fiber (Borri et al., 2003), placed on both sides of the panel, following the scheme presented in Figure 2.4.3.
Figure 2.4.3 - Reinforcing masonry with unidirectional carbon/glass fibers sheets (Borri et al., 2003).
2.4.2.3 Encasement of Masonry Buildings in Fiber-Reinforced Polymers Fiber wrapping or encasement of masonry buildings in FRP shells (Borri et al., 2003), may significantly enhance the strength and ductility of masonry structures. Most masonry walls are not correctly connected to each other, for this reason these structures are particularly vulnerable to seismic action.
Figure 2.4.4 - Fiber wrapping/encasement of masonry buildings in FRP shells (Borri et al. 2003).
The application of carbon fiber reinforced polymers (CFRP), is carried out after having spread an epoxy-primer and an epoxy-mortar on the surface of the panels. The bands of CFRP are applied along the external perimeter I order to wrap the masonry cell with one band near the base and with another near the upper border.
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2.4.2.4 Use of Polymer Grids The reason why polymer grids may be successfully applied for restoring masonry are, from mechanical point of view, the elastic and plastic properties which present quite the same proportions. Due to the fact that these two materials have similar moduli of elasticity, they will deform in similar manner, while the grids supply the system with convenient levels of strength and high capacity of dissipation of energy (Sofronie R, 2004). From a geometric point of view, the grids are shaped as bars of equal tension strength on the two principal directions. The ribs are stiff enough to transmit both tension and shear stresses, while the joints are solid and together with the ribs are integrated in grids. The applications of these grids may differ, from embedding them in bed joints, confining the masonry by wrapping around with polymer grids and then by rendering either buildings bodies as such or only some of their structural members (Figure 2.4.5).
Figure 2.4.5 - Polymer grids used to confine masonry and wrapping around the masonry building, as presented by R. Sofronie, 2004.
2.4.3 Structural Repointing of Masonry Walls Structural repointing mainly addresses the interventions to joints, by replacing some material from which they are made with FRP systems, in order to improve the capacity of URM wall to overtake loadings developed both in or out-of-plane. The main advantage of these system is that the original aspect of the wall is not affected. 2.4.3.1 Epoxy Injections The aim of injections is to restore the original integrity of the retrofitted wall and fill the voids and cracks, which are present in the masonry due to physical and chemical deterioration and/or mechanical actions. The epoxy injection is a method used for small cracks (ElGawady et al., 2004). The success of this technique depends on the injectability of the mix used and on 23
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the injection technique adopted. The injectability of the mix, its properties and the physical chemical compatibility with the masonry are important aspects to be considered for this consolidation technique. 2.4.3.2 Joints Reinforcement The aim of reinforcing the joints, as they represent the weak planes of masonry, is to increase the tensile strength of the bed joints and reduce and distribute more uniformly the transverse tensile stresses in the brick because of the inhibition of lateral expansion of the mortar within the bed joint. a) Micro reinforcement of masonry joints. The micro-reinforcement of masonry joints may be achieved by adding in the cement lime reach mortar mix short polypropylene/polymer fibers of 6 đ?‘šđ?‘š length (Bosiljkov, 2006). The objective of the technique is to reduce cracks induced by the process of mortar hardening and improve mortar toughness and flexibility. b) Macro reinforcement of masonry joints This method consists of introducing two layers of cement lime reach mortar with an embedded resin coated glass fiber mesh between them (Bosiljkov, 2006). The expected improvements are similar to the micro-reinforcement of joints. c) Near Surface Mounted (NSM) Technique Near surface mounted (NSM) FRP is a technique in which pre-cured strips, bars, or rods are inserted into pre-cut grooves in the surface of the strengthened member. The grooves are usually cut large enough to contain the FRP and surround it on three sides with a thin layer of epoxy or some other bonding agent. Advantages of this technique include the limited aesthetic impact and the potential for the development of greater strain in the FRP prior to debonding due to better confinement from the three bonded sides than comparable EB applications which are usually not confined and are bonded only on one sides.
24
Chapter 2 - STATE OF ART
2.5 Experimental characterization of stone masonry The stone masonry is one of the oldest building materials that remained up to our days in old structures. Performance evaluation of stone masonry, in terms of strength and deformation, is particularly relevant due to the increasing demand for the rehabilitation and enhancement of the built heritage. Most of the experimental characterization of stone masonry walls has been performed in the laboratory. However, the construction of stone masonry wall panels has some limitations, in terms of representativeness of real buildings, mainly due to two aspects: the units of masonry are not exactly the same as the existing buildings and the mortar may also not be very representative of the bonding material. For this reason, the in-situ testing represents an excellent test methodology but on the other side it is a challenge for the scientific community, given the need to mobilize equipment and structures suitable for the test. In terms of in-situ mechanical characterization of stone masonry, Italy has been a pioneer with many researches: Borri et al. (2011), Corradi et al. (2008), Lagomarsino et al. (2009). Their main objective is the classification of the types of buildings in order to create mechanical models. The mechanical characterization has been focused on the mean values of shear and compression strength of double skin masonry of limestone and brick. 2.5.1 Out-of-Plane Behavior The walls subjected to out-of-plane loading are known as “flexural wallsâ€? because the flexure is the predominant effort. The out-of-plane behavior is considerably more complex than inplane behavior. The walls may be subjected to flexure in two directions which becomes statically indeterminate, as shown in Figure 2.5.1. The analysis of these walls is extremely complicated because the tensile strength in horizontal flexure can be several times greater than strength in vertical flexure (Drysdale et al., 1999). This difference can occur because the vertical flexure depends basically on the tensile bond strength of the unit-mortar interface of the bed joints, whereas the horizontal flexure depends on the friction resistance of the bed joints and on the tensile bond strength at vertical joint interface (Lourenço, 2001).
25
Chapter 2 - STATE OF ART
Figure 2.5.1 - Flexure in two directions of a wall subject to out-of-plane loading.
The behavior of flexural walls depends mainly on the boundary conditions of the masonry panel. In unreinforced masonry walls supported on four sides, the vertical bending moment at mid-height of the wall induces tensile stresses perpendicular to the bed joints. When these stresses are higher than the tensile strength, a horizontal crack initiates and the behavior of the cracked wall depends upon the orthogonal flexural strength of the masonry. If the vertical flexure strength is equal to the horizontal flexure strength, there is no additional strength. The crack propagates along the bed joint and the mechanism is immediately formed with only a small residual strength due to the self-weight. In general case, in which the horizontal flexural strength is greater than the vertical strength, a crack propagates along the bed joint under constant load and a stable state is reaches. The panel (ideally) consists of two sub-panels, each simply supported along three sides and free along the cracked bed joint. As load is further increased, each sub-panel behaves as described previously until diagonal cracks occurs (see Figure 2.5.2). These cracks immediately propagate to form a mechanism leading to the collapse of the wall (Drysdale et al., 1999)
Figure 2.5.2 – Crack pattern at failure for walls supported on three and four edges.
The boundary conditions may increase substantially the out-of-plane resistance of masonry walls because they introduce additional compressive forces in the wall panel associated to the denominated “arching� effect, (see Figure 2.5.3). When a wall is built between and in tight contact with supports that are restrained against outward movement, elongation of the tensile
26
Chapter 2 - STATE OF ART
face due to bending cannot occur without inducing a compressive force. Under lateral load, this induced in-plane compressive force results on developing arching mechanism.
Figure 2.5.3 – Arching mechanism of masonry behaving under out-of-plane loading.
As pointed out by Moxon (2004) and Liu et al., (2004), the increase on the axial load increases the out of plane strength but also reduces the ductility. As in shear walls, the tensile strength of masonry is a central property in the flexural behavior of walls submitted to out-of-plane loading. The brittle nature of unreinforced masonry due to its low tensile strength makes it as an inadequate material to stand lateral loads as in seismic active regions. 2.5.2 Out of-Plane investigations The bending stress can be developed for in-plane and out-of-plane lateral loads applied to the wall, even if in relation to distinct stiffness conditions of the walls. The bending out-of-plane develops when the lateral action is applied in the perpendicular direction to the wall. In a seismic event it is usual that walls are loaded, both by in-plane and out-of-plane action resulting from the seismic loading. Costa et al., reported an in-situ experimental test campaign on out-of-plane testing of masonry walls, belonging to an ancient building based on selfequilibrated system, avoiding the need of an external reaction structure. The testing configuration (Figure 2.5.4) takes use of a strong wall that serves as a reaction structure, whereas the other wall is the tested element. Hydraulic devices are placed at the top of the walls and connected to them through hinged links ensuring well-known acting loads and restraint conditions (see Figure 2.5.4 b)).
27
Chapter 2 - STATE OF ART
a)
b)
Figure 2.5.4 – Test setup scheme of out of plane action: a) schematic representation; b) acting forces during the test (Costa A., Arede A., Costa A. & Oliveira C. S., 2011).
More recently Costa et al. adopted another technique using airbags for the application of distributed loading along the surface of the wall, in according to Figure 2.5.5. The reaction system was not a strong wall of the structure itself, but rather, an external structure, versatile and easy to assembly. The structure reaction was carried out with metallic tubes, attached to the reaction wall (parallel to the test wall). There are also two reaction surfaces to the airbags formed by elements of wood and plywood boards. It is applied a cyclic bidirectional distributed load, through the airbags, simulating the seismic action. These authors concluded that the double wall stone masonry tested has a high displacement capacity (approximately 180 đ?‘šđ?‘š), and the test ended by imposition the setup, which had no ability to apply higher displacements. The drift showed a maximum value of 7.45%, reflecting a high ductility of the wall. The maximum surface tension was about 6.2 đ?‘˜đ?‘ƒđ?‘Ž.
a)
b)
Figure 2.5.5 - In-situ test out-of-plane using airbags: a) Initial phase of displacement; b) Final phase of displacement (Costa A., Arede A., Costa A. & Oliveira C. S., 2012).
Dizhur et al. (2010), conducted in-situ testing in buildings affected by an earthquake in 2007 in New Zealand. These researchers presented a model for testing out-of-plane slightly different from the situations set out above. They selected a double wall brick masonry and 28
Chapter 2 - STATE OF ART
isolated a panel of the remaining wall, due to the presence of a mezzanine floor (see Figure 2.5.6 a)). This option has been taken to simplify the test and subsequent comparison of results from laboratory tests.
a)
b)
Figure 2.5.6 – Out of plane testing: a) location of the wall; b) test scheme (Dizhur et al., 2010).
These investigators adopted an airbag system adjacent to the panel for loading, leaving a gap of 50đ?‘šđ?‘š between the panel and the protective plywood structure of the airbag, enabling a correct accommodation of this, according to Figure 2.5.6 b). The plywood backing consisted of an assemblage of plywood sheets and steel angles and was supported by a reaction frame. The reaction structure has a different configuration of the test presented by Costa et al. and consists of vertical and diagonal elements of wood bolted to the floor of the wooden beams to the transfer of horizontal loads to the ground floor. The load applied from the airbags was transferred to the plywood backing and to the reaction frame using load cells, which were attached between the plywood backing and reaction frame and provided horizontal stability to the frame. To ensure that the entire load was transferred through the load cells, frictionless plates were used underneath the plywood backing. The displacement was measured using three LVDTs placed: at mid-height, at centerline, and 1000 đ?‘šđ?‘š below the top of the wall.
29
Chapter 2 - STATE OF ART
30
Chapter 3
EXPERIMENTAL PROGRAM
3.1 Introduction The present experimental campaign was carried out within the research program “INOTEC� (Innovative materials with ultra-high ductility for the rehabilitation of the built heritage), promoted by the company CiviTest in collaboration with the University of Minho. The aim of the project is to characterize and to validate an appropriate reinforcement system for schist masonry. In particular it is expected that the research will provide a practical methodology for the application of the strengthening system and it will allow also a realistic and accurate definition of the parameters of the materials adopted. These parameters are the ones necessary for the preparation of the numerical models used in the analysis and validation of this type of structures under seismic loads. The methodology considered for the development of the project consists in the combination of the following items: laboratory tests for the characterization of the adopted materials; laboratory tests for the investigation of the behavior of strengthened and un-strengthened schist masonry elements; numerical simulation with detailed finite element models.
31
Chapter 3 - EXPERIMENTAL PROGRAM
3.2 Materials properties An important aspect of this campaign involved the choice of materials and constructive methodology. In particular, traditional masonry schist walls made of schist stones connected with natural lime-based mortar were analyzed. In this first phase, a physical and mechanical characterization of the adopted materials is given in order to acquire information on the behavior of the single elements originating the schist masonry and the reinforcement system that will be applied on it. 3.2.1 Schist Stones Schist’s result from regional metamorphism, i.e., metamorphism related to deformation processes over large areas with pressure as the dominant factor and the cause of the planar preferred orientation. Variations on pressure and temperature define different regional metamorphism faces and textural variations (namely granularity). The schist stones used in the experimental campaign were collected in Ovar, in the NorthWest of Portugal. They have an irregular shape with dimensions ranging from a few centimeters up to some tens of centimeters in all directions (see Figure 3.2.1).
Figure 3.2.1 - Schist stones used.
3.2.1.1 Physical properties Over the years many authors have investigated the physico-chemical properties of the schist. An important contribution in this campaign was given by Noronha et al. (2011) who carried out some tests examining physical properties such as: water absorption at atmospheric pressure, water absorption by capillarity, density and porosity. The determination of water absorption at atmospheric pressure was carried out according to the đ??¸đ?‘ 13755 standard and compared with other type of rocks studied by Reis (2010). 32
Chapter 3 - EXPERIMENTAL PROGRAM
Rock type
Water absorption (%)
Schist 1 Granite Basalt
[0.10-2.30] 2
[0.20-0.50]
2
[0.10-0.30]
Sandstone
2
[0.20-9.00]
Limestone
2
[0.20-0.60]
Marble
2
Quarzite
[0.20-0.60] 2
[0.20-0.50]
Table 3.2.1 – Water absorption at atmospheric pressure of diverse rocks. 1Noronha et al. (2011), 2Reis(2010).
Regarding density and porosity, table 3.2.2, presents values for the schist studied by Noronha et al, as well as for different rocks. Rock type
Density (mg/m3)
Porosity (%)
[2.51-2.88]
[0.30-2.30]
[2.60-2.80]
[0.40-1.50]
Schist 1 Granite
2
Basalt 2
[2.90-3.00]
[0.30-0.90]
3
[1.30-3.60]
[0.50-40.00]
Limestone 2
[2.60-2.80]
[0.60-2.00]
[2.70-2.80]
[0.50-3.00]
[1.10-1.70]
[25.00-60.00]
Sandstone Marble
2
Quarzite 2 1
Table 3.2.2 – Density and porosity of diverse rocks. Noronha et al. (2011), 2Manuale di Progettazione Edilizia (2007), 3
Kobranova (1989).
Another important contribution was given by Barros R. S. (2013) whose studies were focused on the same properties previously mentioned but on a wide variety of schist rocks from five different regions in the North of Portugal. The values obtained in his work are presented below. Region 1st - Vila Nova de Foz Coa
Av. water absorption (%) Density (g/cm3) Porosity (%) 0.57
2.76
1.60
2 - Serra de Arga
2.99
2.53
7.40
3rd - Carrazedo de Montenegro
1.48
2.66
3.90
4 - Sobral de Sao Miguel
3.55
2.82
10.00
5th - Barqueiros
1.82
2.61
4.70
nd
th
Table 3.2.3 – Results from test of: water absorption at atmospheric pressure, density and porosity.
33
Chapter 3 - EXPERIMENTAL PROGRAM
3.2.1.2 Mechanical properties The investigation of the mechanical properties of the schist in scientific literature is mainly based on two types of test: the axial compression test and the point load test. According to the đ??¸đ?‘ 1926 standard, the test of uniaxial compressive strength allows evaluating the performance of samples placed between two parallel plates and subjected to a uniaxial load (see Figure 3.2.2).
Figure 3.2.2 – Axial compressive strength machine.
Table 3.2.4 shows the uniaxial compressive strength of schist’s from studies by Burcio and Noronha et al. It also presents the values of uniaxial compressive mechanical strength of different rocks studied by different authors. Rock type
Compressive strength (Mpa)
Schist 1
[31.00-221.00]
Granite 2
[26.00-159.80]
Basalt
3
[40.00-413.00]
Sandstone 3
[22.00-82.00]
3
[15.60-96.40]
Limestone Slate 3
[72.30-96.40]
Marble 4
[48.90-65.70] 1
Table 3.2.4 – Compressive strength of diverse rocks. Noronha et al. (2011) and Burcio (2004), 2 Vasconcelos et al. (2005), 3 Bell (2007), 4Mogi (2007).
The point load strength test consists of determining the strength of a sample to a uniaxial point charge deployed by two conical metal tips on the sample. This test has advantages over other compression tests, due to the fact that its implementation does not require prior preparation of the sample and it is possible both in situ and in laboratory (see Figure 3.2.3). 34
Chapter 3 - EXPERIMENTAL PROGRAM
Figure 3.2.3 - Point load test machine.
In the table below the values of point load strength of schist’s studied by Pinho are shown. It also presents ranges of values of the point load strength of diverse rocks. Rock type
Rebound index (Mpa)
Schist 1 Granite Basalt
[0.94-10.33] 2
[10.30-12.00]
2
[1.00-14.50]
Sandstone
2
[0.20-13.00]
Limestone
2
[1.20-3.50]
Slate 2
[4.20-7.90]
Table 3.2.5 - Point load strength of diverse rocks. 1Pinho (2003), 2Bell (2007).
The wide range of values obtained with the tests previously reported is a clear consequence of the anisotropic behavior of the schist. Indeed schist rocks, due to their geological formation, may have a great directional variability in terms of their properties such as the deformation modulus, strength, and permeability. Furthermore, due to its schistosity, schist is very difficult to cut, not only due to its fragility but also due to the existence of multiple anisotropy planes (depending on geological history). All this means that depending on the studied direction, the properties of the schist will be different. This is clearly evident in the experimental campaign carried out by Barros et al. in which he investigated samples with an anisotropy plane that was parallel to one of the faces of the sample. Therefore he considered only two test directions: the direction that is normal to the anisotropy plane and the direction that is parallel to the anisotropy plane (see Figure 3.2.4).
35
Chapter 3 - EXPERIMENTAL PROGRAM
a)
b)
Figure 3.2.4 – Test directions: a) normal to the anisotropy plane; b) parallel to the anisotropy plane.
Taking into consideration these two directions the results obtained for schist rocks coming from five different areas, showed values with appreciable variations.
Test type
1 st Area // ┴
Compressive strength [MPa] 144.9 151.9 5.0 4.8 Point load [MPa]
2 nd Area ┴ //
3 rd Area ┴ //
4 th Area ┴ //
5 th Area // ┴
46.0 45.4 1.5 1.1
79.1 98.4 1.9 1.3
53.6 29.7 2.1 0.5
142.3 88.6 4.0 1.8
Table 3.2.6 – Results from tests of mechanical characterization.
36
Chapter 3 - EXPERIMENTAL PROGRAM
3.2.2 Natural Hydraulic Lime (NHL) Mortar In traditional schist constructions, mortar plays an important role in the structural response and performance at the various mechanical stresses. Currently, in this type of buildings, different types of mortar connecting the schist stones can be found, such as lime or simple earth mortar. A natural hydraulic lime-based mortar has been used in this campaign and it was denoted with the acronym of NHLM. A physical characterization of the single components and a mechanical characterization of the behavior of the mortar will be presented in the following sections. 3.2.2.1 Composition For the realization of the mortar, adopted in the present experimental program, were used: clay with medium granulometry as aggregate, a hydraulic lime Sical HL5 as binder and water.
a)
b)
c)
Figure 3.2.5 – Components of NHLM. a) Aggregate; b) Binder; c) Final aspect.
The quantity proportions of these materials were kept similar for all the castings. In the table below three casting are reported as example. CASTING 1 Material Clay Lime H2O
CASTING 2
CASTING 3
Weight Quantity Weight Quantity Weight Quantity Average C.V [kg] [%] [kg] [%] [kg] [%] [%] [%] 85.54 79.27 85.08 82.61 82.65 78.70 80.20 2.63 12.63 11.70 12.20 11.85 13.57 12.92 12.16 5.48 9.74 9.02 5.71 5.54 8.80 8.37 7.65 24.23 Table 3.2.7 – Mortar quantity proportions.
37
Chapter 3 - EXPERIMENTAL PROGRAM
3.2.2.2 Granulometric analysis A predominant aspect in the physical characterization of the mortar used was the definition of the granulometry of its aggregate. Therefore a granulometric analysis was carried out according to đ??´đ?‘†đ?‘‡đ?‘€ đ??ˇ422. The sample, weighing 1006 đ?‘”đ?‘&#x;, was subjected to the following test steps: - washing with hands. During this procedure the sample was divided into two portions: one portion contained only particles retained on the đ?‘›Â°200 sieve (2.00 đ?‘šđ?‘š) while the other portion contained only particles passing the đ?‘›Â°200 sieve (see Figure 3.2.6 a)); - drying in oven at 110°đ??ś for at least 16 hours. With this operation, the sample has undergone a weight loss equal to the 7.6% compared to the initial weight; - sieving operation by means of a lateral and vertical motion of the sieves (see Figure 3.2.6 b)); - determination of the net weight retained on each sieve on a balance. At the end of weighing, the sum of the masses retained on all the sieves used was equal (Âą2%) to the original mass of the quantity sieved. Moreover, the weight of the particles passing the đ?‘›Â°200 sieve was less than 10 % of the total weight, therefore a sedimentation analysis was not necessary as required by the standard;
a)
b)
c)
Figure 3.2.6 - Granulometric analysis. a)particles retained on the sieve n°200; b)adopted sieves; c)sieves contents after sieving operation.
A summary table is reported below: Sample Gross Weight [g] GRANULOMETRIC ANALYSIS WITH SIEVES Tare [g] Net Weight [g]
38
2384 1454 930
Chapter 3 - EXPERIMENTAL PROGRAM
Sieve N°
1/2' 1'' 3/4'' 3/8'' 4 8 16 30 50 100 200 Bottom
Diameter Tare Sieve [mm] [g] 37.500 25.000 19.000 9.500 4.750 2.360 1.180 0.600 0.300 0.15 0.075 Bottom
Gross weight Net Weight Retained Passing Particles Retained Retained [g] [g] % %
488.0 539.0 582.0 442.0 435.0 392.0 354.0 349.0 358.0 336.0 334.0 431.0
488.0 539.0 582.0 442.0 473.0 537.0 574.0 583.0 499.0 393.0 359.0 451.0 Passing n° 200 Total
0.0 0.0 0.0 0.0 38.0 145.0 220.0 234.0 141.0 57.0 25.0 20.0 50.0 930.0
0.0 0.0 0.0 0.0 4.1 15.6 23.7 25.2 15.2 6.1 2.7 2.2
100.0 100.0 100.0 100.0 95.9 80.3 56.7 31.5 16.3 10.2 7.5 5.4
94.6
Table 3.2.8 - Summary table of the granulometric analysis.
Based on the data obtained it was possible to draw the granulometric curve:
Granulometric Curve 100 90 80 Passing Particles %
70 60 50 40 30 20 10 0 100.0
10.0
1.0
0.1
0.0
Sieve Diameter[mm]
2 Gravel
0.075 Sand
Silt
Figure 3.2.7 - Granulometric Curve.
39
Chapter 3 - EXPERIMENTAL PROGRAM
3.2.2.3 Mechanical properties The mechanical properties of the NHLM were assessed according to the đ??śđ??¸đ?‘ 2007 − đ??¸đ?‘ 1015 − 11. The preparation, storage, testing and analysis are all explained in detail in the code. From each casting, reported in Table 3.2.7, three samples (dimensions: 160 Ă— 40 Ă— 40 đ?‘šđ?‘š3 ) were obtained filling special metal molds with NHLM (see Figure 3.2.8). The internal faces of these molds were previously lubricated with a thin layer of mineral oil to prevent the adhesion of the mortar.
Figure 3.2.8 – Molds casted.
The specimens casted were then tested by means of compressive and flexural tests at different curing ages (28, 60, 127 days) in order to evaluate the development of strength over the time and to allow a comparison with the other tests performed in this campaign. 3.2.2.3.1 Flexural Strength Three prisms for each age studied were tested. Flexural tests were performed in the machine đ?‘€đ?‘–đ?‘?đ?‘&#x;đ?‘œđ?‘Ąđ?‘’đ?‘ đ?‘Ą đ??¸đ?‘€2/500/đ??šđ?‘… with a load cell of 10 đ?‘˜đ?‘ . The test were performed in displacement control, with a velocity of 0.2 đ?‘šđ?‘š/min. The only measured quantities were the actuator force and his displacement. The experimental setup for the flexural test is shown in the figure below:
40
Chapter 3 - EXPERIMENTAL PROGRAM
Figure 3.2.9 – Flexural strength test setup.
The results are presented in the next table.
Age
Sample
1_1NHLM 28 days 2_1NHLM 3_1NHLM 1_2NHLM 60 days 2_2NHLM 3_2NHLM 1_3NHLM 127 days 2_3NHLM 3_3NHLM
Test values Density F ult Ďƒ ult [kN/m3] [kN] [MPa] 18.20 0.099 0.232 18.20 0.104 0.244 18.28 0.100 0.234 17.93 0.099 0.232 18.24 0.131 0.307 18.16 0.135 0.316 18.16 \ \ 18.13 0.107 0.251 17.77 0.173 0.405
Report values Density F ult Ďƒ ult AVG C.V. [%] Avg C.V. [%] Avg C.V. [%] 18.23
0.25
0.101
2.62
0.237
2.62
18.11
0.90
0.122
16.22
0.285
16.22
18.02
1.19
0.140
33.34
0.328
33.34
Table 3.2.9 – Flexural strength results.
During the following ages examined, the resistance has reached a value of 0.328 đ?‘€đ?‘ƒđ?‘Ž at 127 days, i.e., an increase of 38.6% compared to the initial value at 28 days. Further considerations on the results obtained are shown in the table below. Average values Variation Density F ult Ďƒ ult Density F ult Ďƒ ult Age Mold [kN/m3] [kN] [MPa] [%] [%] [%] 28 days 1NHLM 18.23 0.101 0.237 0.0 0.0 0.0 60 days 2NHLM 18.11 0.122 0.285 -0.6 20.5 20.5 127 days 3NHLM 18.02 0.140 0.328 -1.1 38.6 38.6 Table 3.2.10 – Results variation over the time.
In order to better evaluate the development of the flexural strength of mortar with the time, the results presented above are shown in a graph:
41
Chapter 3 - EXPERIMENTAL PROGRAM 0.34 Flexural Strength [MPa]
0.32 0.30 0.28 0.26 0.24 0.22 0.20 0
20
40
60
80
100
120
140
Age [days]
Figure 3.2.10 - Evolution of the flexural strength of NHLM over time
3.2.2.3.2 Compressive Strength Compression tests on the two fragments produced by each flexion test were performed to obtain the compressive strength of the mortar. The tests were performed in the machine đ?‘€đ?‘–đ?‘?đ?‘&#x;đ?‘œđ?‘Ąđ?‘’đ?‘ đ?‘Ą đ??¸đ?‘€2/500/đ??šđ?‘… with a load cell of 100 đ?‘˜đ?‘ . Once again the test modality was in displacement control but the velocity was lower than the flexural test: 0.1 đ?‘šđ?‘š/min. The only measured quantities were the actuator force and his displacement. The experimental setup for the compressive test is shown in Figure 3.2.11:
Figure 3.2.11 - Compressive strength test setup.
The results are presented in the next table.
42
Chapter 3 - EXPERIMENTAL PROGRAM
Age
Sample
1A_1NHLM 1B_1NHLM 2A_1NHLM 28 days 2B_1NHLM 3A_1NHLM 3B_1NHLM 1A_2NHLM 1B_2NHLM 2A_2NHLM 60 days 2B_2NHLM 3A_2NHLM 3B_2NHLM 1A_3NHLM 1B_2NHLM 2A_3NHLM 127 days 2B_3NHLM 3A_3NHLM 3B_3NHLM
Test values Density F ult Ďƒ ult [kN/m3] [kN] [Mpa] 18.75 3.08 1.13 18.47 2.91 1.07 18.94 3.12 1.18 18.37 2.66 1.01 18.47 2.73 1.03 18.56 2.46 0.95 17.99 2.80 1.06 18.28 3.23 1.22 18.49 3.85 1.32 18.85 3.07 1.22 18.55 2.60 1.05 18.21 3.26 1.18 20.90 5.85 2.18 21.69 6.91 2.54 19.20 5.86 2.12 19.30 7.41 2.32 19.56 7.05 2.29 19.02 6.08 2.20
Report values Density F ult Ďƒ ult AVG C.V. [%] AVG C.V. [%] AVG C.V. [%]
18.59
1.14
2.83
9.07
1.06
8.05
18.39
1.63
3.14
13.82
1.18
8.84
19.94
5.46
6.53
10.40
2.28
6.49
Table 3.2.11 – Compression test results.
The dispersion of results is quite small, therefore tests can be considered satisfactory. Moreover an evaluation of the Young’s modulus was carried out analyzing the linear-elastic portion of the đ?œŽ − đ?œ€ curves. Probably due to the size of the samples, it is possible that this measure underestimates the real value of Young’s Modulus. In fact usually the specimens used for the assessment of Young’s modulus are bigger and do not undergo an interference of the steel plates, as in this case.
Age
Sample
1A_1NHLM 1B_1NHLM 2A_1NHLM 28 days 2B_1NHLM 3A_1NHLM 3B_1NHLM 1A_2NHLM 1B_2NHLM 2A_2NHLM 60 days 2B_2NHLM 3A_2NHLM 3B_2NHLM
Young's Modulus [Mpa] AVG C.V. [%] 55.06 53.18 78.67 58.06 20.75 65.77 47.50 48.19 47.63 60.84 67.63 58.15 11.38 59.74 55.27 57.76 43
Chapter 3 - EXPERIMENTAL PROGRAM
1A_3NHLM 1B_2NHLM 2A_3NHLM 127 days 2B_3NHLM 3A_3NHLM 3B_3NHLM
76.63 101.72 64.28 75.55 68.73 56.31 85.62
21.60
Table 3.2.12 - Young's Modulus Evaluation.
The NHLM exhibited an increase of the compressive strength at 127 days equal to 114.3% as shown in the next table. Average values Density F ult Ďƒ ult Age Mold [kN/m3] [kN] [MPa] 28 days 1NHLM 18.59 2.83 1.06 60 days 2NHLM 18.39 3.14 1.18 127 days 3NHLM 19.94 6.53 2.28
Variation Density F ult Ďƒ ult E [Mpa] [%] [%] [%] 0.0 0.0 0.0 58.06 10.9 10.6 58.15 -1.1 7.3 130.9 114.3 75.55
E [%] 0.0 0.1 30.1
Table 3.2.13 - Results variation over the time.
In order to better evaluate the development of the compressive strength of mortar with the time, the results presented above are shown in a graph:
Compressive strength [MPa]
2.5 2.1 1.7 1.3 0.9 0.5 0
20
40
60
80
100
120
Age [days]
Figure 3.2.12 - Evolution of the compressive strength of NHLM over time
44
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Chapter 3 - EXPERIMENTAL PROGRAM
3.2.3 Fiber Reinforced Mortar (FRM) The reinforced mortar used in the experimental campaign has been developed within the project “INOTECâ€? promoted by the company CiviTest in collaboration with the University of Minho. It is a fiber-reinforced mortar created with the purpose of structural reinforcement of cultural heritage therefore, in this experimental program, an application on the typical historical schist masonry has been investigated. Particular attention has been paid in the definition of the physical-mechanical characteristics of the mortar when subjected to vertical casting, in fact, the typical intervention technique on historical masonry involves the application of such mortar via spray. In the next sections this type of mortar will be indicated with the acronym of FRM. 3.2.3.1 Composition Base components for the FRM are: cement, fly ash, fine sand, water, various types of fibers and additives. The cement used is the 42.5đ?‘… cement type I, it has suitable characteristics for FRM as: moderate to low heat hydration allows an appropriate fluidity and hence a lower heat of hydration helping to maintain the rheological characteristics required for projection for a while. The fly ash due to the pozzolanic properties can partially replace cement. Their spherical shape allows for a greater fluidity of the composition of the RFM. The fine sand has as main feature the ability to provide a mixture filling compact, contributing to decrease the capillarity and permeability of the mixing. The composition adopted was made up of: Cement type I 42.5đ?‘…, fly ash, fine sand , water, super plasticizer (Sika Viscocrete 3002), viscosity controller (VMA), glass fiber and PP fiber (polypropylene). The quantities adopted are reported in the table below: Quantity Material Percentage [kg] [%] Cement 42.5R 546.50 25.13 Fly ash 668.75 30.75 H2O 389.83 17.93 Sand 437.17 20.10 VMA 3.42 0.16 SP3002 21.00 0.97 Glass Fiber 96.00 4.41 PP Fiber 11.90 0.55 Total 2174.57 100.00 Material
Table 3.2.14 – Adopted composition (per m3 of FRM).
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Chapter 3 - EXPERIMENTAL PROGRAM
a)
b)
c)
Figure 3.2.13 – FRM composition. a) components; b) glass fibers; c) final aspect.
In this phase of the campaign, the main object was the optimization of the mixture in order to present rheological, mechanical and materials properties appropriate for the projection of mortars for the rehabilitation of structures made up of brittle materials. 3.2.3.2 Adhesive strength: Pull off test A first study dealt with FRM has been the investigation of the adhesion between this mortar and a schist substrate. The assessment has been addressed through the pull-off test method, i.e., one of the tensile test methods commonly used to assess the adhesion between the repair overlay and the existing substrate. Principles, apparatus, samples preparation and test procedures are carefully illustrated in the đ??¸đ?‘ 1015 − 12, reference document for experiments in coatings. The test technique consisted in the application of a tensile load, applied by means of a defined pull-head plate glued with epoxy resin to the test area of the mortar surface. First of all, an adequately big rock was chosen in order to obtain at least 5 specimens as required into the standard. In addition, the rock presented a surface as flat and smooth as possible so that the applied layer of FRM had a thickness as homogeneous as possible. The thickness of the mortar layer was approximately 20 đ?‘šđ?‘š.
a)
b)
c)
Figure 3.2.14 – Sample preparation: a) Stone cleaned; b)Creation of the mold; c)FRM layer thickness.
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Chapter 3 - EXPERIMENTAL PROGRAM
As shown in Figure 3.2.15, seven test specimens were obtained respecting the constraints imposed by the standard, i.e., the minimum distance between the rings and the free edges of the rendered substrate, and the free distance between the individual rings shall be 50đ?‘šđ?‘š.
Figure 3.2.15 – Sample preparation.
The preparation of the test areas was performed cutting the reinforced layer of FRM with a core drilling machine until a depth of approximately 2 đ?‘šđ?‘š into the substrate. Before this operation a very thin layer was removed from the surface in order to remove oil, free particles, dust and produce a regular surface. The test areas presented circular shape of approximately 50 đ?‘šđ?‘š of diameter. Moreover the pull-heads were glued centrally on the test areas, preventing any excess adhesive from bridging the cut around the test areas.
Figure 3.2.16 – Pull-heads glued to the FRM layer.
Afterwards tensile load was applied perpendicularly to the test area through the pull-head plates. A đ??ˇđ?‘Śđ?‘›đ?‘Ž 216 test machine was used to carry out the test (see Figure 3.2.17). The load was applied without shock and at uniform rate according to the table 2 of the đ??¸đ?‘ 1015 − 12 reported in the table below:
47
Chapter 3 - EXPERIMENTAL PROGRAM
Expected adhesive strength [N/mm2] < 0.2 0.2 to < 0.5 0.5 to 1.0 >1.0
Loading rate [N/mm2s] 0.003 to 0.010 0.011 to 0.025 0.026 to 0.050 0.050 to 0.100
Table 3.2.15 - Loading rate.
Figure 3.2.17 â&#x20AC;&#x201C; Proceq Dyna 216 test machine.
During the tests the failure loads were noted for each samples. Therefore the individual adhesive strengths (đ?&#x2018;&#x201C;đ?&#x2018;˘ ) were calculated as the quotient between the failure load (đ??šđ?&#x2018;˘ ) and the test area (đ??´): đ?&#x2018;&#x201C;đ?&#x2018;˘ =
đ??šđ?&#x2018;˘ đ??´
At this point, the assessment of the adhesive strength was carried out by evaluating the different fracture patterns recorded at the end of each test. In fact, as shown in Figure 3.2.18 the failure can occur in three different types: a) Adhesion fracture: fracture at the interface between mortar and substrate. Therefore test value equals the adhesive strength; b) Cohesion fracture: fracture in the mortar itself. The adhesive strength is greater than the test value. Therefore the result shall be considered as lower bound value; c) Cohesion fracture: fracture in the substrate material. The adhesive strength is greater than the test value. Therefore the result shall be considered as lower bound value;
a)
b)
c)
Figure 3.2.18 â&#x20AC;&#x201C; Fracture patterns. 1-Pull-head plate; 2 â&#x20AC;&#x201C; adhesive layer; 3 â&#x20AC;&#x201C; mortar; 4 â&#x20AC;&#x201C; substrate.
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The adhesive strength was obtained as the mean value from the individual values of the specimens to the nearest 0.1 đ?&#x2018; /đ?&#x2018;&#x161;đ?&#x2018;&#x161;2 . The results of the test are presented below: Test Pull Off - Results Sample n° 1 2 3 4 5 6 7
Diameter [mm] 50.0 50.0 50.0 50.0 50.0 50.0 50.0
Area Duration Fu Fracture Type [mm2] [s] [kN] 1963.5 135.4 3.92 cohesion 1963.5 127 3.65 cohesion 1963.5 58 1.65 adhesion 1963.5 35.6 0.79 adhesion 1963.5 35.7 1.33 adhesion 1963.5 41 1.27 adhesion 1963.5 - incorrect coring
fu [MPa] 1.996 Not considered 1.859 Not considered 0.840 0.402 0.677 0.647 -
Average 0.64 Std.dev 0.18 Coeff. Variation 28.17 Table 3.2.16 - Pull off test results.
Figure 3.2.19 â&#x20AC;&#x201C; Different samples fracture.
According to Bonaldo E. (2005), a notable limitation of this type of test is its relative poor precision, evidenced by the large variation values obtained with different types of apparatus. Since pull off strength depend on instrumental parameters, results obtained from different devices may not be comparable. 49
Chapter 3 - EXPERIMENTAL PROGRAM
3.2.3.3 Projection technology of FRM The projection method of fiber-reinforced mortar is standardized in many countries; in Europe there are several standards that address the projection of this type of material. The ones that stand out most are đ??ľđ?&#x2018;&#x2020; đ??¸đ?&#x2018; 14487: â&#x20AC;&#x153;Sprayed concreteâ&#x20AC;? and đ??ľđ?&#x2018;&#x2020; đ??¸đ?&#x2018; 14488: â&#x20AC;&#x153;Testing sprayed concreteâ&#x20AC;?. The use of mortars reinforced with fibers in USA is a reality with a few decades, initially with the use of metallic fibers and more recently with the addition of synthetic fibers, the report of the American Concrete Institute â&#x20AC;&#x153;đ??´đ??śđ??ź 506. 1đ?&#x2018;&#x2026; â&#x2C6;&#x2019; 98: Report on Fiber Reinforced Shotcreteâ&#x20AC;? is a evidence of this practice. Based on the documents reported above a wide investigation of this technique applied to the FRM material was carried out. Therefore, particular attention has been given to the analysis of the most appropriate composition of this mortar. Indeed, the presence of super plasticizers, viscosity controller and additives (see Table 3.2.14) has led to obtain a material that has characteristics compatible for the spray system. Furthermore, the use of appropriate equipment has allowed to make the spray technique even more efficient. In particular, the adopted system, provided the combined use of: đ??źđ?&#x2018;&#x20AC;đ??¸đ?&#x2018;&#x2026; 120 đ?&#x2018;?đ?&#x2018;&#x2122;đ?&#x2018;˘đ?&#x2018; mixer, đ?&#x2018;&#x2021;đ?&#x2018;&#x2C6;đ?&#x2018;&#x2026;đ??ľđ?&#x2018;&#x201A;đ?&#x2018;&#x2020;đ?&#x2018;&#x201A;đ??ż đ?&#x2018;&#x2021;7 spraying machine connected to a compressor đ?&#x2018;&#x192;đ??¸đ?&#x2018;&#x2026;đ??źđ??şđ?&#x2018;&#x201A; đ?&#x2018;&#x2026;đ?&#x2018;&#x2C6;đ??ľđ??¸đ?&#x2018;&#x2021;đ??¸ 24đ?&#x2018;&#x2026;2 (see Figure 3.2.20). The FRM when mixed was channeled into the pomp and sprayed with a pressure of 8 đ?&#x2018;?đ?&#x2018;&#x17D;đ?&#x2018;&#x; and a velocity of 360 đ??żđ?&#x2018;Ą/đ?&#x2018;&#x161;đ?&#x2018;&#x2013;đ?&#x2018;&#x203A;.
a)
b)
c)
Figure 3.2.20 - Spray equipment: a)IMER 120 plus mixer; b)TURBOSOL T7 spraying machine; c) RUBETE R24 compressor.
3.2.3.3.1 Casting For the assessment of mechanical properties of FRM, subjected to spray system, the first problem faced was the casting from which to obtain test samples. With this intent, it was decided to carry out an area of sprayed mortar with dimensions approximately 1 Ă&#x2014; 1 đ?&#x2018;&#x161;2 and a thickness of 0.03 đ?&#x2018;&#x161;. However, given the extreme complexity 50
Chapter 3 - EXPERIMENTAL PROGRAM
of the spray system (correct mix, pressure, distance between the operator and the surface), several attempts were made. A first attempt was to achieve such surface spraying the mortar on four steel molds, each with dimensions of 0.6 Ă&#x2014; 0.6 đ?&#x2018;&#x161;2 , arranged in vertical position (see Figure 3.2.21).
a)
b)
Figure 3.2.21 â&#x20AC;&#x201C; First attempt: a)Steel molds in vertical position; b)Spraying operation.
However, the complete absence of roughness of the mold surfaces caused the slipping of the mortar that did not stick to the surface although the pressure was increased until the maximum value (8 đ?&#x2018;?đ?&#x2018;&#x17D;đ?&#x2018;&#x;) and the operator reduced, as much as possible, the distance between him and the sprayed surface.
Figure 3.2.22 - Slipping of the mortar
Therefore a second attempt was made spraying on four plywood panels with the same area and arranged vertically (see Figure 3.2.23).
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Chapter 3 - EXPERIMENTAL PROGRAM
a)
b)
Figure 3.2.23 - Second attempt: a)Plywood panels; b)Spraying operation.
In this case the surface roughness was greater than that one of the previous molds so the mortar adhered to the support, however, once exceeded the thickness of 1 đ?&#x2018;?đ?&#x2018;&#x161; occurred that the mortar detached itself from the plywood panel because of its weight. For this reason more layers were sprayed, until the thickness of 3 đ?&#x2018;?đ?&#x2018;&#x161; was reached. These layers were sprayed at intervals of, at least 12 hours so that the mortar became more solid. The result also in this case was not positive since the mortar detached itself because of the presence of voids. Another attempt was made repeating the above procedure on a plywood panel with dimension of 0.7 Ă&#x2014; 1.4 đ?&#x2018;&#x161;2.
a)
b)
Figure 3.2.24 - Third attempt: a) Plywood panel; b) Spraying operation.
In this case, an important operation was introduced: after the spraying of each layer a roller was passed on the surface in order to compact the mortar and decrease the voids. The roller
52
Chapter 3 - EXPERIMENTAL PROGRAM
was passed only in vertical direction (from the bottom to the top of the panel) to give a preferential orientation of the fibers.
Figure 3.2.25 â&#x20AC;&#x201C; Surface treated with the roller.
The final result is reported in the figure below.
Figure 3.2.26 - Final panel â&#x20AC;&#x201C; dimensions 0.7 x 1.4 m2.
3.2.3.3.2 Flexural Strength The assessment of the flexural strength of the FRM, when subjected to vertical casting was performed by means of 4 points bending test, according to đ??´đ?&#x2018;&#x2020;đ?&#x2018;&#x2021;đ?&#x2018;&#x20AC; đ??ś1609. The testing samples with a cross section approximately of 6 Ă&#x2014; 3 đ?&#x2018;?đ?&#x2018;&#x161;2 and length of about 27 đ?&#x2018;?đ?&#x2018;&#x161;, were obtained cutting the panel created with the vertical casting (see Figure 3.2.27). In particular in order to investigate the behavior of the FRM in different directions, samples were cut with an inclination of 0°, 30°, 45°, 60°, 90° compared to the direction applied with the roller. In this way, it was possible to understand if the fiber, when subjected to spray, had a preferential disposition and therefore the material presented a stronger behavior in one direction than in another. 53
Chapter 3 - EXPERIMENTAL PROGRAM
a)
b)
Figure 3.2.27 â&#x20AC;&#x201C; Samples preparation: a) Available surface; b) layout of the strips.
The 4 points bending test was performed in the machine đ?&#x2018;&#x20AC;đ?&#x2018;&#x2013;đ?&#x2018;?đ?&#x2018;&#x;đ?&#x2018;&#x153;đ?&#x2018;Ąđ?&#x2018;&#x2019;đ?&#x2018; đ?&#x2018;Ą đ??¸đ?&#x2018;&#x20AC;2/500/đ??šđ?&#x2018;&#x2026; with a load cell of 10 đ?&#x2018;&#x2DC;đ?&#x2018; . The tests were performed in displacement control, with a velocity of 0.2 đ?&#x2018;&#x161;đ?&#x2018;&#x161;/min. The measured quantities were the actuator force, his displacement and the displacements registered by a LVDT positioned in the middle of each sample as shown in Figure 3.2.28. The specimens casted were then tested at 28 and 50 days age of curing.
Figure 3.2.28 - 4 point bending setup (dimensions in cm).
Each sample before being tested was measured and weighed. The results for the samples at 28 days are shown below: Angle Sample
0° 30° 54
1_FRM 2_FRM 3_FRM 1_FRM 2_FRM
Weight Length Width Height Density [kg] [mm] [mm] [mm] [kN/m3] 0.641 270 54 25 17.59 0.822 270 60 31 16.37 0.811 270 57.5 31 16.85 0.761 272 59 27.5 17.24 0.899 272 59 33 16.98
Chapter 3 - EXPERIMENTAL PROGRAM
1_FRM 2_FRM 3_FRM 1_FRM 2_FRM 1_FRM 2_FRM 3_FRM
45° 60° 90°
1.143 1.202 1.08 0.905 0.932 1.007 0.984 0.926
274 267 263 270 270 273 272 274
61 61 58 55 57 59 59 56
42 44 43 36 34 38 38 36
16.28 16.77 16.47 16.93 17.81 16.45 16.14 16.76
Table 3.2.17 â&#x20AC;&#x201C; Vertical casting - Geometrical properties at 28 days.
Afterwards, using the following equation, the flexo-traction strength was calculated at the different curing ages: đ??š â&#x2C6;&#x2122;đ?&#x2018;? đ?&#x2018;&#x20AC; = 2 2 đ?&#x153;&#x17D;= đ?&#x2018;&#x160; đ??żâ&#x2C6;&#x2122;â&#x201E;&#x17D; 6 where: đ??&#x2C6; â&#x20AC;&#x201C; flexo-traction strength; đ?&#x2018;´ â&#x20AC;&#x201C; moment; đ?&#x2018;ž â&#x20AC;&#x201C; flexural modulus; đ?&#x2018; â&#x20AC;&#x201C; applied force; đ?&#x2019;&#x192; â&#x20AC;&#x201C; distance between the point load and the support; đ?&#x2018;ł â&#x20AC;&#x201C; width of the sample; đ?&#x2019;&#x2030; â&#x20AC;&#x201C; thickness.
Angle Sample
0° 30° 45° 60° 90°
1_FRM 2_FRM 3_FRM 1_FRM 2_FRM 1_FRM 2_FRM 3_FRM 1_FRM 2_FRM 1_FRM 2_FRM 3_FRM
Test values FMAX Ď&#x192;MAX [kN] [Mpa] 1.40 9.98 2.36 9.81 2.13 9.27 1.52 8.19 1.69 6.31 2.78 6.19 3.12 6.35 2.28 5.10 2.20 7.42 2.25 8.19 1.96 5.53 1.28 3.61 1.48 4.88
Report Values F MAX Ď&#x192; MAX AVG C.V. [%] AVG C.V. [%] 1.97
25.37
9.69
3.85
1.61
7.40
7.25
18.28
2.73
15.54
5.88
11.54
2.23
1.43
7.80
6.98
1.57
22.26
4.68
20.84
Table 3.2.18 - Results vertical casting at 28 days
Moreover, this test method provides for the determination of the stress-deflection curves reported in the next figure.
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Chapter 3 - EXPERIMENTAL PROGRAM
Stress - Displacement (middle) - 28 days 12 1_FRM_0° 2_FRM_0°
10
3_FRM_0° 1_FRM_30°
σ [MPa]
8
2_FRM_30° 1_FRM_45°
6
2_FRM_45° 4
3_FRM_45° 1_FRM_60°
2
2_FRM_60° 1_FRM_90°
0
2_FRM_90° 0
1
2
3
4
5
6
3_FRM_90°
Displacement [mm] Figure 3.2.29 – Stress – Displacement behavior at 28 days.
The same operations were repeated for the samples at 50 days, however in this case, the absolutely casual presence of voids has revealed to be so significant as to disturb the reader’s comprehension. Thus, it was decided to report the tests data obtained from the 50 days samples in Annex A and consider more reliable the ones obtained at 28 days. In particular this decision is even more justified by the table showed below that highlights that all the 50 days specimens are more lightweight than the 28 days specimens due to the higher presence of voids. In conclusion, the behavior showed in Figure 3.2.29 will be considered representative of the FRM vertical casted, however a numerical comparison with the data obtained at 50 days of curing will not be avoided in next sections in order to demonstrate how the voids presence influences the flexural strength.
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Chapter 3 - EXPERIMENTAL PROGRAM
28 days Angle Sample 1_FRM 2_FRM 3_FRM 1_FRM 2_FRM 1_FRM 2_FRM 3_FRM 1_FRM 2_FRM 3_FRM 1_FRM 2_FRM 3_FRM
0° 30° 45° 60° 90°
50 days
Density Average Density Average [kN/m3] [Mpa] [kN/m3] [Mpa] 17.59 16.30 16.37 16.93 15.65 15.92 16.85 15.83 17.24 15.49 17.11 15.15 16.98 14.81 16.28 15.48 16.77 16.51 15.76 15.72 16.47 15.92 16.93 16.42 17.37 17.81 14.40 15.69 \ 16.26 16.45 15.51 16.14 16.45 13.23 14.37 16.76 14.38
Increment Density Average [%] [%] -7.33 -4.37 -5.96 -6.09 -10.18 -11.47 -12.78 -4.95 -6.05 -4.77 -3.30 -3.03 -19.14 -9.66 \ -5.75 -18.01 -12.64 -14.25
Table 3.2.19 - Vertical casting - density comparison.
Considering the flexo-traction strength, a brief comparison of the results obtained at different ages is provided. 28 days Angle Sample
0° 30° 45°
60°
90°
1_FRM 2_FRM 3_FRM 1_FRM 2_FRM 1_FRM 2_FRM 3_FRM 1_FRM 2_FRM 3_FRM 1_FRM 2_FRM 3_FRM
50 days
Increment
σMAX Average σMAX Average σMAX Average [Mpa] [Mpa] [Mpa] [Mpa] [%] [%] 9.98 7.84 -21.44 9.81 9.69 7.82 7.95 -20.33 -17.94 9.27 8.19 -11.64 8.19 6.16 -24.81 7.25 5.34 -26.37 6.31 4.52 -28.39 6.19 5.01 -19.12 6.35 5.88 7.01 6.05 10.44 2.86 5.10 6.13 20.10 7.42 9.77 31.70 7.80 8.19 6.87 9.01 -16.15 15.48 \ 10.40 \ 5.53 8.88 60.60 3.61 4.68 5.88 6.28 62.66 34.43 4.88 4.09 -16.11 Table 3.2.20 – Results comparison.
Comparing the data reported above in Table 3.2.19 and Table 3.2.20, what have been stated previously can be easily demonstrated. At 28 days, for instance, the FRM samples exhibited the strongest behavior at 0° but this is not maintained at 50 days in fact the values decrease with an average of 18 % due to a density decrease approximately of 6%. Another case where the randomness of the voids 57
Chapter 3 - EXPERIMENTAL PROGRAM
presence leads to obtained strange values and confuses the reader, concerns the samples 60° inclinated. In this case in fact on one hand an increase of 32% has been recorded, on the other hand the sample show a decrease of 16%. Once again, the cause of this behavior must be researched also in the density variation. Therefore in order to simplify the reading and even the comprehension of the data, it will be considered that the strongest behavior of the FRM vertical casted is that one showed by the 0° samples, whereas the weakest is exhibited by the 90° samples. A further demonstration of the voids presence can be sought in the images below that showed some samples at 50 days of curing.
Figure 3.2.30 - Presence of voids in the 50 days samples.
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Chapter 3 - EXPERIMENTAL PROGRAM
Another assessment of the flexural strength of FRM was carried out according to the đ??śđ??¸đ?&#x2018; 2007 â&#x2C6;&#x2019; đ??¸đ?&#x2018; 1015 â&#x2C6;&#x2019; 11. Three molds with the composition reported in table 3.2.14 were casted, therefore 9 samples were obtained (dimensions: 160 Ă&#x2014; 40 Ă&#x2014; 40 đ?&#x2018;&#x161;đ?&#x2018;&#x161;3 ) and then tested at different curing ages (28, 48, 104 days) in order to evaluate the development of strength over the time and to compare the results with the other tests carried out in this campaign. Three prisms for each age studied were tested in the machine đ?&#x2018;&#x20AC;đ?&#x2018;&#x2013;đ?&#x2018;?đ?&#x2018;&#x;đ?&#x2018;&#x153;đ?&#x2018;Ąđ?&#x2018;&#x2019;đ?&#x2018; đ?&#x2018;Ą đ??¸đ?&#x2018;&#x20AC;2/500/đ??šđ?&#x2018;&#x2026; with a load cell of 10 đ?&#x2018;&#x2DC;đ?&#x2018; and in displacement control, with a velocity of 0.2 đ?&#x2018;&#x161;đ?&#x2018;&#x161;/min. The only measured quantities were the actuator force and his displacement. The experimental setup is shown in the figure below:
a)
b)
Figure 3.2.31 â&#x20AC;&#x201C; 3 point bending test: a) samples; b) test setup.
The results are presented in the next table.
Age
Sample
1VC_FRM_1 28 days 1VC_FRM_2 1VC_FRM_3 2VC_FRM_1 48 days 2VC_FRM_2 2VC_FRM_3 3VC_FRM_1 104 days 3VC_FRM_2 3VC_FRM_3
Test values Density F ult Ď&#x192; ult [kN/m3] [kN] [MPa] 16.84 4.87 11.41 17.34 5.56 13.02 17.03 4.64 10.88 17.34 6.46 15.15 17.58 6.88 16.11 17.11 7.28 17.06 16.37 6.75 15.82 16.52 6.29 14.73 16.45 7.36 17.25
Report values Density F ult Ď&#x192; ult AVG C.V. [%] AVG C.V. [%] AVG C.V. [%] 17.07
1.50
5.02
9.44
11.77
9.44
17.34
1.35
6.87
5.96
16.11
5.96
16.45
0.48
6.80
7.93
15.93
7.93
Table 3.2.21 - Flexural strength test results
The dispersion of results is quite small, therefore tests can be considered satisfactory. During the following ages examined, the resistance has reached a value of 15.93 đ?&#x2018;&#x20AC;đ?&#x2018;&#x192;đ?&#x2018;&#x17D; at 104 days, 59
Chapter 3 - EXPERIMENTAL PROGRAM
i.e., an increase of 35.3% compared to the initial value at 28 days. Below, the variations of the main parameters are shown. Average values Variation Density F ult Ď&#x192; ult Density F ult Ď&#x192; ult Age Mold [kN/m3] [kN] [MPa] [%] [%] [%] 28 days 1VC_FRM 17.07 5.02 11.77 0.0 0.0 0.0 48 days 2VC_FRM 17.34 6.87 16.10 1.6 36.8 36.8 104 days 3VC_FRM 16.45 6.79 15.93 -3.7 35.3 35.3 Table 3.2.22 â&#x20AC;&#x201C; Results variation over the time
In order to better evaluate the development of the flexural strength of the FRM with the time, the results presented above are shown in a graph: 17 Flexural Strength [MPa]
16 15 14 13 12 11 10 0
20
40
60
80
100
120
Age [days]
Figure 3.2.32 - Evolution of the flexural strength of FRM over time.
3.2.3.3.3 Compressive strength Compression tests on the two fragments produced by each flexion test were performed in the machine đ?&#x2018;&#x20AC;đ?&#x2018;&#x2013;đ?&#x2018;?đ?&#x2018;&#x;đ?&#x2018;&#x153;đ?&#x2018;Ąđ?&#x2018;&#x2019;đ?&#x2018; đ?&#x2018;Ą đ??¸đ?&#x2018;&#x20AC;2/500/đ??šđ?&#x2018;&#x2026; with a load cell of 100 đ?&#x2018;&#x2DC;đ?&#x2018; . The test modality was displacement control with a velocity of 0.1 đ?&#x2018;&#x161;đ?&#x2018;&#x161;/min. The measured quantities were the actuator force and his displacement.
Age
Sample
1VC_RFM_1A 1VC_RFM_1B 1VC_RFM_2A 28 days 1VC_RFM_2B 1VC_RFM_3A 1VC_RFM_3B 60
Test values Report values Density F ult Ď&#x192; ult Density F ult Ď&#x192; ult [kN/m3] [kN] [Mpa] AVG C.V. [%] AVG C.V. [%] AVG C.V. [%] 17.52 66.01 25.00 16.95 64.53 24.44 17.81 61.20 25.50 17.26 2.15 67.43 6.87 25.73 5.45 16.94 74.41 24.48 16.94 67.98 27.41 17.38 70.44 27.52
Chapter 3 - EXPERIMENTAL PROGRAM
2VC_RFM_1A 2VC_RFM_1B 2VC_RFM_2A 48 days 2VC_RFM_2B 2VC_RFM_3A 2VC_RFM_3B 3VC_RFM_1A 3VC_RFM_1B 3VC_RFM_2A 104 days 3VC_RFM_2B 3VC_RFM_3A 3VC_RFM_3B
17.11 17.60 17.53 17.80 17.16 16.77 18.43 18.01 17.98 18.05 17.92 19.03
73.15 95.72 87.56 91.61 71.19 96.94 91.68 73.59 71.98 91.13 95.52 91.71
29.98 31.49 30.40 17.33 31.81 28.25 31.27 29.77 27.06 27.68 18.24 28.48 31.84 34.74
2.18
86.03
13.07
30.53
4.30
2.36
85.94
12.01
29.93
9.71
Table 3.2.23 - Compression strength results.
Moreover an evaluation of the Youngâ&#x20AC;&#x2122;s modulus was carried out analyzing the linear-elastic portion of the đ?&#x153;&#x17D; â&#x2C6;&#x2019; đ?&#x153;&#x20AC; curves. Also in this case, as for the NHLM the consideration on this evaluation are the same. The results are presented in the next table. Age
Sample
1VC_RFM_1A 1VC_RFM_1B 1VC_RFM_2A 28 days 1VC_RFM_2B 1VC_RFM_3A 1VC_RFM_3B 2VC_RFM_1A 2VC_RFM_1B 2VC_RFM_2A 48 days 2VC_RFM_2B 2VC_RFM_3A 2VC_RFM_3B 3VC_RFM_1A 3VC_RFM_1B 3VC_RFM_2A 104 days 3VC_RFM_2B 3VC_RFM_3A 3VC_RFM_3B
Young's Modulus [Mpa] AVG C.V. [%] 887.68 835.06 918.38 896.72 5.18 859.52 913.98 965.67 1122.53 1082.23 1107.68 1094.45 6.55 966.23 1184.16 1103.86 1660.17 1629.65 1683.26 1656.31 2.36 1672.92 1699.15 1592.73
Table 3.2.24 - Young's Modulus evaluation.
As for the flexural test, the dispersion of results is small, therefore the tests can be considered satisfactory. The FRM exhibited an increase of the compressive strength at 104 days equal to 16.3%. Further consideration on the variations of the results are shown below:
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Average values Variation Density F ult σ ult Density F ult σ ult E E Age Mold [kN/m3] [kN] [MPa] [Mpa] [%] [%] [%] [%] 28 days 1VC_FRM 17.26 67.43 25.73 896.72 0.0 0.0 0.0 0.0 48 days 2VC_FRM 17.33 86.03 30.53 1094.45 0.4 27.6 18.7 22.1 104 days 3VC_FRM 18.24 85.94 29.93 1656.31 5.7 27.4 16.3 84.7 Table 3.2.25 – Results variation over time.
The variation of the compressive strength over the time is reported in the figure below:
Compressive Strength [MOa]
31 30 29 28 27 26 25 0
20
40
60
80
100
Age [days]
Figure 3.2.33 - Evolution of the compressive strength of FRM over time.
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3.2.3.4 Normal casting In order to compare the properties obtained from the sprayed samples, two steel molds with dimensions of 0.6 Ă&#x2014; 0.6 đ?&#x2018;&#x161;2 were carried out with traditional casting, i.e., with the molds horizontally positioned on the ground (see Figure 3.2.34a)). Afterwards, samples were obtained cutting the panels according to the geometry shown in Figure 3.2.34b). The samples cross section were approximately of 6 Ă&#x2014; 3 đ?&#x2018;?đ?&#x2018;&#x161;2 and length of about 27 đ?&#x2018;?đ?&#x2018;&#x161;. As for the vertical casting, the samples were cut with different inclination 0°, 30°, 45°, 60°, 90° in order to investigate the isotropy of the material.
a)
b)
c)
Figure 3.2.34 - Normal casting: a) Steel molds; b) samples orientation; c) samples cut.
Similarly to what stated at § 3.2.3.3.2, the assessment of the flexural strength was carried out by means of 4 point bending test according to the đ??´đ?&#x2018;&#x2020;đ?&#x2018;&#x2021;đ?&#x2018;&#x20AC; đ??ś1609. The test setup and the test ages were kept equal to that seen for the sprayed samples. At first, a physical and geometrical analysis of the samples were executed. The results obtained for the samples at 28 days are reported in next table:
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Angle Sample
0° 30° 45° 60° 90°
1_FRM 2_FRM 3_FRM 1_FRM 2_FRM 1_FRM 2_FRM 3_FRM 1_FRM 2_FRM 1_FRM 2_FRM 3_FRM
Weight Length Width Height Density [kg] [mm] [mm] [mm] [kN/m3] 0.815 273 62 28 17.20 0.833 274 58 30 17.47 0.862 274 58 31 17.50 1.001 272 61 35 17.24 1.016 265 61 36 17.46 0.974 267 64 32.5 17.54 0.935 268 65 33 16.26 0.962 268 60 34 17.60 0.877 271 56 33 17.51 0.88 272 56.5 33 17.35 0.87 271 57 32 17.56 0.91 270 60 32.5 17.23 0.91 271 60 32.5 17.18
Table 3.2.26 - Normal casting - geometrical analysis at 28 days
Afterwards, using the equation reported at the § 3.2.3.3.2, the flexo-traction strength were calculated:
Angle Sample
0° 30° 45° 60° 90°
1_FRM 2_FRM 3_FRM 1_FRM 2_FRM 1_FRM 2_FRM 3_FRM 1_FRM 2_FRM 1_FRM 2_FRM 3_FRM
Test values FMAX σMAX [kN] [Mpa] 1.54 7.59 2.03 9.34 2.40 10.34 1.68 5.39 1.94 5.88 2.03 7.19 1.97 6.69 1.57 5.42 2.12 8.35 2.03 7.93 1.78 7.30 1.49 5.66 2.10 7.96
Report Values F MAX σ MAX AVG C.V. [%] AVG C.V. [%] 1.99
21.81
9.09
15.33
1.81
10.09
5.64
6.12
1.86
13.54
6.44
14.18
2.08
3.03
8.14
3.66
1.79
17.02
6.97
17.03
Table 3.2.27 - Results normal casting at 28 days
The stress-displacement curves are reported in the next graph:
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Stress - Displacement (middle) - 28 days 12 1_FRM_0° 10
2_FRM_0° 3_FRM_0°
σ [MPa]
8
1_FRM_30° 2_FRM_30° 1_FRM_45°
6
2_FRM_45° 3_FRM_45°
4
1_FRM_60° 2_FRM_60°
2
1_FRM_90° 2_FRM_90°
0 0
1
2
3
4
5
6
7
3_FRM_90°
Displacement [mm]
Figure 3.2.35 - Stress - displacement behavior at 28 days.
The same operations were repeated for the samples at 50 days Angle Sample
0° 30° 45° 60° 90°
1_FRM 2_FRM 3_FRM 1_FRM 2_FRM 1_FRM 2_FRM 3_FRM 1_FRM 2_FRM 1_FRM 2_FRM 3_FRM
Weight Length Width Height Density [kg] [mm] [mm] [mm] [kN/m3] 1.116 274 56 37 19.66 1.013 273 57.5 37.5 17.21 1.042 272 60 37 17.26 1.022 270 59 37 17.34 1.076 278 62 36 17.34 1.028 277 57.5 38 16.98 1.035 271 59 38 17.03 1.07 267 61 38 17.29 0.909 268 57 34 17.50 0.982 270 61 34 17.54 0.961 270 58 37 16.59 0.968 269 58.5 36 17.09 0.93 270 58.5 36 16.36
Table 3.2.28 - Normal casting - geometrical analysis at 50 days
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Angle Sample
0° 30° 45° 60° 90°
1_FRM 2_FRM 3_FRM 1_FRM 2_FRM 1_FRM 2_FRM 3_FRM 1_FRM 2_FRM 1_FRM 2_FRM 3_FRM
Test values FMAX σMAX [kN] [Mpa] 3.25 10.16 3.95 11.74 3.87 11.31 3.04 9.04 3.41 10.19 3.01 8.71 2.36 6.65 3.03 8.26 2.81 10.25 2.45 8.35 4.19 12.65 3.81 12.06 3.52 11.15
Report Values F MAX σ MAX AVG C.V. [%] AVG C.V. [%] 3.69
10.49
11.07
7.36
3.23
8.09
9.61
8.46
2.80
13.65
7.87
13.76
2.63
9.70
9.30
14.46
3.84
8.66
11.95
6.33
Table 3.2.29 - Results normal casting at 50 days
The stress-displacement curves are reported in the next graph: Stress - Displacement (middle) - 50 days 14 1_FRM_0° 12
2_FRM_0° 3_FRM_0°
σ [MPa]
10
1_FRM_30° 2_FRM_30°
8
1_FRM_45° 6
2_FRM_45° 3_FRM_45°
4
1_FRM_60° 2_FRM_60°
2
1_FRM_90° 2_FRM_90°
0 0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
Displacement [mm] Figure 3.2.36 - Stress - displacement behavior at 50 days.
Moreover, a comparison between the values obtained at different ages is shown:
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Chapter 3 - EXPERIMENTAL PROGRAM
28 days
Angle Sample
0° 30° 45° 60° 90°
1_FRM 2_FRM 3_FRM 1_FRM 2_FRM 1_FRM 2_FRM 3_FRM 1_FRM 2_FRM 1_FRM 2_FRM 3_FRM
50 days
Increment
σMAX Average σMAX Average σMAX Average [Mpa] [Mpa] [Mpa] [Mpa] [%] [%] 7.59 10.16 33.90 9.34 9.09 11.74 11.07 25.68 21.79 10.34 11.31 9.39 5.39 9.04 67.56 5.64 9.61 70.51 5.88 10.19 73.21 7.19 8.71 21.04 6.69 6.44 6.65 7.87 -0.67 22.31 5.42 8.26 52.36 8.35 10.25 22.63 8.14 9.30 14.13 7.93 8.35 5.19 7.30 12.65 73.22 5.66 6.97 12.06 11.95 113.23 71.39 7.96 11.15 39.99 Table 3.2.30 - Results comparison.
In contrast to what was seen previously for the FRM vertical samples, in this case, the 28 days behavior of the normal casted samples is confirmed at 50 days. In fact, for instance, the specimens with inclination of 0° and 90° prove to be the strongest both to 28 days and to 50 days and the same happens for the 45° samples which are the weakest at both studied ages. In particular it should be pointed out the important increase occurred at 0° and 30° while for the remaining directions the increment is smaller.
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3.2.3.5 Vertical and normal casting comparison After reporting the results obtained by testing on samples of FRM subjected to vertical and normal casting, a comparison between the two methodologies must be carried out. A first consideration is the presence of voids in the samples. As previously stated, the vertical casting consist in the alternation of two phases: spray and compaction by roller. However, the compaction, although very important, has not led to the formation of homogeneous sample and it has not prevented the formation of voids. In particular were carried out: areas more compacted and areas less compacted. This is clear from the density analysis of the samples reported in the following tables where the maximum rate of variation between normal casted samples and vertical casted is approximately −7.16% at 28 days and −22.58% at 50 days. normal Angle Sample
0° 30° 45° 60° 90°
1_FRM 2_FRM 3_FRM 1_FRM 2_FRM 1_FRM 2_FRM 3_FRM 1_FRM 2_FRM 1_FRM 2_FRM 3_FRM
vertical
Variation
Density Average Density Average Density Average [kN/m3] [Mpa] [kN/m3] [Mpa] [%] [%] 17.20 17.59 2.26 17.47 17.39 16.37 16.93 -6.32 -2.61 17.50 16.85 -3.69 17.24 17.24 0.04 17.35 17.11 -1.37 17.46 16.98 -2.77 17.54 16.28 -7.16 16.26 17.13 16.77 16.51 3.12 -3.65 17.60 16.47 -6.42 17.51 16.93 -3.33 17.43 17.37 -0.36 17.35 17.81 2.65 17.56 16.45 -6.31 17.23 17.32 16.14 16.45 -6.33 -5.04 17.18 16.76 -2.44 Table 3.2.31 - Density comparison at 28 days.
normal Angle Sample
0° 30° 45° 60° 68
1_FRM 2_FRM 3_FRM 1_FRM 2_FRM 1_FRM 2_FRM 3_FRM 1_FRM 2_FRM 3_FRM
vertical
Variation
Density Average Density Average Density Average [kN/m3] [Mpa] [kN/m3] [Mpa] [%] [%] 19.66 16.30 -17.10 17.21 18.04 15.65 15.92 -9.04 -11.73 17.26 15.83 -8.29 17.34 15.49 -10.68 17.34 15.15 -12.65 17.34 14.81 -14.62 16.98 15.48 -8.88 17.03 17.10 15.76 15.72 -7.49 -8.09 17.29 15.92 -7.91 17.50 16.42 -6.20 17.52 17.54 14.40 15.69 -17.88 -10.42 16.26 \
Chapter 3 - EXPERIMENTAL PROGRAM
1_FRM 2_FRM 3_FRM
90°
16.59 17.09 16.36
16.68
15.51 13.23 14.38
14.37
-6.50 -22.58 -12.11
-13.83
Table 3.2.32 - Density comparison at 50 days.
However, despite the rate variation mentioned above, specimens obtained by vertical casting always presented a lower density compared to the specimens normal casted. A second consideration concern the strength of the FRM when subjected to the two different casting. As reported in the tables 3.2.33-34 the variation of the đ?&#x153;&#x17D;đ?&#x2018;&#x161;đ?&#x2018;&#x17D;đ?&#x2018;Ľ undergone very important changes with fluctuation ranging from â&#x2C6;&#x2019;38.7% to +51.8% at 28 days and from +5% to â&#x2C6;&#x2019;63% at 50 days. Furthermore, contrary to what was expected, in some cases occurred even an increase of the đ?&#x153;&#x17D;đ?&#x2018;&#x161;đ?&#x2018;&#x17D;đ?&#x2018;Ľ between the normal casting and the vertical casting. Once again, this is due to the creation of two different kind of areas in the sprayed sample: areas more compacted with a behavior similar or even better than the normal casting and areas less compacted with a worst behavior than the normal casting. normal
Angle Sample
0° 30° 45° 60° 90°
1_FRM 2_FRM 3_FRM 1_FRM 2_FRM 1_FRM 2_FRM 3_FRM 1_FRM 2_FRM 1_FRM 2_FRM 3_FRM
vertical
Variation
Ď&#x192;MAX Average Ď&#x192;MAX Average Ď&#x192;MAX Average [Mpa] [Mpa] [Mpa] [Mpa] [%] [%] 7.59 9.98 31.56 9.34 9.09 9.81 9.69 5.06 6.58 10.34 9.27 -10.38 5.39 8.19 51.81 5.64 7.25 28.62 5.88 6.31 7.35 7.19 6.19 -13.89 6.69 6.44 6.35 5.88 -5.17 -8.62 5.42 5.10 -5.90 8.35 7.42 -11.22 8.14 7.80 -4.20 7.93 8.19 3.20 7.30 5.53 -24.28 5.66 6.97 3.61 4.68 -36.12 -32.97 7.96 4.88 -38.71
Table 3.2.33 â&#x20AC;&#x201C; Normal vs Vertical casting at 28 days.
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normal
Angle Sample
0° 30° 45° 60° 90°
1_FRM 2_FRM 3_FRM 1_FRM 2_FRM 1_FRM 2_FRM 3_FRM 1_FRM 2_FRM 3_FRM 1_FRM 2_FRM 3_FRM
vertical
Variation
σMAX Average σMAX Average σMAX Average [Mpa] [Mpa] [Mpa] [Mpa] [%] [%] 10.16 7.84 -22.81 11.74 11.07 7.82 7.95 -33.40 -28.19 11.31 8.19 -27.61 9.04 6.16 -31.88 9.61 5.34 -44.46 10.19 4.52 -55.61 8.71 5.01 -42.46 6.65 7.87 7.01 6.05 5.43 -23.16 8.26 6.13 -25.82 10.25 9.77 -4.65 9.30 8.35 6.87 9.01 -17.73 -3.07 10.40 \ 12.65 8.88 -29.79 12.06 11.95 5.88 6.28 -51.27 -47.43 11.15 4.09 -63.28
Table 3.2.34 - Normal vs Vertical casting at 50 days.
It should be noted that the presence of voids in the samples is absolutely independent from the age of the samples and their orientation, it depends only on the location of the sample where it was cut. Finally all samples subjected to 4 points bending test, showed a similar crack pattern. The main fracture has always occurred in the central area, between the two points of load application where the moment is maximum (see Figure 3.2.37) Normal casting
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Figure 3.2.37 – Normal casting - Samples crack pattern.
Vertical casting
Figure 3.2.38 – Vertical casting - Samples crack pattern.
Only in few cases the rupture was different, mainly in the 50 days samples. As shown below the presence of voids in correspondence of the support has allowed the fracture moved diagonally towards the support.
Figure 3.2.39 - Diagonal fracture in the sample 2_FRM_90° tested at 50 days.
For a more detailed presentation of the 50 days vertical samples crack patterns, see Annex A.
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3.3 Flexural Strengthening efficiency The main purpose of this experimental campaign was to characterize and quantify, as much as possible, the increase of the load carrying capacity and deformation of old schist masonry once subjected to a strengthening system based on Fiber Reinforced Mortar. In particular, a typical behavior of masonry under seismic loads, i.e. out-of plane behavior, was analyzed. With this target, bending tests on vertical masonry schist elements were carried out. Samples preparation and setup of the tests performed are shown in the next sections. 3.3.1 Specimen construction The main test carried out in this experimental program had the objective to investigate the out-of-plane behavior of schist masonry, strengthened with layers of FRM. This assessment was carried out performing a three point bending test on schist masonry prisms, with dimensions of 30 đ?&#x2018;?đ?&#x2018;&#x161; Ă&#x2014; 35 đ?&#x2018;?đ?&#x2018;&#x161; Ă&#x2014; 200 đ?&#x2018;?đ?&#x2018;&#x161;, strengthened with two symmetrical layers of FRM both 2.5 đ?&#x2018;?đ?&#x2018;&#x161; thick. These dimensions are justified because the aim was to reproduce as much as possible the real behavior of a structural element of this weak masonry once strengthened. However, due to the size of the samples, the tests were performed in a non-standard configuration, i.e., with the specimens vertically arranged and not horizontally as in a traditional three point bending test. In particular, three specimens were casted: two strengthened with Fiber Reinforced Mortar and the remaining one without any type of reinforcement (being the reference beam). The first step addressed, was the realization of a wooden support for each specimen, in order to prevent any possible damages during their positioning in the testing machine and to allow a straight construction of the sample.
Figure 3.3.1 - Wooden support.
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Chapter 3 - EXPERIMENTAL PROGRAM
Subsequently, in the bottom part of each column, two steel plates (dimensions 1.5 đ?&#x2018;?đ?&#x2018;&#x161; Ă&#x2014; 35 đ?&#x2018;&#x161; Ă&#x2014; 35 đ?&#x2018;&#x161; ) and two sheets of Teflon with oil between, were introduced (see Figure 3.3.2) in order to minimize the friction due to the deadweight of the specimen.
Figure 3.3.2 â&#x20AC;&#x201C; Positioning of the steel plates in the bottom of each specimen.
After this first phase, the construction of the columns was carried out according to the following steps (see Figure 3.3.3): - Preparation of the NHLM using the composition shown in Table 3.2.7. In particular three molds were filled from three different mixing of NHLM as reported at § 3.2.2.3; - Positioning of the first layer of NHLM above the steel plate; - Arrangement of schist rocks, placing them before in the corners and then in the central part. Each rock was obtained breaking larger rocks in order to obtain elements as representative as possible; - Repetition of the steps described above, up to the realization of 0.5 đ?&#x2018;&#x161; of sample. In this way mortar joints with equal thickness were obtained avoiding thus that the lower ones were crush from the upper weight.
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Chapter 3 - EXPERIMENTAL PROGRAM
Figure 3.3.3 â&#x20AC;&#x201C; Steps of the specimens construction.
Once completed the construction of the columns it was possible to continue with the application of the reinforcement system. Therefore after 28 days from the building of the last specimen, two columns were strengthened using spray technique and carrying out these steps: - Spraying of the first layer of FRM (see composition in Table 3.2.14) with an approximate thickness of 10 đ?&#x2018;&#x161;đ?&#x2018;&#x161;; - Use of a spatula to level and smoothen the mortar layer surface; - Spraying of a second layer of 10 đ?&#x2018;&#x161;đ?&#x2018;&#x161; of thickness (1 day after the application of the previous one) and leveling with spatula; - Application of the last layer of 5 đ?&#x2018;&#x161;đ?&#x2018;&#x161; after 1 day from the previous and leveling. These operations were repeated for the two faces not confined by the wood of each strengthened column. Thus the final cross section area of the reinforced columns was 35 Ă&#x2014; 35 đ?&#x2018;?đ?&#x2018;&#x161;2 .
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Chapter 3 - EXPERIMENTAL PROGRAM
a)
b)
c)
Figure 3.3.4 â&#x20AC;&#x201C; Application of the reinforcement system: a)Spray operation; b) Levelling with spatula; c)Final result.
3.3.2 Test Setup As previously stated, due to the size of the specimens, the test was performed adopting a vertical configuration, therefore different expedients, regarding load cell, supports and đ??żđ?&#x2018;&#x2030;đ??ˇđ?&#x2018;&#x2021;đ?&#x2018; have been taken. Firstly, a testing frame with a load cell of 500 đ?&#x2018;&#x2DC;đ?&#x2018; disposed in horizontal position was designed (see Figure 3.3.5 a) & b)). Then, support points and point load application were made. In particular this operation always occurred once positioned the specimen in the frame and it consisted in fixing a steel cylinder with grout directly to the exterior part of the beam. In the case of support points, cylinders were fixed at a distance of 15 đ?&#x2018;?đ?&#x2018;&#x161; from the extremities (top and the bottom) of the beam, whereas in the case of the point load application, the cylinder was fixed in the middle of the column aligned with the actuator (see Figure 3.3.5 e) & f)).
a)
b)
c)
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Chapter 3 - EXPERIMENTAL PROGRAM
d)
e)
f)
Figure 3.3.5 â&#x20AC;&#x201C; Test setup: a) & b)Testing frame; c) & d)Point load application; e) & f)Support.
Afterwards the wood structure was removed and ten đ??żđ?&#x2018;&#x2030;đ??ˇđ?&#x2018;&#x2021;đ?&#x2018; were positioned according to the configuration shown in Figure 3.3.6. In particular, đ??żđ?&#x2018;&#x2030;đ??ˇđ?&#x2018;&#x2021;đ?&#x2018; able to record a large range of displacements were positioned in the central part of the beam where it was expected the maximum displacement, whereas the đ??żđ?&#x2018;&#x2030;đ??ˇđ?&#x2018;&#x2021;đ?&#x2018; with smaller range were arranged to the extremities. The placement of the đ??żđ?&#x2018;&#x2030;đ??ˇđ?&#x2018;&#x2021;đ?&#x2018; was possible through the use of magnetic bases. Each test was performed using displacement control of the actuator cross-head. The applied displacement rate was kept constant at 0.01 đ?&#x2018;&#x161;đ?&#x2018;&#x161;/đ?&#x2018; .
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Figure 3.3.6 â&#x20AC;&#x201C; Test setup (dimensions in cm).
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Chapter 3 - EXPERIMENTAL PROGRAM
Figure 3.3.7 â&#x20AC;&#x201C; LVDTâ&#x20AC;&#x2122;s disposition.
Every specimen was subjected to monotonic test performed with the following characteristics of the samples: - Un-strengthened column (1đ?&#x2018;&#x2020;đ??ś_đ?&#x2018;&#x2C6;đ?&#x2018;&#x2026;): the NHLM was 68 days old; - Strengthened column (1đ?&#x2018;&#x2020;đ??ś_đ??šđ?&#x2018;&#x2026;đ?&#x2018;&#x20AC;): the NHLM was 63 days old and the FRM was 28 days old. - Strengthened column (2đ?&#x2018;&#x2020;đ??ś_đ??šđ?&#x2018;&#x2026;đ?&#x2018;&#x20AC;): the NHLM was 66 days old and the FRM was 31 days old.
78
Chapter 4
EXPRIMENTAL RESULTS
4.1 Introduction This chapter will examine the adopted reinforcement system effectiveness through the analysis of the data obtained from the bending tests performed on the vertical prototypes of schist masonry previously described. In particular, the load-displacement responses and the crack patterns for each specimen will be showed and analyzed. Afterwards, a comparison of the different results will be carried out in order to determine the reinforcement improvement in terms of load carrying capacity and displacements. As will be fully described in the following sections, the enhancement is evident and the strengthened samples show practically the same behavior, reaching similar peak load values. However, two critical issues emerge: the first concerning the thickness of the reinforcement layers and the second regarding the adopted configuration in the samples bottom. These experimental evidences confirm what have been already recognized by many researchers, i.e., performing out-of-plane tests in masonry walls is a difficult task since it requires special cares. In fact the stability conditions of the specimen during the test become a critical issue when the wall begins to be damage. Thus, the out-of-plane tests conducted on horizontal specimens, have been preferred in relation to the vertical specimens. 79
Chapter 4 â&#x20AC;&#x201C; EXPERIMENTAL RESULTS
4.2 Results and analysis of the Flexural strengthening 4.2.1 Introduction As previously mentioned, in order to assess the effectiveness of the FRM reinforcement once applied to old schist masonry, three specimens were tested under three points bending test. The setup, already discussed above, provides that the specimens are vertically positioned with a load applied horizontally in the middle, thus simulating an out-of-plane behavior. In the next sections the results obtained will be presented, as well as the failure modes observed during each test. 4.2.2 Unreinforced specimen (1 SC_UR) The reference sample, without any type of reinforcement, was tested after 68 days from the end of its construction. At that time, according to the §3.2.2.3, the NHLM has flexural strength of 0.285 đ?&#x2018;&#x20AC;đ?&#x2018;&#x192;đ?&#x2018;&#x17D; and compression strength of 1.18 đ?&#x2018;&#x20AC;đ?&#x2018;&#x192;đ?&#x2018;&#x17D;. Being the un-strengthened specimen, it presented a cross section area of 350 Ă&#x2014; 300 đ?&#x2018;&#x161;đ?&#x2018;&#x161;2 . After its placement in the test frame and the creation of the supports, the lateral wood necessary for the sample transportation has been removed and the đ??żđ?&#x2018;&#x2030;đ??ˇđ?&#x2018;&#x2021;đ?&#x2018; were positioned according to the figure 3.3.6. Before the test start, the column was carefully analyzed identifying with a black marker the water shrinkage cracks.
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Chapter 4 - EXPERIMENTAL RESULTS
a)
b)
c)
d)
e)
Figure 4.2.1 â&#x20AC;&#x201C; Unreinforced Sample: a) General view; b) Intrados beam-top; c) Intrados beam-bottom; d) Extrados beam-top; e) Extrados beam-bottom.
4.2.2.1 Load â&#x20AC;&#x201C; Displacement response The load vs displacement responses for the different đ??żđ?&#x2018;&#x2030;đ??ˇđ?&#x2018;&#x2021;đ?&#x2018; are shown in Figure 4.2.2. The curves obtained show that the larger displacements were recorded by the đ??żđ?&#x2018;&#x2030;đ??ˇđ?&#x2018;&#x2021;đ?&#x2018; centrally positioned (đ??żđ?&#x2018;&#x2030;đ??ˇđ?&#x2018;&#x2021; 1 and đ??żđ?&#x2018;&#x2030;đ??ˇđ?&#x2018;&#x2021; 2) and, gradually moving away from the column middle, the displacements became smaller. Besides, the graph shows that the specimen behavior was not symmetrical, in fact the đ??żđ?&#x2018;&#x2030;đ??ˇđ?&#x2018;&#x2021;đ?&#x2018; 3, 4, 5 had smaller displacements compared to the respective đ??żđ?&#x2018;&#x2030;đ??ˇđ?&#x2018;&#x2021;đ?&#x2018; 6, 7, 8. Furthermore it should be pointed out that the đ??żđ?&#x2018;&#x2030;đ??ˇđ?&#x2018;&#x2021;đ?&#x2018; placed in correspondence of the supports, in order to verify their effectiveness, have not recorded remarkable shifts.
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Chapter 4 â&#x20AC;&#x201C; EXPERIMENTAL RESULTS
Load - Displacement 2.3 Lvdt 8
2.2
Lvdt6
Load [kN]
2.1
Lvdt 7
2
Lvdt 1
1.9
Lvdt 2
1.8
Lvdt 3
1.7
Lvdt4
1.6
Lvdt 5
1.5
Lvdt Top 0
2
4
6
8
10
12
Displacement [mm]
14
Lvdt Bottom
Figure 4.2.2 - Load vs displacement responses.
From the analysis of the curves obtained from the test, it is evident as the unreinforced specimen has a particularly low resistance, reaching the peak load of 2.2 đ?&#x2018;&#x2DC;đ?&#x2018; after only 4â&#x20AC;˛ and 21â&#x20AC;˛â&#x20AC;˛ from the beginning of the test. The specimen after having reached the peak very quickly, proving an irrelevant elasto-plastic behavior, showed a post peak response with a low slope and high fluctuations. This was due to the creation of a significant number of fractures in the column inner core where the schist stones started to lose their bond with mortar. Because of the large movements recorded, some đ??żđ?&#x2018;&#x2030;đ??ˇđ?&#x2018;&#x2021;đ?&#x2018; were removed during the test as soon as they reached the upper limit of their measureable range. 4.2.2.2 Failure mode After few minutes since the test start it was possible to identify, on the unreinforced sample lateral sides, a first crack having appeared exactly in the middle of the column, aligned with the actuator. In particular, this crack gradually increased its opening until the test end, rising to a size of approximately 10 đ?&#x2018;&#x161;đ?&#x2018;&#x161;. Furthermore, the crack occurred at the interface between the schist stones and the NHLM, demonstrating the weakness of the connection between the two elements and the independent behavior of units and joints once subjected to this type of load. The crack patterns observed in the lateral surfaces of the specimen at the peak load are presented in red color in the next figure: 82
Chapter 4 - EXPERIMENTAL RESULTS
a)
b)
Figure 4.2.3 – Crack pattern at the peak load: a) lateral side - front; b) lateral side - back.
Subsequently, after having reached the peak load, an additional crack (marked in red) occurred in the bottom part of the unreinforced sample, aligned with the support as shown in Figure 4.2.4:
a)
b)
Figure 4.2.4 – Additional crack in the bottom part of the sample: a) lateral side - front; b) lateral side – back.
The appearance of this new crack, was clearly due to the hindered rotation of the lower part of the specimen. In fact, having observed the column behavior during the test, it was evident 83
Chapter 4 â&#x20AC;&#x201C; EXPERIMENTAL RESULTS
that, once the first crack in the middle appeared, the top part start to rotate while the bottom part could not move because of the lower support. Therefore, it was revealed that the new crack existence may result from the bottom part configuration adopted, as the steel plates with sheets of Teflon and oil between, did not prevent the existence of friction, and therefore the specimen deadweight contributed to the restriction of the deformation of the sample and created a partially fixed support instead of a free edge. The crack patterns observed at the end of the test are presented in red color in the figure below:
a)
b)
Figure 4.2.5 - Crack pattern at the end of the test: a) lateral side front; b) Opening of the crack in the middle of the lateral side back
Finally, the unreinforced column demonstrated a very brittle and weak behavior having showed the reaching of a low peak load in a short period and a main crack exactly in the same alignment of the load cell.
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4.2.3 Reinforced specimen (1 SC_FRM) The first reinforced sample, was tested when the NHLM was 63 days old and the FRM was 28 days old. The physical and mechanical properties of these materials at that curing time had been previously studied and described in the paragraphs 3.2.2.3 and 3.2.3. The strengthened specimen cross-section area was made of schist and mortar inner core, and two external layers of FRM both 25 đ?&#x2018;&#x161;đ?&#x2018;&#x161; thick. Therefore, the final area was approximately of 350 Ă&#x2014; 350 đ?&#x2018;&#x161;đ?&#x2018;&#x161;2. As it was the first specimen tested, the real effectiveness of the reinforcement as well as the behavior of the schist and mortar inner part hadnâ&#x20AC;&#x2122;t been known, thus, it was decided to pause the test once the peak was reached. All the equipment were removed from the column, leaving only the displacement control of the actuator as recorder. Furthermore the đ??żđ?&#x2018;&#x2030;đ??ˇđ?&#x2018;&#x2021;đ?&#x2018; aligned with the supports to control their movements, were not positioned. The aspect of the sample before the test is showed below.
a)
b)
c)
d)
e)
Figure 4.2.6 â&#x20AC;&#x201C; First reinforced sample: a) General view; b) Intrados beam-top; c) Intrados beam-bottom; d) Extrados beam; e) Extrados beam-point load detail.
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4.2.3.1 Load â&#x20AC;&#x201C; Displacement response The load vs displacement responses for the different đ??żđ?&#x2018;&#x2030;đ??ˇđ?&#x2018;&#x2021;đ?&#x2018; are shown in Figure 4.2.7. As consequence of what stated earlier, the curves obtained from the records of the đ??żđ?&#x2018;&#x2030;đ??ˇđ?&#x2018;&#x2021;đ?&#x2018; , were interrupted few moments after the peak load, whereas the load-displacement curve recorded by the actuator continued until the end of the test (see Figure 4.2.8).
Load - Displacement 25
20
Load [kN]
Lvdt 8 Lvdt 6
15
Lvdt 7 Lvdt 1 10
Lvdt 2 Lvdt 3 Lvdt 4
5
Lvdt 5 0 0
1
2
3
4
5
6
Displacement [mm] Figure 4.2.7 - Load vs displacement responses â&#x20AC;&#x201C; LVDTs.
Load - Displacement 25
Load [kN]
20 15 10
ACTUATOR
5 0 0
2
4
6
8
10
Displacement [mm]
Figure 4.2.8 - Load vs displacement responses â&#x20AC;&#x201C; Actuator.
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The larger displacements were recorded by the đ??żđ?&#x2018;&#x2030;đ??ˇđ?&#x2018;&#x2021; 1 and 2, centrally positioned, while the others had smaller displacements. In particular, it should be noted that the movements recorded from the đ??żđ?&#x2018;&#x2030;đ??ˇđ?&#x2018;&#x2021;đ?&#x2018; 3, 4, 5 in the bottom part of the column were smaller than those recorded in the upper part. Consequently, even in this case the column behavior was not symmetrical. For example, the đ??żđ?&#x2018;&#x2030;đ??ˇđ?&#x2018;&#x2021; 8 had higher displacements than đ??żđ?&#x2018;&#x2030;đ??ˇđ?&#x2018;&#x2021; 4 despite they were positioned symmetrically in the specimen. The peak load was reached after 11â&#x20AC;˛ and 58â&#x20AC;˛â&#x20AC;˛ since the test start and the value obtained was đ??šđ?&#x2018;?đ?&#x2018;&#x2019;đ?&#x2018;&#x17D;đ?&#x2018;&#x2DC; = 23.8 đ?&#x2018;&#x2DC;đ?&#x2018; . Furthermore, analyzing the graphs reported above, it is possible to infer that the specimen exhibited a quite short linear elastic field (up to 9 đ?&#x2018;&#x2DC;đ?&#x2018; ), demonstrating subsequently a long plastic branch up to the peak. Considering then the curve recorded by actuator, it can be underlined that, after the peak load reaching, there was an initial sudden load drop that proves a very brittle behavior of the column. Moreover, after the pause happened approximately at 19 đ?&#x2018;&#x2DC;đ?&#x2018; , the specimen showed a very small increase of the load and finally a decrease up to the test end. During the pause, that was about 30â&#x20AC;˛â&#x20AC;˛, therefore the sample continued to deform with constant load and then it continued again its fast decrease. 4.2.3.2 Failure mode Once the test started, first cracks were observed on the column lateral sides few minutes before the peak load. They emerged in the inner part made of schist stones and mortar. These cracks appeared initially in the column upper half and then in the bottom half. In particular they connected the specimen central area to the upper/lower support, showing a trend with inclination greater than 30°. Furthermore, in this first phase, no cracks were identified in the reinforced layer. The crack patterns observed in the specimen lateral surfaces at the peak load are displayed in red color in the next figure:
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Chapter 4 – EXPERIMENTAL RESULTS
a)
b)
Figure 4.2.9 – Crack pattern at the peak load in the lateral side –front: a) General view; b) Detail of the middle of the column.
Subsequently, with the test progress, the cracks, developed in the upper part of the inner core, increased their size and number, whereas those appeared in the bottom part did not have important variations. The crack patterns observed at the specimen surface at the end of the test are indicated in blue in the figure below:
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Chapter 4 - EXPERIMENTAL RESULTS
a)
b)
Figure 4.2.10 â&#x20AC;&#x201C; Crack pattern at the end of the test in the lateral side â&#x20AC;&#x201C; front: a) Bottom part; b) Top part.
After having removed the đ??żđ?&#x2018;&#x2030;đ??ˇđ?&#x2018;&#x2021;đ?&#x2018; and having allowed the test to continue, a single crack was observed in the layer of FRM, in the column intrados (see Figure 4.2.11). The crack formation just in the final phase of the test (after the peak), makes us to understand that some cracks surely occurred in the FRM inner layers. Considering that the reinforcement was made up of three not continuous layers (see paragraph 3.3.1) is very likely that the FRM inner layers had some cracks at the moment of the peak load and then, these fractures had been propagated up to the outer layer where they emerged with delay.
89
Chapter 4 â&#x20AC;&#x201C; EXPERIMENTAL RESULTS
Figure 4.2.11 - Crack in the reinforced layer - intrados of the Column.
In conclusion, the crack patterns shown during the test on the first strengthened sample are probably due to the occurrence of two main factors: - the different thickness of the FRM layers between the top and the bottom part of the column. It was difficult, in fact, during the spraying phase, to apply the same thickness of reinforced mortar along all the specimen; - the column bottom configuration adopted (steel plates with sheets of Teflon and oil) that had led to the formation of a smaller number of cracks in the lower part of the sample, thus having avoided free movements and having created a fixed support. Furthermore, with the deadweight, the bottom part of the column was subjected to bending but with a higher axial load that reduced the tensile stress due to the bending and prevented cracks to appear (like a pre-stress effect).
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Chapter 4 - EXPERIMENTAL RESULTS
4.2.4 Reinforced specimen (2 SC_FRM) The second reinforced specimen, was tested 31 days after the FRM last layer spray when the NHLM was 66 days old. The physical-mechanical characteristics of these materials are reported above in the paragraphs 3.2.2.3 and 3.2.3. The specimen geometry as well as the test setup for the second reinforced sample was the same adopted for the first reinforced one, already illustrated in the § 4.2.3. In this case, however, the đ??żđ?&#x2018;&#x2030;đ??ˇđ?&#x2018;&#x2021;đ?&#x2018; , aligned with the supports to control their movements, were positioned as in Figure 3.3.6. Furthermore, unlike the first reinforced column, the test had not been paused after having reached the peak load. As a precaution based on the previously results, it was decided to stop the test when the load decreased up to 10 đ?&#x2018;&#x2DC;đ?&#x2018; . Before the test start, the column was carefully analyzed identifying with a black marker the water shrinkage cracks. The sample aspect before the test is reported below.
a)
b)
c)
d)
e)
Figure 4.2.12 - Second reinforced sample: a) General view; b) Intrados beam-top; c) Intrados beam-bottom; d) Extrados beam-middle; e) Extrados beam-point load detail.
91
Chapter 4 â&#x20AC;&#x201C; EXPERIMENTAL RESULTS
4.2.4.1 Load â&#x20AC;&#x201C; Displacement response The load vs displacement responses for the different đ??żđ?&#x2018;&#x2030;đ??ˇđ?&#x2018;&#x2021;đ?&#x2018; are shown in Figure 4.2.13. As indicated in the graph below, once again, the larger displacements were recorded by the đ??żđ?&#x2018;&#x2030;đ??ˇđ?&#x2018;&#x2021; 1 and 2, positioned in the middle of the sample. Whereas, gradually moving from the center to the extremities of the column, the đ??żđ?&#x2018;&#x2030;đ??ˇđ?&#x2018;&#x2021;đ?&#x2018; recorded smaller movements. The smallest displacements were obtained from the đ??żđ?&#x2018;&#x2030;đ??ˇđ?&#x2018;&#x2021;đ?&#x2018; placed in correspondence of the supports, thus demonstrating their effectiveness. Furthermore, even the second reinforced sample behavior was not symmetrical as demonstrated from the recordings of the đ??żđ?&#x2018;&#x2030;đ??ˇđ?&#x2018;&#x2021;đ?&#x2018; 3, 4, 5, arranged in the bottom part, that are lowers than those placed in the upper part. In particular, it should be pointed out that đ??żđ?&#x2018;&#x2030;đ??ˇđ?&#x2018;&#x2021; 6 recorded significant displacements, due to the specimen failure mode which will be explain in the next paragraph. As can be seen from the graph reported below, the đ??żđ?&#x2018;&#x2030;đ??ˇđ?&#x2018;&#x2021;đ?&#x2018; 8, 6, 3, were removed before the test end as they had reached the upper limit of their measureable range.
Load - Displacement 26
21
Lvdt 8
Load [kN]
Lvdt 6 Lvdt 7
16
Lvdt 1 Lvdt 2 11
Lvdt 3 Lvdt 4 Lvdt 5
6
Lvdt Top Lvdt bottom
1 0
2
4
6
8
10
12
Displacement [mm] Figure 4.2.13 â&#x20AC;&#x201C; Load â&#x20AC;&#x201C; displacement responses.
The peak load was reached after 11â&#x20AC;˛ and 30â&#x20AC;˛â&#x20AC;˛ since the beginning of the test and the value obtained was đ??šđ?&#x2018;?đ?&#x2018;&#x2019;đ?&#x2018;&#x17D;đ?&#x2018;&#x2DC; = 23.9 đ?&#x2018;&#x2DC;đ?&#x2018; .
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Chapter 4 - EXPERIMENTAL RESULTS
The pre-peak behavior of the second reinforced sample, proved to be totally similar to the one shown by the first reinforced sample. In fact an elastic field had developed up to 10 đ?&#x2018;&#x2DC;đ?&#x2018; followed by a long plastic branch until the peak analogous to the first strengthened sample. Regarding the post peak section, instead, it is evident the difference from the previous sample. In this case, in fact, no load drop was recorded once passed the peak, but rather almost all the đ??żđ?&#x2018;&#x2030;đ??ˇđ?&#x2018;&#x2021;đ?&#x2018; recorded a decrease with a constant slope except for the đ??żđ?&#x2018;&#x2030;đ??ˇđ?&#x2018;&#x2021; 7. It had an anomalous behavior, registering in the final part even a decrease of displacement. 4.2.4.2 Failure mode During the test on the second strengthened sample, it was possible to observe that no cracks appeared in the schist stones and mortar inner part, until few moments before the peak load. Only at the peak load time, a crack developed suddenly in the specimen upper zone connecting the central area of the column to the upper support, with a trend with inclination greater than 30°. Furthermore, at that time, no cracks were identified neither in the lower part of the specimen and neither in the reinforced layers. The crack patterns observed are reported here below:
a)
b)
Figure 4.2.14 â&#x20AC;&#x201C; Crack pattern at the peak load: a) lateral side â&#x20AC;&#x201C; front; b) lateral side â&#x20AC;&#x201C; back (middle of the sample).
93
Chapter 4 â&#x20AC;&#x201C; EXPERIMENTAL RESULTS
Once passed the peak load, during the test progress, no remarkable changes has been recorded in the central band between the two FRM layers. In fact only few cracks appeared in the sample upper part and no cracks occurred in the bottom part until the test end. However, despite this poor crack pattern, the failure mode was clearly evident due to the opening of an inclined crack in the column upper part (see Figure 4.2.15 a)). This fracture has led to the formation of two cracks in the FRM parallel layers, thus compromising the response of the entire sample (see Figure 4.2.17). This event is also clearly demonstrated by the recordings obtained from the đ??żđ?&#x2018;&#x2030;đ??ˇđ?&#x2018;&#x2021;đ?&#x2018; placed in that area, for example: - đ??żđ?&#x2018;&#x2030;đ??ˇđ?&#x2018;&#x2021; 8, positioned approximately at the crack top extremity, recorded very high values of displacement reaching very shortly the upper limit of its measureable range; - đ??żđ?&#x2018;&#x2030;đ??ˇđ?&#x2018;&#x2021; 7 positioned approximately at the crack bottom extremity, recorded high values of displacement but especially a post peak behavior totally different to the other đ??żđ?&#x2018;&#x2030;đ??ˇđ?&#x2018;&#x2021;đ?&#x2018; ; Therefore the crack patterns at the end of the test are reported below:
a)
b)
Figure 4.2.15 â&#x20AC;&#x201C; Crack pattern at the end of the test (lateral side â&#x20AC;&#x201C; front): a) Detail (cracks in blue); b) General view.
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Chapter 4 - EXPERIMENTAL RESULTS
As stated above the main crack developed in the specimen increasing its opening until the end of the test, rising to a size of about 10 đ?&#x2018;&#x161;đ?&#x2018;&#x161;.
a)
b)
Figure 4.2.16 â&#x20AC;&#x201C; Crack details at the end of the test: a) lateral side â&#x20AC;&#x201C; front; b) lateral side â&#x20AC;&#x201C; back.
The correspondent cracks of the reinforcement system, are reported in red color here below:
a)
b)
Figure 4.2.17 â&#x20AC;&#x201C; Cracks in the FRM layers: a) extrados of the beam; b) intrados of the beam.
95
Chapter 4 â&#x20AC;&#x201C; EXPERIMENTAL RESULTS
However, despite the test failure mode was a little more noticeable in comparison to the previous one, the sample behavior proved to be the same as the previous sample, therefore, in conclusion: - the different thickness of the FRM layers between the top and the bottom part of the column has created a higher number of cracks in the upper part; - the configuration adopted in the bottom of the column (steel plates with sheets of Teflon and oil) has led to the formation of a smaller number of cracks in the sample lower part, avoiding thus free movements and creating a fixed support; - in the FRM inner layers some cracks surely occurred before the instant when they appeared in the outer layer.
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Chapter 4 - EXPERIMENTAL RESULTS
4.3 Discussion of results 4.3.1 Introduction In this paragraph we will compare and discuss the results related to the performed tests on schist vertical elements.. In order to assess the real effectiveness of the applied reinforcement system, will be compared the vertical prototypes behaviors (in terms of load and displacements), subjected to out-ofplane actions. 4.3.2 Comparison of results of Flexural strengthening Analyzing the data, obtained from the out-of-plane tests on the schist samples, two different types of evaluations on the elements responses should be carried out: the first concerning the load and the second in terms of displacements. Regarding the load applied, it is evident that the increment of the load carrying capacity was absolutely high, once the reinforcement system was introduced, (see Table 4.3.1). In fact both the reinforced samples reached a peak load value approximately 10 times higher than the reference specimen. 1UR_SC 1FRM_SC 2FRM_SC [kN] [kN] [kN] 2.22 23.77 23.95 Table 4.3.1 - Comparison of the peak load data.
However, the enhancement could be observed also analyzing the displacements detected at the peak load time shown in the table below.
Lvdt 1 Lvdt 2 Lvdt 3 Lvdt 4 Lvdt 5 Lvdt 6 Lvdt 7 Lvdt 8 Lvdt Top Lvdt Bottom
1UR_SC [mm] 2.01 1.87 1.25 0.37 0.44 1.18 1.55 0.66 0.22 0.04
1FRM_SC [mm] 5.16 5.11 3.58 1.52 1.53 4.74 4.13 2.77 \ \
2FRM_SC [mm] 4.92 3.99 3.50 1.65 2.23 4.72 3.91 2.92 1.54 0.95
Table 4.3.2 - Displacements at the Peak load.
97
Chapter 4 â&#x20AC;&#x201C; EXPERIMENTAL RESULTS
The data presented above, prove that the reinforced specimens reached the peak load with twice or even more displacements than the unreinforced sample. In particular the increments are displayed in the next table as percentage:
Lvdt 1 Lvdt 2 Lvdt 3 Lvdt 4 Lvdt 5 Lvdt 6 Lvdt 7 Lvdt 8 Lvdt Top Lvdt Bottom
1FRM_SC vs 1UR_SC
2FRM_SC vs 1UR_SC
Average
[%]
[%]
[%]
61.0 63.4 65.0 75.4 71.4 75.1 62.5 76.1 \ \
59.1 53.1 64.2 77.3 80.4 75.0 60.4 77.4 85.6 96.1
60.0 58.3 64.6 76.3 75.9 75.0 61.5 76.8 85.6 96.1
Table 4.3.3 - Increment of the displacement at the peak load.
The different behaviors of the schist vertical elements are more clear considering the Annex B that compares the load-displacement responses of the different đ??żđ?&#x2018;&#x2030;đ??ˇđ?&#x2018;&#x2021;đ?&#x2018; for each test performed. Analyzing the Annex B it appears clearly the improvement made by the strengthening system. The strengthened samples showed a considerably longer elastic field compared to the reference specimen. Furthermore, evaluating the inclination of the curves, it has to be inferred that the reinforcement created a more stiff element. Finally, once the reinforcement was applied, the schist elements had developed a good plastic behavior from 10 đ?&#x2018;&#x2DC;đ?&#x2018; up to fail. Considering the post-peak phase, however, the three samples exhibited different behaviors. The reference specimen, for instance, has developed a long branch with a very low slope and high fluctuations immediately after the peak (see Figure 4.2.2). This was due to the numerous internal fractures creation as consequence of the de-bond between stones and mortar. However, it should be noticed that the load cell used in the test has proved to be too powerful (500 đ?&#x2018;&#x2DC;đ?&#x2018; ) to record exactly what happened and therefore part of these fluctuation maybe were due to the actuator imprecision. Concerning the first strengthened sample, a sudden load drop, interrupted at the moment when the test was paused (approximately around 19 đ?&#x2018;&#x2DC;đ?&#x2018; ) characterized its post-peak phase. Finally the second strengthened sample, showed a more regular load decrease, without sudden falls but with regular and constant slope except for the records obtained from the đ??żđ?&#x2018;&#x2030;đ??ˇđ?&#x2018;&#x2021; 7. In particular in its post-peak decrease the sample exhibited a curve inclination increment 98
Chapter 4 - EXPERIMENTAL RESULTS
approximately around 20 đ?&#x2018;&#x2DC;đ?&#x2018; that proves the opening of the main crack in the column inner core. A comparison between the two strengthened samples has been carried out lately and the results are reported in the next table. It shows that, the behavior of the two samples is very similar, considering that the displacement variations for the different đ??żđ?&#x2018;&#x2030;đ??ˇđ?&#x2018;&#x2021;đ?&#x2018; are all smaller than 10% except for the đ??żđ?&#x2018;&#x2030;đ??ˇđ?&#x2018;&#x2021;đ?&#x2018; 2 and đ??żđ?&#x2018;&#x2030;đ??ˇđ?&#x2018;&#x2021;đ?&#x2018; 5 that had recorded higher percentage. 1FRM_SC vs 2FRM_SC [%] 4.6 Lvdt 1 22.0 Lvdt 2 2.2 Lvdt 3 -8.5 Lvdt 4 -45.9 Lvdt 5 0.4 Lvdt 6 5.4 Lvdt 7 -5.3 Lvdt 8 \ Lvdt Top \ Lvdt Bottom Table 4.3.4 - Displacements variation in the strengthened samples.
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Chapter 4 â&#x20AC;&#x201C; EXPERIMENTAL RESULTS
100
Chapter 5
NUMERICAL ANALYSIS
5.1 Introduction Finite element models (FEM) are able to capture some aspects which are unable to be captured in the experimental testing. To perform the numerical analysis it is necessary to know the mechanical parameters of the materials constituting the model. These parameters are the compressive strength, tensile strength, Youngâ&#x20AC;&#x2122;s modulus, Poisson ratio, compressive fracture energy and tensile fracture energy. In order to perform the numerical analysis on the schist masonry prototypes, two main parts need to be carefully examined: the historical masonry behavior and the reinforcement system behavior. In the following sections the finite element modelling will be used with a main purpose: obtaining the mechanical parameters of the materials used in the present experimental campaign, namely schist masonry and FRM, through the validation of the laboratory results and the laboratory observations.
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Chapter 5 â&#x20AC;&#x201C; NUMERICAL ANALYSIS
5.2 Nonlinear finite element analysis In the first part of this section, the finite element computer code used in this study is briefly described. In the second part of this section, a brief introduction to the nonlinear analysis of structures using the finite element method is given. A comprehensive description of this method can be found elsewhere, e.g., Zienkiewicz and Taylor (1989, 1991) and Bathe (1996). 5.2.1 Software used for nonlinear material analysis. FEMIX 4.0 is a computer code whose purpose is the analysis of structure by the Finite Element Method (FEM). This code has a large library of types of finite elements available, namely 3đ??ˇ frames and trusses, plane stress elements, flat or curved elements for shell, and frames and trusses, plane stress elements, flat or curved elements for shell, and 3đ??ˇ solid elements. Linear elements may have two or three nodes, plane stress and shell elements may be 4, 8 or 9-noded and 8 or 20 noded hexahedra may be used in 3đ??ˇ solid analyses. This element library is complemented with a set of point, line and surface springs that model elastic contact with the support, and also a few types of interface elements to model interelement contact. Embedded line elements can be added to other types of elements to model reinforcement bars. All these types of elements can be simultaneously included in the same analysis, with the exception of some incompatible combinations. The analysis may be static or dynamic and the material behavior may be linear or nonlinear. Data input is facilitated by the possibility of importing CAD models. Post processing is performed with a general purpose scientific visualization program named Drawmesh. In the same nonlinear analysis several nonlinear models may be simultaneously considered, allowing, for instance, the combination of reinforced concrete with strengthening components, which exhibit distinct nonlinear constitutive laws. Interface elements with appropriate friction laws and nonlinear springs mat also be simultaneously considered. The global response history is recorded in all the sampling points for selected post-processing. The system of nonlinear equations arising from the incremental-iterative procedure are solved by the Newton-Raphson method (see Section 5.2.2). The analysis can be performed using a path dependent or a path independent strategy, with load or displacement control. Others techniques, such as arc-length control or indirect displacement control, are also available.
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Chapter 5 â&#x20AC;&#x201C; NUMERICAL ANALYSIS
5.2.2 Iterative techniques for the solution of nonlinear problems The displacement formulation of the finite element method leads to (Zienkiewicz and Taylor, 1989): đ??žđ?&#x2018;&#x17D;=đ??š
(5.1)
where đ??ž is the stiffness matrix, đ?&#x2018;&#x17D; is the vector of the nodal displacement and đ??š is the vector of the nodal forces which are equivalent to the loads acting on the finite element. The stiffness matrix can be computed with the following expression: đ??ž = â&#x2C6;Ťđ?&#x2018;&#x2030; đ??ľ đ?&#x2018;&#x2021; đ??ˇ đ??ľ đ?&#x2018;&#x2018;đ?&#x2018;&#x2030;
(5.2)
where đ??ˇ is the constitutive matrix, đ??ľ is a matrix that depends on the finite element type and đ?&#x2018;&#x2030; is the volume of the finite element. Commonly, numerical integration is used to evaluate the integral in (5.2). When Gaussian or Newton-Cotes quadrature is adopted, the integrand function is evaluated in predefined integration points. In linear elasticity equation (5.1) corresponds to a system of linear equations, whose solution can be obtained using several techniques. The most common algorithms are based on direct methods, such as Gaussian elimination (Zienkiewicz and Taylor, 1989) or iterative methods, like the conjugate gradient method (Azevedo and Barros, 1990). In the context of non-linear analysis, equation (5.1) is no longer linear, since the stiffness matrix depends on the values of the displacements, đ?&#x2018;&#x17D;. In order to obtain the evolution of the structural response, đ??š must be applied in small steps. In the present work the total load at the end of each step is named combination. The solution at combination đ?&#x2018;&#x203A; can be computed by solving the system of nonlinear equations, đ?&#x153;&#x201C;đ?&#x2018;&#x203A; = đ?&#x153;&#x201C;( đ?&#x2018;&#x17D;đ?&#x2018;&#x203A; ) = đ??š đ?&#x2018;&#x203A; â&#x2C6;&#x2019; đ??š â&#x20AC;˛ ( đ?&#x2018;&#x17D; đ?&#x2018;&#x203A; ) = 0
(5.3)
where đ?&#x153;&#x201C;đ?&#x2018;&#x203A; is the residual force vector, which is calculated as the difference between đ??š đ?&#x2018;&#x203A; = đ??š đ?&#x2018;&#x203A;â&#x2C6;&#x2019;1 + â&#x2C6;&#x2020;đ??š đ?&#x2018;&#x203A; and the internal equivalent nodal forces, đ??š â&#x20AC;˛ (đ?&#x2018;&#x17D; đ?&#x2018;&#x203A; ). Equation (5.3) can be solved by the Newton-Raphson method. The first two terms of the Taylor series expansion of đ?&#x153;&#x201C;( đ?&#x2018;&#x17D;đ?&#x2018;&#x203A; ) can be used in (5.3) as an approximation, yielding đ?&#x153;&#x2022;đ?&#x153;&#x201C; đ?&#x2018;&#x17E;â&#x2C6;&#x2019;1
đ?&#x153;&#x201C;(đ?&#x2018;&#x17D;đ?&#x2018;&#x203A;đ?&#x2018;&#x17E; ) â&#x2030;&#x2C6; đ?&#x153;&#x201C;(đ?&#x2018;&#x17D;đ?&#x2018;&#x203A;đ?&#x2018;&#x17E;â&#x2C6;&#x2019;1 ) + ( đ?&#x153;&#x2022;đ?&#x2018;&#x17D; )
đ?&#x2018;&#x203A;
đ?&#x203A;żđ?&#x2018;&#x17D;đ?&#x2018;&#x203A;đ?&#x2018;&#x17E; = 0
(5.4)
In this equation đ?&#x2018;&#x17E; is the iteration counter. The initial solution of the Newton-Raphson method is đ?&#x2018;&#x17D;đ?&#x2018;&#x203A;0 = đ?&#x2018;&#x17D;đ?&#x2018;&#x203A;â&#x2C6;&#x2019;1 . In equation (5.4) đ?&#x153;&#x2022;đ?&#x153;&#x201C; đ?&#x2018;&#x17E;â&#x2C6;&#x2019;1
( đ?&#x153;&#x2022;đ?&#x2018;&#x17D; )
đ?&#x2018;&#x203A;
đ?&#x153;&#x2022;đ??šâ&#x20AC;˛
= â&#x2C6;&#x2019; ( đ?&#x153;&#x2022;đ?&#x2018;&#x17D; )
đ?&#x2018;&#x17E;â&#x2C6;&#x2019;1 đ?&#x2018;&#x203A;
đ?&#x2018;&#x17E;â&#x2C6;&#x2019;1
= â&#x2C6;&#x2019; (đ??ž đ?&#x2018;&#x2021; )đ?&#x2018;&#x203A;
(5.5) 103
Chapter 5 â&#x20AC;&#x201C; NUMERICAL ANALYSIS
is the Jacobian matrix, which in this context corresponds to tangential stiffness matrix. The iterative correction đ?&#x203A;żđ?&#x2018;&#x17D;đ?&#x2018;&#x203A;đ?&#x2018;&#x17E; is obtained by solving the system of linear equations (5.4), i.e., đ?&#x2018;&#x17E;â&#x2C6;&#x2019;1
đ?&#x2018;&#x17E; đ?&#x2018;&#x17E;â&#x2C6;&#x2019;1 (đ??ž đ?&#x2018;&#x2021; )đ?&#x2018;&#x203A; đ?&#x203A;żđ?&#x2018;&#x17D;đ?&#x2018;&#x203A; = đ?&#x153;&#x201C;(đ?&#x2018;&#x17D;đ?&#x2018;&#x203A; )
(5.6)
The vector of the displacement is updated with đ?&#x2018;&#x17D;đ?&#x2018;&#x203A;đ?&#x2018;&#x17E; = đ?&#x2018;&#x17D;đ?&#x2018;&#x203A;â&#x2C6;&#x2019;1 + â&#x2C6;&#x2020;đ?&#x2018;&#x17D;đ?&#x2018;&#x203A;đ?&#x2018;&#x17E; = đ?&#x2018;&#x17D;đ?&#x2018;&#x203A;đ?&#x2018;&#x17E;â&#x2C6;&#x2019;1 + đ?&#x203A;żđ?&#x2018;&#x17D;đ?&#x2018;&#x203A;đ?&#x2018;&#x17E;
(5.7)
where â&#x2C6;&#x2020;đ?&#x2018;&#x17D;đ?&#x2018;&#x203A;đ?&#x2018;&#x17E; = â&#x2C6;&#x2018;đ?&#x2018;&#x17E;đ?&#x2018;&#x2013;=1 đ?&#x203A;żđ?&#x2018;&#x17D;đ?&#x2018;&#x203A;đ?&#x2018;&#x2013;
(5.8)
The Newton Raphson method is illustrated in Figure 5.2.1:
Figure 5.2.1 â&#x20AC;&#x201C; Newton-Raphson method.
The iterative procedure described above is interrupted when a certain parameter becomes smaller than a predefined tolerance. The convergence criterion can be based on the force norm, the displacement norm or the energy norm (Zienkiewicz and Taylor, 1991). In the present work a force norm is adopted, and the iterative procedure is successfully terminated when the following condition is verified đ?&#x2018;&#x2021;
đ?&#x2018;&#x2013; ) (đ?&#x153;&#x201C;đ?&#x2018;&#x2013; ) â&#x2C6;&#x161;(đ?&#x153;&#x201C;đ?&#x2018;&#x203A; đ?&#x2018;&#x203A; đ?&#x2018;&#x2021;
â&#x2C6;&#x161;(đ??šđ?&#x2018;&#x203A; ) đ??šđ?&#x2018;&#x203A;
< 10â&#x2C6;&#x2019;3
(5.9)
In the incremental-iterative procedure two stress update strategies were implemented, which lead to a path dependent (PD) or a path independent (PI) behaviors. According to Cristifield 104
Chapter 5 â&#x20AC;&#x201C; NUMERICAL ANALYSIS
(1991), the path dependent strategy is not recommended since it may lead to â&#x20AC;&#x153;spurious unloadingâ&#x20AC;? during the iterative process, therefore only the path independent is adopted, in spite of both strategies (PD and PI) being available in the finite element computer code used in the present study. When a path independent strategy is adopted, the iterative variation of the displacements of the current iteration, đ?&#x203A;żđ?&#x2018;&#x17D;đ?&#x2018;&#x203A;đ?&#x2018;&#x17E; , is also calculated using the information of the previous iteration, đ?&#x2018;&#x17E; â&#x2C6;&#x2019; 1. The new stress state, đ?&#x153;&#x17D; đ?&#x2018;&#x17E; , is calculated as an update of the stress state at the end of the iterative process of the previous combination, đ?&#x153;&#x17D; đ?&#x2018;&#x203A;â&#x2C6;&#x2019;1. 1. Calculate the iterative displacements: đ??žđ?&#x2018;&#x2021;đ?&#x2018;&#x17E;â&#x2C6;&#x2019;1 đ?&#x203A;żđ?&#x2018;&#x17D;đ?&#x2018;&#x17E; = đ?&#x153;&#x201C; đ?&#x2018;&#x17E;â&#x2C6;&#x2019;1 2. Update the incremental displacements: â&#x2C6;&#x2020;đ?&#x2018;&#x17D;đ?&#x2018;&#x17E; = â&#x2C6;&#x2020;đ?&#x2018;&#x17D;đ?&#x2018;&#x17E;â&#x2C6;&#x2019;1 + đ?&#x203A;żđ?&#x2018;&#x17D;đ?&#x2018;&#x17E; 3. Calculate the incremental strain: â&#x2C6;&#x2020;đ?&#x153;&#x20AC; đ?&#x2018;&#x17E; = đ??ľâ&#x2C6;&#x2020;đ?&#x2018;&#x17D;đ?&#x2018;&#x17E; 4. Calculate the incremental stress: â&#x2C6;&#x2020;đ?&#x153;&#x17D; đ?&#x2018;&#x17E; = đ??ˇđ?&#x2018;&#x2021; â&#x2C6;&#x2020;đ?&#x153;&#x20AC; đ?&#x2018;&#x17E; 5. Update the stress: đ?&#x153;&#x17D; đ?&#x2018;&#x17E; = đ?&#x153;&#x17D; đ?&#x2018;&#x203A;â&#x2C6;&#x2019;1 + â&#x2C6;&#x2020;đ?&#x153;&#x17D; đ?&#x2018;&#x17E; 5.2.3 Arc-length method Within the nonlinear analysis of the present work, an incremental load procedure was used. Considering a generic system with one degree of freedom, the nonlinear relationship between force and displacement can be represented as:
Figure 5.2.2 â&#x20AC;&#x201C; Arc-length technique â&#x20AC;&#x201C; system with one degree of freedom (b=1.0).
Figure 5.2.2 represents also the force displacement variation corresponding to the load increase between the combinations đ?&#x2018;&#x203A; â&#x2C6;&#x2019; 1 and đ?&#x2018;&#x203A;. The use of the load increment, â&#x2C6;&#x2020;đ??šđ?&#x2018;&#x203A; , 105
Chapter 5 â&#x20AC;&#x201C; NUMERICAL ANALYSIS
nevertheless, leads to a solution that starts from point đ??´, exceeding the peak corresponding to point đ??ś. In this way the evolution of the structure behavior, from point đ??´ to point đ??ˇ, is not considered. In order to get to know this behavior, the load increment is multiplied by a factor đ?&#x153;&#x2020; whose value is defined through the following constraints, which corresponds to obtaining a solution located on the radius of the arc â&#x2C6;&#x2020;đ??ż showed in Figure 5.2.3. (â&#x2C6;&#x2020;đ?&#x2018;&#x17D;đ?&#x2018;&#x203A; )2 + đ?&#x153;&#x2020;2 đ?&#x2018;? 2 (â&#x2C6;&#x2020;đ??šđ?&#x2018;&#x203A; )2 = â&#x2C6;&#x2020;đ??ż2
(5.10)
where đ?&#x2018;? is a scalar factor that converts the force magnitude in the displacement magnitude. According to Figure 5.2.3, the following equation defines, in terms of đ?&#x153;&#x2020;, the exterior force value in combination đ?&#x2018;&#x203A; đ??šđ?&#x2018;&#x203A; (đ?&#x153;&#x2020;) = đ??šđ?&#x2018;&#x203A;â&#x2C6;&#x2019;1 + đ?&#x153;&#x2020;â&#x2C6;&#x2020;đ??šđ?&#x2018;&#x203A;
(5.11)
The no-equilibrated force (residuo) in combination đ?&#x2018;&#x203A;, i.e. đ?&#x153;&#x201C;đ?&#x2018;&#x203A; , is defined as follow. đ?&#x153;&#x201C;đ?&#x2018;&#x203A; = đ??šđ?&#x2018;&#x203A; (đ?&#x153;&#x2020;) â&#x2C6;&#x2019; đ??š â&#x20AC;˛ (đ?&#x2018;&#x17D;đ?&#x2018;&#x203A; )
(5.12)
where đ??š â&#x20AC;˛ (đ?&#x2018;&#x17D;đ?&#x2018;&#x203A; ) is the internal force obtained basing on the displacement that corresponds to the current combination đ?&#x2018;&#x17D;đ?&#x2018;&#x203A; . According to equations (5.11) and (5.12) the annulment of the noequilibrated forces corresponds to: đ?&#x153;&#x201C;đ?&#x2018;&#x203A; = đ?&#x153;&#x201C;(đ?&#x2018;&#x17D;đ?&#x2018;&#x203A; , đ?&#x153;&#x2020;) = đ??šđ?&#x2018;&#x203A; (đ?&#x153;&#x2020;) â&#x2C6;&#x2019; đ??š â&#x20AC;˛ (đ?&#x2018;&#x17D;đ?&#x2018;&#x203A; ) = đ??šđ?&#x2018;&#x203A;â&#x2C6;&#x2019;1 + đ?&#x153;&#x2020;â&#x2C6;&#x2020;đ??šđ?&#x2018;&#x203A; â&#x2C6;&#x2019; đ??š â&#x20AC;˛ (đ?&#x2018;&#x17D;đ?&#x2018;&#x203A; ) = 0
(5.13)
In the Newton-Raphson method it is expected that in the iteration đ?&#x2018;&#x17E;, the equations (5.10) and (5.13) will be respected obtaining thus: đ?&#x153;&#x201C;(đ?&#x2018;&#x17D;đ?&#x2018;&#x203A;đ?&#x2018;&#x17E; , đ?&#x153;&#x2020;đ?&#x2018;&#x17E; ) = đ??šđ?&#x2018;&#x203A;đ?&#x2018;&#x17E; (đ?&#x153;&#x2020;đ?&#x2018;&#x17E; ) â&#x2C6;&#x2019; đ??š â&#x20AC;˛ (đ?&#x2018;&#x17D;đ?&#x2018;&#x203A;đ?&#x2018;&#x17E; ) = đ??šđ?&#x2018;&#x203A;â&#x2C6;&#x2019;1 + đ?&#x153;&#x2020;đ?&#x2018;&#x17E; â&#x2C6;&#x2020;đ??šđ?&#x2018;&#x203A; â&#x2C6;&#x2019; đ??š â&#x20AC;˛ (đ?&#x2018;&#x17D;đ?&#x2018;&#x203A;đ?&#x2018;&#x17E; ) = 0 2
đ?&#x2018;&#x201C;(â&#x2C6;&#x2020;đ?&#x2018;&#x17D;đ?&#x2018;&#x203A;đ?&#x2018;&#x17E; , đ?&#x153;&#x2020;đ?&#x2018;&#x17E; ) = (â&#x2C6;&#x2020;đ?&#x2018;&#x17D;đ?&#x2018;&#x203A;đ?&#x2018;&#x17E; ) + đ?&#x2018;? 2 (đ?&#x153;&#x2020;đ?&#x2018;&#x17E; )2 (â&#x2C6;&#x2020;đ??šđ?&#x2018;&#x203A; )2 â&#x2C6;&#x2019; â&#x2C6;&#x2020;đ??ż2 = 0
(5.14đ?&#x2018;&#x17D;) (5.14đ?&#x2018;?)
The Newton-Raphson iterative process with the arc-length method is represented in next Figure:
106
Chapter 5 â&#x20AC;&#x201C; NUMERICAL ANALYSIS
Figure 5.2.3 â&#x20AC;&#x201C; Arc-length iterative procedure for a system with one degree of freedom (b=1.0).
In this project load combinations treated with Newton-Raphson without arc-length method along with combinations with arc length using constant â&#x2C6;&#x2020;đ??šđ?&#x2018;&#x203A; have been implemented. In this context the increase of external force is designated by â&#x2C6;&#x2020;đ??š. In Figure 5.2.4 is shown the application of the Newton-Raphson method with and without arc-length.
107
Chapter 5 â&#x20AC;&#x201C; NUMERICAL ANALYSIS
Figure 5.2.4 â&#x20AC;&#x201C; Newton-Raphson method with and without arc-length technique.
The arc-length method application to technical problems with more than one degree of freedom is obtained generalizing the equation (5.14), which leads to the following system of nonlinear equations. đ?&#x153;&#x201C;(đ?&#x2018;&#x17D;đ?&#x2018;&#x203A;đ?&#x2018;&#x17E; , đ?&#x153;&#x2020;đ?&#x2018;&#x17E; ) = đ??šđ?&#x2018;&#x203A;đ?&#x2018;&#x17E; (đ?&#x153;&#x2020;đ?&#x2018;&#x17E; ) â&#x2C6;&#x2019; đ??š â&#x20AC;˛ (đ?&#x2018;&#x17D;đ?&#x2018;&#x203A;đ?&#x2018;&#x17E; ) = đ??š đ?&#x2018;&#x203A;â&#x2C6;&#x2019;1 + đ?&#x153;&#x2020;đ?&#x2018;&#x17E; â&#x2C6;&#x2020;đ??š â&#x2C6;&#x2019; đ??š â&#x20AC;˛ (đ?&#x2018;&#x17D;đ?&#x2018;&#x203A;đ?&#x2018;&#x17E; ) = 0 đ?&#x2018;&#x2021;
2
đ?&#x2018;&#x201C;(â&#x2C6;&#x2020;đ?&#x2018;&#x17D;đ?&#x2018;&#x203A;đ?&#x2018;&#x17E; , đ?&#x153;&#x2020;đ?&#x2018;&#x17E; ) = [â&#x2C6;&#x2020;đ?&#x2018;&#x17D;đ?&#x2018;&#x203A;đ?&#x2018;&#x17E; ] â&#x2C6;&#x2020;đ?&#x2018;&#x17D;đ?&#x2018;&#x203A;đ?&#x2018;&#x17E; + đ?&#x2018;? 2 (đ?&#x153;&#x2020;đ?&#x2018;&#x17E; )2 [â&#x2C6;&#x2020;đ??š] â&#x2C6;&#x2020;đ??š â&#x2C6;&#x2019; â&#x2C6;&#x2020;đ??ż2 = 0
(5.15đ?&#x2018;&#x17D;) (5.15đ?&#x2018;?)
According to Crisfield (1991), in this problem, factor đ?&#x2018;? can be null. 5.2.3.1 Arc-length technique in FEMIX 4.0 In the numerical simulations where arc-length technique is implemented, it begins to operate starting from the last combination founded in the data file (đ?&#x2018;&#x203A;đ??š ). In the following combinations, the load increment between (đ?&#x2018;&#x203A;đ??š â&#x2C6;&#x2019; 1) and đ?&#x2018;&#x203A;đ??š (â&#x2C6;&#x2020;đ??š), is kept constant. The maximum number of combinations with or without arc-length is đ?&#x2018;&#x203A; = đ?&#x2018;&#x203A;đ??š â&#x2C6;&#x2019; 1 + đ?&#x2018;&#x203A;đ??´ , where đ?&#x2018;&#x203A;đ??´ is the maximum number of combinations corresponding to arc-length method. In each đ?&#x2018;&#x203A;đ??´ combinations with arc-length technique, the load increment â&#x2C6;&#x2020;đ??š is multiplied by factor đ?&#x153;&#x2020; previously introduced (see Figure 5.2.4). As in the first iteration of each combination with arc-length, the load factor is equal to 1.0 (đ?&#x153;&#x2020;â&#x20AC;˛ = 1.0), this is considered as a classical iteration of the Newton-Raphson method (see Figure 5.2.3). However, in some cases, the initial load factor is not equal to 1.0, therefore the external forces vector, đ??šđ?&#x2018;&#x203A;1 (đ?&#x153;&#x2020;1 ), the displacement vector, â&#x2C6;&#x2020;đ?&#x2018;&#x17D;1đ?&#x2018;&#x203A; and the initial load factor must be corrected in order to respect the constrain equation of each case. 108
Chapter 5 â&#x20AC;&#x201C; NUMERICAL ANALYSIS
In Figure 5.2.5 the procedure used in the first iteration of each increment is schematically presented. In particular a corrective factor đ?&#x153;&#x201A; is used, according to the configuration â&#x2C6;&#x2020;đ??ż
considered: constant arc-length (đ?&#x153;&#x201A; = â&#x2C6;&#x2020;đ??ż (đ?&#x153;&#x2020;=1.0)), displacement control at a specific variable â&#x2C6;&#x2020;đ?&#x2018;&#x17D;đ?&#x2018;&#x2014;â&#x2C6;&#x2019;đ?&#x2018;&#x2013;
â&#x2C6;&#x2020;đ?&#x2018;&#x17D;
(đ?&#x153;&#x201A; = đ?&#x203A;żđ?&#x2018;&#x17D;1 ) , relative displacement control between two specific variables (đ?&#x153;&#x201A; = 1 đ?&#x203A;żđ?&#x2018;&#x17D;
1 đ?&#x2018;&#x203A;,đ?&#x2018;&#x2014; â&#x2C6;&#x2019;đ?&#x203A;żđ?&#x2018;&#x17D;đ?&#x2018;&#x203A;,đ?&#x2018;&#x2013;
đ?&#x2018;&#x203A;,đ?&#x2018;&#x2013;
).
Figure 5.2.5 â&#x20AC;&#x201C; Load increment correction through the Ρ factor.
A brief description of the incremental/iterative algorithm corresponding to the NewtonRaphson with arc-length method used in FEMIX 4.0 computer code, can be found elsewhere (Azevedo A., Barros J. A. O., Sena-Cruz J. S., 2003). 5.2.4 Elasto-plastic multi fixed smeared crack model This model corresponds to the coupling of the multi-fixed smeared crack model and the elasto-plastic model. The multi-fixed smeared crack model is a generalization of the single-fixed smeared crack model where only one fixed smeared crack was allowed to form at each integration point. On the other hand, elasto-plastic based models depend on the concept of yield surface, flow rule and hardening (or softening) law. More details can be found elsewhere (Sena-Cruz J. M., 2004). 5.2.4.1 Yield surface Two types of yield surface are combined in the proposed numerical model: the Rankine criterion for concrete in tension, and the Owen and Figueiras (1983) yield surface for concrete in compression. Figure 5.2.6 represents the initial and the limit yield surfaces. This initial surface is the limiting surface for elastic behavior. Experimental results from Kupfer et al. (1969) are also included. 109
Chapter 5 â&#x20AC;&#x201C; NUMERICAL ANALYSIS
Figure 5.2.6 â&#x20AC;&#x201C; Yield surface adopted in the elasto-plastic multi-fixed smeared crack model.
The yield surface proposed by Rankine governs the crack initiation, i.e, when the maximum principal stress, đ?&#x153;&#x17D;đ??ź , exceeds the uniaxial tensile strength, đ?&#x2018;&#x201C;đ?&#x2018;?đ?&#x2018;Ą , a crack is formed. This assumption is justified by the experimental results obtained by Kupfer et al. (1969) when the tensile cracking is not accompanied by significant lateral compression. The yield surface proposed by Owen and Figueiras (1983) is suitable to simulate the concrete compressive behavior under monotonic loading, admitting that the tensile stresses do not exceed the concrete tensile strength. 5.2.4.2 Constitutive equation After crack initiation, the basic assumption of this model is the decomposition of the incremental strain vector, â&#x2C6;&#x2020;đ?&#x153;&#x20AC;, into an incremental crack strain vector, â&#x2C6;&#x2020;đ?&#x153;&#x20AC; đ?&#x2018;?đ?&#x2018;&#x; , and an incremental strain vector of the concrete between cracks, â&#x2C6;&#x2020;đ?&#x153;&#x20AC; đ?&#x2018;?đ?&#x2018;&#x153; . This vector is decomposed in an elastic reversible part, â&#x2C6;&#x2020;đ?&#x153;&#x20AC; đ?&#x2018;&#x2019; , and an irreversible or plastic part, â&#x2C6;&#x2020;đ?&#x153;&#x20AC; đ?&#x2018;? , resulting â&#x2C6;&#x2020;đ?&#x153;&#x20AC; = â&#x2C6;&#x2020;đ?&#x153;&#x20AC; đ?&#x2018;?đ?&#x2018;&#x; + â&#x2C6;&#x2020;đ?&#x153;&#x20AC; đ?&#x2018;?đ?&#x2018;&#x153; = â&#x2C6;&#x2020;đ?&#x153;&#x20AC; đ?&#x2018;?đ?&#x2018;&#x; + â&#x2C6;&#x2020;đ?&#x153;&#x20AC; đ?&#x2018;&#x2019; + â&#x2C6;&#x2020;đ?&#x153;&#x20AC; đ?&#x2018;?
(5.16)
Constitutive equations from the multi-fixed smeared crack model Assuming linear elastic behavior for the concrete between cracks (undamaged concrete), the constitutive relationship between â&#x2C6;&#x2020;đ?&#x153;&#x20AC; đ?&#x2018;?đ?&#x2018;&#x153; and â&#x2C6;&#x2020;đ?&#x153;&#x17D; is given by, â&#x2C6;&#x2020;đ?&#x153;&#x17D; = đ??ˇđ?&#x2018;?đ?&#x2018;&#x153; â&#x2C6;&#x2020;đ?&#x153;&#x20AC; đ?&#x2018;?đ?&#x2018;&#x153; where đ??ˇđ?&#x2018;?đ?&#x2018;&#x153; is the constitutive matrix according to Hookeâ&#x20AC;&#x2122;s law.
110
(5.17)
Chapter 5 â&#x20AC;&#x201C; NUMERICAL ANALYSIS
In a similar way, a relationship between â&#x2C6;&#x2020;đ?&#x153;&#x17D; đ?&#x2018;?đ?&#x2018;&#x; and â&#x2C6;&#x2020;đ?&#x153;&#x20AC; đ?&#x2018;?đ?&#x2018;&#x; is established to simulate the crack opening and shear sliding using, â&#x2C6;&#x2020;đ?&#x153;&#x17D; đ?&#x2018;?đ?&#x2018;&#x; = đ??ˇđ?&#x2018;?đ?&#x2018;&#x; â&#x2C6;&#x2020;đ?&#x153;&#x20AC; đ?&#x2018;?đ?&#x2018;&#x;
(5.18)
where đ??ˇđ?&#x2018;?đ?&#x2018;&#x; is the crack constitutive matrix, assumed to be diagonal. Its diagonal terms are đ??ˇ đ?&#x2018;?đ?&#x2018;&#x; đ??ź and đ??ˇ đ?&#x2018;?đ?&#x2018;&#x; đ??źđ??ź , i.e., mode I and mode II stiffness modulus associated with the crack behavior. Combining the equations presented above, a constitutive law for cracked concrete can be obtained. Extending the formulation in order to simulate the formation of more than one fixed smeared crack at each integration point, happen that the strain field in a cracked integration point is submitted to an increment, â&#x2C6;&#x2020;đ?&#x153;&#x20AC; đ?&#x2018;&#x161; , and the stress state of the integration point is also modified and must be updated (đ?&#x153;&#x17D; đ?&#x2018;&#x161; ). In conclusion, the incremental stress vector can be computed from the incremental elastic strain vector, đ?&#x2018;&#x2019; â&#x2C6;&#x2020;đ?&#x153;&#x17D; đ?&#x2018;&#x161; = đ??ˇđ?&#x2018;&#x2019; â&#x2C6;&#x2020;đ?&#x153;&#x20AC;đ?&#x2018;&#x161;
(5.19)
Constitutive equations from the elasto-plastic model đ?&#x2018;&#x2019; The incremental elastic strain vector, â&#x2C6;&#x2020;đ?&#x153;&#x20AC;đ?&#x2018;&#x161; , multiplied by the elastic constitutive matrix, đ??ˇđ?&#x2018;&#x2019; ,
is used to update the stress vector, which leads to đ?&#x2018;&#x2019; đ?&#x153;&#x17D; đ?&#x2018;&#x161; = đ?&#x153;&#x17D; đ?&#x2018;&#x161;â&#x2C6;&#x2019;1 + â&#x2C6;&#x2020;đ?&#x153;&#x20AC;đ?&#x2018;&#x161;
(5.20)
In conclusion the behavior of the cracked concrete is governed by the multi-fixed smeared crack model. In each sampling point several non-orthogonal cracks can arise. The equilibrium equations involved in the constitutive material model leads to a system of nonlinear equations. This system is solved using the Newton-Raphson method. The developed model includes implicit Euler backward algorithms and consistent tangent operators. 5.2.4.3 Crack status According to Bazant and Oh (1983), the most suitable approach to simulate the crack propagation under the finite element framework is by taking into account the concrete fracture parameters, namely, the shape of the tensile-softening diagram and the fracture energy. Two distinct tensile-softening diagrams are available in the developed computational code: tri-linear and exponential diagrams (see Figure 5.2.7). The tri-linear diagram is the defined by the following expressions
111
Chapter 5 â&#x20AC;&#x201C; NUMERICAL ANALYSIS
đ?&#x153;&#x17D;đ?&#x2018;&#x203A;đ?&#x2018;?đ?&#x2018;&#x; (đ?&#x153;&#x20AC;đ?&#x2018;&#x203A;đ?&#x2018;?đ?&#x2018;&#x; )
=
đ?&#x2018;?đ?&#x2018;&#x; with, đ??ˇđ??ź,đ?&#x2018;&#x2013; = â&#x2C6;&#x2019;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2013;
đ?&#x2018;?đ?&#x2018;&#x; đ?&#x2018;?đ?&#x2018;&#x; đ?&#x153;&#x20AC;đ?&#x2018;&#x203A; đ?&#x2018;&#x201C;đ?&#x2018;?đ?&#x2018;Ą + đ??ˇđ??ź,1
đ?&#x2018;?đ?&#x2018;&#x; đ?&#x2018;&#x2013;đ?&#x2018;&#x201C; 0 < đ?&#x153;&#x20AC;đ?&#x2018;&#x203A;đ?&#x2018;?đ?&#x2018;&#x; < đ?&#x153;&#x2030;1 đ?&#x153;&#x20AC;đ?&#x2018;&#x203A;,đ?&#x2018;˘đ?&#x2018;&#x2122;đ?&#x2018;Ą
đ?&#x2018;?đ?&#x2018;&#x; đ?&#x2018;?đ?&#x2018;&#x; đ?&#x2018;?đ?&#x2018;&#x; đ?&#x203A;ź1 đ?&#x2018;&#x201C;đ?&#x2018;?đ?&#x2018;Ą + đ??ˇđ??ź,2 (đ?&#x153;&#x20AC;đ?&#x2018;&#x203A; â&#x2C6;&#x2019; đ?&#x153;&#x2030;1 đ?&#x153;&#x20AC;đ?&#x2018;&#x203A;,đ?&#x2018;˘đ?&#x2018;&#x2122;đ?&#x2018;Ą )
đ?&#x2018;?đ?&#x2018;&#x; đ?&#x2018;?đ?&#x2018;&#x; đ?&#x2018;&#x2013;đ?&#x2018;&#x201C; đ?&#x153;&#x2030;1 đ?&#x153;&#x20AC;đ?&#x2018;&#x203A;,đ?&#x2018;˘đ?&#x2018;&#x2122;đ?&#x2018;Ą < đ?&#x153;&#x20AC;đ?&#x2018;&#x203A;đ?&#x2018;?đ?&#x2018;&#x; < đ?&#x153;&#x2030;2 đ?&#x153;&#x20AC;đ?&#x2018;&#x203A;,đ?&#x2018;˘đ?&#x2018;&#x2122;đ?&#x2018;Ą
đ?&#x2018;?đ?&#x2018;&#x; đ?&#x2018;?đ?&#x2018;&#x; đ?&#x2018;?đ?&#x2018;&#x; đ?&#x203A;ź2 đ?&#x2018;&#x201C;đ?&#x2018;?đ?&#x2018;Ą + đ??ˇđ??ź,3 (đ?&#x153;&#x20AC;đ?&#x2018;&#x203A; â&#x2C6;&#x2019; đ?&#x153;&#x2030;2 đ?&#x153;&#x20AC;đ?&#x2018;&#x203A;,đ?&#x2018;˘đ?&#x2018;&#x2122;đ?&#x2018;Ą ) { 0
2 â&#x201E;&#x17D; đ?&#x2018;&#x201C;đ?&#x2018;?đ?&#x2018;Ą
đ??şđ?&#x2018;&#x201C;
đ?&#x2018;?đ?&#x2018;&#x; đ?&#x2018;?đ?&#x2018;&#x; đ?&#x2018;&#x2013;đ?&#x2018;&#x201C; đ?&#x153;&#x2030;2 đ?&#x153;&#x20AC;đ?&#x2018;&#x203A;,đ?&#x2018;˘đ?&#x2018;&#x2122;đ?&#x2018;Ą < đ?&#x153;&#x20AC;đ?&#x2018;&#x203A;đ?&#x2018;?đ?&#x2018;&#x; < đ?&#x153;&#x20AC;đ?&#x2018;&#x203A;,đ?&#x2018;˘đ?&#x2018;&#x2122;đ?&#x2018;Ą đ?&#x2018;?đ?&#x2018;&#x; đ?&#x2018;&#x2013;đ?&#x2018;&#x201C; đ?&#x153;&#x20AC;đ?&#x2018;&#x203A;đ?&#x2018;?đ?&#x2018;&#x; < đ?&#x153;&#x20AC;đ?&#x2018;&#x203A;,đ?&#x2018;˘đ?&#x2018;&#x2122;đ?&#x2018;Ą
(5.21)
and where:
đ?&#x2018;&#x2DC;1 =
(1â&#x2C6;&#x2019;đ?&#x203A;ź1 )(đ?&#x153;&#x2030;1 +đ?&#x203A;ź1 đ?&#x153;&#x2030;2 â&#x2C6;&#x2019;đ?&#x203A;ź2 đ?&#x153;&#x2030;1 +đ?&#x203A;ź2 )
đ?&#x2018;&#x2DC;2 =
(đ?&#x203A;ź1 â&#x2C6;&#x2019;đ?&#x203A;ź2 )(đ?&#x153;&#x2030;1 +đ?&#x203A;ź1 đ?&#x153;&#x2030;2 â&#x2C6;&#x2019;đ?&#x203A;ź2 đ?&#x153;&#x2030;1 +đ?&#x203A;ź2 )
đ?&#x2018;&#x2DC;3 =
đ?&#x203A;ź2 (đ?&#x153;&#x2030;1 +đ?&#x203A;ź1 đ?&#x153;&#x2030;2 â&#x2C6;&#x2019;đ?&#x203A;ź2 đ?&#x153;&#x2030;1 +đ?&#x203A;ź2 ) 2(1â&#x2C6;&#x2019;đ?&#x153;&#x2030;2 )
2đ?&#x153;&#x2030;1
(5.22)
2(đ?&#x153;&#x2030;1 â&#x2C6;&#x2019;đ?&#x153;&#x2030;2 )
đ?&#x2018;?đ?&#x2018;&#x; The ultimate crack normal strain, đ?&#x153;&#x20AC;đ?&#x2018;&#x203A;,đ?&#x2018;˘đ?&#x2018;&#x2122;đ?&#x2018;Ą , is given by, đ??şđ?&#x2018;&#x201C;
đ?&#x2018;?đ?&#x2018;&#x; đ?&#x153;&#x20AC;đ?&#x2018;&#x203A;,đ?&#x2018;˘đ?&#x2018;&#x2122;đ?&#x2018;Ą = đ?&#x2018;&#x2DC;4 đ?&#x2018;&#x201C;
(5.23)
đ?&#x2018;?đ?&#x2018;Ą â&#x201E;&#x17D;
where đ?&#x2018;&#x2DC;4 = đ?&#x153;&#x2030;
2
(5.24)
1 +đ?&#x203A;ź1 đ?&#x153;&#x2030;2 â&#x2C6;&#x2019;đ?&#x203A;ź2 đ?&#x153;&#x2030;1 +đ?&#x203A;ź2
a)
b)
Figure 5.2.7 â&#x20AC;&#x201C; Tensile softening diagram: a)Tri-linear; b)Exponential (Cornelissen et al., 1986).
The concrete fracture energy, đ??şđ?&#x2018;&#x201C; , is the energy required to propagate a tensile crack of unit area. Generally, đ??şđ?&#x2018;&#x201C; is assumed to be a material parameter and according to the CEB-FIB (1993) it can be estimated from the concrete compressive strength, đ?&#x2018;&#x201C;đ?&#x2018;? , and maximum aggregate size. 112
Chapter 5 â&#x20AC;&#x201C; NUMERICAL ANALYSIS
Depending on the followed đ?&#x153;&#x17D;đ?&#x2018;&#x203A;đ?&#x2018;?đ?&#x2018;&#x; â&#x2C6;&#x2019; đ?&#x153;&#x20AC;đ?&#x2018;&#x203A;đ?&#x2018;?đ?&#x2018;&#x; path, a crack can assume one of six crack statuses as shown in Figure 5.2.8 .The first (1) is named initiation and corresponds to the crack initiation. The opening status occurs when the crack is in the softening branch (2). In the present model a secant branch is assumed to simulate the unloading (3) and the reloading (5) phases. The closing status designates the unloading phase while the reopening status is attributed to the crack in the reloading phase. This assumption does not correspond to the most realistic approach, since cyclic tests reveal the occurrence of a hysteretic behavior (Hordijk 1991). Since the present model was developed to simulate the behavior of concrete structures under monotonic loading, this simple approach is sufficiently accurate. If a crack closes, i.e., đ?&#x153;&#x20AC;đ?&#x2018;&#x203A;đ?&#x2018;?đ?&#x2018;&#x; = 0, the crack status receives the designation of closed (4). The fully open (6) status occurs when in the crack the mode I fracture energy is fully exhausted.
Figure 5.2.8 â&#x20AC;&#x201C; Crack status.
The stress update procedure described in the previous section is only applied to the active cracks, i.e., when đ?&#x153;&#x20AC;đ?&#x2018;&#x203A;đ?&#x2018;?đ?&#x2018;&#x; > 0. When a crack initiates ( đ?&#x153;&#x17D;đ??ź > đ?&#x2018;&#x201C;đ?&#x2018;?đ?&#x2018;Ą and đ?&#x153;&#x192;đ??źĚ&#x2026; â&#x2030;Ľ đ?&#x203A;ź ), when a crack close (đ?&#x153;&#x20AC;đ?&#x2018;&#x203A;đ?&#x2018;?đ?&#x2018;&#x; < 0) or when a closed crack reopens (đ?&#x153;&#x17D;đ?&#x2018;&#x203A;đ?&#x2018;?đ?&#x2018;&#x; > 0), the incremental strain vector â&#x2C6;&#x2020;đ?&#x153;&#x20AC; must be successively decomposed in order to accurately simulate the crack status evolution.
113
Chapter 5 â&#x20AC;&#x201C; NUMERICAL ANALYSIS
5.3 Modelling of the unreinforced schist masonry prototype In this section the numerical simulation of the experimental test carried out on the unstrengthened schist masonry prototype, is presented. The main purpose has been to obtain the mechanical properties of schist masonry and investigate its flexural behavior, performing a non-linear analysis with finite element modeling, using the computer code FEMIX 4.0. In the following sections the adopted mesh, the material properties and the simulation results will be defined, showing in particular the sample crack patterns, the load-deflection response and comparing then with the test results presented in the previous chapter. 5.3.1 Modelling Masonry can be modelled in three types. The first type is micro-modelling where unit, mortar and interface layer, are individually analyzed. The second type is the meso-scale modelling where interface and units are clubbed together in order to be studied as single entity whereas the mortar is considered separately. The final type is the macro-modelling where units and mortar are homogenized as a continuum. The present numerical simulation was performed with a macro-modeling. The reason of this choice lies primarily in the dimensions of the sample, too large for a detailed analysis, and secondly in the irregular and chaotic arrangement of the stones in the specimen, too difficult to be accurately represented. The first step in the numerical modeling has been the creation of a single rectangular mesh with dimensions of 300 đ?&#x2018;&#x161;đ?&#x2018;&#x161; Ă&#x2014; 2000 đ?&#x2018;&#x161;đ?&#x2018;&#x161; representing the sample. Subsequently the original mesh has been refined in order to create a structured 8 node quadrilateral mesh with 2 Ă&#x2014; 2 Gauss-Legendre integration scheme. The size of each mesh was 5 đ?&#x2018;?đ?&#x2018;&#x161; in both đ?&#x2018;&#x2039; and đ?&#x2018;&#x152; direction, resulting 240 elements and 813 nodes (see Figure 5.3.1). In particular, this operation has been facilitated by the possibility of importing CAD models. At this point, once the model geometry has been created and the coordinates data file has been written, it was necessary to define the element type used for the finite element modelling. A plane stress element type was implemented. Afterwards the boundary constrains were analyzed. The sample lateral supports were firstly implemented fixing the translation in đ?&#x2018;&#x2039; â&#x2C6;&#x2019; đ?&#x2018;&#x152; direction in order to create a simple supporthinge scheme. Subsequently, regarding the configuration adopted in the bottom part of the sample, it was decided to fix only the vertical translation allowing instead the horizontal one. 114
Chapter 5 â&#x20AC;&#x201C; NUMERICAL ANALYSIS
In this way the theoretical behavior expected of the steel plates-Teflon-oil system was simulated.
b)
a)
c)
Figure 5.3.1 â&#x20AC;&#x201C; Unreinforced numerical model (supports in blue): a) Complete mesh; b) Top part; c) Bottom part.
Finally the load application was addressed. Two load cases were created: the gravity load and the horizontal load, implemented as edge load acting in the element centrally positioned. Then, two combination were made: the first, simulated the self-weight where the only load acting was the gravity force; the second, represented the real behavior of the specimen during the test where gravity and horizontal load acted together. In order to simulate the real load conditions (see paragraph 3.3.2) the arc-length method was introduced. In this way the load was applied in displacement control, imposing an horizontal displacement equal to the test velocity, i.e., 0.01 đ?&#x2018;&#x161;đ?&#x2018;&#x161;/đ?&#x2018; . As previously stated (see § 5.2.3.1) the arc-length method acts on the last load combination for a number of times equal to the number of combinations fixed for the method, therefore the complete response of the sample was obtained. 115
Chapter 5 â&#x20AC;&#x201C; NUMERICAL ANALYSIS
Another step, presented in the next section, was the introduction of the material properties. Once this last point was carried out, the numerical simulation was performed. 5.3.2 Material properties As mentioned above, in this numerical simulation, schist stones and mortar were considered as a continuum. The mechanical properties of this â&#x20AC;&#x153;systemâ&#x20AC;? have been investigated by few authors, mainly Barros R. S. (2013) and Luso E. C. (2012), whose researches have allowed to obtain reference values of Youngâ&#x20AC;&#x2122;s modulus (đ??¸) and compressive strength (đ?&#x2018;&#x201C;đ?&#x2018;?đ?&#x2018;&#x161; ) by means of uniaxial compressive test on historical schist masonry (see Table 5.3.1). Rock type - Region
Mortar type
Schist - Vila Nova de Foz Coa 1 Artificial (hydraulic + hydrated lime) 1 Schist - Vila Nova de Foz Coa 2 Earth mortar 2 Schist - Vila Nova de Foz Coa 2 Artificial (hydraulic lime) 2
fcm [Mpa] 1.37 3.76 3.88
E [Mpa] 490.3 164.57 373.31
Table 5.3.1 â&#x20AC;&#x201C; Schist masonry mechanical properties. 1Luso E. C., (2012). 2Barros R. S., (2013).
However no researches were carried out with the aim of evaluating the shape of the tensilesoftening diagram and the fracture energy of this kind of continuum. In the present work, the quadri-linear stress-strain diagram, represented in Figure 5.3.2 is used to simulate the post cracking behavior of the adopted material. The main advantage of this diagram is the possibility of changing the post-peak points coordinates (đ?&#x153;&#x2030;đ?&#x2018;&#x2013; , đ?&#x203A;źđ?&#x2018;&#x2013; ), thus providing enough flexibility in order to model the most important aspects of the tensionstiffening effect. Since no previous research could be found regarding the selection of appropriate values for the referred parameters, several attempts were made with the aim of fitting the numerical results with experimental results, in terms of load-deflection behavior. The starting point of this analysis was to assume for each parameter a reasonable range, basing on the results obtained from the experimental test. The hypothesized values and the correspondent đ?&#x153;&#x17D; đ?&#x2018;Ą â&#x2C6;&#x2019; đ?&#x153;&#x20AC;curves are showed below:
116
Chapter 5 – NUMERICAL ANALYSIS
Tensile strength Fracture energy 1st post peak 2nd post peak 3rd post peak
fct [Mpa] [ 0.1 ÷ 0.5 ] Gf [N/mm] [ 0.05 ÷ 0.1 ] ξ1 [-] [ 0.005 ÷ 0.05 ] α1 [-] [ 0.2 ÷ 0.4 ] ξ2 [-] [ 0.1 ÷ 0.5 ] α2 [-] [ 0.05 ÷ 0.1 ] ξ3 [-] [ 0.5 ÷ 1.0 ] α3 [-] [ 0.0 ÷ 0.05 ]
Table 5.3.2 – Quadri-linear tensile softening parameters range.
Quadri-linear tensile softening Max
Average
Min
0.50 0.45 0.40
Stress [MPa]
0.35 0.30 0.25 0.20 0.15 0.10 0.05 0.00 0
0.2
0.4
0.6
0.8
1
Strain [-]
Figure 5.3.2 - Quadri-linear tensile softening diagrams.
As reported in Figure 5.3.2, the hypothesized behavior provides an abrupt decay of the material system until the first post-peak point, followed by a more soft decrease until the ultimate strain. This hypothesis comes from the crack patterns observed during the test that shown a sudden failure in the interface between stones and mortar therefore it was reasonable to suppose that, once the tensile strength was reached, the schist-mortar system offered a considerably low resistance with a sudden decrease of 60 − 80%. Moreover considering a very weak and fragile behavior of the sample, low values of tensile strength and fracture energy were assumed. In conclusion, starting from the hypotheses made, numerous simulations were performed with the aim of fitting the experimental load-displacement curve with the numerical one. The results are presented in the next section. 117
Chapter 5 â&#x20AC;&#x201C; NUMERICAL ANALYSIS
5.3.3 Numerical results During the several simulations carried out, it has been observed that the shape of the numerical curve was mainly governed by đ?&#x2018;&#x201C;đ?&#x2018;?đ?&#x2018;Ą , đ?&#x153;&#x2030;1 , đ?&#x203A;ź1 , and đ??şđ?&#x2018;&#x201C; . In particular, the tensile strength, (đ?&#x2018;&#x201C;đ?&#x2018;?đ?&#x2018;Ą ), and the 1st post-peak point coordinates, (đ?&#x153;&#x2030;1 , đ?&#x203A;ź1 ), influenced the pre-peak trend of the curve, whereas the fracture energy, (đ??şđ?&#x2018;&#x201C; ), conditioned mostly the post-peak branch. Afterwards, in order to fit the numerical curve, it has been noticed that an increase of the tensile strength, (đ?&#x2018;&#x201C;đ?&#x2018;?đ?&#x2018;Ą ), needed to be followed by a reduction of đ?&#x153;&#x2030;1 , đ?&#x203A;ź1 values, allowing in this way the sudden creation of a first crack in the sample as was observed in the test (see paragraph 4.2.2.2). However, the increase of the tensile strength could not exceed 0.15 đ?&#x2018;&#x20AC;đ?&#x2018;&#x192;đ?&#x2018;&#x17D; because, with that value, some peaks have been occurred at the beginning of the curve even if đ?&#x153;&#x2030;1 , đ?&#x203A;ź1 were considerably decreased. Concerning the final part of the curve, the parameter controlling its shape was mainly đ??şđ?&#x2018;&#x201C; whose values could not be lower than 0.13 đ?&#x2018; /đ?&#x2018;&#x161;đ?&#x2018;&#x161; otherwise the numerical curve showed too deviation with the experimental one. Finally, it was observed that an increase of the fracture energy caused a little increase of the tensile strength, therefore đ??şđ?&#x2018;&#x201C; was carefully adjusted. In conclusion, changing the aforementioned parameters, it was possible to obtain the following load-deflection numerical curves, evaluated in the actuator point load and in the opposite point of the sample where đ??żđ?&#x2018;&#x2030;đ??ˇđ?&#x2018;&#x2021; 1 was positioned. Before presenting the results, it should be clarified that since the accuracy of the actuator was not high, the experimental curve taken as reference was that one recorded by the đ??żđ?&#x2018;&#x2030;đ??ˇđ?&#x2018;&#x2021; 1 showed in Figure 5.3.3. However, in order to present a complete analysis, even the comparison between actuator and numerical results is showed below:
118
Chapter 5 â&#x20AC;&#x201C; NUMERICAL ANALYSIS
LVDT 1 Experimental
Numerical
2.5
Load [kN]
2
1.5
1
0.5
0 0
2
4
6
8
10
12
Deflection [mm] Figure 5.3.3 - Load-Displacement behavior (LVDT 1): experimental and numerical curves.
The peak load obtained with the numerical simulation was 2.2 đ?&#x2018;&#x2DC;đ?&#x2018; equal to the experimental value that was 2.215 đ?&#x2018;&#x2DC;đ?&#x2018; . Actuator point load Experimental
Numerical
2.5
Load [kN]
2
1.5
1
0.5
0 0
2
4
6
8
10
12
14
16
Deflection [mm] Figure 5.3.4 - Load-Displacement behavior (Actuator): experimental and numerical curves.
119
Chapter 5 â&#x20AC;&#x201C; NUMERICAL ANALYSIS
The correspondent material properties of the schist-mortar system are showed below: E fcm fct Ξ1 Îą1 Ξ2 Îą2 Ξ3 Îą3 Gf [Mpa] [Mpa] [Mpa] [-] [-] [-] [-] [-] [-] [N/mm] 500 1.0 0.1 0.003 0.33 0.6 0.1 0.85 0.035 0.15 Table 5.3.3 â&#x20AC;&#x201C; Adopted parameters for schist masonry.
Quadrilinear tensile-softening 0.1
stress [Mpa]
0.08 0.06 0.04 0.02 0 0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
strain [-] Figure 5.3.5 â&#x20AC;&#x201C; Quadri-linear tensile-softening diagram â&#x20AC;&#x201C; adopted material.
Once the parameters of the schist-mortar system were defined, the numerical analysis has been continued with the aim of validate the data ranges previously hypothesized (see Table 5.3.2). Thus new values of đ?&#x2018;&#x201C;đ?&#x2018;?đ?&#x2018;Ą , đ?&#x153;&#x2030;đ?&#x2018;&#x2013; , đ?&#x203A;źđ?&#x2018;&#x2013; , and đ??şđ?&#x2018;&#x201C; were implemented in order to verify if the solution previously achieved was unique and the ranges supposed were appropriates. After several attempts it was observed that increasing the fracture energy and decreasing consequently the tensile strength, the numerical curve fitted much better to the experimental one. However, this was possible only increasing drastically the 1 st post-peak point coordinates, namely simulating a slower propagation of the first crack in the sample with a small loss of energy, approximately 20 â&#x2C6;&#x2019; 30% (see Figure 5.3.6). Therefore, while in the first case a brittle behavior of the sample with a sudden tensile strength decrease was simulated, in the second case a more homogeneous material was modelled. The values obtained from the new analysis are showed below. E fcm fct Ξ1 Îą1 Ξ2 Îą2 Ξ3 Îą3 Gf [Mpa] [Mpa] [Mpa] [-] [-] [-] [-] [-] [-] [N/mm] 500 1.0 0.037 0.1 0.7 0.5 0.3 0.8 0.1 0.28 Table 5.3.4 - Adopted parameters for schist masonry â&#x20AC;&#x201C; 2nd analysis.
120
Chapter 5 â&#x20AC;&#x201C; NUMERICAL ANALYSIS
Quadri-linear tensile softening 0.04 0.035
Stress [MPa]
0.03 0.025 0.02 0.015 0.01 0.005 0 0
0.2
0.4
0.6
0.8
1
Strain [-]
Figure 5.3.6 â&#x20AC;&#x201C; Quadri-linear tensile softening diagram - 2nd analysis.
Performing the analysis with this new material, the following load-deflection numerical curves were obtained: LVDT 1 Experimental
Numerical
2.5
Load [kN]
2
1.5
1
0.5
0 0
2
4
6
8
10
12
Deflection [mm] Figure 5.3.7 - Load-Displacement behavior (LVDT 1): experimental and numerical curves.
121
Chapter 5 â&#x20AC;&#x201C; NUMERICAL ANALYSIS
Actuator point load Experimental
Numerical
2.5
Load [kN]
2
1.5
1
0.5
0 0
2
4
6
8
10
12
14
16
Deflection [mm] Figure 5.3.8 - Load-Displacement behavior (Actuator): experimental and numerical curves.
As can be observed from the figure showed above, the numerical curves exhibit a more regular trend compared to Figures 5.3.3 â&#x20AC;&#x201C; 5.3.4, in fact no oscillations occurred. In conclusion as expected, given the complexity of the schist-mortar system, the behavior initially assumed has proved to be not appropriate especially as regards đ?&#x2018;&#x201C;đ?&#x2018;?đ?&#x2018;Ą , đ??şđ?&#x2018;&#x201C; , and đ?&#x153;&#x2030;1 , đ?&#x203A;ź1 . In particular, the system exhibited very low tensile strength since stones and mortar have reacted independently to the applied load, thus the tensile strength of the continuum is actually the strength of the interface between schist and mortar. Even the fracture energy has assumed very different values from those expected. The reason should be found in the chaotic arrangement of stones that have given to the system a certain ductility since the fractures did not propagate suddenly in the sample but they developed slowly encountering area more resistant alternated with area less resistant. As regards the adopted values of Young-s modulus and compressive strength they have proved to be appropriate since they not influenced the results of the performed analysis. Therefore it is possible to state that the schist-mortar continuum adopted in this experimental project has the mechanical properties presented below:
122
Chapter 5 – NUMERICAL ANALYSIS
Young's Modulus Compressive strength Tensile strength Fracture energy 1st post peak 2nd post peak 3rd post peak
E [Mpa] fcm [Mpa] fct [Mpa] Gf [N/mm] ξ1 [-] α1 [-] ξ2 [-] α2 [-] ξ3 [-] α3 [-]
500 1.0 [ 0.037 ÷ 0.1 ] [ 0.15 ÷ 0.28 ] [ 0.003 ÷ 0.1 ] [ 0.33 ÷ 0.7 ] [ 0.5 ÷ 0.6 ] [ 0.1 ÷ 0.3 ] [ 0.8 ÷ 0.85 ] [ 0.035 ÷ 0.1 ]
Table 5.3.5 – Final ranges for schist masonry mechanical properties.
5.3.4 Comparison between experimental and numerical results Additional analyzes were performed in order to obtain the deformed mesh and the crack patterns of the numerical model and to compare then with the experimental ones. These analyzes were performed using the material whose properties are reported in Table 5.3.3. This decision was made since it was more reasonable to simulate o brittle behavior of the historical schist masonry rather than an homogenous one as provide the values of Table 5.3.4. The deformed mesh observed at the peak point and at the end of the numerical analysis are reported below:
a)
b)
Figure 5.3.9 – Deformed mesh: a) Peak load; b) End of the analysis.
123
Chapter 5 – NUMERICAL ANALYSIS
Finally the crack patterns were analyzed at the peak point and even at the end of the simulation and compared to the results presented at § 4.2.2.2. Being the load applied monotonically, according to the paragraph 5.2.4.2 the opening and the fully open crack statuses are represented. The comparison is reported below:
a)
b)
Figure 5.3.10 – Opening crack status at the peak load: a) Numerical model; b) Experimental test.
124
Chapter 5 â&#x20AC;&#x201C; NUMERICAL ANALYSIS
a)
b)
c)
Figure 5.3.11 â&#x20AC;&#x201C; Crack patterns at the end of the analysis: a) Opening status; b) Fully open status; c) Experimental test.
Analyzing the figures above, it is possible to notice that both the deformed mesh and the crack patterns obtained at the peak load show some inconsistencies with those observed experimentally. In fact, while the fracture in the middle of the sample reflects what happened in reality, on the other hand, the fracture in the lower part of the numerical model occurred before the peak load achievement on the contrary to what happened in the test. The reasons for this visible inconsistency should be found in the configuration adopted in the bottom part of the sample and in the homogenization of the sample material. The combination of these two simplifications, necessary for the modelling, and the possibility of slight imperfections in the prototype geometry or even in the experimental test, have led to record these differences. Therefore for these reasons, the comparison between experimental and numerical behavior has been made considering the closest points to the load application, where the interferences were definitely less. However, despite these considerations, the numerical model reflects the overall behavior of the unreinforced prototype, showing a main fracture in the middle, responsible of the failure mechanism (see Figure 5.3.11 c)).
125
Chapter 5 â&#x20AC;&#x201C; NUMERICAL ANALYSIS
5.4 Modelling of the reinforced schist masonry prototype In this section the numerical analysis of the strengthened prototype is presented. Since the mechanical properties of the historical schist masonry have been already defined, the main purpose of this analysis is to investigate the FRM properties, trying to fit the numerical load-deflection responses with the experimental ones. In particular, the reference prototype considered was the 2 đ?&#x2018;&#x2020;đ??ś_đ??šđ?&#x2018;&#x2026;đ?&#x2018;&#x20AC; as it exhibited a more complete response compared to the 1 đ?&#x2018;&#x2020;đ??ś_đ??šđ?&#x2018;&#x2026;đ?&#x2018;&#x20AC;. Moreover, deformed mesh and crack patterns were obtained and analyzed. 5.4.1 Modelling The numerical simulation of the reinforced sample has been carried out with a macromodelling. The prototype was simply outlined with an inner part made up of schist and mortar, covered by two symmetrical layers of FRM. In particular, the inner core has been considered as a continuum as previously stated in paragraph 5.3. The creation of the numerical model was made adding to the unreinforced sample model two symmetrical rectangular mesh with dimensions of 25 đ?&#x2018;&#x161;đ?&#x2018;&#x161; Ă&#x2014; 2000 đ?&#x2018;&#x161;đ?&#x2018;&#x161; representing the reinforcement system. Afterwards, these mesh were refined thus obtaining a model with two type of mesh: the first, modelling the inner core, with dimensions of 5 Ă&#x2014; 5 đ?&#x2018;?đ?&#x2018;&#x161;2, and the second, modelling the FRM layers, with dimensions of 2.5 Ă&#x2014; 5 đ?&#x2018;?đ?&#x2018;&#x161;2 (see Figure 5.4.1). In conclusion, a structured 8 node quadrilateral mesh with 2 Ă&#x2014; 2 Gauss-Legendre integration scheme was obtained. It was composed by 320 elements and 1057 nodes. Moreover, a plane stress element type was implemented. As regards the boundary constrains, the setup adopted for the unreinforced sample was kept equal for the present analysis. The figures below showed the sample configuration.
126
Chapter 5 â&#x20AC;&#x201C; NUMERICAL ANALYSIS
b)
a)
c)
Figure 5.4.1 - Reinforced numerical model (supports in blue): a) Complete mesh; b) Top part; c) Bottom part.
Even the loading conditions have been the same adopted for the previous model. Two load cases were created: the gravity load and the horizontal load. Then, two combination were made: the first, simulating the self-weight and the second where gravity and horizontal load acted together. Afterwards through the introduction of the arc-length method the load was applied in displacement control, with a velocity of 0.01 đ?&#x2018;&#x161;đ?&#x2018;&#x161;/đ?&#x2018; equal to the experimental test. Finally, the numerical simulation was performed, but only after having implemented the FRM properties, presented in the next section. 5.4.2 Material properties Since schist stones and mortar were assumed as a continuum whose mechanical properties are reported in table 5.3.3, the characterization of the materials constituting the reinforced prototype was actually the definition of the FRM properties. However, being a material undergoing trials, as regards both its composition and its application, the FRM mechanical properties have not yet been defined. This means that in the present analysis the parameters 127
Chapter 5 â&#x20AC;&#x201C; NUMERICAL ANALYSIS
values have been assumed basing on the experimental observations conducted in laboratory and on the results obtained in this project. The starting point of the FRM properties investigation, even in this case, was the assumption of the quadri-linear stress-strain diagram, represented in Figure 5.4.4, used to simulate the post cracking behavior of the reinforcement system. Regarding the selection of appropriate post-peak points coordinates (đ?&#x153;&#x2030;đ?&#x2018;&#x2013; , đ?&#x203A;źđ?&#x2018;&#x2013; ), several attempts were made, however in this analysis no initial ranges were assumed as it would have led to a too dispersive analysis, but rather, it was tried to implement the FRM behavior observed in the present project and in other parallels works not yet published. In particular, the experimental observations shown that the FRM once reached the tensile strength, (approximately around 2.5 á 3 đ?&#x2018;&#x20AC;đ?&#x2018;&#x192;đ?&#x2018;&#x17D;) firstly developed a sudden but small loss of strength and subsequently it exhibited an hardening behavior with a considerable increase of the strength, reaching a 2nd post-peak point even higher than the tensile strength. Concerning then the last part of the curve, the FRM showed a descendent branch until the ultimate strain. However these observations did not considered the application via spray, that could have influenced the above supposed behavior. Not all parameters have been hypothesized since the beginning of the modelling. The Youngâ&#x20AC;&#x2122;s modulus value, for instance, was assumed basing on the results presented by Barros J. A. O., Frazao C., Gonçalves D., Valente. T (2014). Even the compressive and the flexotraction strength had some initial values obtained from the material characteristics at 28 days, reported in paragraph 3.2.3.3. 5.4.3 Numerical results The numerical simulation performed for the reinforced prototype has shown significant sensibility to all parameters involved in the analysis. The main problem faced was the implementation of the 2nd post-peak point coordinates, defining the hardening behavior of the material. It was difficult in fact to implement values of đ?&#x203A;ź2 greater than 1.0 since the model did not converge even modifying the iterative algorithm parameters. Even for the 1st post-peak point coordinates particular attention was required, imposing values of đ?&#x153;&#x2030;1 not greater than 0.01 thus allowing a sudden achievement of the first post-peak. In addition, it was observed that đ?&#x153;&#x2030;2 , đ?&#x203A;ź2 were particularly sensitive to the variations made to đ?&#x153;&#x2030;1 , đ?&#x203A;ź1 . After several attempts the equilibrium has been found obtaining the parameters showed in table 5.4.1. 128
Chapter 5 â&#x20AC;&#x201C; NUMERICAL ANALYSIS
As regards the tensile strength and the Youngâ&#x20AC;&#x2122;s modulus, the values assumed initially proved to be overestimated as expected since they have been obtained from a not sprayed material research. In particular, these parameters were the first ones to be adjusted as they governed the shape of the pre-peak branch. In conclusion, changing the aforementioned parameters, it was possible to obtain the following load-deflection numerical curves, evaluated where đ??żđ?&#x2018;&#x2030;đ??ˇđ?&#x2018;&#x2021; 1 was positioned and in the actuator point load. LVDT 1 Experimental
Numerical
25
Load [kN]
20
15
10
5
0 0
2
4
6
8
10
12
Deflection [mm]
Figure 5.4.2 - Load-Displacement behavior (LVDT 1): experimental and numerical curves.
Even in this case, since the accuracy of the actuator was not high, the experimental behavior taken as reference for the comparison with the numerical analysis was that one recorded by the đ??żđ?&#x2018;&#x2030;đ??ˇđ?&#x2018;&#x2021; 1 showed in Figure 5.4.2. However, in order to present a complete analysis, even the comparison between actuator and numerical results is showed below:
129
Chapter 5 â&#x20AC;&#x201C; NUMERICAL ANALYSIS
Actuator point load Experimental
Numerical
25
Load [kN]
20
15
10
5
0 0
2
4
6
8
10
12
14
16
Deflection [mm]
Figure 5.4.3 - Load-Displacement behavior (Actuator): experimental and numerical curves.
As reported in the figures above, the numerical analysis showed a non-homogeneous loaddeflection response comparing to the experimental one. In particular three important oscillations occurred: the first approximately at 12 đ?&#x2018;&#x2DC;đ?&#x2018; of load, the second at 18 đ?&#x2018;&#x2DC;đ?&#x2018; and the third around 22 đ?&#x2018;&#x2DC;đ?&#x2018; . Since these oscillations occurred especially in the pre-peak branch, they simulate the numerous fractures that have been appeared in the inner core, before the occurrence of the final crack in the FRM layer. The peak load obtained with the numerical simulation was 23.9 đ?&#x2018;&#x2DC;đ?&#x2018; equal to the experimental value that was 23.94 đ?&#x2018;&#x2DC;đ?&#x2018; . Once the numerical curves have been fit with the experimental ones it was possible to state that the material properties assumed in the numerical analysis (see table 5.4.1), simulated as much as possible the real material used in the experimental campaign. The FRM mechanical properties and the correspondent quadri-linear diagram are reported below: E fcm fct Ξ1 Îą1 Ξ2 Îą2 Ξ3 Îą3 Gf [Gpa] [Mpa] [Mpa] [-] [-] [-] [-] [-] [-] [N/mm] 11 26.0 3.4 0.005 0.77 0.4 0.9 0.9 0.1 7.0 Table 5.4.1 â&#x20AC;&#x201C; FRM mechanical properties adopted.
130
Chapter 5 â&#x20AC;&#x201C; NUMERICAL ANALYSIS
FRM - Quadri-linear tensile-softening 3.5 3
stress [MPa]
2.5 2 1.5 1 0.5 0 0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
strain [-]
Figure 5.4.4 â&#x20AC;&#x201C; FRM Quadri-linear tensile softening diagram.
5.4.4 Comparison between experimental and numerical results In conclusion additional analyzes were performed in order to obtain the deformed mesh and the crack patterns of the numerical model and to compare then with the experimental ones showed at paragraph 4.2.4.2. The deformed mesh observed at the peak point and at the end of the numerical analysis are reported below:
131
Chapter 5 â&#x20AC;&#x201C; NUMERICAL ANALYSIS
a)
b)
Figure 5.4.5 - Deformed mesh: a) Peak load; b) End of the analysis.
As made in the previous numerical analysis, the crack patterns at the peak point and even at the end of the simulation were analyzed and then compared to the results observed in the 2 đ?&#x2018;&#x2020;đ??ś_đ??šđ?&#x2018;&#x2026;đ?&#x2018;&#x20AC; samples test (see § 4.2.4.2). The opening and fully open crack statuses obtained are reported below.
132
Chapter 5 â&#x20AC;&#x201C; NUMERICAL ANALYSIS
a)
b)
Figure 5.4.6 â&#x20AC;&#x201C; Opening crack status at the peak load: a) Numerical model ;b) Experimental test.
a)
b)
c)
d)
Figure 5.4.7 - Crack patterns at the end of the analysis: a) Opening; b) Fully open; c) & d) Experimental test.
133
Chapter 5 â&#x20AC;&#x201C; NUMERICAL ANALYSIS
Analyzing the crack patterns and the deformed mesh resulting from the numerical modelling it is evident that the model does not reflect what was observed experimentally. The main fracture, for instance, appears in the intrados lower-middle part of the sample (see Figure 5.4.7 b) contrary to what happened in the experimental test where the fractures appeared in the top part. Moreover, no cracks were observed during the test in the bottom of the sample aligned with the support, as reported instead in Figure 5.4.7 a. The causes of these inconsistencies between the numerical and the experimental flexural behavior, once again, can be found in the geometry imperfections of the strengthened prototypes, in the loss of perfect correspondence between the numerical constrains and the real ones and even in the homogenization of the inner core, reported in § 5.3.2. However, despite these considerations, it is possible to state that the numerical modelling has produced satisfactory results since it demonstrates: the fitting of the numerical load-deflection responses with the experimental ones; a similar crack patterns in the model inner core with the appearance of shear cracks as observed in the real sample (see paragraph 4.2.3.2 and 4.2.4.2).
134
Chapter 6
CONCLUSIONS 6.1 Summary In the present thesis three main sections can be recognized. The first macro-section provides a complete and detailed analysis of the materials adopted. Firstly the physic-mechanical properties of the historical schist masonry, namely stones and mortar, are characterized. Subsequently the same characterization involves the strengthening material whose innovative application (via spray) is deeply investigated. The second macro-section addresses the main objective of this project, i.e., the assessment of the strengthening system effectiveness once applied to schist masonry elements subjected to out-of-plane loads. The main idea have been to perform a classic three point bending test but with the sample vertically positioned, since its dimensions and its weakness excluded completely the possibility to rotate. This unusual configuration involves the introduction of some expedients that have led to numerous evaluations. Thus, three prototypes were studied with the aim of evaluating the increase of the load carrying capacity and deformation once the strengthened system was applied. The thesis ends with the numerical analysis whose objective is to validate the results obtained experimentally, in terms of load-deflection responses and crack pattern, through the FE modelling. Indicative values of the mechanical properties of both materials used in the present research, namely schist masonry and fiber reinforced mortar, are provided.
135
Chapter 6 â&#x20AC;&#x201C; CONCLUSION
6.2 Conclusions In the light of the results obtained and of the observations made during the tests, it is possible to draw the following conclusions. The Fiber Reinforced Mortar (FRM) demonstrated an anisotropic behavior both with normal and vertical casting. As regards the normal casting, the FRM showed a stronger behavior along the parallel (0°) and the orthogonal direction (90°) compared to the preferential direction applied. In particular, this behavior is confirmed over the time. Concerning the vertical casting instead, the mortar showed the strongest behavior along the direction applied with the roller (0°) but this have not been confirmed over the time since the samples presented too many voids too be considered reliable. Concerning the out-of-plane tests performed on the schist masonry prototypes the more relevant aspects are presented below: - the unreinforced sample (1 đ?&#x2018;&#x2020;đ??ś_đ?&#x2018;&#x2C6;đ?&#x2018;&#x2026;) demonstrated a very brittle behavior since the failure occurred very quickly and with small values of displacement; - the reinforced samples showed an extraordinary increasing of the load carrying capacity reaching a peak load 10 times higher. Even the displacements increased considerably, recording at the peak-load time an increment of 60 %; - the crack patterns of the strengthened sample showed the occurrence of an higher number of cracks in the sample upper part due to the different thickness of the FRM layers. It was difficult, in fact, during the spraying phase, to apply the same thickness of reinforced mortar along all the specimen; - since the schist masonry prototypes were tested in a vertical configuration they have showed to suffer the deadweight in fact the bottom part of the column was subjected to bending but with a higher axial load that reduced the tensile stress due to the bending and prevented cracks to appear (like a pre-stress effect). - in the FRM inner layers some cracks surely occurred before the instant when they appeared in the outer layer since at the peak load in the intrados of the sample no cracks were observed; Finally, regarding the numerical modelling it is possible to state that both FE-models have produced satisfactory results since they demonstrated: the fitting of the numerical loaddeflection responses with the experimental ones. However, only the unreinforced model showed a similar crack patterns corresponding to the reality. 136
Chapter 6 â&#x20AC;&#x201C; CONCLUSION
Although the numerical model is still in a preliminary status, it was possible to define reasonable parameters for all the materials adopted in the present research.
6.3 Suggestions for future work Based on the results obtained from the numerical model and the experimental works, the following suggestions can be carried out to deepen the information regarding the research topic. The key point for a further improvement of the strengthening system regards the spray technique. The composition of the material should be reviewed in order to obtain a drier and lighter mixture. In this way, even spraying at the same pressure is expected to create a more compact layer devoid of several voids. Moreover it is expected to reach the same thickness avoiding an interruption in the application as occurred in this project. As have been noted during the numerical analysis, an experimental characterization of the tensile behavior of the fiber reinforced mortar should be carried out. This will allow a complete definition of the tensile softening diagram and therefore an easily numerical modelling. Concerning the out-of-plane tests, two main improvements are recommended. Firstly to use a less powerful load cell, able to record with more accuracy the responses of the specimens especially that one of the unreinforced sample whose elastic behavior is almost absent. Subsequently, try to improve the bottom configuration (steel plates, Teflon and oil) since it create a constrain and not a free edge as expected. This could be possible, for instance, decreasing the weight bearing upon the base through the reduction of the sample dimensions or the substitution of the steel plates with wooden boards. In order to have a wider framework of the strengthening system effectiveness once applied to the historical schist masonry, it could be interesting to investigate the in-plane behavior; Regarding the numerical modelling, it is suggested to: use a more refined mesh, more onerous but it could lead to more accurate results, then improving the boundary constrain in the bottom. Finally, in order to define more precisely the schist masonry parameters, it might be interesting to perform a micro-modelling of the sample simulating the different components such as: stones, mortar and interface between them. 137
Chapter 6 â&#x20AC;&#x201C; CONCLUSION
138
Annex A FLEXURAL STRENGTH â&#x20AC;&#x201C; VERTICAL CASTING
139
Annex A
This annex summarizes the data obtained from the analysis of the vertical casted specimens with a curing age of 50 days. Using the same procedure illustrated in paragraph 3.2.3.3.2, a geometrical analysis is firstly showed: Angle Sample
0° 30° 45°
60°
90°
1_FRM 2_FRM 3_FRM 1_FRM 2_FRM 1_FRM 2_FRM 3_FRM 1_FRM 2_FRM 3_FRM 1_FRM 2_FRM 3_FRM
Weight Length Width Height Density [kg] [mm] [mm] [mm] [kN/m3] 0.847 270 55 35 16.30 1.046 270 55 45 15.65 0.83 270 55.5 35 15.83 1.265 270 55 55 15.49 1.23 275 57 53 14.81 1.031 269 63.5 39 15.48 1.052 270 57.5 43 15.76 1.122 270 58 45 15.92 0.835 272 55 34 16.42 0.941 270 55 44 14.40 0.928 271 54 39 16.26 1.147 268 60 46 15.51 1.042 267 59 50 13.23 1.242 266 58 56 14.38
Table A.1 - Vertical casting - Geometrical properties at 50 days.
Then, the flexo-traction strength was calculated:
Angle Sample
0° 30° 45°
60°
90°
1_FRM 2_FRM 3_FRM 1_FRM 2_FRM 1_FRM 2_FRM 3_FRM 1_FRM 2_FRM 3_FRM 1_FRM 2_FRM 3_FRM
Test values FMAX σMAX [kN] [Mpa] 2.20 7.84 3.63 7.82 2.32 8.19 4.27 6.16 3.02 4.52 2.02 5.01 3.11 7.01 3.00 6.13 2.59 9.77 3.05 6.87 3.56 10.40 4.70 8.88 3.61 5.88 3.10 4.09
Report Values F MAX σ MAX AVG C.V. [%] AVG C.V. [%] 2.72
29.12
7.95
2.62
3.64
24.29
5.34
21.65
2.71
22.19
6.05
16.57
3.06
15.84
9.01
20.91
3.80
21.41
6.28
38.49
Table A.2 - Results vertical casting at 50 days
Finally, the stress-deflection curves are reported below:
140
Annex A
Stress - Displacement (middle) - 50 days 12 1_FRM_0° 2_FRM_0°
10
3_FRM_0° 1_FRM_30°
8 σ [MPa]
2_FRM_30° 1_FRM_45°
6
2_FRM_45° 3_FRM_45°
4
1_FRM_60° 2_FRM_60°
2
3_FRM_60° 1_FRM_90° 2_FRM_90°
0 0
1
2
3
4
5
6
3_FRM_90°
Displacement [mm] Figure A.1 - Stress - Displacement behavior at 50 days.
As stated in paragraph 3.2.3.3.2 the curves showed in Figure A.1 can not be considered representatives of the FRM behavior since the presence of voids proved to have too much influence on the results. This is confirmed by the images reported below that highlight the voids presence and as this determines unusual crack patterns.
a)
b)
Figure A.2 – 50 days sample – 30°: a) Starting configuration; b) Crack pattern.
141
Annex A
a)
b)
Figure A.3 – 50 days sample – 30°: a) Starting configuration; b) Crack pattern.
a)
b)
Figure A.4 – 50 days sample – 45°: a) Starting configuration; b) Crack pattern.
a)
142
b)
Annex A
c)
d)
e)
f)
Figure A.5 – 50 days sample – 90°. Starting configuration: a)Front; b)Back. Crack pattern: c) & d) Back; e) & f) Front.
143
Annex A
144
Annex B FLEXURAL STRENGTHENING COMPARISON
145
Annex B
146
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