From Corbel Arches to Double Curvature Vaults : Analysis, Conservation and Restoration of Architectural Heritage Masonry Structures

The book focuses on all typological aspects of arches and vaults within the heritage of design and construction, while bringing attention to new “green” materials, promoting a circular economy informed by limitations caused by global warming. The multidisciplinary approach involves several different competences in architecture, structural engineering, conservation and restoration, geomatics, BIM, building engineering, the technology and history of construction, graphical methods of assessment, and innovative design that utilizes non-polluting materials. After an overview of the technical and aesthetic advantages of masonry vaults, there is a review of the most up-to-date trends in historic preservation. Classic methods of static assessment and innovative building technologies are detailed. Surveying methods and data acquisition are discussed, particularly laser scanning technology and its applications in heritage masonry curved structures. Next comes the experimental static and dymanic behavior of masonry vaults, followed by a critical revision of Distinct Element innovative computerized Methods. An explanation as to how to pass from classic stability analysis to an adaptive Finite Element Method limit analysis procedure is offered. Reinterpretation of the past is then undertaken, with an eye towards emphasizing sustainability. Finally, the conclusion examines still existing gaps in knowledge and recommends avenues of future research. Contents 6 Introduction 8 Outline of the Book Chapters 24 References 25 Historical Review of Masonry Arches and Vaults. Trends in Historic Preservation and the Relevance of Understanding Curved Masonry Structures 28 1 Introduction 28 2 Masonry Analysis: Geometry, Composition, Quality 28 2.1 Short Notes on Masonry Typologies 29 2.2 Investigation Tests for Masonry Walls 32 3 Masonry Typologies Diffused in Como Lake Area 33 4 The Building Traditions of Masonry Vaults in Como and Its Territory 37 5 Conclusion 42 References 43 Survey and Monitoring Methods for Masonry Arches and Vaults 46 1 Introduction 46 2 Objectives of Survey and Monitoring 48 3 Approaches for Survey and Monitoring 49 4 Measurement Methods and Engineering Cases 51 4.1 Vision-Based Methods 51 4.2 Terrestrial Laser Scan 53 4.3 Ground Penetrating Radar (GPR) 56 4.4 Sonic Tests 57 4.5 Infrared (IR) Thermography 59 4.6 Ambient Vibration Testing (AVT) 60 5 Conclusion 62 References 62 Digital Setting Out Techniques for Tile Vaults Without Formwork 68 1 Introduction 68 2 Tile Vaults 69 2.1 Construction and Structural Behaviour 70 2.2 Digital Modelling for Tile Vaults 72 3 Setting Out Through Cameras and Markers Detection Systems 74 3.1 Implementation of the System 75 3.2 Vault Positioning and Setting Out Procedure 77 3.3 Precision of the System 78 3.4 Case Studies 83 4 Conclusions 84 References 85 Experimental Behaviour of Masonry: Static and Dynamic Behaviour of Arches and Vaults 86 1 Introduction on the Experimental Works on Arches and Vaults 86 2 Damage and Collapse Mechanisms in Masonry Arches and Vaults 87 3 Literature Review on Experimental Campaigns of Masonry Arches and Vaults 92 4 Experimental Behaviour of Masonry Vaulted Structures 98 4.1 Scaled Dry-Joint Arch 99 4.2 Scaled Dry-Joint Groin Vault 103 5 Insight on the Design Process of a Full-Scale Mortared Masonry Groin Vault According to the Rule of Thumbs 112 5.1 Preparation of the Mock-Up 112 5.2 Bricks: Bond and Interlocking 115 5.3 Mortar 118 6 Case Studies: Hostelry Cloister, Tomar and Cathedral of Porto, Portugal 120 7 Conclusion 123 References 124 Revisiting Classic Methods for the Equilibrium Analysis of Masonry Arches and Domes 129 1 Introduction 129 2 The Method of Maxima and Minima (Coulomb 1776) 130 3 A Parallel Formulation: The Principle of Virtual Work (Mascheroni 1785) 134 4 Towards the Limit Analysis of Masonry Structures 137 5 The Thrust Line Method: A Brief Review on Historical Literature 140 6 Durand-Claye’s Method for the Stability of Masonry Arches and Domes and Its Modern Re-Visitation 149 7 Modern Contributions on the Equilibrium Analysis of Masonry Arches and Domes 162 8 Concluding Remarks 168 References 169 Rigid Block Limit Analysis of Masonry Arches with Associated and Non-associated Slides 175 1 Introduction 175 2 General Modeling of the Collapse of the Arch 180 2.1 Equilibrium Condition 180 2.2 Geometric Compatibility 182 2.3 Constitutive Laws at the Interfaces: Associated and Non-associated 184 2.4 Mathematical Programming Formulations 186 3 Associated Problem 187 3.1 Lower Bound (LB) Theory and Upper Bound (UB) Theory 187 3.2 Relation Between LB and UB Formulation: Duality 188 3.3 Relation Between the LB/UB Formulations and the LCP Problem 189 3.4 Example 190 4 Non-associated Problem 191 4.1 Linear Complementary Programming 192 4.2 Sequential Linear Programming (SLP) 193 4.3 Example 195 5 Reinforcement 200 5.1 Formulation 200 5.2 Example 202 6 Conclusions 206 References 207 NURBS-Based Limit Analysis of Masonry Vaults 210 1 Introduction 210 2 NURBS Parametric Representation 213 3 Limit Analysis of NURBS-Based Rigid Blocks 216 3.1 Lower Bound Approach 217 3.2 Upper Bound Approach 220 4 Genetic Algorithm Mesh Adaptation 223 5 Some Numerical Examples 224 5.1 Three-Centered Masonry Arch Bridge 224 5.2 Gothic Arches in the Convent of Our Lady of Mount Carmel, Lisbon 226 5.3 Masonry Dome in L’Aquila 229 6 Conclusions 231 References 232 Discrete Element Modelling of Masonry Arch Bridges, Arches and Vaults 237 1 Introduction 237 2 DEM Modelling of Masonry Structures 240 2.1 Contact Formulation in 2D 240 2.2 Contact Detection in 3D 241 2.3 Constitutive Models for Contacts 243 2.4 Equations of Motion for Rigid Blocks 245 2.5 Equations of Motion for Deformable Blocks 246 2.6 Mechanical Damping 247 2.7 Numerical Stability 247 3 Static Analysis of Arches and Vaults 248 3.1 Arch Models 248 3.2 Vault Models 249 3.3 Analysis of a Reinforced Masonry Arch Bridge 250 4 Dynamic Analysis of Arches 252 5 A Simple Example of Modelling a Masonry Arch with 3DEC 254 6 Conclusions 257 References 258 Complex Simplicity—Design of Innovative Sustainable Thin-Shell Masonry Structures 261 1 Introduction 261 1.1 King’s College Chapel: Practice and Analysis 261 1.2 Cesar Martinell: Utility and Structural Innovation 262 1.3 Eladio Dieste: Advanced Masonry 263 2 Thin Tile Vaulting 264 2.1 Guastavino and Thin Tile Vaults in America 265 2.2 Craft and Industry 265 3 Complex Simplicity 266 3.1 Crossway House (Low Stresses-High Performances) 266 3.2 Pines Calyx 267 3.3 Sussex Cellar 270 3.4 Mapungubwe 271 4 Rwanda Cricket Stadium 274 4.1 Background 274 4.2 Context 280 4.3 Architectural Design and Program 280 4.4 Structural Design 281 4.5 Construction 283 References 285