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Discrete Element Analysis of Single Span Skew Stone Masonry Arches

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Discrete Element Analysis of Single Span Skew Stone Masonry Arches DIPLOMA WORK DISCRETE ELEMENT ANALYSIS OF SINGLE SPAN SKEW STONE MASONRY ARCHES TAMÁS FORGÁCS – KMEA2K SUPERVISORS: DR. KATALIN BAGI, FULL PROFESSOR - DEPARTMENT OF STRUCTURAL MECHANICS DR. VASILIS SARHOSIS - CARDIFF UNIVERSITY BUDAPEST, 2015 Discrete element analysis of single span skew stone masonry arches Acknowledgements The author wishes to acknowledge the support given to the below diploma work through the Educational Partnership by ITASCA Consulting Group. The author is also grateful for the many discussions and valuable feedback from the PhD students of Department of Structural Mechanics, namely Gábor Lengyel and Ferenc Szakály. Finally, the author would also like to show his gratitude to Vasilis Sarhosis and Katalin Bagi for sharing their pearls of wisdom with him during the course of this work. 2 Discrete element analysis of single span skew stone masonry arches Abstract Masonry arch bridges are inherent elements of Europe’s transportation system. Many of these bridges have spans with a varying amount of skew. Most of them are well over 100 years old and are supporting traffic loads many times above those originally designed, but the increasing traffic loads may endanger their structural integrity so the need arises to understand the mechanical behaviour in order to inform repair and strengthening options. There are three main construction methods mostly used in such bridges. The differences in geometry lead to differences in strength and stiffness. The diploma work to be presented investigates the mechanical behaviour of single span masonry arches. The analysed construction methods were the so-called false skew arch, the helicoidal and the logarithmic method. The three-dimensional computational software 3DEC based on the discrete element method was used: this software allows for the simulation of frictional sliding and separation of neighbouring stone blocks. The behaviour of the structures was simulated under gravity and under an external full width vertical line load. Types of failure modes, stress levels at the joints will be compared and discussed in the diploma work. The minimum necessary thickness which can resist the self-weight of the skew arch was also determined. The investigated parameters of the skew arches were: - method of construction, - angle of skew, - width of the arch, - element shape and size, - angle of friction. KEYWORDS: skew arch, stereotomy, 3DEC 3 Discrete element analysis of single span skew stone masonry arches Összefoglaló A falazott szerkezetű ívhidak Európa közlekedési rendszerének szerves részét képezik. Ezen hidak közül viszonylag sok rendelkezik kisebb-nagyobb mértékű ferdeséggel. A falazott ívek kora jellemzően meghaladja a 100 évet, míg a rájuk ható forgalmi terhek az idők során jelentős mértékben megnövekedtek, így veszélyeztetve a szerkezetek integritását. Ezért egyre nagyobb az igény a falazott ívek mechanikai viselkedésének megértésére azon célból, hogy a felújításokat és megerősítéseket mind hatékonyabb módon tudjuk elvégezni. Ferde ívek építésére három különböző módszer alakult ki a XIX. század elején. A geometriai kialakítások közti különbségek hatással vannak a szerkezetek teherbírására és merevségére egyaránt. A bemutatott diplomamunka egynyílású, kőből készült, falazott szerkezetű ferde ívek mechanikai viselkedését vizsgálja. A vizsgált építési módszerek: a hamis ferde ív, a helikális módszer és a logaritmikus módszer. A munka során egy háromdimenziós, diszkrét elemek módszerén alapuló szoftver (3DEC) került alkalmazásra, mely lehetővé teszi a súrlódásos megcsúszások szimulálását, továbbá figyelembe veszi a szomszédos elemek szétnyílásának lehetőségét is. A szerkezetek viselkedését gravitációs teher és teljes szélességű, egyenletesen megoszló vonal menti teher hatására vizsgáltam. Az egyes módszerekhez tartozó tönkremeneteli módok, kontakt felületeken létrejövő normál- és nyírófeszültség-eloszlások összehasonlításra kerültek. Emellett meghatározásra került az ívek azon minimális falvastagsága, amely az önsúly egyensúlyozásához szükséges. A ferde ívek vizsgált paraméterei: - eltérő építési módszerek, - ferdeség szögének hatása, - ív szélességének hatása, - elemméret hatása, illetve elemek oldalarányainak hatása, - súrlódási szög hatása. KULCSSZAVAK: ferde ív, falazott szerkezetek, diszkrét elemek módszere, 3DEC 4 Discrete element analysis of single span skew stone masonry arches Content Abstract ..................................................................................................................................... 3 Összefoglaló ............................................................................................................................... 4 1. Introduction ......................................................................................................................... 7 1.1 Background to the research ............................................................................................ 7 1.2 Research aims and objectives ......................................................................................... 8 1.3 Layout of the work ......................................................................................................... 9 2 Methods of construction .................................................................................................... 10 2.1 The false skew arch ...................................................................................................... 10 2.2 Helicoidal method ........................................................................................................ 11 2.2.1 Peter Nicholson’s helicoidal method in stone ....................................................... 12 2.2.2 Charles Fox’s English method in brick ................................................................. 12 2.3 Logarithmic method ..................................................................................................... 15 2.4 Comparison on the three methods ................................................................................ 17 3 Assessment of masonry arch bridges ............................................................................... 18 3.1 The MEXE method ....................................................................................................... 19 3.2 Limit state analysis ....................................................................................................... 20 3.2.1 LimitState:RING ................................................................................................... 20 3.3 Finite Element Models ................................................................................................. 23 3.4 The Discrete Element code - 3DEC ............................................................................. 24 3.4.1 Elements ................................................................................................................ 24 3.4.2 Identification of neighbours .................................................................................. 24 3.4.3 Contacts ................................................................................................................. 25 3.4.4 Constitutive models for contacts ........................................................................... 28 3.4.5 Rigid block motion ................................................................................................ 29 3.4.6 Mechanical damping ............................................................................................. 31 3.4.7 Numerical stability ................................................................................................ 32 4 Development of the computational model ....................................................................... 33 4.1 Model geometry ............................................................................................................ 33 4.1.1 False skew arch ..................................................................................................... 33 4.1.2 Helicoidal method ................................................................................................. 35 5 Discrete element analysis of single span skew stone masonry arches 4.1.3 Logarithmic method .............................................................................................. 37 4.2 Material properties, boundary conditions, loading ....................................................... 41 4.3 Verification ................................................................................................................... 45 5 Results and discussion ....................................................................................................... 47 5.1 Determination of the critical barrel thickness .............................................................. 50 5.1.1 Displacements ....................................................................................................... 51 5.1.2 Joint normal and shear stress distributions ............................................................ 54 5.1.3 Collapse mechanisms ............................................................................................ 57 5.2 Effect of live load ......................................................................................................... 61 5.2.1 Critical position of the live load ............................................................................ 62 5.2.2 Effect of the width of the arch ..............................................................................
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