Finite element analysis of tubular track system

Verlinde, Karel Jef Stefaan (2012-12)

Thesis (MScEng)--Stellenbosch University, 2012.

Thesis

ENGLISH ABSTRACT: The Tubular Track (TT) railway system is a twin beam modular railway system consisting of two reinforced concrete (RC) beams on which steel rails are continuously supported. The beams are linked with galvanised steel gauge tie bars and continuously supported by soil foundations, and can be used to replace conventional sleeper and ballast railway support. The TT railway system has in the past been analysed with various analysis methods, but were found to obtain con icting results. The con icting results means that one of the analysis methods used for the analysis and design of TT railway sections is either an underestimation or overestimation of section displacements, forces, and stresses; or both methods could even be incorrect. The main emphasis of this investigation is therefore to develop and verify static and dynamic analysis methods and modeling techniques which can be used to simulate the TT railway system accurately. The results and models of the previous analyses are not explicitly investigated in this dissertation, but serve as a motivation for this investigation. The TT system is supported by several soil strata providing vertical support, but geometrically modeling the subgrade strata in the analysis models adds a high level of complexity, and is not feasible for general analysis where soil conditions are mostly unknown. The elastic foundation theory is therefore used to accurately simulate the interaction between beam and foundation and therefore su ciently simpli es the analysis models. Simpli cation of a subgrade foundation by simulating a soil sti ness supporting the TT beam is investigated and analysed by comparing nite element analysis (FEA) results of various soil models using parameters of four known soil formations currently in use at TT railway sections. The FEA of the subgrade formations indicates that there is a linear relationship between the modulus of subgrade reaction for a square plate bearing test and a rectangular, in nitely long plate representing the subgrade support for the TT beams. A square plate bearing test can therefore be performed on site and modi ed to represent the actual subgrade support sti ness of the TT railway structure, whereafter it can be used for the analysis and design of the TT system using one of the proposed analysis methods. The analysis models used range from simple theoretical models based on elastic foundation principles, to two-dimensional (2D) beam elements, and ultimately to complex three-dimensional (3D) solid nite element models. The models used for the analyses are the Single and Double Beam elastic foundation, PROKON 2D beams, ABAQUS 2D beams and ABAQUS 3D solid element models. The alternative analysis methods considered should provide a clear indication of which analysis methods are accurate and feasible for design of the TT system. An in-situ reference model with known de ections and design parameters speci c to a TT railway section is used to analyse the di erent analysis methods' accuracy and validity. The Double Beam, ABAQUS 2D and ABAQUS 3D models were found to provide very similar displacements, bending moments and shear forces for a static analysis, whereas the PROKON and Single Beam models provide unsatisfactory results. The PROKON beam model underestimates the bending moments and shear forces in the rail, and overestimates bending moments and shear forces in the RC beam by a considerably margin. This result can lead to the underdesigning of the rail which could possibly force the RC beam to be subjected to larger maximum bending moments and shear forces than for what it was originally designed for, thereby nullifying or possibly even exceeding the amount for which it was overdesigned. This e ectively accelerates material fatigue, which might be the possible cause of the small cracks in the RC beams which have been found on some TT railway sections, which is currently being investigated. A graphical user interface of the Double Beam method is provided for quick and e cient analysis. Empirical methods used to simulate the dynamic nature of a railway system are often used in the industry to simplify the dynamic loading by determining a dynamic amplitude factor (DAF) to be applied to a static load. An implicit dynamic FEA is therefore performed to obtain the DAF for the reference section, which is subsequently used for the comparison with in-situ de ection results. The results of dynamic analysis validates the proposed empirical analysis method, as the displacements obtained were very similar to actual eld test results, thereby also verifying the accuracy of the proposed analysis methods. The sensitivity of the TT system to design parameters is also investigated to indicate to which parameters the design is sensitive to and where small variations of these parameters require due consideration for future and analysis of the TT railway system.

AFRIKAANSE OPSOMMING: Die Tubular Track (TT) spoorweg stelsel is 'n dubbel balk modulêre treinspoor sisteem bestaande uit twee gewapende beton balke waarop staal spore voortdurend ondersteun word. Die balke word gekoppel deur gegalvaniseerde staal stawe vir laterale styfheid en word deurlopend ondersteun deur grond fondamente, en kan gebruik word om konvensionele dwarslêer en ballast spoorweg ondersteuning te vervang. Die TT spoorweg stelsel was in die verlede met verskeie analiseringsmetodes ontleed, maar het teenstrydige resultate gewerf. Die teenstrydige resultate beteken dat een van die analise metodes wat gebruik word vir die analisering en ontwerp van TT spoorweg seksies 'n onderskatting of oorskatting van verplasings, kragte, en spannings is; of beide metodes kan selfs verkeerd wees. Die hoofklem van hierdie ondersoek is dus die ontwikkeling en veri kasie van statiese en dinamiese analitiese metodes en modellering tegnieke wat gebruik kan word om die TT spoorweg stelsel akkuraat te simuleer. Die resultate en modelle van die vorige ontledings word nie uitdruklik in hierdie proefskrif ondersoek nie, maar dien as 'n motivering van hierdie ondersoek. Die TT stelsel word ondersteun deur verskeie grond strata wat vertikale ondersteuning verskaf, maar meetkundige modellering van die grond strata in die ontledingsmodelle veroorsaak 'n hoë vlak van kompleksiteit wat nie bruikbaar is vir algemene analises waar grondeienskappe meestal onbekend is. Die elastiese fondament teorie word daarom gebruik om die interaksie tussen die balk en die fondament akkuraat te simuleer, en vereenvoudig dus die analitiese modelle voldoende. Vereenvoudiging van 'n grond fondament deur 'n grond styfheid ondersteuning van die TT balk te simuleer is ondersoek en ontleed deur die resultate van eindige element analises van verskillende grond modelle te vergelyk. Bekende ontwerp parameters van vier bekend grondformasies wat tans gebruik word by TT spoorweg seksies word vir hierdie analises gebruik. Die eindige element analises van die grondformasies dui daarop aan dat daar 'n lineêre verwantskap tussen die modulus van grond reaksie vir 'n vierkantige plaat dratoets en 'n reghoekige, oneindige lang plaat dratoets bestaan. 'n Vierkantige plaat dratoets kan dus op terrein uitgevoer en aangepas word om die werklike styfheid van die grond ondersteuning van die TT spoorweg sisteem voor te stel. Die analitiese modelle wat gebruik word wissel van eenvoudige teoretiese modelle wat gebaseer is op elastiese fondament beginsels, twee-dimensionele (2D) balk elemente, asook komplekse driedimensionele (3D) soliede eindige element modelle. Die modelle wat gebruik is vir die ondersoek is die Enkel en Dubbel Balk elastiese fondament, PROKON 2D balke, ABAQUS 2D balke en ABAQUS 3D soliede element modelle. Hierdie reeks bied 'n duidelike aanduiding watter analiseringsmetodes akkuraat en haalbaar is vir die ontwerp van die TT stelsel. 'n In-situ verwysingsmodel met bekende de eksies en ontwerp parameters wat spesi ek is vir 'n TT spoorweg seksie word gebruik om die akkuraatheid en geldigheid van die verskillende analitiese metodes te analiseer. Die Dubbel Balk, ABAQUS 2D en ABAQUS 3D modelle verkry baie soortgelyke verplasings, buigmomente en skuifkragte vir 'n statiese analise, terwyl die PROKON en Enkel Balk modelle onbevredigende resultate verkry. Die PROKON model onderskat die maksimum buigmomente en skuifkragte in die staal spoor, en oorskat buigmomente en skuifkragte in die gewapende beton balk. Hierdie resultaat kan moontlik lei tot die onderontwerp van die staal spoor en dwing moontlik vir die gewapende beton balk om blootgestel te word aan groter buigmomente en skuifkragte as vir wat dit oorspronklik ontwerp is, en verontagsaam sodoende moontlik die kragte waarvoor dit oorontwerp is. Dit versnel e ektief materiaal vermoeiing, wat die moontlike oorsaak is van die klein krake wat gevind is in die gewapende beton balke op sommige TT spoorweg seksies wat tans ondersoek word. 'n Gra ese gebruikerskoppelvlak van die Dubbel Balk model is verskaf vir vinnige en doeltre ende ontleding. Empiriese metodes om die dinamiese aard van 'n spoorweg-stelsel te simuleer word dikwels gebruik in die bedryf om dinamiese belasting te vereenvoudig deur middel van die gebruik van 'n dinamiese amplitude faktor (DAF) wat op 'n statiese belasting aangewend word. 'n Implisiete dinamiese eindige element analise word dus uitgevoer om die DAF te ondersoek, wat daarna gebruik word vir die vergelyking met die in-situ de eksie resultate van die in-situ verwysingsmodel. Die resultate van die dinamiese analise bevestig dat die voorgestelde empiriese analise metode gebruik kan word, omdat die verplasings wat verkry baie soortgelyk was aan werklike veld toets resultate, en daardeur ook die veri ëring van die akkuraatheid van die voorgestelde analise metodes bewerkstellig. Die sensitiwiteit van die TT stelsel vir ontwerp parameters word ook ondersoek om aan te dui watter parameters die ontwerp voor sensitief is, en waar klein variasie in hierdie ontwerp parameters behoorlike oorweging vereis vir die toekomstige analisering en ontwerp van die TT spoorweg stelsel.

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