Model uncertainty in the prediction of crack widths in reinforced concrete structures and reliability implications

McLeod, Christina Helen (2019-04)

Thesis

ENGLISH ABSTRACT: This research concerns the assessment of model uncertainty of serviceability limit state (SLS) crack models in reinforced concrete structures, where SLS cracking governs design. SLS are treated nominally in design standards without the extensive probabilistic calibration utilised for the ultimate limit state (ULS). Such nominal treatment is not necessarily appropriate when SLS is the governing limit state. A probabilistic approach is therefore taken in assessing SLS cracking in reinforced concrete structures such as liquid retaining structures (LRS), as a precursor to developing a safe but economical design crack width formulation for application in South Africa. In a reliability study of the current Eurocode crack model undertaken by McLeod (2013), model uncertainty displayed a significant influence on reliability. However, it was found that there is little information on the model uncertainty statistical parameters, providing motivation for this research to quantify the model uncertainty of crack models. A probabilistic approach to SLS cracking is employed. The reliability crack model or General Probabilistic Model (GPM) may be described in this context as the best probabilistic description of expected crack widths. This research therefore included the assessment of the crack models of BS 8007 (1987), BS EN 1992-1 (2004), fib MC 2010 (2013) and the proposed amended EN 1992-1 model (Perez Caldentey, 2017) to establish the GPM. Model uncertainty is defined as the ratio of the maximum experimental to predicted crack widths, wexp/ wpredict. Experimental data on load-induced cracking is assembled into a database to quantify model uncertainty, including the statistical quantification of the bias and uncertainty of the prediction model under consideration. The interaction between selected model parameters and model uncertainty is investigated by means of Pearson’s correlations and linear regression analyses. The crack width model for the GPM is chosen by using the model uncertainty quantification results. Reliability analyses using the First Order Reliability Method (FORM) are done to assess the importance of the respective random variables, including model uncertainty. The study confirms that model uncertainty is the dominant influence on the crack model. Factors such as the relationship between the target reliability and the reliability of the crack width formulations, and the influence of long-term shrinkage strain on reliability are also investigated. Recommendations for future research are also made.

AFRIKAANSE OPSOMMING: Die navorsing ondersoek model onsekerheid van kraakwydte voorspellings in gewapende beton strukture, wat veral relevant is vir die diensbaarheid limietstaat (DLS) waar beheer van kraakwydtes die ontwerp bepaal. Nominale voorsiening vir diensbaarheid is tipies in ontwerpstandaarde, terwyl ‘n heelwat meer omvattende probabilistiese aanslag gevolg word in die voorsiening vir die uiterste limietstaat (ULS). Sulke nominale voorsiening is waarskynlik onvanpas waar DLS die ontwerp bepaal. ‘n Probabilistiese aanslag word hier geneem in die assessering van DLS kraakvorming in gewapende beton waterhoudende strukture, om die ontwikkeling van ‘n veilig maar ekonomiese ontwerpformulering vir Suid-Afrika te ondersteun. ‘n Betroubaarhiedstudie deur McLeod (2013) van die huidige Europese kraakontwerp formulering het getoon dat model onsekerheid die betroubaarheid beduidend beinvloed. Daar was egter onvoldoende informasie om die model onsekerhede statisties te kwantifiseer, ‘n leemte wat deur hierdie navorsing gevul word. ‘n Probabilistiese aanslag word gevolg waar die verwagte kraakwydtes deur die sogenaamde Algemene Probabilistiese Model (APM) beskryf word. Die voorgestelde gewysigde EN 1992-1 model (Perez Caldentey, 2017) bied die beste voorspellings en vorm dus die basis vir die APM. Kraakmodelle van BS 8007 (1987), BS EN 1992-1 (2004), fib MC 2010 (2013) word met behulp van die APM geassesseer. Die model faktore word bereken as die verhouding van die maksimum gemete tot voorspelde kraakwydtes, wexp / wpredict. ‘n Databasis van eksperimentele kraakvorming onder las is vir die doel versamel, waaruit die model onsekerheid kwantifiseer is deur gemiddelde waardes en standaard afwykings van die model faktore te bepaal vir elk van die voorspellingsmodelle. Dit vorm die basis vir die keuse van APM. Korrelasie tussen model faktore en inset parameters kon ook bepaal word deur Pearson korrellasies en lineêre regressie analise. Die relatiewe belangrikheid van verskillende onseker inset parameters (wat model onsekerheid insluit) is bepaal deur gebruik te maak van die Eerste Orde Betroubaarheid Metode (EOBM). Die studie bevestig die belangrikheid van model onsekerheid as die primere invloed op betroubaarheid vir kraakwydte ontwerp. Die betroubaarheid van die verskillende kraak ontwerp formulerings word assesseer en vergelyk met teikenwaardes. Die invloed van langtermyn krimp onsekerheid op die betroubaarheid word ondersoek. Laastens word aanbevelings gemaak vir toekomende navorsing.

Please refer to this item in SUNScholar by using the following persistent URL: http://hdl.handle.net/10019.1/105884
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