Reliability Analysis of Reinforced Concrete using Non-Linear Finite Element Analysis
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The purpose of the thesis is to investigate methods that may be used for assessing thereliability in large concrete structures in combination with non-linear nite element analyses(NLFEA). Reliability methods are applied to a simple beam with various lengths, and evaluated withrespect to applicability, accuracy and feasibility. The reliability is assessed by a responsesurface method in combination with a rst order reliability method (RSM-FORM), anda small-sample Monte Carlo type using Latin hypercube sampling with curve tting toa normal distribution (LHS-t). For greater insight, these methods are investigated usingboth NLFEA and analytic limit state function evaluations (LSFE). Analytic MonteCarlo simulations are used as benchmarks. For very strong or weak material parameters,NLFEA yield inconsistent results. Only two stochastic variables are introduced, namelythe concrete in-situ compressive strength and the steel yield strength. Thus, only materialuncertainties are implemented in the reliability assessments. Since load eects are treateddeterministically, this study only regards reliability of the resistance. In the region where NLFEA is consistent and when only bending failure mode is prevalent,results from NLFEA RSM-FORM yield quite similar results compared to the benchmarks.Similarly, NLFEA LHS-t provides decent, conservative results although less accuratethan RSM-FORM. Analytic results show two important ndings: (1) RSM-FORM accuracydecreases with two failure modes, and (2) the choice of distribution seems importantfor LHS-t, however an optimal choice may still not provide as accurate results as RSMFORM. RSM-FORM shows promising results for a simple beam with one failure mode. However,for large concrete structures with several failure modes, this method might struggle tocreate an accurate response surface. This is further impeded by the diculties in producingconsistent NLFEA response. In terms of feasibility, RSM-FORM normally requires10-25 LSFEs for one reliability assessment, while LHS-t with 50 LSFEs provide the fullpicture of the structural reliability. LHS-t is not as accurate as RSM-FORM, however, itis simpler to grasp and results show that it provides reasonable accuracy for preliminaryreliability assessments. The literature provides a variety of optimizations and improvements on the methods,which might increase their applicability for large scale reliability assessments. Resultsherein are promising, and should be further investigated on more complex models usingimproved RSMs found in the literature.