Reliability of Ultimate Limit State Design in Finite Elements and Compliance with Eurocode 7

Abstract

Geotechnical design problems may be characterized by a certain degree of uncertainty, due to insufficient soil data and transformation of test results in soil parameters. In common practice, engineers perform deterministic analyses according to design standards as Eurocode 7, where the uncertainties are taken into account through partial factors for loads and soil properties to attain certain specified target reliabilities. Forcomplexsoilstructureinteractionproblems, partialfactormethodis difficult to adopt, as the design standards consider geotechnical standards with singlefailuremechanism. ThisisespeciallyproblematicforUltimateLimitstatedesigns where both stiffness and strength properties are dominant. With the advent of limit state design philosophy in Eurocodes, the use of reliability methods in Finite Element Analysis for complex situations has become more and more of interest. Reliability analyses allow to explicitly define the single uncertainties in the model by using an appropriate probabilistic distribution for each source of uncertainty. The reliability index and the probability of failure with respect to a predefined condition are calculated. The problem with using reliability based probabilistic design is the absence of simple computational approaches that can be easily implemented. MonteCarlosimulationsarecommonly usedto solvesoil structureinteraction problems. For a large and complex soil-structure interaction problem, it is computationally intensive to complete even a single run. This practical disadvantage can be solved only by a computationally efficient method. A special purpose application to perform probabilistic analysis in PLAXIS 2D, called PROBANA has been recently developed at Plaxis B.V. PROBANA performs direct probabilistic calculations in the finite element framework, using First Order Reliability Method or Monte Carlo Method. In this thesis, PROBANA (FORM) is used to perform reliability analysis for three benchmarks, and the results from PROBANA – FORM are compared with Point Estimate Method (PEM) and other stochastic Methods. The results from FORM are found to be comparable with that of PEM. It is concludedthatPEMislessaccurateduetoassumptionsmadebyPEMintheunderlying output distribution and FORM is more accurate and practical as it is computationally less intensive compared to other stochastic methods such as the Monte Carlo analysis. An extensive comparison of the reliability based method with Eurocode design method shows possibilities to implement reliability methods with EC7. One such approach is proposed, and demonstrated with the benchmarks.