Characterisation of model uncertainty for reliability-based design of pile foundations

[摘要] ENGLISH ABSTRACT: To keep pace with international trends, the introduction of geotechnical limit state design inSouth Africa is inevitable. To pave the way for implementation of limit state pile design inthe country, the study quantifies model uncertainty in the classic static pile design formulaunder the Southern African geologic environment. The generated model uncertaintystatistics are used to calibrate partial resistance factors in a reliability-based designframework.A series of pile performance predictions by the static formula are compared with measuredperformances. To capture the distinct soil types for the geologic region of Southern Africaas well as the local pile design and construction experience base, pile load tests andassociated geotechnical data from the Southern African geologic environment are used. Themethodology of collecting, compiling, and analyzing the pile load tests to derive themeasured ultimate pile capacities is described. To facilitate the computation of thetheoretical capacities, the site specific geotechnical data in the database are transformed tothe desired engineering soil properties through well established empirical correlations.For a given pile test case, model uncertainty is presented in terms of a model factorcomputed as the ratio of the measured to the theoretical capacity, leading to n realisations ofthe model factor. To facilitate further interpretation and generalisation of the model factorrealisation data, statistical analysis is carried out. The statistical analysis comprises ofgraphical representation by histograms, outliers detection and correction of erroneousvalues, and using the corrected data to compute the sample moments (mean, standarddeviations, skewness and kurtosis) needed in reliability analysis. The analyses demonstratethat driven piles depict higher variability compared to bored piles irrespective of materialstype. Furthermore, for a given pile installation method (driven or bored) the variability innon-cohesive materials is higher than that in cohesive materials.In addition to the above statistics, reliability analysis requires the theoretical probabilitydistribution for the random variable under consideration. Accordingly it is demonstrated thatthe lognormal distribution is the most appropriate theoretical model for the model factor.Another key basis for reliability theory is the notion of randomness of the basic variables.To verify that the variation in the model factor is not explainable by deterministic variationsin the database, an investigation of correlation of the model factor with underlying piledesign parameters is carried out. It is shown that such correlation is generally weak. Correlation can have a significant impact on the calculated reliability index if not accountedfor. Accordingly, the effects of the exhibited correlation is investigated through an approachbased on regression theory in which systematic effects of design parameters are taken intoaccount (generalised model factor). The model factor statistics from the conventionalapproach and those from the generalised model factor approach are used to determinereliability indexes implied by the current design practice. It is demonstrated that nosignificant improvement in values of the reliability indexes is gained by taking into accountthe effects of the weak correlation.The model factor statistics derived on the basis of the standard model factor approach areused to calibrate resistance factors. Four first order reliability methods are employed for thecalibration of resistance factors. These include; the Mean Value First-Order SecondMoment approach, an Approximate Mean Value First-Order Second Moment approach, theAdvanced First-Order Second Moment approach using Excel spreadsheet, and theAdvanced First-Order Second Moment approach (design point method). The resistancefactors from the various calibration methods are presented for the target reliability indexvalues of 2.0, 2.5, and 3.0. The analyses of the results demonstrate that for a given targetreliability index, the resistance factors from the different methods are comparable.Furthermore, it is shown that for a given material type, the resistance factors are quite closeirrespective of the pile installation method, suggesting differentiation of partial factors interms of materials types only. Finally, resistance factors for use in probabilistic limit statepile design in South Africa are recommended.

[发布机构] Stellenbosch University