Evaluating the pressure-settlement response of a composite foundation at a specific site is important for supporting the safety of superstructures in the design process to determine the bearing performance of the foundation. The uncertainties in the power law regression parameters stem from a significant scattering of pressure-settlement curves when a series of static load tests are conducted for the composite foundations composed of cement–fly ash–gravel piles at a particular site. Thus, in this work, a probability density contour (PDC) of these regression parameters is constructed using a bivariate distribution, which offers great flexibility in fitting the marginal distributions and the dependency between the two regression parameters. Based on an intuitive evolutionary geometry of the PDCs in the original physical space of two dependent random variables, a reliability index is defined as a distance ratio of two PDCs, i.e., the dispersed PDC that just touches the limit state curve and the one standard deviation PDC. These bivariate PDCs are discretized with several segments that adapt to the different spreads of the asymmetric data. Reliability indices are calculated based on the geometric reliability analysis, which offers great transparency for engineers in evaluating the safety of the composite foundation at a site-specific level. By using this reliability technique, the effects of uncertain regression parameters are explicitly explored at six sites consisting of 280 static loading tests.
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