RELIBILITY ANALYSIS OF SIMPLE SLOPES AND SOIL-STRUCTURES WITH LINEAR LIMIT STATES

The first objective of this research was to develop closed-form and numerical probabilistic methods of analysis that can be applied to otherwise conventional methods of unreinforced and geosynthetic reinforced slopes and walls. These probabilistic methods explicitly include random variability of soil and reinforcement, spatial variability of the soil, and cross-correlation between soil input parameters on probability of failure. The quantitative impact of simultaneously considering the influence of random and/or spatial variability in soil properties in combination with cross-correlation in soil properties is investigated for the first time in the research literature. Depending on the magnitude of these statistical descriptors, margins of safety based on conventional notions of safety may be very different from margins of safety expressed in terms of probability of failure (or reliability index). The thesis work also shows that intuitive notions of margin of safety using conventional factor of safety and probability of failure can be brought into alignment when cross-correlation between soil properties is considered in a rigorous manner. The second objective of this thesis work was to develop a general closed-form solution to compute the true probability of failure (or reliability index) of a simple linear limit state function with one load term and one resistance term expressed first in general probabilistic terms and then migrated to a LRFD format for the purpose of LRFD calibration. The formulation considers contributions to probability of failure due to model type, uncertainty in bias values, bias dependencies, uncertainty in estimates of nominal values for correlated and uncorrelated load and resistance terms, and average margin of safety expressed as the operational factor of safety (OFS). Bias is defined as the ratio of measured to predicted value. Parametric analyses were carried out to show that ignoring possible correlations between random variables can lead to conservative (safe) values of resistance factor in some cases and in other cases to non-conservative (unsafe) values. Example LRFD calibrations were carried out using different load and resistance models for the pullout internal stability limit state of steel strip and geosynthetic reinforced soil walls together with matching bias data reported in the literature.

Minorities, Measured Cognitive Skills and the Earnings of Canadians (Working Paper 26)

This paper uses the Statistics Canada Survey of Literacy Skills in Daily Use (LSUDA) to investigate minority-“white”(i.e., non-minority) income differences and the role education and English/French literacy and numeracy skills play in those patterns. There are three principal sets of findings. First, among males, some visible minority groups have substantially lower levels of the measured language and number skills than whites and other more economically successful minorities, and in some cases these differences play a significant role in explaining the observed income patterns. The minority-white income gaps are, however, much smaller for women, and the literacy and numeracy variables do not have much of a role to play in explaining those differences. Second, for men, the minority-white income gaps are largely confined to immigrants, and there are no significant differences amongst the native-born once various factors which affect incomes (including education and the literacy and numeracy measures) are taken into account. For women, though, minority-white income differences only emerge for certain Canadian-born groups when they are differentiated from immigrants, for whom different gaps become apparent. Finally, the measured returns to literacy and numeracy differ significantly by ethnic group and sex. Various implications of the findings are discussed.