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.

Long-term hydroclimatic change and interannual variability in water sources, Apex River (Iqaluit), Baffin Island, Nunavut

The eastern Canadian Arctic is home to Canada’s largest Indigenous population, which depends on local freshwater sources for drinking water. However, small watersheds have rarely been analyzed for long-term hydrologic response to changing climate. This study aims to address this issue by examining the Apex River, a small watershed with a long hydroclimatic record, near Iqaluit, Nunavut. Particular emphasis was placed on the long-term changes in climate and river discharge, and the seasonal variability of water sources between two snapshots in time, 1983 and 2013. Long-term hydrological data were obtained from gauge station 10UH002, operated by Environment and Climate Change Canada, and long-term meteorological data were acquired from Environment Canada–operated stations near Iqaluit Airport. Breakpoint analysis suggested that long-term mean annual surface air temperatures have increased since 1994. In contrast, no long-term total precipitation or annual discharge changes were observed. However, river flow initiation and cessation analyses of the Apex River flow season indicates that flow extended into the autumn since the 2000s. The 2013 flow season lasted 44 days longer than the 1983 flow season. Systematic river sampling was undertaken throughout the 2013 thaw season to determine contributing proportions of event (snowmelt or rainfall) and pre-event (baseflow) water to river runoff. Results from the stable isotope hydrograph separation for 2013 were compared to findings for 1983. Snow was the main source of water to the river during the snowmelt period in 1983 and 2013, however baseflow was still an important contributor. Although there was high similarity of water sources early in the season in 1983 and 2013, the two years differed during the autumn. In 2013 there was a high rainfall runoff response that was not present in 1983, suggesting high release of late-season sub-surface water storage and an increased sensitivity to late-season rainfall events in 2013. This research provides insights into the hydrologic response of the Apex River to long-term climatic change, and highlights the need for high-quality precipitation and discharge data for effective long-term hydrological assessment.