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.

Examining Cognitive Processing in Children with an Arithmetic Disability

Currently there is no consensus as to the specific cognitive impairments that characterize mathematical disabilities (MD) or specific subtypes such as an arithmetic disability (AD). The present study sought to address this concern by examining cognitive processes that might undergird AD in children. The present study utilized archival data to conduct two investigations. The first investigation examined the executive functioning and working memory of children with AD. An age-matched achievement-matched design was employed to explore whether children with AD exhibit developmental lags or deficits in these cognitive domains. While children with AD did not exhibit impairments in verbal working memory or colour word inhibition, they did demonstrate impairments in shifting attention, visual-spatial working memory, and quantity inhibition. As children with AD did not perform more poorly than their younger achievement-matched peers on any of these tasks, impairments in specific areas of executive functioning and working memory appeared to reflect a developmental lag rather than a cognitive deficit. The second study examined the phonological processing performance of children with AD compared to children with comorbid disabilities in arithmetic and word recognition (AD/WRD) and to typically achieving (TA) children. Results indicated that, while children with AD did demonstrate impairments on all isolated naming speed tasks, trail making digits, and memory for digits, they did not demonstrate impairments on measures of phonological awareness, nonword repetition, serial processing speed, or serial naming speed. In contrast, children with AD/WRD demonstrated impairments on measures of phonological awareness, phonological short-term memory, isolated naming speed, serial processing speed, and the alphabet a-z task. Overall, results suggested that phonological processing impairments are more prominent in children with a WRD than children with an AD. Together, these studies further our understanding of the nature of the cognitive processes that underlie AD by focusing upon rarely used methods (i.e., age-matched achievement-matched design) and under-examined cognitive domains (i.e., phonological processing).