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.

Karst hazard analysis towards the development of predictive karst models for southern Ontario

An investigation into karst hazard in southern Ontario has been undertaken with the intention of leading to the development of predictive karst models for this region. The reason these are not currently feasible is a lack of sufficient karst data, though this is not entirely due to the lack of karst features. Geophysical data was collected at Lake on the Mountain, Ontario as part of this karst investigation. This data was collected in order to validate the long-standing hypothesis that Lake on the Mountain was formed from a sinkhole collapse. Sub-bottom acoustic profiling data was collected in order to image the lake bottom sediments and bedrock. Vertical bedrock features interpreted as solutionally enlarged fractures were taken as evidence for karst processes on the lake bottom. Additionally, the bedrock topography shows a narrower and more elongated basin than was previously identified, and this also lies parallel to a mapped fault system in the area. This suggests that Lake on the Mountain was formed over a fault zone which also supports the sinkhole hypothesis as it would provide groundwater pathways for karst dissolution to occur. Previous sediment cores suggest that Lake on the Mountain would have formed at some point during the Wisconsinan glaciation with glacial meltwater and glacial loading as potential contributing factors to sinkhole development. A probabilistic karst model for the state of Kentucky, USA, has been generated using the Weights of Evidence method. This model is presented as an example of the predictive capabilities of these kind of data-driven modelling techniques and to show how such models could be applied to karst in Ontario. The model was able to classify 70% of the validation dataset correctly while minimizing false positive identifications. This is moderately successful and could stand to be improved. Finally, suggestions to improving the current karst model of southern Ontario are suggested with the goal of increasing investigation into karst in Ontario and streamlining the reporting system for sinkholes, caves, and other karst features so as to improve the current Ontario karst database.