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.

Performance and Assessment of Rehabilitated Steel Culverts

This thesis explores the effects of rehabilitation on the structural performance of corrugated steel culverts. A full-scale laboratory experiment investigated the effects of grouted slip-liners on the performance of two buried circular corrugated steel culverts. One culvert was slip-lined and grouted using low strength grout, while the other was slip-lined and grouted using high strength grout. The performances of the culverts were measured before and after rehabilitation under service loads using single wheel pair loading at 0.45m of cover. Then, the rehabilitated culverts were loaded to their ultimate limit states. Results showed that the low and high strength grouted slip-liners provided strength well beyond requirements, with the low strength specimen failing at a load 2.4 times the fully factored service load, while the high strength specimen did not reach an ultimate limit state before bearing failure of the soil stopped testing. Results also showed that the low strength specimen behaved rigidly under service loads and flexibly under higher loads, while the high strength specimen behaved rigidly under all loads. A second full-scale experiment investigated the effect of a paved invert rehabilitation procedure on the performance of a deteriorated horizontal ellipse culvert. The performance of the culvert before and after rehabilitation was examined under service loads using tandem axle loading at 0.45m of cover. The rehabilitated culvert was then loaded up to its ultimate limit state. The culvert failed due to the formation of a plastic hinge at the West shoulder, while the paved invert cracked at the invert. Results showed that the rehabilitation increased the structural performance of the culvert, increasing the system stiffness and reducing average strains and local bending at critical locations in the culvert under service loads. A sustainability rating tool specifically for the evaluation of deteriorated culvert replacement or rehabilitation projects was also developed. A module for an existing tool, called GoldSET, was created and tested using two case studies, each comparing the replacement of a culvert using a traditional open-cut method with two trenchless rehabilitation techniques. In each case, the analyses showed that the trenchless techniques were the better alternatives in terms of sustainability.