Reliability analysis of slopes with truncated quantile functions from small, truncated/censored samples

Abstract

Truncated and censored samples encountered in geotechnical engineering arise from various factors such as equipment limitations, formation characteristics, sample disturbance, unsuitable sampling methods, environmental conditions, human error, budget constraints, and geological complexities. In addition to this, unprecedented events like the COVID-19 pandemic can impede soil and rock sampling efforts, necessitating engineers and designers to work with truncated samples. The primary objective of the research is to explore novel approaches for probabilistic slope stability analysis and design under small, truncated/censored samples. Landslides represent a prevalent and impactful geo hazard in Canada, particularly in relation to human lives and infrastructure sustainability. Thousands of landslides occur across Canada annually, resulting in direct and indirect damage estimated to range between $200 and $400 million per year. Reliability analysis, specifically utilizing the reliability index, serves as a valuable tool for evaluating engineering uncertainties, especially within the realm of slope stability. This study assesses the challenges posed by probability distribution limitations, emphasizing the relevance of truncated random variables in engineering contexts. The application of maximum entropy principles (MEPs) to estimating quantile functions (QFs) from truncated samples is discussed in the research. By employing MEPs along with partial probability weighted moments (PPWMs), the study demonstrates the effective estimation of truncated quantile functions. The optimization of these functions, determined by the Akaike information criterion (AIC), prevents the use of excessively complex models, thereby ensuring flexibility in model selection. [...]