Probabilistic characterization of Young's modulus of soil using equivalent samples

• We develop an approach to obtain meaningful statistics from limited soil/rock data.
• Such statistics are required in geotechnical reliability analysis/design.
• The approach is based on Bayes’ Theorem and Markov Chain Monte Carlo simulation.
• It is illustrated and validated using both real observation and simulation data.
• The approach is particularly beneficial for projects with medium/ small sizes.

Several probability-based design codes (e.g., load and resistance factor design (LRFD) codes and Eurocode 7) have been developed and implemented around the world recently. A characteristic (or nominal) value of soil/rock properties is used in these design codes, and it is typically defined as a pre-specified quantile (e.g., mean or lower 5% quantile) of the statistical distribution of the soil properties. This poses a challenge in the implementation of the design codes, because the number of soil/rock property data obtained during site investigation is generally too sparse to generate meaningful statistics, rendering proper selection of the characteristic value a very difficult task. This paper aims to address this challenge by developing a Markov Chain Monte Carlo Simulation (MCMCS)-based approach for probabilistic characterization of undrained Young's modulus, Eu, of clay using standard penetration tests (SPT). Prior knowledge (e.g., previous engineering experience) and project-specific test data (e.g., SPT test data) are integrated probabilistically under a Bayesian framework and transformed into a large number, as many as needed, of equivalent samples of Eu. Subsequently, conventional statistical analysis is carried out to estimate statistics of Eu, and the characteristic value of the soil property is selected accordingly. Equations are derived for the proposed approach, and it is illustrated and validated using real SPT and pressuremeter test data at the clay site of the US National Geotechnical Experimentation Sites (NGES) at Texas A&M University.