Interpretation and Simulation of Geotechnical Data from Sparse Measurements Using Bayesian and Compressive Sampling Methods

Abstract

Due to geological formation processes that geo-materials have undergone, properties of geo-materials vary spatially and exhibit spatial auto-correlation. Proper characterization and interpretation of such variability and correlation generally require extensive measurements from geotechnical site characterization. In geotechnical engineering, measurements from a specific site are usually sparse and limited. It is therefore a challenging task to interpret properly geotechnical properties from sparse measurements or to rationally simulate geotechnical properties considering spatial variability and spatial correlation. Note that simulated geotechnical properties using such as random field theory have been increasingly used in geotechnical engineering in the past three decades to account for the effects of the variability and uncertainties in geotechnical properties.

To address these challenges, several methods are developed for the interpretation and simulation in this study under two scenarios: 1) when the spatial auto-correlation of geotechnical properties is not explicitly considered and 2) when the spatial auto-correlation is explicitly considered. Because spatial auto-correlation of geotechnical properties is of great importance to geotechnical design and analysis, emphasis is placed on the second scenario although the first scenario is also covered in the study. As the spatial variability and spatial auto-correlation of geotechnical properties are explicitly reflected in geotechnical properties profiles (i.e., variation of geotechnical properties over depth), a method based on compressive sampling/sensing (CS) is developed for objective interpretation of geotechnical properties profile from sparse measurements (e.g., about 10 data points). The interpreted profile from sparse measurement by the CS-based method is realistic and reflect the underlying variation of geotechnical properties over depth in a specific site, and it explicitly takes the spatial auto-correlation of geotechnical properties into account.

Because only sparse measurements are used to interpret geotechnical properties profile, the interpreted profile via the CS-based method may contain significant statistical uncertainty. The statistical uncertainty further propagates to and significantly affects geotechnical design or analysis when the interpreted profile is used as input. It is therefore important to quantify the statistical uncertainty in the interpreted profile. To this end, a Bayesian compressive sampling (BCS) approach, i.e., a probabilistic extension of the CS-based approach, is developed in the study. The BCS approach provides not only the best estimate of a geotechnical property profile of interest, but also a vehicle to explicitly and rationally quantify the statistical uncertainty in the interpreted profiles caused by sparse measurements. The quantified statistical uncertainty offers an explicit and objective measure of the accuracy and reliability of the interpreted soil property profile.

Building on the quantified statistical uncertainty from BCS, a method is further developed to facilitate the determination of characteristic values for geotechnical parameters from a purely statistical point of view. Characteristic values of geotechnical properties are required in geotechnical codes (e.g., Eurocode 7), and their determination in an objective manner has been a challenging task due to the limited and spatially varying pattern of measurements. Moreover, the results obtained from the BCS approach are further formulated as a truncated Karhunen-Loève (KL) expansion for development of a random field generator, denoted as a BCS-KL generator in this study. This generator requires only sparse measurements as input but offers hundreds of thousands of site-specific random field samples (RFSs) as output. It bypasses the difficult of using random field theory which generally requires extensive measurements to estimate the corresponding random field parameters. Moreover, the simulated RFSs are realistic and statistically characterize the spatial auto-correlation and variation of a soil property of interest within the site of interest.

Date of Award	21 Aug 2017
Original language	English
Awarding Institution	City University of Hong Kong
Supervisor	Yu WANG (Supervisor)