Due to time, budget, and/or technical constraints, geotechnical site investigation data from a specific site are often limited and sparse, leading to a long-lasting challenge in characterization of spatially varying geotechnical properties. During preliminary stages of site characterization, geotechnical data from neighboring sites or sites with similar geological conditions are often collected and used as valuable prior knowledge in geotechnical engineering practice. Nevertheless, existing methods for spatial variability characterization often rely solely on site-specific data and cannot effectively incorporate prior knowledge or existing databases. To address this issue, this study proposes a novel machine learning method that systematically combines sparsely measured data at a specific site with existing data from neighboring sites or sites with similar geological settings for characterization of property spatial variability in a data-driven manner. The proposed method starts with the construction of a dictionary that draws the dominant spatially varying patterns from a property measured at sites with similar geology under a dictionary learning framework. Leveraging the developed dictionary, the spatial variability of a property is interpreted from sparse site-specific measurements using Bayesian learning. The effectiveness of the proposed method is demonstrated using real data, and improved performance over existing methods is observed.

A profile of geotechnical properties is often needed for geotechnical design and analysis. However, site-specific data might be characterized as MUSIC-X (i.e., Multivariate, Uncertain and Unique, Sparse, Incomplete, and potentially Corrupted with “X” denoting the spatial/temporal variability), posing a significant challenge in accurately interpreting geotechnical property profiles. Different sources, or types, of data are commonly available from a specific site investigation program, and they are usually cross-correlated, and thus can provide complementary information. This leads to an important question in geotechnical site investigation: how to integrate multiple sources of sparse data for enhancing the profiling of different geotechnical properties. To address this issue, this study proposes a novel method, called fusion Bayesian compressive sampling (Fusion-BCS), for integrating sparse and non-co-located geotechnical data. In the proposed method, the auto- and cross-correlation structures of different sources of data are exploited in a data-driven manner through a joint sparse representation. Then, profiles of different geotechnical properties are jointly reconstructed from all measurements under a framework of compressive sampling/sensing. The proposed method is illustrated using simulated and real geotechnical data. The results indicate that the accuracy of the interpreted geotechnical property profiles may be significantly improved by integrating multiple sources of site investigation data.

Cross-correlated random fields are an essential tool for simultaneously modeling both auto- and cross-correlation structures of spatial or temporal quantities in stochastic analysis of structures or systems. Existing cross-correlated random field simulation methods often require explicit information about random field parameters as inputs. However, in engineering practice, site-specific measurements of different quantities are often limited, non-co-located and irregularly distributed within a given site because of time, budget, or space constraints as well as missing data. It is notoriously difficult to properly estimate reliable random field parameters from limited non-co-located measurements with an irregular spatial pattern, particularly the auto-correlation and cross-correlation structures of a two-dimensional (2D) cross-correlated random field. To deal with this issue, this study proposes a novel 2D cross-correlated random field generator for simulating 2D cross-correlated random field samples (RFSs) directly from sparsely measured non-co-located data points with unequal measurement intervals. Using a joint sparse representation, auto- and cross-correlation structures of different spatial/temporal quantities are exploited simultaneously from sparse measurements, followed by the generation of cross-correlated RFSs using Bayesian compressive sampling (BCS) and Markov chain Monte Carlo (MCMC) simulation in a data-driven manner. The proposed generator is demonstrated using 2D data of two correlated geotechnical properties. The results indicate that the RFSs generated using the proposed method from sparse measurements can properly characterize the spatial auto- and cross-correlation structures of different geotechnical properties.

In engineering practice, simplified procedure based on cone penetration test (CPT) results is widely used for evaluating soil liquefaction potential. Since the CPT-based simplified procedure was developed from observations during past earthquakes, it is semi-empirical and involves significant uncertainty (e.g., model uncertainty). In addition, due to time, budget and access constraints, CPTs are often sparsely conducted at a specific site, leading to a significant uncertainty associated with interpolation of the limited CPT soundings, particularly along horizontal direction. Furthermore, it is well-recognized that spatial variability of soil properties has a remarkable effect on soil liquefaction. All these variability and uncertainties greatly affect the seismic liquefaction assessment results, particularly spatial distribution of liquefiable soils in a site, and liquefaction-induced damage. This underscores a question of how to properly incorporate these variability and uncertainties in liquefaction assessment, e.g., how to characterize spatial distribution of soil liquefaction potential in a site with quantitative consideration of the abovementioned variability and uncertainty. To address this issue, this paper develops a novel probabilistic method for characterizing spatial distribution of soil liquefaction potential through factor of safety, FS against liquefaction in a vertical cross-section using Bayesian compressive sampling and Monte Carlo simulation. Using the proposed method, many random field samples of FS cross-section are obtained directly from limited CPT measurements. The proposed method is illustrated using both a simulated data example and a set of real CPT data from Christchurch, New Zealand. It is shown that the proposed method performs well and provides reasonable liquefaction assessment results.