Unsupervised and Simultaneous Stratigraphic Interpretation of CPT Soundings at Site Scale
Publication: International Journal of Geomechanics
Volume 21, Issue 8
Abstract
This paper presents a novel Bayesian machine-learning approach for unsupervised and simultaneous soil stratigraphic interpretation of cone penetration test (CPT) soundings at the site scale. The proposed approach interprets numerous CPT soundings in a joint manner, and it leverages the statistical similarity of the measured sounding data in feature space (i.e., the Robertson chart) and the spatial constraints induced from spatial correlations of the sounding data both vertically along a single CPT sounding and horizontally across multiple soundings in physical space. The mathematical core of the proposed approach consists of the following two parts: (1) a quasi-3D (or 3D axial-symmetric) hidden Markov random field (HMRF) model describing both the statistical and spatial patterns of the CPT soundings; and (2) a model inference process, in which the statistical and spatial patterns are extracted from the dataset using a Bayesian unsupervised learning algorithm. The joint interpretation strategy of the proposed approach facilitates the use of rich statistical information and spatial constraints contained in an ensemble of CPT soundings to enhance the accuracy and consistency of a stratigraphic interpretation at the site scale. The proposed approach has been tested in a real-world case consisting of 44 CPT soundings collected from a geotechnical investigation site. The interpretation results show that the proposed approach can extract the soil spatial and statistical patterns from multiple CPT soundings and significantly increase the accuracy and consistency of the soil stratigraphic interpretation results.
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Acknowledgments
This work was partially supported by the Ohio Department of Transportation under Agreement Number 31795 Subtask 6: A Study of AI Based Methods for Characterization of Geotechnical Site Investigation Data and partially supported by the STEM Catalyst grant from the University of Dayton. The financial support was gratefully acknowledged.
Notation
The following symbols are used in this paper:
- dmax
- predefined threshold horizontal distance;
- Fr
- normalized friction ratio;
- fs
- sleeve friction;
- i, j
- index of a soil element, where i denotes the identification number of a sounding, and j denotes the discretized element depth;
- L
- set of soil labels;
- log10
- base 10 logarithmic function;
- Qtn
- normalized tip resistance;
- qc
- tip resistance;
- S
- set of soil elements in a group of CPT soundings;
- U(·)
- energy function associated with an MRF;
- Vc(·)
- clique potential associated with an MRF;
- clique potential for horizontal cliques;
- clique potential for vertical cliques;
- x
- soil stratification configuration of the CPT soundings;
- xt
- sample of x at MCMC simulation iteration t;
- x0
- initial estimates of x in MCMC simulation;
- x*
- maximum posterior estimates of x;
- mean-field configuration of a soil stratification configuration x;
- y
- observed scatter CPT sounding points in the feature space;
- β
- granularity coefficients;
- βt
- sample of β at MCMC simulation iteration t;
- β0
- initial estimates of β in MCMC simulation;
- β*
- maximum posterior estimates of β;
- βh
- horizontal granularity coefficients;
- βv
- vertical granularity coefficients;
- θ
- set of GMM parameters;
- θt
- sample of θ at MCMC simulation iteration t;
- θ0
- initial estimates of θ in MCMC simulation;
- θ*
- maximum posterior estimates of θ;
- μ
- means of GMM components;
- covariance matrices of GMM components;
- horizontal neighbor set of a neighborhood system;
- ∂ij
- neighborhood system of a soil element (i, j); and
- vertical neighbor set of a neighborhood system.
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Published In
International Journal of Geomechanics
Volume 21 • Issue 8 • August 2021
Copyright
© 2021 American Society of Civil Engineers.
History
Received: Sep 13, 2020
Accepted: Mar 29, 2021
Published online: May 20, 2021
Published in print: Aug 1, 2021
Discussion open until: Oct 20, 2021
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