Stratigraphic uncertainty characterization using generalized coupled Markov chain

Stratigraphic uncertainty widely exists in geotechnical structures. An efficient generalized coupled Markov chain (GCMC) model was proposed to simulate the stratigraphic uncertainty in the past. This model, however, cannot be directly applied to geotechnical problems because of the difficulty in directly estimating the horizontal transition probability matrices (HTPMs) of the GCMC from boreholes with large hole-to-hole distance. This paper, therefore, aims at addressing the above problem by using a maximum likelihood estimation (MLE) method and utilizing the MLE modified GCMC model to characterize stratigraphic uncertainty. In the framework of the GCMC, the validity of the proposed method is verified, and information entropy method is adopted to quantify the stratigraphic uncertainty. As an illustration, the proposed model is applied to a construction site in Hong Kong to characterize the stratigraphic uncertainty. A systematic comparison of coupled Markov chain (CMC) and GCMC model for stratigraphic uncertainty simulation was conducted. The influences of borehole layout scheme on transition probability matrices (TPMs) estimation and stratigraphic uncertainty simulation are explored. Results showed that the result of stratigraphic uncertainty simulation of the GCMC model is more reasonable than that of the CMC model. The borehole layout scheme is very important for estimating TPMs and significantly influences the stratigraphic uncertainty simulation. The information entropy map has the potential to become a useful guideline for the design of the borehole layout scheme in geotechnical engineering practice.