Estimation of horizontal transition probability matrix for coupled Markov chain

Xiao Hui Qi, Dian Qing Li, Kok Kwang Phoon

Research output: Contribution to journalConference articlepeer-review

2 Citations (Scopus)


Geologic uncertainty appears in the form of one soil layer embedded in another or the inclusion of pockets of different soil types within a more uniform soil mass. An efficient coupled Markov chain (CMC) model has been proposed to simulate geologic uncertainty in the literature. This model, however, cannot be directly applied to geotechnical engineering. The primary problem lies in the estimation of horizontal transition probability matrix (HTPM), one key input of the CMC model. The HTPM is difficult to estimate due to the wide spacing between boreholes in the horizontal direction. Hence, a practical method for estimating the HTPM is verified using artificial borehole data. The effectiveness of this method is evaluated using the approach as follows. Several virtual boreholes are created using a set of prescribed HTPM and vertical transition probability matrix(VTPM). The HTPM estimated from the virtual boreholes is compared with the prescribed (or actual) HTPM. The evaluation results show that the estimated HTPM agrees well with the prescribed HTPM if the prescribed HTPM and VTPM are both highly diagonally dominant (diagonal element is larger than the sum of off-diagonal elements) Key words: geologic uncertainty, coupled Markov chain, horizontal transition probability matrix.

Original languageEnglish
Pages (from-to)2423-2428
Number of pages6
JournalJapanese Geotechnical Society Special Publication
Issue number71
Publication statusPublished - 2016
Externally publishedYes
Event15th Asian Regional Conference on Soil Mechanics and Geotechnical Engineering, ARC 2015 - Fukuoka, Kyushu, Japan
Duration: 9 Nov 201513 Nov 2015


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