TY - JOUR

T1 - Estimation of horizontal transition probability matrix for coupled Markov chain

AU - Qi, Xiao Hui

AU - Li, Dian Qing

AU - Phoon, Kok Kwang

N1 - Funding Information:
This work was supported by the National Science Fund for Distinguished Young Scholars (Project No. 51225903), the National Basic Research Program of China (973 Program) (Project No. 2011CB013506) and the National Natural Science Foundation of China (Project No. 51329901).

PY - 2016

Y1 - 2016

N2 - 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.

AB - 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.

KW - Coupled Markov chain

KW - Geologic uncertainty

KW - Horizontal transition probability matrix

UR - http://www.scopus.com/inward/record.url?scp=84971442598&partnerID=8YFLogxK

U2 - 10.3208/jgssp.TC304-03

DO - 10.3208/jgssp.TC304-03

M3 - Conference article

AN - SCOPUS:84971442598

VL - 2

SP - 2423

EP - 2428

JO - Japanese Geotechnical Society Special Publication

JF - Japanese Geotechnical Society Special Publication

IS - 71

T2 - 15th Asian Regional Conference on Soil Mechanics and Geotechnical Engineering, ARC 2015

Y2 - 9 November 2015 through 13 November 2015

ER -