Estimation of horizontal transition probability matrix for coupled Markov chain

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 geological 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 prescribed HTPM. 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).