Simulation of geologic uncertainty using coupled Markov chain

Geological uncertainty appears in the form of one soil layer embedded in another or the inclusion of pockets of different soil type within a more uniform soil mass. An efficient coupled Markov chain (CMC) model has been proposed to simulate geological uncertainty in the past. 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 proposed based on borehole data. The effectiveness of this method can be evaluated using the following approach. Several virtual borehole outcomes are simulated using artificial HTPM. The HTPM estimated from the virtual boreholes is compared with the artificial HTPM. Boreholes collected from Perth, Australian are adopted to illustrate the proposed method for HTPM estimation. The results show that the estimated HTPM agrees well with the artificial HTPM if the artificial (real) HTPM or vertical transition probability matrix (VTPM) is strongly diagonally dominant (diagonal element is larger than the sum of off-diagonal elements). The estimated HTPM is not sensitive to the borehole layout scheme as the diagonal dominancy of the HTPM is strong.