Estimation of Horizontal Transition Probability Matrix for Coupled Markov Chain Based on Borehole Data

Geological uncertainty widely exists in many landslide cases. It appears in the forms of one soil layer embedded in another or the inclusion of pockets of different soil type within a more uniform soil mass. An effective simulation method for the geological uncertainty is still absent in the geotechnical practice. Hence, borehole data from various sites are collected to verify the first-order Markovian property. A practical method is proposed to estimate the horizontal transition probability matrix (HTPM) for the couple Markov chain (CMC) model. Several virtual boreholes are created by means of simulating realizations of CMC using a prescribed HTPM. The effectiveness of the proposed method is evaluated by comparing the prescribed HTPM and the HTPM estimated from the virtual boreholes. The borehole data from Perth city, Australia is adopted to illustrate the estimation process of the HTPM. The results indicate that first-order Markovian property in soil transitions is quite common in reality. The estimation error of HTPM decreases with the increasing diagonal dominancy of the HTPM or VTPM. The method facilitate the application of the coupled Markov chain model in the simulation of the geological uncertainty. It provides a basis for uncertainty analysis of geotechnical problems considering geological uncertainty.