An analytical method for estimating horizontal transition probability matrix of coupled Markov chain for simulating geological uncertainty

Geological uncertainty exists widely in nature, which has a pivotal influence on the deformation and stability of the geotechnical structure. The coupled Markov chain (CMC) model is a widely used method to simulate the variability of strata. However, the difficulty to determine the horizontal transition probability matrix (HTPM), one of the important input parameters for the CMC model, limits its direct application to geotechnical engineering problems. In this study, an analytical method for estimating the HTPM is proposed and the CMC model is enhanced by integrating the analytical HTPM estimation method for simulating geological uncertainty. The validity of the analytical method for the HTPM and the accuracy of the strata simulated by the enhanced CMC model are evaluated through a typical stratum in literature. The results show that the estimated HTPMs are in good agreement with the real values and not sensitive to borehole schemes. The CMC model enhanced by the proposed analytical method for estimating the HTPM is well capable of simulating the strata based on given borehole data.