Simulation of Geological Uncertainty Using Coupled Markov Chain: A Case Study at a Manually Filled Loess Site

Stratigraphic variability contributes significantly to the deformation and stability of geotechnical structures. In this case study, the stratigraphic variability of a typical deep manually filled site in Lanzhou New District, Gansu Province, China is simulated. By applying Walther's law, the relationship between vertical and horizontal transition counting matrices is established to calculate the vertical and horizontal state-transition probability matrices using a coupled Markov chain model. The Monte Carlo simulation method is used to predict the distribution of soil layers. Based on borehole data, the effects of different borehole layout schemes on the estimation of the transfer probability matrix and prediction of the soil layer distribution are investigated. The results indicate that to obtain accurate estimations for the state transition probability matrix and predictions for the soil layer distribution, more evenly distributed borehole data should be selected. When the values of the diagonal elements in the matrix are high, the sensitivity of the transition probability matrix estimation to the borehole layout scheme is low. Multiple predictions of soil layer distributions using the same borehole layout scheme yield different results primarily because of the significant spacing between the boreholes.