Simulation of geological uncertainty using modified generalized coupled Markov chain

The traditional generalized coupled Markov chain (GCMC) is an effective model for the simulation of geological uncertainty. However, it cannot be directly applied to geotechnical problems. The reason lies in that one important parameter of GCMC, namely horizontal transition probability matrix (HTPM), is hard to be estimated due to the typical large distance between boreholes. Hence, In the framework of GCMC, a maximum likelihood estimation method for HTPMs based on borehole data is proposed. The validity of the method is verified. On this basis, the information entropy plot is adopted herein to quantify geological uncertainty. In addition, the borehole data from Dun Laoghaire Harbour, Dublin City, Ireland is used to simulate the geological uncertainty. The influences of layout schemes of boreholes on HTPMs are investigated. Moreover, those on simulation of geological uncertainty are explored. The results show that the proposed method can effectively estimate HTPM, which lays a foundation for analysis of geological uncertainty based on borehole data. The layout scheme of boreholes is very important for the estimation of the transition probability matrix in all directions and the simulated results of the geological uncertainty. Adequate borehole data should be provided to obtain accurate transition probability matrices. The boreholes should be designed in the key research area to minimize the simulation of geological uncertainty. The information entropy plot can visually quantify the stratigraphic simulation uncertainty, which can be used to guide the design of borehole schemes.