Abstract:

As a explicit behaviors of the complicated nonlinear dynamic system，the displacement of landslide is characterized with many uncertain factors. In order to reduce the limitation of traditional method, the set pair analysis (SPA) theory combined with fuzzy-Markov theory is introduced to describe the landslide dynamic system, and then the SPA-fuzzy-Markov prediction model for landslide displacement is set up. In this new model, the fuzzy-Markov theory is applied to analyze and predict the state transition of the uncertain factor in SPA model. By this way, the precision can obtained a significant improvement. Based on the correlation coefficient and mean square deviation of eigenvalue, two verify methods for fuzzy-Markov fitting in multidimensional space are suggested. Furthermore, based on these two verification methods; the sensitivity analysis for fuzzy-Markov model in two factors, such as fuzzy interval overlap and state transfer steps, can be done. By this way, the optimal parameter combination can be recommended. As a test，the SPA-fuzzy-Markov composite model is used to analyze the displacement of Liujiatuo landslide. The results indicate that the state transfer step is more sensitive than fuzzy interval overlap in this case. It is proved this new model can conspicuously improve the short-term prediction precision than just single SPA model; and this new model is worth popularizing in geotechnical monitoring. Moreover, the introducing of fuzzy-Markov guides a new way to develop basic research of SPA theory. This new method has theoretical and practical values not only in geotechnical monitoring, but also in other related fields.

Key words: rock and soil mechanics, landslide, prediction, set pair analysis, fuzzy, Markov chain, sensitivity analysis