Nat. Hazards Earth Syst. Sci., 18, 1187–1199, 2018 https://doi.org/10.5194/nhess-18-1187-2018 © Author(s) 2018. This work is distributed under the Creative Commons Attribution 4.0 License. State fusion entropy for continuous and site-specific analysis of landslide stability changing regularities Yong Liu, Zhimeng Qin, Baodan Hu, and Shuai Feng School of Mechanical Engineering and Electronic Information, China University of Geosciences, Wuhan, 430074, China Correspondence: Zhimeng Qin ([email protected]) Received: 6 October 2017 – Discussion started: 1 November 2017 Revised: 21 March 2018 – Accepted: 23 March 2018 – Published: 19 April 2018 Abstract. Stability analysis is of great significance to land- fiths and Fenton, 2004). Saito’s method is an empirical fore- slide hazard prevention, especially the dynamic stability. cast model and is suitable for the prediction of sliding ten- However, many existing stability analysis methods are dif- dency and then the failure time. Based on homogeneous soil ficult to analyse the continuous landslide stability and its creep theory and displacement curve, it divides displacement changing regularities in a uniform criterion due to the unique creep curves into three stages – deceleration creep, stable landslide geological conditions. Based on the relationship creep and accelerating creep – and establishes a differential between displacement monitoring data, deformation states equation for accelerating creep. The physical basis of Saito’s and landslide stability, a state fusion entropy method is herein method helped it to successfully forecast a landslide that oc- proposed to derive landslide instability through a comprehen- curred in Japan in December 1960, but also makes it strongly sive multi-attribute entropy analysis of deformation states, dependent on field observations. LEM is a kind of calcula- which are defined by a proposed joint clustering method tion method to evaluate landslide stability based on mechan- combining K-means and a cloud model. Taking Xintan land- ical balance principle. By assuming a potential sliding sur- slide as the detailed case study, cumulative state fusion en- face and slicing the sliding body on the potential sliding sur- tropy presents an obvious increasing trend after the landslide face firstly, LEM calculates the shear resistance and the shear entered accelerative deformation stage and historical max- force of each slice along the potential sliding surface and de- ima match highly with landslide macroscopic deformation fines their ratio as the safety factor to describe landslide sta- behaviours in key time nodes. Reasonable results are also bility. LEM is simple and can directly analyse landslide sta- obtained in its application to several other landslides in the bility under limit condition without geotechnical constitutive Three Gorges Reservoir in China. Combined with field sur- analysis. However, this neglect of geotechnical constitutive vey, state fusion entropy may serve for assessing landslide characteristic also restricts it to a static mechanics evalua- stability and judging landslide evolutionary stages. tion model that is incapable of evaluating the changing regu- larities of landslide stability. LEM involves too many physi- cal parameters, such as cohesive strength and friction angle, which makes it greatly limited in landslide forecast. As a typ- 1 Introduction ical numerical simulation method, FEM subdivides a large problem into smaller, simpler parts that are called finite ele- Landslides are some of the greatest natural hazards, account- ments. The simple equations that model these finite elements ing for massive damages of properties every year (Dai et al., are then assembled into a larger system of equations that 2002). Analysis of landslide stability as well as its chang- models the entire problem. FEM then uses variational meth- ing regularities plays a significant role in risk assessment at ods from the calculus of variations to approximate a solu- site-specific landslides (Wang et al., 2014). For this concern, tion by minimising an associated error function. In landslide many stability analysis methods have been proposed, such as stability analysis, FEM not only satisfies the static equilib- Saito’s method, limit equilibrium method (LEM) and finite rium condition and the geotechnical constitutive characteris- element method (FEM) (Saito, 1965; Duncan, 1996; Grif- Published by Copernicus Publications on behalf of the European Geosciences Union. 1188 Y. Liu et al.: State fusion entropy for continuous analysis of landslide stability changing regularities tic but also adapts to the discontinuity and heterogeneity of based on original data and personal engineering geological the rock mass. However, FEM is quite sensitive to various in- experience. volved parameters and the computation will increase greatly Entropy has been widely used to describe the disorder, to get more accurate results. If parameters and boundaries imbalance and uncertainty of a system (Montesarchio et al., are precisely determined, LEM and FEM can provide results 2011; Ridolfi et al., 2011). Previous works have introduced with high reliability. Other stability analysis methods such as entropy into landslide susceptibility mapping to evaluate the the strength reduction method also have been rapidly applied weights of indexes (Pourghasemi et al., 2012; Devkota et al., (Dawson et al., 2015). These methods provide the theoretical 2013). From the viewpoint of system theory, a landslide can basis for analysing landslide stability and have been widely be regarded as an open system that exchanges energy and in- applied in engineering geology (Knappett, 2008; Morales- formation with external factors. Shi and Jin (2009) proposed Esteban et al., 2015). a generalized information entropy approach (GIE) to eval- Despite of the great contributions made by these stabil- uate the “energy” of multi-triggers of landslide and found ity analysis methods, there are a few matters cannot be ne- that the GIE index showed a mutation before landslide fail- glected. Firstly, the safety factor is the most adopted index ure in a case study. But this GIE method is aimed at landslide to indicate landslide stability (Hsu and Chien, 2016), but triggering factors and thus cannot directly indicate landslide it mainly indicates safe (larger than 1) or unsafe (smaller stability. than 1) and is incapable of showing the degree of stabil- In this paper, a state fusion entropy (SFE) approach is pro- ity or instability (Li et al., 2009; Singh et al., 2012). Sec- posed for continuous and site-specific analysis of landslide ondly, external factors such as rainfall (Priest et al., 2011; stability changing regularities. It firstly defines deformation Bernardie et al., 2015; Liu et al., 2016) and fluctuation of states as an integrated numerical feature of landslide defor- water level (Ashland et al., 2006; Huang et al., 2017b) will mation. Considering the multiple attributes of deformation also change landslide stability. However, currently only a few states, entropy is adopted for landslide stability (instability) studies have mentioned real-time landslide stability (Mon- analysis. Correspondingly, a historical maximum index is in- trasio et al., 2011; Chen et al., 2014). Thirdly, methods like troduced to identify key time nodes of stability changes. LEM and FEM involve too many physical parameters whose uncertainties make these methods hard to match with the real-time conditions of landslide. It becomes of great inter- 2 Methods est to find a new method to evaluate landslide stability that only requires a few parameters, can easily be matched with In this paper, a landslide is regarded as an open dynamic landslide real-time conditions and can indicate the extent as system, and landslide stability (instability) is the source of well as the changing regularities of landslide stability. the system. Under the influence of external factors, landslide Displacement is the most direct and continuous manifes- stability will respond to these triggers by generating defor- tation of landslide deformation promoted by external factors mation states. Eventually, deformation states will be mani- and has been widely used in landslide analysis (Asch et al., fested in the form of landslide displacement. Therefore, to 2009; Manconi and Giordan, 2015; Huang et al., 2017a). analyse landslide stability based on displacement monitor- Due to its easy acquisition, quantification and high reliabil- ing data, defining deformation states is the primary founda- ity, displacement monitoring data have become some of the tion. In order to adapt to the unique geological conditions most recognised evidence for landslide stability analysis and of different landslides, a joint clustering method combining early warning. Macciotta et al. (2016) suggested that veloc- K-means clustering and cloud modeling is proposed. Aiming ity threshold be used as a criterion for an early warning sys- for three typical characteristics of deformation states, entropy tem and that the annual horizontal displacement threshold analysis is then conducted and fused to analyse landslide in- for Ripley landslide (GPS 1) can be 90 mm and that between stability and its changing regularities. A result interpretation May and September can be 25 mm. Based on the analysis method is proposed correspondingly. The flow chart is shown of a large number of displacement monitoring data, Xu and in Fig. 1. Zeng (2009) proposed that deformation acceleration be used as an indicator of landslide warning; the