And fast Lagrange element method follows the continuum hypothesis, which adopts difference format.
Nowadays, the most popular methods are finite element, discrete element and fast Lagrange element methods at home and abroad (Liu et al., 2007). Until now, a variety of numerical simulation methods have been applied in dynamic analysis successfully, including finite element, finite difference, discrete element, fast Lagrange element, discontinuous deformation analysis, manifold element, boundary element, unbounded element and semi-analytical element methods (Qi et al., 2004). While numerical simulation is an economical and convenient alternative method. Due to complicated topography and slope structure, results from in-situ test are difficult to obtain and the conclusion from model tests cannot reflect the natural slope. And results obtained by model test and in-situ test methods are limited to be generalized.
However, analytical solutions encounter serious limitations when the problem geometry is complicated and a great number of influencing parameters are to be incorporated (Gong, 2000 Qi, 2006). Meanwhile, the analysis method of dynamic response of rock slopes can be classified as analytical, numerical and model test methods. The classification of rock slope stability under earthquakes has been studied in different views (Babanouri et al., 2013 Hong & Xu, 2005 Liu et al., 2001 Liu et al.,2005 Liu et al.,2007 Qi, 2002), from which we can conclude that the classification mainly includes pseudo-static, sliding block, numerical, model test and probability analysis methods etc. Meanwhile, the paper (Li et al., 2003) points out five significant issues about dynamic loading in the area of geotechnical engineering, which includes the study of rock slope stability under earthquakes, and the dynamic response of rock slopes is one of its important study issues. Thousands of geological disasters are triggered by the Wenchuan Earthquake in Sichuan Province, and the majority of the disasters are landslides induced (Xu et al., 2009). China is a mountainous country accompanied with many earthquakes.
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