Block toppling is one of the typical failure types of the rock slopes caused by overturning of the slender, layered rock blocks on the slope under gravitational or seismic conditions. For the stability assessment against the block toppling, limit equilibrium methods are conventionally used. However, in case of the earthquakes, rocking vibration of each rock mass, and the interaction among them may affect the stability of the whole slope. Thus, to evaluate the seismic safety of the toppling slopes, it is appropriate to use a numerical method that can incorporate the above mentioned phenomena precisely.

In this study, the discontinuous deformation analysis (DDA) is focused as a method to simulate rocking motion of the rock mass during the earthquakes. Since DDA is an implicit type numerical method for discontinua, robust computation of the discontinuous behaviors of jointed rock masses is possible. In the past studies, however, it was pointed out that decision of appropriate numerical parameters in DDA to reproduce the rocking motion with high accuracy is difficult. Therefore, the purpose of this study is to reveal the cause of the accuracy degradation of DDA in rocking motion analysis, and to propose an improvement scheme of the DDA for the rocking motion analysis.

The reason of the accuracy degradation in DDA is discussed based on the fundamental rocking problem. From the simulated results with the conventional DDA, it is found that the contact treatment by applying the constraint condition on the normal gap, so-called non-penetration condition, induces unnatural vibration of the contact point after the collision and loses the accuracy. Based on this insight, the new method is developed formulating the contact with zero gap rate condition to avoid the vibration of the contact point. In addition, to satisfy this constraint condition strictly, Augmented Lagrangian method (ALM) is also introduced instead of the conventional penalty method. The new DDA is applied to the fundamental rocking analysis, and showed good agreement with the solution of the rocking theory.

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