This paper presents the modeling of rockfalls using the lumped mass method and the DDA method. In the lumped mass method, the block is treated as a lumped mass which neglects the three-dimensional aspects of the block such as the block shape and the subsequent block orientation at the instant of impact on the slope. On the contrary, the DDA method for rigid blocks, which is a two-dimensional deterministic discrete element analysis, is adopted to study the rockfall problem if it is of importance to investigate the effects from the shape and size effects of the falling rock. Results obtained demonstrate that the proposed method with the combination of using the lumped mass method and the DDA method can greatly increase the reliability of predicting rockfall trajectories using the high resolutionDEMand exhibit great potential for practical applications in the future.


Due to the effects of global climate change in recent years, Taiwan has seen increasing extreme rainfall events, which dramatically increase the occurrence of rockfall hazards. The rockfall problem poses a continuous hazard in mountain areas worldwide (Schweigl et al., 2003; DAMOCLES, 2003). Rockfall dynamics, which is a function of the location of the detachment point, geometry, and mechanical properties of both the rock block and the slope, plays a crucial role in modeling the rockfall problem. However, reliable rockfall prediction is usually a difficult task because it is difficult to determine the initial conditions, the actual natural or engineered slope geometry, and the relationships describing the energy loss at impact in space and time, even after a rockfall has occurred. In reality, the geometrical and mechanical characteristics of the surface material may vary dramatically along a slope. Accordingly, modeling rockfalls should involve high resolution Digital Elevation Model (DEM) and probabilistic analysis.

The lumped mass method was proposed by Piteau and Clayton (1976). Their program, called Computer Rockfall Model, can deal with four motions (free fall, bouncing, rolling, and sliding), and assumes that a falling rock is an infinitely small mass point to simulate velocity reduction after a collision without contributions from the shape and the size of the falling rock. Many researchers have continued to use the lumped mass method to develop rockfall analysis programs, such as CADMA (Azzoni et al., 1995), RocFall (Steven, 1998), CRSP (Pfeiffer and Bowen, 1989). In Taiwan, the RocFall and the CRSP are often adopted for analyzing the rockfall problem. Although two-dimensional models are preferable from an operational and computational point of view, the interpretation of their results and their extension to neighboring areas are subjective. With the significant improvement in satellite imaging and digital terrain production technology recently, countries with serious rockfall problems have conducted increasing research on rockfalls. The STONE program published in 2003 is based on a three-dimensional rockfall analysis model. Due to the limitations of DEM data accuracy, the applications of the STONE program are mostly for large area analyses. Also, most rockfall programs are limited to the deterministic analysis. In a deterministic analysis it is assumed that all input parameters are exactly given (e.g. the coefficients of restitution, slope friction, and the location and velocity of where the rocks originate, etc) and the analysis does not take the probabilities of different event sequences into account.

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