Analysis and prediction of rockfalls using a mathematical model

This paper deals with the study of rockfalls using a mathematical model, codified for computer use. Called CADMA, it allows predictions to be made of fall trajectories and of the relevant parameters (energy, height of bounce, run out distance of the falling blocks) for the design of remedial works. Designed with the experience gained from several in situ tests, this model is based on rigid body mechanics, and statistically analyses a fall in a two-dimensional space. The main features of the program are presented in this paper, as well as the criteria for choosing the trajectory to be studied, and the techniques for the assessment of the most relevant parameters required for the execution of the rockfall analysis (particularly the dynamic parameters: restitution and rolling friction coefficients). Some practical aspects of the rockfall mathematical analysis are also discussed. These include the effect of topographical detail on the results and the optimal number of simulations to be carried out. The characteristics and potentials of the program were evaluated by comparing the results of in situ tests: in all cases, the program supplied generally accurate predictions in terms of fall velocity, energy, height of bounce and stopping distance.