A numerical model has been developed for the study of the spatial movement of blocks striking a three-dimensional topography. The generalized movement of such blocks is determined by fundamental equations of the dynamics of rigid solids. When a block touches the topographical surface, a condition of either instantaneous contact (impact) or permanent contact (rolling or sliding) is imposed upon it. The geometry of the blocks may be defined as prisms with polygonal section or ellipsoids. The block is taken to be absolutely rigid and the topography has either an inelastic or plastic behaviour coupled with a surface roughness. The model has been fitted to the results of a case-study of a real rockfall, in which a million cubic meters are involved. The study permits a delimitation of risk zones in cultivated areas and underlines practical protection steps which may be implemented when rockfalls are at a minimum due to winter freezing.


Un modèle numerique a ete developpe pour l'etude du mouvement spatial de blocs impactant une topographie tridimensionnelle. Le mouvement general d'un bloc est regi par les equations fondamentales de la dynamique du solide rigide. Quand le bloc touche la surface topographique, on impose des conditions de contact instantane (impact) ou permanent (roulement ou glissement). La geometrie des blocs peut être choisie en forme de prisme à section polygonale ou d'ellipsoïde. Le bloc est considere comme indeformable, la topographie presente un comportement au choc soit inelastique, soit plastique, tout en possedant une rugosite de surface. Le modèle a ete cale sur un eboulement reel de l'ordre de un million de mètres cubes, sur la base d'observations faites in situ. L'etude doit servir à delimiter les zones de risques dans des culturea en exploitation et preconiser des mesures de protection à mettre en oeuvre durant la periode de gel hivernal où l'activite de chutes est pratiquement stoppee.


Es wurde ein numerisches Modell zur Untersuchung der raumlichen Bewegung von Blöcken entwikkelt, die auf eine dreidimensionale Topographie prallen. Die allgemeine Bewegung eines Blocks wird durch die Grundgleichungen der Dynamik starrer Körper beschrieben. Wenn der Block die Gelandeoberflache beruehrt, wird augenblicklicher (Stoss) oder Dauernder (Rollen oder Gleiten) Kontakt vorgegeben. Die Blöcke können prismatische form mit polygon-Querschnitt oder ellipsoïdische form aufweisen. Der Block wird starr angenommen, und die Gelandeoberflache verhalt sich entweder inelastisch oder plastisch mit Beruecksichtigung einer Oberflachenrauheit. Das Modell wurde mittels der Ergebnisse eines reellen felssturzes von 1 Mio m3 Ausmass geeicht. Die Untersuchung erlaubt die festlegung von Risikozonen in landwirtschaftlich genutztem Gelande und von Schutzmaasnahmen, die wanrend der Winterfröste, die die felsstuerze praktisch zum Stillatand bringen, ausgefuehrt werden können.


Near rock cliffs in mountainous regions, falling rocks and rockslides make dynamic studies of possible block trajectories necessary for the evaluation of the extent of the threatened zones as well as for the definition of adequate measures of protection. Until now, existing models of computation are essentially two-dimensional (CUNDALL, 1971, AZIMI et al., 1982, BOZZOLO and PAMINI, 1982, HACAR et al., 1977, LOPEZ-CARRERAS, 1981, PITEAU and CLAYTON, 1976). They simply apply to a ground profile selected in a vertical plane or along the line of the deepest slope, without being able to take care of the lateral dispersion of the block trajectories. In many cases of complex topography, with corridors, funnels, conic slopes or any other shape, the modelling of a single profile can be very misleading. Faced with a real rockfall of considerable extent, in which a million cubic meters are involved, the authors have developed a numerical model for the study of the spatial movement of blocks striking a three-dimensional topography.


The numerical model applies rigid body dynamics to simulate the motion of ellipsoidal or polygonal blocks. The driving force is gravity. During its motion the block encounters successive impacts on the topography. These impacts involve frictional contact and elastoplastic response.


During the late spring of 1985, signs of instability of an important rock mass of carboniferous black schists were observed. The mass was situated some 1'000 meters above the Rhone Valley, near Riddes, with a mean dip of the general slope of about 40°. A site survey showed velocities of displacement on the order of one centimeter per day, with a large scattering. There was, however, no significant correlation with the weather conditions.

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