Magnitude–frequency relation for rockfall scars using a Terrestrial Laser Scanner

The analysis of the three-dimensional rockfall scar geometry provides clues for the understanding of the failure mechanisms acting on cliffs, of the conditioning factors, and on the frequency of the events. In this paper, a supervised step-by-step methodology is presented for establishing the statistical magnitude–frequency relation of rockfall scar volumes, using a point cloud from Terrestrial Laser Scanner (TLS) data. The methodology includes a procedure for identifying discontinuity surfaces, calculating the areas of those which are exposed, and the height of rockfall scars. In the estimation of the rockfall scar volume a key issue is the consideration of the minimum spacing of the discontinuity sets to differentiate between step-path surfaces and undulated ones. Having obtained the distributions of both the basal area and height of the scar across the slope, the volume of the rockfall scars is calculated stochastically by multiplication of these two parameters by means of a Monte Carlo simulation. Both distributions of the basal area and of the rockfall scar volume are found to be power-law, with the exponent b ranging from 0.9 to 1.2. The relation obtained might be used as a first approach of rockfall magnitude–frequency curves in large cliffs.