Mode analysis for spatial distribution of reach probability of earthquake-induced rockfall

Abstract

Using a rock-slope model constructed on a shaking table, six cases were conducted by varying initial postures of rock and peak ground accelerations (PGA). The result was used to investigate the spatial distribution of reach probability for rockfall trajectory. In this study, mode analysis using singular value decomposition (SVD) was applied to clarify the relationship between the spatial distribution and rockfall conditions such as initial posture and PGA. The spatial modes from the first mode to the third mode can explain 97.9% of the whole spatial distribution of rockfall reach probability. The result showed that the rockfall trajectory exhibits an primary distribution in a specified area with a dispersion of 31.88˚ from the initial rockfall position. Furthermore, it was suggested that the initial posture of rock affects the lateral distribution of rockfall trajectory. In the case of posture A of rock (face to ground), the rockfall showed a significant lateral distribution with a dispersion angle of 31.88˚, while in the case of posture B of rock (vertex down to ground), the rockfall showed a strong longitudinal distribution along the downslope direction with a relatively small dispersion angle of 5.45˚.