Abstract
A mathematical model for the development of talus slopes was constructed. The model is characterized by the following three points: (1) the balance of the erosional volume of the cliff and the depositional volume of the talus; (2) changing ratio of volumes by the parallel recession of the cliff to volumes by the recession due to the decline slope angle of the cliff; (3) variable angles of the slopes bordering the cliff at the top (slope above the cliff) and at the foot (slope below the cliff). The above second and third points are not clearly included in the previous mathematical models of the slope development. These features are particularly indispensable to apply the model to the development of actual talus slopes. The present model consists of four initial landform factors (slope angle above the cliff, slope angle below the cliff, angle of the initial cliff, and height of the initial cliff) and four variable topographic factors (angle of the talus slope, horizontal retreat distance of the cliff owing to the parallel recession, reduction angle of the cliff owing to the recession due to the slope angle declination, and volume change ratio owing to the cliff-talus transformation). The computational results show the developmental process of the talus slope, and are comparable with field data. The model has, therefore, potential to apply to the development of actual talus slopes, although there is a problem that the retreat rates of the cliff set constant with time.
