In the lumped mass model which is used in various commercial software (eg. CRSP and Rocfall 4.0), the division of kinetic energy into translational and rotational components is done through a combination of energy balance and empirical relationships. Other than slope geometry, the required input data are the normal coefficient of restitution, the tangential coefficient of restitution and the coefficient of rolling friction. In order to accommodate shape and rotational effects in lumped mass models, two empirical factors related to size and normal impact velocity are employed. Using the lumped mass model, values of normal coefficient of restitution greater than 1 were reported in many field observations, with values as large as 2 obtained. This makes the application of the lumped mass model questionable in some situations. We have proposed a two-dimensional shape-dependent mechanistic model where only two material parameters, namely the normal coefficient of restitution and the friction coefficient, are used. The proposed model uses the shape, size and point of contact of the rock to calculate the translational and rotational components of the kinetic energy. Through this new approach which incorporates complete two-dimensional rigid body dynamics, we are able to predict an apparent normal coefficient of restitution greater than 1 while, at the same time, not violating the principle of conservation of energy.
Rockfalls are natural hazards that can cause great damage to human life and infrastructure. In current practice it is common to model the rockfall as a point mass that is rigid, dimensionless and circular. The modelling of a rock in this manner is inherently phenomenological as this representation does not mimic actual rock-slope impact conditions. Significantly, there can be no description of shape or an emulation of the actual mechanism of rock-slope impact, including induced rotation and the effect of size.