Modeling of the impact of rigid ellipsoidal blocks by means of an elastic-visco-plastic constitutive model

Rockfall is one of the most common hazards in mountain areas causing severe damages to structures/infrastructures and, human lives. For this reason, numerous are the papers published in the last decades on this subject, both introducing reliable approaches to simulate the boulder trajectory and defining design methods for sheltering structures. As is well known, the most popular strategy to simulate the block trajectory and velocity is based on the lumped mass material point approach. This is capable of describing the block trajectory, before either its natural arrest or impact against an artificial/natural obstacle, by suitably considering its interaction with soil/rock materials, interaction always dynamic, very often highly dissipative and defined, according to its nature, as sliding, rolling or impact.

In this framework, this study focusses on impacts and, in particular, on the role of block geometry in affecting the block kinematic response. The problem is approached numerically; by modifying a previously conceived elastic-viscoplastic constitutive model, based on the macro-element concept. and capable of satisfactorily simulating impacts of spherical blocks.

The modified constitutive model relaxes the assumption of spherical block by assuming an ellipsoidal shape and by allowing for the boulder rotation. These two changes make the problem more complex but allow to model more realistically the impact. For the sake of simplicity, the results shown in this work consider the block motion to be planar, but the model already allows to include general three dimensional conditions.

In this work, the model is briefly outlined and the procedure for calibrating the model constitutive parameters described. Then, the results of an extensive parametric analysis, employing constitutive parameters calibrated on experimental data taken from the literature, are discussed. In particular, the role of (i) the inner block orientation, and (ii) the inner impact angle is considered in terms of both kinematic variables and restitution coefficients. Finally, interpolation functions to compute restitution coefficients, once both block shape and inner impact block orientation are known, are provided.