M. Spadari

Prediction of the bullet effect for rockfall barriers: a scaling approach

The so-called “bullet effect” refers to the perforation of a rockfall protection mesh by impact of a small block, which has a kinetic energy lower than the design value, where the design value is determined through tests with relatively large blocks. Despite playing a key role in the overall performance of a flexible rockfall barrier, this phenomenon is still poorly understood at present. An innovative approach for quantitatively characterizing this effect based on dimensional analysis is proposed in this paper. The analysis rests on a hypothesis that the relevant variables in the impact problem can be combined into three strongly correlated dimensionless parameters. The relationship between these dimensionless parameters (i.e., the scaling relationship) is subsequently investigated and validated by means of data generated with a finite element model. The validation process shows that the dimensionless parameters are apt and that the proposed scaling relationship characterizes the bullet effect with a reasonable level of accuracy. An example from the literature involving numerical simulation of a full rock barrier is considered, and satisfactory agreement between the calculated performance of the barrier and that predicted by the established scaling relationship is observed.

Laboratory Investigation on High Values of Restitution Coefficients

Restitution coefficients are used to quantify the energy dissipation upon impact when predicting rock fall events. These coefficients can be determined in situ or in the laboratory. In any case, the usual values for the normal restitution coefficient kn are below unity. Values greater than one are quite rare, seen as unusual and barely explained. Previous experimental research conducted in Australia has shown consistent and systematic values of the normal restitution coefficient greater than one. This was tentatively explained by a combination of parameters such as low impacting angle, rotational energy and block angularity. The study presented in this paper aims at (1) identifying the critical parameters conducting to high kn values and (2) at explaining the associated motion mechanisms. The objective was reached with values of kn up to almost 2. In addition, the study has confirmed the significance of low impacting angle, rotational energy and block shape in this context.

Perforation of Flexible Rockfall Barriers by Normal Block Impact

Flexible rockfall barriers are a common form of protection against falling blocks of rock and rock fragments (rockfall). These barriers consist of a system of cables, posts, and a mesh, and their capacity is typically quantified in terms of the threshold of impact (kinetic) energy at which the barrier fails. This threshold, referred to here as the “critical energy,” is often regarded as a constant. However, several studies have pointed out that there is no single representative value of critical energy for a given barrier. Instead, the critical energy decreases as the block size decreases, a phenomenon referred to as the “bullet effect.” In this paper, we present a simple analytical model for determining the critical energy of a flexible barrier. The model considers a block that impacts normally and centrally on the wire mesh, and rather than incorporate the structural details of the cables and posts explicitly, the supporting elements are replaced by springs of representative stiffness. The analysis reveals the dependence of the critical energy on the block size, as well as other relevant variables, and it provides physical insight into the impact problem. For example, it is shown that bending of the wire mesh during impact reduces the axial force that can be sustained within the wires, thus reducing the energy that can be absorbed. The formulas derived in the paper are straightforward to use, and the analytical predictions compare favorably with data available in the literature.