ABSTRACT
The stabilization of rock slabs by means of anchoring systems (e.g. rockbolts or cables) is a complex problem involving not only geometrical issues, but also mechanical issues. In particular, the main points to be considered are (i) the degradation of mechanical properties of the block-bedrock interface, (ii) the dependence of the block-anchor interaction loads on the block displacements and (iii) the technical/economical optimization of the stabilizing system. In addition, whilst conventional design approaches usually tackle the problem by adopting a “force-based” method, the most recent design approaches require a “performance-based” analysis of the system, respecting both Ultimate Limit State (ULS) and Serviceability Limit States (SLS), capable of modelling even the passive behaviour of the stabilizing system. From a theoretical point of view, this implies that neither traditional limit equilibrium methods nor hybrid methods can be adopted in the design, since a displacement based design approach taking into account the block-anchor coupling is rather required. The interaction forces in fact directly depend on the block displacement field, which, on its turn, depends on the supporting forces given by the anchoring system. Moreover, although the behaviour of the block is usually modelled by adopting a small displacement scheme, the mechanical response of the anchor in the neighborhood of the sliding plane has to be modelled by means of a large displacement scheme, accounting even second order effects. Traditional finite element or finite difference 3D numerical analyses implementing such aspects are often too demanding (both from a computational and an economical point of view) to be considered actual cost-effective design tools for the engineers, especially during the early stages of the design process. In this paper a simplified displacement based procedure for analyzing the stability against sliding of an unstable rock block is presented, by comparing the performances of a rockbolt ad of a cable. The mechanical behaviour of the anchor is reproduced by means of a finite element approach and its transversal and axial interaction with the rock is modelled by means of non-linear springs, lumping the interaction forces in each node. An explicit finite difference scheme is implemented to solve the motion equation of the rock block. Several examples and numerical analyses are shown in order to highlight the importance of second order effects and to clarify the role of the bending stiffness of the anchor. Such approach is particularly useful for the optimization of the intervention measure.
