ABSTRACT
A 1D model describing the response of unsupported or supported blocks or wedges of rock near an excavation to an incoming stress wave is presented. The model is based on a non-linear force-displacement relation which includes an elastoplastic positive branch (corresponding to displacement into the excavation) and an elastic negative branch (corresponding to displacement towards the rock mass). The model is characterized by the following parameters: mass of block of ground and its location (back, sidewall or floor), yield displacement and yield force of support, ultimate displacement and stress wave damping coefficient. The response of unsupported ground and ground reinforced with typical bolts (split set, bonded and debonded rebars, cable bolt, MDX bolt) is studied. The time histories of incoming stress waves are simulated for scaled finite fault-slip sources reconstructed for real large seismic events in a hard rock mine. The probabilistic relations between the characteristics of the incoming stress wave (Peak Ground Velocity PGV, Cumulative Absolute Displacement CAD) and residual displacement of unsupported or supported block of ground relative to the host rock are established. The Peak Ground Velocities corresponding to the initiation of yielding (triggering of shakedown) and exceedance of the ultimate displacement (survival limit) are compared with the theoretical triggering and survival limits suggested in the Canadian Rockburst Support Handbook (1996). The results of these dynamic analyses can be used to establish fragility functions for various ground support designs. The fragility functions prescribe the probability of a specific level of shakedown damage (e.g. ranging from slight damage to collapse) as a function of ground motion intensity quantified using PGV and CAD (or other ground motion parameter). These functions provide a means to convert ground motion hazard (expected future annual rates of exceedance of various levels of ground motion at locations of interest) into probabilities of shakedown damage for various types of ground support.
