Probabilistic analysis of crushed zone for rock blasting

Transmission of explosion waves through a rock medium causes a severe vibration that stimulates the mechanical behavior of rock mass. This stimulation imposes highly concentrated stresses on the ends of existing fine joints and depending on the toughness of the rock, causes them to propagate rapidly. Consequently, the propagation and joining of cracks form a crushed zone around the blast hole. Several studies are available in the literature to estimate the radius of crushed zone, deterministically. In this paper, however, a probabilistic approach has been adopted. This is because the initiation and propagation of cracks have a probabilistic nature, and neither the initial state of the rock nor the explosion load could be expressed in a fully deterministic way. Thus, after generating random values for involved parameters, including explosive density, detonation velocity, dynamic Young's modulus, dynamic Poisson's ratio, uniaxial compressive strength, and borehole radius, the Monte-Carlo sampling method was adopted to calculate the exceeding probability of the crushed zone radius from desired values. The results showed that the exceedance probability for the growth of cracks falls sharply by the increase in the crushed zone radius so that the probability of crushed zone radius longer than 0.5 m is less than one percent. The results of this study, compared to the deterministic models, provide advantages in that they are not only limited to a certain value for the crushed zone radius and show the probability of exceedance for any desired radius.