The 3D shape of the loosening zone above multiple draw points in block caving through plasticity model with a dilation front

The thorough understanding of the loosening zone created by the interaction of the flow of multiple draw points in block caving mines is of utmost importance, because this knowledge would help to improve the operation of these mines reducing the mining costs. However, this loosening zone is usually roughly estimated by superimposing multiple single loosening zone centered at each draw point, without considering the interaction of the associated flows. In this article we extended the loosening zone for a single isolated draw point, determined by the plasticity model and a dilation front, to calculate the shape of the loosening zone created by multiple draw points including the interaction of the individual flows. We observed that the interaction of flows created by two draw points breaks the symmetry of the loosening zone shape, and increase its height within the interaction region. At constant extracted volume or mass drawn the strength of this interaction is mainly controlled by the separation distance between draw points. In the limit where positions of both draw points coincide, the resulting loosening zone shape resembles the one created by an isolated single draw point, with twice the extracted volume for one single draw point. In the case of a linear array of multiple draw points we observed two different behaviors depending on the location of draw points. On the one hand, the width of the loosening zone for the inner draw points saturates to a value corresponding to the addition of the half separation distance to the nearest neighbors. On the other side, the draw points located at the ends of the linear array reduces the ratio of growth of the width of the loosening zone because the side located near the interaction region stops to growth due to the interaction with the neighbor draw point. The plasticity model with a dilation front captures the experimental results for a linear array of five draw points obtained by an independent group. It is also observed that the top surface of the inner draw points is more even, suggesting that a mass flow might be observed above these draw points when they are separated a distance smaller than 1.5 times the width of the isolated loosening zone, contradicting the Laubscher criterion. Although the plasticity model with a dilation front does not include the whole complexity found in the actual underground mines or even in the experimental scaled models, it is a useful tool to study the interaction of complex arrangement of draw points both qualitatively and quantitatively.