Calculated isolated extracted and movement zones compared to scaled models for block caving

In this article is presented a comparison between the measured isolated extracted and movement zones from scaled models for block caving, with the corresponding zones calculated from the kinematic and plasticity models. The isolated movement zone is determined by introducing the dilation effect into the kinematic and plasticity models for gravity flow. For both models, we show that the resulting isolated movement zone is similar to the isolated extracted zone scaled by a factor that depends only on the density change taking place during the flow. This result provides analytical support to early observations of Janelid and Kvapil, who found experimentally such relation in a flat bottomed hopper. When comparing the numerical factor obtained with the kinematical model with the estimated by Janelid and Kvapil a difference of 60% is found. This deviation is mainly because of the assumption of same eccentricity assuming by Janelid and Kvapil that is not fulfilled in the kinematic model. On the other hand, the recent results obtained by Castro and collaborators, referred to the height and width of the isolated extracted zone as a function of the accumulated mass drawn and the width dependence on height in both zones, are compared to the corresponding curves predicted by the dilation-plasticity model. The curves obtained are in good agreement with the experimental data for moderate heights below 2 m, where flow remains radial. Remarkably, a unique value of the angle θGθG limiting the flow is required to fit the whole set of curves obtained by Castro. In this case, the ratio of the height of the movement zone to that of the extracted zone, leads to an estimated density change of 19%.