A hybrid approach to predict hang-up frequency in real scale block cave mining at El Teniente mine, Chile

Highlights

• Evaluation of In-situ ore fragmentation to predict hang-up occurrence probability.

• Uncertainty of rock block geometry and its impact on blockiness level.

• In-situ ore fragmentation prediction at real mine scale and real time.

• Hybrid Predictive modeling of hanging-up frequency in block cave mining.

• Large scale discrete fracture network modeling application at block cave mine.

Abstract

The in-situ ore fragmentation and probability of occurrence of hang-ups at draw points are the most significant factors on the performance of block cave mining. In this study we develop a hybrid methodology to study the uncertainty in the block geometry in the context of blockiness variable and hang-up frequency at a cave mine. This hybrid approach is based on the combination of geostatistical simulation, probabilistic discrete fracture network, geometrical and topological characterization of the fracture networks and supervised Poisson regression models. Our results and hybrid predictive models provide guidance on the systematic characterization of the fractured rock mass at a cave mine for its design, evaluation of production rates, and for risk evaluation purposes. This study can serve as a reference for the rock block geometry analysis in other related fields.

Introduction

The main advantage of the block caving method in underground mining is the utilization of gravity to induce stress by undercutting a rock mass. In-situ, primary and secondary ore fragmentations are the most significant factors on the performance of block cave mining. Then an assessment of fragmentation can be helpful to foresee some of the most important potential difficulties such as hang-ups frequency and migration of fine particles at draw points (Chen, 2000).

The feature governing in-situ block size distribution (the number of closed rock blocks and their volumes) and subsequently primary and secondary block size distributions are parameters of the preexisting fracture network within the rock mass. Therefore, an important part in the evaluation of the fragmentation process of a fractured rock mass and the block cave design is the geometrical, topological, and mechanical characterization of the fractures based on borehole and areal data at early stages of the project (Heslop, 2000, Laubscher, 2001). The formation of closed rock polyhedra (in-situ rock fragmentation) is a complex phenomenon that requires more research to be understood and to assess better design processes at block cave mines. The knowledge about predominant parameters influencing the geometry of rock blocks is essential not only for assessing in-situ fragmentation but also for primary and secondary fragmentation, the probability of the hang-up frequency, and the migration of fine particles as well. Among other parameters, the in-situ block size distribution (IBSD) and the probability of hang-ups in draw points are critical to optimize the design process in block cave mining. A hang-up is defined as the caved polyhedral ore, which, due to its size, obstructs the draw point and temporarily stops production from it. During the last decades, several authors have carried out research related to the critical parameters of discrete fracture network and their influence on the rock block uncertainty. The probability of occurrence of rock blocks is strongly dependent on the likelihood of having fractures intersecting each other (Zhang et al, 2012), itself dependent on the fracture intensity (Jimenez-Rodriguez and Sitar, 2008). Lu et al. (2015) determined the blockiness level of a rock mass around a tunnel with 35 rock mass models considering different sizes and spacings for fractures. Li et al. (2018) analyzed the influence of fracture shapes on rock block geometry, stability analysis of a tunnel and rock mass seepage. The abovementioned studies did not consider the uncertainty of input parameters on the resulting models. Munkhchuluun et al., (2018) used a single variable – the volumetric fracture intensity- to provide a direct link to rock mass fragmentation. They model the variability of the volumetric fracture intensity with a kriging approach that produces a smoothing effect. Nadolski et al. (2018) showed that the hang-up frequency and the migration of fine particles at New Afton mine are controlled by a network of faults. They reported that the height of draw and the boundary of the cave are important as well. All the above formulations consider a single estimated model of the volumetric fracture intensity of discontinuities or network of the faults. However, such an estimation yields smoothed image of the true volumetric fracture intensity and may give rise to unrealistic models of in-situ fragmentation, hang-up frequency, mine plans and unlikely revenue forecasts. Moreover, these models are not able to consider the inherent uncertainty of the discontinuity network. On the other hand, all the analyses of the in-situ fragmentation have been performed for small scale fracture networks within small volume of rock masses due to the limited computational capacity of the applied software. Dirkx et al., (2019) used the delays uncertainty from hang-up frequency into the production scheduling process of cave mining operation. They reported the probability of hang ups occurrence as an important factor for mine planning and for the profitability of cave mining. Hekmatnejad et al. (2020) showed how the error of volumetric fracture intensity (P₃₂) as an input parameter propagates and impacts the resulting discrete fracture network model, in-situ fragmentation, and the potential of formation of removeable blocks around tunnel. But they did not discuss about the relation between the P₃₂ and the geometry of the rock blocks. Hekmatnejad et al. (2021) introduced the circular variance (C.V.) as a complementary variable to the volumetric fracture intensity (P₃₂) that has a high impact on the mean rate of the formation of unstable blocks around a tunnel. In details, they focused on analyzing the relationship between P₃₂ and the circular variance of a fracture system on geometrically possible motions of rock blocks (kinematical state of rock blocks) around a tunnel. The last two studies have reported significant results on that topic and help to better understand the impact of the parameters of fracture networks on geometrical and kinematical properties of rock blocks at specific rock engineering designs.

However, there is still a gap of approaches that allow one to study, understand and combine the several factors governing the uncertainty of rock block geometry and its impact on the probability of the occurrence of hang-ups at draw points for decision making and design processes in cave mine. In this study we develop a hybrid methodology based on the combination of geostatistical simulation, probabilistic discrete fracture network, geometrical and topological characterization of fracture networks and supervised Poisson regression models. We used the R-Dis-Frag (Rock-Discontinuity-Fragmentation) computer package for the geometrical and topological characterization of a fracture network. The supervised Poisson regression model allows predicting the blockiness level of the cave volume as a significant parameter to assess the probability of the occurrence of hang-ups at draw points (inversely, the mean rate of production of the rock material at draw points). The results of this work demonstrate the sensitivity of the blockiness level to the mean number of intersections per each fracture, volumetric fracture intensity P₃₂, circular variance and fracture size.

Here are the key contributions of the present study considering previous works on this topic:

• We introduce a hybrid probabilistic approach based on the combination of geostatistical simulation, probabilistic discrete fracture network, geometrical and topological characterization of fracture networks and supervised Poisson regression models to study the in-situ block size distribution and the hang-up frequency as the two most important parameters at block cave mine.

• Our approach used thousands of discrete fracture network models at mine scale (100 m × 100 m × 100 m) to study and quantify the uncertainty in the block geometry in the context of blockiness variable and hang-up frequency at cave mine.

• The application of R-Dis-Frag package allows the geometrical and topological characterization of thousands of real scale fracture network models at real time.

Our results and hybrid predictive models provide guidance on the systematic characterization of the fractured rock mass at a cave mine for its design, evaluation of production rates, and for risk evaluation purposes. This study could serve as a reference for the rock block geometry analysis in other related fields.