Objectives of the training:
•Understand the FLAC2D/ FLAC3D numerical approach and the types ofproblems it can solve•Know how to manipulate the FLAC2D/ FLAC3D user interface to access andinterpret results•Follow the recommended solution procedure to simulate a simple case
This project was developed for an open-pit copper mine located in Brazil and proposes blast design optimization based on numerical modeling of the blasting process using the code Blo-Up. The analysis in Blo-Up involved calibration of the model in terms of fragmentation of a documented blasting. This calibration included characterization of the rock mass and of the explosives being used, the real drillhole pattern used, and the designed blasting sequence. The calibrated model allowed testing of different configurations for different blasting strategies to achieve a desired P80 size in the resulting muck pile. Due to the versatility of testing different blasting strategies, new opportunities to use Blo-Up have arisen in open pit mining in order to optimize blast designs.
The open-pit copper mine was facing difficulties finding an optimum drill and blast design to optimize the mine-to-mill chain. According to the mine-to-mill layout, an optimum 80% passing size (P80) for the mining system was around 0.55 m. Based on documented testing at the site, the main difficulty with achieving this objective was the occurrence of over-sized fragments (boulders) that affect the extraction rates and increase the mine costs due to secondary fragmentation requirements.
As part of the Hybrid Stress Blast Model (HSBM) project, Itasca has developed a software tool to model the rock blasting process. The code, named Blo-Up (Itasca, 2012), uses a unique combination of three-dimensional continuum and discontinuum numerical methods to represent the key processes occurring in non-ideal detonation, rock fracturing, and muck pile formation. In this context, Itasca suggested using Blo-Up to address the problem described above through numerical modeling of the blasting process.
This project was aimed at optimizing the blasting parameters to improve fragmentation as indicated above.
As stated previously, the Blo-Up code was developed by Itasca as part of the HSBM research project, which is still open. In order to understand the construction of the models, the calibration stage, optimization of the design, and some details on the software and the numerical method used by Blo-Up are presented in this section, along with the overall methodology.
Motivated by the need to better understand the blasting process, a group of mining companies, universities, and explosives suppliers have collaboratively supported the HSBM (Hybrid Stress Blasting Model) research project since 2001. One of the outcomes of this project has been the development of a numerical modeling tool that covers the entire blasting process. In this matter, Itasca has contributed to creating a fragmentation and fracture modeling software named Blo-Up.
Blo-Up is currently capable of reproducing general trends in fracturing and fragmentation observed in the field but is not capable of reproducing every detail of a real blast (Furtney, 2011). However, by predicting realistic trends in fracturing according to the variation in blasting design parameters, it is a relevant research and awareness tool for optimizing design parameters.
The Blo-Up software is a three-dimensional modeling tool that represent the blasting process through a combination of continuum and discrete numerical methods.
The software works by coupling three numerical components (Figure 1):
The representation of rock in Blo-Up is discrete, meaning a lattice node represents a discrete volume of rock. One of the simplifications that speeds up the calculation is that all the lattice nodes represent the same volume. When the size distribution is calculated, the lattice is divided into fragments. When the model is first created, all the lattice nodes are connected, and as fracturing occurs, the springs that connect the nodes are broken. Blo-Up
keeps track of these fragments and of the total volume in fragments of different sizes. The size of a fragment is the cube root of the volume of a fragment. The volume of a fragment is the number of nodes that make up the fragment times the nodal volume. The nodal volume is the lattice resolution cubed. This means that the minimum fragment size reported always corresponds to the actual lattice resolution (the smallest dimension in the size distribution curve corresponds to the lattice size or resolution of the model). For the tail of the size distribution (fragment sizes below the lattice size), Itasca uses a method to project the curve to smaller sizes by adjusting probability distributions of Rosin-Rammler (Equation 1) or Swebrec (Equation 2) (Ouchterlony & Sanchidrián, 2019).
Regarding the above, note that the finer the resolution of the model, the better the distribution will be fitted to fine zones but at a higher computational cost (longer running times).
The flowchart summarizing the work method for the overall project is shown in Figure 2.
After the calibration process, the best-case scenario (BC) obtained is shown in Figure 3 and Table 1.
In Table 1, four models are presented:
The low error was achieved by incorporating two further assumptions: 1) the introduction of vertical blast-induced damage by running the model twice, which attempts to reproduce the damage induced in the rock mass by the blasting that took place in the bench above; and 2) the upper 3 m of the bench were modeled assuming that the rock mass in this zone would have a reduced tensile strength (1 MPa less), in order to account for degradation of the intact rock due to previous blasting, in addition to the induced damage considered above.
As shown in Table 1, in terms of P80 the model shows variability related to the scale. When the model extends from small to large, new interactions make the model coarser. The model tends to be more conservative in the range of sizes between 0.2 and 0.4 m, while showing a reasonable representation of the rest of the curve (towards the fines). This overall gives a calibrated model with an error of 4% when compared to the observed dataset.
Figure 4 (top) shows the fragment contour of the blasted rocks considering fragment sizes ≥ 0.5 m for the BC Large Model. A vertical cross-section was included to show the fragmentation along the height of the bench, which is shown in Figure 4 (Middle). Both figures demonstrate that larger fragments concentrate in the upper part of the bench, in a volume that includes the damaged area and the area below. Figure 4 (bottom) presents a horizontal section located 5 m below the height bench. The fragment contour shows that larger fragments concentrate in the maximum spans between drill holes. In both views, large fragments can be located at the boundary conditions (back of the model); however, the methodology applied to measure fragmentation filtered data located in these areas.
After several tests, an optimized design was found to give a P80 of approximately 0.53 m. This was obtained by implementing blasting with the following parameters:
In forming the blasting design, the following is recommended:
The best calibrated results were found when a Swebrec distribution was fitted to the Blo-Up data, which shows that the overall error of the best calibrated model is 4%. This was made by incorporating two further assumptions:
In terms of optimization of the design parameters, the best case showed a P80 of ~0.53 m.
Furtney, J. K., P. A. Cundall, I. Onederra and E. Sellers. (2011) “Numerical Modeling of Rock Blasting: Validation Tests for Blo-Up 2.5,” in Continuum and Distinct Element Modeling in Geomechanics — 2011 (Proceedings, 2nd International FLAC/DEM Symposium, Melbourne, February 2011), 359–367, D. Sainsbury, R. Hart, C. Detournay, and M. Nelson, Eds. Minneapolis: Itasca.
Itasca Consulting Group, Inc. (2012) Blo-Up User’s Guide. Release 2.7. Minneapolis: Itasca.
Ouchterlony, F., J.A. Sanchidrián. (2019) “A review of development of better prediction equations for blast fragmentation,” Journal of Rock Mechanics and Geotechnical Engineering. 11(5) 1094-1109.
Mining
Blo-Up