Optimisation of the undercut level elevation in block caving mines using a mathematical programming framework
Bibliographic record
Abstract
The selection of an elevation for the placement of the undercut level is a decisive initial step in the planning and design of block caving mines. It is key for the success of a caving project to define the undercut elevation that will most likely yield the highest possible net present value (NPV) of the operation, considering the discounting periods from both the vertical draw rate extraction of the ore and the horizontal mining direction advancement. This paper outlines a mathematical programming framework to determine the best undercut elevation by formulating a simplified linear integer programming (IP) model that captures the discounting of the profits from the vertical draw rate extraction and the horizontal advance direction that can be applied at the early stages of a caving project. The IP model comprises a simplified block caving scheduling algorithm that considers ‘mining units’ (MU), which are groupings of blocks within each column based on the minimum draw rate condition and the undercut elevation considered. The formulation considers the following constraints: mining capacity, minimum and maximum draw rate, vertical precedence within columns and a horizontal precedence based on a concave mining advancement front. The model is set on an iterative loop over the different possible levels. The model is tested on a case study, where it provides a tool to evaluate the potential mineable reserves, define the optimal undercut elevation, and a starting schedule for future detailed engineering design.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".