Webinar: Stope Optimization Technologies – Modern Tools & Algorithms

K-MINE is a mining software and consulting company established in 1994 in Ukraine, with offices across Europe, the United States, and Canada. The team includes developers, geologists, and mining engineers, many of whom are certified under NI 43-101 and JORC reporting standards. K-MINE serves clients ranging from small exploration groups to major corporations with cost-effective mining software solutions.

The K-MINE platform comprises 12 adaptable modules for both open-pit and underground mining operations, covering geological data management, surveying, mine design, production scheduling, and real-time monitoring through IoT and dispatch system integration.

As shallow deposits become depleted, the mining industry faces increasing reliance on deeper underground operations. This shift demands smarter underground mine planning and more precise stope boundary optimization to maximize project profitability while managing rock stability and physical constraints.

The floating stope algorithm determines stope boundaries by creating a virtual floating stope that moves within the ore body to find the most economically beneficial location. The process involves evaluating the economic value of each ore block based on a predetermined cut-off grade, then creating two envelopes: an inner envelope representing the area of highest ore quality, and an outer envelope encompassing all possible stope positions. The optimal result is selected as close as possible to the inner envelope while remaining within the outer boundary.

Limitations of the floating stope algorithm include the lack of geomechanical constraints, which can result in overlapping stopes where adjacent blocks share high-grade ore. It also requires significant manual adjustments by engineers and does not always generate stope geometries that align with real mining conditions.

The MVN algorithm optimizes stope boundaries by considering the economic value of blocks using a fixed three-dimensional block model. It identifies the best neighborhood - a group of adjacent blocks providing the highest economic benefit - by first calculating individual block values, then analyzing combinations with surrounding blocks. The highest-value combination is selected as the most profitable option.

The key advantage of the MVN algorithm is that it prevents overlapping stopes. However, results depend on the starting point of the search, meaning different initial conditions can lead to different solutions. The method uses rigid economic block models and does not consider the impact of mining cost based on stope shape or size. It also lacks consideration for stope wall stability.

This stope boundary optimization method operates in three stages: block conversion, optimization, and visualization. In the first stage, the deposit model is converted into a standardized block model with uniform element sizes. The optimization process then analyzes all possible stope configurations, creating a table of potential stopes and their economic parameters. The algorithm selects the most profitable stopes while eliminating redundant and overlapping blocks.

The Sens and Topal method allows for both fixed and variable stope sizes, as well as different selection strategies. Its main advantage is the elimination of overlapping stopes, making it more precise than the floating stope algorithm. However, stopes are selected in descending order of economic value rather than through global optimization, which can limit the identification of more advantageous stope combinations.

This algorithm creates three-dimensional optimized stope layouts that maximize economic value while complying with physical and geomechanical constraints. The process begins with block model regularization to ensure uniform element sizes, followed by conversion into an economic model and step-by-step analysis of possible block combinations. All possible stopes are generated and assigned parameters such as ore grade and material density. Unprofitable stopes are discarded, and the remaining ones are grouped into sets that provide maximum value.

The main advantage is the generation of unique, non-overlapping stopes while considering both economic and geotechnical parameters. Unlike other algorithms, it allows for variable stope sizes and considers barrier pillars and levels. The primary limitation is significant computational resource requirements, especially for large-scale deposits.

Each method has distinct trade-offs. The floating stope algorithm is the simplest to implement but least efficient due to the lack of constraints. The MVN algorithm offers a good balance between accuracy and computational speed but lacks flexibility. The Sens and Topal approach achieves high detail but does not always provide globally optimal solutions. The Sandanayake and Topal approach delivers the highest profitability but requires the most computational power and time. The choice of algorithm depends on deposit conditions, required calculation accuracy, and available computational resources. In some cases, the most effective approach may combine multiple methods.

The Mathews stability graph method assesses stope wall stability based on empirical data from previously mined stopes. It classifies rock mass using the stability number defined by three key parameters: Rock Quality Designation (RQD), joint set orientation, and stress conditions. Engineers determine stope stability by plotting the stability number against the hydraulic radius - the ratio of a stope's volume to its exposed surface area. This method adjusts for rock quality and provides practical guidelines for stope sizing. Its limitations include reliance on historical data and the absence of direct economic factor integration.

The NPV approach evaluates the profitability of different stope configurations by calculating revenue from extracted ore and subtracting operational costs. Cut-off grades determine the boundary between ore and waste. Studies show that using flexible cut-off grades rather than fixed values improves resource utilization and economic performance. By adjusting stope designs based on market conditions and ore prices, mines can retain more profit over the project life.

Barton limit span theory determines the maximum permissible span of unsupported openings based on rock mass properties. It establishes the relationship between unconfined compressive strength (UCS), Joint Roughness Coefficient (JRC), and Joint Alteration Coefficient (JAC). These parameters define the stability of rock bridges within the stope. A key insight is that weaker rock masses require narrower stopes and additional support structures. The Barton approach is often used alongside the Mathews stability graph to refine stope design criteria for deposits with highly variable geological conditions.

Numerical modeling using finite element or finite difference methods simulates stress distribution and deformation patterns around stopes. These models account for anisotropic rock behavior, pore pressure effects, and excavation sequences to predict potential failure zones. By iterating through different stope geometries and analyzing stability indicators such as the Factor of Safety (FoS) and displacement vectors, engineers optimize stope layouts to maximize extraction while minimizing geotechnical risk.

The ELOS method quantifies expected overbreak based on rock mass rating and excavation technique. It estimates the thickness of overbreak around stope boundaries, allowing for adjustments in stope dimensions to minimize dilution. Research indicates that using ELOS predictions to refine stope boundary placement can reduce unwanted waste extraction by up to 15%, leading to significant increases in processing efficiency.

Backfilling plays a critical role in stope layout optimization. Hydraulic backfill and paste backfill provide structural