Webinar: Application of Cut-Off Grade for Pit Optimization

Cut-off grade is a limit indicator of mineral content that divides mineralized material into ore and waste (overburden). There are many methods to determine the cut-off grade, each with its own advantages and limitations. By selecting the right cut-off grade, a mining company can achieve specific economic objectives – from immediate profits to maximization of Net Present Value (NPV) over the entire life of mine.

It is important to understand that cut-off grade is not a fixed number with a single definitive answer. It is a strategic variable with major implications for mine design and long-term planning. Cut-off grade changes as the economic environment changes – metal prices, mining costs, processing costs, and the presence of unwanted material in ore blocks all affect the profitability of the operation.

Four major milestones shaped the development of the cut-off grade concept from the 1950s to 2014.

Mortimer was one of the first to formalize the cut-off grade concept. He established that material is classified as ore when two criteria are met:

• The average grade should bring the mining company a certain minimum income per ton of processed ore, including a standard profit margin.
• The lowest grade material should also pay for itself – covering its own mining and processing costs.

When both criteria are satisfied, the mining company achieves a bare minimum: it receives profit, and every sample contains a grade that justifies its extraction and processing.

According to Mortimer's evaluation, two parameters define the cut-off grade, and planning should be based on the highest one. Each parameter has its own associated costs and goals. However, Mortimer did not detail the full list of costs that should be considered when calculating these parameters. Neither of Mortimer's cut-off grade definitions accounts for the productivity of mining, processing, and marketing stages at different points in the mine's life, nor for important factors like ore extraction sequence and opportunity costs.

The calculation sequence involves building a tonnage-grade relationship from the block model, fitting a regression line, and then determining the required average grade of ore flow at the enrichment plant. Both of Mortimer's definitions are determined by break-even calculations with different costs included, and the required profit margin is treated as a cost. The corporate goal is explicitly stated: achieve a minimum level of profitability while ensuring that no processed material generates a loss.

This approach was a significant improvement over simple break-even cut-offs, but it does not guarantee the maximization of any measured project value.

Mathematician Kenneth Lane is recognized as one of the founders of modern cut-off grade optimization. In his 1988 work "The Economic Definition of Ore," he developed a fundamentally new theory that remains the benchmark for mathematically describing the cut-off grade solution using the maximum Net Present Value criterion.

In addition to the financial and geological parameters used in break-even and Mortimer's assessments, Lane's theory accounts for a third critical component: the ability of the production system to control the flows of three types of material – rock mass, ore, and final product.

Lane's methodology defines six potential cut-off grades: three marginal grades and three balanced grades. The marginal grades are calculated using break-even formulas that take into account the limiting effect of each individual production stage on overall productivity. Lane identifies the following cost categories:

• Operational costs – variable costs calculated per unit of output
• Constant costs – calculated per unit of time
• One-time costs – independent of time and production volume
• Capital costs – design and investment costs
• Costs required to maintain the production process

Lane was the first to demonstrate the importance of opportunity costs in cut-off grade estimation. Opportunity cost arises when alternative options must be considered for supplying raw materials to a production stage with limited capacity. It is the main economic driver that pushes producers to maximize profits.

Balanced cut-off grades come into play when two stages of production must operate in harmony. For example, the pit has a maximum capacity to extract rock mass (expressed in tonnes per year), and the processing plant has a maximum capacity to process ore. These two components are in balance when the ratio of ore to rock mass supplied equals the ratio of processing capacity to mining capacity.

The optimal cut-off grade is determined by ranking three cut-off grade values for each pair of production stages and choosing the average values. This results in an optimal cut-off grade policy for the reviewed period.

Despite worldwide recognition, Lane's theory is not widely used in mining practice. The reasons include the complexity of the mathematical formulas, the difficulty of representing opportunity costs in practical mining terms, and the dependence of results on the discount rate and the ratio of prices to costs – which change frequently and require regular recalculation.

Hall considered cut-off grade as the least understood criterion for mining profitability. He argued that determining the cut-off grade is an integral part of optimizing the overall production strategy – it cannot be a simple input but should be the end result of the strategic planning and optimization process.

Hall examined increasingly complex models for determining and optimizing cut-off grade, eventually combining them with full optimization of mining company strategy. His work focused on several key aspects:

• Input parameters necessary for evaluating the full optimization strategy
• Methods for selecting the appropriate block identifier – the value assigned to each block of rock to describe its worth relative to other blocks (actual metal grades, metal equivalents, or monetary equivalents)
• Creation of project performance criteria, such as NPV, real option value, and alternative costing methods

Hall's monograph provides practical tools that mining engineers can use to translate corporate goals into actionable mine plans. His work goes far beyond Lane's mathematics, explaining how mining is planned and optimized using modern tools and technology.

Jean-Michel Rendu used maximum NPV as the optimization criterion but proposed an iterative approach to cut-off grade determination:

1. Calculate cash flow or NPV based on a pre-accepted cut-off grade without opportunity costs.
2. Use the calculated opportunity cost and cash flow to recalculate the cut-off grade.
3. The new cut-off grade creates new mining plans, new cash flow values, and new opportunity costs.
4. Repeat until the cut-off grade and cash flow stabilize.

Rendu's theory is similar to Lane's in that the main focus is on maximizing NPV. However, there are differences in methodology and application of cost types. Rendu's calculations account for changes in NPV and cash flows in the form of direct costs and opportunity costs, but also include environmental, social, economic, ethical, and political factors.

The main difficulty of Rendu's approach is the need for many iterations before reaching a stable solution.

Cut-off grade has a direct impact on virtually every aspect of mine planning and operations:

• Mineral reserves – the amount of material classified as ore changes significantly with the cut-off grade
• Ore quality – the average grade of processed material depends on where the cut-off line is drawn
• Rock mass removal – the volume of overburden removed from the pit and its quality are directly affected
• Scale of operations – the size of the mining enterprise depends on the cut-off grade choice
• Mining method – drastic changes in cut-off grade can affect which mining method is appropriate
• Capital and operating costs – higher productivity requires more productive (and expensive) equipment
• Life of mine – lower cut-off grade extends mine life; higher cut-off grade shortens it
• Physical infrastructure – the size of waste dumps, stockpiles, warehouses, and processing plants are all affected
• Cash flows and economic indicators – profitability, payback period, and NPV are all sensitive to the cut-off grade

An incorrectly high cut-off grade reduces ore reserves, shortens the life of mine, and can leave significant value in the ground. An incorrectly low cut-off grade increases the volume of low-quality material sent for processing, inflating enrichment costs and reducing the profitability of final products.

When developing a new deposit, the main task is to determine the optimal starting point – an area that corresponds to the best quality and largest volume of ore with the lowest stripping ratio. The goal is to generate maximum profit during the first stages of mine development, which increases NPV and speeds up the return on investment.

If the goal is to maintain profitability without losing the potential of the processing plant, the cut-off grade should be increased by the percentage of dilution. The volume of ore extracted should also account for ore losses.

When the NPV is maximized and all production stages are fully loaded with maximum-quality material, there is often a surplus of lower-grade ore. If the processing plant has spare capacity, this lower-grade material can be utilized. If there is no spare capacity, the cut-off grade must be increased to improve the quality of the final product.

Lower-quality materials are typically stored in temporary stockpiles – either active (depleted over time) or cumulative (awaiting changes in technology or market conditions). Associated costs such as re-excavation, transportation, bulldozer work, and royalties should be included in the warehousing strategy calculation.

For medium- and short-term planning in single-metal deposits, Lane's balanced cut-off grade method is preferred where possible. In situations where Lane's theory is impractical, Mortimer's method provides a workable approach that ensures a minimum acceptable profit and some income for shareholders.

In critical situations where the required ore is not available in the pit and the processing plant is idle, the break-even cut-off grade can be used as a last resort. This approach carries a high risk of not meeting corporate goals, but it can serve as a bridge while the mine returns to its planned cut-off grade level.

Cut-off grade values at each production stage should be calculated using an iterative method or optimization software with the maximum NPV criterion applied over the entire life of mine. Only small temporary deviations from the optimal cut-off grade policy should be allowed, with a mandatory return to the guide values once conditions stabilize.

To demonstrate how K-MINE software handles cut-off grade tasks, a scenario-based analysis was performed using the following input data:

• Pit slope angles: 44° (hard rock), 32° (soft rock)
• Final product price: $90/ton
• Cut-off grade range: 10% to 20% (magnetic iron)
• Mining cost: approximately $4.5/ton (varies by rock type and elevation)
• Ore losses: 2%, dilution: 2%
• Discount rate: 10%
• Annual production: 5 million tons of ore
• Enrichment cost and product yield: determined by quality-dependent formulas

Eleven scenarios were created in K-MINE, each with a different cut-off grade while keeping all other parameters constant. This allowed direct comparison of results across all scenarios.

Comparing the highest (20%) and lowest (10%) cut-off grade scenarios revealed significant differences. Since the block model contained several ore bodies, one of which had a substantially lower grade of magnetic iron, a notable difference in optimal pit contours was observed along the western wall of the pit.

Key findings across all 11 scenarios:

• Ore volume ranged from 55.5 million tons (10% cut-off) to 20.4 million tons (20% cut-off)
• Overburden volume ranged from 150 million tons to 84 million tons
• Profit ranged from approximately $700 million to $370 million
• NPV ranged from $392 million to $223 million
• Life of mine ranged from 11 years to 4 years

K-MINE's diagram functionality displays these indicators in both cumulative and differential modes, helping engineers perform preliminary analysis of each scenario.

Based on the NPV maximization analysis:

• A cut-off grade below 13% is not rational, since ore volume remains unchanged while the processing plant receives material that is more difficult to enrich.
• A cut-off grade of 15% and above significantly reduces the life of mine, which increases the number of negative economic factors.
• The 13% cut-off grade region ensures profitability, high NPV, maximum ore volume for processing, and maximum life of mine.
• The 17% cut-off grade limits the amount of low-quality ore sent for processing and provides faster return on investment, but at the cost of reduced life of mine.

The final decision depends on the company's strategic goals: whether to prioritize longer mine life with balanced returns, or shorter mine life with faster capital recovery.

Cut-off grade must be flexible and adaptable to changing conditions. All indicators involved in its calculation change continuously as each ton of rock is removed. This creates a constant need for monitoring and recalculation.

The decision to adopt an optimal cut-off grade should be made jointly by mine planners, production teams, management, and marketing specialists – everyone directly involved in the production and sale of the final product. Cut-off grade is a strategic decision that affects the entire life of mine.

The frequency of cut-off grade review depends on which type of cut-off grade is being considered. Break-even cut-off grade and Mortimer's minimum-profit cut-off grade should be monitored continuously.

Cut-off grade should be reviewed whenever there is a significant change in any part of the production cycle. For example, if mine productivity increases, the company must decide whether to send more material to the processing plant, increase stripping activities to open future mining areas, or raise the cut-off grade to reduce pressure on the plant and increase profitability.

The most important trigger for cut-off grade review is a significant change in the final product price. When it changes substantially, the cut-off grade and the overall mine strategy should be reassessed.

Break-even cut-off grade cannot guarantee that all production rates and economic indicators will remain at a high level. The main reasons include unpredictable changes in prices, costs, and ore characteristics. Break-even cut-off grade is highly variable and raises several unresolved questions:

• How to account for limited processing plant or marketing capacity
• How to handle variable recovery and processing rates
• How to include ore losses, dilution, and stripping ratio in the formulas
• How to ensure company interests and shareholder returns
• What cost categories to include – fixed, variable, capital, direct, or indirect

As Hall noted, break-even cut-off grade and break-even level are fundamentally different concepts. It is the company management's responsibility to determine the appropriate cut-off grade that serves the company's strategic interests. Break-even cut-off grade should not blindly follow random fluctuations in prices and costs – it should only be used as a reference parameter and applied as a last resort in critical situations.