Webinar: The impact of pit wall stability on mining economics

Thank you so much for joining our live stream today. My name is Anya, and I'm a Business Development Manager at K-MINE. Before we begin, I'd like to remind everyone to follow our LinkedIn page where we post announcements for future streams.

Today we're going to be talking about a very important topic for mining companies, especially those in development and production stages. We'll be discussing the impact of pit wall stability on mining economics.

As you all know, slope stability is a critical factor that directly affects mining operations, safety, and profitability. Without proper management, mining companies can face high costs, lost production, and serious accidents. So if you're looking to improve your mining operations, reduce costs, and ensure the safety of your workers, this webinar is for you.

Let me give you a short overview of what we as a software company that specializes in the mining industry offer. Besides the functionality we will discuss further, we have been on the market for almost 30 years and provide one standalone application that is customizable and adaptable for each company's needs.

Our solution is model-based, and it allows us to work with companies of any size and provide reasonable prices as well. Our application is based on our patented graphic core, which processes information faster. We aim to cover most operational needs such as 3D modeling, resource estimation, and planning.

Today we have built 12 modules for companies that are in exploration, development, or production stages. Each of these modules can be configured, adjusted, and enhanced for each deposit - for open pit or underground mining as well.

Each of these 12 modules can be used as a standalone module or in conjunction with each other. That allows different departments of a company to exchange information within one space without the need to create shared drives, fight compatibility issues, or waste time on import/export processes and data adjustment.

We also offer custom solutions and end-to-end planning to automate production stages.

At K-MINE, we understand the uniqueness of each mining project. That's why we offer additional services to mining companies that are in development and production stages. With a team of mining engineers, geologists, planners, surveyors, and other professionals, we provide services such as resource modeling, mining engineering, and audit.

Our engineers not only set up the whole company's infrastructure during the implementation of our solution but also assist our clients at any stage of work - building 3D models, planning schedules, and estimating resources and reserves.

Today we'll cover the importance of calculating slope stability indicators in mining operations. We will discuss the methods of calculation and features of K-MINE's stability analysis module. We will present a use case to demonstrate how the stability analysis calculation is performed and how the optimal resulting slope angles of pit walls are found. Then we'll discuss the evaluation of the influence on key economic measures and finish the webinar analyzing the results.

When mining companies use an open pit method, it's critically important to make sure that the rocks don't collapse at the edges and the sides of the pit. The angle of the slope is what determines how stable it is.

If the slope angle is too steep, the design can lead to a sudden collapse of the pit walls or benches. But if the angle is too low and the pit is really deep, then it can be too expensive to mine.

For example, in a pit that is up to 300 meters deep, decreasing the wall inclination angle by just a few degrees can increase the volume of overburden by millions of cubic meters per kilometer of pit wall.

So geomechanics engineers have to figure out how to balance rock safety with productivity. They use the same methods and tools as they do for underground mines.

The stress in the soil making up the slope depends on how heavy the rocks are and anything else - like buildings or machines - sitting on the side of the slope.

When the slope gets steeper, the tangential stresses go up. If they go too high and exceed the shear resistance limit of the rocks, then the slope goes out of balance and slides along a specific surface.

When the height of the bench increases, we need to make sure the slope stays stable by reducing the angle of inclination. But the slope height and angle are affected by a number of natural factors: how strong the rocks are, how fractured and layered they are, the orientation of cracks and layers in relation to the slope, as well as other things like groundwater level and technological factors.

That's why we need to do geotechnical surveys to assess the stability of existing slopes and calculate safe angles for planned objects. Even though the rocks can be complex and hard to work with, we can still calculate the slope elements with minimal errors.

When we determine stability, the composition of rocks that make up the pit sides is the most important factor.

If the rocks are homogeneous and possess constant physical and mechanical properties, we can use analytical dependencies to evaluate stability.

However, if the pit sides are made up of layered rocks of varying thicknesses and orientation to the horizontal plane, and atmospheric precipitation affects the physical and mechanical properties of the rock mass, along with the additional load from heavy mining and transport equipment - then the calculation models become much more complicated.

In these scenarios, closed analytical dependencies are no longer applicable, and researchers must turn to numerical or digital models to assess the stress-strain state of pits and dumps with various shapes and compositions. These numerical models allow us to evaluate pits and dumps composed of rocks with arbitrary structures and variable physical and mechanical properties.

As far as K-MINE software, our tools allow users to manage rock masses, helping them tackle complex issues such as slope stability, deformation in open pit rocks, and geomechanics in general.

Geomechanics is a multi-disciplinary field as it includes mechanics of deformable media, geology, hydrogeology, geotechnics, engineering geology, and seismic events impact.

In mining geomechanics, we utilize various methods to determine the slope stability by computing the stability coefficient. One of the useful tools in identifying the sliding surface present within the structure is the theory of limit equilibrium, as it allows us to ensure safe and stable mining operations.

Holding and engineering forces also play a significant role in geomechanics, which we address through the application of algebraic addition and polygonal forces techniques. These methods enable us to deal with challenging rock mass management issues and maintain the stability of mining operations.

We utilize various methods to determine the slope stability factor while also creating graphical representations of prisms that may collapse.

To get started, we require some initial information:

• Physical, mechanical, and strength properties of the rocks in the area of interest
• The structure of the benches located at different elevations
• The calculation area boundary

This information serves as a foundation for our assessment, allowing us to evaluate the stability of the slopes accurately. With this critical information in hand, we can determine the risk of potential rock collapses and take necessary measures to ensure the safety of operations.

In order to determine the calculation area, we need to create two limiting lines that are perpendicular to the edges. These lines can be set using the polyline object. When constructing these lines, we need to make sure that they cross all of the edges along which we need to perform the calculation.

The method of algebraic addition of forces involves graphically displaying prisms of possible collapse that help us determine whether a slope is safe or not.

To use this method, we need to specify or select the physical and mechanical properties of the rocks and then divide the calculated prism of potential collapse into a number of smaller prisms. Additionally, we can utilize a filter to take into account seismicity by enabling the appropriate flag.

In addition to the safety factor, we can also calculate the slope angle for a given stability factor. This information is incredibly valuable because it allows us to design and implement slope stabilization measures that are effective and efficient.

Overall, the algebraic addition of forces method is an essential tool in slope stability analysis, providing valuable insights into slope behavior.

This method is used to determine the stability of slopes in areas such as dump sites or tiers, taking into account holding and shear forces caused by foundation uplift and plantar deformation from a weak foundation of high power.

The stability calculation starts with the search for the most stressed sliding surface in the rock area. Then an iterative construction is carried out from the minimum possible sliding prisms, limited by the sliding surface approximated by three arcs of circles.

To perform calculations using this method, we need to enter rock properties for the foundation and upper layer separately. The calculation is performed using two selected polar lines drawn along the normal to the analyzed slope.

The result obtained while calculating slopes on a weak foundation covers only the slope from the first lower edge (the boundary of the rocks of the weak foundation) to the last upper edge that intersects the calculated profile.

The force polygon method is another way to calculate stability in a homogeneous area by taking into account shearing and holding forces through vector addition.

Once you choose this method, you need to enter data about physical, mechanical, and strength properties of rocks - similar to the algebraic addition of forces method.

Apart from a typical stability calculation, this technique considers hydrostatic conditions and water slope conditions for first unbound rocks. To account for hydrostatic conditions in the calculations, we have to indicate the layer in which the groundwater level is located and the upper boundary of the aquifer.

This method is very helpful in assessing the stability of various structures and ensuring the safety of mining projects.

The force polygon method in anisotropic medium is used to calculate the stability of a heterogeneous massive, taking into account the shearing and holding forces by using the vector addition of forces.

This method considers various properties of the rock that fall into the prism of possible collapse. The search for the most stressed sliding surface is carried out by an iterative method.

What distinguishes this method from calculating stability in a homogeneous massive is that the rock properties needed for the calculation are automatically extracted from the block model. Furthermore, seismic impact, water slope conditions, and the presence of weakening surfaces are accounted for similarly to the polygonal forces method in a homogeneous medium.

The FEM stability task is used to determine the stability factor and stress-strain state of slopes, pit walls, and dumps.

This method makes use of the finite element method - a numerical technique that involves dividing the area of analysis into a finite number of sub-areas or elements. This helps in carrying out elastoplastic calculations to determine the factor of stability. We use the strength reduction method, which involves finding a stable solution to the problem while simultaneously reducing the strength characteristics of the rocks in the massive.

In order to begin the FEM stability calculation, it is necessary to construct a geological section using surface objects with a double fill and build polyline objects to act as boundary conditions.

Our objective is to optimize the angle of inclination of the pit wall to achieve an economic benefit.

To start, we determine the current stability coefficient and then proceed to optimize it. We make use of the initial design coordinates of the conditional open pit, as well as the framework of the open pit and the rock formations that contain the mineral deposit.

The stability calculation using FEM is performed section by section. This allows us to utilize the cross-section tools to obtain a slope section that takes into account the mining location and the rock formations.

We trim the superfluous portions of the sections, switch to the working view, and then initiate the FEM stability calculation task. In the task menu, we upload the rock list, define their characteristics, and establish the association between the surfaces on the section and the rocks mentioned in the list.

Once we've taken the limiting factors into account, the next step is to create a grid of a certain size, determine the number of iterations, and set the required accuracy. After that, all we have to do is hit the "Apply" button, which within a few seconds will produce our results.

Each result comes with its own stability map, which has its own legend and stability factor.

We perform the task in two stages: first for the stable rocks, and then for the weaker overburden.

The stability factor of the overburden is 1.79, indicating that this section is not extremely stable. While the coefficient is considered normal, there is no need to reduce it at this time.

However, we can optimize the factor of 3.64 for the rock formations, which presents an opportunity for improvement. To achieve this, we use the "Calculate Slope Stability" task for our section. We pick the prism that connects the lower and upper benches from the result list, and then input the required safety factor (for example, 2.7) in the required stability factor field and run the calculation.

Using this approach, we arrive at a stability factor of 3.7, which closely matches the factor derived from the FEM method. Additionally, a prism that could potentially collapse emerges on the section, along with the slope angle of the pit wall that achieves a stability factor of 2.7. In our specific case, this angle is 42.3 degrees, and we can incorporate this angle into our design to observe any resulting differences in the outcome.

In the process of optimizing the resulting pit slope, we need to pay close attention and make final decisions only after considering all the factors. It's crucial to have complete confidence in the input information and calculations to avoid any mistakes and risks associated with the destabilization of the rock mass.

Now let's examine how slight changes of the resulting pit angle can affect the economics of a small iron ore pit. We create different scenarios in the Pit Optimizer module to illustrate this.

To develop a project to search for optimal contours, we require a block model and the current mining position in the pit. To consider the present state of mining operations during the optimization process, we must restrict the block model to a wireframe before incorporating it into a project. We use the "Set Property" command and choose the appropriate geometric constraints.

We initiate the project creation process via the "Optimal Pit Boundary" command and complete the primary fields, including the project name and the save location.

We configure the display of calculation results to present values in millions with a single decimal point. We incorporate the restricted block model into the project, indicate the fields for quality indicators and material class attributes, and input the specific weights for the block model rocks along with valuable components for each mineral type.

For pit angle indicators, we set 39 degrees for rocks and 30 degrees for soft rocks. These angles can be defined by filling in two fields: the default field and the angle of inclination for soft rocks from the material class attribute.

To conduct a comprehensive analysis, we establish a price adjustment coefficient step of 0.02 within the range. Let's assume that we are mining iron ore to produce a concentrate and then high-quality direct reduction pellets, each worth $150.

The cost of enrichment is set at $12. The cut-off grade is 12.5% and above. Recovery factors are set at 0.38 and 0.3 for high- and low-quality ore respectively. Excavation cost is set for each rock group, and transportation costs use a fixed value of $2 per ton. We set the discount factor and annual productivity, then run the calculation.

The results show that there isn't a substantial increase in minerals after the seventh coefficient. We select this price adjustment coefficient (0.72) for comparison with future calculations.

We create a similar scenario with one variation: we choose an angle of 42 degrees as the resulting angle for rocks. All other settings remain unchanged to make a reliable comparison.

The differential graph presents a slightly different pattern. For the specified pit wall inclination angle, a distinct coefficient will be optimal - we choose coefficient 0.68 and compare it with 0.72 from the first scenario.

We can conclude that the increase in the angle has optimized the shell. This means that the same quantity of ore can be extracted with less overburden. With the same price adjustment factor of 0.72, we obtain more ore.

We create wireframes based on the scenarios and coefficients we're interested in:

• Red: angle of 39 degrees, coefficient of 0.72
• Purple: angle of 42 degrees, coefficient of 0.68
• Blue: angle of 42 degrees, coefficient of 0.72

We construct a cross-section along the guideline and examine the distinctions between the shells.

Initial observation reveals that when the pit wall has the smallest inclination angle (39 degrees), a larger quantity of both soft and hard overburden is extracted. For an inclination angle of 42 degrees, shells with coefficients 0.72 and 0.68 are nearly parallel. However, the shell with coefficient 0.72 is deeper throughout, indicating that more rocks will be extracted.

The key issue remains the numerical expression of these indicators. Even minor discrepancies over broad areas may result in significant variations in volume. Consequently, choosing the optimal contour should be done carefully.

The option with a steeper slope angle removes 12 million tons more rock mass. The ore is 3 million tons more, and the overburden is 9 million tons more. The stripping ratio for the increment is 3 tons per tonne, which is not attractive given that the total stripping ratio for the deposit is up to 2.55 tons per tonne.

More rock mass means more cost for removal and processing: $88 million more (8% increase). However, there is also an increase in profit of $60 million (7%) and an increase in NPV of about $11 million (3%). As a percentage, these costs are still higher. Considering the result of financial activity for a long period, we can't ignore the discounted income, but the increase is not significant.

The difference in rock mass export is only 2.3 million tons, and the ore export indicators are the same. This means the entire difference lies in the removal of overburden.

This is a great result - it means we get a decrease in the stripping ratio for the entire field, and the costs are optimized. In terms of economic indicators, the trend is clear: less overburden with the same value of ore will result in a reduction of total cost, leading to an increase in the main economic indicators such as profit and NPV.

Increasing the angle of inclination of the pit wall by three degrees leads to an optimization in terms of reducing the cost of overburden and opens up new prospects for considering optimal contours if necessary.

However, it's worth noting that this result is applicable to smaller and not significantly deep pits. The deeper the pit, the more significantly this indicator affects the economics.

When it comes to optimizing the pit slope, caution is essential. On one hand, we want to minimize costs, optimize slope parameters, and reduce the cost of finished products. On the other hand, we need to avoid irreparable losses that can be caused by wrong calculations or incomplete understanding of rock occurrence conditions.

These losses can lead to the suspension of pit operations, freezing the entire mine, and even loss of equipment and personnel. Safety should always be the top priority, and the margins of safety should be respected and never violated.

There's a joke that suggests the pit should collapse the day after equipment and personnel are removed - to allow for the maximum possible angle of inclination. But of course, we don't want to bring our mine to such a state.

What if tomorrow the price of the finished product increases, giving new prospects for development of the field? The global trend shows that prices are rising because resources are being depleted.

Looking at our example of optimizing the resulting angle of inclination of the pit wall, we can conclude that even a slight change in this indicator can have a significant impact on the volume of rock excavation.

In our case, increasing the angle by three degrees allowed us to:

• Reduce costs by minimizing overburden excavation by 2.5 million tons
• Obtain the same volume of minerals
• Extract more minerals and extend the life of the pit and the enterprise as a whole with an additional 3 million tons of ore

Most mining companies are commercial organizations and aim to increase profits. That's why the optimization process must be carried out continuously for all possible parameters while adhering to geotechnical conclusions to ensure the safety of life, property, and profitability.

When should stability and optimization work be carried out?

Stability work should be performed at minimum in three different cases:

1. To gather knowledge of the deposit before starting mining activities at the site
2. To clarify the physical and mechanical properties in underexplored areas
3. In cases of observed instability, to clarify data and decide on future actions

Stability monitoring should be performed on a regular basis. This serves as a signal about incoming danger - the deeper the pit, the more relevant the issue becomes.

Optimization is usually performed once a year using updated information. But if the updated information is significantly different from the data on which the optimization was based, the optimization should be revised as soon as possible.

Were the same calculation methods used for rocks and overburden?

No, we used different methods. To calculate the stability factor of hard rock, we followed the Hoek-Brown failure criterion. For the sediments of the overburden, we used the Mohr-Coulomb theory, which is more appropriate for weaker rocks. The selected theory determines the list of physical and mechanical properties to be specified.

Does K-MINE have a solution for dump stability?

Yes. K-MINE offers two tasks to calculate dump slope stability:

1. Using the calculation method with foundation uplift in the slope stability task
2. Using the finite element method (FEM)

The difference lies in the calculation method, 2D/3D mode, and result output method.

What if the optimized pit contour encroaches on expensive infrastructure?

In this case, a comprehensive approach is necessary. You need to consider as many factors as possible - all expenses and profits.

If the expanded contour is related to additional profits, then planning has to be done by relocating the infrastructure to a new position, taking into account all expenses, and comparing the NPV in both cases.

If the extension is related to global stability - meaning the revised slope angles indicate that the pit wall may become unstable - then there is no question of making additional profits. The pit wall must be kept stable regardless of the cost. Additional measures must be taken to stabilize the part of the open pit until the rock mass becomes safe.

Each case is unique and the solution depends on the skills and expertise of the staff involved.

How is geological variability accounted for in stability analysis?

Geological variability can be accounted for using a block model and information from solid models (like polygons on the sections). We set the correspondence between the rock list and the polygons in a section when using the finite element method. The block model must contain all necessary information - the quality of the input determines the quality of the output.