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Volume Calculations (Open-cut Mine Surveying Duties)

Volume calculations are very important in mining to not only estimate the efficiency of machines and mining methods, but also to determine how much contractors should be paid if they are paid on a material-moved basis. Generally surveyors will be required to conduct these calculations once per month (it's referred to as 'End of Month' volumes) and provide them to various sections of the mining company. The process of calculating these volumes is by conducting survey 'pickups' or 'locations' using various methods such as:

- Total Stations
- RTK GPS (Real-Time Kinematic - Global Positioning System), or 'Surveying GPS'
- Automatic Laser Scanners
- Aerial Flyover Laser Data

In order to calculate a volume of moved material, both a 3D 'top' and 'bottom' surface are required. Top surfaces could be the bottom of a previous dig, or a shot ground surface which is always surveyed following a blast. As blasted material expands as compared to its solid state, it has varying densities and therefore a calculation is required to accommodate for the expansion of the material when completing volume calculations (you don't want to overpay or underpay contractors or provide inadequate data). It is part of the surveyors duty to monitor what happens in the pit to ensure that volume calculations don't allow a machine to receive 'payment' for moving the same material twice (e.g. if material is moved to an in-pit dump, it should only be paid the first time it is moved). The first movement of the material is referred to as 'prime', subsequent movements is referred to as 'rehandle'.

The creation of surfaces is probably one of the more exciting parts of the role. It allows you to construct something using real-world data which you have collected. The end result will always provide a sense of a achievement and provide something you can look at and say 'I created that'.
Volumes are calculated by using 3D surfaces, examples of different construction methods for surfaces are shown below.


Example #1: Data (point cloud) collected with an Automated Laser Scanner with photographic rendering


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Not all mines will have automated laser scanners available for use. However, they do make life a lot easier. When large amounts of data is required (e.g. the surface of blasted ground (shot ground)), they will ensure the capture of all visible data. Combining scans together is generally an easy process and the station (where the scanner is set up) is generally surveyed using GPS. Scanners intended for mining use are generally not super-accurate (they can't be used for engineering/construction surveying), however given the distance they can measure and the data collected they can allow for more accurate data collection as compared to conventional methods. Some automated scanners such as the one used in the pickup above have the ability to take a continuous photo while scanning and render the points to a photographic colour. This produces a realistic 3D point cloud environment, making it easier to determine what data is required and what to remove (e.g. machines in the way of the scan). It also allows for the collection of data and 'tracing' of particular features while the processing the data. The laser used for this particular scan is a Maptek iSite 4400LR laser.


Example #2: Triangulated surface from above point cloud


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Simply put, triangulation refers to a 3D surface which is constructed using best-fit triangles between points in the data. This process allows you to produce a 3D surface which can be used for volume calculations when compared against another surface. For more detailed information about triangulations, click here.


Example #3: Data (point cloud) collected with an Automated Laser Scanner with photographic rendering


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Example #4: Triangulated surface from above point cloud


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Example #5: Triangulated surface example from aerial laser data


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Example #6: Data (point cloud) produced by an aerial laser survey


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The data in the above image was collected from an aerial flyover. This process involves a plane flying over the pit with a powerful laser scanner capable of collecting many points from the sky. The system used to produce this particular data is a Trimble Harrier LIDAR.


Example #7: Triangulated surface from above point cloud


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Example #8: Contours produced by the above point cloud


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Example #9: Data collected using total stations and GPS


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The above example demonstrates a more conventional method of data collection in a mine. It comprises a combination of total station setup's and RTK GPS. The surveyor will collect the information as they determine is required. Each of the stations and backsights used for the data collection are generally positioned with GPS.


Example #10: Triangulated surface of above data with points overlaid


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Example #11: Triangulation of above data without points overlaid


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Example #12: Top and Bottom surface used for volume calculation


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To calculate a volume of material moved, you need to have a 'top' and 'bottom surface. Top surfaces may include shot ground data (see next example), a previous pit surface, or simply by using a surface from the previous month. You will generally use the same top surface while excavations progress month to month to achieve an 'overall' volume and to ensure that rehandle is automatically factored into the calculation (because it will automatically cause a lesser resulting volume if the material is still within the extents of the shape, therefore being paid at a later date).


Example #13: Using shot-ground as a top surface


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Shot-ground (blasted material) is also commonly used as a top surface. When materials are blasted they expand, so 'swell' has to be factored into volume calculations. Typically volume reports will be completed as 'solid' - referring to the actual material removed if it was in it's natural solid shape. Since blasting the material causes it to break up it is no longer solid and can't be calculated as solid unless a swell factor is bought into the calculation. Some surveying operations will have swell factors calculated for each blast, while others will determine an average swell factor to apply to all calculations when using shot-ground as a top surface.

Example #14: Another Top and Bottom surface used for volume calculation


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Example #15: Another Triangulated surface with source points


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Example #16: Multiple seam surfaces displayed


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Example #17: Multiple seam surfaces displayed with points


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Example #18: Multiple seam surfaces displayed with points (opposite direction)


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Example #19: Multiple seam surfaces displayed with points (different colour scheme)


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Generally coal mining operations will involve multiple seams being mined simultaneously. However volumes are generally calculated separately to provide accurate information on what machine excavated what material. Separation in this way allows accurate analysis to determine which machines or contractors are performing or underperforming, and provides a means of comparing costs associated with each machine to the amount of material removed or minerals mined. Not only does it also allow engineers to determine what mining methods are most effective in each mine, but they are able to allocate machine schedule accurately in advanced by knowing their capabilities.

Example #20: Data (point cloud) collected with an Automated Laser Scanner with machine interaction


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When using automated scanners you will often capture machines in the scan. A filtering process must be established to remove the machines before creating surfaces over the data.

Open-cut Mine Surveying Duties