Calculating Volumes of Sand Piles Using Pix4D and ESRI Tools

Introduction

  Volumetric analysis is the process of calculating the volume of objects using software. It can be used to calculate the volume of buildings, mine piles. river valleys, canyons, and more. To calculate the volume of an object using volumetric analysis x,y, and z values are needed. They do not need to be coordinates and elevation. They can be cartesian values. UAS data is a great source to perform volumetric analysis on. Processing imagery through Pix4D creates an orthomosaic and a DSM. The DSM contains elevation values which can be used to calculate volume. Volume measurements can be very accurate and precise when using UAS imagery, especially if GCPs were used.
  In this lab the volume of three sand piles chosen from the Litchfield sand mine will be calculated using Pix4D, 3D analyst tools, and TIN tools. The tools used for the 3D analyst method include Extract by Mask and Surface Volume. For the TINs, the tools used include Raster to TIN, Add Surface Information, and Polygon Volume. After calculating the volumes of the sand piles, a table and a map of the average volume values will be created. The difference between the methods and values will then be discussed.

Methods

Use Pix4D to Calculate Volumes
  To do this, the Litchfield Mine GCP project was opened. Then, the volumes tab was used to create a polygon around the three sand piles. After that, the volume was calculated. Piles two and three are shown below in figure 7.0. Their calculated volumes can be seen in the left part of the image. Pile one's calculated volume is 1086.17 m³, pile two's calculated volume is 18.59 m³, and pile three's calculated volume is 32.20 m³.

Fig 7.0: Using Pix4D to Calculate Volumes for Sand Piles 2 and 3.

Use a DSM Clip to Calculate Volumes

  First, three different feature classes needed to be created in ArcCatalog and edited in ArcMap so that the DSM could be clipped to only the area needed to calculate the volume. These were name Pile1, Pile2, and Pile3. Then, the Extract by Mask tool was used to clip the DSM to the corresponding feature class. The Extract by Mask tool is used to clip a raster (the DSM) to a specific feature class (Pile1, Pile2, or Pile3)  or a different raster dataset. After this, the Surface Volume tool was used to calculate the volume of the three sand piles. The Surface Volume tool calculates the volume based off a specific surface. In this case, the volume wanted is the area above the lowest value of the DSM clip for each sand pile. Using this method, the calculated volumes were 1191.85 m³ for pile 1, 23.76 m³ for pile 2, and 48.04 m³ for pile 3. 

Use a TIN to Calculate Volumes

  For this, the three DSM clips were converted to TINs using the Raster to TIN tool. This tool creates a TIN based on an input raster. Then, the Add Surface Information tool was used to add the minimum elevation value (Z-Min) to the TINs. These minimum elevations values were imported from the DSM clip features. In general, the Add Surface Information creates a new feature class which imports information into its attribute table. After the Z-Min value feature class was created for each pile, the Polygon Volume tool was used to calculate the volumes. This tool used both the TINs and the Z-min feature classes. The Polygon Volume tool is ordinarily used for calculating the volume and surface area between a polygon feature class and a TIN. After doing this for each pile, the calculated volumes were 1202.46 m³ for pile 1, 24.31 m³ for pile 2, and 48.96 m³ for pile 3.

Results / Discussion

  While calculating the volumes of the sand piles using the different methods, the results were entered into an Excel spreadsheet. This can be seen below in figure 7.1. An average and standard deviation field were also added. Overall, all three methods seemed to be within reasonable accuracy of each other. The TIN and 3D analyst methods churned out extremely similar results with the Pix4D volumes having lower values across all three piles. Looking at the difference in the calculated volumes for each pile, it seems that the difference between the methods grow as the size of the sand pile increases. For example, there is a greater difference between the volumes of pile 1 across the three methods than there is between the volumes of pile 2. This is probably because each method is consistent in the way it calculates the volume so larger pile volumes are going to differ more than smaller pile volumes.

Fig 7.1: Sand Pile Volume Table

  A map was created showing the locations of the sand piles and the average calculated volumes using the three different methods. This map is shown below in figure 7.2. Because of the table in figure 7.1, there aren't any surprises in the map. By far, pile 1 is the largest pile by both area and volume. Piles 2 and 3 are similar in surface area so they have more similar volumes.

Fig 7.2: Average Sand Pile Volume Map

Conclusion

   In conclusion, UAS imagery can be used to calculate volumes in at least three different ways. It is interesting to see how similar the 3D analyst and the TIN calculated volumes area. These values are very close to each other because the TINs were derived from the DSM which was used to calculate the 3D analyst volume. The volumes calculated in this lab could be used by the mining company to see how much sand is left in the piles and to see how much time they have before they need to replace the pile with more sand. Volumetric analysis is a much more efficient and cheaper way to get this estimate than actually measuring the pile.  Based off of the three methods in this lab, no conclusion can be made seeing which method is the most accurate. Even though the 3D analyst and TIN methods were similar, that doesn't mean that those methods are more accurate than using Pix4D. A comparison between the actual volume of the sand piles and the calculated volumes using each method would need to be done to test the accuracy.