Calculation Method for the Integral Method¶
Below we describe how volume calculations are performed using the integral method in Gemini Terrain.
Basis for the Calculation¶
The basis for calculation with the integral method is physical layers, i.e., application layers defined as strata, and theoretical layers, i.e., layers built in excavation pits or intersections.
Calculation Principle¶
The calculation principle used is that we calculate the volume for the terrain integrals where the grid point lies within the boundary contour. The volume is then adjusted by the ratio between the total area and the area for which the volume was calculated. It is the total area (exact area within the boundary contour) that is documented in the report.
Calculation Formula
Total volume = Calculated_volume × (total area / volume area)
Figure explanation: A = Boundary contour, Light yellow = Volume area, Orange = Total area
Calculation Accuracy¶
The uncertainty in this volume calculation will be reduced by reducing the grid size.
The correction factor (total area / volume area) is a measure of how well the area of the grid matches the area of the boundary contour. The ideal value is 1. We will see that the correction factor changes when we change the grid size. The main rule will be that it approaches the value 1 more and more as we reduce the grid size.
About Calculation Accuracy
When discussing the calculation accuracy of volumes, we must also consider how accurate the data we are working with originally is. Errors or uncertainty of a few centimeters in height and a few centimeters in the horizontal plane in the original data also introduce uncertainty in the volumes.
Boundary Contour¶
In mass calculation, an edge is defined vertically from the boundary contour to the layer against which the calculation is made.
Figure explanation: A = Layer 1, B = Layer 2, C = Boundary contour
A directly measured boundary contour creates inaccuracies between the two terrain layers (1 and 2) involved. This is due to inaccuracies in both the measurement data for the boundary contour and in the base data for the other layer.
Illustration of how volume calculation is performed along the boundary contour
Possible Inaccuracies
From the edge of the boundary contour, volumes are calculated vertically against the other layer. This can result in fill masses appearing where there should only be cut masses.