# Fuel-Efficient Road Classification Methodology for Sustainable Open Pit Mining
## 2 Materials and Methods
### IRI Model  
IRI is the standard roughness index of pavement management employed to acquire quantitative longitudinal surface-bump data of road surfaces [25; 26]. The longitudinal profile elevation data of roads reflects the undulation of the road surface to a certain extent, making it a cross-sectional type of smoothness evaluation indicator.  
As defined in The International Road Roughness Experiment Standard for Measurements, a technical paper published by the World Bank [27], the value of IRI reflects the smoothness of the road surface. A smaller IRI value indicates a smoother road, with an ideal road condition reflected when IRI equals 0. The physical meaning of IRI is that when the vehicle steadily drives through the measured road section at a specific speed, the cumulative vertical displacement of the vehicle (measured in meters) to the distance traveled (measured in kilometers). Its unit is m/km. The specific derivation of IRI is based on a quarter-car model that employs the same road-vehicle vibration equations to establish a unified evaluation metric, exhibiting excellent applicability. The basic principle is shown in Figure 4.  
Figure 3: LiDAR system.  
Based on the model shown in Figure 4, the standard IRI calculation formula is given by Equation (1) as follows:  
\[IRI=\frac{1}{L}\int_{0}^{L}\lvert z_{u}-z_{s}\rvert dx \tag{1}\]  
where \(z_{s}\) is the spring mass displacement, \(z_{u}\) is the unspring mass displacement; and \(L\) is the total length of the tested road.  
The specific application process of Equation (1) was to achieve the calculation of the vertical cumulative displacement by installing the corresponding sensors on the vehicle. Whereas, with the adoption of Lidar, Equation (1) needs to be adjusted accordingly, as in Equation (2):  
\[IRI=\frac{1}{L}\int_{0}^{L}\lvert\lvert H_{u}-H_{s}\rvert-L_{p}\tan\alpha \rvert dx \tag{2}\]  
where the elevation of the former sample point is \(H_{s}\), the latter is \(H_{u}\), \(L_{p}\) is The horizontal spacing between sampling points \(\alpha\) is the slope gradient of the inclined surface, such as a ramp.  
It is important to emphasize that the calculation must be performed separately for horizontal and inclined road segments, as mixed-type sections should not be included in the analysis.  
In the practical application of Equation (2), the process of obtaining continuous sample points for IRI calculation from the mine road surface model involves the following steps: First, UAV-acquired point cloud data of the mining area is obtained. However, as the spacing between point cloud data points is non-uniform, while Equation (2) requires equal intervals between sample points, further processing is necessary. The point cloud model is therefore converted into a DEM (Digital Elevation Model). This conversion enables the generation of continuous, equally spaced sample points by projecting a line composed of uniformly distributed points onto the DEM surface. Once these regularly spaced sample points are acquired, the IRI can be calculated. The complete workflow is illustrated in Figure 5.  
Naturally, given the substantial elevation variations characteristic of open-pit mine haul roads, the analysis requires segmentation of the road into multiple sections. Each  
Figure 4: A quarter-car model.  
Figure 5: Lidar-based IRI calculation process.  
segment is then individually evaluated using Equation (2) to compute discrete IRI values. The resulting series of IRI measurements effectively captures the progressive variation in road surface roughness.