# A New Method for Haul Road Design in Open-Pit Mines to Support Efficient Truck Haulage Operations
## 3 Methods
### Road Layout Analysis Using LCPA  
Researchers have developed various LCPA methods to derive the least-cost path between the point of departure and the destination. Representative examples include methods for deriving the least cost path by integrating multiple influencing factors [16; 33], for deriving a new optimal path considering existing physical roads [15; 34], for increasing the number of movable cells to avoid the formation of zigzag-shaped roads [35], and for searching for the optimum path by considering vertical influencing factors such as terrain slope and horizontal influencing factors such as wind direction and strength [13; 14; 36; 37]. The present study analyzes the road layout in open-pit mines by using the LCPA algorithm proposed by [PERSON] and [PERSON] [25]. This method is appropriate for the road layout optimization in open-pit mines or construction sites because it allows for consideration of the terrain slope (vertical friction) and the rotational angle of trucks, both of which greatly affect the travel time and fuel consumption of dump trucks. The input data required for the LCPA method include the topographic data of the mine, the point of departure and destination, the cost map, and the vertical and horizontal factor models. The final pit analysis and bench design data can be used as the topographic data of an open-pit mine in the planning and design stage. The input type of the mine terrain is a digital elevation model (DEM) that assigns the terrain altitude to grids divided into the same size. The departure point of the truck was set as the area at the bottom of the open-pit mine, and the destinations of the truck were set as the respective entrances to the stockpile and the waste dump, where the ore and waste are unloaded. The place of departure and the destination are entered as points. The cost map takes the form of raster data, which is the cost of moving by a unit of distance recorded in every grid. The types of costs generated when the trucks move include the truck travel time, physical distance, fuel consumption, risk, and resistance. The Vertical Factor model calculates the weights for terrain slopes (see Figure 5a). Haul roads with a slope greater than the slope limit make it difficult to run trucks stably and increase the travel time and fuel consumption of trucks. Therefore, the terrain slope must be considered in order to design a haul road with a slope that does not exceed the slope limit. The appropriate slope limit for haul roads is 8% to 11% (approximately 5\({}^{\circ}\) to 6\({}^{\circ}\)) and should be determined by considering the performance and efficiency of trucks used in the mine [5]. The Vertical Factor model assigns an infinite weight to terrain slopes exceeding the slope limit (see Figure 5b). The Horizontal Factor model calculates weights for the rotational angle of trucks (see Figure 5c). The weight of a rotational angle is determined by considering the difference between the angle of the path entering Cell C and the angle of the path leaving Cell C. The Horizontal Factor model assigns an infinite weight when the angle difference exceeds the angle limit (see Figure 5d). The 2D haul road layout is analyzed through the LCPA using the generated input data (see Figure 6). First, the cell containing the departure point is set as the current processing cell, and the travel costs incurred when the truck moves from the current processing cell to the neighboring cells in the orthogonal and diagonal directions are calculated using Equation (2). The travel cost calculations are divided into the orthogonal and diagonal directions when moving to the neighboring cells. \[Cost_{C\to N}= \begin{cases}0.5\times\sqrt{{D_{0}}^{2}+(Elv_{N}-Elv_{C})^{2} \times VF_{C\to N}}\times(C_{C}\times HF_{C\to N}+C_{N})&\text{ \emph{Orthogonal connection}}\\ 0.5\times\sqrt{\left({D_{0}}\times\sqrt{2}\right)^{2}+(Elv_{N}-Elv_{C})^{2}} \times VF_{C\to N}\times(C_{C}\times HF_{C\to N}+C_{N})&\text{\emph{Diagonal connection}}\end{cases}