Advanced Mass Haul Diagram Optimization: Mathematical Models for Balances and Haul Distances
Learn the mathematical principles of mass haul diagrams to balance cut and fill volumes and reduce earthwork hauling costs.
Earthworks represent a significant portion of highway construction budgets. Balancing cut and fill volumes along an alignment minimizes the need for borrow pits (bringing in soil) and waste sites (disposing of excess soil). The **Mass Haul Diagram** is a key tool for planning these earthwork operations.
Analyzing the mass haul curve allows engineers to establish balance lines, identify cut and fill zones, and calculate haul costs. Below we detail the mathematical equations used in mass haul analysis.
1. Cumulative Mass Ordinate Equation
The mass ordinate Mx at any station x represents the cumulative net volume of earthwork from the start of the project:
Where:
- SF = Shrinkage Factor (typically 0.80 to 0.95 for compacted fill)
- BF = Bulking Factor (used when excavated rock expands in volume)
2. Haul and Overhaul Analysis
The haul cost is calculated by multiplying the moved volume by the distance transported. The area under the mass haul curve represents the total transport effort in m3-stations:
By drawing balance lines, we identify haul loops. The average haul distance (D) for a loop is calculated as the area of the loop divided by the maximum ordinate value:
If D exceeds the contract freehaul distance limit (e.g. 100m), the excess distance is billed as overhaul, which is monitored closely during earthwork planning.