Mass-Haul Diagrams: The Economics of Earthwork Distribution

Overview

In large-scale infrastructure projects like highways and railways, the cost of moving soil can dominate the budget. A Mass-Haul Diagram (MHD) is a continuous curve where the vertical ordinates represent the algebraic sum of corrected earthwork volumes (cut being positive, fill being negative) 1. By plotting this against the horizontal distance of the project, surveyors and engineers can visualize the movement of material and optimize the distribution of "cut" to "fill."

Why This Matters

Transporting soil is expensive. An MHD allows you to identify exactly where soil should be moved from and to, minimizing the "haul distance" 1. It provides a mathematical basis for deciding whether to move excavated soil to a distant fill site or simply "waste" it locally and "borrow" new material from a closer pit 2.

Background

The MHD works in tandem with the longitudinal section of a route. The peaks and valleys of the diagram correspond directly to Grade Points: the locations where the natural ground intersects the proposed formation level 1.

Theory

The diagram is governed by several fundamental economic definitions:

• Haul: The product of the volume of material moved and the distance it is moved 1.
• Freehaul: The maximum distance through which excavated material can be moved without additional cost beyond the basic excavation rate 2.
• Overhaul: The movement of material beyond the freehaul distance, which incurs an additional "overhaul rate" 1.
• Waste: Material excavated from cuts that is not used for embankments 2.
• Borrow: Material required for embankments that is secured from outside the roadway excavation 2.

Mathematical Principles

1. Bulking and Shrinkage

Soil volume changes when moved. Excavation loosens soil (bulking), while compaction in a fill site reduces its volume (shrinkage) 1. Ordinarily, earth is less by about 10% after filling, while rock bulks by 20% to 30% 1. A correction factor must be applied to the volumes before plotting the MHD.

2. Overhaul Calculation

The total haul in a section is calculated as: $\text{Total Haul} = \text{Volume} \times \text{Distance}$ Overhaul is specifically the volume moved beyond the freehaul limit: $\text{Overhaul} = \text{Overhaul Vol} \times (\text{Average distance between centroids} - \text{Freehaul distance})$ 3.

Field Workflow

Step-by-Step Example

Problem: Calculate the overhaul cost for a 1200m section where:

• Freehaul distance = 300 m.
• Basic rate = 30 p/m³.
• Overhaul rate = 2 p/stn m (1 stn m = 1 m³ moved 100m).
• Total volume in a loop ($CD$) = 3932 m³.
• Distance between centroids ($JK$) = 450 m 6.

1. Identify Freehaul Volume: The volume $CC'$ within the 300m limit is found from the MHD 3.
2. Calculate Overhaul Volume: Assume $EG = 1257.6 \text{ m}^3$ 6.
3. Determine Overhaul Distance: $450\text{ m} - 300\text{ m} = 150\text{ m}$ 3.
4. Calculate Overhaul Cost:$\text{Cost} = \frac{EG \times (JK - \text{Freehaul})}{100} \times \text{Overhaul Rate}$$\text{Cost} = \frac{1257.6 \times (450 - 300)}{100} \times 2 = 3772.8 \text{ p}$ 6.

Formula Breakdown

• Limit of Economical Haul: The maximum distance beyond which it is cheaper to waste material and borrow from a new pit. $\text{Limit} = \text{Freehaul Distance} + \frac{\text{Cost of Borrow}}{\text{Overhaul Rate}}$ 2.
• Haul sign: If the MHD curve rises above the balance line, movement is from left to right; if it falls below, movement is from right to left 7.

Practical Tips

• Centroid Positioning: The horizontal positions of the centroids of cut and fill can be approximated by bisecting the lines representing the freehaul distance and the total haul distance on the MHD 7.
• Balance Line Selection: Adjust the balance line to minimize the area between the curve and the line, as this area represents the total haul of the project 1, 8.

Common Mistakes

• Plotting Between Stations: Mass ordinates must always be plotted at the stations, never between them 5.
• Ignoring Bulking: Failing to correct for rock bulking will result in a surplus of material that the MHD did not predict, leading to unexpected disposal costs 1.

FAQ

Conclusion

The Mass-Haul Diagram is an indispensable tool for the economic management of civil engineering projects. By mathematically linking the physical terrain to the costs of machinery and transport, it transforms raw survey data into a strategic financial plan.

References

Schofield, W. (2001). Engineering Surveying. 5th ed. Butterworth-Heinemann.