Mass haul and earthwork balancing

Knowing how much cut and fill a project contains is only half of the earthwork problem. The other half is where the material goes. Cut from one end of a road might build the embankment at the other end, two kilometers away; surplus from a building excavation might be wasted off site at a tipping fee; a shortfall might have to be imported from a borrow pit. Each choice has a cost, and haul distance drives much of it. The mass haul diagram is the classic tool for planning earthwork movement along a linear project, and the same thinking applies to balancing a building site. This lesson shows how to adjust cut and fill to a common basis, build a mass diagram, read balance points and haul distances, and decide between hauling, borrowing and wasting.

Putting cut and fill on the same basis

Cut is measured in bank volume. Fill is measured in compacted volume. To balance them, both must be expressed in the same units. The usual approach is to convert fill into the bank volume needed to make it, by dividing by (1 − shrinkage). Some engineers instead multiply cut by a shrinkage factor to get its compacted equivalent; either works as long as it is consistent. Rock, which bulks rather than shrinks, is handled with its own factor.

Other adjustments may be needed: unsuitable material in the cut that cannot be used in fill (such as topsoil, organic soil or wet clay) is subtracted from the usable cut; material needed for other purposes, such as backfill or landscaping berms, is set aside; and the volume of pavement structure, imported granular base and topsoil replacement is accounted for in the design surfaces.

The mass ordinate

The mass ordinate at any station is the running total of cut minus adjusted fill from the start of the project to that station. Starting at zero, add each interval's cut and subtract its adjusted fill. A rising mass ordinate means the project is in cut; a falling ordinate means it is in fill.

The mass diagram

Plotting the mass ordinate against station gives the mass diagram, usually drawn directly below the profile so the two can be read together. The diagram has a few properties that make it powerful.

• Rising segments correspond to cut; falling segments to fill.
• A maximum point marks a change from cut to fill; a minimum point marks a change from fill to cut. These are the grade points on the profile where cut and fill meet.
• Any horizontal line drawn across the diagram is a balance line. Where it intersects the diagram, the stations between consecutive intersections have equal cut and fill: the material in one part of that loop exactly fills the other part.
• The vertical distance from the balance line to the peak or trough of a loop is the volume moved within that loop.
• A loop above the balance line means material moves forward (in the direction of increasing stations); a loop below means it moves backward.
• The difference between the mass ordinate at the end and the balance line is the surplus to waste (if positive) or the shortfall to borrow (if negative).

Average haul distance

The cost of moving earth depends on how far it travels. The average haul distance in a loop is the distance between the center of mass of the cut and the center of mass of the fill it supplies. On the mass diagram, it equals the area of the loop (between the diagram and the balance line) divided by the volume moved (the height of the loop). In practice, software computes it, but a quick estimate is the horizontal width of the loop at half its height.

Freehaul and overhaul

Many unit-price contracts pay excavation at a single rate that includes hauling up to a stated distance, the freehaul distance. Material hauled further earns an additional payment for overhaul, measured as volume times the distance beyond the freehaul. Overhaul is common on highway contracts, and less common on private site work, where hauling is usually included in the unit rates. Whether or not overhaul is paid separately, the contractor's costs rise with distance, so the concept matters to every estimate.

US specifications traditionally measure overhaul in cubic yard-stations (one cubic yard moved 100 feet beyond freehaul), and some agencies use cubic yard-miles.

Borrow, waste and the economic haul limit

Balancing cut and fill is not always the cheapest solution. If cut must travel a long way to reach a fill, it may cost less to waste the cut nearby and import borrow close to the fill. The economic haul limit is the distance beyond which it is cheaper to waste and borrow than to haul.

Adding the freehaul distance gives the limit of economic haul. On the mass diagram, the engineer can move the balance line up or down, or use several balance lines, so that no loop is wider than the economic haul limit. Material outside those loops is wasted or borrowed.

Real decisions also consider the quality of the material (cut may be unsuitable for fill), the schedule (borrow may allow two fronts to work at once), haul road conditions, environmental approvals for borrow pits and waste sites, truck traffic through neighborhoods, and the cost and availability of disposal sites for surplus soil, which is often regulated.

Excess soil regulation

Moving soil off a site is increasingly regulated. Many states and municipalities require testing and documentation before excess soil can be taken to another site, and soils with any contamination must go to permitted facilities. Some jurisdictions, such as Massachusetts and New Jersey, have detailed soil management rules. These rules can change the economics of a project significantly, favoring designs and grading plans that balance on site.

For building projects the mass diagram is rarely drawn, but the same thinking applies: estimate the cut, the fill and the unsuitable material; decide what can be reused on site and where it will be stockpiled; and price off-site disposal and imported fill realistically. A site that balances, with reuse of excavated material for landscaping and berms, can save substantial trucking cost and community disruption.

Planning the earthwork operation

The mass diagram also helps plan the sequence and the equipment. Short hauls within a loop are suited to dozers (up to about 100 meters) and to loaders and scrapers for middle distances. Long hauls suit trucks. Loops in different directions may run with different crews at the same time. Borrow and waste sites need haul roads, and the haul road grades and surfaces affect cycle times, which are covered in Lesson 11.

Finally, earthwork plans change. Weather, unexpected unsuitable material, rock and design revisions all upset the original balance. A good practice is to update the earthwork quantities and mass diagram monthly from progress surveys, so that the team knows whether the site is trending toward surplus or shortfall, and can adjust borrow, waste and equipment before it becomes expensive.