The Mass Haul Diagram

Take the cut and fill volume at each station, treat cut as positive and fill as negative, and add them up as you move along the alignment. Plot that running total against chainage. That is the whole construction.

The value at any point is therefore not the volume at that station — it is the net surplus or deficit of material accumulated from the start of the diagram up to that point. This is why the curve is read by its slope and its shape rather than its individual values.

Before the volumes are summed they should be corrected for swell and shrinkage, because a cubic metre in the cut is not a cubic metre in the fill. Skipping that correction makes the whole diagram optimistic about how far the material goes.

Where the curve rises, the alignment is in cut — material is being produced. Where it falls, the alignment is in fill — material is being consumed. A steep section means a lot of earth over a short distance; a flat section means the alignment is close to balanced there.

A peak is where cut turns into fill, and a trough is where fill turns into cut. Both are points where the direction of haul reverses: material to the left of a peak moves one way, material to the right moves the other. That is the single most useful thing the diagram tells a site.

If the curve ends above where it started, the job produces surplus material that has to go somewhere. If it ends below, the job is short and material has to be brought in. The vertical distance between start and end is the size of that surplus or deficit.

Draw a horizontal line across the curve. Wherever it cuts the curve, the volume between those two intersections balances: the cut on one side exactly fills the fill on the other. The horizontal length of that segment is the distance the material travels.

Contracts usually pay for a certain haul distance within the basic excavation rate — the free haul. Drawing the balance line at exactly the free haul distance separates the material that is already paid for from the material that travels further, which is the overhaul and is paid separately.

The area enclosed between the curve and the balance line is proportional to volume multiplied by distance — the haul effort. This is why two alignments with identical total quantities can cost very differently: the totals are the same, but the areas under their curves are not.

Moving surplus cut a long way to fill a deficit is not automatically the right answer. Past a certain distance it becomes cheaper to waste the surplus nearby and borrow fresh material near the fill instead. That break-even is the economic haul distance.

It is a cost comparison, not a geometric property: the cost of hauling a cubic metre the extra distance against the combined cost of wasting one and borrowing another. Because it depends on local rates, haul road condition and the cost of a borrow area, it is a number the project sets — not one the diagram computes for you.

What the diagram does is make the decision visible. Once the economic haul distance is drawn as a balance line, every segment longer than it is a candidate for borrow-and-waste rather than haul.

It is one-dimensional. Every quantity is collapsed onto the alignment, so the curve says a segment needs three thousand cubic metres but not whether that material sits left or right of the centreline, or whether a haul road can actually reach it. A plan and the cross-sections still have to answer that.

It inherits every weakness of the station quantities it was built from. If the sections were spaced too widely, or the side slopes were seated on interpolated rather than measured ground, those errors are already inside the curve — and summing them makes the drift accumulate rather than cancel.

It also says nothing about sequence. The diagram shows that a cut balances a fill; it does not know that the cut is excavated in month six and the fill is needed in month two. On a phased job that ordering can override what the diagram suggests.

The station table gives quantities, the grid plan gives a map, and the mass haul diagram gives movement. They are three views of the same earthwork, and each answers a question the other two cannot.

In practice the diagram is worth drawing as soon as the vertical alignment is provisional, not at the end. Raising or lowering the profile by a small amount changes the balance dramatically, and the curve is the fastest way to see whether a change made the job cheaper or simply moved the problem along the alignment.