The cross-section method has gaps. Here is how to close them.

How the cross-section method works

Along the road centreline, cross-sections are cut at each station. On every section, the area between the existing ground line and the design line is measured — that is the cut or fill area at that station. The volume between two adjacent sections is the average of their areas multiplied by the distance between them. The total is the sum of all such reaches, station by station.

Volume between adjacent sections: V = (A1 + A2) ÷ 2 × L

(A1 and A2 are the cut or fill areas at two adjacent sections; L is the distance between them.)

This is the standard method for linear works — roads, municipal streets, embankments — where the longitudinal profile rises and falls along the alignment and each cross-section carries its own cross-fall. The section method maps directly onto that geometry.

Where the cross-section method falls short

1. The method assumes the ground changes linearly between two sections. Where there is a ditch, a mound, or a hollow between stations, that feature is averaged away and the volume it represents is missed.

2. The larger the section spacing and the more broken the ground, the larger the error. Widely spaced sections on rough terrain are where the method loses the most.

3. If the section is cut at the wrong angle — not normal to the curve on a horizontal curve — the measured area is distorted and the resulting volume is wrong.

How I close the gap

I use a station densification method. Where the existing ground is broken, extra stations are added and the spacing is reduced. Every horizontal-curve transition point and every vertical-profile change point gets its own station and is included in the calculation (worked in EICAD and road-survey-master software).

Each section then corresponds exactly to the design, and the recovered volume approaches the true value — no overlap, no gap, no over-counting.