Earthwork involves the excavation (cut) and placing (fill or embankment) of soil and rock to create a finished grade for a civil engineering project, such as a highway, railway, or canal. Profiling and cross-sectioning are the fundamental surveying techniques used to quantify these volumes, which are critical for cost estimation, contractor payment, and resource planning.

A cross-section is a profile of the ground surface taken at right angles to the longitudinal centerline of the route. By combining the natural ground profile with the proposed design template (the shape of the finished roadbed, including lanes, shoulders, and side slopes), the area of cut or fill at any specific station can be determined.

1. Level Section: The ground surface is horizontal transversely. Only the centerline cut/fill depth is needed to compute the area.
2. Three-Level Section: The ground slopes uniformly from the centerline to both side stakes. It is defined by three points: the centerline depth and the horizontal/vertical coordinates of the two slope stakes.
3. Five-Level Section: Used when the ground is highly irregular, requiring intermediate elevation shots between the centerline and the slope stakes.
4. Side-Hill Section: A cross-section where the proposed grade line intersects the natural ground slope, resulting in excavation (cut) on one side of the centerline and embankment (fill) on the other.

Once the coordinates (offsets from centerline and elevations relative to grade) of a cross-section are known, the area can be calculated. The most common method used in route surveying is the Coordinate Method (Shoelace Formula).

For a cross-section defined by vertices $(x_1, y_1), (x_2, y_2), \dots, (x_n, y_n)$ ordered consecutively around the perimeter:

The volume of earthwork is calculated between successive cross-sections along the route.

The Average End Area method is the most widely used technique for earthwork volume calculations due to its simplicity. It assumes that the volume between two cross-sections is exactly the average of their two areas multiplied by the distance between them.

When higher accuracy is required, or when the ground is highly irregular causing significant differences between adjacent areas, the Prismoidal formula is used. A prismoid is a solid whose ends are parallel polygons and whose sides are quadrilaterals or triangles.

Rather than computing $A_m$ directly, it is often easier to compute the volume using the Average End Area method and then apply a Prismoidal Correction ($C_p$) to obtain the exact prismoidal volume.

For a standard three-level section, the correction formula is:

When there is an odd number of cross-sections (meaning an even number of intervals) spaced at a constant distance $L$, Simpson's 1/3 rule can be applied to calculate the total volume. It generally yields a more accurate result than applying the average end area method repeatedly, as it inherently approximates the prismoidal volume over parabolic profiles.

Earthwork materials change volume during excavation and compaction. This must be accounted for when balancing cut and fill volumes.

• Swell: When rock or dense soil is excavated, it breaks up and increases in volume.
• Shrinkage: When loose excavated material is placed in a fill and mechanically compacted, it usually occupies less volume than it did in its original natural state.

To equate cut and fill volumes, a Shrinkage Factor or Swell Factor is applied, usually to the fill volume, to determine the equivalent volume of required excavation (bank measure).

A mass haul diagram (or simply mass diagram) is a continuous curve showing the accumulated algebraic sum of earthwork volume (cut being positive, fill being negative) from an initial station to any succeeding station along the route profile.

It is a powerful graphical tool used by engineers and contractors to plan the movement of excavated material, determine haul distances, and select equipment.

1. Rising and Falling: The curve rises where there is an excess of excavation (cut) and falls where there is a deficiency (fill).
2. Peaks and Valleys: A peak occurs where a cut transitions into a fill (grade line is above the ground line). A valley (lowest point) occurs where a fill transitions into a cut.
3. Balance Lines: Any horizontal line drawn to intersect the mass curve at two points indicates a balance between cut and fill between those two stations. The material excavated between those stations exactly equals the material required for fill.
4. Area under the Curve: The area between the mass curve and a balance line represents the haul (volume $\times$ distance) required to move the balanced material.

• Freehaul: The maximum distance earth can be moved without extra compensation to the contractor. It is considered part of the basic excavation cost. The freehaul volume is calculated from the balance points on the mass diagram separated by the freehaul distance ($FHD$).
• Overhaul ($OH$): If material must be moved further than the freehaul distance to balance the cut and fill, the extra distance is termed "overhaul." The contractor is paid a premium for overhaul, usually calculated in units of station-meters.

When a project is not perfectly balanced (the mass diagram ends above or below zero):

• Borrow: Material obtained from outside the project limits when there is a deficiency of cut (excess fill).
• Waste: Excavated material that cannot be used on the project (excess cut) and must be disposed of elsewhere.

The choice to overhaul existing material versus wasting it and borrowing new material depends entirely on the relative cost.

The Limit of Economic Haul is the distance at which the cost of overhauling excavated material equals the cost of obtaining borrow material from nearby pits. If the required haul distance exceeds the LEH, it is cheaper to waste the cut and borrow new material for the fill.