Question 8 of 9: Route Cross-Section and Its Relation to the Profile

Question 8: Route Cross-Section and Its Relation to the Profile (10 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

A route cross-section is a section of the ground taken transverse (perpendicular) to the route centreline at a specific station (chainage). It records the existing-ground elevations at a series of offsets left and right of the centreline — taken at regular intervals and at every significant break of slope — out to the limits of the proposed works. Superimposed on that natural-ground line is the design template: the finished formation width, side slopes (e.g. 2:1), ditches and, where relevant, superelevation. The area enclosed between the existing ground and the template is the cut area (ground above grade) or fill area (ground below grade) at that station. Cross-sections are commonly plotted with an exaggerated vertical scale so small height differences are legible.

The profile, by contrast, is a longitudinal section taken along the centreline. It plots, against chainage, the natural-ground elevation of the centreline (the ground profile) together with the proposed grade line (vertical alignment) — its tangent grades and the vertical curves joining them.

How they relate. The two are orthogonal cuts through the same terrain model that together fix the earthworks in three dimensions:

• The profile supplies, at each station, the grade (formation) elevation of the centreline. That single elevation is the anchor point about which the cross-section’s design template is drawn — so a cross-section cannot be completed until the profile grade at its station is known.
• Cross-sections are taken at the stations laid out along the profile (full stations, plus breaks and transitions). Each gives a cut or fill area $A_i$.
• Successive areas are turned into volumes using the spacing between stations (the along-route distance measured on the profile), by the average-end-area rule $V=\dfrac{L}{2}(A_1+A_2)$ or, more precisely, the prismoidal formula. Summing gives the cut and fill quantities and the mass-haul diagram.

In short, the profile controls the vertical geometry along the line and the cross-sections describe the shape across it at each station; the profile’s grade elevation seeds each cross-section, and the cross-section areas combined with the profile’s station spacing yield earthwork volumes.