A longitudinal section, also termed as a structure’s Side Elevation, is a section taken through the lengthwise dimension of a structure.

Quantity of Earth Fill and Cut is required in various construction projects like Railways, Road works, Canals, Dams, etc. Accurate quantity estimation is essential in saving a lot of money on leveling the existing surface for construction work.

There are various methods of quantity estimation like Simpson’s 1/3rd Rule, Average Depth method, Trapeziodal Rule, Net Area method, etc.

Using Trapezoidal Rule (high accuracy): In trapezoidal method, each segment of the section is divided into various trapezoids and triangles. The sum of the areas of these segments is calculated to arrive at the area of the section.

Earthwork Estimate Trapezoidal Rule
Trapezoidal Rule

In the figure above, the 7 points marked with dark circles are the initial levels. The red circled points (4 in number) denote the Proposed or Final levels. The above section is divided into 10 segments and the intermediate points are interpolated for both initial and design levels. The area of the trapezoids 1,2,3,8,9,10 and the area of the triangles 4 and 7 determine the cutting quantity for the above section. Similarly the area of the triangles 5 and 6 determine the filling quantity.

LXQ-CAD software uses the highly accurate trapezoidal rule to calculate earth cutting and filling quantity.