Earthwork Quantity Computation – Valid Methods Used in Highway and Irrigation Projects In engineering surveying and quantity estimation, the volume of earthwork between two cross-sections (or between multiple sections) may be calculated using which of the following established methods?

Introduction:
Accurate earthwork quantity estimation underpins cost, planning, and payment in road, railway, and canal works. Surveyors compute volumes between successive cross-sections using standard mathematical methods. This question tests recognition of the commonly accepted formulas and when they are used.

Given Data / Assumptions:

• Two or more cross-sections at known chainages are available.
• Areas are measured from field notes or CAD.
• Ground varies more or less regularly between sections.

Concept / Approach:

The 'end areas' and 'trapezoidal' approaches assume linear variation, while the 'prismoidal' formula fits a parabolic variation of the surface between sections and is more accurate when curvature exists. The 'mean areas' framing is a practical variant when intermediate shapes are averaged. Choice depends on section spacing and smoothness of terrain, but all are legitimate in practice and in specifications.

Step-by-Step Solution:

Verification / Alternative check:

Using both trapezoidal and prismoidal methods on a curved surface typically shows the prismoidal result slightly smaller (more accurate) than trapezoidal when areas curve concavely between sections, aligning with numerical integration theory.

Why Other Options Are Wrong:

Each named method is valid under suitable assumptions; therefore, selecting a single one would be incomplete. 'All of the above' correctly captures accepted practice.

Common Pitfalls:

Applying the trapezoidal rule over long intervals where ground curvature is significant; ignoring the necessity of closer section spacing on irregular terrain.

Final Answer:

All of the above