For a highway formation having a uniform gradient over a length where the existing ground also has a longitudinal slope, which earthwork computation methods are acceptable for calculating quantities?

Introduction / Context:
Highway earthwork is often computed between successive cross-sections where both formation level and ground profile vary. The selection of a volume formula balances accuracy with the available sectional data.

Given Data / Assumptions:

• Uniform formation gradient over the considered length.
• Ground exhibits a longitudinal slope (not necessarily uniform across the entire project).
• Cross-sections are available at regular intervals.

Concept / Approach:
The mid-section and trapezoidal formulae are straightforward and widely used; the prismoidal (Simpson’s) formula offers higher accuracy when area variation is approximately parabolic. For routine highway works with reasonably spaced sections, all three methods are acceptable, with the prismoidal formula preferred where curvature in area change is significant.

Step-by-Step Solution:
1) Compute areas at section faces from formation-ground geometry.2) Choose a formula: Mid-section (average of areas at midpoints), Trapezoidal (average of end areas), or Prismoidal (Simpson’s 4–2 weighting with D/3 factor).3) Apply consistently over intervals and sum volumes.

Verification / Alternative check:
Spot-check a segment with both trapezoidal and prismoidal; differences are typically small if intervals are short or areas vary nearly linearly.

Why Other Options Are Wrong:

• Each of A–C is valid; selecting only one unnecessarily restricts acceptable practice.

Common Pitfalls:

• Using large intervals where area curvature demands prismoidal accuracy.
• Failing to maintain equal spacing when applying Simpson’s rule.

Final Answer:
All the above..