In earthwork estimation using the mid-section (mean-section) method, which of the following statements correctly describe how areas and volumes are determined between two consecutive sections?

Introduction / Context:
For routine roadway and canal projects, earthwork volumes between stations can be computed by simple approximate methods when the cross-section shape is consistent. The mid-section (mean-section) method is one such technique, lying conceptually between the average-end-area and prismoidal approaches.

Given Data / Assumptions:

• Two consecutive sections at a known spacing L.
• Sectional geometry (e.g., formation width and side slopes) remains the same, while depths vary.
• Mean depth is representative for computing a mid-section area.

Concept / Approach:
The method first computes a representative depth as the simple average of depths at the two stations. Using that mean depth and the section geometry, one evaluates the “mid-section area.” The earthwork volume over the interval is then approximated as this mid-section area multiplied by the spacing L between the same two sections.

Step-by-Step Solution:
Compute mean depth: d_mean = (d1 + d2) / 2.Compute mid-section area A_m using d_mean in the standard area formula (e.g., for a trapezoidal cutting).Compute volume: V ≈ A_m * L, where L is the distance between the two consecutive sections under consideration.Recognize that the “original sections” phrase in option (d) is a distractor; the spacing used is the same pair’s spacing.

Verification / Alternative check:
For small differences between d1 and d2, the mid-section result approaches the prismoidal value; for larger differences, the prismoidal formula gives improved accuracy over this approximation.

Why Other Options Are Wrong:

• Option (d) is incorrect because volume must refer to the distance between the same two sections whose depths were averaged.

Common Pitfalls:
Using inconsistent geometry when forming A_m; confusing section spacing; applying the method where section shape changes significantly.

Final Answer:
(a), (b) and (c) of the above.