Q4. Which of the following methods is NOT in use for earthwork estimation?
📚 Detailed Explanation: The Crossing Method Is Not Used for Earthwork Estimation
Earthwork estimation involves computing cut and fill volumes along roads, railways, canals, embankments, and other linear civil engineering works. Several well-established methods exist for this, each suited to different conditions. The Crossing Method does not belong to this group — it is an architectural/building estimation technique.
The Four Recognised Earthwork Volume Methods
| Method | How It Works | When Used |
|---|---|---|
| Trapezoidal (Mean Sectional) | Treats the solid between two sections as a trapezoid; averages the two end areas and multiplies by the distance. V = D × [(A&sub1;+A&sub2;)/2] | Quick estimates; overestimates for tapered sections |
| Prismoidal (Simpson’s) | Uses three sections (end + mid); V = (D/6)(A&sub1; + 4Aₑ + A&sub2;). Most accurate for prismoids. | Accurate volumes for irregular cross-sections |
| Mid-Section | Finds the average depth at mid-point, computes the cross-section area at that depth, multiplies by the interval distance. | Widely used when mid-section data is available |
| Cross-Section Method | Surveys full cross-sections at regular intervals along the alignment; plots and planimeters each section area, then applies trapezoidal or prismoidal rule. | Standard for road/railway earthwork |
What the Crossing Method Actually Is
In building estimation, the Crossing (or Centre-Line) Method is used to compute the total length of walls along the centre-line of a building plan, accounting for overlaps at corners and T-junctions. It has nothing to do with soil volumes, embankments, or excavation.
Why the Other Options Are Wrong
A (Trapezoidal): This is one of the most widely used earthwork methods. Fully valid.
B (Prismoidal): The prismoidal formula is the gold standard for earthwork volume accuracy. Fully valid.
C (Mid-section): A standard earthwork method that uses the average depth between two sections to find the mid-section area. Fully valid.
Key Concepts for Students
- Cross-section vs crossing: “Cross-section method” (taking perpendicular sections along a route) is valid for earthwork. “Crossing method” (handling wall length at building corners) is not. These sound similar but are completely different domains — a classic exam word-trap.
- Accuracy ranking: For earthwork volume accuracy: Prismoidal > Mid-section > Trapezoidal. The trapezoidal method always overestimates for solids that taper from top to bottom (frustums), while the prismoidal formula is exact.
- Practical application: In road earthwork surveys, cross-sections are taken every 20–30 m (or at changes in ground level). The surveyed areas are computed by planimeter or coordinate method, then summed using trapezoidal or prismoidal rules to get total cut/fill volume.