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Earthwork and Volume Example

Easy DifficultyFE Surveying

Estimate the volume of cut or fill between two cross sections using the average end-area method.

Concept

In earthwork, cross-sectional areas are computed at stations along the alignment. The average end-area method estimates volume between two sections as the average of the two areas times the distance between them: V = \frac{A _{1} + A _{2}}{2} \times L . For better accuracy over a stretch with three sections (two segments), the prismoidal formula uses the middle area: V = \frac{L}{6} (A_{1} + 4 A_{m} + A_{2}) . V = \frac{A _{1} + A _{2}}{2} \times L V = \frac{L}{6} (A_{1} + 4 A_{m} + A_{2}) Notation: A_{1}, A_{2} = cross-section areas at stations 1 and 2, A_{m} = area at mid-section (prismoidal), L = horizontal distance between sections, V = volume.

Two cross sections along a road cut are 50 ft apart. The cut area at the first section is 120 yd² and at the second section is 80 yd². Find: The volume of cut between the two sections (yd³) using the average end-area method.

A_{1} = 120 yd^{2} A_{2} = 80 yd^{2} L = 50 ft (distance between sections)

Use consistent units: areas in yd² and L in yards so volume is in yd³. L = 50 ft = 50/3 yd . V = \frac{A _{1} + A _{2}}{2} \times L V = \frac{120 + 80}{2} \times \frac{50}{3} = 100 \times \frac{50}{3} = \frac{5000}{3} \approx 1667 yd^{3}

Volume of cut: V \approx 1670 yd^{3} .

End-area: V = \frac{A _{1} + A _{2}}{2} \cdot L; Prismoidal: V = \frac{L}{6} (A_{1} + 4 A_{m} + A_{2})