Earthwork Calculation: Excavation and Filling

Introduction

Earthwork includes excavation (cutting) and filling (embankment). It is measured in cubic metres as per IS 1200 and forms a major part of foundation and road estimates.

This guide covers:

• Simple excavation (foundations, trenches)
• Trapezoidal and prismoidal formulae for linear earthwork
• Bulking and compaction factors

Units (IS 1200)

Item	Unit	Payment
Earthwork in excavation	cum	per cum
Earthwork in filling (foundation trenches)	cum	per cum
Earthwork in filling (plinth)	cum	per cum

Simple Excavation (Buildings)

For foundation trenches, use:

Volume = Length × Breadth × Depth

• Length, breadth – At bottom of excavation (or average of top and bottom)
• Depth – From ground level to bottom of excavation

For stepped excavation, find volume of each step and add.

Example: Foundation Trench

Single room, centre line 19.2 m, trench width 0.9 m, depth 1.4 m.

Volume = 19.2 × 0.9 × 1.4 = 24.192 cum

See quantity takeoff methods for long wall–short wall and centre line approaches.

Trapezoidal Formula (Mean Area Method)

For roads, canals, or any linear work with cross-sections at regular intervals:

V = (D/2) × (A₁ + 2A₂ + 2A₃ + ... + 2Aₙ₋₁ + Aₙ)

Where:

• A₁, A₂, ... Aₙ = areas of consecutive cross-sections (sq m)
• D = distance between sections (m)
• n = number of sections

Simplified (Two Sections)

V = (D/2) × (A₁ + A₂)

Example

Chainage	Area (sq m)
0	20
10 m	25
20 m	18
30 m	22

D = 10 m
V = (10/2) × (20 + 2×25 + 2×18 + 22) = 5 × 128 = 640 cum

Prismoidal Formula

More accurate when cross-sections change. Use when number of sections is odd (3, 5, 7...):

V = (D/6) × (A₁ + Aₙ + 4×(A₂ + A₄ + A₆ + ...) + 2×(A₃ + A₅ + A₇ + ...))

Odd subscript: multiply by 4
Even (middle): multiply by 2

Example (5 sections)

A₁=20, A₂=25, A₃=18, A₄=22, A₅=19, D=10 m

V = (10/6) × (20 + 19 + 4×(25+22) + 2×18)
= (10/6) × (39 + 188 + 36) = (10/6) × 263 ≈ 438 cum

Bulking and Compaction

Bulking

Excavated soil occupies more volume than in-situ:

• Sand: ~10–15%
• Ordinary soil: ~15–25%
• Clay: ~20–30%

Bulking factor = Volume after excavation / Volume in-situ
e.g., 1.2 means 20% bulking.

Compaction

Fill is compacted to required density. Compaction factor = In-situ volume / Compacted volume
Often 0.9–0.95 (i.e., 1 cum fill needs 1.05–1.1 cum loose soil).

Application

• Excavation to fill:
  Fill volume (compacted) × (1 + bulking) ≈ Excavation required
• Borrow pit:
  Order more excavated material than fill volume if transporting from elsewhere.

Volume from Spot Levels

For irregular terrain (e.g., building site):

1. Take grid of spot levels.
2. Find cut/fill at each grid point (depth below/above formation).
3. Use formula:

V = (A/4) × (Σ h at corners)

Where A = area of one grid cell, h = cut/fill depth.
For prismoid over each cell: V = (A/4) × (h₁ + h₂ + h₃ + h₄).

Side Slopes

For trapezoidal cross-section (road in cutting/filling):

Area = (B + s×h) × h
(approximate for uniform slope)

Where:

• B = bottom width
• h = depth of cut or fill
• s = horizontal distance per 1 m vertical (e.g., 1.5:1 → s = 1.5)

Measurement Rules

1. Linear – to nearest 0.01 m

2. Area – to nearest 0.01 sq m

3. Volume – to nearest 0.01 cum

4. Same work, different conditions – measure separately (e.g., soft soil vs hard rock excavation).

Cost Considerations

• Rock excavation – Paid separately, much higher rate than soil.
• Water in excavation – De-watering may be an extra item.
• Lead for disposal – If soil is carted away, lead affects cost.

Next Steps

• Quantity Takeoff Methods – Long wall, short wall, centre line for building foundations
• Detailed Estimates – Full estimate including earthwork