6.5 Excavation, Earthwork Volumes, Hauling & Compaction

6.5 Excavation, Earthwork Volumes, Hauling & Compaction

Earthwork Volumetric Calculations & Cut/Fill Balancing

Earthwork engineering focuses on cut and fill balancing—calculating earth volumes to ensure that soil excavated from high elevations (cuts) matches the soil volume needed for low elevations (fills), minimizing expensive off-site borrow import or waste export hauling.

1. Average End-Area Method

The Average End-Area method is the standard engineering formula used for calculating earthwork volumes for linear excavations—including utility trenches, roadways, pipeline ditches, and drainage swales:

V = ((A_1 + A_2) / 2) * (L / 27)

Where:

• V = Volume of earth in Cubic Yards (cu yd).
• A_1 = Cross-sectional area of cut or fill at the first station (in square feet, sq ft).
• A_2 = Cross-sectional area of cut or fill at the second station (in square feet, sq ft).
• L = Horizontal distance between station 1 and station 2 (in feet).
• 27 = Conversion factor (27 cubic feet = 1 cubic yard).

2. Grid Method (Borrow Pit Method)

The Grid Method is used to calculate cut and fill volumes for broad, non-linear areas such as commercial building pads, parking lots, and site mass grading. The site plan is divided into uniform square grids (e.g., 50 ft x 50 ft, where Grid Area A = 2,500 sq ft):

V = A * ((sum h_1 + 2sum h_2 + 3sum h_3 + 4*sum h_4) / (4 * 27))

Where:

• A = Area of a single grid square (in square feet).
• h_1 = Cut or fill depths at corner stakes shared by only 1 grid square.
• h_2 = Cut or fill depths at corner stakes shared by 2 adjoining grid squares.
• h_3 = Cut or fill depths at corner stakes shared by 3 adjoining grid squares.
• h_4 = Cut or fill depths at corner stakes shared by 4 adjoining grid squares.

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Soil Volume Phase Transitions: BCY, LCY, CCY

Soil volume changes substantially during earthmoving operations due to variations in air void ratios. Contractors must account for three distinct volumetric states:

   ┌───────────────────────┐       Excavation (Swell)       ┌───────────────────────┐
   │   BANK CUBIC YARD     │ ─────────────────────────────► │   LOOSE CUBIC YARD    │
   │        (BCY)          │                                │        (LCY)          │
   │  Natural In-Situ Soil │ ◄───────────────────────────── │  Excavated / Hauled   │
   └───────────┬───────────┘          Load Factor           └───────────────────────┘
               │
               │ Compaction (Shrinkage)
               ▼
   ┌───────────────────────┐
   │ COMPACTED CUBIC YARD  │
   │        (CCY)          │
   │  Engineered Fill Pad  │
   └───────────────────────┘

1. Bank Cubic Yards (BCY)

Soil in its natural, undisturbed in-situ state prior to excavation. All engineering plans, cut depths, and baseline surveys are measured in BCY.

2. Loose Cubic Yards (LCY)

Soil after excavation and loading. When soil is disturbed, particle bonds break and air voids enter, causing the soil to expand or "swell":

LCY = BCY * (1 + S_w) Swell Factor (S_w) = (LCY - BCY) / BCY = (Density_bank / Density_loose) - 1 Load Factor = BCY / LCY = 1 / (1 + S_w)

3. Compacted Cubic Yards (CCY)

Soil after mechanical compaction in fill lifts. Compaction expels air voids and forces particles into dense packing, resulting in a volume smaller than the original bank volume:

CCY = BCY * (1 - S_h) Shrinkage Factor (S_h) = 1 - (CCY / BCY) = 1 - (Density_bank / Density_compacted)

Soil Volume Properties Table

Hauling & Fill Calculation Example

• Problem: A commercial site requires placing and compacting 10,000 CCY of dense clay fill. The clay has a bank-to-compacted shrinkage factor of 20% ($S_h = 0.20$) and an excavation swell factor of 30% ($S_w = 0.30$). How many Bank Cubic Yards must be excavated, and how many Loose Cubic Yards must be hauled by 18-LCY dump trucks?
• Step 1: Calculate Bank Volume (BCY): BCY = CCY / (1 - S_h) = 10,000 / (1 - 0.20) = 10,000 / 0.80 = 12,500 BCY
• Step 2: Calculate Loose Volume (LCY): LCY = BCY * (1 + S_w) = 12,500 * (1 + 0.30) = 16,250 LCY
• Step 3: Calculate Truckloads: Truckloads = 16,250 LCY / (18 LCY/truck) = 902.78 -> 903 Truckloads

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Geotechnical Soil Mechanics, Proctor Tests & Compaction Equipment

Cohesive vs. Cohesionless Soils

• Cohesive Soils (Clays & Silts): Characterized by fine microscopic platelets bound by electrochemical forces. Possess high plasticity, slow drainage, and cohesive shear strength. Susceptible to volumetric shrinking when dried and swelling when saturated. (Prevalent across the Georgia Piedmont region as weathered crystalline "Georgia red clay").
• Cohesionless Soils (Sands & Gravels): Composed of granular particles with no internal chemical cohesion. Shear strength derives entirely from internal friction between interlocking particles. Highly permeable with rapid drainage.

Proctor Moisture-Density Testing

To achieve structural stability, soil fill must be compacted to a specified percentage of its Maximum Dry Density (MDD) at its Optimum Moisture Content (OMC), determined in geotechnical laboratories via Proctor tests:

                    PROCTOR MOISTURE-DENSITY CURVE

       Dry Density (pcf) 
          ▲
          │                Peak = Maximum Dry Density (MDD)
          │                      ┌─────┐
          │                    ┌─┘     └─┐
          │                  ┌─┘         └─┐
          │                ┌─┘             └─┐
          │              ┌─┘                 └─┐
          │            ┌─┘                     └─┐
          │          ┌─┘                         └─┐
          │        ┌─┘                             └─┐
          └────────┴─────────────┬───────────────────┴──► Moisture Content (%)
                                 │
                       Optimum Moisture Content (OMC)

• Optimum Moisture Content (OMC): The specific water content percentage at which soil particles are sufficiently lubricated to slip into their densest possible packing configuration under compaction. Placing soil significantly dry of OMC prevents full compaction due to friction; placing soil wet of OMC causes water to fill pore spaces, resulting in soil "pumping" and shearing failure.
• Compaction Specification: Commercial building pads typically mandate compaction to 95% to 98% of Maximum Dry Density per ASTM D1557, placed in loose lifts of 6 to 8 inches within +/- 2% to +/- 3% of OMC.

Compaction Equipment Matrix

Dewatering Methods

• Open Sump Pumping: Direct pumping from sumps excavated in low points; suitable for coarse gravels and low water inflows.
• Wellpoint Systems: Series of small-diameter (1.5" to 2") slotted pipe points driven at 3- to 6-foot intervals around the excavation perimeter, connected to a common header pipe and vacuum pump; effective for lowering water tables up to 15 to 20 feet in sandy soils.
• Deep Wells: Drilled holes containing submersible turbine pumps; used for deep excavations in permeable strata.