9.6 Excavation and Embankment (Cut and Fill)

Excavation and Embankment (Cut and Fill)

Why This Topic Matters for the PE Construction Exam

Earthwork operations—moving dirt from where it is (cut) to where it needs to be (fill)—often represent the largest variable cost on heavy civil projects like highways, dams, and site developments. The PE exam tests your ability to accurately estimate earthwork volumes using geometric methods, account for soil swelling and shrinkage, and plan the logistics of moving the material using Mass Haul Diagrams.

Earthwork Volume Calculations

The Average End Area Method

This is the most common method used for linear projects like roads and pipelines. Cross-sections of the existing ground and proposed grade are taken at regular intervals (stations). The area of cut or fill at each station is calculated.

The volume ($V$) between two adjacent stations is calculated by averaging their cross-sectional areas ($A_1$ and $A_2$) and multiplying by the distance ($L$) between the stations.

$V = \frac{A_1 + A_2}{2} \times L$

Crucial Unit Conversion: Cross-sectional areas are typically in square feet, and distance is in feet, giving a volume in cubic feet. Earthwork is universally measured in cubic yards (CY). You must divide the cubic feet by 27 to get cubic yards.

$V (\text{in CY}) = \frac{(A_1 + A_2) \times L}{2 \times 27} = \frac{(A_1 + A_2) \times L}{54}$

Borrow Pit (Grid) Method

For large, open site excavations (like a basement or a borrow pit), the grid method is used. The site is divided into a grid of squares or rectangles. Elevations are surveyed at the grid intersections before and after excavation.

The volume of each grid cell is calculated by taking the average of the depth of cut at its four corners and multiplying by the area of the cell. The total volume is the sum of all cell volumes.

$V = Area \times \frac{h_1 + h_2 + h_3 + h_4}{4}$

Incorporating Soil States

When calculating cut and fill, you must remember that a cubic yard of dirt in a cut (Bank Cubic Yards, BCY) does not equal a cubic yard of dirt in a fill (Compacted Cubic Yards, CCY).

If you need 10,000 CCY of fill for an embankment, you cannot just excavate 10,000 BCY from a hillside. Due to shrinkage, you will need more bank material.

Required Cut Volume (BCY) = Required Fill Volume (CCY) / (1 - Shrinkage Factor)

Similarly, when sizing the hauling fleet, you must convert the Bank volume to Loose volume (LCY) using the swell factor.

Mass Haul Diagrams

A Mass Haul Diagram is a continuous curve showing the cumulative volume of earthwork along the centerline of a project.

Key Features of a Mass Diagram:

• Y-Axis: Represents cumulative volume (usually in cubic yards). Cut volumes are considered positive (+), and fill volumes are considered negative (-).
• X-Axis: Represents distance along the project (Stations).
• Rising Curve: Indicates a section where cut exceeds fill.
• Falling Curve: Indicates a section where fill exceeds cut.
• Peaks: The highest points on the curve. A peak indicates a transition from cut to fill.
• Valleys: The lowest points on the curve. A valley indicates a transition from fill to cut.
• Balance Line: Any horizontal line drawn across the curve intersecting it at two points. The cut volume exactly matches the fill volume between those two points (a balance point).

Using the Mass Diagram

Mass diagrams are used to determine:

1. Haul Direction: Earth is hauled "forward" (increasing stationing) on a descending curve and "backward" (decreasing stationing) on an ascending curve.
2. Average Haul Distance: Determined by finding the horizontal distance between the centers of mass of the cut and fill segments.
3. Equipment Selection:
   • Short hauls (e.g., < 300 ft): Dozers.
   • Medium hauls (e.g., 300 - 5,000 ft): Scrapers.
   • Long hauls (e.g., > 5,000 ft): Excavators and Haul Trucks.
4. Borrow and Waste: If the mass curve ends above the zero line, there is excess cut (waste). If it ends below the zero line, there is a deficit requiring imported material (borrow).

Worked Example: Average End Area Calculation

Scenario: A road contractor is excavating a trench between Station 10+00 and Station 11+50.

• The cross-sectional area of the cut at Station 10+00 is 450 sq ft.
• The cross-sectional area of the cut at Station 11+50 is 300 sq ft.

Question: What is the total volume of excavation in cubic yards?

Step 1: Determine the distance between stations.

• Station 11+50 is 1,150 feet. Station 10+00 is 1,000 feet.
• Distance ($L$) = 1,150 - 1,000 = 150 feet.

Step 2: Apply the Average End Area formula.

• $A_1 = 450$ sq ft
• $A_2 = 300$ sq ft
• $V (in CF) = ((450 + 300) / 2) \times 150$
• $V = (750 / 2) \times 150 = 375 \times 150 = 56,250$ cubic feet.

Step 3: Convert to cubic yards.

• $V (in CY) = 56,250 / 27 = 2,083.3$ cubic yards.

The total excavation volume is approximately 2,083 cubic yards.