2.1 Earthwork Construction and Estimating

1.1 Earthwork Construction and Estimating

Earthwork is one of the most critical phases in civil engineering projects, governing the economics, equipment selection, and scheduling of roadway, foundation, and sitework construction. To perform accurate estimations for earthwork operations, a design or construction engineer must understand that soil is not a rigid body with a static volume; rather, its volume changes significantly depending on its physical state. In construction and estimating, soil exists in one of three mutually exclusive states: the bank state, the loose state, and the compacted state.

The Three States of Soil

Soil volume is directly influenced by the arrangement of its solid particles and the voids (air and water) between them. The three states represent different stages of the earthwork process:

1. Bank state: This refers to soil in its natural, undisturbed, in-situ condition before excavation. Volume in this state is measured in bank cubic yards (BCY) or bank cubic meters (BCM). It represents the parent material that must be cut or excavated.
2. Loose state: When soil is excavated, the mechanical action of the bucket breaks the soil structure, dispersing the particles and introducing air voids. This causes the soil to expand or swell. The volume in this disturbed state is measured in loose cubic yards (LCY) or loose cubic meters (LCM). Haul units (dump trucks, scrapers) carry soil in its loose state, making this volume critical for transportation estimating.
3. Compacted state: When soil is placed as fill and subjected to mechanical compaction (using rollers, tampers, or compactors), water and air are forced out of the voids, and the soil particles are packed tightly together. This process, known as compaction, reduces the volume below both the loose volume and, typically, the original bank volume. This state is measured in compacted cubic yards (CCY) or compacted cubic meters (CCM). Structural embankments, road bases, and foundation backfills are specified in compacted volumes.

Volumetric Conversion Relationships

Converting volumes between bank, loose, and compacted states is essential for determining equipment productivity, haul costs, and borrow pit requirements. The relationship is governed by swell and shrinkage factors.

Swell Calculations

The percent swell (Sw) represents the fractional increase in soil volume when transitioning from the bank state to the loose state:

Sw (%) = ((V_L / V_B) - 1) * 100 Sw (%) = ((Density_B / Density_L) - 1) * 100

Where V_L is the loose volume, V_B is the bank volume, Density_B is the bank density, and Density_L is the loose density. The swell factor (also called the volumetric swell coefficient) is expressed as:

Swell Factor = 1 + (Sw / 100) = V_L / V_B

Alternatively, estimators use the load factor (Lf), which is the ratio of bank volume to loose volume (the reciprocal of the swell factor):

Lf = V_B / V_L = Density_L / Density_B = 1 / (1 + Sw)

To find the loose volume from a known bank volume: V_L = V_B * (1 + Sw) = V_B / Lf

Shrinkage Calculations

The percent shrinkage (Sh) represents the fractional decrease in soil volume when compacted, relative to its original bank state:

Sh (%) = (1 - (V_C / V_B)) * 100 Sh (%) = (1 - (Density_B / Density_C)) * 100

Where V_C is the compacted volume, and Density_C is the compacted density. The shrinkage factor (Sf) is the ratio of compacted volume to bank volume:

Sf = V_C / V_B = 1 - Sh

To find the compacted volume from a known bank volume: V_C = V_B * (1 - Sh) = V_B * Sf

To calculate the required bank volume (borrow pit excavation) to satisfy a required compacted fill volume: V_B = V_C / (1 - Sh) = V_C / Sf

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Haul Unit Capacity and Fleet Estimating

When estimating the transportation of excavated material, haul units are limited by either volume or weight. The volumetric capacity of a truck can be described as struck capacity (the volume of the truck bed filled level to the top) or heaped capacity (the volume including a heap of material piled above the sides, typically at a 2:1 slope). The gravimetric capacity is the maximum safe operating weight limit.

An estimator must check both limits:

1. Volumetric limit: Max Load (LCY) = Heaped capacity of haul unit.
2. Weight limit: Max Load (LCY) = Weight capacity (lbs) / Loose density (lb/LCY).

The lesser of these two volumes controls the haul unit capacity per trip. Once the controlling capacity is determined, the number of loads required is: Number of loads = Total loose volume to haul / Controlling capacity per truck

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Worked Examples

Example 1: Excavation and Hauling

A roadway excavation project requires the removal of 12,000 BCY of dry common earth. The material has a swell of 25% and a loose density of 2,100 lb/LCY. The contractor plans to haul the excavated material using dump trucks with a heaped capacity of 18 LCY and a maximum payload weight limit of 16.5 tons. Calculate the total loose volume to be hauled and the minimum number of truck loads required.

Solution:

1. Calculate the loose volume (V_L): V_L = V_B * (1 + Sw) V_L = 12,000 BCY * (1 + 0.25) = 15,000 LCY

2. Check the truck capacity limits:

   • Volumetric capacity = 18 LCY.
   • Weight capacity = 16.5 tons = 16.5 * 2,000 lbs = 33,000 lbs.
   • Max volume based on weight capacity = Weight capacity / Loose density Max volume = 33,000 lbs / 2,100 lb/LCY = 15.71 LCY.

3. Determine the controlling capacity: Since 15.71 LCY (weight limit) is less than 18 LCY (volume limit), the truck is weight-limited. The controlling capacity per truck is 15.71 LCY.

4. Calculate the required number of loads: Number of loads = 15,000 LCY / 15.71 LCY/load = 954.8 loads Rounding up to the nearest whole integer, the minimum number of loads is 955.

Example 2: Embankment and Borrow Pit

A structural embankment requires 8,500 CCY of compacted clay. The borrow source material has a shrinkage of 12% and a swell of 30%. Determine the bank volume that must be excavated from the borrow pit and the loose volume that must be hauled to the fill site.

Solution:

1. Calculate the required bank volume (V_B) to be excavated: V_B = V_C / (1 - Sh) V_B = 8,500 CCY / (1 - 0.12) = 8,500 / 0.88 = 9,659.09 BCY

2. Calculate the loose volume (V_L) to be hauled: V_L = V_B * (1 + Sw) V_L = 9,659.09 BCY * (1 + 0.30) = 12,556.82 LCY

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Quantity Take-Off Methods

Estimating earthwork quantities requires calculating the volume of cut and fill from drawings, profiles, and survey data. Three standard mathematical methods are utilized:

1. Average End Area Method

Used for linear projects like highways, railways, and trenches. It calculates the volume between two parallel vertical cross-sections separated by a distance L:

V = L * ((A_1 + A_2) / 2) / 27 (for volume in cubic yards, where A_1 and A_2 are in square feet and L is in feet)

The average end area method is an approximation. It assumes a linear transition in cross-sectional area between the two stations. It slightly overestimates the volume if one end area is significantly larger than the other, particularly when one area approaches zero (forming a pyramid or cone shape).

2. Prismoidal Formula

For greater accuracy, especially when the transition between end areas is highly non-linear or where high precision is required (such as rock excavation), the prismoidal formula is used:

V = (L / 6) * (A_1 + 4*A_m + A_2) / 27 (where A_m is the cross-sectional area at the midpoint)

Note that A_m is not the average of A_1 and A_2. Instead, the dimensions of the midpoint cross-section must be determined by averaging the linear dimensions of the end cross-sections, and then calculating A_m from those averaged dimensions.

3. Grid Method (Borrow Pit Method)

Used for mass excavations, grading sites, or borrow pits. The site is divided into a grid of squares or rectangles of equal area. Elevational measurements of the original ground and final grade are taken at each grid corner. The height of cut or fill (h) is computed at each node. The volume is calculated as:

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

Where:

• A is the area of a single grid cell (sq ft).
• h_1 represents corner heights shared by only 1 grid cell.
• h_2 represents corner heights shared by 2 grid cells.
• h_3 represents corner heights shared by 3 grid cells.
• h_4 represents corner heights shared by 4 grid cells.

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Mass Diagrams

A mass diagram is a graphical representation of the cumulative volume of earthwork along the centerline of a linear project. The horizontal axis represents the project stations (distance), and the vertical axis represents the cumulative algebraic sum of excavation (cut, assigned a positive sign) and embankment (fill, adjusted for shrinkage and assigned a negative sign) starting from station 0+00.

Key Characteristics of a Mass Diagram:

1. Rising slopes represent areas of cut (excavation exceeding fill).
2. Falling slopes represent areas of fill (embankment exceeding cut).
3. Peaks (maximum points) indicate transitions from cut (excavation) to fill (embankment).
4. Valleys (minimum points) indicate transitions from fill (embankment) to cut (excavation).
5. A balance line is a horizontal line drawn across the mass curve. Any two points where the mass curve intersects the balance line indicate that the volume of cut between those two stations is exactly equal to the volume of fill required (adjusted for shrinkage). The net earthwork volume between these points is zero.
6. The horizontal distance between the centroid of the cut and the centroid of the fill represents the haul distance.
7. Free haul distance (FHD) is the maximum distance over which excavated material can be hauled without extra charge (specified in the contract, e.g., 500 feet). The cost of this haul is included in the base excavation price.
8. Overhaul distance is the distance beyond the free haul limit. The contractor receives additional payment for hauling material over this distance, usually paid in units of station-yards (1 cubic yard hauled 100 feet).