10.3 Compaction, Excavation, and Mass Diagrams

Compaction, Excavation, and Mass Diagrams

In transportation engineering, earthwork constitutes a major portion of highway construction costs. Effective management of excavation, hauling, and compaction operations dictates project efficiency. This section delves into the mechanical stabilization of soils via compaction, field density verification methods, and the strategic planning of earthmoving using mass diagrams.

1. Compaction Equipment Selection and Operations

Compaction is the densification of soil by the removal of air, requiring mechanical energy. It increases shear strength, decreases permeability, and minimizes future settlement. The effectiveness of compaction depends on soil type, moisture content, compaction effort, and the type of equipment used. Selecting the correct roller is critical for achieving the required dry unit weight.

Types of Rollers and Soil Suitability:

• Smooth-Wheel (Drum) Rollers: These provide 100% coverage under the wheel with contact pressures typically between 40 and 60 psi. They are suitable for well-graded sand-gravel mixtures, crushed rock, and asphaltic concrete. However, they are not effective for deep layers because their compaction effect is shallow. They are often used for proof-rolling subgrades and finishing operations to provide a smooth surface.
• Pneumatic Rubber-Tired Rollers: These consist of heavily loaded wagons with several rows of closely spaced tires. They provide both pressure and a kneading action. They are highly versatile and effective for sandy and clayey soil compacts, as well as granular base courses. The tire pressure can be adjusted to vary the contact pressure.
• Sheepsfoot Rollers: Distinguished by numerous drum projections (feet), these rollers provide high contact pressure (up to 1,000 psi). The feet penetrate the soil layer and compact from the bottom up, creating a kneading action that destroys soil clods. They are specifically designed for cohesive soils (clays and silts). They are highly ineffective in clean sands or gravels.
• Vibratory Rollers: These rollers impart dynamic forces to the soil in addition to static weight. The vibration frequency and amplitude can be adjusted. They are exceptionally effective for granular soils (sands, gravels, and crushed stone), as the vibrations reduce internal friction, allowing particles to rearrange into a denser state. They can also be effective on cohesive soils if operated at lower frequencies with high amplitudes.

Compaction Operations: Optimal compaction occurs near the Optimum Moisture Content (OMC), determined by the Standard or Modified Proctor test. In the field, soil is spread in "lifts" (layers). The lift thickness must be compatible with the roller's depth of influence—typically 6 to 12 inches for loose material. If the lift is too thick, the lower portion will not be adequately compacted.

2. Field Density Testing Methods

Once a lift is compacted, field testing verifies that the required relative compaction (usually expressed as a percentage of the maximum dry density from the Proctor test) has been achieved. Common field methods include:

• Sand Cone Method (ASTM D1556): A traditional, destructive test. A hole is excavated in the compacted soil, and the extracted soil is weighed and tested for moisture content. The hole is then filled with a standardized, uniform sand of known dry density from a calibrated cone apparatus. The volume of the hole is calculated from the weight of sand used. It is highly accurate but slow and sensitive to vibration during the test.
• Nuclear Density Gauge (ASTM D6938): The most common modern method. It is fast and non-destructive (or requires only a small probe hole). The gauge emits gamma radiation to measure bulk density (based on radiation scattering by soil particles) and neutrons to measure moisture content (based on thermalization of neutrons by hydrogen atoms in water). While efficient, it requires strict safety protocols, licensing, and periodic calibration.
• Balloon Density Method (ASTM D2167): Similar to the sand cone method, but a water-filled rubber balloon is used to measure the volume of the excavated hole. The volume is read directly from a graduated cylinder. It is faster than the sand cone but the balloon can snag on sharp rocks or fail to fill irregular voids in gravelly soils.
• Drive Cylinder Method (ASTM D2937): A thin-walled steel cylinder is driven into the soil and extracted to obtain an undisturbed sample of known volume. The sample is weighed and its moisture content determined. This method is rapid and reliable but is only suitable for fine-grained, cohesive soils that will stick together in the cylinder; it cannot be used in gravels or hard soils.

3. Earthwork Volumes and Prismoidal Computations

Earthwork volumes are typically calculated along a highway alignment using cross-sections taken at regular stations. The most common volume calculation method is the Average End Area Method: $V = \frac{A_1 + A_2}{2} \cdot L$ Where $A_1$ and $A_2$ are the cross-sectional areas at two stations, and $L$ is the distance between them.

However, when cross-sections change rapidly (e.g., from a deep cut to a high fill), the Average End Area Method overestimates the volume. In such cases, the more accurate Prismoidal Formula is used: $V = \frac{L}{6} (A_1 + 4A_m + A_2)$ Where $A_m$ is the area of the section midway between $A_1$ and $A_2$. Note that $A_m$ is not simply the average of the two areas; its dimensions must be interpolated from the dimensions of the end sections before calculating the area.

4. Mass Diagram and Haul Optimization

A mass diagram is a continuous curve representing the cumulative volume of earthwork along the linear profile of a roadway. Cuts are considered positive, and fills are negative. The diagram helps engineers plan the most economical movement of material.

Key Mass Diagram Concepts:

• Profile vs. Mass Diagram: An ascending mass diagram curve indicates a cut section (accumulation of material), while a descending curve indicates a fill section (depletion of material).
• Balance Points: Points where the mass diagram intersects the baseline (or any horizontal line) represent locations where the cut volume exactly equals the fill volume within that interval. No material needs to be imported or exported between balance points.
• Free Haul Distance (FHD): Contract specifications often define a distance over which hauling earth is included in the unit price of excavation. This is the Free Haul.
• Overhaul: Hauling material beyond the FHD is termed Overhaul. It is generally paid by the unit volume-distance (e.g., station-yards). The cost of overhaul increases with distance.
• Limit of Economical Haul (LEH): The maximum distance it is financially viable to haul material from a cut to a fill. Beyond this distance, it is cheaper to waste the cut material locally and borrow material from a nearby source for the fill. $LEH = FHD + \frac{\text{Cost of Borrow}}{\text{Cost of Overhaul per unit distance}}$
• Borrow and Waste: If the total cut exceeds total fill (plus shrinkage), the excess is waste. If fill requirements exceed available cut, material must be brought in from a borrow pit. Shrinkage and swell factors must be applied because soil density changes when excavated and compacted (e.g., 1 cubic yard of bank material may only yield 0.85 cubic yards of compacted fill).

Optimization Walkthrough: To optimize hauling on a mass diagram, engineers draw a horizontal line of length equal to the LEH within the loops of the mass diagram curve.

1. Any horizontal chord drawn within a loop represents a balance line. The area bounded by the mass diagram curve and this balance line represents the haul (in station-yards).
2. Within this area, place the FHD chord. The area above (or below) the FHD chord represents the free haul, while the remaining area within the balance loop represents overhaul.
3. By setting the balance line to exactly the LEH, the contractor minimizes costs. Material outside the LEH balance line is designated as waste (from the cuts) or requires borrow (for the fills).

Mastery of these concepts ensures that highway earthworks are executed structurally soundly, utilizing appropriate machinery, verified by rigorous testing, and optimized for minimal financial expenditure during the hauling process.