Mass Diagram and Earthwork Concepts
Introduction
A Mass Diagram is an essential tool in civil engineering for efficiently managing earthwork. It provides a graphical representation of the distribution of cutting and filling along a project alignment, such as roads, railways, or irrigation works.
Key Terms and Concepts
1. Mass Diagram
- Purpose: Predict the distribution of excavated earth and identify the location of borrow pits and waste banks.
- Key Components:
- Abscissae (X-axis): Represents the chainages (distances) along the alignment.
- Ordinates (Y-axis): Represents the cumulative algebraic sum of cutting (+) and filling (-) volumes.
- Special Considerations: For hilly areas with transverse slopes, both cutting and filling may occur at the same chainage. Use the net difference of cutting and filling, and assign the sign of the larger volume.
2. Balancing Line
A line on the mass diagram that represents the equalization of cutting and filling over specific alignment lengths. It minimizes unnecessary cutting or filling.
3. Lead
The horizontal distance excavated earth is transported from a borrow pit to the embankment. A lead of 30 m is considered normal, and additional rates apply for longer distances.
4. Lift
The vertical height through which excavated earth is lifted. A 1.5 m lift is normal, and additional rates apply for higher lifts.
5. Haul Distance
The distance between the cutting face and the toe of the embankment.
6. Average Haul Distance
The distance between the center of gravity of cutting and the center of gravity of filling.
Steps for Preparing a Mass Diagram
- Calculate the volumes of cutting and filling using cross-sectional data along the alignment.
- Plot chainages along the X-axis using a suitable horizontal scale.
- Plot cumulative volumes of cutting (+) and filling (-) along the Y-axis using a suitable vertical scale.
- Join the plotted points with a smooth curve to form the mass diagram.
- Analyze the curve to determine the distribution of excavated earth.
- Draw the balancing line to minimize unnecessary cutting and filling.
Example of a Mass Diagram
Given Data
| Chainage (m) | Volume of Cutting (m³) | Volume of Filling (m³) | Net Volume (m³) | Cumulative Volume (m³) |
|---|---|---|---|---|
| 0 | 500 | 0 | +500 | +500 |
| 50 | 400 | 0 | +400 | +900 |
| 100 | 0 | 700 | -700 | +200 |
| 150 | 0 | 300 | -300 | -100 |
| 200 | 600 | 0 | +600 | +500 |
Mass Diagram Interpretation
- Positive Slope: Indicates cutting; surplus earth is available.
- Negative Slope: Indicates filling; earth is required.
- Flat Slope: Represents balance between cutting and filling.
- Balancing Line: Represents alignment length where cutting and filling are equalized.
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