Short Answer:

To determine volume in surveying, surveyors measure the surface levels of land before and after excavation or filling. The volume is calculated based on the difference in these levels. Common methods include the cross-section method, grid method, and contour method, depending on the shape and size of the land.

In simple terms, volume is calculated by multiplying the average area of the surface with the depth or height. These calculations help in planning earthwork for roads, canals, and construction projects, ensuring the right amount of material is added or removed from the site.

Determining volume in surveying

Volume determination in surveying is essential for earthwork estimation. Whether you are constructing a dam, road, or cutting/filling land, it is important to know how much soil needs to be excavated or filled. Surveyors achieve this by measuring the land surface and using certain techniques to calculate the amount of material involved.

Common Methods for Volume Calculation

1. Cross-Section Method
   This method involves taking cross-sections of the ground at regular intervals along a reference line, such as a road alignment or canal centerline. The area of each cross-section is calculated using geometric formulas or by dividing it into regular shapes. Then the volume between each pair of cross-sections is calculated using:

Volume = (A₁ + A₂) / 2 × Distance

Where A₁ and A₂ are the areas of two successive cross-sections. The total volume is the sum of all segment volumes. This method is widely used in roadwork and canal projects.

1. Grid Method (Spot Leveling)
   In this method, the area is divided into small squares or rectangles by marking grid points on the ground. The elevation at each grid point is measured. Using these heights, the average depth is calculated. The area of each grid is multiplied by the average height to get the volume.

Volume = Area of each grid × Average height difference

This method is suitable for large, level areas like construction sites or airports.

1. Contour Method
   This method is based on contour maps. Volume is calculated by measuring the area within each contour line and applying formulas:

Volume = (h / 3) × [A₁ + Aₙ + 4(sum of even A) + 2(sum of odd A)]

Where h is the contour interval and A are the areas enclosed by contours. This is suitable for calculating volumes of reservoirs, hills, and valleys.

1. Prismoidal Method
   Used for more accurate volume calculation between two irregular surfaces. It considers the shape of the volume as a prismoid (a 3D shape with top and bottom faces not parallel). This gives better results than averaging areas.

Important Considerations

• Accuracy of level measurement is critical.
• Proper grid spacing affects final precision.
• Selection of method depends on land condition and purpose.

Conclusion

Determining volume in surveying is crucial in construction and earthwork projects. Methods like cross-section, grid, and contour are chosen based on site shape and size. Accurate measurement and suitable method ensure proper planning and cost estimation.