Calculating Embankment Volume: Formulas and Procedures Explained! Key Points for Choosing Between the Average Cross-Section Method and the Contour Method

Embankment work at construction sites is not merely transporting and piling soil; it is an extremely important process that requires meticulous management based on accurate volume calculations. With conventional surveying methods, cross-sections were created from multiple measurement points and volumes calculated from them, but this approach had many challenges and limitations. The more complex the site's topography, the more subjectivity enters into setting the measurement points, and errors accumulate in the final volume calculations. Furthermore, even when multiple surveyors perform the same work, results can vary, undermining consistency in management. However, by utilizing 3D point cloud data, this problem can be greatly improved. A 3D point cloud refers to coordinate information of millions to tens of millions of points acquired by laser scanning or drones; by analyzing this data with advanced processing techniques, more accurate and reliable volume calculations have become possible.

In this article, we provide a detailed explanation of the primary methods for calculating embankment volumes, their principles, formulas, application conditions, and practical points for choosing among them. Focusing on the average cross-section method and the contour method, we clarify the characteristics and applicable situations of each approach. From the three perspectives of pursuing accuracy, improving efficiency, and reducing costs, we explain the value of using 3D point clouds for volume calculation.

Conventional Methods for Calculating Embankment Volume and Their Challenges

Traditional embankment volume calculations have been carried out mainly by combining two methods: the cross-section method and the longitudinal-section method. In the cross-section method, multiple sections perpendicular to the construction alignment are established, the amount of soil in each section is calculated, and the total embankment volume is obtained by summing them. This approach is particularly effective for linear projects such as road construction and has been a reliable method adopted at many sites for many years. Generally, cross sections are set at intervals of 10 m to 20 m (32.8-65.6 ft), and the ground surface elevation at each location is estimated from multiple measurement points. However, when site topography is complex—for example, when valley terrain is intricately incised, existing structures are scattered, or rock is exposed—judgment is required to determine appropriate section locations.

At the stage of selecting cross-section locations, there is a serious problem in which the surveyor's experience and judgment can greatly affect the results. For example, if cross-sections are taken at 10 m (32.8 ft) intervals at one site but at 15 m (49.2 ft) intervals at another site, calculations may differ even for the same terrain. In the worst case, calculation errors can reach 5 percent or more, which in large-scale projects can translate into differences in earthwork volumes of hundreds of cubic meters or more. Furthermore, fine topographic variations between cross-sections cannot be captured by the cross-section method. When the ground surface changes in a wavy pattern, has locally deep depressions, or when fill has been placed to accommodate complex terrain such as alluvial fans, these features are not reflected in the calculations, resulting in systematic errors in the final volume.

The longitudinal section method suffers from the same problems. In this approach, cross-sections are drawn along the project alignment and volumes are calculated from terrain changes before and after construction. However, terrain changes in directions perpendicular to the alignment are difficult to capture accurately with these sectional methods. In particular, when the terrain changes abruptly near the edge of an embankment, accurately capturing those changes requires many measurement points, which greatly increases the surveying workload. Also, because the terrain can change slightly over time, it is difficult to verify that no unintended terrain changes occurred between the pre-construction and post-construction surveys.

Characteristics and Advantages of 3D Point Cloud Data

3D point cloud data has the potential to fundamentally solve the problems of conventional cross-section methods. A 3D point cloud is a digital recording of the coordinates of countless points in space, with each point containing three-dimensional information: X coordinate, Y coordinate, and Z coordinate (elevation). Such dense point cloud data can be efficiently acquired through a combination of laser scanners, cameras and IMUs (inertial measurement units) mounted on drones, and GNSS receivers. Importantly, this point cloud data captures even subtle variations in the ground surface. Terrain changes on the order of millimeters (inches) are also recorded and stored as data.

The greatest advantage of 3D point cloud data is its overwhelming density of measurement points. With traditional surveying, depending on site conditions, it was common to have tens to hundreds of measurement points per hectare. By contrast, a 3D point cloud can provide tens of thousands to hundreds of thousands of points, and in some cases millions of points, over the same area. This dramatic difference in density records all subtle changes in terrain, enabling volume calculations with much higher accuracy. In addition, once 3D point cloud data is acquired, it can be analyzed from various angles and viewpoints. The high reproducibility—different surveyors analyzing the same data will obtain the same results—is another significant advantage that conventional methods could not achieve. Because the objectivity of the data is guaranteed, if questions later arise about calculation results, the data can be easily reused for recalculation.

Furthermore, 3D point cloud data make comparisons over time very easy. By acquiring data at multiple points in time—such as the initial, mid, and completion stages of embankment work—and overlaying them, it becomes possible to understand in detail which parts of the embankment have progressed and by how much, or whether uneven construction has occurred. This kind of time-series analysis enables improved construction quality and early detection of unexpected problems. Moreover, if a quality issue is found, tracing its cause also becomes straightforward. For example, if it is discovered that the fill height at a certain location is below the planned level, data analysis can help infer whether the reason is equipment failure, operator error, or ground settlement.

On-site 3D Point Cloud Data Acquisition Methods

There are several options for efficiently acquiring 3D point cloud data at embankment construction sites. The first is the use of drones equipped with laser scanners. This approach has the major advantage of being able to survey large areas in a short time. Since drones can be operated without manual intervention, they can safely carry out measurements on steep slopes or in areas that are difficult to access. Typically, they are flown to an altitude of around 100 m (328.1 ft) above ground and pass over the construction area multiple times to acquire measurement data. Drone surveys can cover several hectares in a single day, making them especially time-efficient for large construction areas. However, drone surveys have the drawback of being susceptible to weather conditions. Flight can be difficult on rainy or windy days, and because the sun’s position differs significantly between morning and afternoon, shadow patterns change, which can affect the quality of the point cloud data.

The second option is the use of ground-based laser scanners. In this method, the scanner is mounted on a tripod and measurements are taken sequentially from multiple positions on site. Ground-based scanners have the advantage of higher accuracy than drones. Typically, errors are kept to a few centimeters or less (a few inches or less), and measurement accuracy at short ranges is particularly good. They can also obtain relatively accurate data around complex terrain and existing structures. However, because the area that can be covered in a single scan is limited, many measurement positions are required on large construction sites, which increases the time required for surveying. Furthermore, registration (the process of aligning multiple scans obtained from different positions to a unified coordinate system) is necessary, and this processing involves technical effort.

The third option is to use photogrammetry. By processing high-resolution images taken from multiple angles, it generates a 3D point cloud. This approach has the major advantage of being low-cost to implement, and with a drone equipped with a high-performance camera, sufficient accuracy can be achieved. However, on soil surfaces with uniform texture, extracting feature points can be difficult, which carries the risk of reduced measurement accuracy. In particular, newly deposited soil often has a uniform surface, and photogrammetry algorithms may fail to find feature points, so caution is required. The choice of the optimal method should be determined by comprehensively considering multiple factors such as project scale, site terrain, accuracy requirements, budget allocation, and weather conditions.

Process for calculating volume from 3D point cloud data

When 3D point cloud data is acquired, the subsequent data-processing stage becomes extremely important. First, the acquired point cloud data contains noise, and this noise must be removed. Noise refers to points generated by measurement errors rather than the actual ground surface. For example, points captured while a drone was vibrating, points reflected from low-reflectivity objects, points that captured particles such as atmospheric dust, or points where parts of existing structures were mistakenly recorded all correspond to noise. By properly removing these, the accuracy of subsequent processing can be greatly improved. Statistical methods that automatically detect outliers are often used for noise removal.

Next, it is necessary to distinguish between embankment areas and non-embankment areas. This is called the classification process, in which a computer either automatically extracts embankment regions from terrain features or an operator manually specifies the areas. Automatic classification is fast, but its accuracy is not always perfect, so verification is essential. Manual specification takes time but produces more reliable results. In practice, a hybrid approach—checking the results of automatic processing and making adjustments as needed—is the most efficient. For example, workers visually confirm the boundary lines of embankment areas and correct any discrepancies with the automatic classification results.

Once the embankment area has been determined, compare the two point cloud datasets—the pre-construction ground surface and the post-construction ground surface—and calculate the volume difference. This calculation is performed by aligning both point clouds in a unified coordinate system, determining the elevation difference at each point, and aggregating those differences on a grid. The calculation results can be obtained not only as the total volume of the embankment area but also as volumes for each sub-area, enabling a detailed understanding of construction progress. For example, by dividing the construction area into 5 m (16.4 ft) square grids and calculating the volume within each grid, it becomes immediately clear which parts of the work are falling behind.

Steps for Practical Application in the Workplace

When actually using 3D point cloud data at an embankment construction site, a step-by-step approach is effective. First, as the initial stage, record the pre-construction conditions in detail. Because the measurement accuracy at this stage will serve as the reference for all subsequent comparative calculations, it is necessary to exercise sufficient care. It is also important to perform multiple measurements and verify the consistency of the data. Recording all conditions—such as measurement time, weather conditions, and the drone's flight parameters—will be useful as a reference when conducting quality assessments later.

In the second stage, after construction begins, data are acquired periodically. Generally, measurements are taken when the embankment volume reaches a predetermined reference amount, or when it reaches progress milestones (for example, 30 percent, 60 percent, 90 percent of the plan). These periodic measurements allow verification of whether construction is proceeding according to plan. If deviations from the plan are detected, their causes can be identified and the construction plan adjusted. For example, if it is found that embankment progress in a particular area is substantially below the plan, an investigation can determine whether the cause is equipment placement issues or unexpected changes in soil properties, and appropriate countermeasures can be implemented.

In the third stage, the final volume is measured after construction is completed and compared with the design values. This comparison provides a basis for evaluating construction accuracy and, if necessary, making decisions about additional work or corrections. Typically, embankment construction requires accuracy within ±5 percent of the design values, but by utilizing 3D point cloud data this accuracy requirement can be reliably met. Furthermore, this data can be used to improve accuracy in future similar projects. By analyzing accumulated data to understand construction difficulty under specific terrain conditions, personnel allocation and scheduling for future projects can be made more rational.

Practical Tips for Improving Accuracy

To improve the processing accuracy of 3D point cloud data, there are several practical tips. The first is the installation of ground control points (GCPs). This involves placing multiple points on site with known coordinates and linking them to the measured data to enhance overall positional accuracy. Especially for large construction areas, the number and placement of these ground control points greatly affect data accuracy. Generally, it is recommended to place them at the four corners and the center of the construction area. Ground control points should be made of highly reflective materials and be clearly identifiable during measurement. In drone aerial surveys, especially over large areas, it has been reported that using multiple ground control points can improve accuracy by more than five times.

The second point is consideration of environmental conditions during measurement. Measuring at the same time of day standardizes the direction of sunlight and minimizes the effects of shadows. Also, measurements on rainy days or days with high humidity should be avoided. Under such conditions, lasers and cameras can operate unreliably, increasing the risk of reduced data quality. Furthermore, the ambient temperature during measurement also has an impact. In extremely low-temperature environments, a drone’s battery performance degrades and flight time is shortened. When planning measurements, it is important to fully take weather conditions into account and select the optimal measurement day.

The third is the selection of data processing software and its proper configuration. Point cloud processing software comes in a variety of products, each employing different algorithms. By selecting the software best suited to your site conditions and appropriately adjusting parameters, higher accuracy can be achieved. Comparing and reviewing results processed with multiple software packages is also an effective quality assurance method. For example, processing the same point cloud data with several software packages and checking the differences in calculation results can reveal that a particular software is not suited to the characteristics of the site.

The Path to Streamlining Embankment Volume Management

By utilizing 3D point cloud data, the entire process of managing embankment volumes can be greatly streamlined. Traditional methods could take anywhere from several days to several weeks from surveying to volume calculation. In contrast, leveraging 3D point clouds can significantly shorten the time from measurement to report creation. Furthermore, because the data are managed digitally, multiple stakeholders can share the same information, greatly improving the transparency of construction management. Project owners, designers, contractors, and supervisors can all access the same data and monitor construction progress in real time.

The benefits of such digitalization are not limited to mere time savings. Because it enables decision-making based on accurate and detailed data, it leads to optimization of construction planning and early detection of problems. In addition, the accumulated data can be used as benchmark information for future similar projects, contributing to overall quality improvement of operations. For example, if data on embankment settlement and compaction characteristics under specific terrain conditions are accumulated, prediction accuracy for new projects will improve.

Currently, many construction companies are advancing the adoption of embankment management systems that utilize 3D point cloud data. These companies are realizing substantial cost savings and quality improvements through automation of surveying, increased efficiency in data processing, and standardization of reporting processes. At your site as well, you can expect significant benefits by introducing such cutting-edge technology.

The Potential of High-Precision Measurement Using Smartphones

In recent years, devices that add high-precision positioning measurement functions to smartphones have emerged, and they are poised to revolutionize embankment measurement. Conventional drones and scanners were very expensive and their maintenance was complex, but smartphone-based solutions significantly lower the barriers to adoption. By leveraging equipment such as iPhone-mounted GNSS high-precision positioning devices, field workers can obtain position information with centimeter-level accuracy (half-inch accuracy) from devices small enough to carry. These mobile devices require relatively low initial investment, making it economically feasible to deploy multiple units.

By using such mobile devices at multiple measurement points and collecting their coordinate information, it is possible to achieve an information density equivalent to point cloud data. Furthermore, a workflow can be realized in which data is sent to the cloud in real time and processing results can be checked while on site. By leveraging smartphones, on-site staff who have not received special training can participate in measurement tasks, resulting in greatly increased on-site flexibility. In addition to improving work efficiency, worker safety is also enhanced. Measurements using conventional surveying instruments required carrying heavy equipment and working on hazardous slopes, but by utilizing mobile devices, lightweight and safer measurements can be achieved. Going forward, such mobile-based high-precision measurement systems are expected to become mainstream for embankment volume management.