Table of Contents

• Scenes where volume calculation is needed and its importance

• Traditional volume calculation methods and their challenges

• What is 3D measurement? Overview of a new surveying method

• Benefits of volume calculation using 3D measurement

• The role and importance of high-precision positioning (RTK)

• Procedure for volume calculation using 3D measurement

• Use cases across various fields

• Conclusion: The future brought by 3D measurement and high-precision positioning

• FAQ (Frequently Asked Questions)

Scenarios where volume calculation is needed and its importance

In civil engineering and construction sites, volume calculations of terrain and structures are indispensable. For example, understanding how much soil has been placed in earthworks (the volume of fill) or how much soil has been removed by excavation (the volume of cut) is essential for construction planning and cost control. Accurately calculating volumes allows precise estimation of required fill materials and the number of dump trucks. Furthermore, in as-built verification (the process of checking whether the completed shape matches the design), measuring the volume difference between fill and cut is used to check discrepancies between plans and actual results. These volume measurement results are also important as reporting materials to clients and as the basis for progress-based payment settlements. If there are errors in volume calculation, it can lead to various problems such as delays due to incorrect material ordering, cost overruns, or rework due to inconsistencies with the design. Therefore, the field strongly demands rapid and accurate volume calculations. Especially in recent years, with the Ministry of Land, Infrastructure, Transport and Tourism promoting i-Construction (ICT construction), digitization and efficiency of surveying have become emphasized. On-site 3D data and the use of GNSS (satellite positioning) that can be measured instantly are key to supporting construction management DX (digital transformation). In this way, volume calculation plays an extremely important role in site planning and management.

Traditional volume calculation methods and their challenges

Although volume measurement is crucial, the work was traditionally far from simple. Conventional surveying typically uses optical total stations or levels, relying on manual measurements in the field and then calculating volumes back at the office based on drawings. Naturally, volumes are not immediately known on site; only after bringing the measured data back can quantities be calculated, causing a time lag before construction decisions can be made. For example, methods such as measuring multiple cross-sections and calculating volume by the average-end area method, or taking survey points in a mesh and averaging heights per grid to determine volume, are used. These tasks require skilled technicians and considerable effort, and measurement and calculation take time. In particular, total station surveying involves heavy equipment and effort for setup and line-of-sight maintenance, typically requiring multiple personnel. Regular maintenance and calibration of equipment are also indispensable. On the other hand, attempting volume calculation using GPS positioning as an easy method faces the problem that ordinary standalone positioning can produce errors of 5-10 m (16.4-32.8 ft), which is insufficient for civil surveying accuracy. Recently, photogrammetry using drones and point cloud measurement using 3D laser scanners have emerged, but these often require dedicated operators and high-performance PCs for data processing, making them costly and time-consuming and not easily adoptable for routine fieldwork. In short, conventional methods had many challenges in terms of manpower, accuracy, and post-processing, and there was a strong demand for a method to measure volumes more easily and accurately on site.

What is 3D measurement? Overview of a new surveying method

Against this background, a new surveying method that performs 3D measurement of terrain has emerged. As the name implies, 3D measurement is a method of measuring objects three-dimensionally to obtain point cloud data or 3D models. Traditionally, shapes were understood fragmentarily by measuring point by point, but 3D measurement acquires the shape of the entire target area with high-density data. Specifically, common technologies include using laser scanners (LiDAR) to measure many laser points or reconstructing 3D models from drone aerial photos via photogrammetry. Recently, it has also become possible to easily perform 3D scanning using LiDAR sensors or high-performance cameras built into smartphones and tablets. Point clouds and 3D models obtained by 3D measurement represent surfaces of terrain and structures with countless points or meshes (triangulated networks). Using these, you can analyze the shape differences needed for volume calculations in detail. For example, you can overlay the current ground model with the design model to calculate differential volumes, or automatically measure fill and cut volumes relative to a reference plane. The acquired 3D data can be processed and analyzed with CAD software on a PC or with dedicated tools, and can also be shared and intuitively reviewed via cloud-based 3D viewers. The ability to visually "render visible" the amount of fill or excavation, which is hard to grasp from numbers alone, is another major advantage of 3D measurement.

Benefits of volume calculation using 3D measurement

By utilizing 3D measurement technology, the process of volume calculation gains several advantages that conventional methods do not offer. The main benefits are summarized below.

• High accuracy: Because the entire terrain can be measured at high density, there are fewer oversights or omissions compared to cross-section methods, enabling more accurate volume calculations. There is no need to interpolate between measured points or rely on experience, reducing errors.

• Improved work efficiency: Large areas can be measured in a short time, and data processing and volume calculation are often automated by software, making the process markedly faster than before. This reduces cumbersome manual calculation work, leading to savings in labor costs and time.

• Improved safety: Even steep slopes or unstable fills where people cannot safely enter can be measured remotely with 3D scanning, safely capturing the shape. This reduces risky measurement work at heights or dangerous locations and lowers the risk of occupational accidents.

• Intuitive visualization: The obtained 3D models can be used to display volume differences in color or explain to stakeholders with three-dimensional visuals. Information that is hard to convey with text or tables can be shared visually, facilitating smoother communication.

• Data reusability: Recorded point cloud data is useful for future verification or other analyses. Once surveyed, you can later create additional cross-sections or calculate volumes for other areas, allowing repeated effective use of the data.

The role and importance of high-precision positioning (RTK)

One of the technologies supporting high-precision volume calculation by 3D measurement is high-precision positioning. Using satellite positioning (GNSS) you can measure your location (latitude, longitude, altitude) anywhere on Earth, but ordinary GPS has errors of several meters and cannot be used for precise surveying. The correction technology used for this is RTK (Real Time Kinematic). RTK-GNSS surveying uses correction data from a base station and signals provided by the quasi-zenith satellite "Michibiki" (such as CLAS in Japan) to improve positioning accuracy in real time to the order of a few centimeters. This allows GNSS to obtain three-dimensional coordinates of points with accuracy comparable to optical surveying instruments. Furthermore, GNSS can observe height (elevation) simultaneously, so it is possible to calculate cut and fill volumes from differences relative to a reference elevation without performing separate leveling. High-precision positioning from RTK is indispensable for giving the 3D measurement data a correct scale and alignment. For example, in drone photogrammetry, using known points measured in advance by RTK as references ensures dimensional accuracy of the model. Similarly, combining RTK positioning information with scanned point clouds makes the acquired point cloud have absolute coordinates (real-world coordinate systems). This enables volume calculations that accurately reflect ground elevation data. In addition, because the acquired data shares the same coordinate system as existing design data or other survey data, differential calculations with the design and comparisons of data from multiple time points can be performed smoothly. High-precision positioning is a key technology that maximizes the value of 3D measurement and makes its results dependable.

Procedure for volume calculation using 3D measurement

Finally, let’s review the general flow of calculating volume using 3D measurement.

• Confirm and prepare the measurement area: First, identify the area or object for which you want to measure volume and, if necessary, plan the survey. If flying a drone, prepare a flight plan; for ground scanning, consider the measurement start positions and routes. Also prepare any reference elevations (e.g., surrounding ground surface) or comparison data (e.g., as-built design drawings) if available.

• On-site data acquisition: Perform 3D measurement on site. For drone photogrammetry, photographs are taken during automatic flight; for laser scanning, the scanner is rotated or moved toward the target to acquire point clouds. Recently, solutions have appeared that attach RTK-capable devices to smartphones and generate point clouds automatically from camera footage simply by walking around. The important points are to cover the target fully and, when necessary, measure from multiple directions to prevent data gaps.

• Data processing and 3D model generation: Generate a 3D model (point cloud or mesh) from the acquired data. For drone photos, dedicated software or cloud services stitch photos into a point cloud; for laser or smartphone scanning, acquired data is similarly converted into point clouds automatically. If high-precision positioning information is included, the model will be assigned the correct scale and coordinates at this stage. The completed 3D model faithfully reproduces the current terrain and target object.

• Volume calculation: Calculate volume from the generated 3D data. There are several calculation methods. One is to compute the volume between a specified reference plane (horizontal plane or an arbitrary elevation) and the model surface. If you specify the measurement area with a polygon, the software can automatically quantify the amount of rise (or excavation) in that region. Another method is to compute the difference in volume between the current model and another model. For example, by calculating the difference between pre- and post-construction terrain models or between a design model and the current model, you can evaluate whether the prescribed excavation/fill volumes have been achieved. In any case, you can select the required area in the software and often compute volumes with a single click.

• Review and utilize results: Verify the calculated volume values. In addition to the numerical volume (cubic meters), if possible display where and how much fill or cut occurred on the 3D model with color gradation to intuitively grasp excesses or shortages. You can also compile these results into drawings or reports to share with stakeholders or decide whether additional on-site surveying is required. With systems that provide results in real time, the information can be used immediately for construction management decisions on site.

Use cases across various fields

Volume calculation using 3D measurement is being applied in many areas beyond civil engineering sites. Some examples are introduced below.

• Civil engineering and construction: Measurement of fill and cut volumes in roadworks and land development, management of muck (excavated material) in tunnel excavation, verification of soil volumes in dams and levees, and use across many civil works. It contributes to enhanced as-built management and streamlined progress-based settlement.

• Mining and plant industries: In mines and quarries, the volumes of extracted ore or aggregate stockpiles are regularly measured to assist inventory management and production tracking. Ore pile volumes that were once measured by people in dangerous conditions can now be safely measured by drones or ground LiDAR.

• Disaster response: 3D measurement is used to rapidly assess volumes of debris from landslides or volcanic eruptions. Measuring the volume of collapsed slopes or sediment accumulation in rivers helps plan earthmoving work and consider measures to prevent secondary disasters. In large-scale disasters, three-dimensional modeling of damage can also serve as reference material for restoration planning.

• Environmental and infrastructure management: Needs for volume measurement exist in areas such as landfill capacity management, estimation of stored grain or feed in agriculture, and measurement of dredged materials in ports. Regular 3D measurement makes it possible to monitor long-term changes and formulate efficient operation plans. Thus, 3D measurement and volume calculation technologies contribute to improved efficiency and safety in various field applications.

Conclusion: The future brought by 3D measurement and high-precision positioning

The fusion of 3D measurement technology and high-precision positioning technology is set to dramatically change the field of volume calculation. Precision surveying that once relied only on specialist surveyors can now be made efficient and less labor-intensive by digital tools. As described in this article, using 3D scanners, drones, and RTK-GNSS enables rapid acquisition of large amounts of data and accurate volume calculation. This not only speeds up operations but is transforming the nature of surveying itself. Recently, solutions enabling anyone to survey easily using smartphones have also emerged. For example, the simplified surveying with LRTK, where a pocket-sized high-precision GNSS receiver is attached to a smartphone, allows on-site 3D measurement and volume calculation without complicated operations. By pointing to the area to be measured on the screen and pressing a button, area and soil volume are instantly calculated on site, making the system easy for even inexperienced technicians to use. After a short training course, anyone can capture wide-area point clouds with one hand and check as-built shapes in 3D. Using these latest tools, on-site surveying will become increasingly simple and accurate. As DX in surveying tasks such as volume calculation advances, further sophistication and labor savings in construction management are expected. Moreover, amid concerns about the aging and shortage of experienced survey technicians, leveraging digital technologies enables efficient surveying that does not rely on experience or intuition, thereby contributing to the sustainability of future site management.

FAQ (Frequently Asked Questions)

Q: How accurate can volume calculations using 3D measurement be? A: Accuracy depends on the equipment and conditions used, but 3D measurement combined with RTK-GNSS can achieve horizontal positions on the order of a few centimeters (a few inches) and vertical errors on the order of a few centimeters to a dozen or so centimeters (a few inches to several inches). Capturing the entire terrain in detail dramatically improves the accuracy of volume calculations. However, measurement conditions (for example, dense vegetation) and the size of the survey area also affect accuracy, so it is important to add measurement points as needed and perform accuracy verification.

Q: What equipment and software are required to perform volume calculation by 3D measurement? A: Generally, 3D laser scanners, drones (+ high-precision GPS), or smartphone-based 3D scanning devices can be used. Software (dedicated apps or cloud services) is also needed to process captured photos or point cloud data, but recently integrated solutions that can compute results in real time on site have appeared. Choose equipment that best fits the intended use and scale.

Q: Can it be used without specialized knowledge? A: In the past, expertise in surveying and photogrammetric analysis was indispensable, but current tools have become more user-friendly. Once you learn the basic procedures, advanced calculations are handled automatically by the software. Systems like LRTK are designed for intuitive operation so anyone can start surveying quickly. However, it is advisable to have knowledge of safe drone operation and basic training in data interpretation.

Q: How long does it take from measurement to results? A: It varies depending on the measurement area and method. For drone photogrammetry, flight time may be 10–20 minutes, and data processing can take tens of minutes or more. On the other hand, a simple ground scan can complete point cloud acquisition in a few minutes, and some systems can display volume calculation results on site. In any case, it is significantly shorter than traditional manual measurement and calculation.

Q: Is the investment cost worthwhile? A: Initial investment includes equipment costs and software fees, but the benefits can outweigh these. Time savings in surveying, reduced personnel costs, prevention of rework due to calculation errors, and shortened construction schedules thanks to rapid as-built recognition yield significant advantages. Additionally, inexpensive devices and cloud services have become more available recently, making adoption feasible even for small sites.