Table of contents

• Traditional volume calculation methods and their challenges

• What is 3D surveying?

• What is high-precision positioning (RTK)?

• How volume calculation changes with 3D surveying × high-precision positioning

• Use cases for volume calculation using 3D technology

• Volume calculation anyone can do with simple surveying using LRTK

• FAQ

Volume calculation is indispensable on construction sites and civil engineering projects. For example, accurately knowing how much fill was placed in earthworks (fill volume) or how much material was excavated and removed (cut volume) is essential for construction planning and cost control. Measurement results serve as documentation for completion management and progress-based payment calculations, so quick and accurate volume calculation is required on site. In recent years, with the push for *i-Construction* (ICT construction) by the Ministry of Land, Infrastructure, Transport and Tourism, digital surveying that uses GNSS and 3D data is becoming widespread on sites. As a result, volume calculations that once relied on specialist technicians are being dramatically streamlined, and an era in which “anyone can easily” perform them is approaching. This article reviews traditional volume calculation methods and their challenges, and explains how combining 3D surveying and high-precision positioning changes volume calculation.

Traditional volume calculation methods and their challenges

Measuring volume used to often require manual work by experienced surveyors. A typical approach was to take multiple cross-sections of the terrain in the field using surveying instruments, then return to the office and calculate volume from those cross-sectional areas and the intervals between them. For road works and the like, the “average cross-section method” is used: multiply the average of the cross-sectional areas by the distance to compute earthworks volume. However, this method can fail to capture undulations between cross-sections (for example, deep depressions), leading to discrepancies from the actual volume. Achieving accuracy requires increasing the number of measurement points, which in turn increases the workload of surveying.

Traditional surveying used optical instruments such as total stations and levels, typically requiring tripod setup and careful observations by multiple people. Transporting and installing heavy equipment, securing personnel for measurements, and regularly calibrating instruments were all necessary. After field surveying, data had to be taken back to the office for drafting and calculations, so volumes were not available immediately. As a simple alternative, commercially available GPS receivers (handheld GNSS) could be used, but standalone positioning traditionally had errors of about 5-10 m (16.4-32.8 ft), making them unusable for accuracy-demanding volume calculations. More recently, photogrammetry using drones and point cloud measurement with 3D laser scanners have emerged, but these also require specialist knowledge and time- and cost-intensive data processing, so they have not been something easily used for routine site work. Thus, conventional methods had many issues in terms of manpower, accuracy, and post-processing, and sites have long awaited “an easier and more accurate way to calculate volume.”

What is 3D surveying?

3D surveying is a general term for technologies that measure the shape of objects and terrain in three dimensions and acquire digital 3D models (such as point cloud data). By measuring countless points that make up an object’s surface and assigning X, Y, and Z coordinates (including elevation) to each, complex shapes can be recorded in 3D exactly as they are. Main methods include using laser scanners or reconstructing 3D models from multiple photos via photogrammetry. Terrain irregularities that were difficult to grasp from conventional 2D drawings or cross-section sketches can be intuitively and precisely reproduced with high-density point cloud data obtained by 3D surveying. From the point cloud, you can later create arbitrary cross-sections, recalculate volumes and areas, and generally enjoy high data reusability.

3D surveying is rapidly being adopted in civil engineering and construction, proving useful from design and construction through to maintenance. For example, if a construction site is aerially photographed by drone and a terrain point cloud model is created, the fill and cut volumes can be immediately calculated from changes in the ground surface before and after construction. Volume calculations that once required a surveyor’s craft can now be obtained automatically on software using 3D models. Also, if point cloud data are saved as evidence for completion control, future verification and information sharing with other industries become easy. Recently, smartphones equipped with LiDAR sensors have appeared, enabling 3D scanning over ranges of several meters with familiar devices. However, smartphone-only scans can gradually drift when measuring wide areas, and this weakness can be offset by combining them with the high-precision positioning described below.

What is high-precision positioning (RTK)?

High-precision positioning refers to techniques that measure position using satellite positioning systems (GNSS) with centimeter-level errors. GNSS includes systems such as the U.S. GPS and Russia’s GLONASS as well as Japan’s quasi-zenith satellite system, and with dedicated receivers you can obtain latitude, longitude, and altitude anywhere on Earth. However, ordinary positioning accuracy is on the order of several meters, so error correction techniques are required for precise surveying. A representative method is RTK (Real Time Kinematic), which uses correction information from a base station and augmentation signals from satellites to reduce positioning errors in real time to a few centimeters. In Japan, using the centimeter-level augmentation service (CLAS) broadcast from the “Michibiki” quasi-zenith satellites operated by the Ministry of Land, Infrastructure, Transport and Tourism makes RTK positioning possible even in mountain areas outside conventional communication zones. By employing such advanced GNSS correction technologies, you can measure your current position with accuracies of about 2-3 cm (0.8-1.2 in) horizontally and about 3-4 cm (1.2-1.6 in) vertically.

With high-precision position information from RTK, various measurements can be automated from that data. For example, measuring multiple points allows you to instantly calculate distances between them and the area enclosed, and if you record ground elevations in detail, you can easily compute volumes (earthworks) from differences against a reference surface. Area calculations and earthwork estimates that once required manual labor and time can now produce results at the push of a button using high-precision GNSS. Also, GNSS surveying allows movement and measurement without needing line-of-sight between points as optical methods do, enabling rapid acquisition of many points even in sites with many obstacles. For these reasons, RTK-GNSS positioning is highly practical in civil engineering and is becoming the new standard for surveying.

How volume calculation changes with 3D surveying × high-precision positioning

Combining 3D surveying and high-precision positioning dramatically improves the efficiency and accuracy of on-site volume calculations. Because 3D surveying can digitize the entire shape of the target without omission, it enables accurate volume calculation without the sampling limitations of the cross-section method mentioned earlier. Incorporating RTK’s high-precision coordinates gives the 3D data an exact scale (dimensions) and position information. Traditionally, photogrammetry required placing several known control points on site to scale the model, but using RTK-enabled drones or equipment can largely eliminate the need for such control point surveying. By digitizing the entire process from 3D shape acquisition to volume computation, results can be obtained in a short time even without specialized surveying skills.

What concrete benefits arise from 3D surveying × high-precision positioning? Key advantages include:

• Significant efficiency gains in measurement work: data collection can be completed in a short time even on large sites. Earthwork measurements that once took half a day to several days can be finished quickly with drone flights or scans.

• Reduction in personnel and labor: many devices can be operated by one person, reducing the multi-person work previously required. Small, highly mobile equipment makes it easy to continue other tasks while surveying.

• High-precision results: high-density information such as point cloud data improves volume calculation accuracy. With RTK suppressing positional drift, the obtained volume values are more reliable and easier to reconcile with design values.

• Improved safety: dangerous slopes or areas with large amounts of soil can be measured without directly climbing or approaching them. Drone aerial photography or long-range scanning can ensure both worker safety and measurement.

• Ability to measure frequently: the ease of measurement enables frequent volume checks in line with construction progress. Monitoring daily fill and excavation volumes allows more accurate construction management and progress-based settlements.

• Immediate data sharing and accumulation: digital measurement data can be sent to the cloud or shared with stakeholders on the spot. You can quickly reflect survey results in reporting materials, or store them in a database for future analysis, enabling high-value-added operations.

In this way, combining 3D surveying and high-precision positioning makes it possible to perform volume calculations at speeds and accuracies that far surpass conventional methods. It is fair to say that the conventional wisdom on site is being rewritten.

Use cases for volume calculation using 3D technology

Digital volume calculation is expanding across many scenarios. Here are some representative examples.

• Earthwork management in civil construction: measure fill and cut volumes on construction sites with drone surveys or ground scans, and check differences from design plans. Comparing terrain models before and after construction and calculating volumetric differences can be used immediately as grounds for completion control and progress-based settlement.

• Inventory management in material yards: in stockyards for gravel and crushed stone, periodically measuring the volume of stockpiles is important. 3D surveying allows safe and accurate measurement of large piles that people cannot climb, improving inventory accuracy and leading to better material ordering and cost management.

• Estimating sediment volume at disaster sites: in situations where heavy rains or landslides have caused slope collapse, you can quickly estimate lost soil volume by comparing post-event point cloud data from drones with pre-event data. This enables rapid recovery work planning. There are cases where evaluating sediment outflow based on before-and-after slope data accurately guided the scale of emergency works.

• Soil volume management in building and site development: in building sites and residential development, there is demand to measure volumes of foundation excavations and fill placement. Introducing 3D measurement enables construction management based on accurate figures rather than supervisors’ visual estimates, reducing rework for excess or deficiency and contributing to shorter schedules and cost savings.

Beyond these, volume calculation is used in many fields such as land development in agriculture and extraction estimation at mining sites. As convenient and accurate 3D measurement becomes more accessible, decision-making in these situations is becoming increasingly data-driven.

Volume calculation anyone can do with simple surveying using LRTK

A recent approach that lets sites easily enjoy the benefits of the latest technologies is simple surveying with LRTK. LRTK is a small RTK-GNSS receiver that can be attached to a smartphone, a revolutionary device that realizes centimeter-level positioning—formerly requiring special equipment—with “one smartphone per person.” Just attach the dedicated device to a smartphone and launch the app to perform surveying while obtaining high-precision coordinates in real time. The device fits in a pocket and has a built-in battery, making it ideal for surveying while moving around the site.

The dedicated LRTK app automatically records the coordinates of positioned points and includes functions to immediately measure distances, areas, and volumes. For example, surrounding a pile of soil with multiple positioned points allows you to estimate its approximate volume on site. You can also augment point cloud data obtained by a smartphone camera or LiDAR with position information, generate a detailed 3D model in the cloud, and compute an accurate volume. The ability to complete this workflow in real time on site is a major strength of simple surveying using LRTK. The convenience of being able to measure whenever you want adds new agility to everyday construction management.

Furthermore, the LRTK system makes it easy to upload acquired data to the cloud and share it. You can check field measurements on the office PC or instantly share information with stakeholders, improving the speed of reporting and instructions. The dedicated cloud also allows list management of survey data and export to CAD drawings, enabling a fully digital workflow that replaces traditional analog processes. It is groundbreaking that this much can be done with just a smartphone rather than expensive surveying equipment or special software.

With the advent of simple surveying using LRTK, the technology of 3D surveying × high-precision positioning is becoming accessible to everyone. This new surveying style will increasingly become the new standard in site management. Experience the easy, high-precision volume calculation that LRTK enables on your site—you’ll likely be surprised by its usability and accuracy.

FAQ

Q1. What is volume calculation and why is it important? A1. Volume calculation is determining the volume of three-dimensional objects or terrain. In civil engineering and construction, it is particularly important for calculating the amount of soil moved by filling or excavation (so-called earthworks). Knowing accurate volumes forms the basis for estimating required hauling volumes and truck counts, progress management, cost calculations, and other planning. Errors in volume calculation can lead to material procurement mistakes or cost overruns, so performing them accurately and quickly is essential for site operations.

Q2. What challenges did traditional volume calculation methods have? A2. Traditionally, surveyors created multiple cross-sections of the terrain with total stations and similar instruments and calculated volume from the areas of those sections. This method required time and effort for measurement and drafting, and could not fully capture undulations between sections, limiting accuracy. Large sites often required multiple personnel for surveying, increasing labor costs. Also, the obtained figures could not be produced instantly on site and required office-based processing. These issues of manpower, accuracy, and immediacy were inherent in traditional methods.

Q3. What is 3D surveying? A3. 3D surveying is a method of measuring the shape of targets in three dimensions and converting them into digital data. Representative examples include point cloud data from laser scanners and drone photogrammetry. Because objects are recorded as collections of many points, you can capture terrain and structures comprehensively in 3D. Complex shapes that were difficult to handle with traditional planar surveying can be modeled with high precision using 3D surveying, from which volumes and areas can be calculated.

Q4. What is RTK? A4. RTK (Real Time Kinematic) is a technique that corrects satellite positioning errors in real time to measure position with centimeter-level accuracy. Ordinary GPS has errors of several meters, but RTK greatly reduces those errors using correction information from base stations and signals from quasi-zenith satellites. This enables knowledge of your current position with only a few centimeters of deviation relative to map coordinates. High-precision RTK positioning has revolutionized stakeout and completion control in civil surveying and is indispensable for precise volume calculations.

Q5. Is a drone necessary for volume measurement? A5. Not necessarily. Drones have the advantage of quickly photographing large areas from above and are suitable for measuring earthworks on large sites, but for narrow areas or indoor spaces, ground-based measurements can be effective. For example, tripod-mounted laser scanners or close-range 3D scanning with a smartphone can also be used to determine volumes. In short, measurement methods other than drones are available depending on site size and conditions. Portable surveying tools like LRTK enable efficient, high-precision volume data acquisition even when measuring from the ground.

Q6. Can surveying be done without specialist knowledge or qualifications? A6. Recent simple surveying systems are designed to be usable even by non-specialist surveyors. Once you learn the basic operation steps, the system can automatically acquire and process data without complicated settings. That said, it is desirable to know some points for obtaining more accurate results (such as correct instrument setup and understanding error factors). Nevertheless, unlike traditional optical surveying instruments, advanced skills and adjustments are not required, and the latest simple surveying tools are intuitive for anyone to use. Indeed, some products operate like smartphone apps, and site personnel can begin using them after short training sessions.

Q7. How accurate can volume measurements be? A7. Accuracy depends on the equipment and method used, but with RTK-capable surveying instruments, point coordinates can be acquired with errors of only a few centimeters in both horizontal and vertical directions. Therefore, calculated volumes can theoretically be expected to fall within a few percent error, yielding high accuracy. In practice, accuracy varies somewhat with the shape of the target, data density, and the satellite reception environment. However, compared to traditional cross-section methods, 3D techniques capture shapes far more precisely, greatly reducing human error and oversights. In summary, volume calculations using the latest 3D surveying plus RTK can be considered to provide practically sufficient accuracy for earthwork management.

Q8. What is LRTK? A8. LRTK is the name of a smartphone-sized positioning device and system developed by Refuxia. It consists of an ultra-compact RTK-GNSS receiver that can be attached to a smartphone (the LRTK Phone device) and a dedicated app. With it, a smartphone quickly becomes a surveying instrument with centimeter accuracy. It receives correction information over the Internet and signals from satellites to enable real-time high-precision positioning. Positioned point data can be managed and shared via cloud services, and the app also provides distance, area, and volume calculation functions. “Simple surveying with LRTK” refers to this surveying method using the LRTK device and a smartphone, lowering the technical barrier and improving on-site productivity, and it is attracting attention as a solution.