Volume calculations made this easy! The new standard: 3D surveying × high-precision positioning

Table of Contents

• Traditional volume calculation methods and their challenges

• What is 3D surveying?

• What is high-precision positioning (RTK)?

• How volume calculations change with 3D surveying × high-precision positioning

• Use cases for volume calculations using 3D technology

• Volume calculations anyone can do with simple surveying using LRTK

• FAQ

Volume calculation is indispensable on construction sites and civil engineering works. For example, accurately knowing how much soil has been placed in embankment works (fill volume) or how much soil has been removed by excavation (spoil volume) is essential for construction planning and cost management. Measurement results also serve as documentation for as-built management and quantity assessment, so rapid and accurate volume calculations are required on site. In recent years, driven by the Ministry of Land, Infrastructure, Transport and Tourism’s *i-Construction* (ICT construction) initiative, digital surveying that leverages GNSS and 3D data has been gradually adopted in the field. As a result, volume calculations that used to rely on specialist technicians have become dramatically more efficient, and an era in which “anyone can do it easily” is emerging. This article reviews traditional volume calculation methods and their issues, and explains how the combination of 3D surveying and high-precision positioning changes volume calculations.

Traditional volume calculation methods and their challenges

In the past, measuring volume often required manual work by experienced surveyors. A typical method was to use surveying instruments on site to measure many cross sections of the terrain, then return to the office to calculate volumes from those cross-sectional areas and their spacings. In road works, the “average cross-section method” is often used, where the average of the cross-sectional areas is multiplied by the distance to calculate the earthwork volume. However, this method can fail to reflect irregularities between sections (for example, deep depressions), resulting in discrepancies from the actual volume. Achieving higher accuracy requires increasing the number of measurement points, which in turn increases the surveying workload.

Traditional surveying used optical instruments such as total stations and levels, typically requiring tripod setup and careful observations by multiple people. Transporting and setting up heavy equipment, securing personnel for measurements, and periodic calibration of instruments were all unavoidable. Of course, after surveying on site, data had to be taken back for drafting and calculation processing, so volumes could not be obtained immediately. As a simpler option, commercially available GPS receivers (handheld GNSS) could be used, but standalone positioning traditionally had errors on the order of 5–10 m (16.4–32.8 ft), making it unsuitable for volume calculations that require accuracy. In recent years, photogrammetry using drones and point cloud measurement with 3D laser scanners have appeared, but these also require specialist knowledge and time- and cost-intensive data processing, so they were not something easily used in daily fieldwork. Traditional methods thus had many issues in terms of manpower, accuracy, and post-processing, and the field has long awaited “a simpler and more accurate way to calculate volumes.”

What is 3D surveying?

3D surveying is a general term for technologies that measure the shape of objects or terrain in three dimensions and acquire them as digital 3D models (such as point cloud data). By measuring countless points that make up the surface of the target and assigning X, Y, and Z coordinates (including elevation) to each, complex shapes can be recorded in 3D exactly as they are in reality. Major methods include using laser scanners and reconstructing 3D models from multiple photographs via photogrammetry. Surface irregularities that were difficult to capture in traditional 2D drawings or cross-section sketches can be intuitively and precisely reproduced with high-density point cloud data obtained by 3D surveying. From the resulting point clouds, arbitrary cross-sections can be created later, and volumes and areas can be recalculated freely; the high reusability of the data is also highly valued.

3D surveying is rapidly expanding its use in civil engineering and construction, and it is useful in many stages from design and construction to maintenance. For example, if you aerially photograph a construction site with a drone and create a point cloud model of the terrain, you can instantly calculate fill and cut volumes from the difference between the ground surface before and after construction. Volume calculations that used to require a surveyor’s craftsmanship can be automatically obtained in software using a 3D model. Also, if point cloud data are stored as evidence for as-built management, future verification and information sharing with other industries become easier. Recently, smartphones with built-in LiDAR sensors have appeared, enabling 3D scanning over a range of several meters. However, standalone smartphone scans can exhibit gradual positional drift over wide areas; this weakness can be mitigated by combining them with the high-precision positioning described later.

What is high-precision positioning (RTK)?

High-precision positioning is a technique that uses satellite positioning systems (GNSS) to measure positions with centimeter-class errors. GNSS includes systems such as the U.S. GPS and Russia’s GLONASS and Japan’s quasi-zenith satellite systems; using dedicated receivers, latitude, longitude, and altitude can be obtained anywhere on Earth. However, normal positioning accuracy is on the order of several meters, so error-correction techniques are necessary for precise surveying. A representative method is RTK (Real Time Kinematic), which reduces positioning errors to the centimeter level in real time by using correction information from a base station and augmentation signals from satellites. In Japan, using the centimeter-level augmentation service (CLAS) distributed from the Ministry of Land, Infrastructure, Transport and Tourism’s “Michibiki” satellites makes RTK positioning possible even in mountainous areas outside of communications coverage. 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.

If you can obtain high-precision position information via RTK, various measurements can be automated from that data. For example, measuring multiple points allows you to instantly compute distances and enclosed areas, and if you can record ground elevation in detail, you can easily calculate volumes (earthwork) from differences relative to a reference surface. Area and earthwork calculations that used to require time and manual effort can now deliver results at the press of a button using high-precision GNSS. Also, unlike optical methods, GNSS surveying can obtain many points quickly while moving around without worrying about line-of-sight between survey points, making it advantageous on sites with many obstacles. For these reasons, RTK-GNSS-based positioning is highly practical in civil engineering and is becoming a new standard in surveying.

How volume calculations change with 3D surveying × high-precision positioning

Combining 3D surveying techniques with high-precision positioning dramatically increases the efficiency and accuracy of volume calculations on site. First, 3D surveying digitally captures the entire shape of the target without omission, enabling accurate volume calculation without the sampling approach used in the previously mentioned cross-section method. By incorporating RTK’s high-precision coordinates, you can provide that 3D data with an exact scale (dimensions) and positional information. Traditionally, photogrammetry required placing several known control points on site to scale the model. However, using RTK-capable drones or equipment can greatly reduce the labor of such control point surveys. By digitizing the entire process from 3D shape acquisition to volume calculation, even non-experts can obtain results in a short time.

So what specific benefits arise from 3D surveying × high-precision positioning? Here are the main advantages:

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

• Reduced personnel and effort: Many devices can be operated by one person, reducing the multiple-person tasks that were previously required. Small, mobile equipment makes it easy to proceed with other work between surveying tasks.

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

• Improved safety: Measurements can be taken without climbing or approaching dangerous slopes or large amounts of loose soil. Using drone aerial photography or long-range scanning allows you to secure worker safety while performing measurements.

• Frequent measurements possible: Because measurements are easy to perform, you can conduct frequent volume checks in line with construction progress. Grasping daily fill and excavation volumes enables more accurate construction management and quantity settlement.

• Immediate data sharing and accumulation: Digital measurement data can be uploaded to the cloud on site and easily shared with stakeholders. You can immediately reflect survey results in reports and accumulate them in a database for future analysis, enabling high-value operations.

In this way, the combination of 3D surveying and high-precision positioning enables volume calculations at speeds and accuracies far beyond conventional methods. It’s fair to say that the conventional wisdom on site is being rewritten.

Use cases for volume calculations using 3D technology

Digital volume calculations are being applied in a variety of situations. Here are some representative examples.

• Earthwork management in civil engineering: Measure fill and cut volumes on construction sites via drone surveys or ground scanning and check differences from the design plan. By comparing terrain models before and after construction to compute earthwork volume differences, you can immediately use the results as evidence for as-built management and quantity settlement.

• Inventory control at material yards: Regular measurement of stockpile volumes of gravel and crushed stone is important in material yards. 3D surveying lets you safely and accurately measure the volume of large stockpiles that people cannot climb. This improves inventory awareness and leads to better material ordering and cost control.

• Estimating sediment volume at disaster sites: In cases of heavy rain or landslides, you can quickly estimate the volume of displaced soil by comparing current point cloud data from drones with pre-disaster data to instantly calculate lost soil volume. This enables rapid planning of restoration works. There are actual cases where the volume of soil washed away from a collapsed slope was evaluated from before-and-after data, allowing accurate judgment of the scale of emergency works.

• Earthwork management in building and land development: There is demand to measure volumes of excavated holes for foundations and fill volumes at development sites. Where site supervisors previously made visual estimates, introducing 3D measurement allows construction management based on accurate figures. This reduces rework from excesses or shortages, contributing to shorter schedules and cost reductions.

Other applications include land development in agriculture and estimating excavation volumes at mining sites; the uses of volume calculation are diverse. As easy and accurate 3D measurement becomes more accessible, decision-making in these situations is becoming more data-driven.

Volume calculations anyone can do with simple surveying using LRTK

To let sites easily reap the benefits of the latest technology, an approach called “simple surveying with LRTK” has emerged. LRTK is a small RTK-GNSS receiver that can be attached to a smartphone, a revolutionary device that realizes centimeter-class positioning that previously required specialized equipment with “one smartphone per person.” By attaching the dedicated device to a smartphone and launching an app, you can perform surveying while obtaining high-precision real-time position coordinates. 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 perform distance, area, and volume calculations. For example, if you encircle a spoil pile with multiple positioning points, you can calculate an approximate volume on the spot. You can also supplement position information to point cloud data captured by the smartphone’s camera or LiDAR and generate detailed 3D models in the cloud to obtain precise volumes. The major strength of LRTK simple surveying is that this series of tasks can be completed on site in real time. The convenience of being able to measure whenever you want brings new agility to daily construction management.

Furthermore, LRTK systems make it easy to upload and share acquired data to the cloud. You can check measurement results at the office immediately and share information with stakeholders, improving the speed of reporting and directives. On dedicated cloud services, you can manage lists of survey data and output to CAD drawings, enabling processes that were once analog to be completed digitally. It is revolutionary that you can do so much with just a smartphone, without expensive surveying instruments or specialized 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 and high-precision volume calculations that LRTK makes possible on site—you will surely be impressed by its ease of use and accuracy.

FAQ

Q1. What is volume calculation? Why is it important? A1. Volume calculation is the process of determining the internal capacity (volume) of a three-dimensional object or terrain. In civil engineering and construction, it is particularly important for calculating the amount of soil involved in fills and excavations (so-called earthwork). Knowing accurate volumes provides the basis for estimating required soil transport and truck counts, for quantity management, and for cost calculations. Errors in volume calculation can lead to material procurement mistakes and cost overruns, so performing accurate and prompt calculations is essential for site operations.

Q2. What were the challenges of traditional volume calculation methods? A2. Traditionally, surveyors used total stations and the like to create multiple cross-sections of terrain and calculated volumes from those cross-sectional areas. This method required time and effort for measurement and drafting, and it could not fully capture irregularities between sections, limiting accuracy. Large sites often required multiple personnel for surveying, resulting in high labor costs. Furthermore, the numbers obtained could not be produced immediately on site and needed post-processing back at the office. These challenges of effort, accuracy, and immediacy existed with conventional methods.

Q3. What is 3D surveying? A3. 3D surveying is a method for measuring the shape of a target in three dimensions and digitizing it. Representative examples include point cloud data obtained by laser scanners or drone photogrammetry. By recording an object as a collection of many points, you can capture terrain and structures in their entirety in three dimensions. 3D surveying can model complex shapes that were difficult to handle with traditional planar surveying, and you can calculate volumes and areas from those models.

Q4. What is RTK? A4. RTK (Real Time Kinematic) is a technique that corrects satellite positioning errors in real time to measure positions with centimeter-level accuracy. Ordinary GPS has errors on the order of meters, but RTK uses correction information from base stations and signals from quasi-zenith satellites to greatly reduce those errors. This allows you to know your current position with only a few centimeters of deviation from map coordinates. High-precision RTK positioning has revolutionized the setting out of reference points and as-built management in civil surveying and has become an indispensable technology for precise volume calculations.

Q5. Is a drone necessary for volume measurement? A5. A drone is not always necessary. Drones have the advantage of rapidly photographing large areas from the air, making them suitable for earthwork measurements on large sites, but for narrow areas or indoor environments, ground-based measurements can be effective. For example, you can use tripod-mounted laser scanners or close-range 3D scans from a smartphone to determine volumes. In short, measurement methods other than drones can be selected depending on the scale and situation of the site. Using portable surveying tools like LRTK, you can efficiently obtain high-precision volume data even by ground-based manual measurement.

Q6. Can surveying be done without specialized knowledge or qualifications? A6. Recent simplified surveying systems are designed to be usable even by non-specialist surveyors. As long as you learn the basic operating procedures, the systems will automatically acquire and process data without complicated settings. However, it is desirable to know some points for obtaining more accurate results (such as correct instrument setup and understanding error factors). That said, advanced skills and adjustments required by traditional optical surveying instruments are not necessary, and the latest simple surveying tools are characterized by being intuitive for anyone to use. In fact, many products are operated like smartphone apps, allowing site personnel to start using them after short training.

Q7. How accurate can volume measurements be? A7. Accuracy depends on the equipment and methods used, but when using RTK-capable surveying instruments, point coordinates can be obtained with errors of only a few centimeters in both horizontal and vertical directions. Therefore, calculated volumes can theoretically be expected to have errors on the order of a few percent. In practice, accuracy varies somewhat depending on the shape of the target, data density, and satellite reception environment. However, compared to conventional cross-section methods, the much more detailed shape capture significantly reduces human error and oversight. In summary, volume calculations using the latest 3D surveying + RTK can be expected to provide earthwork quantities with practically sufficient accuracy for most uses.

Q8. What is LRTK? A8. LRTK is the name of a smartphone-compatible small positioning device and system developed by Reflexia. It consists of an ultra-compact RTK-GNSS receiver (LRTK Phone device) that can be attached to a smartphone and a dedicated app; with this setup, a smartphone quickly becomes a surveying instrument with centimeter-level accuracy (cm level accuracy (half-inch accuracy)). The device receives correction information via the internet and signals from satellites to enable real-time high-precision positioning. Measured point data can be managed and shared via cloud services, and the app also includes functions to calculate distance, area, and volume directly. “Simple surveying with LRTK” refers to the surveying method anyone can perform easily using the LRTK device and a smartphone, lowering the technical barrier and improving site productivity.