Embankment Volume Calculation: Methods, Errors, and 3D Workflow | LRTK

Table of Contents

• Why calculating embankment volume is important

• Traditional methods for calculating embankment volume

• Issues arising from traditional methods

• Basic knowledge of as-built management and earthwork quantity management

• The new standard brought by ICT and 3D surveying

• What is simple surveying with LRTK?

• FAQ (Frequently Asked Questions)

Why calculating embankment volume is important

In civil and construction works, "embankment" refers to raising the ground with soil to a prescribed height, and accurately calculating and understanding its volume is critically important. Misjudging the quantities of embankment or excavation can greatly affect project planning, costs, and quality. Below are the main situations where embankment volume calculation is required and why it matters.

• Construction planning and logistics management: By accurately calculating how much soil must be transported in, out, or disposed of, you can properly plan the number of dump trucks, transport runs, and the construction schedule. Knowing embankment and excavation volumes in advance prevents rework or delays caused by soil shortages or surpluses.

• As-built management and quality assurance: As-built management verifies at project completion whether the embankment has reached the designed height, shape, and volume. If embankment quantity is insufficient, required bearing capacity or stability may not be achieved; if excessive, it may exceed the design height. Using objective volume data to correct shortages or excesses ensures quality.

• Progress measurement and cost calculation: Earthworks are billed based on the amount of soil brought in or the embankment created. Calculating an accurate embankment volume acceptable to both the client (owner) and contractor is indispensable for preventing contractual disputes and ensuring proper cost control.

• Safety management: The amount of embankment or temporarily stored soil directly affects safety. Excessive embankment can increase load and the risk of collapse, while overly deep cuts can cause surrounding slopes to fail. Controlling soil quantities is important for slope stability calculations and landslide prevention.

As outlined above, calculating embankment volume is indispensable at every stage of a project—planning, construction, inspection, and settlement. Whether timely and accurate soil quantity data can be obtained greatly influences on-site construction efficiency and decision-making speed.

Traditional methods for calculating embankment volume

Various methods have traditionally been used to obtain embankment volumes. Here are representative traditional techniques and an overview of each.

• Approximation by the average cross-sectional area method: The most basic method slices the embankment into cross-sections at regular intervals, measures each cross-sectional area, averages them, and multiplies by the distance between sections to obtain volume (the average cross-sectional area method). For example, if the area at the start of a section is A1, the area at the end is A2, and the section length is L, the volume V is roughly `V = ((A1 + A2) / 2) × L`. On site, heights were measured with a staff or level, cross-sectional areas were calculated on paper drawings, and volumes computed manually. This method has long been used for estimating embankment quantities for railways and roads, but improving accuracy requires subdividing sections finely.

• Calculations using surveying instruments and drawings/CAD: Surveyors use total stations (electro-optical distance meters) or GPS survey instruments to measure ground elevations before and after embankment in a fine mesh, and then calculate volume from the coordinate data. Traditionally, longitudinal and cross-sectional drawings of the existing and design ground were produced and volume calculated from differences in cross-sectional areas. Later, survey data began to be imported into civil design CAD software on PCs, where 3D models of embankment and original ground could be compared and volumes computed automatically. This increases accuracy but requires specialized knowledge and time for surveying and data processing.

• Estimates from machine operation or transported soil quantities: As a rough estimate, sites sometimes back-calculate embankment volumes from machine or truck operation records. For example, using the number of loads moved by 10-ton dump trucks to estimate approximate cubic meters by empirical rules, or estimating soil quantity from excavator bucket capacity and number of loads. However, these are coarse approximations and can deviate significantly from actual volumes, so they are unsuitable for formal verification.

Thus, traditional embankment volume calculations combined everything from manual field measurements to CAD-based calculations and experience-based approximations. Each method can yield results, but there has been room for improvement in accuracy and efficiency, and the issues described below have been pointed out.

Issues arising from traditional methods

The traditional methods described above have raised the following issues and concerns from field teams.

• High labor and time burden: Surveying with tapes and staffs and producing cross-section drawings requires many workers and long hours. Office work to compile survey results into drawings and tables also imposes a large burden on site engineers. With labor shortages, constantly arranging specialized surveyors increases costs and can make it difficult to proceed efficiently within schedule.

• Limited measurement points and accuracy concerns: There is a limit to how many points can be measured manually, making it difficult to fully understand the embankment as a whole. Judging from only limited measurement points risks overlooking localized shortages or excesses in areas not measured. In large embankments, manual measurements can lead to situations where discrepancies are found during inspection and corrective work is rushed.

• Dependence on individuals and human error: Estimates based on experience and intuition vary with the skill of the person in charge and lack objectivity. Busy sites also lead to recording mistakes or forgotten photos. For example, if measurements and photos of buried items are not taken before backfilling, no evidence may remain after completion, potentially leading to disputes. Reliability suffers when accuracy depends on who performs measurements and when human error can occur.

• Lack of real-time results and safety concerns: Traditional methods require taking survey data back to the office for calculation and drawing, so immediate on-site results are not available. Inability to instantly confirm embankment quantities during construction can delay corrective work. Measuring on steep or partially compacted, unstable embankments is also hazardous. Supporting a staff on uneven slopes carries a fall risk, and these safety concerns are significant on-site issues.

Because of these problems, the industry has long demanded "more efficient and reliable methods for managing embankment volumes." The next section explains new solutions using ICT and 3D measurement technologies that are becoming widespread.

Basic knowledge of as-built management and earthwork quantity management

Here we briefly clarify the terms “as-built management” and “earthwork quantity management” that appear in the title. These are important concepts for discussing quality and quantity control on construction sites.

• As-built management: "As-built" refers to the finished shape of structures or created terrain resulting from work. As-built management is the process of verifying and recording, based on measurement data, whether the completed parts conform to the design shape and dimensions. In public works, measurements at prescribed points are taken according to the as-built management standards set by the client (administration) to check errors against design values. These results are used for inspection acceptance and handover decisions, making them key to assuring construction quality.

• Earthwork quantity management: Earthwork quantity management is, as the name implies, managing the amount (volume) of soil handled in the work. In embankment and excavation projects, the actual volumes transported in/out or emplaced are measured and recorded against the planned quantities estimated at the planning stage. Periodic volume measurement during construction to monitor deviations from plan is required. Quantity management is often conducted alongside as-built (shape) verification, and it's common to simultaneously measure progress quantities (embankment and excavation volumes). This allows evaluation and control of project outcomes from both quality and quantity perspectives.

In short, as-built management checks "shape (quality)" while earthwork quantity management checks "quantity (amount)". Traditionally, as-built verification was performed first, followed by separate volume calculations, but recently 3D technologies described below are enabling the integration of shape measurement and volume calculation into a single workflow, becoming the new standard.

The new standard brought by ICT and 3D surveying

Against the background of the issues above, digital technologies for embankment volume management have been increasingly adopted on sites. The key is the introduction of ICT construction methods and 3D surveying technologies. Backed by the Ministry of Land, Infrastructure, Transport and Tourism’s *i-Construction* policy, high-density non-contact measurements using drones and laser scanners have become practical. This has brought changes to as-built and earthwork quantity management that can be called a "new standard."

Benefits of 3D point cloud data measurement

A point cloud is a collection of countless measurement points (XYZ coordinates) that record site geometry. Photogrammetry by drones and ground-based 3D laser scanners can scan wide areas of terrain and structures in a short time and obtain high-precision 3D models. Using point cloud data has the following benefits.

• Comprehensive site coverage: Unlike manual measurements, point clouds can densify data to cover every part of the terrain. They capture surface irregularities and subtle unevenness without omission, enabling detailed detection of deviations from design. This reduces overlooked issues and allows early detection and correction of important quality problems. The Ministry of Land, Infrastructure, Transport and Tourism has introduced a new as-built inspection method called "surface management," which evaluates the entire finished surface with point clouds and promotes more comprehensive inspection than traditional point-by-point checks.

• Immediate volume calculation: By comparing the measured point cloud of current conditions with design data, the volumetric difference for embankment or excavation can be calculated automatically. Previously, manual cross-section calculations or CAD cross-sectional analyses were required, but point cloud measurement allows instantaneous volume calculation within software. For example, a wide development embankment that used to take 2–3 people several days to measure and calculate was completed in under half a day in a case where drone aerial photography and dedicated software were used. Being able to grasp soil quantities on site instantly enables on-the-spot decisions about progress and whether additional embankment is needed.

• Efficiency in inspection and document creation: Acquired point cloud data can be stored and used as a digital 3D record. Some analysis software can automatically display differences from design as color maps or generate pass/fail reports. This enables semi-automation of as-built inspections and progress quantity reports, greatly reducing tasks such as hand-drawing drawings or transcribing numbers into spreadsheets. The ministry’s surveys report that earthworks using ICT construction (3D surveying, machine guidance, etc.) reduced total labor time by about 30% on average, demonstrating efficiency improvements from digitalization.

By adopting 3D surveying technologies, accuracy and speed of embankment volume management have increased dramatically. The era in which "embankment volume measurement is done in 3D as a matter of course" is arriving. Public project inspection standards are being revised accordingly, and 3D as-built management (surface management) is becoming the new standard for earthworks and paving. What used to rely on veteran intuition and manual work is shifting to a new norm where anyone can perform accurate, rapid as-built and quantity management through data use.

What is simple surveying with LRTK?

While 3D surveying is becoming the new standard, there is also growing demand for more user-friendly measurement tools that anyone can use. Drones and high-end laser scanners are effective but have barriers such as required expertise, aviation law constraints, and high equipment costs, making them difficult to adopt for small to mid-sized sites. One solution that has emerged is a new surveying device combining a smartphone with RTK technology. A representative example is LRTK, developed by the Tokyo Institute of Technology spin-off Lefixea Inc.

LRTK (Lefixea RTK) is a high-precision surveying system consisting of a pocket-sized RTK-GNSS receiver that attaches to a smartphone or tablet and a dedicated app. Using the Real-Time Kinematic (RTK) method to correct satellite positioning errors, it achieves centimeter-level positioning accuracy (cm level accuracy (half-inch accuracy)) even with a smartphone. By utilizing the smartphone’s built-in camera and LiDAR sensor (on supported models), it can 3D-scan surrounding terrain and structures and attach high-precision position coordinates to the obtained point cloud, enabling handling as an accurate 3D model. It can also link with cloud-based analysis functions on site and, with a single tap, automatically calculate and display embankment or accumulated soil volumes. LRTK integrates surveying and calculation on the smartphone—processes that were previously separate—making it revolutionary in enabling anyone to easily calculate embankment volumes on site.

The emergence of LRTK has made as-built surveying and volume calculation, which previously required expensive dedicated equipment and skilled technicians, much more accessible. The compact device simply mounts to a smartphone, offering excellent mobility, and workers can quickly measure while walking in narrow sites or on slopes with elevation differences. In a few minutes of scanning, wide-area point cloud data can be acquired and embankment volumes confirmed immediately, dramatically improving on-site decision-making speed. In terms of accuracy, LRTK achieves positional precision that previously required surveying instruments costing several million yen, providing reliability comparable to traditional methods.

There are also substantial benefits in ease of introduction. Because LRTK leverages existing smartphones or tablets, initial costs can be kept down, and non-specialists can learn to operate it with short training. Special flight permissions or licenses are not required, making it easy to incorporate into daily construction management and promoting one-device-per-person use on sites. In advanced construction sites, site supervisors and workers themselves increasingly use LRTK to check as-built and soil quantities, and its simplicity and utility are highly valued.

Thus, simple surveying with LRTK embodies the new on-site standard for embankment volume management. It supports the 3D surveying required by the Ministry’s ICT and i-Construction initiatives, and acquired point cloud data meet the accuracy requirements and delivery formats of as-built management guidelines. LRTK offers substantial labor and time savings compared to traditional methods while enhancing the reliability of quality and quantity management, making it a powerful tool for future site operations. Consider adopting this new standard at your site and step into the next stage of embankment volume management.

FAQ (Frequently Asked Questions)

Q: How is embankment volume calculated? A: Traditionally, embankment volume was obtained by measuring cross-sectional areas and applying the average cross-sectional area method, or by calculating from survey data using drawings or CAD software. First measure the original ground and the finished embankment surface, then obtain volume from their difference. The detailed procedure is to extract cross-sections at regular intervals, calculate each section’s area, compute partial volumes as average cross-sectional area × length for each segment, and sum them. Recently, using 3D models such as point clouds, software can automatically compute volume differences between the embankment and the design surface, which is becoming the mainstream method.

Q: What is the difference between embankment and excavation? A: "Embankment" (fill) means raising low ground with soil, while "excavation" (cut) means lowering high ground by digging. Road construction and land development use both as needed to achieve designed heights and slopes. Embankment and excavation amounts are paired concepts, and project planning considers their balance (the so-called “earthwork balance”). If excavated soil can be reused for embankment, it is economical; if insufficient, soil must be brought in from outside, and if surplus arises, it must be taken to a disposal site.

Q: What is as-built management? A: As-built management is the process of verifying and recording whether the final shape and dimensions of completed structures or terrain conform to design drawings. For instance, road subbase thickness or embankment height are measured at project completion and compared with design values to check if they fall within standards. In public works, measurement at prescribed points according to as-built management guidelines is mandatory, and results are organized into tables and photo logs for submission. Passing as-built management is a crucial inspection item for recognizing project completion and ensuring construction quality.

Q: What technologies can be used for earthwork quantity management? A: Recently, advanced earthwork quantity management methods using ICT have increased. Representative methods are point cloud surveying using drone aerial photography or 3D laser scanners. These can digitize wide areas into 3D data in a short time and accurately calculate embankment and excavation volumes by comparing with design models. Smartphone-integrated simple surveying devices (such as LRTK) are also gaining attention. They obtain high-precision point clouds with a smartphone and GNSS and automate volume calculation in the cloud, enabling immediate on-site quantity assessment. The trend is to perform objective, digital measurement-based quantity management rather than relying on manual work or intuition.

Q: What is LRTK? A: LRTK is a surveying system consisting of a compact RTK-GNSS receiver that attaches to a smartphone and a dedicated app. Using Real-Time Kinematic (RTK) to correct satellite positioning errors, it enables centimeter-level positioning accuracy (cm level accuracy (half-inch accuracy)) with a smartphone. It also uses the smartphone’s camera or LiDAR to scan the site and obtain point cloud data, from which embankment volumes can be calculated instantly. Compared to conventional surveying equipment, LRTK is portable and economical, and designed to be operable by non-specialists, enabling easy as-built and quantity measurements by anyone.

Q: I hear terms like i-Construction and ICT construction—what do they mean? A: i-Construction is the name of the Ministry of Land, Infrastructure, Transport and Tourism’s initiative to revolutionize productivity on construction sites. It aims to streamline and enhance surveying, design, construction, and inspection processes through the use of ICT (information and communication technology). Specifically, it promotes the use of 3D survey data, drones, machine guidance (automatic control of construction machinery), and BIM/CIM (3D model-based design and construction) to digitize construction management that was previously manual. ICT construction refers broadly to construction carried out using these ICT technologies, and in embankment volume management, 3D point cloud-based as-built management (surface management) is becoming the new standard. Digitalization dramatically improves quality, safety, and efficiency in the i-Construction era of construction management.