Table of Contents

• Introduction

• Why You Need to Calculate Embankment Volume

• Basic Methods for Calculating Embankment Volume

• Key Points for As-built Management and Earthwork Quantity Control

• Improving Volume Calculation Accuracy and Cautions

• Measuring Embankment Volume Using the Latest Technologies

• Simple Surveying with LRTK

• FAQ

Introduction

In civil engineering, an "embankment" refers to the act of piling soil or earth in a designated location to form raised ground, as well as the resulting mass of soil. It is performed when raising ground for road construction, land development, and similar works, and is carefully constructed to meet the as-built shape and design elevations. Accurately calculating the amount of embankment, namely the volume of earthwork, is extremely important for site management. Errors in the calculation of embankment volume can lead to misjudging the required quantity of soil, causing excessive costs or rework. This article explains in detail the basic methods to accurately calculate embankment volume and practical tips for as-built and earthwork quantity management that are useful on site.

Why You Need to Calculate Embankment Volume

Accurately calculating embankment volume is indispensable for both construction planning and quality control. First, understanding the appropriate amount of soil enables effective construction cost management. Earthwork often accounts for a large portion of procurement and transportation costs for soil, so accurately estimating the required embankment volume prevents shortages or surpluses of materials and helps avoid unnecessary expenditures. It also contributes to construction schedule management. For example, to arrange additional soil early if there is a shortage or to plan disposal of surplus soil, accurate knowledge of embankment volume is a prerequisite.

Furthermore, grasping embankment volume is directly linked to as-built management (verifying that the completed structure matches the design in shape and dimensions). By comparing the theoretical soil quantities estimated from design drawings with the actual quantities constructed, you can check whether the embankment has been built according to plan. If there is a shortage, additional embankment will be required; if there is an excess, the specified height or shape may have been exceeded. Such verification allows early correction of quality defects or construction errors. Accurate calculation of embankment volume is the foundation for appropriately managing construction progress, cost, and quality.

Basic Methods for Calculating Embankment Volume

Representative methods for calculating embankment volume are the average cross-sectional area method (prismoidal/average section method) and the mesh method. The average cross-sectional area method is commonly used for linear embankments such as road construction. First, set cross-sections at regular intervals (for example 10 m (32.8 ft / 33 ft) or 20 m (65.6 ft / 66 ft)), and measure the area of the embankment portion at each section. For each segment, take the average of the two adjacent section areas and multiply by the distance between the sections to obtain the segment volume. Summing these calculations across all segments yields the total embankment volume. Expressed as a formula: `V = (A1 + A2) / 2 × L` (V: segment volume, A1/A2: end section areas, L: distance between sections). This method is relatively simple and convenient for calculating soil quantities.

On the other hand, the mesh method (also called the grid method) is used for planar earthworks such as development sites. Divide the embankment area into a grid like a checkerboard, and survey the ground elevation at each grid point. Determine the embankment thickness (height of placed soil) at each cell, and compute the cell volume as a prismatic volume (height × cell area). Summing the small volumes of all cells yields the total embankment volume. Mesh spacing is typically uniform, for example 5 m × 5 m (16.4 ft × 16.4 ft / 16 ft × 16 ft), but the finer the mesh, the higher the accuracy; however, more surveying is required, so a balance should be struck according to site conditions.

With these traditional, largely manual methods, you need to survey the existing ground (before construction) and the finished embankment ground separately, then produce cross-sections or surface maps and perform area calculations to obtain volumes. Recently it has become common to use Excel or CAD software for calculation and drawing, but in any case, on-site surveying and drawing-based calculation work require time and effort. To obtain accurate embankment quantities, it is important to appropriately set the spacing of survey points and cross-section pitches to capture terrain undulations as much as possible. For example, narrow the section spacing in areas with large undulations, and increase survey points in complex terrain.

Key Points for As-built Management and Earthwork Quantity Control

The results of embankment volume calculations directly affect on-site practices for as-built management and earthwork quantity control. Here are the key points to keep in mind from each perspective.

First, in as-built management, it is essential to confirm whether the embankment matches the design in shape and dimensions. After embankment completion, measure heights and widths at designated survey points and check for deviations from the design cross-sections. Regarding volume in particular, comparing the theoretical values calculated at design with the measured values enables you to determine whether there is an overall surplus or deficit of embankment material. A key practice in as-built management is to conduct surveys by layer or by process as needed and perform intermediate verifications. For example, if embankment is constructed in multiple layers, measuring thickness and cross-sectional shapes after compaction of each layer helps prevent large errors at the final stage. Also, it is important to save the measurement data (cross-sections and survey coordinate data) at completion to assist in quantity confirmation with the client.

From the earthwork quantity control perspective, maintaining a balance of soil across the project is required. If cut and fill are balanced, you can reduce unnecessary import or export of soil, so advance planning of soil allocation is important. Accurate calculation of embankment volume enables precise procurement of required soil.

Note the soil volume change factor (or swell factor/compaction factor). Soil excavated and subsequently placed will change volume due to compaction, so the same 100 cubic meters of soil may occupy different volumes as "excavated soil (loose)" versus "embankment (compacted)". Generally, embankment compaction expels air between particles, reducing volume by a few to several tens of percent compared to the original volume, and this must be considered when ordering or allocating soil. For example, even if the design embankment volume is 1,000 cubic meters, you should plan a margin and prepare more soil on site to avoid shortage.

During construction, it is indispensable to track earthwork quantities by progress. Regularly measuring the achieved embankment volume allows early detection of deviations from the plan. Tracking daily embankment volumes enables proactive decisions such as “order additional soil because we are short” or “arrange transportation because surplus soil will be generated.” Implementing a PDCA cycle for earthwork quantity control improves efficiency and optimizes costs.

Improving Volume Calculation Accuracy and Cautions

To accurately calculate embankment volume, the following points should be observed during surveying and calculation on site.

• Ensure surveying accuracy: The accuracy of the survey data underlying volume calculations is paramount. When measuring elevations with levels or total stations, perform instrument setup and calibration reliably and avoid errors due to long-distance measurements with poor sightlines. Set benchmark coordinates and elevations correctly and measure before and after embankment construction based on the same reference.

• Optimize survey point density: For both cross-section and mesh methods, accuracy depends on the density of survey points. More rugged terrain requires denser surveying, but time constraints require efficient planning. As a rule of thumb, place survey points to cover important terrain change points (boundaries of elevation change, tops and toes of slopes, etc.), and allow wider spacing in flat, less variable areas.

• Choose the calculation method appropriately: Consider accuracy differences due to the calculation method itself. The average cross-sectional area method is convenient but prone to error when unexpected undulations occur between sections. The mesh method evaluates the entire surface by subdividing it and tends to be more accurate but traditionally required dedicated software because it is not suitable for hand calculation. Recently, 3D design data-based earthwork calculations (discussed below) have become common; where possible, using such digital methods is recommended.

• Account for soil properties and compaction: As described earlier, final embankment volume varies with soil type, moisture content, and compaction. When ordering or transporting soil based on calculated volumes, do not accept the calculated numbers uncritically; allow leeway based on site soil conditions. The change rate differs between cohesive soils and sandy soils and with moisture content, so refer to past results or test data if available.

By applying these points and performing multiple checks, you can improve the accuracy of volume calculations. For example, compare results using different calculation methods (compute with both section method and mesh method), or have other site staff cross-check the results. In large projects where earthwork costs are substantial, even small errors can affect cost and schedule. Through careful management and verification, you can bring embankment volume calculations closer to “more reliable” values.

Measuring Embankment Volume Using the Latest Technologies

With recent advances in ICT, the measurement and calculation of embankment volume have become dramatically more efficient. Traditionally, surveys and calculations were conducted manually, but now using 3D surveying technologies you can obtain earthwork quantities quickly and with high accuracy. A representative example is volume calculation using point cloud data. Point cloud data are 3D datasets that cover the terrain surface with many survey points, obtained by laser scanner measurements or drone aerial photography analysis (photogrammetry). Because surface irregularities can be recorded down to the millimeter-level (0.04 in), comparing point cloud datasets before and after work allows accurate calculation of embankment and excavation volume differences.

The greatest advantage of point cloud-based earthwork calculation is the efficiency of surveying and computation. With traditional methods, you would measure elevations at regular intervals on site, create cross-sections, and calculate segment volumes one by one using the average cross-sectional area method. With point cloud measurement, you can—for example—capture the terrain before and after embankment as full point clouds and automatically compute volumes on a computer by differencing the two datasets. This eliminates the need to manually produce numerous cross-sections and, because the calculations use data that measure the entire terrain comprehensively, there are fewer oversights and higher accuracy.

Moreover, once point cloud data are obtained and saved, they can be reused for re-calculation with the mesh method or for partial area volume calculations as needed. Measurements themselves are also rapid, and significant time savings compared to traditional surveys have been reported. For example, at one site, earthwork measurement and calculation that took four people seven days (28 person-days) was completed in 2 people 1 day (2 person-days) by introducing drone photogrammetry plus point cloud analysis. While greatly reducing manpower and days, volume calculation accuracy for as-built quantities was found to be comparable to traditional methods (approximately 1% error), demonstrating the practical usefulness of point cloud-based volume measurement.

Other modern technologies include ground-based 3D laser scanners and machine guidance systems mounted on heavy equipment such as bulldozers and excavators. Fixed laser scanners can obtain extremely precise terrain data to the millimeter, and machine guidance systems can be used to monitor cut-and-fill quantities in real time during operation. However, the former involves very expensive equipment and requires specialized operation skills, and the latter is primarily intended as operator assistance and is not always suitable for recording as-built measurements. Amid these options, smartphone- and tablet-based simple 3D measurement has recently attracted particular attention. Many modern smartphones are equipped with LiDAR distance sensors, and with dedicated apps they can scan surrounding terrain in a short time and generate point clouds. In fact, LiDAR scanners are standard on models such as iPhone 12 and later and some iPad Pro units, allowing site supervisors themselves to measure embankment shapes in a few minutes and immediately calculate volumes.

The advantage of smartphone-based point cloud measurement is its ease of use and mobility. Drone flights or fixed laser scanner setups require flight permissions, transportation and installation of equipment, and operator training, but a smartphone is truly a “pocket device” that can be taken out and used on site as needed. No special qualifications or intensive training are required, lowering the barrier to field adoption. For small embankments or temporary stockpile volume checks, site agents or supervisors can quickly scan on the spot without calling a survey team, use the measured volume to arrange heavy equipment or dump trucks, and apply the results immediately. Tasks that could not previously be done in real time—such as immediate revision of earthwork plans or rapid as-built confirmation—are becoming possible with mobile device point cloud measurement.

Recently, services have emerged that upload smartphone-acquired point cloud data to the cloud and automatically generate 3D models and compute volumes. Cloud integration allows on-site measurement data to be instantly shared with office PCs or remote stakeholders, aiding centralized management of construction records. Regularly recording point clouds during construction helps visualize progress quantitatively, and post-completion data can be used to monitor long-term terrain changes. The application range for as-built and earthwork quantity data is expanding. Through these digital technologies, embankment volume measurement is moving to a new stage of being both rapid and reliable.

Simple Surveying with LRTK

To make smartphone-based 3D measurement even more easily usable on site, there is a solution called LRTK. LRTK is a high-precision positioning system provided by Reflexia that transforms a handheld iPhone or similar device into a high-accuracy surveying instrument using a compact, smartphone-mounted device. Specifically, an antenna attached to the smartphone uses network RTK (real-time kinematic) positioning to enhance the phone’s GNSS position information to centimeter-level accuracy (cm level accuracy (half-inch accuracy)). This allows point cloud and photo data obtained by the phone’s LiDAR scanner or camera to be given accurate coordinates, enabling high-accuracy point cloud measurement with location information—a task that was previously difficult—using only a smartphone.

The biggest advantage of introducing LRTK is real-time earthwork measurement on site. Using an LRTK-enabled dedicated app, scanning embankments or stockpiles will automatically compute volumes from the acquired 3D point cloud and display the results on the smartphone screen. The acquired data are also immediately uploaded to the cloud, making it easy to review details on an office PC or share them with a team. Because LRTK point cloud data are high-accuracy data tied to absolute coordinates from the outset, comparisons with design elevations and reference planes can be performed quickly. This greatly shortens the steps that previously required PC-based analysis and calculation after point cloud acquisition, shrinking the time lag from surveying to as-built quantity calculation to nearly zero. As a result, it is possible to make rapid construction decisions such as “decide today whether to arrange disposal of surplus soil” or “confirm backfill volume immediately and order additional soil.”

LRTK also excels at cloud service integration, enabling accumulation of on-site data to manage construction history in a time series. Comparing multiple point cloud datasets allows quantitative evaluation of progress, and future monitoring of terrain changes for maintenance purposes becomes feasible. Enabling site staff to routinely perform 3D measurement that previously required surveying specialists will dramatically improve the accuracy and speed of construction management. LRTK is truly an innovative tool for the era of “one device per person.” If your site is struggling with embankment volume calculations, consider trying this simple surveying using LRTK. You should be able to experience a new form of construction management driven by high-accuracy, high-efficiency as-built quantity control.

FAQ

Q: What is as-built management? A: As-built management is a quality control process that verifies whether the constructed elements (embankments, concrete structures, etc.) conform to the shapes and dimensions specified in the design documents. Measurements of height, thickness, width, volume, and other parameters are taken and compared with design values and standards to determine if they meet the criteria. In embankment works, important as-built management checks include whether soil has been placed to the specified elevation, whether slopes and widths match the design, and whether the volume of placed soil is appropriate.

Q: What is the difference between the average cross-sectional area method and the mesh method? A: The average cross-sectional area method draws cross-sections at regular intervals and derives volume from section areas. It is suitable for elongated embankments such as roads and has relatively simple calculation steps. The mesh method divides the target area into a grid and surveys the elevation (embankment thickness) for each cell, summing volumes across the grid. It is suited for large-area development works and tends to be more accurate than the average cross-sectional method because it can reflect the terrain undulations more finely. However, it is not suitable for hand calculation, so in recent years automatic calculations using software with point cloud data have become more common.

Q: Can embankment volume be calculated from the number of dump truck trips? A: A rough estimate is possible, but accuracy is limited. Multiply the dump truck’s load capacity (cubic meters per truck) by a loading efficiency factor and the number of trips to estimate soil volume approximately. However, actual embankment volume varies with soil moisture and compaction, and loading practices can introduce losses, so errors occur. To accurately determine embankment volume on site, direct surveying and calculation methods (section method, mesh method, point cloud measurement, etc.) are more reliable.

Q: Can smartphones’ LiDAR really be used for surveying? A: LiDAR sensors on recent high-end smartphones (for example, certain iPhone models) can perform simple 3D surveying. There are apps that acquire point cloud data by scanning terrain or structures, allowing measurements and volume calculations. However, a standalone smartphone’s GNSS positioning accuracy is typically on the order of meters, which is coarse for precise surveying. For high accuracy, augmenting the phone with RTK positioning such as LRTK to correct location information can provide centimeter-level surveying accuracy.

Q: What exactly is LRTK used for? A: LRTK is a high-precision positioning system used in combination with smartphones or tablets. A dedicated compact antenna receiver is attached to the device and uses real-time kinematic (RTK) satellite positioning correction techniques to dramatically improve the smartphone’s GNSS accuracy. This enables the point cloud data and photos acquired with the phone to be tagged with accurate coordinates, making measurement at accuracies comparable to professional surveying instruments possible. In short, LRTK’s role is to allow accurate surveying and as-built measurement “anytime, anywhere, by anyone” using just a smartphone.