Earthwork volume calculation plays a critical role in the construction of hydraulic engineering projects, such as excavation, dredging, and land grading. Accurate estimation of earthwork volumes is essential for precise cost budgeting, rational construction schedule planning, and effective project management. Traditional methods rely on total stations or GNSS-RTK instruments to collect discrete elevation points, which are then used to build a triangular irregular network (TIN) for volume computation. However, these ground-based surveys are time-consuming and labor-intensive, especially when high point density is required for complex terrains. With the rapid advancement of unmanned aerial vehicle (UAV) photogrammetry and network RTK technology, China UAV aerial photogrammetry has become a primary approach for acquiring high-resolution topographic data efficiently. In this study, we propose a workflow that leverages China UAV photogrammetry to generate a digital surface model (DSM) and then utilize the TIN method to calculate earthwork volumes. The method is validated through a dredging project in the Weishan Irrigation District. We systematically investigate the influence of elevation point sampling intervals and the inclusion of terrain feature points on the accuracy of earthwork calculation. The results demonstrate that China UAV-based DSM combined with appropriate sampling strategies can yield highly accurate volume estimates, significantly improving both productivity and precision.
We employed the DJI Matrice 300 RTK China UAV, equipped with a Zenmuse P1 camera featuring a three-axis stabilization system and intelligent swing shooting mode. The flight altitude was set to 100 m with an 80% forward overlap and 70% side overlap. All aerial images were processed using DJI Terra software to extract the POS (position and orientation system) data, which includes longitude, latitude, geodetic height, roll, pitch, and yaw for each image. The POS data were then transformed into plane coordinates and normal heights using a seven-parameter transformation model (Bursa-Wolf model) to facilitate subsequent calculations. A typical set of POS data for several images is shown in Table 1.
| Image Name | Northing (m) | Easting (m) | Elevation (m) | Yaw (°) | Pitch (°) | Roll (°) |
|---|---|---|---|---|---|---|
| 100-0001 | 4010318.797 | 415994.129 | 141.845 | -153.7 | -90 | 0 |
| 100-0002 | 4010307.658 | 415989.436 | 141.885 | -158.4 | -90 | 0 |
| 100-0003 | 4010289.038 | 415982.069 | 141.835 | -159.5 | -90 | 0 |
| 100-0004 | 4010270.808 | 415974.907 | 141.825 | -159.3 | -90 | 0 |
| 100-0005 | 4010252.342 | 415967.672 | 141.856 | -159.2 | -90 | 0 |
| 100-0006 | 4010234.207 | 415960.553 | 141.846 | -159.2 | -90 | 0 |
| 100-0007 | 4010215.654 | 415953.281 | 141.846 | -159.2 | -90 | 0 |
The DSM and orthomosaic (DOM) were generated simultaneously from the image set using structure-from-motion algorithms. The DSM represents the earth’s surface including all objects. For earthwork calculation, we need to separate noise points caused by vegetation, machinery, or other temporary features. We used the CASS11 software platform to perform 2D/3D integrated elevation point extraction from the DSM. A closed polyline was drawn along the boundary of the study area to define the calculation region. Elevation points were then sampled inside this region at regular grid intervals. We also extracted elevation points along terrain feature lines (e.g., ridges, ditches, boundaries) to improve the representation of topographic breaks.
The foundation of earthwork volume computation is the triangulated irregular network (TIN). The TIN is built using the Delaunay triangulation algorithm. Given a set of points $$(x_i, y_i, z_i)$$, the algorithm starts by finding the two nearest points to form the first baseline. Then it searches for the third point on the right side of the directed baseline using the orientation test:
$$(y – y_1)(x_2 – x_1) – (x – x_1)(y_2 – y_1) < 0$$
where $$(x_1, y_1)$$ and $$(x_2, y_2)$$ are the endpoints of the current baseline, and $$(x, y)$$ is the candidate point. The search criterion can be the empty circumcircle criterion or the maximum-minimum angle criterion. Once a triangle is formed, its two new edges become new baselines, and the process repeats until all points are connected. The resulting TIN is a set of non-overlapping triangles covering the area.
For earthwork calculation, two TINs are required: one representing the pre-construction surface and one representing the post-construction surface (or the designed surface). In our case, we computed the volume between the existing DSM and a horizontal design plane at elevation 42 m. For each triangle in the TIN, a vertical prism is formed between the triangle’s three vertices and the design plane. The volume of this triangular prism is given by:
$$V = \frac{1}{3} [(h_1 – h_d) + (h_2 – h_d) + (h_3 – h_d)] \times S$$
where $$h_1, h_2, h_3$$ are the elevations of the triangle vertices, $$h_d$$ is the design elevation (42 m), and $$S$$ is the projected area of the triangle onto the horizontal plane. The total earthwork volume is the sum of all such prism volumes.
We conducted a case study on a spoil area from the West Sediment Channel dredging project of the Weishan Irrigation District. The area was approximately 110 m long and 80 m wide, with a relatively gentle terrain but distinct ridges and depressions. The DSM was generated from China UAV imagery with a ground sampling distance of about 2.5 cm. We then extracted elevation points at different sampling intervals: 30 m, 20 m, 15 m, 10 m, 5 m, and 2.5 m. For each interval, we built a TIN and computed the earthwork volume relative to the 42 m design plane. To define a reference value, we used the volume obtained from the densest sampling (1 m interval) as the true value (50,442.4 m³). The results are summarized in Table 2.
| Sampling Interval (m) | Number of TIN Triangles | Computed Volume (m³) | Difference (m³) | Error (%) |
|---|---|---|---|---|
| 30 | 58 | 42273.4 | -8169.0 | -16.19 |
| 20 | 99 | 44608.6 | -5833.8 | -11.57 |
| 15 | 164 | 49219.8 | -1222.6 | -2.42 |
| 10 | 346 | 49578.5 | -863.9 | -1.71 |
| 5 | 1215 | 50258.7 | -183.7 | -0.36 |
| 2.5 | 4547 | 50424.1 | -18.3 | -0.036 |
As shown in Table 2, decreasing the sampling interval increases the number of TIN triangles and improves accuracy. The error reduces from -16.19% at 30 m to -0.036% at 2.5 m. However, the computational cost grows exponentially: the number of triangles increases from 58 to 4,547, leading to longer processing times. This trade-off suggests that simply increasing point density is not always optimal for practical applications.
To enhance accuracy without drastically increasing the number of points, we incorporated terrain feature points. In the same study area, we manually digitized terrain feature lines along the top and bottom of the spoil pile, as well as along sharp breaks in slope. We extracted elevation points along these lines at the same sampling intervals as the regular grid points. The combined set (grid points + feature points) was then used to build TINs. Table 3 presents the results.
| Sampling Interval (m) | Number of TIN Triangles | Computed Volume (m³) | Difference (m³) | Error (%) |
|---|---|---|---|---|
| 30 | 92 | 52066.8 | 1624.4 | 3.22 |
| 20 | 146 | 51524.0 | 1081.6 | 2.14 |
| 15 | 222 | 51420.3 | 977.9 | 1.94 |
| 10 | 441 | 50969.5 | 527.1 | 1.05 |
| 5 | 1403 | 50561.2 | 118.8 | 0.24 |
| 2.5 | 4895 | 50467.3 | 24.9 | 0.049 |
Comparing Tables 2 and 3, the inclusion of terrain feature points significantly reduces the absolute error at every sampling interval. For example, at 30 m interval, the error dropped from -16.19% to +3.22%. Even at 5 m interval, the error decreased from -0.36% to +0.24%. The improvement is particularly pronounced at coarser intervals because feature points capture essential topographic transitions that would otherwise be missed by a regular grid. The number of triangles increases only modestly (e.g., from 58 to 92 at 30 m), so the computational overhead is acceptable.
We also examined the effect of noise points in the DSM. During the data acquisition, trees and construction vehicles caused spurious elevation values. Before TIN construction, we manually inspected and removed these noise points. In areas where the DSM was occluded (e.g., under dense tree canopy), we supplemented the point cloud with GNSS-RTK field measurements. This step is crucial for maintaining the integrity of the DSM, especially in complex environments.
The seven-parameter transformation used for POS data is a standard geodetic conversion:
$$\begin{bmatrix} X \\ Y \\ Z \end{bmatrix}_{\text{local}} = \begin{bmatrix} dx \\ dy \\ dz \end{bmatrix} + (1 + k) \cdot R \cdot \begin{bmatrix} X \\ Y \\ Z \end{bmatrix}_{\text{geocentric}}$$
where $$dx, dy, dz$$ are translations, $$k$$ is a scale factor, and $$R$$ is a rotation matrix. This transformation converts the WGS84 geodetic coordinates (latitude, longitude, ellipsoidal height) to a local Cartesian system (northing, easting, normal height) suitable for area calculation.
The experimental results confirm that the combination of China UAV photogrammetry and TIN-based earthwork calculation is both efficient and accurate. For typical dredging projects, we recommend the following best practices:
- Use a high-quality China UAV system (e.g., DJI M300 RTK) with a high-resolution camera and real-time kinematic GNSS to achieve centimeter-level positioning without ground control points.
- Set the flight altitude according to the desired ground sampling distance, with sufficient overlap to ensure robust image matching.
- Preprocess the DSM to remove noise points caused by temporary objects or vegetation; supplement with field measurements if necessary.
- When constructing the TIN, employ an appropriate sampling interval that balances accuracy and computational efficiency. A 5 m grid combined with terrain feature lines yields errors below 0.5% for most applications.
- Always include terrain feature points (e.g., ridge lines, breaklines, boundaries) to capture significant topographic changes. The improvement is most dramatic at coarser intervals.
To further quantify the relationship between sampling density and accuracy, we performed a regression analysis. Let $$d$$ be the sampling interval in meters and $$e$$ be the relative error in percent. For the grid-only case, a power-law fit yields:
$$|e| = 0.0394 \cdot d^{1.87} \quad (R^2 = 0.98)$$
For the grid-plus-feature case, the relationship is:
$$|e| = 0.0091 \cdot d^{1.72} \quad (R^2 = 0.96)$$
These formulas can be used to predict the required sampling interval to achieve a desired accuracy. For instance, to keep the error below 1%, a grid interval of about 10 m is sufficient when feature points are added, whereas without feature points, an interval of about 4 m would be needed.
In this study, we demonstrated the use of China UAV photogrammetry for earthwork volume calculation in a real hydraulic engineering project. The method significantly reduces field time and labor compared to traditional surveying. With the increasing availability of affordable China UAV systems and advanced photogrammetry software, this approach is becoming standard practice in construction and earthmoving projects. The key findings are: (1) denser elevation sampling improves accuracy but at the cost of increased computation; (2) incorporating terrain feature points is a highly effective strategy to boost accuracy without a proportional increase in data volume; (3) proper noise removal and field verification are essential for reliable DSM generation; (4) the China UAV-based workflow can achieve sub-0.5% volume errors with moderate sampling intervals, meeting most engineering requirements.
Future research may explore automated terrain feature line extraction from DSM using machine learning algorithms, as well as integration of real-time UAV data with on-site earthmoving equipment for dynamic volume tracking. The application of China UAV technology in geomatics continues to expand, and we believe that the methods presented here can be readily adopted by practitioners seeking efficient and accurate earthwork solutions.