In modern civil engineering and water conservancy projects, accurate estimation of earthwork volume is critical for cost control, schedule planning, and resource allocation. Traditional methods relying on total stations or GNSS-RTK for topographic data collection suffer from low efficiency and high labor costs, especially when dense sampling is required. With the rapid advancement of drone technology, unmanned aerial vehicle (UAV) photogrammetry has emerged as a powerful alternative for acquiring high-resolution topographic data. This paper presents a first-person account of a study that leverages drone technology to generate digital surface models (DSM) and employs the triangulated irregular network (TIN) method for earthwork volume calculation. The work focuses on a dredging project within a large irrigation canal, where we systematically investigate the influence of sampling density and terrain feature points on calculation accuracy. Our findings demonstrate that drone technology combined with proper sampling strategies can yield highly reliable earthwork estimates, significantly outperforming conventional approaches in both speed and precision.
The core methodology involves three stages: aerial data acquisition using a UAV, DSM generation via structure-from-motion, and volume computation based on TIN differencing. We used a DJI Matrice 300 RTK quadcopter equipped with a Zenmuse P1 full-frame camera. The drone technology allowed us to capture overlapping images with a forward overlap of 80% and side overlap of 70% at a flight altitude of 100 m. The onboard GNSS receiver integrated with network RTK provided real-time positioning, enabling direct georeferencing without ground control points. After each flight, the POS data (including latitude, longitude, ellipsoidal height, and attitude angles) were extracted and transformed into the local planar coordinate system using a seven-parameter similarity transformation. The transformed coordinates were then used in photogrammetric processing software (DJI Terra) to produce both the orthophoto and the DSM with centimeter-level accuracy.
The DSM serves as the fundamental data source for earthwork calculation. We converted the continuous surface into a set of discrete elevation points and constructed a TIN using Delaunay triangulation. The algorithm starts by selecting the point closest to the geometric center of the region as the first vertex, then finds its nearest neighbor to form an initial baseline. For each baseline, the third point is searched on the right side of the directed line segment according to the following criterion:
$$
(y – y_1)(x_2 – x_1) – (x – x_1)(y_2 – y_1) < 0
$$
where \((x_1, y_1)\) and \((x_2, y_2)\) are the coordinates of the baseline endpoints, and \((x, y)\) is the candidate third vertex. The search also enforces the empty circumcircle condition, ensuring that no other point lies inside the circumcircle of the triangle. This process is repeated recursively until all edges are processed, yielding a network of non-overlapping triangles that optimally represent the terrain surface.
Once the TIN is established, earthwork volume is computed by comparing the pre- and post-construction surfaces. Each triangle in the post-construction TIN forms a triangular prism when vertically projected onto the pre-construction or design plane. The volume of a single prism is given by:
$$
V = \frac{1}{3} \left[ (h_1 – h) + (h_2 – h) + (h_3 – h) \right] \times S
$$
where \(h_1, h_2, h_3\) are the heights of the three triangle vertices on the post-construction surface, \(h\) is the design elevation (or the height of the pre-construction surface at the corresponding projection), and \(S\) is the area of the triangle projected onto the horizontal plane. Summing over all triangles gives the total earthwork volume for the entire region.
To validate the method, we selected a rectangular spoil area (approximately 110 m by 80 m) from the canal dredging project. The area had a relatively smooth topography but with distinct breaklines at its top and bottom boundaries. We first generated a high-resolution DSM from the UAV survey and used it as the reference. We then systematically reduced the sampling interval to create multiple TIN models with different point densities. For each interval, we computed the volume to a uniform design elevation of 42 m. The volume obtained with a sampling interval of 1 m (50,442.4 m³) was taken as the true value because it represents the densest practical sampling. Table 1 summarizes the results for intervals ranging from 30 m down to 2.5 m, without considering terrain feature lines.
| Interval (m) | Number of triangles | Volume (m³) | Difference (m³) | Relative error (%) |
|---|---|---|---|---|
| 30 | 58 | 42,273.4 | -8,169.0 | -16.19 |
| 20 | 99 | 44,608.6 | -5,833.8 | -11.57 |
| 15 | 164 | 49,219.8 | -1,222.6 | -2.42 |
| 10 | 346 | 49,578.5 | -863.9 | -1.71 |
| 5 | 1,215 | 50,258.7 | -183.7 | -0.36 |
| 2.5 | 4,547 | 50,424.1 | -18.3 | -0.04 |
As revealed in Table 1, the computed volume monotonically approaches the reference value as the sampling interval decreases. However, the number of triangles increases dramatically—from 58 at 30 m to 4,547 at 2.5 m—which leads to a quadratic rise in computational cost. More importantly, even at an interval of 5 m, the relative error is only -0.36%, which is acceptable for most engineering applications. This suggests that ultra-dense sampling is unnecessary if the terrain is relatively uniform. Yet, the error at coarser intervals (e.g., -16.19% at 30 m) is unacceptably large, indicating that sampling density must be chosen appropriately based on terrain complexity.
In real projects, terrain often contains sharp breaklines that define boundaries between different slopes. Ignoring these features in the TIN can introduce significant errors. To address this, we developed a strategy that explicitly extracts elevation points along terrain feature lines (such as ridge lines, valley lines, and breaklines) from the DSM and includes them as additional constraint points in the triangulation. We repeated the volume calculation with the same set of sampling intervals but also added a set of feature-line points. The results are presented in Table 2.
| Interval (m) | Number of triangles | Volume (m³) | Difference (m³) | Relative error (%) |
|---|---|---|---|---|
| 30 | 92 | 52,066.8 | +1,624.4 | +3.22 |
| 20 | 146 | 51,524.0 | +1,081.6 | +2.14 |
| 15 | 222 | 51,420.3 | +977.9 | +1.94 |
| 10 | 441 | 50,969.5 | +527.1 | +1.05 |
| 5 | 1,403 | 50,561.2 | +118.8 | +0.24 |
| 2.5 | 4,895 | 50,467.3 | +24.9 | +0.05 |
By comparing Table 2 with Table 1, we observe that the inclusion of terrain feature points significantly improves accuracy at every sampling interval. For instance, at 30 m interval, the error dropped from -16.19% to +3.22%—a reduction of more than 19 percentage points. Even at 10 m, the error decreased from -1.71% to +1.05%. The improvement is most pronounced at coarser intervals because the sparse regular grid fails to capture the abrupt elevation changes at the top and bottom of the spoil area, whereas feature lines precisely embed these changes into the TIN. At very fine intervals (2.5 m), the effect is marginal because the regular grid already resolves the breaklines with sufficient detail. These results highlight the synergy between drone technology and intelligent sampling: the high-resolution DSM provides the raw data, but judicious selection of feature points extracts the essential geomorphic structure, enabling accurate volume calculation even with moderate sampling density.
The underlying reason for this improvement lies in the nature of TIN interpolation. A TIN approximates the terrain by planar facets. When breaklines are not represented, the facets cut across the actual slope changes, leading to systematic underestimation or overestimation of the volume. For example, in our test area, the spoil pile has a relatively flat top and a sloping side. Without feature points, the large triangles at a 30 m interval average out the slope, producing a volume that is far smaller than the true value (as indicated by the -16.19% error). After adding points along the top edge and the toe of the slope, the triangles conform to the actual breakline, and the computed volume becomes slightly larger than the true value (+3.22%), which is actually closer to the true volume than the negative bias. This demonstrates that drone technology not only provides the data but also enables the extraction of meaningful feature information that traditional survey methods may miss due to their limited point density.
It is also worth noting that the total number of triangles in Table 2 is only moderately higher than in Table 1 for the same sampling interval. For example, at 15 m interval, the triangle count increased from 164 to 222—a 35% increase that yields a dramatic error reduction from -2.42% to +1.94%. This suggests that investing effort in identifying and extracting feature lines yields a high return in accuracy without incurring prohibitive computational costs. In practice, we recommend that users of drone technology always perform a feature-line extraction step on the DSM before constructing the TIN for earthwork calculation.
Several practical considerations emerged during our study. First, the raw DSM may contain artifacts caused by vegetation, moving machinery, or water bodies. These noise points must be removed prior to TIN construction. We applied a filtering step that compares each DSM cell with its neighbors and discards points whose elevation deviates more than a certain threshold from the local average. For areas occluded by trees or equipment, we supplemented the DSM with ground measurements obtained via GNSS-RTK.
Second, the POS data from the UAV camera must be carefully transformed from the WGS84 geographic coordinates to the local projection. We used a seven-parameter transformation (three translations, three rotations, one scale factor) that converts latitude/longitude/ellipsoidal height to planar coordinates and orthometric heights. The transformation parameters were derived from a set of control points measured by static GNSS. Any error in this step would propagate into the DSM and ultimately affect the volume calculation. Therefore, we validated the transformed coordinates against independent checkpoints and achieved a root mean square error of less than 3 cm in both planimetry and height.
Third, the TIN algorithm itself can be optimized. We implemented the incremental insertion method with a spatial index to speed up the point location step. For the largest dataset (2.5 m interval with feature points, about 4,895 triangles), the computation finished in less than 2 seconds on a standard desktop computer. This efficiency makes the method suitable for real-time volume estimation during construction progress monitoring.
To further quantify the influence of sampling strategy, we performed a sensitivity analysis. We defined the terrain roughness index as the standard deviation of slope within the area. For our test site, the roughness was 0.12 (radians). Using a 10 m sampling interval without feature points yielded an error of -1.71%. When we introduced artificial breaklines (by adding 20 feature points extracted from the DSM along the top edge), the error dropped to +0.85%. This illustrates that even a small number of strategically placed feature points can compensate for a large reduction in grid density.
We also investigated the effect of the design elevation value. In our test, the design elevation was fixed at 42 m. When we varied this design level by ±1 m, the relative errors remained nearly constant, indicating that the conclusions about sampling density and feature points are robust to changes in the reference plane. This is expected because the error behavior is governed by the geometry of the TIN rather than by the absolute elevation difference.
Another important aspect is the scalability of drone technology. For large canal dredging projects, the total area often spans several square kilometers. In such cases, a single UAV flight may not cover the entire zone. We employed a multi-flight mission planning approach with 30% lateral overlap between strips. The strips were then merged during point cloud generation. We verified that the seam lines did not introduce noticeable discontinuities in the DSM by comparing elevations along overlapping boundaries. The average discrepancy was 1.2 cm, confirming the consistency of the drone technology.
In terms of time efficiency, a conventional RTK survey of the same spoil area (110 m × 80 m) with a 5 m grid would require about 400 points, taking two surveyors approximately 3 hours to complete. In contrast, the UAV flight took 12 minutes, including takeoff and landing, and the subsequent data processing (image alignment, dense matching, DSM generation, and volume calculation) took another 2 hours. Thus, drone technology reduced the total field-to-result time by over 40% while providing far richer data (millions of points instead of hundreds).
Finally, we compiled a summary table that compares the accuracy of various methods used in practice:
| Method | Field time (hours) | Processing time (hours) | Relative error (%) | Point density (pts/m²) |
|---|---|---|---|---|
| RTK 5m grid | 3.0 | 0.5 | -0.8 to +0.6 | 0.04 |
| UAV DSM + TIN (5m grid, no feature) | 0.2 | 1.5 | -0.36 | 0.04 |
| UAV DSM + TIN (10m grid, with feature) | 0.2 | 1.2 | +1.05 | 0.01 |
| UAV DSM + TIN (30m grid, with feature) | 0.2 | 1.0 | +3.22 | 0.001 |
From Table 3, it is clear that drone technology not only accelerates data acquisition but also achieves comparable or better accuracy than conventional RTK surveys when combined with feature-based TIN refinement. Even at a coarse grid of 30 m, the addition of feature points yields an error of only +3.22%, which is acceptable for preliminary estimates or for large-scale earthmoving projects where small relative errors translate into manageable absolute volumes.
We also explored the effect of the type of feature lines used. In the test area, the most critical feature lines are the boundary between the flat top and the sloping side (convex breakline) and the line where the slope meets the natural ground (concave breakline). Using only the top breakline reduced the error from -16.19% to -5.8% at 30 m interval. Adding both top and bottom breaklines further reduced the error to +3.22%. This indicates that all major terrain breaks should be represented.
One limitation of the current study is that it was conducted on a single spoil area with relatively simple topography. Future work should include more complex terrains with multiple slopes, gullies, and irregular boundaries to further validate the robustness of the method. Additionally, we plan to integrate the feature-line extraction step directly into the photogrammetric workflow, automatically detecting breaklines from the point cloud using edge detection algorithms. This would eliminate manual digitization and make drone technology fully autonomous for earthwork applications.
In summary, this paper has demonstrated that drone technology offers a highly efficient and accurate solution for earthwork volume calculation. The key contributions are: (1) establishing a complete workflow from UAV flight to DSM to TIN-based volume computation; (2) quantifying the impact of sampling interval and feature-point inclusion on accuracy; (3) showing that even coarse grids can yield acceptable results when terrain feature lines are properly incorporated. We recommend that practitioners adopt drone technology with the following guidelines: use a flight altitude of 100–150 m with 80% forward and 70% side overlap; apply a seven-parameter coordinate transformation; filter out noise points from the DSM; extract breaklines automatically or manually; and then construct the TIN with a sampling interval of 10–20 m depending on terrain roughness. This approach balances computational efficiency and accuracy, making drone technology a practical tool for routine earthwork management.