# Voxel-Based Digital Twin Framework for Earthwork Construction
## 4 Implementation of the Proposed System
### Graphical Simulation Environment for Model-Equipment Interaction
#### 4.1.3 Model Integration in Platform
This method divides 3D space into uniform points and reduces the computational burden of the model, resulting in a sparser but topologically consistent point cloud. Once filtered and downsampled, the point cloud is converted into a TIN surface representing the current state of information. The TIN surface representing the current state of information and the ground TIN surface are compared, and the solid is extracted. This extracted solid is used as input for voxelization, representing the as-built voxels. However, the transformation from point cloud to TIN introduces minor interpolation errors, particularly in regions with low point density or complex topography. These errors can propagate into the voxel model and must be calculated and controlled. Most importantly, the accuracy of the proposed method must align with construction tolerances; for example, the error of the as-built volume (cut or fill) should not increase the allowable range. For most earthwork projects, an error deviation of 1-3% is typically considered within an acceptable range. For instance, modeling accuracy is greatly affected by the size of the voxel. A smaller voxel size fits the as-built volume, reducing error and enhancing model accuracy. To assess the impact of voxel size and point cloud resolution on model accuracy, multiple experiments were conducted. The raw point cloud was subsampled at varying levels (20%, 30%, 40%, 50%, 60%, and 70%) using a distance-based approach. Similarly, voxel sizes of 3 mm, 6 mm, and 9 mm were considered. The error was calculated by changing the voxel size, and model accuracy was compared with the allowable range. Figure 14 presents the sampling of the point cloud data and the effect of voxel size on model accuracy. The error was calculated against the ground truth point cloud obtained using a laser scanner with mm level accuracy. It was found that smaller voxels can tolerate the error and enhance model accuracy even for a large, sampled dataset. For example, a voxel size of 3 mm provides less than 3% error (allowable range) when the data is subsampled by 60%. On the other hand, a voxel size of 9 mm tolerates the same error when the data is sampled at 40%. Even though smaller voxels provide more accuracy, they increase the computational effort for model creation and model updating when new data is added to the system. Hence, in addition to accuracy, the computational performance of model creation and updating was analyzed. Figure 15 presents the performance of model creation and updating for each voxel size. It can be seen that a smaller voxel size enhances model computation for both model creation and updating. An optimal voxel size can be selected based on accuracy and computational efficiency. A voxel size of 9 mm provides an error of 2.9% when the data is sampled at 40%. The time values for



Figure 14: Subsampling of point cloud data and the effect of voxel size on model accuracy. Figure 15: Performance of model creation and model updating. ## 5 Conclusions

Due to the unique characteristics of earthwork construction, such as inhomogeneous earthwork material information, volumetric modeling, irregular terrain, and the complex nature of earthwork resources, such as model-equipment interaction, developing an earthwork digital twin is a challenging task. This study proposes a digital twin framework that connects the physical earthwork twin with its digital counterpart using a voxel-based representation for earthwork operational simulation, as well as for the visualization and quantification of earthwork progress. The key contribution of this study is the proposed development of a framework consisting of five interconnected modules that generate voxel-based as-planned and as-built models, embedding geotechnical properties of the earthwork site. Furthermore, a structured voxel-to-voxel comparison method is proposed that integrates the as-planned model with automated updating using as-built data derived through photogrammetry or laser scanning.