# Voxel-Based Digital Twin Framework for Earthwork Construction
## 2 Related Research  
### Earthwork Twin Modeling  
Capturing the as-is conditions and simulating earthwork processes demand a context-sensitive modeling approach that accounts for irregular topography, material heterogeneity, and continuous spatial changes. In digital practice, earthwork environments are represented by surface and solid-based models [27]. Triangular irregular network (TIN) surfaces have been used in earthwork terrain modeling; however, they lack volumetric information. Solid data modeling, including boundary representation (B-rep) and decomposition models, was used to create a solid-based volumetric environment [28]. B-rep uses the boundary information to represent a 3D volume, whereas decomposition models segment a 3D volume into smaller units [29]. However, B-rep is a homogeneous model and is not designed to incorporate the varying properties of the earthwork within a model [30].  
A decomposition model can efficiently address this issue and represent inhomogeneous earthwork properties. The tetrahedral network (TEN) is a decomposition model that uses the faces of TIN surfaces to create units, into which information such as material, cost, and quantity is assimilated [31]. However, TEN has limitations in terms of adaptability and refinement to smaller units (Figure 1). For instance, more often, when detailed information is needed, or when the unit size is larger than the equipment-specific dimension, such as bucket size, this cannot be achieved with TEN because of its fixed structure [28].  
Figure 1: Properties of the voxel-based representation and comparison with other geometric models.  
Voxel-based representation offers an efficient solution to address the aforementioned limitations. It divides the model into volumetric, 3D voxel units, providing a consistent data structure. It can represent the varying properties of earthworks by using different voxel sizes that can additionally be manipulated with equipment [24]. For example, the underground construction environment is represented by voxels that offer the incorporation of attribute information at the entity level, enabling the efficient management of uncertain spaces for simulation [4]. This reflects the advantages of voxels in precisely representing material characteristics, such as changes in material type (clay or sand) or properties (densities or moisture level), enabling the model to account for different material properties during manipulation [25].  
In addition to these geometries, point-based representation methods are also used, especially for representing the as-built information collected through photogrammetry and light detection and ranging (LIDAR) [32]. The point data is processed or enriched with classification labels to extract meaningful information and interpreted using a mesh reconstruction algorithm [19]. However, the direct use of point-based modeling lacks inherent topology, which hinders structural simulation or material-specific progress tracking. Moreover, hybrid modeling strategies have also been used in recent years. For instance, homogenous regions are modeled using surface or Brep models, while TEN and voxels are utilized to represent inhomogeneous regions [24; 28]. In other words, boundary information is represented using surface-based models, while volumetric information is modeled through TEN or voxels [33].