# Voxel-Based Digital Twin Framework for Earthwork Construction
## 1 Introduction  
Earthwork operations are critical components of most construction projects and involve significant volumetric modifications of the terrain. These operations are inherently cyclic, as multiple pieces of equipment, such as excavators and dump trucks, are utilized to excavate, transport, and fill earthwork materials. Earthwork construction has a dynamic nature and unique characteristics, including an unstructured work environment such asirregular terrain and inhomogeneous earthwork material properties, the presence of utilities or unstable soil, unexpected rock layers, large-scale operations involving volumetric designs and significant material quantities, difficult scene perception, particularly in underground construction, and limited visibility of machine operators [1]. During construction, two significant challenges arise, as follows: (1) simulating the interaction between an unstructured environment and equipment during earthwork activities, and (2) the difficulty in integrating all the information and dynamically updating the model to reflect the as-built status. These challenges often create safety issues, impacting the productivity and quality of earthwork construction. Hence, a system is needed that can support the integration of all information in an integrated environment, represent earthwork characteristics realistically, and support real-time simulation and dynamic monitoring for efficient earthwork management. The digital twin connects the physical and virtual assets/processes, enabling seamless integration and control. It uses sensing technologies to capture as-built information and utilizes advanced modeling, visualization, and simulation techniques to accurately represent, analyze, and optimize the system during the operation [2]. At its core, the digital twin serves as a manipulable virtual replica, allowing users to gain insights into the behavior and performance of the physical system [3]. To be effective, the virtual twin must be built with a high degree of fidelity, incorporating the spatial, material, and temporal dynamics of its physical counterpart [4]. Additionally, the virtual twin and physical twin are linked in a bidirectional way, meaning that the changes in the physical environment, such as excavation volume and materials, must be reflected in the virtual twin. Equally, insights from the virtual twin should be used to guide the project stakeholders for accurate and timely decisions [5]. Therefore, in the context of earthwork, a realistic and data-rich virtual twin is fundamental, as it could represent dynamic earthwork processes, including the representation of heterogeneous earthwork materials, interactions, and the volumetric changes that occur during the construction. Several review articles provide definitions, challenges, opportunities, and current methods for data acquisition, data integration, data linkage between physical and digital components, twin representations, and advanced tools for improving systems and making decisions effectively [4; 6; 7; 8; 9; 10; 11]. Most of the proposed definitions and frameworks share three fundamental components of a digital twin, as follows: the physical twin, the digital twin, and the connections [12]. [PERSON] et al. [13] proposed a generalized framework of the following five components: digital components, virtual components, data, connection, and services. In recent years, digital twin applications have gained substantial attention in the construction industry, particularly for monitoring, simulation, and optimization of physical processes. For example, a digital twin framework for construction equipment monitoring, progress monitoring, and visualization was developed. It provides information about equipment tracking using Internet of Things (IoT) data and dashboard visualization [14]. Drone-based photogrammetry and computer-aided design (CAD) data were integrated to track road base construction in a digital twin environment [15].