## 5 Multidimensional Virtual Design Models (_uD Modeling_)  
In the context of nD modeling, the term 'n' transcends the three-dimensional space by incorporating multiple layers of data. A BIM model that operates with localized spatial attributes typically represents a three-dimensional (3D) engineered model embedding structural and architectural elements of a building or infrastructure in different layers. BIM models contain geometrical, aesthetic, and valuable semantic data, which provides a detailed understanding of the built environment, from structural composition to functional properties. While recent studies highlight a shift towards BIM as a complement to traditional Computer-Aided Design (CAD) formats [167; 168; 169; 170] the transition towards fully integrated intelligent BIM models is not immediate but is seen as an evolutionary process where digitally captured 3D data are enhancing traditional conceptual design [171; 172; 173; 174; 175]. While 2D and 3D aspects are easy to implement in the traditional CAD designs, nD modeling simply extends the dimension of the BIM by incorporating more aspects of the design considerations and relating to all phases of the infrastructure lifecycle such as scheduling (4D), cost analysis (5D), environmental sustainability (6D), and maintenance operations (7D). In the context of transportation infrastructure, BIM models can be powerful for storing and visualizing inspection data and conducting different analyses, such as estimating pavement-repair cost, clash detection with underground utilities, and material quantity takeoff [176; 177; 178; 179]. The most critical impairment to BIM implementation in managing and maintaining transportation infrastructures is the lack of specialized software [180]. The most common application of 3D modeling is for visualization, as-built documentation, and quality control tasks [181; 182; 183]. Many research studies believe that the adoption of 3D-engineered models is an essential step for agencies employing CIM, leading to more reliable workflow interaction, higher transparency in design, and rework and cost reduction [184; 185; 186; 187]. BIM allows linking a 3D model of a facility to the detailed information of construction activity, which enables a transfer to digital management for civil projects [188; 189; 190; 191; 192; 193; 194]. As part of this digital transformation, a 4D model (3D model + schedule) plays a significant part in the planning phase of a construction project [195]. For instance, a study integrated 3D road design and pavement structure analysis based on BIM tools [196]. This comprehensive utilization of BIM can heavily improve task workflow accuracy during the maintenance phase. A collaboration-based BIM model development management (CBMDM) system was proposed, in which developing, tracking, and communicating regarding BIM models are three key components of the system [197]. For example, in an intricate project such as tunnel construction, a comprehensive BIM documentation system was prepared that entails the shape, specifications, and parametric modeling for applied material quantity takeoffs [198]. Another study developed a preliminary conceptual integration model for the underground built-environment elements by adopting collaborative examination, benefit analysis, and design practices [44]. Moreover, to enable interoperability between the design and construction phases of a bridge project, bridge information models have been developed to facilitate data analysis, decision-making, and management throughout the project lifecycle [199; 200; 201]. These examples further emphasize the value of collaboration in managing complex infrastructure projects, especially between the operation, maintenance, and rehabilitation phases. Addressing the specific model-oriented challenges is key for broadening the scope of BIM implementation in infrastructure projects.