# 3D-Printed Concrete Bridges: Material, Design, Construction, and Reinforcement
## 2 Design Process of 3D-Printed Concrete Bridges
The Castilla-La Mancha Park footbridge in Alcobendas, Madrid, is another example of how topology optimization can be applied to form-finding in the design of 3D-printed bridges [19]. This project employed the D-shape, particle-bed printing method that differs from conventional extrusion-based 3D concrete printing. Parametric design played a central role in optimizing material distribution, minimizing waste through recycling raw materials during production, and enhancing structural performance by placing material only where necessary. Additionally, generative algorithms were used to maintain porosity while enabling the creation of complex geometries, demonstrating the synergy between advanced computational tools and innovative manufacturing techniques [20]. The \"Striatus Bridge\" and its evolution, the \"Phoenix Bridge\", exemplify innovative, iterative design processes that integrate form-finding, performance-based optimization, and rigorous structural analysis to address both aesthetic and structural challenges in 3D-printed concrete bridges [13; 21]. Both bridges share a common goal of minimiz  
Figure 2: Examples of Topology optimization for design of 3D-printed concrete bridges: (**a**) Simply-supported girder design [14] (**b**) FloatArch bridge design [16]. ing tensile stress in unreinforced concrete by utilizing arch forms, which function as transverse span structures designed to transfer loads primarily through compression (see Figure 3a) [22]. The design of the Striatus Bridge began with a skeletal graph connecting its five supports, which served as the foundation for generating a 2D mesh. This mesh was refined using Thrust Network Analysis (TNA) to establish a 3D thrust network of compressive forces in equilibrium with predefined loads, as shown in Figure 3b. The resulting form-found mesh was discretized into individual voussoir blocks, with joints carefully positioned to align with the compressive force flow. Stability was verified through Discrete Element Modeling (DEM), which evaluated the dry-assembled structure under various conditions. Iterative adjustments to block interfaces and thicknesses ensured that the final design met both aesthetic and structural requirements [13]. Integrating form-finding and structural analysis demonstrates the iterative refinement necessary for compression-dominant designs. Building on the Striatus design, the Phoenix Bridge employed a similar iterative approach while incorporating traditional masonry-inspired techniques [21]. The design process emphasized optimizing the arch axis to minimize bending moments, ensuring that the cross-section primarily experienced compressive stress. Finite Element Analysis (FEA) was used in evaluating stress distribution, allowing refinements to the arch geometry and block dimensions to balance structural performance with aesthetic considerations. The \"Design by Testing\" methodology has also been a key approach in several projects. This methodology can complement TO by ensuring experimental validation of design choices and linking computational and physical testing. [PERSON] et al. [23] utilized the \"Design by Testing\" approach to create a 3D-printed bicycle bridge. This approach involved comprehensive testing of materials and structures at every phase, which included characterizing materials (such as assessing compression, tension, modulus of elasticity, creep, and shrinkage), conducting destructive tests on a 1:2 scaled model, and carrying out assembly trials. The design phase began with understanding the constraints their 3D concrete printer posed. Although the entire bridge could theoretically fit within the printer's build space, the team opted for a modular design to ease transportation and assembly. This modularity also enabled optimization of the bridge's cross-section, exploiting the printer's features. The insights gathered during testing led to notable enhancements, such as a 4% reduction in both print path length and material consumption. [PERSON] et al.