Quantifying the complexity of 3D printed concrete elements

Freedom of shape enabled by 3D concrete printing (3Dcp) is often mentioned alongside productivity, technology progress, material optimization, and other benefits of the technology. When doing so, printed structures are described using qualitative terms such as “complex”, “double-curved,” and “geometric freedom”. However, such descriptions depend on the aesthetics and the observers’ interpretation, which renders an objective comparison between concrete objects difficult. To alleviate the ambiguities with such qualitative comparisons, this study proposes a quantitative metric consisting of two complexity coefficients – Intrinsic Complexity Coefficient (ICC) and Fabrication Specific Complexity Coefficient (FSCC). The ICC considers the concrete elements’ geometry using shape coefficient and mean curvature, whilst the FSCC defines the elements’ complexity within the context of 3Dcp (ease of printing, resolution). Thus, the ICC can be used to compare printed elements and the FSCC to determine which element is easier to print. Within this study, 10 pillars with varying complexity were designed and then graded according to the two complexity coefficients. Further, this evaluation was employed to adjust the construction duration consumed when calculating the productivity of elements produced using 3Dcp and traditional construction techniques. In such a way, the coefficients allowed to incorporate geometric complexity when comparing the productivity of various construction techniques, illustrating just one of many applications for ICC and FSCC.