Quantifying the complexity of 3D printed concrete elements

The freedom of shape offered by 3D concrete printing (3Dcp) is often mentioned when considering productivity, technology progress, material optimization, and others. Printed structures are described using qualitative terms such as "complex", "double-curved," and "geometric freedom" due to difficulties in quantifying the design's complexity. Such descriptions depend on the aesthetics as well as the observers' interpretation, which makes an objective comparison between concrete objects difficult. To alleviate the ambiguities with such qualitative comparisons, the purpose of this study is to offer a quantitative metric for evaluating the complexity of the intrinsic geometry of a concrete element and the difficulty of printing it. This was achieved by proposing two complexity coefficients ? Intrinsic Complexity Coefficient (ICC) and Fabrication Specific Complexity Coefficient (FSCC). The ICC considers the geometry of the concrete elements' (shape coefficient, mean curvature), whilst the FSCC defines the elements' complexity within the context of 3Dcp (ease of printing, resolution). This allows the ICC to be used to compare printed elements and the FSCC to determine which element is easier to fabricate using 3Dcp. Within this study, ten 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 used 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 the many applications for the metric proposed in this study.