How homogenous is your 3D printed concrete? A new approach to assessing anisotropy using Weibull statistics

Abstract Material volumes created using extrusion-based 3D concrete printing (3DCP) are inherently anisotropic due to the network of inter-filament regions which are exposed to the ambient environment to varying degrees. Consequently, the strength characteristics are dependent on these factors and the toolpath used during deposition. Additionally, the agglomeration process presents a greater opportunity to embed defects, such as air voids. The strength outcomes in printed material are therefore practically difficult to control and hence significant variability is observed both against cast equivalent and between printed samples. Reliably measuring anisotropy is critical for monitoring production quality and informing structural design calculations. Current anisotropy indices rely on mean strength values, making them sensitive to missing loading orientations, data scatter and test conditions, which is problematic for creating robust measures for practical use. However, the random nature of the presence of defects in printed material aligns particularly well with the weakest link theory, suggesting that the Weibull model is theoretically ideal for characterisation. Using the flexural data from 15 laboratories from the RILEM TC 304-ADC interlaboratory dataset, it is demonstrated that not only can a two-parameter Weibull model be reliably characterised, but its robustness is demonstrated to be superior to the existing approaches, reducing the statistical uncertainty between 48 and 64%. The Weibull modulus, directly captures strength variability and size effects which provides a statistically consistent anisotropy index comparable across different laboratories and test setups, offering a practical method for quality assurance in 3D printed concrete.