For the selective paste intrusion (SPI) method, thin layers of aggregate are locally bound by cement paste where the structure shall arise. After completion of the printing process, the structure is excavated from the particle-bed and the unbound particles are removed. However, for a sufficient layer bonding and shape accuracy, the rheology of the cement paste must be adapted to the flow resistance of the particle-bed. For practical application, that means mostly time and material consuming "trial and error" tests. To prevent that, analytical models can help to predict the penetration of the cement paste. This paper presents four analytical models to calculate the penetration depth of a cement paste into a particle packing. Based on Darcy's law, an already existing model is slightly modified (model A+) and a generalized (model C), an advanced generalized (model D) as well as a simplified model (model B/B+) are developed. Compared to conducted tests on the penetration depth, model B showed good accuracy (deviation <1.5 mm) for pastes with a yield stress ≥8.2 Pa, model A+/B+/C for ≥ 5.4 Pa and model D even for <5.4 Pa. Finally, an application guide for each model for practical use will be given.
Keywords: 3D printing; analytical model; cement; concrete; particle-bed; penetration; selective paste intrusion.