The layer water-loss nomograph

The joint between two layers is the weakest place in a printed wall. Its strength follows how wet the top of the lower layer is when the next layer arrives. Keita et al. (2019) measured that bond against the water the top had lost. A relative water loss of 0.1 % left the strength unchanged, and 1 % cut it by about 40 %.

The nomograph is five panels. Its top half is the ACI chart's top half, and the line leaves it at the moisture deficit. It then meets the air-movement ray at the evaporation rate, and the layer-cycle curve at the water loss on the bar along the foot. The loss axis increases leftward and is logarithmic.

The tool reads five inputs. The first three are the ACI tool's, and you measure them the same way. Air movement is in metres per second, because an indoor anemometer reads that unit. The layer cycle is the perimeter divided by the print speed, or the pause, and a cycle timed at the print is the better value.

The rate is not the ACI 305 value. It is the evaporation from a vertical wet face in a hall, where the air moves slowly and the face moves some of it itself. Buck (1981) gives the vapour pressure, and Churchill and Chu (1975) give the transfer from a vertical face. The loss is that rate times the layer cycle.

The loss is an upper bound. It is the rate times the time, from a surface that stays wet for the whole cycle. The rate under it carries a factor of about 1.5, and most of that is the air over the top of the layer. Both thresholds are provisional, which is why both are adjustable.

Every figure on this page comes from one of these sources. Several are quoted as the named papers report them. The originals are named here so that a reader can check each one.

• Keita, E., Bessaies-Bey, H., Zuo, W., Belin, P. and Roussel, N. (2019). Weak bond strength between successive layers in extrusion-based additive manufacturing: measurement and physical origin. Cement and Concrete Research 123: 105787. The two points that place both thresholds.
• Sanjayan, J. G., Nematollahi, B., Xia, M. and Marchment, T. (2018). Effect of surface moisture on inter-layer strength of 3D printed concrete. Construction and Building Materials 172: 468–475.
• Buck, A. L. (1981). New equations for computing vapor pressure and enhancement factor. Journal of Applied Meteorology 20: 1527–1532. The saturation vapour pressure in this model.
• Churchill, S. W. and Chu, H. H. S. (1975). Correlating equations for laminar and turbulent free convection from a vertical plate. International Journal of Heat and Mass Transfer 18: 1323–1329. The air the face moves itself.
• Churchill, S. W. (1977). A comprehensive correlating equation for laminar, assisting, forced and free convection. AIChE Journal 23(1): 10–16. The blend of the face's air and the hall's.
• Scherer, G. W. (1990). Theory of drying. Journal of the American Ceramic Society 73(1): 3–14. Capillary flow keeps a drying surface wet.
• Lehmann, P., Assouline, S. and Or, D. (2008). Characteristic lengths affecting evaporative drying of porous media. Physical Review E 77: 056309.
• Al-Fadhala, M. and Hover, K. C. (2001). Rapid evaporation from freshly cast concrete and the Gulf environment. Construction and Building Materials 15(1): 1–7. The rate falls away over hours.
• Shah, M. M. (2014). Methods for calculation of evaporation from swimming pools and other water surfaces. ASHRAE Transactions. And (2022), Science and Technology for the Built Environment.
• ACI 305R, Guide to Hot Weather Concreting. American Concrete Institute. The rate this model is compared against.
• ASHRAE Standard 55. The convention that air below 0.1 m/s is still.