EvapMargin

The ACI 305 nomograph

The ACI 305 nomograph estimates evaporativity: the peak rate at which the air can take water from a free water surface (Uno 1998). It is the industry tool to assess the environment during casting of slabs.

In 3D concrete printing, the environment is even more relevant. As 3DCP mixtures do not bleed water as a floor slab does, capillary pressure starts at once. In other words, the ideal evaporativity is zero. The nomograph reads the environment, and how far it is from that ideal. It is most useful as a way to forecast the need for curing and to compare printing conditions. This guide says how to read the figure, what to measure, and how far to trust the number.

Background

The environment has significant effects on concrete, specifically the availability of water for curing, and stresses caused by evaporation. In conventional casting, formwork protects most of the concrete, and in floor slabs bleeding water to the surface protects the rest. This is not true for 3D printed concrete.

Capillary pressure and relative volume changes, when constrained by the printbed or other layers, will often result in cracks. By controlling the environment you can minimize or delay these forces, so the concrete can build sufficient strength to withstand them.

The same environment on cast concrete and on a printed wall Two cases side by side under one band of air. The band names the environment: temperature, humidity and air movement. The same air acts on both cases. On the left is conventional casting. A cast slab stands between formwork on both sides, and a film of bleed water covers its top. One arrow carries water from that film into the air. The formwork protects the concrete, and the bleed water protects the surface. On the right is 3D printed concrete. A printed wall stands on a printbed, with a fresh layer on top, a layer below it, and set layers under that. The wall has no formwork, so arrows carry water off the open top and off both flanks of the fresh layer and of the layer under it. The fresh layer carries capillary pressure and shrinks inward, which two arrows inside it show. A hatched interface bonds it to the layer below, and that layer constrains it. The printbed under the wall constrains it as well. The printed wall has no formwork and no bleed water, and constrained shrinkage opens a crack. Environment temperature, humidity, air movement The same air acts on both Conventional casting 3D printed concrete Formwork Bleed water Cast concrete the surface stays wet Formwork Formwork protects the concrete Bleed water protects the surface Fresh layer capillary pressure Layer below constrains it Set layers Printbed No formwork, no bleed water Constrained shrinkage opens a crack
Figure 01.1The same environment, two cases. Cast concrete with formwork and bleed water, and a printed wall with neither, under one band of air.

How to read it

The nomograph is four panels, read clockwise from the top left. One construction line threads through all four, from the ambient temperature to the evaporation rate. Two carriers join the panels: the air moisture level and the moisture deficit. Each panel also draws both thresholds in its own input, so it says how far that input can move.

The four panels and the two carriers The four panels of the nomograph as boxes, in the two-by-two grid the figure itself uses. Top left is the ambient temperature panel, which control 1, the ambient temperature, and control 2, the relative humidity, govern. Top right is the surface temperature panel, control 3. Bottom right is the air movement panel, control 4. Bottom left is the evaporation panel, a narrow bar against the air movement panel; no control sets it, because it carries the reading. A dashed arrow runs right out of the ambient panel into the surface panel with the air moisture level A, which is the vertical axis of both. A second runs down out of the surface panel into the air movement panel with the moisture deficit D, the horizontal axis of both. A third runs left out of the air movement panel into the bar with the evaporation rate E, the vertical axis of both, and E is the reading. Each pair of panels shares an axis, so the line hands each value on and the reader carries no number. Air moisture level A the vertical axis of both panels Moisture deficit D the horizontal axis of both panels Evaporation rate E the vertical axis of both panels, and the reading 1 Ambient temperature 2 Relative humidity 3 Surface temperature 4 Air movement Evaporation no control sets it Each pair of panels shares an axis: A, then D, then E. The line hands each value on, so you carry no number.
Figure 02.1The four panels and the two carriers. The panels as boxes and the carriers as arrows, in the order the construction line meets them, so the loop closes on the evaporation axis.

What to measure

The tool reads four inputs. Each is a value measured at the print, not a value assumed for the hall. A hall can carry 3 to 5 °C between floor and ceiling. So a sensor on the wall reads a different air from the fresh layer. The surface temperature is the input the equation is most sensitive to.

Table 03.1The four inputs. Each input with its unit, its range, where to take the reading, and the proxy the tool accepts.
Input Unit Range Where to take the reading What the tool accepts
Step 1Ambient temperature °C 5 to 40 In the air beside the printhead, at the height of the fresh layer. None. Enter the temperature you measured.
Step 2Relative humidity % 20 to 100 In the same air as the temperature, clear of the door and of the mixer. None. Enter the humidity you measured.
Step 3Surface temperature °C 5 to 40 On the top of the layer just laid, with an infrared thermometer. The printing temperature, which the control asks for. A face that evaporates cools below it.
Step 4Air movement km/h 0 to 25 At the fresh layer, in the air that crosses its face. Fans, hoods and open doors all count. A preset instead of a measurement.
Indoor 2 km/h.
Outdoor 8 km/h.
Outdoor, windy 20 km/h.

The model

Menzel (1954) measured the rate at which water leaves a free water surface under known air temperature, humidity and air movement. Uno (1998) fitted those measurements to one closed-form equation. This tool computes that equation with no correction for printing, so the chart stays the ACI 305 nomograph. Three assumptions travel with the equation, and each one fails at a printed face.

E = 5 · ( (Ts + 18)^2.5 − r · (Ta + 18)^2.5 ) · (V + 4) · 10^−6
Table 04.1Symbols and units.
Symbol Meaning Unit
E Evaporation rate from the surface kg/m²/h
Ts Surface temperature of the fresh concrete °C
Ta Ambient temperature of the air °C
r Relative humidity divided by 100 none
V Air movement over the surface km/h
From four inputs to the evaporation rate The equation as three boxes, read downward. The first box is the air moisture level A. Control 1, the ambient temperature, and control 2, the relative humidity, enter it on dashed arrows. It gives A as r times the ambient temperature plus 18, raised to the power 2.5, where r is the humidity divided by 100. A solid arrow hands A down to the second box, the moisture deficit D. Control 3, the surface temperature, enters it. It gives D as the surface temperature plus 18, raised to the power 2.5, less A. A negative deficit reads zero. Uno fitted these formulas in 1998, and Menzel measured the rate at open water in 1954. A solid arrow hands D down to the third box, the evaporation rate E. Control 4, the air movement, enters it. It gives E as 5 times D times the air movement plus 4, times 10 to the power minus 6. E is the reading, in kilograms per square metre per hour. Three assumptions close the chain: the equation assumes free water at the surface, it assumes that surface is flat and horizontal, and it assumes one air speed across the whole surface. 1 Ambient temperature 2 Relative humidity 3 Surface temperature 4 Air movement A Uno (1998) fitted these formulas. D Menzel (1954) measured this rate at open water. Air moisture level A A = r · (Ta + 18)^2.5 r is the relative humidity divided by 100. Moisture deficit D D = (Ts + 18)^2.5 − A A negative deficit reads zero. Evaporation rate E E = 5 · D · (V + 4) · 10^-6 The reading, in kg/m²/h. The equation assumes free water at the surface. It assumes that surface is flat and horizontal. It assumes one air speed across the whole surface.
Figure 04.1From four inputs to the evaporation rate. Each step of the equation as one box with its formula, from the two temperatures and the humidity to the rate.

Accuracy and limits

The nomograph and its equations do not estimate the rate at which the concrete surface loses water. They estimate evaporativity: the peak rate at which the air can take water from a free water surface (Uno 1998). The nomograph therefore reads the environment, not the concrete. It is most useful as a way to forecast the need for curing and to compare printing conditions. On a cast surface, bleed water rises and keeps a film of free water on the face. That film holds the assumption behind the ACI limit: the equation matches the concrete only while bleed water covers the face.

Note 05.1Method: no bleed water

A 3DCP mixture bleeds almost nothing. Without a water film, capillary pressure builds from the first minute at any evaporation rate. The strength of the layer must develop fast enough to take it. For the best structural performance, evaporativity should be zero. Capillary action drives a relative volume change in the drying layer, and stresses concentrate where that change is held. Three constraints can hold it: the printbed, a layer below that shrinks at a different rate, or a step in stiffness in the geometry. The 0.25 kg/m²/h working threshold comes from cracking evidence, not from the equation. Nobody holds the calibration data from vertical printed faces that would settle it.

Sources

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.

  • ACI 305R, Guide to Hot Weather Concreting. American Concrete Institute. Source of the nomograph and the 1.0 kg/m²/h limit.
  • ACI 308R-23, Guide to Curing Concrete. American Concrete Institute. The nomograph gives evaporativity, not the loss from concrete. Source of Menzel's measuring conditions, of the ±25 % up to 1.0 kg/m²/h, and of the overestimate above it.
  • Menzel, C. A. (1954). Causes and prevention of crack development in plastic concrete. Portland Cement Association. The equation behind the nomograph.
  • Uno, P. J. (1998). Plastic shrinkage cracking and evaporation formulas. ACI Materials Journal 95(4): 365-375. The closed-form equation used here, and the origin of the 1.0 limit.
  • 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 wind-tunnel work behind the ±25 %, and the fall in the loss after the bleed water.
  • Moelich, G. M., Kruger, J. and Combrinck, R. (2020). Plastic shrinkage cracking in 3D printed concrete. Composites Part B 200: 108313. And (2022), the plastic-shrinkage crack-risk model, Cement and Concrete Composites.
  • Markin, S., Combrinck, R. and Mechtcherine, V. (2023). Cement and Concrete Research, and preprint SSRN 4511047. Plastic shrinkage of printed concrete with and without formwork, and the effect of filament thickness.
  • Deysel, Boshoff and Smit (2023). Implementing capillary pressure control measures to prevent plastic shrinkage cracking in concrete. Construction and Building Materials. The cracking evidence that brackets the 0.25 line.
  • Slowik, V., Schmidt, M. and Fritzsch, R. (2008). Capillary pressure in fresh cement-based materials and identification of the air entry value. Cement and Concrete Composites 30(7): 557-565.