# Drying-induced damages in exposed fresh cement-based materials at very early ages: From standard casting to 3D printing

Wenqiang Zuo, Laura Caneda-Martinez, Emmanuel Keita, Patrick Aimedieu, Michel Bornert, Nicolas Roussel

► To cite this version:

Wenqiang Zuo, Laura Caneda-Martinez, Emmanuel Keita, Patrick Aimedieu, Michel Bornert, et al.. Drying-induced damages in exposed fresh cement-based materials at very early ages: From standard casting to 3D printing. Cement and Concrete Research, 2024, 185, pp.107614. 10.1016/j.cemconres.2024.107614. hal-04943079

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Submitted on 12 Feb 2025

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# Drying-induced damages in exposed fresh cement-based materials at very early ages: from standard casting to 3D printing

Wenqiang ZUO<fnref n="1" />,<fnref n="2" />, Laura CANEDA-MARTINEZ<fnref n="1" />,<fnref n="3" />, Emmanuel KEITA<fnref n="1" />, Patrick AIMEDIEU<fnref n="1" />, Michel BORNERT<fnref n="1" />, Nicolas ROUSSEL<fnref n="3" />*

• Corresponding author. nicolas.roussel@univ-eiffel.fr

## Abstract

In this paper, we are studying the shrinkage and microstructural damages induced by drying in samples exposed to drying at very early ages. We measure for two model mortars the average and local shrinkage through microtomography images subtraction along with microstructure evolution through microtomography radiographs. Our measurements showcase the role played by the kinetics of propagation of drying-induced capillary stresses on shrinkage distribution. They moreover show the existence of two distinct types of microstructural damages in such exposed samples occurring at the onset of the sample desaturation after a period as short as a couple of hours. Our analysis allows for a first-order understanding of the scaling of the main stress, length and time scales of the problem with some material parameters such as compressibility and permeability. We finally extrapolate and discuss the consequences of the above features on standard concrete casting and on concrete 3D printing.

## 1. INTRODUCTION

Let us first start, for the purpose of locating the scope of the present paper, by drawing here a rough and simplistic picture of water fluxes, volume and internal stress variations in

<footnote n="1">¹ Navier laboratory (UMR 8205), CNRS, ENPC, Gustave Eiffel University, France.</footnote>

<footnote n="2">² School of Materials Science and Engineering, Southeast University, Nanjing, China.</footnote>

<footnote n="3">³ CPDM Laboratory, Gustave Eiffel University, France.</footnote>
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cement-based materials at very early ages. Please note that this picture is putting the emphasis on the drying physics of a “soft” porous medium simplifying therefore some aspects from literature dealing with hydration-induced features, which are more relevant for the understanding of longer time scales of observation.

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There exists in a cement-based system some chemical shrinkage due to the well-known difference between the volume of the reacting components and the one of the final products of the hydration reaction [1]. This is expected to lead to an overall decrease of the material volume. However, the strong interactions between the constitutive elements of the system partially prevent such a contraction. The water consumption leads therefore to a desaturation of the porosity, to the formation of capillary menisci and to the generation of capillary stresses. The effective magnitude of the material so-called “autogenous” shrinkage [2–4] results then from a complex interplay between the above chemical shrinkage, these capillary stresses and the constantly evolving rigidity of the solid particles network, the level of which increases with the advancement of the same hydration reaction. On top of this complexity, because of the hydration reaction exothermic nature, some temperature variations may induce some additional volume variations. All these features are finally driven by boundary conditions that dictate how much freedom a cement-based matrix has to shrink and deform or, if unable or partially unable, how much internal stress is generated leading potentially to some micro and macro cracking or, more generally, to some microstructural damages [5].

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In the above, in practice and in most literature (except for the one dealing with the so-called plastic shrinkage that will be reminded further in this paper), external drying of the fresh material (defined as an exchange of water with the external dry (or drier) environment) is ignored or neglected. This finds its origin in the fact that the manufacturing of cement-based objects is mostly based on a formative process [6]. These objects are therefore protected from external drying by a formwork for the first tens of hours of their life. It is moreover expected that a proper curing of the material for the more exposed cement-based objects such as slabs is able to counteract the loss of water induced by external drying. Once cement-based materials become exposed to a potentially dry environment, the hydration reaction is already advanced and the fresh material has turned into an artificial stone, the rigidity and low permeability of which prevent most drying-based capillary effects from inducing any major microstructural damages with an exception in the case of low W/C ratio materials [3].
Let us try below to assess the amount of water that might be lost to the environment through a typical drying process and compare it to the amount of water consumed by the hydration reaction on the short time scales of interest for this paper (i.e. BEFORE the hydration peak).

- As a reference, it is generally assumed that, at first order, full hydration of cement is requiring around 40% [4] of the cement mass in water. With around 300 kg of cement per cubic meter of concrete, the mass of water consumed by the full hydration of the cement powder is therefore around 100 kg. After 24 hours, with degrees of advancement for the hydration reaction of around 50%, it can be assumed that this amount is of the order of several tens of kg of water per cubic meter of concrete.

- Water evaporation in a typical environment (temperature around 20°C and neglectable winds) leads to water fluxes through the material external surface of the order of several $10^{-8}$ m/s [7,8]. This flux is obviously known to highly depend on temperature and on convection and may vary much with the climatic features of a given local environment, but such dependency is out of the scope of this introduction. Moreover, we assume here that the permeability of the fresh material is high enough for the evaporation rate to be driven by the environment only. It is therefore not limited by the ability of the material to bring water to its surface [9]. Such an assumption may prove wrong in the case of low W/C ratio concretes where evaporation or drying may be limited by the permeability of the fresh material and lead to a propagation of a dry front from the drying surface [9–11].

- In the case of a typical concrete wall protected by a formwork for 24 hours, the surface offered to such water exchange at the top of the form is around $10^{-1}$ m² per cubic meter of concrete. Considering the above water flux through such a surface, the amount of water evaporated in 24 hours is therefore of the order of several tens of grams and is fully neglectable in front of the water later consumed by hydration.

- In the case of a concrete slab in a similar environment, the surface exposed to drying increases up to several square meters per cubic meter of concrete. As a consequence, several kilograms of water per cubic meter of concrete may be lost to the environment at very early ages. This can promote an earlier desaturation of the material and premature high-level capillary stresses, which can, in turn, induce cracks and microstructural damages [12]. This imposes a proper curing procedure for this type of
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concrete elements and may require, in some cases, the use of shrinkage reducing admixtures [13].

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- In the case of printed concrete or any other shaping non-formative additive processes, the specific surface offered to drying varies with the resolution of the shaping processes. This may, for instance, be the size of the lace or filament in extrusion-based 3D printing. In most technologies under scrutiny and development [14,15], the drying specific surface may reach a couple of tens of square meters per cubic meter of concrete. As a consequence, the potential amount of water lost to the environment at very early ages may reach a few tens of kilograms per cubic meter of concrete. This suggests that it is able to threaten not only the microstructure through some drying-induced stresses but also the hydration reaction itself. Such a regime and its consequences on hydration were spotted using SEM in [11].

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The above suggests that ignoring very early drying processes is totally legitimate in the case of standard concretes cast using a formwork for vertical structural applications. These drying processes become non-neglectable features in many horizontal industrial applications, where most of the water is still nevertheless consumed by hydration. The above finally suggests that there potentially exists a regime for extremely "exposed" materials where very early drying processes may become dominant in front of hydration itself.

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It has to be noted here that several authors in literature tackled shrinkage and its consequences in the fresh state for "exposed" materials. Such shrinkage was named "plastic shrinkage" according to the common perception that, in the fresh state, concrete is a "plastic" material [16,17]. Such a semantic predates more recent work showing that fresh concrete is not a simple plastic material but an aging and thixotropic elasto-visco-plastic granular material [18]. Plastic shrinkage seems, in literature, to include any deformations occurring before setting [19]. As such, it may include gravity-induced features such as so-called bleeding and consolidation and all deformations induced by early drying or any water extraction (such as the one induced by the contact with a dry porous substrate). Plastic shrinkage relates therefore more to some deformation occurring during a given and defined period of the life of the material than to a real physical origin for such deformations. In literature, however, drying-induced plastic shrinkage attracted most attention [20] and a more dedicated term, capillary shrinkage, is sometimes used [21]. In most papers, drying and gravity-induced effects are intermixed and interconnected [22]. This finds its origin in the fact that these features of
engineering interest all happen together simultaneously. Gravity is, on one hand, at the origin of some bleeding and consolidation. This is specifically true for average or large W/C ratio [23] or for some large vertical length scales [24]. The formation of a water layer at the top of the samples affects in turn the drying as this layer evaporates first before any water is extracted from the bulk of the material. When drying only was isolated and studied, it was shown that drying induces some capillary pressure inside the material that has the ability to induced some so-called plastic shrinkage cracking [22]. Despite the claim that "free plastic shrinkage would ... not result in cracking" [22], other results show that drying-induced meniscii in the bulk may result in shrinkage and, possibly, in cracking [21]. At a critical capillary pressure, air was shown to penetrate into the system [12]. This so-called "air entry" was suggested to be the origin of strain localization and, consequently, of early age cracking. Typical damage patterns are meshed or parallel cracks in floors or slabs with widths of up to 1 mm [25].

Within the above frame, in this paper, we choose to study "exposed" materials. Such "exposed" materials would correspond in practice to materials fulfilling one or more of the following requirements:

16. The environment is dry or hot and/or convection is strong. The external water demand is therefore high. This often corresponds to outdoor harsh processing conditions (water fluxes higher than $10^{-7}$ m/s or higher than the recommended 1kg/m²/h [26]).

19. The material intrinsic temperature is artificially high and water is readily available for evaporation (for instance, accelerated cement-based materials with internal temperature in the fresh state higher than 35°C).

22. The ratio between the surface exposed to drying and the available water in the element is high (higher than 10 square meters per cubic meter of concrete).

24. It can be noted that 3D printed materials, as discussed above, specifically fulfill the last requirement. When they are chemically accelerated, they moreover often fulfill the second requirement. In the case of outdoor printing, all the above requirements would potentially be fulfilled making printed concretes extremely "exposed" and potentially very sensitive to capillary shrinkage.

29. We moreover choose here to study thin samples of low W/C materials. As a consequence, our samples do not consolidate nor bleed and dimensional variations are expected to originate from drying only.
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In order to study the specific features of drying at very early ages for these exposed materials, we choose in this paper to assess drying rate, average and local shrinkage through microtomography images subtraction along with microstructure through microtomography radiographs on two different exposed mortar samples.

Our measurements showcase the role played by the kinetics of propagation of drying-induced capillary stresses on shrinkage distribution. They moreover show the existence of two distinct types of microstructural damages in such exposed samples occurring at the onset of the ample desaturation after a period as short as a couple of hours.

We finally discuss the consequences of such features on standard casting and 3D printing.

## 2. MATERIALS AND PROTOCOLS

### 2.1. Materials and mix design

A CEM I Cement with a specific gravity of 3.15 was used. The chemical composition of the cement used in this study is shown in **Table 1**. The Particle Size Distribution (PSD) of cement powders was measured using a laser particle size analyzer (Malvern Mastersizer S) and dispersing cement powders in isopropanol (Cf. **Figure 1**). The median particle size of cement powders $d_c$ was around 11.5 µm. Glass beads with a diameter of 0.85 mm were used as a model monodisperse sand in order to produce our mortar samples.
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Table 1

Chemical composition of the cement.

<table><thead><tr><td>Composition</td><td>%Weight</td></tr></thead><tbody><tr><td>SiO<sub>2</sub></td><td>21.81%</td></tr><tr><td>Al<sub>2</sub>O<sub>3</sub></td><td>3.67%</td></tr><tr><td>Fe<sub>2</sub>O<sub>3</sub></td><td>5.54%</td></tr><tr><td>CaO</td><td>64.10%</td></tr><tr><td>MgO</td><td>1.31%</td></tr><tr><td>SO<sub>3</sub></td><td>2.41%</td></tr><tr><td>Cl</td><td>0.04%</td></tr></tbody></table>

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<figure><img src="image_2.png" /><figcaption>Figure 1. The cumulative particle size distribution of the cement studied in this work.</figcaption></figure>

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Thermocouples were used to measure temperature evolution of the cement paste samples (results not shown here). The thermocouple was inserted in the middle of a cylindrical plastic container filled with the fresh cement paste. The container was 7.2 cm in height and 5.3 cm in diameter. The container was sealed during testing. The external temperature was 23 ± 1°C. The peaks in temperature were reached at 14 and 10 hours for the W/C = 0.35 and W/C = 0.2 samples respectively. These peaks were respectively 32 and 34 °C.
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One polycarboxylate-based superplasticizer, Sika Viscocrete Tempo 12, was used in liquid form. Its specific gravity is 1.06 ± 0.02 and its solid content is 29.5% ± 1.4%. Its dosage is expressed in proportion to the mass of cement.

## 2.2. Sample preparation and drying

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The samples were prepared according to the following mixing procedure. Water containing the pre-mixed superplasticizer was first manually mixed for 1 min with cement powder. Glass beads were then added into the cement paste and the mixture was manually mixed for another 1 min before being poured into a 3D printed acrylonitrile butadiene styrene mold with an internal dimension of 50 mm in length, 20 mm in height, and 15 mm in width. The mold was then vibrated for 30 s. In the rest of the paper, the upper surface of this sample is called the "drying surface".

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For each mortar, two drying conditions were applied. One sample was dried at room temperature while the second one was sealed by covering the upper surface of the sample with a paraffin film. After casting, the sample was placed on an analytical balance with a measurement accuracy of 1 mg within the microtomographic device. The mass loss of the fresh samples induced by drying was continuously recorded in situ during the XRCT measurements.

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## 2.3. Microtomography measurements

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XRCT images were obtained on a XRCT laboratory scanner (Ultratom from RX-Solution). The device combines a Hamamatsu L10801 source (230 kV, 200 W, smallest spot size: 5µm) and a Varex Imaging 4343DXV flat-panel imager (3000 × 3000 pixels, pixel size 139µm). Four XRCT scans were performed for each fresh sample: upon casting, 2.5 h, 7 h, and after 24 h. The voltage and current applied in this study were 160 kV and 24 µA, respectively. For the first three scans, 2336 projections were recorded during a 360° scan with two images per second frame rate. At each scanning angle, two radiographs were recorded and averaged. Radiograph projections were recorded to trace the evolution of fresh samples every 10 s between the first two scans. For the last scan, 4672 projections were recorded during 360° scan with a frame rate of two images per second. At each scanning angle, two radiographs were recorded and averaged. The total time for each scan was around 40 min. X-Act software from RX Solutions
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was used to reconstruct the 3D images of the samples. The 3D reconstruction volume of each
sample is about 3000 × 3000 × 2500 voxels, and the voxel size is around 20 µm.

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**2.4. Shrinkage measurements**

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The **free autogenous shrinkage** (i.e., the shrinkage induced by cement hydration [27]) was
measured using a dilatometry technique according to ASTM C1608. However, to prevent the
imbibition of external water in the fresh sample, pure water above the sample was replaced
by silicone oil with a viscosity of 300 mPa·s. 40 ml of the fresh sample was filled in a glass
bottle with a diameter of 43.5 mm and a volume of 125 ml. The shrinkage was obtained by
dividing the measured displacement of the oil meniscus in the pipette by the initial sample
height. During the test, the glass bottle was placed in a water bath with a controlled
temperature of 20 ± 1°C and the room temperature was maintained at 20 ± 2°C.

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The **average vertical shrinkage** of the fresh sample subjected to drying was measured from
the surface settlement of the upper surface measured by X-ray radiographs. Assessment of
the surface position is based on the sharp change in grey level at the transition from the
background to the sample. The mean surface position is then obtained by averaging all the
columns of each radiograph image. Finally, the shrinkage is obtained by dividing the surface
settlement by the initial height of the sample.

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Finally, an in-house Digital Image Correlation (DIC) software developed at Navier Laboratory was used [28] to determine the **local vertical shrinkage profile** in the fresh sample. This method compares a reference radiograph with consecutive radiographs obtained during XRCT measurements at different drying ages. It should be noted that, for all samples studied here, the measured shrinkage in the horizontal direction is of the order of the uncertainty of the DIC and is far lower than vertical shrinkage. More information on the DIC measurement can be found in Appendix A.1. Finally, the computed change in local shrinkage becomes lower than the uncertainty of the DIC once some microstructural damages occur in the sample cracking initiates. Therefore, in this paper, this method is only applied before any microstructural damage initiation.

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## 2.5. Fresh samples mechanical properties assessment

We will be looking in this paper at some water migration within the cement matrix, which will, in turn, lead to some volume variations that will be driven by the material compressibility. We choose therefore here to assess the compressibility of our cement pastes by using centrifugation experiments. Such measurements were shown to relate well to some typical filter pressing techniques [29]. They allow for the assessment of both the compressive yield stress $\sigma_0$ defined as the critical stress needed to extract water from the sample at a given water-to-cement mass ratio along with the compressibility modulus $K_0$ computed as the local first order derivative of the compressive yield stress curve noting that a small variation in solid fraction $d\phi$ relates to a volume strain $\epsilon_v$ following $d\phi = -\phi \cdot \epsilon_v$.

A Sigma 3-16PK centrifuge equipped with a swinging bucket rotor was used [30]. The cement paste was poured in transparent plastic centrifugal tubes with a diameter of 28 mm and a volume of 50 ml. All the tubes were previously filled with some epoxy resin to get rid of the conical section of each tube. The distance between the center of rotation and the flat bottom of the tube was 153 mm. The rotation speed used in the current study was 4500 rpm.

The compressive yield stress at a given solid volume fraction of cement was obtained by a volume fraction profile method as proposed by Miller et al. [30]. The solid volume fraction over the tube was measured by cutting the centrifugal sediment into around 10 thin slices with a thickness of 3 to 5 mm. The pieces were then dried at 105°C until a constant weight was reached. Compressive yield stress as a function of solid volume fraction is plotted for our two types of cement pastes in Fig. 2.
<figure><img src="image_3.png" /><figcaption>**Figure 2.** Compressive yield stress of cement paste as a function of W/C ratio measured using centrifugation for the two PCE dosages studied in this work. The vertical dashed lines correspond to the initial W/C ratio of our two types of samples. The horizontal dashed line stands for the reference capillary pressure $P_{cap}$ in a typical drying fresh cement paste (see text).</figcaption></figure>

In order to extrapolate both compressive yield stress $\sigma_M$ and compressibility modulus $K_M$ at the level of our model mortars from the measured compressive yield stress $\sigma_0$ and compressibility modulus $K_0$ of the paste, we are using here the accepted work of Chateau [31]:

$$K_M = K_0 \left(1 - \frac{\phi_B}{\phi_m}\right)^{-2} \qquad (1)$$

$$\sigma_M = \sigma_0 \sqrt{(1 - \phi_B) \left(1 - \frac{\phi_B}{\phi_m}\right)^{-2}} \qquad (2)$$

Where $\phi_B$ is the glass beads solid fraction (50%) and $\phi_m$ is the maximum dense packing fraction (64% for spherical particles). All measured and computed values for the compressive yield stresses and compressibility moduli of our materials are reported in Tab. 2.
## 2.6. Permeability

The permeability $k$ of our fresh samples is estimated using a Kozeny-Carman type relation [32,33] $k = \phi^3 r^2 / 450(1 - \phi)^2$, which accounts for the pre-factor correction suggested in [34] and attributed to tortuosity. We moreover consider that the typical fresh mixture pore size is one order lower than the mean cement particle size ($r = 1$ µm), neglecting here any effect of the W/C ratio or the fact that there exists a pore size distribution in such heterogeneous materials. We gather in Tab. 2 all computed permeabilities for our two model mortar samples and their constitutive cement matrix. These values are in general agreement with the ones measured in [34] and [35].

<table><caption>Table 2. Samples properties</caption><thead><tr><th></th><th>Porosity</th><th>Solid fraction</th><th>W/C</th><th>PCE dosage</th><th>Compressive yield stress (MPa)</th><th>Compressibility modulus (MPa)</th><th>Permeability (m²)</th></tr></thead><tbody><tr><td>Paste W/C = 0.35</td><td>52%</td><td>48%</td><td>0.35</td><td>0.65%</td><td>0.04</td><td>0.2</td><td>1E-15</td></tr><tr><td>Paste W/C = 0.20</td><td>39%</td><td>61%</td><td>0.20</td><td>2.00%</td><td>0.8</td><td>20</td><td>3E-16</td></tr><tr><td>Mortar W/C = 0.35</td><td>26%</td><td>74%</td><td>0.35</td><td>0.65%</td><td>0.1</td><td>4</td><td>7E-17</td></tr><tr><td>Mortar W/C = 0.20</td><td>19%</td><td>81%</td><td>0.20</td><td>2.00%</td><td>3</td><td>400</td><td>2E-17</td></tr></tbody></table>

# 3. EXPERIMENTAL RESULTS

## 3.1. Drying rate

We first plot in Figure 3 the water-drying velocity at the drying surface as a function of time for the two mortar samples. Such a velocity is computed from the measured mass loss of the samples. Figure 3 leads to the following observations:

- At short time scales, as expected from samples initially having a wet surface and being in contact with the same environment, measured drying rates are equivalent and around $6.10^{-8}$ m/s. This period is called the “constant evaporation rate” period in literature and was shown to lead to evaporation rates equivalent to the one of pure water at an equivalent temperature in the same environment [36].

- The slightly higher initial drying rate (i.e., for time scales of the order of several hundreds of seconds) may be attributed to the higher temperature of the W/C = 0.2
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mortar resulting from the dissolution processes at the contact between cement and water. This effect is noted to vanish after around 30 minutes.

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- The drying rate drops down to values below the accuracy of our measurement technique around the hydration peak time as expected from the massive nucleation of C-S-H and its consequences on both porosity and permeability of the samples. In literature, the evaporation rate decrease after the constant rate period is often indeed reported to be primarily due to the change in the intrinsic permeability caused by cement hydration [37]. It has however to be kept in mind that drying may also induce a partial desaturation of the porous medium that may, in turn, induce a major decrease in permeability even in the absence of any porosity-filling hydration reaction [10].

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- The main feature in Fig. 3 lies in the two samples showing a plateau in drying rate lasting for more than $10^4$ seconds (3 hours). On the main time scale of interest of this paper (i.e., less than $10^4$ seconds or less than 3 hours), both samples drying rates are noted to be similar. Hence, the amount of water leaving the two samples is identical but, as we will see further, the consequences on shrinkage and microstructure of such a water loss are very different.

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<figure><img src="image_4.png" /></figure>

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<caption>**Figure 3.** Water flow in m/s at the upper surface of our fresh samples as a function of time before setting for the two mortars. The vertical lines are used to locate the peak in hydration heat as measured in section 2.1.</caption>
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## 3.2. Shrinkage

<figure><img src="image_5.png" /><figcaption>**Figure 4.** Comparison between average vertical drying-induced shrinkage measured using microtomography and free autogenous shrinkage for the W/C = 0.35 mortar. The vertical dashed line corresponds to the time of the measured peak in hydration heat.</figcaption></figure>

We plot in Fig. 4 the measured free autogenous shrinkage along with the average vertical drying-induced shrinkage computed from the microtomography measurements. We first note that the drying-induced shrinkage is reaching a plateau and is almost over after only around 3 hours. The subsequent increase is suggested to be induced by the hydration onset and its associated autogenous shrinkage. Obviously, this second increase in shrinkage in the exposed sample cannot be directly compared to the autogenous shrinkage measured in a protected sample.

We moreover note that drying-induced shrinkage after around $1E^4$ seconds (2-3 hours) is of the same order of magnitude (around 0.1%) as autogenous shrinkage at the end of the hydration heat peak (around $1E^5$ seconds). We finally note, by simply comparing both types of shrinkage and their respective magnitudes, that our exposed W/C = 0.35 sample may potentially be reaching total shrinkage values of the order of 2%. This suggests that drying-
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induced shrinkage in the case of exposed materials is potentially able to increase the total
shrinkage of the material by a factor 2.

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<figure><img src="image_6.png" /><figcaption>**Figure 5.** Comparison between the average drying-induced shrinkage measured using microtomography and the volume loss corresponding to the measured water loss for the two mortar samples. The white dots show the first observation of microstructural damages in fresh samples by microtomography 2D radiographs (see text).</figcaption></figure>

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We now compare in Figure 5 the average drying-induced shrinkage and the volume loss induced by the measured water loss for the two mortar samples. For around a few thousand seconds (around one hour) for the W/C = 0.35 sample and one thousand seconds (around 20 minutes) for the W/C = 0.2 sample, shrinkage and water volume loss are identical. This suggests obviously that the two samples stay fully saturated in this first regime and are simply shrinking to compensate for the loss of water imposed by the external environment.

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Such an initial regime where water loss and surface vertical settlement are equal was already measured in [36]. It was however attributed to the evaporation of a bleeding water layer. Our microtomographic measurements clearly show however that the vertical displacement of the upper surface is not induced by the evaporation of an upper layer of bleeding water but by the contraction of the granular skeleton itself.
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We remind here that colloidal interactions, early hydrate nucleation or cohesion forces [23,38] allow for the system to be fully stable under the effect of gravity and density differences for reasonable vertical length scales. All the samples prepared in the present paper are clearly in this regime. There is therefore no bleeding and gravity itself cannot deform the particle network. Gravity-induced stresses or buoyancy stresses for samples around 1 cm thick are indeed around a couple of hundreds of Pa while capillary stresses for pores that are around $10^{-6}$ m are in the order of 100 kPa. All gravity effects are therefore neglectable and gravity-induced settlement does not exist as such here, only drying-induced or capillary contraction.

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We suggest therefore here to describe such feature using the term “capillary contraction” and not the term “settlement” from literature where gravity-induced features are mixed with capillary driven ones as discussed in the introduction.

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After this first regime, shrinkage and water loss diverge suggesting that the samples desaturate or, in other words, that some air enters these porous media to replace water. In the first regime, no capillary stress inside the samples was expected, except at the vicinity of the drying surface, which was the only liquid/air interface. For the sake of clarity, it can be noted that some capillary pressure was still expected to propagate downward in the liquid itself in this first regime. However, as soon as the samples desaturate, some liquid/air interfaces appear in the bulk material. Some capillary stresses may then propagate, in turn, inside the sample, potentially damaging its microstructure.

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Indeed, in Fig. 5, the first microstructural damages (shown and discussed further in this paper) do initiate shortly after the end of the first drying regime. They happen after around 2 hours for the W/C = 0.35 sample and after around one hour for the W/C = 0.2 sample. Here again as in Fig. 2, results suggest that, despite the fact that both samples keep on drying and losing water to the environment, drying-induced shrinkage ends after air enters the system and after around $10^4$ seconds (around 3 hours) for the W/C = 0.35 sample and a few $10^3$ seconds (around one hour) for the W/C = 0.2 sample. The above features are similar to the generic concept of “air entry” mentioned in the introduction [12]. However, this air entry follows two different patterns depending on each sample properties as discussed in the next section.

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### 3.3. Microstructural damages

We gather in Tab. 3 microtomographic images of the typically observed microstructural damages in both samples after the end of the first saturated regime. For the sake of comparison, we add to the table the images for a sealed sample (i.e., protected from drying) where no microstructural damages were observed over all the time scales of observation up to 24 hours.

Two different patterns for the microstructural damages appear depending on the mortar W/C ratio.

- Pattern 1 in the W/C = 0.35 mortar is heterogenous but isotropic and displays very specific damages with aspect ratio around 10 or below and a typical width around a few hundreds of micrometers. The present authors are not aware of any pictures of such microstructural damages in literature so far. These damages appear before $10^4$ seconds (before 3 hours) and they do not change much over time after their initiation (at least within our time and spatial resolution). From image analysis (results not shown here), we estimated that they represent around several tenths of percent of additional porosity.

- Pattern 2 in the W/C = 0.20 mortar is clearly anisotropic (Cf. Fig. 6) and displays damages with very large aspect ratio. They initiate at seemingly random locations in the sample before $10^4$ seconds (before 3 hours) and progressively percolate to form elongated cracks. Their average width is around a couple of hundreds of micrometers. As shown in Fig. 6(b), in their final conformation, they are perpendicular both to the evaporating surface and to the longest dimension of the sample. These cracks are very similar to cracks observed in cement-based materials before, during and after setting and are typically attributed to the restrained capillary or autogenous shrinkage induced by either drying or by cement hydration. We remind however here that the damages reported in Tab. 3 are already present after a couple of hours and do therefore appear long before the hydration reaction onset. It is therefore more relevant to compare them to the so-called "plastic" shrinkage cracks observed in [36].
<table><caption>Table 2. Micro tomographic images of sealed and drying mortar samples (horizontal cross section at mid sample height).</caption><thead><tr><th colspan="4">W/C = 0.35 - Sealed sample</th></tr></thead><tbody><tr><td>Scan upon casting</td><td>Scan at 10<sup>4</sup> s<br>(Around 2.5 h)</td><td>Scan at 2.5x10<sup>4</sup> s<br>(Around 7 h)</td><td>Scan after 10<sup>5</sup> s<br>(Around 24 h)</td></tr></tbody></table>

$$W/C = 0.35$$

<table><thead><tr><th></th><th></th><th></th><th></th></tr></thead><tbody><tr><td>Scan upon casting</td><td>Scan at 10<sup>4</sup> s<br>(Around 2.5 h)</td><td>Scan at 2.5x10<sup>4</sup> s<br>(Around 7 h)</td><td>Scan after 10<sup>5</sup> s<br>(Around 24 h)</td></tr></tbody></table>

$$W/C = 0.2$$

<table><thead><tr><th></th><th></th><th></th><th></th></tr></thead><tbody><tr><td>Scan upon casting</td><td>Scan at 10<sup>4</sup> s<br>(Around 2.5 h)</td><td>Scan at 2.5x10<sup>4</sup> s<br>(Around 7 h)</td><td>Scan after 10<sup>5</sup> s<br>(Around 24 h)</td></tr></tbody></table>
<figure><img src="image_7.png" /><figcaption>**Figure 6.** Distribution over depth of the microstructural damages obtained through subtraction of tomographic images of the initial state and after 2.5 h drying: (a) W/C = 0.35; (b) W/C = 0.2.</figcaption></figure>

### 3.4. Initial shrinkage before microstructural damages

We plot in Figure 7 the shrinkage profile reconstructed through digital image correlation (Cf. Appendix A) as a function of depth for the two samples at various time steps before any microstructural damages. We see that, although shrinkage is roughly homogeneous over the depth of the W/C = 0.2 sample, it is stronger in the vicinity of the drying surface in
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the W/C = 0.35 sample. Shrinkage keeps on increasing over time for the W/C = 0.35 sample as expected from Fig. 5 where the average vertical drying-induced shrinkage has not yet reached a plateau whereas it saturates after 1500 s for the W/C = 0.2 sample as expected from Fig. 5 where the timesteps shown here are all on the drying-induced shrinkage plateau.

<figure><img src="image_8.png" /></figure>

<figure><img src="image_9.png" /><figcaption>**Figure 7.** Local vertical shrinkage profile computed through Digital Image Correlation as a function of the distance from the free surface. (a) mortar W/C = 0.35; (b) mortar W/C = 0.2.</figcaption></figure>
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# 4. ANALYSIS AND DISCUSSION

## 4.1. Drying rates and drying regime

The samples studied here are clearly in the exposed regime defined in our introduction with around 50m² of exposed surface per cubic meter of material. As soon as any water above the sample surface is evaporated (none was visually spotted in our experiments), the wet interface between grains, water and air is composed of menisci, which induce a capillary pressure $P_{cap}$ at the top drying surface [9,10,39,40]. This capillary pressure is of the order of $γ/r$ where $γ$ is the surface tension and $r$ is the radius of curvature of the menisci. We assume here for the sake of simplicity that the presence of a superplasticizer does not affect significantly the surface tension of pure water (around 70 mN/m). We moreover assume that the typical meniscus size is of the order of the typical paste pore size ($r = 1$ µm). The resulting order of magnitude for $P_{cap}$ is therefore 100 kPa, which compares well to the measured values in [35].

This capillary pressure $P_{cap}$ is expected to drive water to the upper drying surface to meet the demand for continuous evaporation of water from the environment. The capillary-driven water flow $J_{cap}$ writes:

$$J_{cap} = \frac{kP_{cap}}{\mu H} \qquad (3)$$

where $μ$ is water viscosity, $H$ is the sample depth and $k$ is the sample permeability.

Using Eq. 3 and Tab. 2, the $J_{cap}$ values computed for the W/C = 0.35 and W/C = 0.2 samples are 3×10⁻⁷ m/s and 1×10⁻⁷ m/s, respectively. They are both higher than the measured drying rate in Fig. 3 (around 6×10⁻⁸ m/s). This suggests that the capillary pressure gradient induced by our drying experiments is sufficient (at least initially) to extract water from the entire sample [10]. This suggests, in turn, that water loss in both samples shall be homogeneous and that there shall not be any creation and propagation of a drying front inside the sample [10]. Such a regime may go on even when the porosity stops being saturated as long as the decrease in permeability induced by desaturation does not prevent the material from feeding the evaporating surface. This is confirmed by the fact that the water loss rate for both samples in Fig. 3 is constant for 1E⁴s (around 3 hours). This finally suggests that, in steady
state and for this duration, the water loss is homogeneous and spread over the entire sample and there shall not be any major gradients in capillary pressure or drying stresses in the fresh sample. This is in opposition to the drying of hardened cement-based materials where strong moisture gradients induced by the low permeability of such hardened materials are known to drive strong capillary stress gradients [41].

The above first-order analysis agrees well with the W/C = 0.2 sample where local shrinkage in Fig. 7(b) was measured to be homogeneous. It is however in contradiction with Fig. 7(a) where the shrinkage of the W/C = 0.35 sample was shown to be localized close to the upper drying surface of the sample. This contradiction can however be explained by looking at the kinetics of liquid pressure propagation in the sample as done below.

## 4.2. Capillary pressure propagation

For a finite porous medium of height $H$ saturated by water, a liquid pressure diffusion characteristic time $t_c$ can be defined (Cf. Eq. 4). This characteristic time corresponds to the time required to distribute the drying-induced liquid pressure in the porous medium [42–45]. This time can be estimated as:

$$t_c = \frac{H^2 \cdot \mu}{M \cdot k} \qquad (4)$$
where $M$ is the material compressibility modulus.

Using Eq. 4 and Tab. 2, the $t_c$ values are found to be around 1300 seconds (20 minutes) and 30 seconds for the W/C = 0.35 and W/C = 0.2 samples respectively. Such values suggest in the case of the W/C = 0.35 sample that capillary suction propagates from the evaporating surface to the bottom of the sample during the first 20 minutes of drying. Only after this first 20-minute period, water is homogeneously drained to the evaporating surface from everywhere in the sample. This explains why the measured shrinkage in Fig. 7(a) in this sample is heterogeneous and stronger close to the top of the sample as, for the first 20 minutes, the evaporating water has been drained from these zones only. In the case of the W/C = 0.2 sample, capillary suction propagates in less than one minute and water displacement to the top is then expected to be homogeneous almost from the start of the experiment. This leads, in turn, to the homogeneous local shrinkage measured in Fig. 7(b).
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It can finally be kept in mind in the following that, when the first microstructural damages appear in both samples, this first regime is already over and all the water contained in both mortar samples is being progressively fed to the drying surface from the entire sample at a constant rate.

### 4.3. Stress level in the samples and microstructural damages

As discussed above, the volume loss induced by water evaporation is compensated by two mechanisms, a global unrestrained shrinkage in a first saturated regime followed by some microstructural damages occurring once the so-called "air entry value" is reached [12].

#### 4.3.1. Soft fresh matrix and “cracklets”

As soon as the system gets desaturated, the capillary pressure that initially only acted at the top drying surface of the sample may now act anywhere inside the porous medium where a liquid-air interface is created. This capillary pressure is of the order of $γ/r$ or around 100 kPa. If we compare this value to the compressive yield stress of the various materials and phases studied here, we conclude that this pressure level is higher than the compressive yield stress of the W/C = 0.35 cement paste and lower than the compressive yield stresses of both mortars and of the W/C = 0.2 cement paste. This suggests that such a level of capillary stress is sufficient to induce a phase separation and extract water from the W/C = 0.35 cement matrix. As a consequence, the microstructural damages observed in this case would then find their origin in the reorganization and consolidation of the cement matrix under the effect of capillary suction. All other materials and/or scales of observation are indeed expected to be stable and to stay homogeneous when submitted to such a level of capillary pressure.

The microstructural damages as described in section 2.3 are made of voids with aspect ratio around 10 or below and a typical width around a few hundreds of micrometers. From the above, we suggest therefore that the formation of such voids finds its origin in the local reorganization and consolidation of the soft cement matrix when submitted to the capillary pressure induced by the progressive desaturation of the fresh sample.

This type of damages has never been specifically observed in standard concretes up to the knowledge of the present authors. There may be several reasons behind that.
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- First, most concretes are protected by formworks (or molds in the lab) and are therefore not exposed to the very early drying studied in this paper.

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- Second, concretes are expected to be cured and therefore protected from any early external drying. As such, when they are finally exposed to evaporation, their matrix, through hydration, has reached degrees of rigidity that are far above typical capillary stresses. As a consequence, the cement matrix has become too stiff to be consolidated or reorganized in order to provide water to the evaporating surface.

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- Finally, concrete containing a large volume fraction of aggregates has a lower permeability, even in the fresh state, than the mortars studied here. As a consequence, the material may not be able to provide water to the surface during drying as discussed in section 3.1 and a dry front may then be expected to propagate from the drying surface on distances of the order of some hundreds of micrometers [9,11]. In such a regime, there is no air entry or desaturation induced by an early exposure to a dry environment and the entire material below the dry front is expected to stay saturated. The dry front propagation may however threaten the hydration of the drying surface and potentially lead to some stress gradients at the origin of some other types of microstructural damages.

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It seems from literature that the above damages may have however been indirectly spotted in some printed samples. For instance, Bekaert et al. [46] investigated the effect of curing conditions on the vacuum-saturated porosity of printed samples and reported that the measured porosity decreased when the relative humidity during curing increased (i.e. when the water loss to drying decreased). Moreover, Mohan et al. [47] investigated the pore structure of 3D printed concrete elements and reported that the aspect ratio of pores in regions far from the drying interface increase from unity to significantly higher average aspect ratios (>3) within the dried interlayer region. Elongated pores in printed samples were also reported in [48–52]. Some of these pores may have been the traces of compressed entrapped air voids at interfaces between layers. We however suggest here that, when they are located in the bulk, these measured elongated pores find their origin in the local reorganization and consolidation of the soft fresh cement matrix induced by capillary (or drying-induced) stresses. This further suggests that the conditions to form such microstructural damages include:

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- a “soft” matrix (at least at the time of the exposure to drying),

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- a homogenous drying regime where the material is able to feed the surface with water
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(high permeability in the fresh state as it is often the case for pastes or mortars). If this condition is not fulfilled at the length scale of the entire layer, these microstructural damages are then expected to only appear in the zones closest to the drying interface where water is drained to the evaporating surfaces,

- a sufficient loss of water over a short period of time in order to reach the conditions of air entry (either because of a high material temperature, a dry environment or a high geometric ratio between the surface exposed to drying and the material volume).

In order to allow for an easy reference to these peculiar microstructural defects that seem to be specific to some printing technologies, we suggest here to give them a name. As they are typically small aspect ratio cracks, we suggest to call them **cracklets**.

Finally, all the above discussion is based on a qualitative approach. It can be expected from literature that, in order to predict such features in details, especially the time of air entry, the consolidation of the matrix, its increase in solid fraction and the related increase in mechanical properties shall be accounted for [53]. This effect is limited within the frame of this paper as the water loss before air entry is less than 1% and 0.5% of the initial water for the W/C = 0.35 and W/C = 0.2 samples respectively. This effect is however expected to increase for higher W/C ratio.

### 4.3.2. Stiff fresh matrix and cracks

Contrarily to the above regime, the W/C = 0.2 sample cement matrix is too stiff to be reorganized and consolidated by the capillary pressure. However, the sample, as a whole, is submitted to a low but non neglectable pressure gradient. Consequently, some tensile stresses are induced in the sample. This situation is very similar to what happens during the hydration of cured and/or sealed cement-based materials samples. In the latter case, water is consumed by hydration instead of being drained from the entire sample and evaporated at the surface. The similarity goes further in the sense that water loss is homogenous in both cases. Indeed, hydration is expected to be homogenous at first order and we have shown that the drying regime studied here is homogeneous with the entire W/C = 0.2 sample being under homogenous capillary suction after a couple of minutes (Cf. section 3.2). Finally, both during hydration and drying of a "stiff" fresh cement-based matrix, the level of capillary stresses is
1 not able to extract water from a cement matrix that is not compressible at these levels of
2 stresses.

3 It is therefore not surprising that the observed microstructural damages look very similar
4 to the type of cracks observed during the well-known and documented hydration/autogenous
5 shrinkage process [3]. Contrarily to hydration and setting where many chemical and physical
6 processes are acting simultaneously, it is possible here, as we are faced with external drying
7 alone, to assess the maximum equilibrium tensile stress σm using, once again, the work of
8 Scherrer [45]. This maximum stress is equal to [45]:

$$ \sigma_m = \frac{\mu H J_e}{6k} \qquad (5) $$

9 where J_e is the liquid flow rate.

10 The tensile stress computed from Eq. (5) is here of the order of 10 kPa. It can be compared to
11 a rough assessment of the tensile strength of the matrix from the value of the modulus in Tab.
12 2 and the value of the critical strain, above which cracks have been measured to occur in
13 hardened cement pastes or fresh pastes respectively. This value is reported to be around 10⁻⁴ [38,54,55] and would indeed lead to some maximal tensile strength for the W/C = 0.2 matrix
14 of order 10kPa. The two values being of the same order of magnitude suggests that the tensile
15 stress induced by capillary suction is at the origin of the observed long cracks shown in Fig.
16 6(b).

17 All the above is however in contradiction with some drying-induced cracks that were reported
18 to clearly open from the drying surface [36]. We suggest that the difference between this work
19 and other measurements originates from the studied drying regime itself. The two materials
20 studied here are rather permeable and the studied samples have a low thickness. They are
21 therefore able to feed the evaporating surface with water. As our samples thickness is small,
22 this water is homogenously drained from everywhere in the sample as discussed in section
23 3.1. As a consequence, and as shown in Fig. 3, the drying rate is constant and the material,
24 once the capillary pressure has propagated down to the bottom of the sample, dries
25 homogeneously. In such a case, the pressure gradient is low and the top surface is not
26 expected to specifically suffer from any tensile stress higher than in the bulk [56]. Many
27 materials, in nature or industry or more specifically in concrete construction, have however
28 permeabilities in the fresh state low enough to prevent the material from feeding the
29 evaporating surface with water as discussed in section 3.1. or as illustrated in [9,11] . They
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may moreover be far thicker preventing the water from being drained from everywhere in the sample. Finally, even when they are initially able to feed the evaporating surface with water, the progressive desaturation induced by water loss may limit in time such ability. In such cases, there may exist a zone in the sample where water is not drained or a dry front may even propagate from the evaporating surface. The pressure gradient in the sample would then strongly increase and the stress at the evaporating surface would then be expected to become tensile. Cracks would then, in turn, be expected to start from the top of the sample instead of anywhere in the sample as measured here.

# 5. Back to practical considerations

## 5.1. From glass beads to real sand

We first show in Figure 8 the exact same measurements for the same sample geometry when the glass beads in the W/C = 0.35 mortar are replaced with a 0/4 mm river sand. We observe in this “real” material the same cracklets as the ones observed in our model mortar containing glass beads.

<figure><img src="image_10.png" /><figcaption>**Figure 8.** Micro tomographic images of a mortar with W/C ratio of 0.35, and containing 0/4 mm river sand subjected to drying: (a) scan upon casting; (b) scan at 2.5 h; (c) scan after 24 h.</figcaption></figure>
## 5.2. Standard concrete: heterogeneous drying and shrinkage

We first choose to ignore the protected case of concrete wall casting. For typical concrete slab casting, drying is not expected to be homogeneous. First, the permeability of this highly dense material (made from 80% of non-porous sand and aggregates) is too low for the material to provide water to the evaporating surface and a dry front is expected to propagate from the evaporating surface. Moreover, concrete slabs are expected to be too thick for water to be drained from the entire thickness. Water is then dominantly drained from a zone located right below the evaporating surface. In both cases, the concrete slab undergoes heterogeneous shrinkage and a fast increase in some liquid pressure gradients. As a consequence, it can be expected, from the reasons discussed in the above section, that the stress at the evaporating surface is tensile. Cracking is therefore expected to initiate at the evaporating surface and propagate on a finite length through the drying front or through the zone where water is drained. The cracklets observed in this paper may still potentially be observed in the zone where water is drained from but local capillary stresses are expected to be fully dominated by liquid-pressure-gradient induced stresses. Cracks propagating from the evaporating surface are therefore the most expectable and most obvious microstructural damage as observed in practice and studied in the plastic shrinkage cracking literature gathered in the introduction. The concepts of heterogeneous shrinkage induced by the kinetics of capillary stress propagation and the one of the diffusion of a dry front induced by the inability of the material to provide water to the evaporating surface are however absent from that literature.

## 5.3. Printed concrete: cracks and cracklets

For the generic 3D printing of a filament, the material is considered as extremely "exposed" as the geometric ratio between the drying surface and the material volume is high. In the case of low water-to-binder ratio materials or extremely detrimental environmental conditions, water demand may be higher than the ability of the material to provide water to the evaporating surface. This shall in turn lead to the propagation of a dry front that may threaten cement hydration and potentially affect layer interfaces as studied and demonstrated in [11]. However, in most cases, because these materials are often mortars with
1 higher permeabilities in the fresh state than concretes and because the filament thickness is
2 typically low, we expect that water will be homogeneously drained from everywhere in the
3 sample. We distinguish here between two typical printing strategies, the mono-component
4 printing (1K) and the two-components printing (2K) where an accelerator is dispersed in the
5 material at the level of the printhead. In the case of 1K printing strategy, it can be expected
6 that the cement matrix is initially soft enough for cracklets to appear in the material whereas
7 the very fast stiffening of 2K solutions shall probably protect these materials from such
8 microstructural damages. In the 2K solutions, however, the competition between the
9 development of liquid pressure gradient and the strength growth is expected to drive the
10 initiation of cracks. Depending on the material permeability and its evolution along with the
11 thickness of the filaments, these cracks may initiate from the evaporating surface or from
12 anywhere in the bulk material. No matter the technology, it is worth keeping in mind from the
13 above that drying in the case of printed materials will be a key driver of the final
14 microstructure and that its mitigation or the mitigation of its consequences will be key issues
15 to tackle [57].
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## 6. Conclusions
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19 We have studied in this paper the very early age drying of "exposed" fresh cement-based
20 model mortars (i.e. samples for which the ratio between drying surface and sample volume
21 was higher than 10 m²/m³). In such conditions, drying-induced effects, that are usually
22 neglectable when compared to hydration-induced effects in standard concrete elements,
23 dominate.

24 Our results suggest that, in a first regime, fresh cement-based materials are initially
25 deformable enough to simply shrink when they dry without any desaturation of their porosity.
26 We suggest to describe such feature using the term "capillary contraction" and not the term
27 "settlement" from literature where gravity-induced features are mixed with capillary driven
28 ones. In this first regime, the sample volume decrease is then equal to the water volume lost
29 to the external environment. This initial drying-induced shrinkage is occurring over a period
30 of a couple of hours and, depending on the rigidity and permeability of the fresh material, it
31 may either result into a homogenous local shrinkage in a "stiff" fresh mortar or into a
32 shrinkage strongly localized close to the drying surface in a "soft" fresh mortar.
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We moreover measured, after this first regime, the initiation of some drying-induced microstructural damages long before hydration onset. In the “stiff” fresh mortar, damages were found to be similar to the well-known hydration-induced high-aspect-ratio microcracks usually observed in cement-based samples after a couple of days. In the “soft” fresh mortar, however, damages had an aspect ratio of around 10 and a typical width of a few hundreds of micrometers. Because of this peculiar shape, we suggested to name them “cracklets”. Both types of microstructural damages appear as early as after one hour. They are therefore fully linked to external drying and are not related at all to hydration.

We finally emphasized in our discussion that the conditions required for early drying to induce such microstructural damages in the bulk of the material are fulfilled in the case of most recently developed 3D printing concrete technologies.

## Acknowledgments

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The authors would like to acknowledge the financial support of the DiXite project and Alluvium project, which is supported by a public grant overseen by the French National Research Agency (ANR) as part of the « Investissements d'avenir » program (reference: ANR-16-IDEX-0003) in addition to the contributions of the institutions and partners involved. L. Caneda-Martínez is supported by the "Postdoctoral fellowship funded by Xunta de Galicia (ED481B-2021-001). The authors would also like to thank P. Belin for his help designing and producing some parts of the experimental set-up.

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## Appendix A

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To assess the drying-induced shrinkage of samples before setting, an in-house software CMV was used to perform DIC on the samples. This method is based on the comparison of a reference radiograph with consecutive radiographs obtained during XRCT measurements at different drying ages.

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Firstly, the reference image is discretized into a grid of points to be correlated. The correlation domain of the selected points is then prescribed according to the available local contrast and spatial resolution of the images. The DIC computation is then performed through finding the most similar domain in the deformed images based on optimizing the so-called zero centered normalized cross-correlation coefficient as presented in [58].
The strain field is then obtained via performing Green formula employing a contour integration, on the measured displacement of the surrounding points of a given point. This DIC approach for detecting local and overall strain was previously developed, and in-depth details can be found in previous work such as [28].

Moreover, the uncertainties of the DIC-based measurement of radiographs can be attributed to the noise in the image, i.e., the imperfection of the image acquisition, and the systematic error, i.e., the interpolation of grey levels within the correlation domain to acquire the sub-pixel accuracy of the displacement [28,59]. In the current study, a bi-linear grey level interpolation was used. To decrease the DIC random error, which is proportional to the ratio between the noise and available local contrast within the correlation domain, a rather large size, i.e., 100 voxels, was selected, which corresponds to the typical size of the beads and bubbles in the sample. Furthermore, the local vertical shrinkage is obtained by computing the average vertical shrinkage of every two rows of correlated points, e.g., every two rows of points with the same color in Fig. A1 allows to obtain the mean local vertical shrinkage of the height lies in the middle of the rows.

The correlation coefficient criterion was set to 0.7, which allows correlating most of the points. For the points that exceed the correlation coefficient criterion, the correlated locations were extrapolated according to well-correlated points. The measurement uncertainty of the DIC was estimated by comparing the errors of DIC measurement with the imposed displacement, i.e., performing the DIC measurement of the radiographs before and after a small imposed magnification variation [28,59–61]. Measurement uncertainty of around 0.05 pixel was considered in the current study.

<figure><img src="image_11.png" /></figure>
1 **Fig. A1.** Illustration of 2D DIC measurement for the consecutive radiographs.

2

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7 [2] C.G. Lynam, Growth and movement in Portland cement concrete, Oxford University Press, London, 1934.

9 [3] D.P. Bentz, O.M. Jensen, Mitigation strategies for autogenous shrinkage cracking, Cem Concr Compos 26 (2004) 677-685.
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17 [6] R.A. Buswell, W.R.L. da Silva, F.P. Bos, H.R. Schipper, D. Lowke, N. Hack, H. Kloft, V. Mechtcherine, T. Wangler, N. Roussel, A process classification framework for defining and describing Digital Fabrication with Concrete, Cem Concr Res 134 (2020). https://doi.org/10.1016/j.cemconres.2020.106068.

21 [7] ACI 305, ACI 305R-99 Hot Weather Concreting Reported by ACI Committee 305, Journal of American Concrete Institute (2000) 1-20.

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