EVOLUTION OF PORTLAND CEMENT
MECHANICAL PROPERTIES EXPOSED TO
CO2-RICH FLUIDS: INVESTIGATION AT
DIFFERENT SCALES

Brice Lecampion, James Vanzo, Franz-Josef Ulm, Bruno Huet, C Germay, Ines Khalfallah, Justin Dirrenberger

► To cite this version:

Brice Lecampion, James Vanzo, Franz-Josef Ulm, Bruno Huet, C Germay, et al.. EVOLUTION OF PORTLAND CEMENT MECHANICAL PROPERTIES EXPOSED TO CO2-RICH FLUIDS: INVESTIGATION AT DIFFERENT SCALES. Mechanics and Physics of Porous Solids (MPPS) -A tribute to Pr. Olivier Coussy, IFSTTAR, pp.129-152, 2011, 9782720825934. hal-04847884

HAL Id: hal-04847884

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# EVOLUTION OF PORTLAND CEMENT MECHANICAL PROPERTIES EXPOSED TO CO₂-RICH FLUIDS: INVESTIGATION AT DIFFERENT SCALES

B. LECAMPION*, J. VANZO†, F.J. ULM†, B. HUET**, C. GERMAY◦, I. KHALFALLAH**, J. DIRRENBERGER**

* Schlumberger Doll Research
One Hampshire Street
Cambridge, MA 02139, USA
e-mail: BLecampion@slb.com

† Dept. of Civil & Environmental Engineering
Massachusetts Institute of Technology,
77 Massachusetts Avenue
Cambridge, MA 02139, USA

** Schlumberger Riboud Product Center
1 rue Henri Becquerel
Clamart 92142, France

◦ Epslog S.A.
Bat. PIMW, Bvd de Colonster 4/P56
Liège 4000, Belgium

**Key words:** Cement Carbonation, Scratch tests, Nano-indentation grid technique, Chemical analysis, Micro-poroelasticity, CO₂ storage

**Abstract.** Macroscopic scratch tests and nano-indentation grid tests on carbonated Portland cement pastes are reported. A chemical analysis (Electron Probe Micro Analysis) is also briefly presented. The scratch tests probe the macroscopic evolution of the material failure properties between the un-reacted and carbonated parts of the samples, while grid of nano-indentation tests investigate the material evolution at a smaller scale. The results are put in perspective via a micro-poroelastic analysis. The material becomes stiffer and stronger macroscopically with carbonation while a large re-organization of the microstructure takes place at small scale.

## 1 MOTIVATIONS

The interest in carbon dioxide (CO₂) geological storage as well as enhanced-oil recovery applications via CO₂ injection has grown steadily in recent years. The sealing proper-
ties of wells -both injectors, producers and abandoned- during the life-span of a project is a critical factor for performance and risk assessments. Portland cement - the sealing components of oil wells- is known to react when exposed to CO₂. This is also a matter of concern in civil engineering with respect to armature corrosion due to atmospheric carbonation. In deep cemented wells, fluid composition, temperature and pressure are different from atmospheric conditions although the main mechanisms of carbonation remain similar and may ultimately endanger the sealing properties of the cemented annulus between the formation and the steel casing [1]. Cement carbonation via CO₂ exposure can be roughly split in the following stages. First, CO₂ dissolves in water forming carbonic acid (dissociation) which then reacts with Portlandite (CH) to form calcite. It also reacts with Calcium-Silicate Hydrates (C-S-H) forming calcite and silica gel:

$$Ca(OH)_2 + CO_2 \rightarrow CaCO_3 + H_2O \quad (1)$$

$$CaO_x \cdot SiO_2 \cdot nH_2O + xCO_2 \rightarrow xCaCO_3 + SiO_2 + nH_2O \quad (2)$$

$$CaCO_3 + CO_2 + H_2O \rightarrow Ca^{2+} + 2HCO_3^- \quad (3)$$

For any fugacity of CO₂, the Gibbs free energy of reactions 1 and 2 is negative and hydrates carbonation proceeds completely until depletion of one of the reactant. After depletion of cement hydrates, i.e. for an excess of CO₂ with respect to hydrates, the solubility of carbonates is increased (reaction 3) therefore allowing for some significant calcium mass transfer. Finally, for an excess of water with respect to cement hydrates and CO₂, calcium is leached out of the system and calcite dissolution is complete. Previous publications have thus referred to a carbonation stage and a dissolution stage. The first stage was mainly observed in the high pressure and high temperature closed system experiments [2], [1] and a dissolution stage with no leaching was also suggested in the latter conditions for long time of exposure (beyond 3 months) [3]. The second stage including calcium leaching was observed for open system experiments, i.e for infinite supply of water and CO₂, at room temperature and pressure [4] (see [5] for a review).

In this paper, we restrict to relatively short CO₂ exposure of samples carbonated at high pressure and temperature in closed systems (i.e. no "leaching") and focus on the evolution of mechanical properties of the material. The carbonated samples (see Fig. 1) clearly exhibits inhomogeneities which prohibit the quantitative analysis of conventional mechanical tests such as uniaxial compression. Inhomogeneities of mechanical properties in a cylindrical core under tri-axial compression imply a non-uniform state of stress and strain. The "macroscopic" values of elastic and strength properties obtained from such conventional tests therefore integrate all the inhomogeneities (size, structure of the carbonated zones and properties). The values obtained can not be extrapolated to a different geometry, providing therefore little value for practical applications. In order to properly investigate the evolution of the mechanical properties associated with chemical changes in the cement paste, an approach based on finer experimental tests, sampling only particular zones (unreacted, carbonated rim etc.), is investigated. Repetitive scratch tests of the
<figure><img src="image_2.png" /><figcaption>Figure 1: Cement cores cut in half after CO₂ exposure for two distinct durations (top: wet super-critical CO₂, bottom: CO₂-saturated with water), the carbonated rims are clearly visible.</figcaption></figure>

surface of the core are performed in order to reveal the evolution of failure properties at a scale of about a millimeter. Nano-indentation grid tests are also performed on different zones of the exposed sample. This experimental technique samples a smaller lengthscale of the material (few tenth of micrometers), and is well suited to probe the C-S-H matrix mechanical properties in the unreacted and carbonated zones of a sample. Some chemical analyses are also reported. The results are put in perspective via a micro-poroelastic analysis.

# 2 MATERIALS AND CARBONATION

## 2.1 Materials

The material used for this study is an oil-field class G cement paste with a slurry density of 1.89g/cm³, which corresponds to a water-to-cement ratio of 0.45. Class G cement is a classic blend used in the cementing of oil-wells and is very similar to CEM I system but slightly coarser [6]. The cement slurry is prepared according to ISO/API specifications [6], cured in cubic molds for 72 hours at a temperature of 90°C and a pressure of 28MPa. This particular cement is exactly similar to the one used in [3, 7]. The large characterization of the behavior of this system with respect to CO₂ exposure already reported in several publications will be completed here by a detailed investigation of its mechanical properties.

An investigation of the cement mineralogy via XRD has been performed on a unreacted
<table><caption>Table 1: Mechanical properties of the unreacted material obtained from conventional tests. $f_{rupt}$ denotes the failure load for a given confining pressure.</caption><tr><td>UCS direct</td><td>43 ± 2 MPa</td></tr><tr><td>Young's Modulus</td><td>16.4 GPa [7]</td></tr><tr><td>Poisson's ratio ν</td><td>0.24 [7]</td></tr><tr><td>f<sub>rupt</sub></td><td>63MPa @ 30MPa of Confinement [7]</td></tr></table>

sample. A quantitative analysis (Rietveld method) allows to estimate the composition (see Table 2) in terms of the weight ratio of the constituents of a dry "powder" of the hydrated paste (i.e dry cement minus its porosity). From these results and the knowledge of the density of the cement slurry $\rho_s = 1.89SG$, it is possible to obtain an estimate of the overall porosity $\phi$ of the hydrated material as: $\rho_s = \phi\rho_w + (1 - \phi)\rho_{powder}$, where $\rho_w$ and $\rho_{powder}$ denotes respectively the density of water and of the dry powder of hydrated cement. The density of the dry powder of hydrated cement can also be estimated from the XRD results: $1/\rho_{powder} = \sum_j W_j/\rho_j$ where $W_j$ denotes the mass fraction of components $j$ of density $\rho_j$ in the dry powder. We finally obtain a value of total porosity of 33%, which is in close agreement with the value obtained from MIP on the same material [3]. Finally, Table 1 summarizes the mechanical properties obtained from conventional tests (uniaxial and triaxial tests) on the initial material. These properties are in the usual range for such a cement mix.

<table><caption>Table 2: Quantitative XRD estimates of the weight fraction of the different mineralogical component of a dry powder of hydrated cement.</caption><thead><tr><td>Components</td><td>Density (SG)</td><td>Weight fraction W<sub>j</sub> (%)</td></tr></thead><tbody><tr><td>C4AF</td><td>3.76</td><td>16.38</td></tr><tr><td>Quartz</td><td>2.62</td><td>1.21</td></tr><tr><td>Calcite</td><td>2.71</td><td>2.65</td></tr><tr><td>Portlandite</td><td>2.25</td><td>31.89</td></tr><tr><td>Ettringite</td><td>1.8</td><td>5.72</td></tr><tr><td>Katoite</td><td>2.76</td><td>9.15</td></tr><tr><td>Amorphous content (C-S-H)</td><td>2.03</td><td>33</td></tr></tbody></table>

## 2.2 CO$_2$ exposure

The cured cubic molds were either cored in order to obtain small diameters cylinders (1.25 and 2.5 cm) or left as such for some initial tests. Table 3 summarizes the five class of samples used throughout this study depending on their exposition to CO$_2$. A set of 20 samples (6 samples of 1.25 cm diameter and 14 samples of 2.5 cm diameter) was placed in a CO$_2$ reactor at constant Temperature (90°C) and pressure (28MPa) for either 4 days
<table><caption>Table 3: The five different types of samples, the carbonation rim thickness is measured directly after cutting the core in 2 parts along its axis (see Fig. 1).</caption><thead><tr><th rowspan="2">Sample Family<br>#</th><th colspan="2">Exposure to CO<sub>2</sub> [in hours]</th><th rowspan="2">Carbonation rim<br>thickness [mm]</th></tr><tr><th>Wet supercritical CO<sub>2</sub></th><th>CO<sub>2</sub>-saturated water</th></tr></thead><tbody><tr><td>1</td><td>-</td><td>-</td><td></td></tr><tr><td>2</td><td>88</td><td>-</td><td>2</td></tr><tr><td>3</td><td>-</td><td>88</td><td>3</td></tr><tr><td>4</td><td>523</td><td>-</td><td>5</td></tr><tr><td>5</td><td>-</td><td>523</td><td>6-7</td></tr></tbody></table>

(88 hours) or 3 weeks (523 hours). A detailed presentation of the CO₂ reactor and the experimental procedure is reported in [8]. We briefly recall here its main characteristics. The set-up is designed to expose cement samples to two types of CO₂-rich fluids: wet supercritical CO₂ in the upper part and CO₂-saturated water in the lower part of the reactor. After placement of the samples and addition of the required amount of liquid fluid, the reactor is closed, the heating system starts and the CO₂ is slowly injected to reach a constant pressure. After about two hours, the temperature and pressure have reached their desired value (90°C, P = 28 MPa) and are held constant for the duration of the test. At the end of the test, particular care is taken to slowly depressurized the system in order to avoid sudden cracking of the samples via the well-known Mandel-Cryer poroelastic effect [9]. In the two test durations reported here, the volume of water is of 625 mL, the volumetric ratio of cement over water is of 0.15 and the volumetric ratio of the CO₂ over cement is about 0.11.

# 3 MACROSCOPIC EVOLUTION: SCRATCH TESTS

## 3.1 Principles

The scratch test consists in cutting a grove on the surface of a specimen via a Poly-crystalline Diamond Composites (PDC) cutter. The test is conducted under kinematic control, namely with a constant depth *d* (referred to as the depth of cut), constant cutter width *w* and a constant speed of the cutter. The two components of the force acting on the cutter are recorded continuously during the scratch; both in the scratch direction *F*<sub>s</sub> and normal to the scratch surface *F*<sub>n</sub>. These forces are typically averaged on a length-scale of a few times the depth of cut. This test has been extensively used on sedimentary rocks. It provides an efficient and continuous measurement of the material strength as very little damage is caused to the sample. A more complete description can be found in [10, 11]. It is important to stress that such tests completely removes a known volume of rock. It involves order one strain, and material behavior beyond failure. It is not an incipient failure test.

The total force acting on the cutter generally has a pure "cutting" as well as a frictional
<figure><img src="image_3.png" /><figcaption>Figure 2: Sketch of the forces acting on a sharp cutter (from [12]).</figcaption></figure>

component [12]. However, when using a "sharp" cutter (see Fig. 3.1), the total force acting on the cutter is mostly devoted to the pure cutting process (process of rock destruction), any frictional processes being negligible. All the tests reported in this paper have been performed with sharp cutters. It is also important to note that there is a transition from ductile to brittle failure as the depth of cut increase (at fixed cutter width). The brittle mode of failure is associated with the appearance of macro-chips (see [10]). All the tests reported here were performed at low depth of cut. In the ductile mode of failure, the horizontal $F_{cs}$ and vertical $F_{cn}$ components of the total force experienced by the sharp cutter are proportional to the cross area of the cut $A = wd$ (where $w$ is the cutter width and $d$ the depth of cut) and the specific energy $\epsilon$ of the specimen [12] (see Fig. 3.1):

$$F_{cs} = \epsilon A \quad F_{cn} = \zeta \epsilon A \qquad (4)$$

The ratio between the vertical and horizontal force $\zeta$ is a function of the cutter inclination (see [12] for details). The specific energy $\epsilon$ is defined as the minimum energy required to destroy a unit volume of rock. Such a material property has been found to be directly related to the uniaxial compressive strength of a large number of sedimentary rocks, mortar etc. [11]. For scratch tests performed with sharp cutters at different depth of cut, the specific energy is estimated by computing the coefficient of proportionality between the horizontal component of the force $F_{cs}$ averaged a distance of over about four times the depth of cut and the cross-sectional area of the cut.

## 3.2 Validation

An initial series of scratch tests was performed on unreacted cement in order to validate the use of relatively small cutter widths as well as to assess the repeatability of the procedure. The requirement of a small cutter width is linked to the relatively small size of the samples put in the CO₂ reactor (half an inch diameter). Fig. 3 displays the evolution of the horizontal force averaged over the length of the cut versus the cross sectional area of the cut $A = wd$ for the three different cutter widths tested. For a given width of the cutter, a clear linear variation of the mean horizontal force with the depth of cut (at $w$
<figure><img src="image_4.png" /><figcaption>Figure 3: Cutting force versus cross area of the cut for the unreacted material: effect of the cutter width.</figcaption></figure>

constant) can be observed. However, the coefficient of proportionality between the force and the cross-sectional area (i.e. the specific energy $\epsilon$ given by eq.(4)) is different for each cutter width: a factor of 1.42 (2.13) is obtained between the specific energy obtained from tests conducted with a cutter width of 5mm (2.5mm) compared the value obtained from tests conducted with a cutter of 10mm width. Such a cutter width effect (i.e. the loss of the self-similar scaling $F/A$) clearly illustrates a non-local failure mechanism although without the appearance of macro-cracks. Such a non-local mechanism has also been observed on some rocks exhibiting large dilatancies [13]. A recent analysis of the test in terms of fracture energy has been developed in order to take into account such a non-local mechanism, indicating that fracture toughness could be extracted from scratch tests [14]. It is worthwhile to point out that any theory trying to explain such an effect must recover the linearity of the cutting forces with the depth of cut for a given cutter width. Such a cutter-width effect attenuates as the width of the cutter increases, and the failure property obtained from wide cutter asymptotes toward the "intrinsic" material property. In the following, we will present all the results in terms of the horizontal force averaged
<figure><img src="image_5.png" /><figcaption>Figure 4: Principle of repetitive scratch tests (left), mean horizontal forces versus cumulated depth of cut with 3 different cutter widths for an unreacted cement sample (right). The core is carbonated from all sides (see Fig. 1), the left carbonated edge is not displayed here in order to highlight the carbonated rim visible within the middle part of the sample.</figcaption></figure>

over the cut for a given depth of cut and cutter width.

In order to capture the variation of the mechanical properties as one moves deeper inside the material from the initial surface, repetitive scratch tests are performed with the same *incremental* depth of cut and same cutter width. For an unreacted cement sample, Fig. 4 displays the horizontal force averaged over the length of the specimen as a function of the cumulated depth of cut from the initial surface of the sample. The first millimeter exhibits a lower value of the horizontal force which then stabilizes. This ultimately proves the repeatability of the test and the possibility to detect changes in mechanical properties within the sample. The lower forces obtained close to the surface may be due to dessication / hydration effects, although the samples were carefully kept in water. The impact of coring has to be excluded for the test reported in Fig. 4 as the sample was simply an uncored cube directly out of the curing chamber. Nevertheless, possible micro-cracks induced by coring may be present on samples exposed to CO₂ as cylindrical cores were placed in the CO₂ reactor. It is important to highlight that based on these results, a change of mechanical properties will only be detectable from repetitive scratch tests at a depth larger than 1 / 1.25 mm from the initial sample surface.

## 3.3 Samples exposed to CO₂

Several cylindrical cores of 25.4mm diameter and 50.8mm in length have been tested by repetitive scratching for each type of CO₂ exposure (see Table 3), amounting to a total of eight cores. Fig. 5 displays an example of the "log" (variation along the length of the cut) of the horizontal cutting force component across a sample of type # 4 for an incremental depth of cut of 0.25mm at a depth of 8 mm from the sample surface. At such a depth,
<figure><img src="image_6.png" /><figcaption>Figure 5: Continuous record of the horizontal force along the length of the cut, for a cumulated depth of cut of 8mm and an incremental depth of cut of 0.25mm. The red continuous line is an example of a moving average of the signal over 0.2mm. The mean forces for a given cut are taken in the middle part of cut for each depth, excluding the left and right carbonated edges.</figcaption></figure>

<table><caption>Table 4: Average of the different scratch tests results in the unreacted and carbonated zone for the different type of samples (Incremental depth of cut 0.25mm, cutter width of 2.5mm).</caption><thead><tr><th rowspan="2">Sample<br>Family<br>#</th><th colspan="2">Unreacted zone</th><th colspan="2">Carbonated zone</th><th rowspan="2">rim<br>(mm)</th></tr><tr><th>Horizontal force<br>μ (N)</th><th>s (N)</th><th>Horizontal force<br>μ (N)</th><th>s (N)</th></tr></thead><tbody><tr><td>2 (a)</td><td>39.18</td><td>1.89</td><td>55.21</td><td>3.8</td><td>1.75-2.25</td></tr><tr><td>2 (b)</td><td>40.30</td><td>1.44</td><td>53.16</td><td>2.06</td><td>2-2.25</td></tr><tr><td>3 (a)</td><td>40.66</td><td>1.19</td><td>56.51</td><td>1.06</td><td>2-2.5</td></tr><tr><td>3 (b)</td><td>42.31</td><td>0.95</td><td>55.34</td><td>3.81</td><td>1.75-2.25</td></tr><tr><td>4 (a)</td><td>39.78</td><td>1.60</td><td>50.52</td><td>1.93</td><td>6.5-7.25</td></tr><tr><td>4 (b)</td><td>40.01</td><td>0.54</td><td>49.06</td><td>1.45</td><td>6.25-6.75</td></tr><tr><td>5 (a)</td><td>40.06</td><td>1.05</td><td>52.23</td><td>2.72</td><td>6.75-7</td></tr><tr><td>5 (b)</td><td>38.5</td><td>1.63</td><td>49.48</td><td>1.87</td><td>7-7.5</td></tr><tr><td>Mean</td><td>40.09</td><td>1.28</td><td>52.68</td><td>2.33</td><td>-</td></tr></tbody></table>

carbonated zones at both ends of the cut are clearly visible on the force signal. For each scratch test, the forces are averaged over the center area of the core in order to avoid the edge effects. The variation of the averaged horizontal forces versus the cumulated depth of cut for samples submitted to two different duration of exposure can be seen on Fig. 6. If we disregard the first millimeter where evolution of the force is related to the surface effects previously mentioned, two clear zones appears: a stronger zone which
<figure><img src="image_7.png" /><figcaption>Figure 6: Evolution of the averaged horizontal force versus the cumulated depth of cut for a sample exposed to wet supercritical CO₂ during 88 hours (left) and 523 hours (right). The incremental depth of cut for these tests is of 0.25mm.</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>Figure 7: Evolution of the averaged horizontal force versus the cumulated depth of cut for a sample exposed to CO₂-saturated water during 88 hours. The incremental depth of cut is of 0.1 mm, providing a more detailed evolution of cement properties.</figcaption></figure>
<figure><img src="image_9.png" /><figcaption>Figure 8: Cutting force for different depth of cuts and cutter width (2.5mm left, 5mm right) in the carbonated zone of a sample exposed to CO₂-saturated water during 512 hours.</figcaption></figure>

extend coincides with the carbonated rim, and a zone in the center of the core where the averaged horizontal cutting force is exactly similar to the unreacted material. It is also interesting to point out, that for short CO₂ exposure (i.e. shorter carbonation rim), a decrease in strength can be observed between the carbonated and unreacted part of the sample. Such a decrease in strength is associated with a dissolution front where porosity is much larger. Such a dissolution front is visible on SEM images [3]. It is important to point out, that in the case where the carbonation rim is larger (longer exposure), due to the finite geometry of the cylindrical core such a dissolution front is "averaged" between reacted and unreacted materials: the curvature of the boundary between the unreacted and carbonated zone becomes too large compared to the width of the cutter. Fig. 7 displays, for a sample of class #2, a more refined variation of the mean horizontal force as a value of 0.1 mm was used for the incremental depth of cut. A slight increase in the mean horizontal force ahead of the dissolution front can be seen. Such a "dipole" like shape around the carbonation front is profoundly similar to the one obtained from local porosity measurements from SEM images [3].

For all samples, the horizontal forces can be further averaged in both the carbonated and unreacted zones. Table 4 summarizes the results. The averaged horizontal force and its standard deviation for both the carbonated and unreacted parts of each type of sample tested are reported. The thickness of the carbonation rim obtained from scratch tests appear consistent with the thickness measured visually from the cores (Table 3). It is important to note that the value of the cutting forces in the unreacted zone of all samples is similar to the values obtained on the unreacted material. The values of the cutting forces in the carbonated zone are always larger and consistent between the different carbonated samples. On one of the samples with a long duration of exposure to CO₂, for which the carbonated rim is sufficiently large, two series of tests with different depth of cut were performed: one with a cutter width of 2.5mmm and the other with
<figure><img src="image_10.png" /><figcaption>Figure 9: Element mapping (Ca, Si, O maps) via EPMA of a carbonated 1.9 SG class G paste cured at 90°C, exposed to CO₂ for a month. The surface of the sample is to the right, unreacted paste is visible on the left.</figcaption></figure>

a cutter width of 5mmm. Fig. 8 displays the results. Again a clear linearity of the
averaged horizontal forces with the depth of cut is visible for a given cutter width but the
coefficient of proportionality differs for the two series ,similarly to what was observed for
the unreacted material. If we compare the specific energy of the carbonated and unreacted
zones, we obtain a ratio of about 1.5 for a cutter width of 2.5 mm and a ratio of 1.26
for a cutter width of 5mm. These results confirm that the carbonated cement is stronger
than the unreacted cement, a fact accepted in the case of carbonation under atmospheric
conditions [15].

4 MICROSTRUCTURE EVOLUTION

**4.1 Chemical Analysis by EPMA**

A detailed chemical analysis by Electron Probe Micro Analysis (EPMA) has been
performed at MIT in the unreacted and carbonated parts of the samples (see [16] for
a complete detailed and quantitative analysis). The primary benefit of EPMA is the
ability to acquire precise, quantitative elemental analyses at very small "spot" sizes (as
little as 1-2 micrometers), primarily by wavelength-dispersive spectroscopy (WDS). We
report here, very briefly, a semi-quantitative analysis performed on similar samples (same
density Class G mix, cured at 90°C) *but* exposed longer to CO2 (one month) performed by
Schlumberger [?]. The observed behavior observed is similar to the one reported in [16],
although not as detailed and quantitative. In the results presented here, Calcium (Ca),
Silicon (Si), Iron (Fe), Aluminum (Al) and Oxygen (O) were mapped using a so-called
rastering mode which is less quantitative than the point mode. Fig. 9 displays a map of
<figure><img src="image_11.png" /><figcaption>Figure 10: CaO SiO₂ map for an unreacted (left) and carbonated (right) 1.9 SG class G paste cured at 90°C, exposed to CO₂ for a month.</figcaption></figure>

the Ca, Si and O elements for a strip across the Class G sample exposed to CO₂ for a month. This strip spans the entire carbonated zone from the unreacted core to the initial cement, fluid interface. Calcite and silica gel nodules of different sizes up to 30 to 50 micrometers can be identified in the carbonated part.

The data were further analyzed assuming a system containing only Calcium and Silicon Oxides. In Fig. 10, we display a map of CaO versus SiO₂ atomic content only, for the unreacted and carbonated material. The purpose is to distinguish between three phases, C-S-H, calcite and silica gel, based on a two component measurement, carbon is not measured by EPMA. The distribution of chemical composition may be related to two main mechanisms. First, this distribution may correspond to the composition of a single phase, e.g. a solid solution such as the C-S-H phase. In this case the distribution of composition is expected to be quite centered (i.e. low standard deviation) because a large distribution would not be consistent with chemical equilibrium. Indeed C-S-H with large Ca to Si ratio (Ca/Si ≈ 1.5) do not coexist with C-S-H of low Ca/Si (≈ 1.0) at equilibrium. Secondly, the distribution may be related to the size of two or more phases (pure phases or solid solution) of distinct composition. Indeed if the average size of a phase is of the order of the beam interaction volume, more than one phase is identified at each point in space.

The signature of the unreacted sample is typical of a Portland cement: the distribution of composition in the CaO/SiO₂ plane is clearly centered on the C-S-H phase (CaO=62%, SiO₂=38%, i.e. Ca/Si ≈ 1.65). From this main C-S-H pole, one observes two main lines towards a pure calcium pole (CaO=100%, SiO₂=0%) and towards a SiO₂ depleted pole (CaO=20%, SiO₂=0%). These two lines are respectively characteristic of C-S-H – Portlandite mixture and a C-S-H – aluminate hydrates mixture.

For the carbonated material, on the other hand, the data spread along the line between the pure CaO pole (CaO=100%, SiO₂=0%) and Calcium depleted pole (CaO=0%,
SiO$_{2}$=60%). No clear C-S-H pole is visible anymore. The distribution of composition around the pure CaO pole supports the formation of large calcite nodules. This pole can not be attributed to Portlandite since this pole is absent in the unreacted cement core. Similarly, the distribution of composition around the Calcium depleted pole supports the formation of large pure SiO$_{2}$ nodule. XRD data of the carbonated zone (not reported here) did not indicate any increase of the Quartz content (or any other crystalline polymorph). Therefore, we suggest that these SiO$_{2}$ nodules are made of silica gel. For a composition between the initial C-S-H pole and the calcium depleted pole, it is difficult to differentiate between the coupled effect of the degree of carbonation, which is equivalent to the degree of decalcification, and the growth of nodules of calcite and silica gel. However, the large spread of the composition distribution along the latter line, as opposed to being close to the centered initial distribution, supports an advanced degree of carbonation of the cement hydrates.

The chemical analysis of the carbonated material shows that 1) the carbonated matrix is primarily made of partially decalcified C-S-H, calcite and silica gel, and 2) the characteristic length scale of the representative elementary volume is increasing (i.e. a more disordered material at small scale).

## 4.2 Nano-indentation campaign

Multiple nano-indentation performed on a grid allows the investigation of complex heterogeneous material via a statistical analysis of the results [17]. This technique has been applied with success to a large number of different cement pastes and has brought new insight in the mechanical properties of the C-S-H matrix [17]. In order to properly investigate the C-S-H matrix, a large number of indentation tests was performed on samples of the different type (see Table 3). Each tests are usually spaced at about 20 micrometers apart. All the results can be de-convoluted using an a priori unknown finite number of phases. The experimental cumulative distribution function (CDF) of the measured indentation modulus *M* and hardness *H* are fitted by a linear combination of a finite number of Gaussian CDF corresponding to the number of phases present in the material. Such an analysis provides an estimation of the number of mechanical phases in the material, the mean and variance of the indentation modulus and hardness of each mechanical "phases" as well as their respective surface fraction. For a randomly organized materials like cement paste, surface fraction can be assimilated to volume fraction. The first point of interest is of course the difference between the unreacted and carbonated samples with respect to different mechanical phases present in the material.

The analysis of the nano-indentation results can also be carried a step further by recognizing that each indentation modulus and hardness (*M*<sub>i</sub>, *H*<sub>i</sub>) obtained on the grid represents a stiffness and strength response of a composite porous material composed of a solid phase (C-S-H particle) and pore space. Some micromechanical model links the indentation values to the properties of the solid particle (contact stiffness *m*<sub>s</sub> = *E*<sub>s</sub>/(1−*ν*<sub>s</sub><sup>2</sup>) and hardness *h*<sub>s</sub>) and the solid packing density η ('one minus porosity') of the composite
material. We refer to [18] for more details. These micro-macro relations permit to probe
the microstructure sensed by the large number of indentation tests. In particular, it is
possible to determine the packing density distributions of the different hydration phases
assuming that all mechanical phases are made of a similar solid particle. In the case of
carbonated cement paste, it is unclear if the assumption of a similar solid particle for all
mechanical phases still holds.

In this study done at MIT and reported in detail in [16], a number of nano-indentation
grids (20 by 20 with a spacing of 20 µm) have been performed on the unreacted sample
and the samples exposed to CO2 (samples exposure described in Table 3). The different
steps of the analysis described previously will allow a detailed investigation of the evo-
lution of the C-S-H matrix properties. We refer to [16] for a complete presentation and
discussion of the results. Three distinct groups with similar mechanical signature have
been distinguished: i) unreacted sample and the center of the short term exposed sample,
ii) the center of the long term exposed sample (i.e. near the carbonation front) and iii)
the carbonated rim of all exposed samples.

4.2.1 Unreacted materials

Table 5 summarizes the results of the deconvolution of the nano-indentation tests performed on the unreacted materials, namely of the reference sample #1, and of the indentation tests performed on the unreacted zones of samples #2 and #3. The different mechanical phases are recognized as low-density, high density, ultra-high density C-S-H packing and residual clinkers. The results show a fair amount of consistency with previous reported results of cement pastes in terms of mean indentation modulus, mean indentation hardness [23, 20]. This consistency holds for both the reference material and the unreacted center of the carbonated samples. There is however some difference in terms of volume fraction and appearance of the low density phase between samples. This may be due to a smaller number of tests for sample #3 notably. The mean packing density values obtained by deconvolution of the data with an indentation modulus lower than the C-S-H ’solid’ (m_s = 65GPa, h_s = 3GPa) using a composite model are also consistent with reported values: η\_LD = 0.66 – 0.73, η\_HD = 0.7 – 0.77, η\_UHD = 0.74 – –0.791. Fig. 11 displays a typical deconvolution of the packing fraction of these three mechanical ”phases”. Overall, we can conclude that the micromechanical signature is very similar to other cement pastes tested [20]. It is also important to note that the center of the samples #2-#3 (short CO₂ exposure) indicates no significant changes over the initial material. A conclusion in line with the results of macro scratch tests.

4.2.2 Partially carbonated material

Due to their size and long exposure, the sample of type #4 and #5 have their center
in close interaction with the carbonation front. Nano-indentation grids performed in
the center part of those samples have a different micromechanical signature, as well as
<table><caption>**Table 5:** Summary of the nano-indentations grid results for the unreacted material</caption><thead><tr><th>Sample</th><th></th><th>#1</th><th>#2</th><th>#3</th><th>Literature [20]</th></tr></thead><tbody><tr><td rowspan="3">LD C-S-H</td><td>M (GPa)</td><td>-</td><td>-</td><td>20.59</td><td>16-26</td></tr><tr><td>H (GPa)</td><td>-</td><td>-</td><td>0.69</td><td>0.27-0.88</td></tr><tr><td>vf (%)</td><td>-</td><td>-</td><td>49.8</td><td></td></tr><tr><td rowspan="3">HD C-S-H</td><td>M (GPa)</td><td>30.9</td><td>27.48</td><td>33.24</td><td>17-40</td></tr><tr><td>H (GPa)</td><td>1.7</td><td>1.02</td><td>1.24</td><td>0.74-1.45</td></tr><tr><td>vf (%)</td><td>58.7</td><td>78.4</td><td>38.6</td><td></td></tr><tr><td rowspan="3">UHD C-S-H</td><td>M (GPa)</td><td>35.25</td><td>54.86</td><td>-</td><td>36-54</td></tr><tr><td>H (GPa)</td><td>1.83</td><td>2.34</td><td>-</td><td>1.15-2.35</td></tr><tr><td>vf (%)</td><td>33.2</td><td>14.2</td><td>-</td><td></td></tr><tr><td rowspan="3">Clinker</td><td>M (GPa)</td><td>105.3</td><td>100.33</td><td>85.61</td><td></td></tr><tr><td>H (GPa)</td><td>9.89</td><td>7.78</td><td>6.78</td><td></td></tr><tr><td>vf (%)</td><td>8.1</td><td>7</td><td>11.6</td><td></td></tr></tbody></table>

a different chemical signature. The chemical analysis reported in [16] have shown that although a strong C-S-H pole was still present for these material, no Portlandite was visible. Four mechanical phases can be defined from the nano-indentation grid tests (for more details, see [16]):

* a phase with an average indentation modulus of 19GPa and hardness of 0.78GPa. These properties compare well with those of a Low-Density C-S-H, although the indentation hardness is slightly higher. The volume fractions of this component vary widely between samples.

* the second phase has a modulus and hardness of 27GPa and 1.3 GPa respectively. These values correspond to a High-Density C-S-H. This class is not identified on all grids, but when present it is dominant.

* the third phase has a broad range of moduli (M=41–64GPa) and hardness (H=3.14–3.81GPa). This phase has a hardness much higher than the ultra-High Density C-S-H although the modulus is similar.

* the last phase has a range of moduli (M=74-93GPa) and hardness (H=5.5–9.1GPa) well above the range of usual hydration products. Its volume fraction is relatively low.

## 4.3 Carbonated zones

The average phases properties of the carbonated materials identified from nano-indentation grid are summarized in Table 6 (again, see [16] for complete details). The different mechanical phases are classified with respect to the range of the indentation modulus. Five phases were identified, two being present only in some tests.
<figure><img src="image_12.png" /><figcaption>Figure 11: Packing Density Distributions of sample #2: (top) unreacted zone; (bottom) carbonated zone - taken from [16].</figcaption></figure>

* phase C1 (M<10GPa, H<0.5GPa) probably represents macroporosity and is not present in all tests.

* phase C2 (M=10–25 GPa, H=0.5–1.1GPa) is the second most represented phase in all the carbonated materials. Its mean properties are not too different from those of Low Density C-S-H.

* phase C3 (M=25–35 GPa, H=1.1–2GPa) is present in about half of the tests. Its mean modulus and hardness appear somehow similar to High Density C-S-H.

* phase C4 (M=35–55GPa, H=2–4GPa) is the dominant phase in all the carbonated materials. Its mean modulus (M 50GPa) is somewhat similar to the one of Ultra High Density C-S-H but its mean hardness (H~ 2.78GPa) is much higher.

* phase C5 is the stiffest mechanical phase (M>55GPa, H>4GPa), its volume fraction is relatively low. This phase may represent residual clinkers.

A series of tests was also performed at different distances from the carbonation front and no clear evolution of the mechanical signature was found. This indicates a homogeneous
<figure><img src="image_13.png" /><figcaption>Figure 12: The distribution of indentation modulus of all the tests performed on unreacted (left) and carbonated materials (right) - taken from [16].</figcaption></figure>

state of carbonation in all the carbonated zones. A micro-mechanical model based on the packing of a CSH particle (of single mechanical properties) can be used to further analyze the nano-indentation data. The result of the deconvolution of that data in distributions of packing densities as presented in Fig. 11. There is a wide-spread distribution of packing densities in the carbonated zone. This is an indication that the carbonation process introduces more disorder in the microstructure. It therefore appears that the carbonated zone have a complex structure, the different mechanical phases do not seems to have the same basic 'solid' constituent. It is also interesting to visualize all the indentation modulus for the unreacted and carbonated materials (Fig. 12). One can easily see that the carbonated material have a much larger and wider distribution of indentation modulus.

# 5 MICROMECHANICAL DISCUSSION

In this section, we investigate a micromechanical analysis of the evolution of the cement properties when exposed to CO₂. We restrict ourselves to the estimation of linear poroelastic properties of cement pastes, following the approach described in [21]. We will not detail here the machinery of microporomechanics. One can refer to the pioneering work of [22] for multiphases material with internal eigenstresses. We use the multi-scale conceptual model of cementitious material developed in [23, 21], where the macroscopic properties of the cement paste are obtained via a two-steps procedure. First, the properties of the C-S-H matrix are obtained from the knowledge of the volume fraction of the different C-S-H phases (LD, HD and UHD) and their mechanical properties. Then, a second up-scaling is performed incorporating the macro-porosity, unhydrated clinkers and other minerals such as Portlandite and calcite.

## 5.1 Unreacted material

The drained elastic properties of the C-S-H matrix can be estimated from the results of the nano-indentation campaign. The volume fraction of the three phases LD, HD and
<table><caption>Table 6: Summary of the results performed on the carbonated zone of the different sample type. Multiple tests were performed on most samples (see [16] for details), we only report range of values (extrema of the different grids) for each sample type here. A value of x indicates that the phase was not present in all grids performed on this sample.</caption><thead><tr><th>Phase</th><th>Sample</th><th>#2</th><th>#3</th><th>#4</th><th>#5</th></tr></thead><tbody><tr><td rowspan="3">C1</td><td>M (GPa)</td><td>-</td><td>-</td><td>-</td><td>x-8.9</td></tr><tr><td>H (GPa)</td><td>-</td><td>-</td><td>-</td><td>x-0.37</td></tr><tr><td>vf (%)</td><td>-</td><td>-</td><td>-</td><td>x-27</td></tr><tr><td rowspan="3">C2</td><td>M (GPa)</td><td>14.4-14.79</td><td>18.6</td><td>13.-17</td><td>16-21</td></tr><tr><td>H (GPa)</td><td>0.54</td><td>0.94</td><td>0.5-0.7</td><td>0.6-1.03</td></tr><tr><td>vf (%)</td><td>15.9-27.7</td><td>31.2</td><td>15-25.8</td><td>10.9-30</td></tr><tr><td rowspan="3">C3</td><td>M (GPa)</td><td>26.6-27.3</td><td>-</td><td>x-30.9</td><td>x-30.4</td></tr><tr><td>H (GPa)</td><td>1.25</td><td>-</td><td>x-1.46</td><td>x-1.6</td></tr><tr><td>vf (%)</td><td>24.8-21.7</td><td>-</td><td>x-29</td><td>x-15.8</td></tr><tr><td rowspan="3">C4</td><td>M (GPa)</td><td>49.4-51.2</td><td>47.18</td><td>47.8-51.25</td><td>45-53</td></tr><tr><td>H (GPa)</td><td>2.5-2.8</td><td>2.39</td><td>2.45-3.45</td><td>2.04-2.9</td></tr><tr><td>vf (%)</td><td>46-55</td><td>51.6</td><td>42-71</td><td>61-78</td></tr><tr><td rowspan="3">C5</td><td>M (GPa)</td><td>88.7-95.9</td><td>57-133</td><td>72-111</td><td>77-95</td></tr><tr><td>H (GPa)</td><td>6.9-7.3</td><td>4-11</td><td>5-11</td><td>4.8-7.19</td></tr><tr><td>vf (%)</td><td>3.5-4.3</td><td>2.7-14</td><td>2.3-11</td><td>4.6-7.1</td></tr></tbody></table>

UHD making up such a matrix are taken as the averaged value for all samples in the unreacted zone taking out the stiffer phase made of unhydrated clinkers. One obtains respectively $vf(LD) = 32\%$, $vf(HD) = 56\%$, $vf(UHD) = 12\%$ for the three types of C-S-H. The value of their elastic moduli (K, G) have been taken from the deconvolution of nano-indentation tests and a poro-mechanical upscaling in all points similar to the one described [17] using a self-consistent scheme. The consistency of such an approach can be checked by comparing the measured indentation modulus (see Table 5) with the predicted one (see Table 7). The up-scaling of the C-S-H matrix properties (made of the different C-S-H types) is then performed using a matrix based Mori-Tanaka scheme where the dominant phase is taken as that of the largest volume fraction, the HD C-S-H. The results are summarized in Table 7. The porosity of the C-S-H matrix is simply obtained from the "packing" density and volume fraction of the different phases and is equal to 28%.

On top of the C-S-H matrix, the material at the larger scale contains, macro-porosity and all the minerals detected via the XRD analysis (see Table 2). The volume fractions can be estimated as follows. The macro-porosity $\phi_{mp}$ of the cement paste can be estimated via a pixel analysis of SEM images on the center part of the exposed samples [3]; a value of $\phi_{mp} = 14\%$ is obtained. This value is consistent with the one estimated with the Powers-Brownyard model and a hydration degree of 0.8. Using such a value for
<table><caption>Table 7: Poroelastic properties of the different C-S-H phases and results of the upscaling of the C-S-H matrix properties.</caption><thead><tr><th></th><th>φ</th><th>K (GPa)</th><th>G (GPa)</th><th>K<sub>u</sub> (GPa)</th><th>b (-)</th><th>M (GPa)</th><th>v<sub>f</sub> (%)</th></tr></thead><tbody><tr><td>Low-Density</td><td>0.36</td><td>10.55</td><td>6.7</td><td>13.72</td><td>0.78</td><td>17.6</td><td>32</td></tr><tr><td>High-Density</td><td>0.26</td><td>19.68</td><td>11.3</td><td>21.13</td><td>0.59</td><td>30.59</td><td>56</td></tr><tr><td>Ultra-High Density</td><td>0.17</td><td>28.9</td><td>15.43</td><td>28.9</td><td>0.4</td><td>42.5</td><td>12</td></tr><tr><td>C-S-H Matrix</td><td>0.28</td><td>16.62</td><td>9.88</td><td>18.9</td><td>0.66</td><td>-</td><td>-</td></tr></tbody></table>

the macroporosity, we obtain the volume fraction $f_{C-S-H}$ of the C-S-H matrix from the split of the *known* total porosity of the cement paste between C-S-H porosity and the macro-porosity: $\phi = \phi_{C-S-H} f_{C-S-H} + \phi_{mp}$. The volume fraction of the other constituents (non-amorphous) are then obtained from the XRD results and the value of the porosities. Table 8 summarizes the results as well as the mechanical properties of the different constituents found in the literature. Using a Mori-Tanaka up-scaling scheme, we obtain a value of 19.5 GPa for the drained cement paste Young's modulus and a Poisson's ratio of 0.26 for the unreacted material (see also Table 8). Such a value appears slightly larger than the one obtained from static measurements on the similar material [7] and can be explained by the presence of defects at a larger core scale (e.g. cracks) which significantly lower the elastic moduli. The up-scaled sonic velocities of 3670 m/s and 2060 m/s for compressional and shear waves respectively compare well with typical values for such a material [7].

<table><caption>Table 8: Poroelastic Properties and volume fraction of the different constituents together with the up-scaled properties of the cement paste. Undrained bulk moduli of the minerals constituents are equal to their drained value (i.e. non porous phases). Note *: these estimates assumes no-evolution of the C-S-H matrix properties during carbonation; Note **: this estimate uses the properties of a carbonated matrix (see Table 9).</caption><thead><tr><th rowspan="2">Constituents</th><th rowspan="2">K (GPa)</th><th rowspan="2">G (GPa)</th><th rowspan="2">K<sub>u</sub> (GPa)</th><th rowspan="2">b (-)</th><th colspan="3">Estimated Vol. fraction v<sub>f</sub>(%)</th></tr><tr><th>Unreacted</th><th>Diss. front</th><th>Carb.</th></tr></thead><tbody><tr><td>C-S-H Matrix (Tab. 7)</td><td>16.62</td><td>9.88</td><td>18.9</td><td>0.66</td><td>67</td><td>67</td><td>67</td></tr><tr><td>Quartz[24]</td><td>37</td><td>44</td><td>-</td><td>0</td><td>0.3</td><td>0.3</td><td>0.3</td></tr><tr><td>C4AF [25]</td><td>104.16</td><td>48.07</td><td>-</td><td>0</td><td>2.9</td><td>2.9</td><td>2.9</td></tr><tr><td>Portlandite</td><td>33.3</td><td>15.38</td><td>-</td><td>0</td><td>9</td><td>0</td><td>0</td></tr><tr><td>Calcite [24]</td><td>76.3</td><td>32</td><td>-</td><td>0</td><td>0.6</td><td>0.6</td><td>11</td></tr><tr><td>Katoite[24]</td><td>28</td><td>10.1</td><td>-</td><td>0</td><td>2.2</td><td>2.2</td><td>2.2</td></tr><tr><td>Ettringite[24]</td><td>27.3</td><td>9.9</td><td>-</td><td>0</td><td>2.1</td><td>2.1</td><td>2.1</td></tr><tr><td>Pores</td><td>0</td><td>0</td><td>0</td><td>1</td><td>14</td><td>23.7</td><td>13</td></tr><tr><td>Unreacted</td><td>13.9</td><td>7.7</td><td>15.47</td><td>0.66</td><td></td><td></td><td></td></tr><tr><td>Dissolution front*</td><td>10.5</td><td>5.7</td><td>12.14</td><td>0.75</td><td></td><td></td><td></td></tr><tr><td>Carbonated*</td><td>15.3</td><td>8.4</td><td>16.8</td><td>0.67</td><td></td><td></td><td></td></tr><tr><td>Carbonated**</td><td>18.38</td><td>11.03</td><td>19.43</td><td>0.63</td><td></td><td></td><td></td></tr></tbody></table>
## 5.2 Carbonated material

As previously observed experimentally, the microstructure of the material undergoes a large re-organization during carbonation: the C-S-H matrix is partly decalcified, silica gel and calcite are also present.

A simple approach that assumes no evolution of the C-S-H matrix properties can be first tested. We will simply assume that all the Portlandite crystals get dissolved and re-precipitate as calcite. The change of the volume fraction of calcite can be easily obtained, also taking into account the change of molar volume at the expense of macro-porosity. The elastic properties of the dissolution front and carbonated zones can then be easily estimated from an up-scaling similar that used for the unreacted paste. The results are summarized in table 8. Although, we have estimated the poroelastic properties of the material and *not its strength*, it is interesting to compare the ratio of the modulus of the carbonated and unreacted zones with the ratio of the specific energy of these two zones obtained via scratch tests. The ratio $\epsilon_{carbonated}/\epsilon_o$ obtained from scratch is in average about 1.4, while the ratio of the bulk modulus obtained via the up-scaling procedure $K_{carbonated}/K_o$ is about 1.2. If one assumes that the ratio between elastic moduli and strength properties remains roughly of the same order of magnitude for cementitious material (a fact often observed), such a difference necessarily results in modifications at the level of the C-S-H matrix which have not been taken into account in such a simplistic estimate.

<table><caption>Table 9: Poroelastic properties of the different mechanical phases and results of the upscaling for the model of a carbonated matrix.</caption><thead><tr><th></th><th>φ</th><th>K (GPa)</th><th>G (GPa)</th><th>K<sub>u</sub> (GPa)</th><th>b (-)</th><th>M (GPa)</th><th>v<sub>f</sub>(%)</th></tr></thead><tbody><tr><td>Low-Density C2</td><td>0.36</td><td>10.55</td><td>6.7</td><td>13.72</td><td>0.78</td><td>17.6</td><td>20</td></tr><tr><td>C4</td><td>0</td><td>39.9</td><td>18.1</td><td>39.9</td><td>0.</td><td>50</td><td>63</td></tr><tr><td>Silica Gel</td><td>1.</td><td>0</td><td>0</td><td></td><td>1</td><td>-</td><td>17</td></tr><tr><td>Carbonated Matrix</td><td>0.24</td><td>20</td><td>11.33</td><td>20.99</td><td>0.51</td><td>-</td><td>-</td></tr></tbody></table>

As a first refinement, we model the carbonated matrix as follows: a mixture of decalcified C-S-H, silica gel and a phase dominated by calcite. Silica gel has a vanishing small stiffness and we thus model it as porosity. The decalcified C-S-H is identified as phase C2 (see subsection 4.3), and we assume its mechanical properties to be similar to the Low Density C-S-H. Obviously calcite is not in its pure mineral form and is present as a "mixture", we identified the phase C4 as representing it. We take the mean value of its indentation modulus 50GPa, and arbitrarily assume a Poisson's ratio of 0.3 - we also assume zero porosity for this phase. Table 9 summarizes the properties of such a model of the carbonated C-S-H matrix (The volume fractions are taken from the mean of the nano-indentation tests). Taking the upscaled value of such a carbonated matrix, keeping the same volume fraction for the C-S-H matrix and other constituents at the larger scale as before, we re-perform the upscaling (see the last line of Table 8). We obtain a stiffer
macroscopic modulus compared to the hypothesis of a non-carbonated matrix. The ratio $K_{carbonated}/K_o$ is now of 1.39 - closer to the experimental ratios of specific energies reported by scratch test. However, one has to note that the model of the carbonated matrix used here is very crude and definitely requires further refinement. It shows nevertheless the importance of taking into account the decalcification of the C-S-H.

# 6 CONCLUSIONS

We have reported a series of experimental results geared toward the understanding of the evolution of mechanical properties of Portland cement exposed to CO₂-rich fluids. Both scratch and nano-indentation tests have proven to be useful, and confirm that i) the center of the exposed cores have properties identical to the initial unreacted material, ii) the carbonated zone appears stiffer and stronger than the initial material. The dissolution front between the carbonated zone and the unreacted material exhibits a lower strength as seen from scratch tests. Such a front will be a surface of weakness where deformation might localize in structural applications (e.g. cement annulus of oil wells). However the presence of such a front is intimately linked to the geochemical conditions and may -in some cases- disappears. At a lower scale, for the type of CO₂ exposure investigated, a combination of chemical and mechanical analysis has shown that the C-S-H matrix significantly evolves and becomes more disordered. It is made of silica gel, calcite nodules (at different scales) and decalcified C-S-H. We have also reported some multiscales micro-poroelastic estimates of the macroscopic properties which allow to quantify the changes of the poroelastic properties during carbonation. We can use this information in practical mechanical calculations involving a moving carbonation front and different geometries.

In this work, we have not addressed the possible detrimental effect of the crystallization pressure associated with calcite crystallization in the pore space [26]. Such an effect is particularly difficult to observe experimentally for carbonation, but should somehow be addressed in further research. Ultimately, we believe that the integration of geochemical and micro-poromechanical modeling validated with experiments at different scales is a promising approach to better understand the evolution of mechanical properties of cement exposed to various CO₂ conditions. The work reported here is a tiny "scratch" in that direction.

**Acknowledgments** The authors would like to thank Schlumberger (NYSE:SLB) for the permission to publish this work. The samples were "carbonated" by G. Rimmelé. Fruitful discussions with Matteo Loizzo and Jean Desroches are greatly acknowledged.

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