my work. In Figures 3.9, a two-coated sphere morphology is used to represent the cement paste and mortar microstructures, as also proposed in other studies [Stora et al., 2009, Bary and Béjaoui, 2006]. At the cement paste level, the hydrating particle is embedded in a high-density (HD) products layer, which is, in turn, embedded in a low-density (LD) products layer. At the mortar scale, the sand particle is embedded in an Interface Transition Zone (ITZ) layer, which is, in turn, embedded in the cement paste layer. The Generalized Self-Consistent (GSC) scheme [Herve and Zaoui, 1993] is used to obtain the homogenized properties of the cement paste and mortar. Mori-Tanaka (MT) [Mori and Tanaka, 1973] scheme is used to estimate the properties within each coat. Numerical homogenization is used to estimate the properties at the concrete scale adopting a matrix/polyhedral inclusion morphology, with the mortar functioning as matrix and coarse aggregate particles as inclusions. This microstructure representation allows accounting for the existence of high and low C-S-H products (or inner and outer products, respectively). The scale separation at the cement paste level can be questioned since the typical size of some crystalline phases overlaps the size of cement particles and capillary pores.

In a more recent study [Honorio et al., 2022c], 16 microstructure representations are compared in order to fully explore the relevant representations mostly adopted for cement systems. The representations are shown in Figure 3.10 (8 representations assume only spherical inclusions, the other 8 adopt similar scale separation but with ellipsoidal inclusions). Each representation combines different assumptions regarding the number of scales to be considered, the shape of the constituent phases, or the model to describe phase assemblage. For phase assemblage, Powers [Powers and Brownyard, 1946], Tennis and Jennings (TJ) [Tennis and Jennings, 2000], and Königsberger-Hellmich-Pichler (KHP) [Königsberger et al., 2016] models. Self-Consistent [Hill, 1965] or MT schemes are deployed to upscale cement paste elastic properties.

In the application of analytical micromechanics, the philosophy of "as simple as possible as complex as necessary" helps understanding the relative contribution of the main input variables (associated with the composition and microstructure representation). Simple representations with spherical inclusions can already capture most of the first-order effects in cement-based materials. Increasing the complexity of the model representation by may improve the precision of predictions. For example, adopting non-spherical inclusions for some phases lead to a better description of mechanical properties [Pichler et al., 2009, Königsberger et al., 2021].

In the case of a cement system in which the simple models as Powers' are not necessarily valid, thermodynamic models (e.g., [Lothenbach and Winnefeld, 2006] arise as a powerful tool to provide phase assemble in a material agnostic way.

Finally, in studies using Strategy 2, the information from the molecular simulations is directly used as input in Micromechanics models. In the case of C-S-H, the anisotropies at the molecular level need to be accounted for, and representations of the microstructure as in Figure 3.11 are adopted [Honorio et al., 2022b, Honorio, 2022a, Ait Hamadouche et al., 2022].
<figure><img src="image_45.png" /><figcaption>Figure 3.11: Representation of the microstructure of C-S-H gel following Strategy 2 (when information from the molecular simulations is directly used as input Micromechanics models) [Honorio et al., 2022b, Honorio, 2022a, Ait Hamadouche et al., 2022].</figcaption></figure>

## 4.2 Conductivity-like properties

By mathematical analogy, various physical properties can be seen as akin to conductivity type and, therefore, the same mathematical expressions for the homogenization schemes apply [Torquato, 2002]. Table 3.2 summarizes the conductivity-like properties. All the problems listed relate an average flux to an average (or applied) intensity via an effective property. This effective property is a scalar in the case of isotropy or a 2 × 2 matrix in the anisotropic case. Note that the fluid permeability (or hydraulic conductivity) can be treated as a different class of property by other authors [Torquato, 2002], and approaching this problem as a conductivity-like problem is an approximation that can be useful in capturing the permeability of cement systems [Cui and Cahyadi, 2001].

### 4.2.1 Schemes based on Eshelby-like solution

Eshelby's strategy in elasticity (see Section 4.3) can be adapted to deal with conductivity-like properties [Hatta and Taya, 1985]. The effective conductivity of a N-phase heterogeneous material is given by:

$$ \bar{\lambda} = \sum_{p=1}^{N} f_p \lambda_p : A_p \qquad (3.8) $$

where $\lambda_p$ and $f_p$ are the conductivity tensor (assuming a uniform conductivity per phase) and volume fraction, respectively, of phase $p$; and $A_p$ is the localization tensor of phase $p$.
<table><caption>**Table 3.2:** Mathematical analogy of the linear forms describing the problems of conductivity-like properties: Thermal conductivity, electrical conductivity, dielectric permittivity, diffusivity, hydraulic conductivity.</caption><thead><tr><th>Effective property</th><th>Constitutive law</th><th>Average flux</th><th>Average intensity</th></tr></thead><tbody><tr><td>Thermal conduct.<br>λ</td><td>Fourier<br>q = -λ∇T</td><td>Heat flux<br>q</td><td>Temperature gradient<br>∇T</td></tr><tr><td>Electrical conduct.<br>σ<sub>e</sub></td><td>Ohm<br>J = σ<sub>e</sub>∇V<sub>e</sub></td><td>Electric current<br>J</td><td>Electric field<br>∇V<sub>e</sub> = E</td></tr><tr><td>Dielectric permit.<br>ε</td><td>Clausius-Mossotti<br>D<sub>e</sub> = -ε∇V<sub>e</sub></td><td>Electric displ.<br>D<sub>e</sub></td><td>Electric field<br>∇V<sub>e</sub> = E</td></tr><tr><td>Diffusivity<br>D</td><td>Fick<br>J = -D∇c</td><td>Mass flux<br>J</td><td>Concentration gradient<br>∇c</td></tr><tr><td>Hydraulic conduct.<br>K</td><td>Darcy<br>J = -K∇i</td><td>Mass flux<br>J</td><td>Hydraulic gradient<br>∇i</td></tr></tbody></table>

In the case of elliptical inclusions randomly distributed and oriented in a representative elementary volume (REV), a solution based on the Eshelby approach gives an approximation for $A_p$:

$$A_p \approx A_p^d \left( \sum_{r=1}^{N} f_r A_r^d \right)^{-1} \qquad (3.9)$$

where

$$A_p^d = (I + S_p^E ((\lambda^{ref})^{-1} \lambda_p - I))^{-1} \qquad (3.10)$$

is the localization tensor in the dilute case, with $I$ being the (second-rank) identity matrix, and $S_p^E$ the (second-rank) Eshelby-like tensor [Hatta and Taya, 1985]. The variable $\lambda^{ref}$ stands for the conductivity of the reference medium. According to the choice of a reference medium, one obtains the following homogenization schemes

* **Mori-Tanaka (MT, or Maxwell Garnet) scheme:** the matrix is chosen as the reference medium $\lambda^{ref} = \lambda_0$, i.e., all interactions among phases are mediated by the matrix, which is a good approximation for materials with a matrix/inclusion morphology with a moderate volume fraction of inclusions.

* **Self-Consistent (SC, or Bruggeman) scheme:** the effective medium itself is chosen as the reference medium $\lambda^{ref} = \bar{\lambda}$, i.e., all phases have the same status and the effective medium itself mediate the interactions among phases. This solution functions for morphologies in which a matrix cannot be clearly identified but can also be helpful in modeling materials with matrix/inclusion morphology, especially when there is a change of the hosting matrix phase according to evolution parameters (e.g., the electrical conductivity of cement systems as discussed below).
In the case of spherical inclusion exhibiting a microscopic isotropic behavior, and for heterogeneous materials macroscopically isotropic, the tensorial expressions above reduce to expressions below.

* For MT scheme:

$$ \frac{\bar{\lambda} - \lambda_0}{\lambda + 2\lambda_0} = \sum_{r=1}^{N} f_r \frac{\lambda_r - \lambda_0}{\lambda_r + 2\lambda_0} \qquad (3.11) $$

* For SC scheme:

$$ \sum_{r=1}^{N} f_r \frac{\lambda_r - \bar{\lambda}}{\lambda_r + 2\bar{\lambda}} = 0 \qquad (3.12) $$

where the subscript 0 denotes the (isotropic) matrix phase.

### 4.2.2 Schemes based on multilayered composite spheres

The presence of interphases can be modeled with the Generalized Self-Consistent (GSC) scheme based on the composite-sphere morphology. GSC scheme has been deployed to model the transport properties of the ITZ [Caré and Hervé, 2004] and also in microstructure representations of cement system separating high-density, and low-density product layers [Honorio et al., 2018a]. The GSC results for effective conductivities is the recursive equation [Herve, 2002, Caré and Hervé, 2004]:

$$ \overline{\lambda_{i}^{GSC}} = \lambda_{i} + \frac{1 - f_{i}}{\frac{1}{\overline{\lambda_{i-1}^{GSC}} - \lambda_{i}} + \frac{f_{i}}{3\lambda_{i}}} \qquad (3.13) $$

where $\overline{\lambda_{i}^{GSC}}$ is the effective conductivity of a matrix/composite-sphere composite in which the composite-sphere is constituted of ($i-1$) concentric coats and a core (associated here to subscript 0), all embedded in a matrix (here, represented by the subscript $i$). With simple manipulations, it is possible to show that this form for a 2-phase material is equivalent to that of a 2-phase MT scheme under micro- and macro-isotropy.

### 4.2.3 Properties of C-S-H gel

To upscale the conductivity-like properties of C-S-H gel using input from molecular simulations, the SC scheme was deployed but assuming a locally transverse isotropic behavior. Other authors used a similar strategy to upscale the thermal conductivity of C-S-H [Qomi et al., 2015, Sarkar and Mitra, 2021].

In a slit pore with an infinite slab of fluid confined between two walls, the conductivity-like properties can be written as a function of the parallel and perpendicular components in a Cartesian frame, as already discussed in the previous Chapter. In the case of diffusion, the local behavior writes (as in Eq. 2.22):
<figure><img src="image_46.png" /><figcaption>Figure 3.12: Effective (A) diffusion and (B) permeability of C-S-H gel for various effective gel pore sizes $H_g$ [Honorio, 2023].</figcaption></figure>

$$D = \begin{pmatrix} D_{\parallel} & 0 & 0 \\ 0 & D_{\parallel} & 0 \\ 0 & 0 & D_{\perp} \end{pmatrix} \qquad (3.14)$$

The C-S-H gel microstructure is assumed to be composed of two phases: micro-porous solid particles (subscripts ,s) and gel porosity (subscript ,g). The pore size associated with microporous solid particles should be the equilibrium basal spacing (here, $d_{eq} = 13.7$ Å, which is the most prevalent pore size in C-S-H layers stacks for the C-S-H model used in most of my works [Honorio et al., 2021b], as discussed in the previous Chapter). Typical gel pore sizes range from 2 to 10 nm diameter (e.g., [Abdolhosseini Qomi et al., 2021]). For a two-phase material and under the assumption of macroscopically isotropic behavior (which implicates that all orientations of the anisotropic equiaxed inclusions are equiprobable), the expression for the SC scheme with microscopically transverse isotropic behavior for both phases simplifies into the following implicit equation:

$$\bar{D} = \frac{\frac{7(1-f_g)D_{\parallel,s}}{D_{\parallel,s}+2D} + \frac{5(1-f_g)D_{\perp,s}}{D_{\perp,s}+2D} - \frac{7f_gD_{\parallel,g}}{D_{\parallel,g}+2D} - \frac{5f_gD_{\perp,g}}{D_{\perp,g}+2D}}{\frac{7(1-f_g)}{D_{\parallel,s}+2D} + \frac{5(1-f_g)}{D_{\perp,s}+2D} - \frac{7f_g}{D_{\parallel,g}+2D} - \frac{5f_g}{D_{\perp,g}+2D}} \quad (3.15)$$

where $f_g$ is the gel porosity. (I recall that the packing density $\eta_g = 1 - f_g$ of low and high-density C-S-H is generally assumed to be $\eta_g=0.64$ for low density (LD) and $\eta_g=0.74$ for high density (HD) C-S-H [Constantinides and Ulm, 2004]). An explicit solution for the non-negative real root of this expression can be obtained but is not reported here because too lengthy (the complex and negative solutions
are not physical for conductivities). This solution was used in the upscaling of the
following C-S-H gel properties:

* **Diffusion.** The perpendicular component of self-diffusion in C-S-H (as shown in Fig. 2.7) is one order of magnitude lower than the parallel component, so it can be fairly approximated as zero in homogenization procedure [Honorio, 2023]. Figure 3.12(A) shows the effective diffusion as a function of the packing density of the gel. The effective diffusivity computed for LD and HD C-S-H is 0.012*D<sub>bulk</sub>* and 0.0034*D<sub>bulk</sub>* respectively. These values compare well with experimental data from the literature: 0.02–0.05*D<sub>bulk</sub>* from Quasi-Elastic Neutron Scattering experiments [Li et al., 2012]; 0.017*D<sub>bulk</sub>* from Incoherent Elastic Neutron Scattering experiments [Fratini et al., 2013]; and 0.03*D<sub>bulk</sub>* from Pulsed Field Gradient Nuclear Magnetic Resonance experiments [Korb et al., 2007]. In ref. [Honorio et al., 2022b] the results were obtained using as input the non-zero perpendicular component obtained from MD simulations; this choice yields results similar to the ones above.

<figure><img src="image_47.png" /><figcaption>**Figure 3.13:** Effective frequency-dependent dielectric permittivity of C-S-H gel: (A) real and (B) imaginary part for various packing densities ηg and interlayer distance of gel pore dg [Ait Hamadouche et al., 2022].</figcaption></figure>

* **Permeability.** The perpendicular component of local permeability in C-S-H is strictly zero. Figure 3.12(B) shows the effective permeability as a function of the packing density of the gel. The effective permeability computed for LD and HD C-S-H are 10-15 ×10⁻²³ m² and 8.5-10×10⁻²³ m², respectively. These results are in good agreement with the value of 7 ×10⁻²³ m² calculated by Powers based on experiments [Powers, 1958]. The low permeability of C-S-H
gel is explained by negative slip boundary conditions, loss of dimensionality,
and viscosity increase with confinement [Honorio, 2022a].

* **Dielectric permittivity.** The perpendicular component of local permittivity is also approximately zero [Ait Hamadouche et al., 2022], and this anisotropy ($\epsilon_{||} \neq \epsilon_{\perp}$) would persist in pore thickness up to the hundreds of nanometers [de Luca et al., 2016]. Figure 3.13 shows the effective permeability as a function of the frequency of both real and imaginary parts of the dielectric permittivity for various packing densities of the gel. The values at the static limit of LD and HD C-S-H are within the range of 2-20 obtained from inverse analysis based on micromechanics and experiments [Guihard et al., 2020]. The Cole-Cole model [Cole and Cole, 1941] (Eq. 2.43) also fits well the results at the gel scale [Ait Hamadouche et al., 2022].

4.2.4 Properties of cement paste, mortar and concrete

Conductivity-like properties at larger scales were upscaled following Strategy 1.

<figure><img src="image_48.png" /><figcaption>**Figure 3.14:** Thermal conductivity at cement paste level [Honorio et al., 2018a]: estimates (full lines) compared to experimental data (symbols) [Mounanga, 2003] according to four different w/c ratios. The inset shows the evolution of the degree of hydration for each w/c (points are experimental data and full lines are the fitted evolutions).</figcaption></figure>

* **Thermal Conductivity.** Micromechanical estimates of the thermal conduc-
tivity of cement pastes (following a microstructure representation similar to
the one in Figure 3.9) are shown in Figure 3.14 [Honorio et al., 2018a]. The
thermal conductivity estimates monotonously decrease with time in agreement
with the observation of other authors [Bentz, 2007, Qomi et al., 2015], while
the experimental results [Mounanga, 2003] used for comparison instead show a slight increase with time. The trend observed in the estimates is expected since the solid phases conduct more heat than the liquid water in the conditions considered. In both cases, only a minor variation of the thermal conductivity with time is observed. This aspect reinforces the argument of Bentz [Bentz, 2007] in adopting a constant 1.0 W/m.K value as a reasonable estimation of the thermal conductivity of cement pastes at all ages (which is the recommendation made for thermo-mechanical modeling of concrete at early-ages [Azenha et al., 2021]). Experimental data seems to suggest a decrease in thermal conductivity with $w/c$. At the same time, in the analytical estimates, this is a clear trend in agreement with the results reported by other authors [Bentz, 2007, Qomi et al., 2015].

<figure><img src="image_49.png" /><figcaption>**Figure 3.15:** (A) Effective electrical conductivity of the cement paste with $w/c = 0.4$: comparison of micromechanics estimates with experimental results from [Christensen et al., 1994]. SC estimates obtained with MCM (using as input log-normal distributions for the conductivities of the solids and pore solutions, and a standard deviation of the pore solution conductivity of 1 S/m is adopted) and from least square fitting of the experimental data are shown; Hashin-Shtrikman upper and lower bounds are identical to the MT estimates using the pore solution as a matrix and using the solid as the matrix, respectively. The pore solution's conductivity results using the master curve presented in [Honorio et al., 2020b] (Fig. 1) are used in the homogenization. (B) Formation factor $F = \sigma/\sigma_{PS}$ of a cement paste with $w/c = 0.5$ as a function of the capillary porosity: comparison between experimental [Christensen et al., 1994] and model data. The inset shows the effective electrical conductivity of the cement paste with $w/c = 0.5$ and the associated standard deviation as computed with MCM.</figcaption></figure>

* **Electrical conductivity.** The estimates of the electrical conductivity of cement pastes (with a microstructure representation as the case "SC1s" in
Figure 3.10) are shown in Figure 3.15 [Honorio et al., 2020b] in comparison with the experimental data of [Christensen et al., 1994]. Monte Carlo Micromechanics (MCM) is introduced in this study [Honorio et al., 2020b] as a method to quantify uncertainty/ variability in the electrical conductivity using micromechanics. The variability observed in the electrical conductivity of the pore solutions [Vollpracht et al., 2016, Honorio et al., 2020c] was used as input in a Monte Carlo approach, in which the distribution of the electrical conductivity of the pore solutions was assumed to be log-normal (to avoid sampling negative conductivities). The effective electrical conductivity of the paste was computed with the SC and MT schemes. In the latter case, estimates in which the pore phase is assumed as the hosting matrix (HS+) and the case in which the solid phase (here assumed to exhibit a low, but non-zero, conductivity similar to that attributed to C-S-H of 0.0246 S/m [Honorio et al., 2020b]) is chosen as the hosting matrix (HS-) are shown (these scenarios correspond to the Hashin-Shtrikman bounds [Hashin and Shtrikman, 1963]). The first case gives estimates close to the experimental data before the setting; the second case is at late ages. SC scheme captures reasonably well the experimental data following the transition from the complex fluid before setting to a porous solid. Variability computed with MCM is also reported. Comparison with the experimental formation factor $F = \sigma/\sigma_{PS}$ of a cement paste with $w/c = 0.5$ is also provided as a function of the capillary porosity.

<figure><img src="image_50.png" /><figcaption>**Figure 3.16:** Effective static permittivity of a cement paste: comparison against the experimental data of [Andrade et al., 1999] on water-saturated cement paste with $w/c$ of 0.4 and 0.5 (the authors report results on three samples for each age tested).</figcaption></figure>

* **Dielectric permittivity.** Using input from molecular simulations for the pore solution (composition associated with a $w/c$ of 0.4), estimates of the effective static dielectric constant of a cement paste are shown in Figure 3.16
in comparison with the experimental data of [Andrade et al., 1999] on water-saturated cement pastes with a w/c 0.4 (at 7 days of age) or 0.5 (for various ages). A good agreement is observed between the model estimates and the experimental data for a paste with w/c = 0.4 at 7 days. Due to a dilution effect, cement pastes with higher w/c are expected to exhibit a lower dielectric response. Note, however, that the tendency of a decreasing effective static permittivity is observed in both experimental and model results.

## 4.3 Elastic properties properties

As for conductivity-like properties, schemes based on Eshelby solution and composite sphere morphology are briefly recalled. By mathematical analogy, the linear elasticity problem is similar to the viscosity problem [Torquato, 2002].

### 4.3.1 Schemes based on Eshelby solution

The effective stiffness and compliance tensors of a heterogeneous material composed of N anisotropic inclusions are given, respectively, by:

$$ \bar{\mathbb{C}} = \sum_{p=1}^{N} f_p \mathbb{C}_p : \mathbb{A}_p \qquad (3.16) $$

$$ \bar{\mathbb{S}} = \sum_{p=1}^{N} f_p \mathbb{S}_p : \mathbb{B}_p \qquad (3.17) $$

where $\mathbb{C}_p$ and $\mathbb{S}_p$ are the stiffness and compliance tensors (assuming a uniform behavior per phase), respectively, of phase $p$; $\mathbb{A}_p$ and $\mathbb{B}_p$ are the strain and stress localization tensors, respectively; $f_p$ is the volume fraction. The localization relations allow estimating the average mechanical fields per phase (or interphase variability of stresses):

$$ \bar{\sigma}_p = \mathbb{B}_p : \mathbf{\Sigma} \qquad (3.18) $$

$$ \bar{\epsilon}_p = \mathbb{A}_p : \mathbf{E} \qquad (3.19) $$

For a macroscopically applied stress $\mathbf{\Sigma}$ or strain $\mathbf{E}$ on REV contour.

In the case of elliptical inclusions randomly distributed and oriented in a representative elementary volume (REV), the solution proposed by Eshelby [Eshelby, 1961] gives an approximation for $\mathbb{A}_p$:

$$ \mathbb{A}_p \approx \mathbb{A}_p^d : \left( \sum_{r=1}^{N} f_r \mathbb{A}_r^d \right)^{-1} \qquad (3.20) $$

where

$$ \mathbb{A}_p^d = (\mathbb{I} + \mathbb{S}_p^E : ((\mathbb{C}^{ref})^{-1} : \mathbb{C}_p - \mathbb{I}))^{-1} \qquad (3.21) $$
is the strain localization tensor in the dilute case, with $\mathbb{I}$ being the (fourth-rank) identity element, and $S_p^E$ the (fourth-rank) Eshelby tensor [Eshelby, 1961]. The variable $\mathbb{C}^{ref}$ stands for the stiffness of the reference medium. According to the choice of a reference medium, one obtains the schemes again

* **Mori-Tanaka (MT) scheme:** the matrix is chosen as the reference medium $\mathbb{C}^{ref} = \mathbb{C}_0$

* **Self-Consistent (SC) scheme:** the effective medium itself is chosen as the reference medium $\mathbb{C}^{ref} = \bar{\mathbb{C}}$, i.e., all phases have the same status and the effective medium itself mediate the interactions among phases.

In the case of spherical inclusions exhibiting a microscopic isotropic behavior, and for a heterogeneous materials macroscopically isotropic, the tensorial expression above reduces to the system of two equations below.

* For MT scheme:

$$ \frac{\bar{K} - K_0}{\bar{K} + \frac{4}{3}G_0} = \sum_{r=1}^{N} f_r \frac{K_r - K_0}{K_r + \frac{4}{3}G_0}; \quad \frac{\bar{G} - G_0}{\bar{G} + \frac{4}{3}H_0} = \sum_{r=1}^{N} f_r \frac{G_r - G_0}{G_r + \frac{4}{3}H_0} \quad (3.22) $$

* For SC scheme:

$$ \sum_{r=1}^{N} f_r \frac{K_r - \bar{K}}{K_r + \frac{4}{3}\bar{G}} = 0; \quad \sum_{r=1}^{N} f_r \frac{G_r - \bar{G}}{G_r + H_{SC}} = 0 \quad (3.23) $$

where with $H_r = \frac{\frac{3}{2}K_r + \frac{4}{3}G_r}{K_r + 2G_r} G_r$, and the subscript 0 denotes the (isotropic) matrix phase.

### 4.3.2 Schemes based on multilayered composite spheres

As in the case of conductivity-like properties, the GSC scheme in elasticity has been deployed to model the ITZ [Ulrik Nilsen and Monteiro, 1993, Hashin and Monteiro, 2002, Honorio et al., 2017a, Nadeau, 2002, Nadeau, 2003] and also in microstructure representations of cement system separating high-density and low-density product layers [Honorio et al., 2016b]. The GSC estimate for the bulk modulus is a simple recursive equation [Herve and Zaoui, 1993]:

$$ \overline{K_i^{GSC}} = K_i + \frac{1 - f_i}{\frac{1}{K_{i-1}^{GSC}} - K_i + \frac{3f_i}{3K_i + 4G_i}} \quad (3.24) $$

where $\overline{K_i^{GSC}}$ is the effective conductivity of a matrix/composite-sphere composite in which the composite-sphere is constituted of ($i-1$) concentric coats and a core (associated here to subscript 0) embedded in a matrix (here, represented by the
subscript *i*). With simple manipulations, it is possible to show that this estimate for the bulk modulus for a 2-phase material is equivalent to that of a 2-phase MT scheme under micro- and macro-isotropy. The expression for the shear modulus requires the solution of a non-linear implicit equation [Herve and Zaoui, 1993].

### 4.3.3 Properties of C-S-H and cement paste

The SC scheme, as presented above, was used to estimate the effective elastic constant at the C-S-H gel scale in comparison with coarse-grained simulation in Figure 3.8 accounting for the 2D shape of layers.

<figure><img src="image_51.png" /></figure>

**Figure 3.17:** Comparison of the experimental data and simulation results for different models proposed in the benchmark of COST TU1404 action [Wyrzykowski et al., 2017] for (a) dynamic and static elastic Young's modulus and (b) dynamic shear modulus. Experimental results from the dynamic measurements are presented with open square markers, and from the static measurements with open triangle markers. Model 4 refers to my results.

Analytical homogenization was proposed as one method to estimate the elastic constants development in cement pastes at an early age in a benchmark promoted within COST action TU 1404. In my participation, I have adopted the microstructure representation as in Figure 3.9 together with the simplest form of the schemes
presented above (i.e., assuming micro- and macro-isotropic behavior and spherical inclusions). The results ("model 4" in the benchmark) exhibit a good agreement with the experimental data, as shown in Figure 3.17, when the hydration is previously fitted. In an additional scenario, I have also used a cement hydration kinetics model (based on boundary nucleation and growth kinetics [Honorio et al., 2016c]) (here denoted as "Model 4 (no kinetics fitting)") to get the hydration kinetic function. Even though the initial kinetics agreed well with the experimental data, and hence the modeled cumulative heat curve almost overlapped with the experimental data, a relatively poor agreement was obtained in the deceleration phase of hydration kinetics, where the rate of hydration and the cumulative heat were considerably underestimated. The estimations of the model rejoin the experimental curve in the diffusion-driven stage of the model.

Considering all the microstructure representations in Figure 3.10, micromechanics-based estimates of elastic constants were compared with experimental data in a database collected considering various authors as detailed in [Honorio et al., 2022c]. The results concerning the microstructure representations with better performance (among the 16 representations) are shown in Figure 3.18. These results confirm the better performance of the SC scheme in capturing early-age property development. Overall the precision in estimates of early-age behavior (degree of hydration DOH < 0.7) was lower than the estimated at late ages. The estimates obtained from micromechanics-based estimates were compared with the ones predicted by data science techniques; and the opportunities of using both techniques as allies were discussed [Honorio et al., 2022c].

## 4.4 Aging linear viscoelasticity

The homogenization of the aging linear viscoelastic behavior can be performed using the correspondence principle early proposed by Mandel [Mandel, 1958], which can be written in terms of Volterra integral [Volterra, 1959] operators. This operator is defined as the multiplication operator "∘":

$$ (f \circ g)(t, t_0) \equiv \int_{t=-\infty}^{t} f(t, t')d_{t'}g(t', t_0) \qquad (3.25) $$

for time-dependent functions f and g. In a set F of functions, the ring (F; +, ∘) satisfies the conditions of a division ring: all nonzero elements have a multiplicative inverse, but the multiplication is not necessarily commutative. Analogously, division rings for a set of matrices F and the Volterra matrix inner product (F; +, ⋆), and for a set of tensors F and the Volterra double contraction products (F; +, ⋇) can be defined.

Using the correspondence principle and these definitions, the stress-strain relationships in aging linear viscoelasticity are written as [Sanahuja, 2013]:
<figure><img src="image_52.png" /><figcaption>**Figure 3.18:** Micromechanics-based estimate performances for elastic prediction of the training set for some of the microstructure representations in Fig. 3.10 (only the representations with the best performance are shown here) [Honorio et al., 2022c]: experimental elastic constants from the training dataset (Young modulus *E*, Poisson ratio *ν*, bulk *K* and shear *G* moduli) plotted against the estimated values using various homogenization methods. Influence of the degree of hydration on the performances: the empty blue circles correspond to DOH <0.7, and the solid black circles correspond to DOH >0.7, i.e., predictions at late ages.</figcaption></figure>
$$ \epsilon(x,t) = \mathbb{S}(x,t,.) \overset{\circ}{\overleftarrow{\circ}} \sigma(x,.), \forall x \in \Omega \quad (3.26) $$

$$ \sigma(x,t) = \mathbb{R}(x,t,.) \overset{\circ}{\overleftarrow{\circ}} \epsilon(x,.), \forall x \in \Omega \quad (3.27) $$

where the relaxation and compliance tensors, $\mathbb{R}$ and $\mathbb{S}$, respectively, can be obtained from each other by the inversion with respect to the operator $\overset{\circ}{\overleftarrow{\circ}}$: $\mathbb{S} \overset{\circ}{\overleftarrow{\circ}} \mathbb{R} = \mathbb{R} \overset{\circ}{\overleftarrow{\circ}} \mathbb{S} = H_{t'}(t)\mathbb{I}$, where the identity elements are $H_{t'}(t)\mathbb{I}$ with $H_{t'}(t)$ being the Heaviside function and $\mathbb{I}$ being the fourth order identity tensor.

Using this correspondence principle, the MT, SC, and GSC schemes can be rederived in an aging linear viscoelasticity framework. The MT and SC solutions in aging linear viscoelasticity were proposed by Sanahuja [Sanahuja, 2013]. As a result of my PhD, I have proposed the solution for the GSC scheme in aging linear viscoelasticity [Honorio et al., 2017a] using tools of non-commutative algebra.

<figure><img src="image_53.png" /><figcaption>**Figure 3.19:** Basic creep at concrete scale [Honorio et al., 2016b]: comparison of homogenization estimates with experiments from [Craeye et al., 2009]. Mesostructures with spherical (full lines) and Voronoï (dashed lines) inclusions for scenarios with (right) and without (left) space-filling are shown.</figcaption></figure>

This theory was applied to get the aging viscoelastic behavior of cement-based materials at early-age [Honorio et al., 2016b]. Analytical schemes were used to estimate the properties at the level of hydration products, cement paste, and mortar following the microstructure representation in Figure 3.9. Numerical homogenization was used to study the concrete scale. This combined approach allowed investigating two mechanisms leading to an aging behavior: simulations taking into account
the space-filling process as leading to an intrinsically aging behavior of C-S-H were compared to simulations in which this effect was not considered. Figure 3.19 shows the estimates of basic creep of concrete compared to experimental results [Craeye et al., 2009]. The estimates of basic creep were in agreement with the usual values obtained experimentally for similar concretes. At all levels (cement paste, mortar, and concrete), the material creeps more at the very early age when the behavior accounting for the space-filling is adopted.

The theory developed above generalizes linear viscoelasticity and, therefore, can also apply to non-aging viscoelasticity. Within the COST Action TU1404, I have participated in a modeling benchmark on upscaling non-aging viscoelasticity of cement-based materials [Königsberger et al., 2021]. In this benchmark, three micromechanics creep models with different microstructure representations have been compared with experimental data. All estimates yielded errors below 5% with respect to various experimental datasets. Model adopting non-spherical shapes for hydrates yielded better predictions.

## 4.5 Thermal expansion

The coefficient of thermal expansion (CTE) can be obtained from the stress localization tensor $\mathbb{B}$ (e.g., [Zaoui, 1998]):

$$ \bar{\alpha} = \sum_{p=1}^{N} f_p \mathbb{B}_p : \alpha \qquad (3.28) $$

The problem of thermal expansion is analogous to the others in poromechanics (e.g., drying strains) and can also be applied to the cases in which one phase exhibits swelling (as is the case of some durability problems in cement systems).

In the case of micro- and macro-isotropy and assuming N spherical inclusions, the solution of MT and SC schemes are given, respectively, by [Honorio et al., 2018a]:

$$ \alpha_{MT} = \left[ f_0 \alpha_0 + \sum_{i=1}^{N} f_i \frac{\alpha_i K_i (4G_0 + 3K_0)}{4G_0 + 3K_i} \right] / \left[ f_0 + \sum_{i=1}^{N} f_i \frac{K_i (4G_0 + 3K_0)}{4G_0 + 3K_i} \right] \qquad (3.29) $$

$$ \alpha_{SC} = \left[ \sum_{i=1}^{N} f_i \frac{\alpha_i K_i (4G^{SC} + 3K^{SC})}{4G^{SC} + 3K_i} \right] / \left[ f_0 + \sum_{i=1}^{N} f_i \frac{K_i (4G^{SC} + 3K^{SC})}{4G^{SC} + 3K_i} \right] \qquad (3.30) $$

In the case of a two-phase material, the expression of MT reduces to the expression provided in [Wang et al., 2019].

Micromechanics estimates using the microstructure representation of Figure 3.9 are compared with the experimental data from [Wyrzykowski and Lura, 2013] on the evolution of the CTE of cement pastes and mortar at early-age. Hydration kinetics and phase assemblage were modeled following the clinker composition of the cement
<figure><img src="image_54.png" /><figcaption>**Figure 3.20:** Linear CTE of cement paste and mortar at early age [Honorio et al., 2018a]: estimates (full and dashed lines) compared to experimental data (dots) from [Wyrzykowski and Lura, 2013]. Full lines are "sealed" estimations, and dashed lines are "saturated" estimations. The corresponding estimations of the linear CTE of ITZ are shown in the upper inset. The lower inset shows the experimental heat flux as provided by [Wyrzykowski and Lura, 2013] in the context of COST TU 1404 Action.</figcaption></figure>

provided by the authors and fitted on simple Johnson-Mehl-Avrami-Kolmogorov exponential expressions with characteristic times adjusted by means of a more refined hydration model [Tennis and Jennings, 2000]. ITZ is accounted for adopting a 20 µm thickness. It is assumed that water contributes actively to the thermal expansion before setting. Then, after setting, drained behavior is adopted for LD C-S-H and capillary pores while HD C-S-H remains in an undrained state. With these assumptions, a minimum observed within the first day can be obtained. No minimum is observed with fully 'undrained/saturated' conditions, and the effective CTE is expected to decrease with time since water CTE is much higher than solids CTE.

## 4.6 Heat capacity

Since the heat capacity refers to the ratio of extensive quantities: heat and mass (or volume) (or more precisely, to the amount of heat needed to increase in a Kelvin the temperature of a given amount of material), rigorously a simple weighted average with respect to the mass fraction $f_i^m$ (or volume fraction, or molar fraction if the heat capacity is given per volume or per mol) applies to get the "effective" heat capacity (e.g. [Qomi et al., 2015]):
$$c_P = \sum_{i}^{N} f_{i}^{m} c_{p,i} \qquad (3.31)$$

The same expression can be written for $c_V$ and similar properties such as the density. In these cases, no Micromechanics *per se* needs to be applied.

<figure><img src="image_55.png" /><figcaption>**Figure 3.21:** Heat capacity for cement paste [Honorio et al., 2018a]: estimations (full and dashed lines) compared to experimental data (symbols) from [Mounanga, 2003] according to four different $w/c$ ratios. Full lines are estimations without accounting for the coupling with thermal expansion; dashed lines are estimations accounting for the coupling with thermal expansion.</figcaption></figure>

The estimates of the heat capacity of cement pastes were compared with experimental results [Mounanga, 2003] under ambient conditions, as shown in Figure 3.21. All the errors exceed 30%. These high errors can be explained by (i) the lack of data concerning the thermal properties of some hydrates, (ii) the variations of the thermal properties of confined water, and (iii) the simplified description of hydration kinetics (only a few points are furnished by [Mounanga, 2003], and some evolutions are proposed in terms of empirical relations). As in the experimental data, the estimations monotonously decrease with time, tending to an asymptotic value at late ages. Measured heat capacity at the very early age can be more than 150%, this asymptotic value; the variations in the model estimations are less pronounced. Experimental data do not establish a clear relation between $w/c$ ratio and the heat capacity (for a given time). On the other hand, estimations of heat capacity show a clear tendency: the higher the $w/c$, the higher the heat capacity. This tendency is expected in non-dried samples since the porosity is larger in high $w/c$ samples, and the heat capacity of water occupying the porosity is much bigger than solids'. Other
experimental [Bentz, 2007] and simulation [Qomi et al., 2015] results in the literature report the same trend. Understanding why the rigorous framework providing the homogenized heat capacity seems to not work in the case of cement system is one goal of the ANR THEDESCO (as detailed in Section 2.2.4 in the next Chapter).

## 4.7 Local information in elasticity and strength estimates

### 4.7.1 Fluctuations of fields: estimations of intraphase field distributions

Besides averaged information per phase (or interphase distribution of fields as in Eqs. 3.18 and 3.19), more precise local information regarding the intraphase estimations of the distribution of fields can be obtained using analytical homogenization methods. The fluctuation or covariance (forth-rank) tensor of a stress field within phase i is

$$Q_i \equiv \langle \delta\sigma \otimes \delta\sigma \rangle_i \qquad (3.32)$$

where " ⊗ " denotes the dyadic product. The fluctuations are larger in the applied stress or strain load direction and smaller in the perpendicular direction. The standard deviation $\omega_i$, or the statistical variability, of a field in a given direction klmn can be approximated by the square root of the components of the fluctuation tensor defined in Eq. 3.32 [Bobeth and Diener, 1987]:

$$\omega_{i, klmn} \equiv (Q_{i, klmn})^{1/2} \qquad (3.33)$$

As shown in the last sections, the average stress $\langle \sigma \rangle_i$ per phase can be obtained through localization relations. In order to compute the second moment (i.e. $\langle \sigma \otimes \sigma \rangle_i$), the definitions of local u and effective U elastic energies can be used [Brenner et al., 2001]:

$$u(\mathbf{x}) = \frac{1}{2} [\sigma(\mathbf{x}) : (\varepsilon(\mathbf{x}) - \varepsilon^{(0)}(\mathbf{x}))] = \frac{1}{2} [\sigma(\mathbf{x}) \otimes \sigma(\mathbf{x})] :: \mathbb{S}(\mathbf{x}) \qquad (3.34)$$

$$U = \langle u(\mathbf{x}) \rangle = \frac{1}{2} [\Sigma : \mathbb{S}^{\text{eff}} : \Sigma - \langle \sigma^{\text{res}}(\mathbf{x}) : \varepsilon^{(0)} \rangle] \qquad (3.35)$$

where the effective elastic energy is obtained from the local energy by applying Hill's lemma [Brenner et al., 2001].

The second moment of stress field in a phase i can be then obtained by deriving U with respect to the local compliance $\mathbb{S}_i$ [Buryachenko and Rammerstorfer, 1998]:

$$\langle \sigma \otimes \sigma \rangle_i = -\frac{2}{f_i} \frac{\partial U}{\partial \mathbb{S}_i} \qquad (3.36)$$

Assuming $\varepsilon^{(0)}$ constant per phase, the second moment of stresses is [Buryachenko and Rammerstorfer, 1998, Brenner et al., 2004, Brenner et al., 2001]:
$$ \langle \sigma \otimes \sigma \rangle_i = \frac{1}{f_i} \left[ \Sigma \otimes \Sigma :: \frac{\partial \mathbb{S}^{\text{eff}}}{\partial \mathbb{S}_i} + \sum_{i=1}^{N} f_i \varepsilon_i^{(0)} : \left( 2\Sigma : \frac{\partial^t \langle \mathbb{B} \rangle_i}{\partial \mathbb{S}_i} + \frac{\partial \langle \sigma_{\text{res}} \rangle_i}{\partial \mathbb{S}_i} \right) \right] \quad (3.37) $$

This result can be used with different homogenization schemes. Strategies to solve this derivative are provided in [Buryachenko and Kreher, 1995, Brenner et al., 2004]. In the previous equations, it can be seen that in the absence of external mechanical loading $\Sigma$, fluctuations within the phase exist if the residual stresses are non-zero. These results regarding second moments are valid to any degree of anisotropy [Buryachenko and Rammerstorfer, 1998]. In the macro-isotropic case, for spherical inclusions, the expressions are reduced [Buryachenko and Rammerstorfer, 1998] to the ones presented by [Bobeth and Diener, 1986] in the absence of transformation fields or [Bobeth and Diener, 1987] in the presence of transformation/residual fields.

This analytical approach to calculate mechanical field intraphase variability was compared with the stress field distribution obtained from finite elements simulation as shown in Figure 3.22. The finite elements simulation considered numerical inclusion/matrix samples with spherical, convex Voronoi polyhedral, and convex Voronoi polyhedral flattened inclusions. Uniaxial stress was applied in both numerical and analytical approaches. The standard deviation of both approaches yielded standard deviation of the same order, with analytical results giving larger deviations. Compared to the case with spherical inclusions, the stress distribution curves in the composite with Voronoi inclusions are broadened. As expected, the flattened polyhedral inclusions lead to still broader distributions of stresses within the aggregates considering all directions.

Applying the analytical approach to cement-based materials, it is possible to quantify how stiffer aggregates lead to larger fluctuations in stress distribution. Two effects are observed in a multiscale framework: (i) localization of stresses in stiffer phases to the detriment of less stiff phases; (ii) propagation of fluctuations towards smaller scales as detailed in [Honorio et al., 2018b]. These effects compete in determining the statistical variability of stresses within hydration products. For C-S-H, the standard deviation of stresses for a hydrostatic load are on the order of magnitude of the stresses applied at the concrete scale even if C-S-H is much less stiffer than other phases (aggregates, clinker). Concerning the effect of age, different behaviors can be observed according to the scale considered. Discounted the very early-age (before 1 day), the standard deviation of stresses decreases with age (due to solidification) at concrete and mortar scales, and increases in hydration products scales (due to the decrease of contrast of stiffness)[Honorio et al., 2018b].

A direct way of using the estimations of the fluctuations of stresses is in the computation of the strength of composites (as discussed in the next section) or to understand cracking overall and processes involving stress relaxations or creep. The numerical results in Figure 3.22 exhibit a clearly non-symmetric distribution of mechanical fields also observed in coarse-grained simulations (Figure 3.3). In a forthcoming work [Babaei et al., 2022] in collaboration with SCK-CEN (Belgium),
asymmetrical distribution with similar shapes were also observed under drying, and thermal expansion (self-equilibrated) loads in numerical samples fo cement paste obtained from microstructural modeling. Determining the functional form of the probability distributions of the stress fields in heterogeneous materials and their dependence on load and composition is still to be fully worked out.

<figure><img src="image_56.png" /><figcaption>**Figure 3.22:** Effects of inclusion shape [Honorio et al., 2018b]: At the top, comparison of analytical estimates of stress distributions in matrix and inclusions with results from 3D finite element simulations on numerical samples with three different inclusion shapes. The Young moduli of the matrix and inclusion are $E_{mat} = 20$ GPa and $E_{inc} = 65$ GPa, respectively; the Poisson ratio of all phases is 0.2. A uniaxial load is applied in the x-direction. The analytical estimations are shown, assuming a normal distribution of stresses. At the bottom, numerical samples considered in 3D finite elements simulations: (a) spherical, (b) convex Voronoi polyhedral, and (c) convex Voronoi polyhedral flattened inclusions (with an aspect ratio of 3).</figcaption></figure>

## 4.7.2 Estimation of compressive strength

The mechanical strength can be estimated from the intraphase distribution of stresses associated with a (stress) failure criterion. Here, a normal distribution of stress fields is assumed (in the lack of a more precise choice capturing the asymmetry
mentioned above). Being stresses a tensorial quantity, it is necessary to deal with a multivariate distribution $\wp(\langle\sigma\rangle_i, q_i)$ of the stress tensor in a given constituent phase $i$. For compressive strength, adopting the Von Mises criterion, which corresponds to the second invariant of stresses:

$$ \sigma_{VM}^2 = \frac{1}{2} \left[ (\sigma_{11} - \sigma_{22})^2 + (\sigma_{22} - \sigma_{33})^2 + (\sigma_{33} - \sigma_{11})^2 + 6 (\sigma_{23}^2 + \sigma_{31}^2 + \sigma_{12}^2) \right] \quad (3.38) $$

the resulting distribution is 6-variate, with each degree of freedom corresponding to one term on the right-hand side of the equation. In the following, it is assumed that the stress components are independent random variables. The distribution of the difference of two random independent variables $X_1(\langle X_1 \rangle, q_1)$ and $X_2(\langle X_2 \rangle, q_2)$ is $X_{1-2}(\langle X_1 \rangle - \langle X_2 \rangle, q_1 + q_2)$. Note that in the resulting distribution of the difference, the variances are summed. The product of a random variable $X_1$ and a scalar $a$ verifies $aX_1(\langle X_1 \rangle, q_1) = X_1(a \langle X_1 \rangle, a^2 q_1)$. With these properties of independent random variables, the distributions of Von Mises stress can be computed from the Euclidean norm (or 2-norm) of a multivariate distribution with $k_\chi = 6$ degrees of freedom accounting for each term of the right-most side of Eq. 3.38. The multivariate distribution of normally distributed random variables $\langle X_i \rangle^2/q_i$ is given by the noncentral chi-squared distribution whose PDF is:

$$ f_{\chi}(k_{\chi}, \lambda; x) = \frac{1}{2} \exp\left(-\frac{x+\lambda}{2}\right) \left(\frac{x}{\lambda}\right)^{\frac{k_{\chi}}{4}-\frac{1}{2}} J_{\frac{k_{\chi}}{2}-1}\left(\sqrt{\lambda x}\right) \quad (3.39) $$

where $J_v(y) = (y/2)^v \sum_{j=0}^{\infty} \frac{(y^2/4)^j}{j!\Gamma(v+j+1)}$ is the modified Bessel function of the first kind. The mean of the noncentral chi-squared distribution is the sum of the degrees of freedom $k_\chi$ and non-centrality parameter $\lambda = \sum_{i=1}^{k_\chi} (\langle X_i \rangle)^2$. The variance of noncentral chi-squared distribution is $q_\chi = 2(k_\chi + 2\lambda)$.

In a REV $\Omega$, a given phase $i$ with compressive strength $f_{c,i}$ is expected to fail in a uniaxial test if in a volume fraction $f_{cr}$ the von Mises stress exceeds $(2/3)f_{c,i}^2$ [Lavergne et al., 2018]. The compressive strength of the REV is, therefore:

$$ f_{c,\Omega} = \min_{\forall i \subseteq \Omega} \left[ \frac{f_{c,i} \sqrt{\frac{2}{3}}}{\sqrt{\frac{q_{\chi}}{k_{\chi}} F_{\chi}^{-1}(1-f_{cr})}} \right] \quad (3.40) $$

where $F_{\chi}^{-1}$ is the inverse of the Cumulative Distribution Function (CDF) of the noncentral chi-squared distribution $f_{\chi}$ in Eq. 3.39. The value of the critical volume fraction $f_{cr}$ must be chosen so that the strength of the composite $f_{c,\Omega}$ does not exceed the strength $f_{c,i}$ of the constituent phases $i$ [Lavergne et al., 2018].

With this approach, the analytical estimates of the compressive strength of cement pastes are computed and compared against experimental data in Figure 3.23.
<figure><img src="image_57.png" /><figcaption>**Figure 3.23:** Comparison of analytical estimates [Honorio et al., 2018b] with experimental compressive strength of cement pastes obtained from the literature [Wyrzykowski et al., 2017, Honorio et al., 2016a, Pichler et al., 2013, Termkhajornkit et al., 2014, Lam et al., 2000]. At left, the results of Wyrzykowski et al. [Wyrzykowski et al., 2017] refer to a *w/c* of 0.3; at the center, the results of Honorio et al. [Honorio et al., 2016a] refer to a *w/c* of 0.5. In both cases, the evolution of Young moduli with age is presented in the respective articles. Analytical estimations are provided as a function of the critical volume fraction *f*<sub>cr</sub> and homogenization scheme (MT ou SC) used to get the effective properties of the hydration product layer scale.</figcaption></figure>

The estimations are made at hydration layer scales, and both SC and MT schemes are used for homogenizing each hydration product's layer. At this scale, the adopted intrinsic compressive strength of hydrates is $f_{c,0}$ = 141.5 MPa [Wyrzykowski et al., 2017]. Various values of the critical volume fraction $f_{cr}$ are considered. As in [Lavergne et al., 2018], $f_{cr}$ nearing 0.1 returns reasonable estimations of compressive strength (larger $f_{cr}$ lead to overestimations of the strength). The results show that the strength estimations are scheme-dependent, notably at early ages. The hydration products' layer homogenized by SC scheme provides better estimations at the very early ages than with the MT scheme. It must be noted, however, that at the very early age, the assumption of spherical (or equiaxed) inclusions and isotropy of phases seem insufficient to capture the cement paste's strength. This aspect was observed by Pichler et al. [Pichler et al., 2009], which propose acicular inclusions to model hydrates in cement paste scale. Improvements could also be obtained by accounting for the fluctuations coming from the anisotropy of inclusions. The results presented here indicate, however, that these simplifying assumptions of spherical (or equiaxed) inclusions and (micro-)isotropy seem enough to capture the compressive strength of cement paste at late ages. In this direction, the estimates of compressive strength at late ages are compared with experimental data [Honorio et al., 2016a, Pichler et al., 2013, Termkhajornkit et al., 2014, Lam et al., 2000] provided as a function of the gel-space ratio. The gel-space ratio $\gamma_g$ is defined as the
ratio between the volume of gel (i.e. hydration products plus "gel" micropores) and the sum of the volumes of gel and capillary pores [Powers and Brownyard, 1946]. This parameter is often associated with the strength of cement-based materials. For instance, the compressive strength of the cement pastes $f_{c,cp}$ is reported to scale with $\gamma_g^n$ with $n$ between 2 and 3 [Bentz, 2005]. As can be seen in Figure 3.23(right), The estimates provided here at late ages are in agreement with other results regarding the relation of the compressive strength of cement pastes with gel-space ratio.

# 5 Conclusion

In this chapter, upscaling methods dealing with the various mesoscales of interest in cement systems research were presented. These methods provide an way of establishing composition-(micro)structure-property correlations in cement systems in good agreement with experiments. The gel mesoscale is highlighted as a critical scale. This scale arises an open-to-adventure playground to promote the handshake between the techniques better suited to model the molecular scale and the techniques better suited to model the continuum.

In my works, the upscaling strategies 1 to 3 (as schematized in Figure 3.1) have been deployed in a multi-physics framework. Investigation of various properties can benefit from adopting strategies 2 or 3, in which multiscale modeling uses input information from the molecular scale. This is yet to be fully worked out for thermal properties and electrical conductivity. Effects of unsaturated conditions and related sorption-induced deformations are still poorly understood in a complete bottom-up framework. The multiscale multi-technique multi-physics strategies outlined here can be extended to cope with these conditions in future work.

Local information about mechanical fields variability is key to understanding mechanical failure. Molecular simulations have been used to shed light on failure mechanics of simple materials [Brochard et al., 2018]. Reactive force fields furnish a way to analyze failure at the local level. In applications to cement systems, Mohr-Coulomb failure criterion is shown valid to describe the failure of C-S-H at the molecular scale [Qomi et al., 2014a]. Looking at the characteristic length of the process zone, only failure in very brittle materials can be fully understood at the molecular level [Souguir et al., 2020]. A multiscale multi-technique framework is yet to be fully worked out in this topic.
# Chapter 4

## Conclusion and perspectives

### 1 Conclusions

This manuscript discusses strategies to establish composition-(micro)structure-property correlations for cement-based materials in a multi-physics and multiscale framework. This framework requires a multi-technique approach since each scale of interest demands adapted techniques. Micromechanics and statistical physics combined provide a robust multiscale, multi-technique framework to cope with all the complexities of cement-based materials. Modeling what is happening at the molecular scale and proposing upscaling strategies to quantify the repercussion at larger scales is crucial to understanding the behavior of cement-based materials.

In chapter 2, the molecular scale is shown to play a critical role in determining the origins of key phenomena in cement-based materials. Molecular simulations are presented as a toolbox to compute missing properties of phases present in cement systems. The elucidation of the origins of mechanical, thermal, transport, and electromagnetic response and their coupling with sorption-related processes can benefit from analyses starting from the molecular scale.

Chapter 3 presents upscaling methods dealing with the various mesoscales of interest in cement systems research. These methods provide a way of establishing composition-(micro)structure-property correlations in cement systems in good agreement with experiments. The gel mesoscale is highlighted as a critical scale. This scale arises an open-to-adventure playground to promote the handshake between the techniques better suited to model the molecular scale and the techniques better suited to model the continuum.

### 2 Perspectives

The perspectives of this work concern both materials science and materials engineering frameworks applied to civil engineering materials. Critical features of cement-based materials behavior still need to be fully worked out and will benefit
from a multiscale, multi-technique framework. This manuscript contributes in the direction of completing constituent property tables and understanding the effects of sorption in C-S-H, AF-phases, and ASR products bottom-up. Once composition-(micro)structure-property correlations are established, one can also look at the opportunities of engineering the materials for a target performance.

On-going work and short to mid-term perspectives ("Other perspectives") are presented in the following.

## 2.1 Ongoing work

### 2.1.1 Temperature and RH-dependence of thermal properties bottom-up

**Associated projects: Master project (2020) and on-going PhD of F. Masara (ANR JCJC THEDESCO)**

Critical questions regarding the thermal behavior of cement-based materials remain unanswered. In particular, the physical origins of the following aspects are still to be addressed:

* Thermal expansion: cement-based materials exhibit at least two non-trivial behaviors: (i) the CTE is a non-monotonous function of the relative humidity, reaching a maximum value at approximately 70% RH [Wang et al., 2018]; and, (ii) the CTE often reach a minimum value at the first days (Fig. 3.20).

* Heat capacity: the effective heat capacity of composites is expected to be the average of the heat capacities of all phases weighted by their (volume or mass) fractions, i.e., described by a mixture law [Qomi et al., 2015]. However, estimations of heat capacity of cement-based materials using mixture laws are not in reasonable agreement with experimental data [Honorio et al., 2018a] (as shown in Fig. 3.21)).

Modeling strategies that can describe these peculiar behaviors of cement-based materials from the underlying physics will represent an advance in the field by enhancing confidence in the predictions of the performance and durability of cement-based materials.

The goal of the project THEDESCO (ANR JCJC funding) is to provide models of the thermal expansion and heat capacity of cement-based materials that are informed by the relevant physical phenomena in a multiscale framework, and that can be used in the engineering practice. The strategy proposed combines classical molecular simulations with poromechanics, homogenization techniques, and finite element (FE) analysis. As presented in the first chapter, the first results concern the thermoelastic properties of water confined in C-S-H [Honorio et al., 2021b], and the temperature and RH-dependence of interfacial behavior in C-S-H [Masara et al., 2023]. Ongoing work copes with the repercussion of the molecular processes in
the heat capacity and thermal expansion of cement-based materials in a multiscale
strategy.

Further developments in the direction of understanding the behavior of cement-
based materials at high temperatures are also envisioned. The goal is to advance the
comprehension of the molecular mechanisms of fire-induced spalling in concrete. The
theories explaining spalling point out to the pore fluid pressurization and/or thermal
stresses build-up (due to restrained thermal strains) as the underlying mechanism
[Liu et al., 2018, Phan, 2008, Dwaikat and Kodur, 2009, Kalifa et al., 2000, Min-
deguia et al., 2015]. Thermodynamic considerations in explosive properties of water
in geomaterials suggest that other mechanisms leading to fluid instability might
also be relevant, including rapid heating of liquid water, liquid decompressions, and
cavitation [Thiéry and Mercury, 2009].

2.1.2 Electromagnetic and transport properties bottom-up in unsatu-
rated conditions

Associated projects: on-going PhD of S. Ait Hamadouche (IDEX, project HYDRA) concerning the dielectric part. Collaboration with UFG (Brazil) concerning electrical conductivity and diffusion. IUF project submitted in 2022.

In the previous chapters, several works coping with the molecular processes at
the origin of electromagnetic and transport properties under liquid-saturated con-
ditions have been discussed. The unsaturated cases have not been fully explored
in bottom-up investigations starting from the molecular scale. Also, further devel-
opments are needed to link self-diffusion to the corrected/collective diffusion, and
macroscopic diffusion [Coasne, 2016]. The corrected (or collective) diffusion coef-
ficient is associated, in the framework of the linear response theory, with the flux
and the chemical potential gradient (e.g., [Coasne, 2016]) and can also be computed
from the velocity correlation function but accounting for cross-correlation terms.
The macroscopic diffusion coefficient links, at equilibrium, the flow to the macro-
scopic concentration gradient. These three diffusion coefficients are equivalent only
under the assumptions of negligible velocity cross-correlation terms with respect to
auto-correlation terms; and linear adsorption isotherm so that the Darker factor is
approximately 1 [Coasne, 2016].

In the case of electromagnetic properties, the frequency-dependent response of
meso and microporous phases such as C-(A)-S-H and AF-phases is yet to be mea-
sured. In the case of impedance measurements (directly related to the frequency-
dependent electrical conductivity), the associated molecular responses are yet to be
investigated. Fundamental questions remain unanswered regarding ion specificity
and the role of interfaces.

Changes in pore saturation are generally accompanied by sorption-induced vol-
ume changes that also need to be considered. At the molecular level, these changes
occur in particular by a reduction of interlayer spacing in the case of C-(A)-S-H and
AFms, which alters the confinement conditions of water and ions, potentially impacting polarization time correlations and dynamics (i.e., the microscopic features driving electromagnetic and transport properties). The same can be said regarding the columnar structure of ettringite. The sorption-induced volume changes also affect the mesocale (gel) structure in the case of C-(A)-S-H. Coarse-grained simulation can be helpful in modeling the structure and resulting electromagnetic and transport properties. However, a well-suited coarse-grained representation for this kind of property must be adopted.

Building on the recent work dealing with the saturated case [Honorio et al., 2022b, Honorio, 2022a, Honorio et al., 2020a, Ait Hamadouche et al., 2022], the unsaturated case can be explored for both electromagnetic and transport properties (diffusion and permeability) of C-S-H at the molecular scale. The same strategy can be applied to AF-phases and their various hydration states. The expected results will provide new physical insights helping in the comprehension of transport processes in cement-based materials and the interpretation of electromagnetic measurements. Well-suited multiscale approaches enabling the linking of atomic-level process to the macroscopic are also to be validated for the unsaturated case. Various compositions of the pore solutions are relevant to cement systems, and the composition is dependent on age, and reactive system composition (cement type, use of supplementary cementitious materials) [Vollpracht et al., 2016]. The study of bulk pore solutions [Honorio et al., 2020a] with complex multi-ionic composition can also be extended to the unsaturated case. Data science techniques can be helpful in these studies by enabling the exploration of correlations among composition (water content, ion nature), microstructure, and electromagnetic and transport properties.

### 2.1.3 Molecular mechanisms of the crystallization pressure

**Associated projects: Master project (2022) and on-going PhD of B.M. Hawchar (CNRS 80 prime, project ESOPE)**

Crystallization in porous materials is a major cause of damage of materials, involved in the degradation of heritage [Flatt et al., 2014, Flatt et al., 2006, Tsui et al., 2003], geotechnical disorders [Sass and Burbaum, 2010], geomorphological processes [Wellman and Wilson, 1965, Serafeimidis and Anagnostou, 2013], and pathologies of cement-based materials. The latter includes ASR [Rajabipour et al., 2015], sulphate attack [Liu et al., 2014], and delayed ettringite formation [Taylor et al., 2001, Zhang et al., 2021]. The mechanisms of crystallization pressure, however, remains one the most poorly understood phenomenon in the mechanics of porous media [Flatt et al., 2006].

In the project ESOPE, the molecular mechanisms at the origins of the crystallization pressure are investigated. Molecular simulation approaches combined with microfluidics experiments will be deployed to unveil the origin and quantify the crystallization pressure phenomena in model systems (NaCl salt/aqueous solutions). Simulations of the solubility of NaCl using free energy methods and thermodynamic
<figure><img src="image_58.png" /><figcaption>**Figure 4.1:** Chemical potential of solid NaCl aqueous solution as a function of the molality [Hawchar, 2022]. The blue dashed lines correspond to Aragones et al. [Aragones et al., 2012] results. The solid magenta curves represent experimental results, and the red curves correspond to Hawchar Master thesis [Hawchar, 2022] simulations. Improved solubility estimations were obtained with new simulations using Yagasaki et al. [Yagasaki et al., 2020] potential.</figcaption></figure>

integration was set up during the Master project of B.M. Hawchar based on the study of Aragones et al. [Aragones et al., 2012]. The approach allows the computation of the chemical potential of aqueous solution and solid NaCl under various stress conditions. The intersection of the chemical potential of the solid and that of the aqueous solution as a function of the molality gives the solubility of the solution (Fig. 4.1). These simulations, combined with thermodynamic considerations, allowed to revisit Correns law (the equation relating supersaturation and crystallization pressure which is often used to describe the process in porous media [Flatt et al., 2006]) accounting for a general stress state in the solid. During his PhD, B.M. Hawchar will tackle the case of the simulation of crystal growth under confinement and the experimental part of the project.

The developments in this project will open the window for future investigations focusing on unveiling the molecular mechanisms associated with crystallization pressure in the durability problems in cement-based materials.

### 2.1.4 Statistical physics tool for understanding the macroscopic structure of cement systems

**Associated projects:** Master project (2021) of L. Renault. A chapter in the PhD of T. Sayari
<figure><img src="image_59.png" /><figcaption>**Figure 4.2:** Simulated aggregate volume fraction profile according to the granulometric curves of three concrete mix designs [Sayari et al., 2023]: F1 VeR-CoRs concrete with Dmax = 25 mm, F2 CETU concrete with Dmax = 25 mm and a different aggregates distribution, and F3 the B11 concrete with Dmax = 12.5 mm (the total volume fraction is the same and is equal to 40%).</figcaption></figure>

The random structure of cement-based materials at the cement paste, mortar, and concrete scale can be simulated using tools for molecular simulations. These techniques can be helpful in simulating aggregate, filler, or reactive powder packing. Increasing the packing density of aggregates in concrete, and therefore reducing the amount of cement, is one of the most straightforward ways of reducing the impact of using cement-based materials [Van Damme, 2018].

The development tools to model the packing of an aggregate mix might help in the optimization of the use of locally available aggregates. Local aggregates may present a large variability in features that are known to affect the packing density, such as aggregate shape and size distribution. Most of the solutions proposed so far in the literature to optimize the packing density relies on empirical approaches or extensive experimental campaigns [de Larrard and Sedran, 2002]. These strategies generally do not properly explore all formulation space regarding the possible combinations of aggregates locally available. In this context, there is a need for simulation tools for optimizing the packing density in which the features of locally available resources can be accounted for.

In the works performed so far, truncated and shifted Mie potential are used to approximate a hard sphere potential [Jover et al., 2012]. This allowed simulating the maximum random packing in mono and polydisperse systems. Grand Canonical Monte Carlo simulations can be used to simulate aggregate packing, and a combination of simulations in different ensembles (in an annealing-like process) can be used to explore high packing density random configurations.

The tool has also been deployed to simulate formwork wall effects in concrete: the formwork perturbs the arrangement of aggregates leading to a microstructure gradation as a function of the distance from the surface. This gradation results in
property variation from the concrete surface: close to the formwork surface, the elastic moduli can be roughly half of the value in the bulk zone, and transport properties are increased in the vicinity of the surface due to high cement paste volume fraction [Bissonnette et al., 2018]. To validate the approach, we verify that the simulation reproduces the profile of highly confined monodisperse particles [Nygård et al., 2012]. Then, confined polydisperse particles following the coarse aggregates granulometric curves and volume fractions of the real concrete formulation are simulated as shown in Fig. 4.2. Molecular simulation codes enable the calculation of density profiles (as a function of center particle counting, which is the same strategy to assess water layering in nanoslit pores) that can be converted into volume fraction profiles through a convolution operation. The results show that the characteristic size perturbed by the presence of the formwork is on the order of half of the maximum aggregate size [Sayari et al., 2023]. Then, property profiles can be estimated using micromechanics and assuming a slowly varying microstructure gradation so that a REV can be approximated (similar assumptions are required when homogenization schemes are applied to get profile property of Functionally-Graded Materials (FGMs) [Paulino, 2007]).

Perspectives of the work include proposing an optimization strategy using as input the volume fraction and granulometric curve of aggregates (fine and coarse) but also filler and cement particles. Future work can also deal with the introduction of interaction to account for small particles flocculation or even go towards the simulation of rheological processes in the fresh state.

## 2.2 Other perspectives

This section concerns projects that are still in their initial stages as well as ideas that are still to be fully worked out.

### 2.2.1 Sorption-induced deformations: multiscale aspects

**Associated projects:** IUF project submitted in 2022; Proposal of a PhD project with ADI funding with Nagoya University/Tokyo University (still in preparation)

Despite the decades of research dedicated to better understanding, modeling, and controlling drying shrinkage, fundamental questions remain unanswered, such as how drying alters C-(A)-S-H molecular and gel structures, how this alteration controls drying deformations extension and reversibility, and what are the origins of heteresis under sorption in cement-based materials [Abdolhosseini Qomi et al., 2021]. Understanding these fundamental aspects is crucial to control drying shrinkage. In this direction, studies using atomistic simulation have proposed solutions to reduce or even eliminate drying shrinkage in cement systems [Moshiri et al., 2020, Yang et al., 2018]. Counterion specific effects might be at the origin of the more pronounced shrinkage observed in cements with increasing alkali content [Wittmann,
[2008]. The effects of other cations need to be investigated, including cesium for nuclear applications and species such as aluminum and magnesium.

Future work will cope with understanding how specific (counter)ions effects affect sorption, disjoining pressures, effective interactions, and hysteresis under sorption in C-(A)-S-H and AFms. Other ions prone to binding in C-(A)-S-H can also be studied, including molecules known as reducing shrinkage agents. A multiscale strategy, including explicit simulation of the gel mesoscale, might add to the comprehension of the repercussions of these nanoscale effects up to the scale of industrial applications of concrete.

### 2.2.2 Ion specific effects, ion exchange, and ion binding

**Associated projects: IUF project submitted in 2022**

Ions in cement-based materials, including potentially aggressive agents, have three possible destinies: (i) being chemically bonded in a hydrate phase, (ii) being physically adsorbed onto hydrates, or (iii) being free ions in the pore solution. Chemical and physical binding concerns mostly C-(A)-S-H and AF-phases. Ion specificity in AF-phases can be related to the variety of AFt and AFm phases: each associated with a different ion chemically bonded in similar structures. The atomic-level processes associated with physical adsorption are yet to be fully understood. Changes in the ionic composition of the pore solution may promote ion exchange. The processes in which AF-phases and C-(A)-S-H exchange chemically and physically bonded ions with the pore solution are poorly understood. These processes are crucial to understanding chloride, carbonate, and sulfate binding for durability purposes [Yuan et al., 2009]. Atomic-level comprehension of ion binding and ion exchange may provide new insights for ion immobilization and materials design for durability.

Future work will cope with understanding ion binding and exchange in C-(A)-S-H and AF-phases using molecular simulation. C-S-H surface is prone to the development of electrical double layers in which both cations (first layers) and anions can be adsorbed. Ion exchange can be evaluated using free energy methods [Rotenberg et al., 2009]. Anions and cations relevant for durability and sorption-induced deformation can be investigated. In the case of AF-phases, sulfate, carbonates, chloride, hydroxide, and aluminosilicate ions are yet to be fully worked out.

### 2.2.3 Phase quantification and experimental techniques assessing small scales

**Associated projects: ANR PCI HEAT COFFEE**

Experimental investigation is the primary technique deployed to establish composition-property correlations in cement systems. Even though my work focus on modeling and simulation, I have participated in the supervision of PhD projects with a (mostly) experimental vocation (PhD projects of P. Saba, M. Razafimbelo, and T. Sayari). I plan to develop skills in experimental techniques that can be
helpful for providing input or for validation of the models across scales. These tech-
niques include notably methods for phase quantification and property measurements
at macro and small scales.

In a forthcoming PhD project (in the context of ANR PCI HEAT COFFEE),
accelerated experiments will be studied for assessing due to ASR and Delayed Et-
tringite Formation (DEF) degradations. Quantification techniques will be deployed.
Techniques to characterize submicroscale will be considered, taking advantage of the
rich environment of the Saclay plateau regarding facilities for small scale character-
ization.

2.2.4 Data science for composition-property correlations

Associated projects: Master project (2021) and ANR JCJC THEDESCO

Machine Learning (ML) techniques arise as promising tools to directly establish composition-microstructure-property correlations without a priori assumption of the microstructure characteristics [Agrawal and Choudhary, 2016]. The huge amount of experimental data produced on cement-based materials in the last century can be used to build databases that can be interrogated by ML.

In cement and concrete research, ML has been deployed since the 90's to predict
generally mechanical properties. Other methods include support vector machines
[Yan and Shi, 2010], decision trees [Behnood et al., 2015], evolutionary algorithms
[Golafshani and Behnood, 2018]. Elastic properties have also been extensively stud-
ied using ML [Ben Chaabene et al., 2020], with a strong focus on the impact of using
recycled aggregates. As input variables, the composition in terms of cement and wa-
ter content, as well as supplementary cementitious materials (SCM) and admixture
mass or volume, are often adopted [Ben Chaabene et al., 2020]. Neither the ef-
fects of the mineralogical composition of cement nor the effects of age (and property
development, especially at early-age) are generally considered in these studies.

A multi-technique modeling approach combining Machine Learning (ML) and Micromechanics-Based (MB) methods has been recently proposed to link cement system composition, and degree of hydration to the elastic properties of the material [Honorio et al., 2022c]. The technique can also be deployed to other properties. In the context of the ANR THEDESCO project, a database of thermal properties is to be built.

Data science techniques can also be helpful in tackling composition variability in-
trinsic to cement systems. For example, these techniques can be deployed to explore
correlations among pore solution composition (in terms of water content, ion nature,
ionic composition) and transport properties. Combinatorial approaches have been
used with reactive force fields to general library of C-S-H atomic structures [Qomi
et al., 2014b]. The approach can be extended to C-A-S-H and other substitutions
in C-S-H.
### 2.2.5 Cement-based materials under irradiation

**Associated projects: PEIR M1 project of M. Trifa; PhD project submitted for funding by CEA Saclay**

Cement-based materials are widely deployed in the nuclear power industry (in power plants and storage/disposal of radioactive waste). When exposed to radiation, concrete exhibits a degradation of mechanical properties originating from the swelling of certain siliceous aggregates, deformations induced or promoted indirectly by irradiation (shrinkage/creep related to temperature-activated drying), order/disorder alterations of phases in cement systems, and structural modifications of the constituent in concrete [Krishnan et al., 2018, Krishnan et al., 2017, Le Pape et al., 2020]. Major efforts have been put into understanding the mechanisms of degradation of cement-based materials under irradiation to extend the service life of nuclear plants. Bottom-up approaches arise as a promising strategy to tackle this topic.

The study of even apparently simple systems such as portlandite reveals complex behavior. Portlandite shows delayed H₂ release under irradiation. The mechanisms of transport of H₂ are not fully understood and might involve swelling of crystal network [de Noirfontaine et al., 2018], and the possible contribution of Grotthuss mechanism (an exchange of a proton and a vacant site between two oxygen [Agmon, 1995, Dupuis et al., 2017]). Reactive force fields are used to understand these processes in an ongoing investigation.

A PhD project proposal has been submitted on this topic. Molecular simulations will be deployed to quantify the effects of irradiation on the main mineral phases of cement-based materials (C-(A)-S-H, portlandite, and AF-phases).

### 2.2.6 AF-phases, M-S-H, C-A-(K)-(N)-S-H etc..

**Associated projects: IUF project submitted in 2022 for AFms, miscellaneous projects proposed to undergraduate students at ENS**

The goal of completing fundamental property data database can benefit from the multiscale multi-physics strategy outlined in this manuscript. Information concerning AF-phases deserves attention since they cover a large number of phases in cement systems. The physical properties of most of these phases remain unknown to date. AF-phases critical for carbonate, sulfate, and chloride immobilization, such as hemi- and mono-carboaluminates and Kuzel salt, are yet to be fully investigated with molecular simulations. The properties of hydrotalcite and thaumasite are also to be quantified. The processes leading to the sorption-induced deformations observed in AF-phases are yet to be fully worked out.

Other phases to be investigated in a multiscale, multi-physics, multi-technique framework are M-(A)-S-H, C-A-(K)-(N)-S-H (i.e., C-(A)-S-H with alkali substitutions/ binding), gels in geopolymer systems, etc.
# Appendix A
## Curriculum Vitae

### Tulio HONORIO DE FARIA

Email: thonorio@ens-paris-saclay.fr

Date of birth: June 20th 1988

ORCID: 0000-0003-0281-4502

Phone: +33 (0)1 81 87 51 02

Nationality: Brazilian and French

Research ID: S-5867-2017

ResearchGate: https://www.researchgate.net/profile/Tulio-Honorio

LinkedIn: https:// linkedin.com/in/tulio-honório-de-faria-2b752546

Google Scholar: https://scholar.google.fr/citations?user=8kHPd58AAAAJ

Github: https://github.com/tuliohf

### EDUCATION

<table><tr><td>10/2012-10/2015</td><td>PhD, Civil Engineering (laude with honors)<br/>École Normale Supérieure de Cachan, France<br/>PhD supervisor: B. Bary. Co-supervisor: F. Benboudjema</td></tr><tr><td>10/2011-09/2012</td><td>M.Sc., Materials Science for Sustainable Construction<br/>École des Ponts Paristech, France<br/>Master project supervisor: B. Huet (Lafarge)</td></tr><tr><td>02/2006-12/2010</td><td>BA, Civil Engineering<br/>Federal University of Goiás, Brazil</td></tr></table>

### CURRENT POSITION

<table><tr><td>From 09/2018</td><td>Associate Professor (Maître de Conférences)<br/>Department of Civil and Environmental Engineering<br/>École Normale Supérieure Paris-Saclay, France</td></tr></table>
PREVIOUS POSITIONS

<table><tr><td>10/2017-08/2018</td><td>Teaching Assistant/Postdoc (ATER)<br>MSME Lab., Université Paris-Est Créteil, France<br>Project: <i>Physical properties of hydroxyapatite from molecular simulations</i></td></tr><tr><td>10/2015-09/2017</td><td>Postdoctoral Researcher<br>Navier Laboratory, École des Ponts Paristech, France<br>Project: <i>Thermal expansion of adsorbing microporous media and application to clay desiccation</i></td></tr><tr><td>10/2012-10/2015</td><td>Doctoral Researcher<br>Concrete and Clay Laboratory, CEA Saclay, France<br>Project: <i>Modelling and numerical simulation of the mechanical behaviour and cracking of concrete at early age.</i> Project funded by ONDRAF/NIRAS (Belgium)</td></tr></table>

RESEARCH FUNDING

<table><thead><tr><td></td><td>Funding</td><td>Value</td><td>Title</td><td>Status</td></tr></thead><tbody><tr><td>2019-2023</td><td>ANR</td><td>284 k€</td><td>THEDESCO: Thermal Deformations of Concrete: predictive modeling for tailored design and adaptation. https://anr.fr/Projet-ANR-19-CE22-0004 (CI: F. Benboudjema, C. Giry)</td><td>PI</td></tr><tr><td>2022-2025</td><td>CNRS 80 Prime</td><td>115 k€</td><td>ESOPE: Damage by salts: origins of the crystallization pressure (PI: L. Brochard (ENPC); Others CI: L. Mercury (ISTO); F. Osselin (ISTO); M. Vandamme (ENPC); J-M. Pereira (ENPC))</td><td>CI</td></tr><tr><td>2021-2024</td><td>IDEX LaSIPS</td><td>115 k€</td><td>HYDRA: Development of a Broad-band Dielectric Approach for the Non-destructive Evaluation of Hydration of Cement-Based Materials. (PI: E. Vourc'h ; Others CI: F. Benboudjema, F. Daout)</td><td>CI</td></tr><tr><td>2022-2025</td><td>CEA funding</td><td>100 k€</td><td>Bottom-up modelling of the mechanical properties of cement-based materials from molecular simulations. (PI: S. Poyet and B. Bary (CEA); Others CI: A. Chartier, T. Chanpentier (CEA))</td><td>CI</td></tr><tr><td>2020</td><td>DIM RE-SPORE</td><td>60 k€</td><td>Capillary Flow Porometer for Multidisciplinary Applications. (Co-PI: E. Vennat (CS); CI: F. Benboudjema (ENSPS), A. Bourdot (ENSPS), J.M. Fleureau (CS)). Funding from <i>Region Ile-de-France</i></td><td>Co-PI</td></tr></tbody></table>

Status: PI = Principal (Lead) Investigator; CI= Co-Investigator
Participation as PhD co-advisor in the following industrial projects:

<table><thead><tr><td></td><td>Funding</td><td>Title</td></tr></thead><tbody><tr><td>2019-2022</td><td>EDF</td><td>Optimization of the reinforcement in massive zones in reinforced concrete under complex loadings. (PI: F. Gatuingt (ENSPS); M. Bottoni and G. Herve-Secourgeon (EDF))</td></tr><tr><td>2019-2022</td><td>Eiffage, CERIB, CETU</td><td>Kinetics of drying in concrete: application to achieving water content equilibrium in fire behavior tests. (PI: F. Benboudjema (ENSPS); F. Robert and S. Mohaine (CERIB))</td></tr><tr><td>2018-2022</td><td>Saint Gobain</td><td>Mechanics of cement-based composites reinforced by glass fibres grid. (PI: F. Benboudjema (ENSPS); X. Brajer (Saint Gobain))</td></tr></tbody></table>

## SUPERVISION

### PhD thesis

#### Ongoing

7. **Marwa Hamze** (2023-) "Use of molecular dynamics for the multi-scale evaluation of the mechanical properties of cement-based materials". Co-supervision: S. Poyet, B. Bary (dir.), A. Chartier, T. Chanpentier (CEA); T. Honorio (LMPS). Funding: CEA

6. **Bilal Mahmoud Hawchar** (2022-) "Study of crystallization pressure by molecular simulation and microfluidics experiments". Co-supervision: L. Brochard (dir.), M. Vandamme, J-M. Pereira (ENPC); L. Mercury, F. Osselin (ISTO); T. Honorio (LMPS). Funding: CNRS 80 Prime

5. **Sofiane Ait-Hamadouche** (2021-) "Development of a Broad-band Dielectric Approach for the Non-destructive Evaluation of Hydration of Cement-Based Materials". Co-supervision: E. Vourc'h (dir.), F. Benboudjema, T. Honorio (LMPS); F. Daout (U. Nanterre). Funding: IDEX LaSIPS

4. **Fatima Masara** (2021-) "Multiscale modelling of the thermo-hydro-mechanical response of concrete informed by the molecular scale". Co-supervision: F. Benboudjema, **T. Honorio (dir. by derogation)** (LMPS), Funding: ANR THEDESCO

3. **Takwa Sayari** (2019-2022) "Kinetics of drying in concrete: application to achieving water content equilibrium in fire behavior tests". Co-supervision: F. Benboudjema (dir.), T. Honorio (LMPS); F. Robert and S. Mohaine (CERIB) - **defense in jan-2023**

#### Defended

2. **Mihaja Razafimbelo** (2019-2022) "Optimization of the reinforcement in massive zones in reinforced concrete under complex loadings". Co-supervision: F. Gatuingt (dir.), T. Honorio (LMPS); M. Bottoni and G. Herve-Secourgeon (EDF)
1. **Pascale Saba** (2018-2022) "Mechanics of cement-based composites reinforced by glass fibres grid". Co-supervision F. Benboudjema (dir.), T. Honorio (LMPS); X. Brajer (Saint Gobain Research)

## Visiting researchers

1. **Waleska Barbosa**, post-doc level (Apr-2020 to Dec-2020) "Molecular modelling of substitutions in and symmetry transitions in tricalcium silicates". Visiting Research From Federal University of Paraná (Brazil)

2. **Saied Babaei**, doctoral level (Apr-2020 to Jun-2020) "Micromechanics of drying and thermal shrinkage in cement-based materials". Visiting Research From SCK-, University of Antwerp (Belgium). (Co-supervision F. Benboudjema).

## Master project

10. **Bilal Mahmoud Hawchar** (Mar-2022 to Jul-2022) "Origins of crystallization pressure by molecular simulation" (Co-supervision L. Brochard (ENPC))

9. **Loric Renault** (Apr-2021 to Jun-2021) "Optimizing the packing density of aggregates in concrete using simulations and machine learning"

8. **Dikra Afkir** (Mar-2021 to Jul-2021) "Topology optimization of the reinforcement in cement-based materials" (Co-supervision F. Gatuingt)

7. **Mohamad Khoder** (Mar-2021 to Jun-2021) "Experimental characterization and micromechanical modelling of the properties of concrete made with seashell aggregates" (Co-supervision A. Bourdot)

6. **Sofiane Ait Hamadouche** (Mar-2021 to Jun-2021) "Nanomechanics of C-S-H and ASR gels: a study by coarse-grained simulations"

5. **Fatima Masara** (Apr-2020 to Jul-2020) "Thermal pressurization and effective interactions in C-S-H under sorption" (Co-supervision F. Benboudjema)

4. **Estefanía Nuñez Del Prado** (Mar-2020 to Jun-2020) "Molecular modelling of the hysteresis under sorption and RH-dependent elastic constants of C-S-H" (Co-supervision F. Benboudjema)

3. **Nejd Hammami** (Mar-2020 to Jun-2020) "Influence of aggregate seashell aggregate shape on concrete properties: experimental characterization and micromechanics modelling" (Co-supervision A. Bourdot, D. Badreddine)

2. **Percy Guerra** (Mar-2019 to Jun-2019) "Dimensional stability of ettringite: molecular dynamics study of the RH- and temperature dependencies" (Co-supervision A. Bourdot)

1. **Reine Fares** (Mar-2015 to Aug-2015) "Numerical estimation of the multiscale thermo-viscoelastic properties of concrete at early-age" (Co-supervision B. Bary)
## Undergraduate Research Projects

14. Marwane Trifa (2022) "Portlandite under irradiation: mechanisms of H₂ diffusion"

13. Bilal Mahmoud Hawchar (2021) "C-A-S-H structure and properties"

12. Marc Vacher (2020) "Cement-based composites with seashells fillers" (Co-supervision A. Bourdot and M. Maroufi)

11. Sofiane Ait-Hamadouche (2020) "Tailoring the composition of cement paste for a target elastic response: using machine learning for the exploration of mix design space"

10. **Wassi Hussain** (2020) "Characterization of the hydration and modelling of phases present in pastes with seashell" (Co-supervision A. Bourdot)

9. **Ornella M. Chemgne Tamouya** (2019) "Molecular modelling of Alkali-Silica Reaction (ASR) products"

8. **Estefanía Nuñez Del Prado** (2019) "Molecular modelling of the elastic constants of C-S-H" (Co-supervision F. Benboudjema)

7. **Sirine Al-Dandachli** (2019) "Energy storage in ettringite: a study based on molecular simulations" (Co-supervision A. Bourdot)

6. **Thibault Ronzaud** (2019) "Valorisation of shell as concrete aggregates: experimental and micromechanics study" (Co-supervision A. Bourdot)

5. **Rodrigo Yanez** (2019) "Effects of drying in concrete structures layouts obtained from topology optimization" (Co-supervision Farid Benboudjema)

4. **Percy Guerra** (2018) "Identification of ettringite behaviour: physical properties estimated by in silico experiments"

3. **Samy Ben-Hamoudi** (2018) "Hydrodynamics in C-S-H nanopores: a molecular dynamics study"

2. **Martin Pegeot** (2018) "Topology optimization of reinforcement in rendering mortars", (Co-supervision F. Benboudjema)

1. **Quentin Laurent** (2018) "Simulation of the evolution of capillary porosity of cement pastes at early age"

## TEACHING ACTIVITIES

Details are given for the courses I'm currently teaching.

<table><tr><td>From 2018</td><td>ENSPS</td><td>Multiscale modelling (M2 level). Correlations composition-structure-property in materials science and engineering. Techniques of multiscale modelling. Molecular simulations. Micromechanics in elasticity, conductivity-like properties and transformation fields. Application to civil engineering materials.</td></tr></table>
**Experimental methods** (M2 level). Practical sessions on gas permeability of concrete.

**Numerical methods** (M2 level). Practical sessions on numerical methods for thermal transport.

**Soil Mechanics** (M1 level). Practical sessions on oedometric and shear failure testing of soils.

**Energy distribution** (Hydraulics /Aeraulics) (M1 level). Practical session on design of hydraulic and aeraulics installations.

**Complex media** (Pre-master level). Correlations composition-structure-property in materials science and engineering. Analytical and numerical homogenization. Application to composites in a multiphysics framework.

**Discontinuous media** (Pre-master level). Molecular simulations: theory and practical sessions.

**Transport in porous media** (Pre-master level). Practical sessions on experimental measurements of gas permeability of concrete and simulation of concrete barriers.

<table><tr><td>2017-2018</td><td>UPEC</td><td>Fluid and Solid mechanics; Thermal science; Numerical analysis and Calculus, Numerical simulation of structures; Dynamics and vibrations; General Mechanics</td></tr><tr><td>2016-2017</td><td>ENPC</td><td>Molecular simulations in materials science</td></tr><tr><td>2013-2015</td><td>ESTP- ESITC</td><td>Construction materials</td></tr></table>

## EDUCATIONAL AND ADMINISTRATIVE RESPONSABILITIES

<table><tr><td>From 2021</td><td>Head of Master 2 "Materials and Structures" and of the common core with Master 2 "Building envelopes and sustainable construction"</td></tr><tr><td>From 2022</td><td>Head of the group "Life-Cycle of materials, buildings and infrastructures for the reduction of environmental impact of constructions" of the OMEIR team at the LMPS</td></tr><tr><td>2019-2020</td><td>Responsible for the organisation of conferences for M1 and M2 FE-SUP level at ENS Paris-Saclay</td></tr><tr><td>From 2019</td><td>Referent "skills-based approach" for the master of the Department of Civil Engineering and Environment</td></tr></table>

## MEMBERSHIP OF SCIENTIFIC AND TECHNICAL COMMITTEES
<table><tr><td>From Oct-2022</td><td>Member, RILEM Technical Committee MMS : Modelling and experimental validation of moisture state in bulk cementitious materials and at the steel-concrete interface</td></tr><tr><td>From Jul-2022</td><td>Member, RILEM Technical Committee CFR : Concrete during Fire - Reassessment of the framework</td></tr><tr><td>From Mai-2022</td><td>Member, RILEM Technical Committee DCS - Data-driven concrete science</td></tr><tr><td>From Aug-2019</td><td>Member, RILEM Technical Committee CCS - Early age and long-term crack width analysis in RC Structures</td></tr><tr><td>From Feb-2019</td><td>Team Leader, LMT, DIM RESPORE (Network of Excellence in Porous Solids - Area of Major Interest of Île-de-France region)</td></tr><tr><td>Jan-2015 to Mar-2019</td><td>Member, RILEM Technical Committee CMS - Thermal cracking of massive concrete structure</td></tr><tr><td>Oct-2017 to Oct-2018</td><td>Executive board, International Association ConCreep (IA-CONCREEP)</td></tr><tr><td>Jan-2016 to Nov-2018</td><td>Member, COST Action TU 1404 Towards the next generation of standards for service-life of cement-based materials and structures</td></tr><tr><td>Oct-2014 to Oct-2017</td><td>Member, NANOCEM: Partner Project on Multiscale estimation of the thermo-viscoelastic properties of cementitious materials at early age</td></tr></table>

## REVIEWING ACTIVITIES

### Grant review (1)

ANR, French Nat. Research Agency (1)

### International journals (86 reviews)<sup>a</sup>

<table><tr><td>1</td><td>ACS Earth and Space Chemistry (1)</td><td>16</td><td>J. Eng. Mechanics (1)</td></tr><tr><td>2</td><td>Advanced Theory and Sim. (2)</td><td>17</td><td>J. Mat. in Civil Eng. (4)</td></tr><tr><td>3</td><td>AIChE Journal (1)</td><td>18</td><td>J. Physical Chemistry (1)</td></tr><tr><td>4</td><td>American Mineralogist (1)</td><td>19</td><td>J. Rock Mech. Geot. Eng. (1)</td></tr><tr><td>5</td><td>Applied Clay Science (5)</td><td>20</td><td>J. Theor. Comp. App. Mech. (1)</td></tr><tr><td>6</td><td>Applied Sciences (8)</td><td>21</td><td>Materials (5);</td></tr><tr><td>7</td><td>Buildings (2)</td><td>22</td><td>Materials & Design (2)</td></tr><tr><td>8</td><td>Cement and Concrete Composites (3)</td><td>23</td><td>Materials Research (1)</td></tr><tr><td>9</td><td>Cement and Concrete Research (12)</td><td>24</td><td>Materials and Structures (5)</td></tr><tr><td>10</td><td>Composite Structures (1)</td><td>25</td><td>Mec. of Time-Depend. Mat. (1)</td></tr><tr><td>11</td><td>Const. and Building Mat. (13)</td><td>26</td><td>Minerals (2)</td></tr><tr><td>12</td><td>Fractal and Fractional (2)</td><td>27</td><td>SN Applied Sciences (1)</td></tr><tr><td>13</td><td>Int. J. Num. An. Met. Geomec. (1)</td><td>28</td><td>Structural Eng. and Mechanics (2)</td></tr><tr><td>14</td><td>Journal of Adv. Concrete Tech. (5)</td><td>29</td><td>Sustainability (1)</td></tr><tr><td>15</td><td>Journal of African Earth Sci. (1)</td><td></td><td></td></tr></table>

## INVITED TALKS (7) AND ADVANCED SCHOOLS (3+1)

<footnote><sup>a</sup> Verification at https://www.webofscience.com/wos/author/record/535317</footnote>
<table><tr><td>May-2023</td><td>Analytical approaches to homogenization micro-to-meso – <b>Advanced school</b> of ETN SUBLime (European Training network – Innovative Training Network Sustainable Building Lime Applications via Circular Economy and Biomimetic Approaches).</td></tr><tr><td>Mar-2022</td><td>Multiphysics behaviour of porous materials from the molecular scale. <b>Invited talk</b> at the Seminar of <i>Quartz Lab of SupMéca, Saint-Ouen, France</i>.</td></tr><tr><td>Mar-2022</td><td>The molecular scale in cement-based materials investigations: contribution to understanding, prediction, and design for durability. <b>Invited talk</b> at the Workshop of the R&D FURNAS-ANEEL (UFG) “Service Life”, <i>Federal University of Goiás, Goiânia, Brazil</i>.</td></tr><tr><td>Mar-2022</td><td>Multiscale, Multiphysics, Multitechnique modelling applied to cement-based materials. <b>Advanced school</b> at for the Doctoral program of Civil engineering at the <i>Federal University of Goiás, Goiânia, Brazil</i>.</td></tr><tr><td>Aug-2020</td><td>The perspective of multi-scale modelling in the research on cement-based materials: contribution for the development of predictive models and non-destructive evaluation. <b>Invited talk</b> at the Workshop of the R&D FURNAS-ANEEL 0394-1504/2015 organized by the <i>Federal University of Goiás, Goiânia, Brazil</i>.</td></tr><tr><td>Mar-2020</td><td>Molecular simulations of nanoporous materials: unveiling the physical origins of the thermo-hygro-mechanical response – <b>Advanced school</b> of ETN ATHOR (European Training network – Innovative Training Network Advanced THERMomechanical multiscale mOdelling of Refractory linings).</td></tr><tr><td>Fev-2020</td><td>How molecular simulations may explain multiphysics phenomena in concrete and clays?, <b>Invited talk</b> at the <i>The University of Queensland, Brisbane, Australia</i> (Funded by BOOSTER project of ENSPS).</td></tr><tr><td>Nov-2019</td><td>Numerical Nano-Twins and Materiomics : elucidating the origins of porous materials behaviour from material « genome », <b>Invited talk</b> at the Seminar “Club of affiliates of the LMT”, <i>ENS Paris-Saclay, Cachan, France</i>.</td></tr><tr><td>May-2019</td><td>Multiscale methods – <b>Advanced school</b> of CSMA Juniors (French Association Calcul des Structures et Modélisation), <i>Ile de Porquerolles, France</i></td></tr><tr><td>May-2019</td><td>Water in cement-based materials, <b>Invited talk</b> at the weekly seminar at the <i>Thomas Young Centre, London, United Kingdom</i>.</td></tr><tr><td>May-2015</td><td>Multiscale Modelling of the thermo-viscoelastic properties of cement-based materials and structures at early-age, <b>Invited talk</b> at the International Workshop of Young Doctors in Gemechanics (W(H)YDOC), <i>ENPC, Champs-sur-Marne, France</i></td></tr></table>

PhD FOLLOW-UP COMMITTEE

<table><tr><td>2018</td><td>Justin Kinda (ENS Paris-Saclay, EDF) - "Impact of drying rate on delayed strain behavior of cement-based materials - experimental and numerical study"</td></tr></table>
<table><tr><td>2021/2022</td><td>Thibaut Herin (CEA, Université Paris-Saclay) - "Mechanisms of radiolysis in cement hydrates and the consequences of the H₂ formation in irradiated materials"</td></tr><tr><td>2022</td><td>Rémy Hoarau Belkhiri (CEA, Université Paris-Saclay) - "Irradiation of cement-based materials at early-age"</td></tr></table>

## AWARDS AND HONORS

<table><tr><td>2015</td><td>PhD laude with honors</td></tr><tr><td>2011</td><td>Lafarge scholarship for M.Sc.</td></tr><tr><td>2011</td><td>M.Sc. scholarship at ENS Cachan – declined.</td></tr><tr><td>2011</td><td>M.Sc. scholarship Erasmus SAHC Advanced master – declined.</td></tr><tr><td>2009</td><td>BRAFITEC exchange scholarship Brazil-France</td></tr></table>

## CONFERENCE AND MINISIMPOSIUM ORGANISATION AND ACTIVITIES

<table><tr><td>2020</td><td>Organization of mini-symposium MS436 Multiscale mechanics and physics of civil engineering porous materials on at the 14th World Congress in Computational Mechanics and ECCOMAS Congress. Co-organization with L. Brochard (ENPC), J. Sanahuja (EDF R&D) and K. Ioannidou (CNRS).</td></tr><tr><td>2020/21</td><td>Member of scientific Committee of the International RILEM conference on early-age and long-term cracking in RC structures.</td></tr><tr><td>2023</td><td>Member of scientific Committee of the Synercrete 23 - The International RILEM Conference on Synergising expertise towards sustainability and robustness of cement-based materials and concrete structures, Milos Island, Greece.</td></tr></table>

## Publications

Ph.D.: Honorio de Faria, T. (2015) Modelling concrete behaviour at early-age: multiscale analysis and simulation of a massive disposal structure. École Normale Supérieure de Cachan. https://tel.archives-ouvertes.fr/tel-01241585

PUBLICATIONS IN PEER-REVIEWED JOURNALS (42, with 39 in SCOPUS indexed journals)

corresponding author; Post-Doc#; PhD candidate*; Master Student**; Undergraduate student***
2023

J42. **Masara, F.***; **Honorio, T.**; Benboudjema, F. Sorption in C-S-H at the molecular scale: disjoining pressure, hysteresis, and cavitation. CEMENT AND CONCRETE RESEARCH 164 pp. 107047. doi: https://doi.org/10.1016/j.cemconres.2022.107047

2022

J41. **Honorio, T.**; Ait Hamadouche, S.**; Fau, A. (2022) Machine Learning and Micromechanics as Allies to Correlate Composition-Property in Cement-Based Materials. JOURNAL OF THEORETICAL, COMPUTATIONAL AND APPLIED MECHANICS 9830. doi: 10.46298/jtcam.9830

J40. **Honorio, T.**; Carasek, H.; Cascudo, O. (2022) Friedel's salt: temperature dependence of thermoelastic properties. CEMENT AND CONCRETE RESEARCH 160 pp.106904. doi: 10.1016/j.cemconres.2022.106904

J39. **Honorio, T.** (2022) Thermal conductivity of ettringite, heat capacity and thermal expansion of ettringite and metaettringite: effects of the relative humidity and temperature. CEMENT AND CONCRETE RESEARCH 159, pp. 106865. doi: 10.1016/j.cemconres.2022.106865

J38. Mahmoud Hawchar, B.**; **Honorio, T.** (2022) C-A-S-H thermoelastic properties at the molecular and gel scales. JOURNAL OF ADVANCED CONCRETE TECHNOLOGY 20 (6) pp. 375-388. doi: 10.3151/jact.20.375

J37. **Honorio, T.**; Brochard, L. (2022) Drained and undrained heat capacity of swelling clays. PHYSICAL CHEMISTRY CHEMICAL PHYSICS. doi: 10.1039/D2CP01419J

J36. Barbosa, W#; **Honorio, T.** (2022) Triclinic tricalcium silicate: structure and thermoelastic properties from molecular simulations. CEMENT AND CONCRETE RESEARCH. doi: 10.1016/j.cemconres.2022.106810

J35. **Honorio, T.**; Carasek, H.; Cascudo, O. (2022) Water self-diffusion in C-S-H: effect of confinement and temperature studied by molecular dynamics. CEMENT AND CONCRETE RESEARCH 155, 106775. doi: 10.1016/j.cemconres.2022.106775

2021

J34. Hervé-Sercougeon, G.; Hervé-Sercougeon, E.; Habib, S.; Razafimbelo, M.*; Bottoni, M.; Escoffier, F.; Mendoza-Chavez, G.; Kameh, A.; Voldoire, F.; Gatuingt, F.; Oliver-Leblond, C.; **Honorio, T.**; Escoffier, F.; Nazé, P-A.; Chatzigogos, C. (2021) On structural Finite Element modelling strategies and their influence on the optimization of final constructability of RC structures. NUCLEAR ENGINEERING AND DESIGN 385, 111541. doi: 10.1016/j.nucengdes.2021.111541

J33. **Honorio, T.**; **Masara, F.**; Benboudjema, F. (2021) Heat capacity, compressibility and thermal expansion of liquid water confined in C-S-H. CEMENT 6, 100015. doi: 10.1016/j.cement.2021.100015

J32. **Honorio, T.**; Maaroufi, M.; Al Dandachli, S.**; Bourdot, A. (2021) Ettringite hysteresis under sorption from molecular simulations. CEMENT AND CONCRETE RESEARCH 150, 106587. doi: 10.1016/j.cemconres.2021.106587
J31. Bore, T.; Mishra, P. N.; Wagner, N.; Schwing, M.; **Honorio, T.**; Revil, A.; Scheuermann, A. (2021) Coupled Hydraulic, Mechanical and Dielectric investigations of fine grained soils during shrinkage. ENGINEERING GEOLOGY 294, 106352. doi: 10.1016/j.enggeo.2021.106352

J30. Abdolhosseini Qomi, M. J.; Brochard. L.; **Honorio, T.**; Maruyama, I.; Vandamme, M. (2021) Advances in atomistic modelling and understanding of drying shrinkage in cementitious materials. CEMENT AND CONCRETE RESEARCH 148, 106536. doi: 10.1016/j.cemconres.2021.106536. **Invited review to the special issue on "Molecular scale modelling of cement and related systems".** (authors in alphabetical order; the authors contributed equally to the manuscript)

J29. Azenha, M.; Kanavaris, F.; Schlicke, D.; Jędrzejewska, A.; Benboudjema, F.; **Honorio, T.**; Šmilauer, V.; Serra, C.; Forth, J.; Riding, K.; Khada, B.; Sousa, C.; Briffaut, M.; Lacarrière, L.; Koendeers, E.; Kanstad, T.; Klausen, A.; Torrenti J.M.; Fairbairn, E.M.R. (2021) Recommendations of RILEM TC 287-CCS: Thermo-chemo-mechanical modelling of massive concrete structures towards cracking risk assessment. MATERIALS AND STRUCTURES 54 (135). doi: 10.1617/s11527-021-01732-8

J28. Königsberger, M.; **Honorio, T.**; Sanahuja, J.; Delsaute, B.; Pichler, B. L. (2021) A. Homogenization of nonaging basic creep of cementitious materials: a multi-scale modeling benchmark. CONSTRUCTION AND BUILDING MATERIALS 290, 123144. doi: 10.1016/j.conbuildmat.2021.123144

J27. Brochard, L.; **Honorio, T.** (2021) Thermo-poro-mechanics under adsorption applied to the anomalous thermal pressurization of water in undrained clays. ACTA GEOTECHNICA. doi: 10.1007/s11440-021-01188-8

J26. **Honorio, T.** (2021) Shear deformations in nanolayered silicates: the role of specific ion effects in the alkali-silica reaction products. MATERIALS AND STRUCTURES 54:86. doi: 10.1617/s11527-021-01671-4

J25. Kanavaris, F.; Jędrzejewska, A.; Sfikas, I.; Schlicke, D.; Kuperman, S.; Šmilauer, V.; **Honorio, T.**; Fairbairn, E.M.R.; Valentim, G.; Funchal de Faria, E.; Azenha, M. (2021) Enhanced massivity index based on evidence from case studies: towards a robust pre-design assessment of early age thermal cracking risk and practical recommendations. CONSTRUCTION AND BUILDING MATERIALS 271, 121570. doi: 10.1016/j.conbuildmat.2020.121570

2020

J24. **Honorio, T.**; Chemgne Tamouya, O. M.***; Shi, Z. (2020) Specific ion effects control the thermoelastic behavior of nanolayered materials: the case of crystalline alkali-silica reaction products. PHYSICAL CHEMISTRY CHEMICAL PHYSICS 22, 27800. doi: 10.1039/d0cp04955g

J23. **Honorio, T.**; Chemgne Tamouya, O. M.***; Shi, Z.; Bourdot, A. (2020) In-termolecular interactions of nanocrystalline alkali-silica reaction products under sorption. CEMENT AND CONCRETE RESEARCH 136, 106155. doi: 10.1016/j.cemconres.2020.106155

J22. **Honorio, T.**; Carasek, H.; Cascudo, O. (2020) May self-diffusion of ions computed from molecular dynamics explain the electrical conductivity of pore solutions in cement-based materials? MATERIALS AND STRUCTURES 53(3): 67. doi: 10.1617/s11527-020-01507-7
J21. **Honorio, T.**; Guerra, P.**; Bourdot, A. (2020) Molecular simulation of the structure and elastic properties of ettringite and monosulfoaluminate. CEMENT AND CONCRETE RESEARCH 135, 106126. doi: 10.1016/j.cemconres.2020.106126

J20. Brochard, L.; **Honorio, T.** (2020) Revisiting thermo-poro-mechanics under adsorption: Formulation without assuming Gibbs-Duhem equation. INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE 152, 103296. doi: 10.1016/j.ijengsci.2020.103296

J19. **Honorio, T.**; Carasek, H.; Cascudo, O. (2020) Electrical properties of cement-based materials: Multiscale modeling and quantification of the variability. CONSTRUCTION AND BUILDING MATERIALS 245, 118461. doi: 10.1016/j.conbuildmat.2020.118461

J18. **Honorio, T.**; Bore, T.; Benboudjema, F.; Vourc'h, E.; Ferhat, M* (2020) Dielectric properties of the pore solution in cement-based materials. JOURNAL OF MOLECULAR LIQUIDS 302, 112548 doi: 10.1016/j.molliq.2020.112548

2019

J17. **Honorio, T.**; Benboudjema, F.; Bore, T.; Ferhat, M*; Vourc'h, E. (2019) The pore solution of cement-based materials: structure and dynamics of water and ions from molecular simulations. PHYSICAL CHEMISTRY CHEMICAL PHYSICS 21, pp. 11111-11121. doi: 10.1039/C9CP01577A

J16. **Honorio, T.** (2019) Monte Carlo molecular modelling of temperature and pressure effects on the interaction between crystalline calcium silicate hydrate layers. LANGMUIR 35(11), pp. 3907-3916, doi: 10.1021/acs.langmuir.8b04156

J15. **Honorio, T.**; Lemaire, T.; Di Tommaso, D.; Naili, S. (2019) Molecular modelling of the heat capacity and anisotropic thermal expansion of nanoporous hydroxyapatite. MATERIALIA 7b03198 doi: 10.1016/j.mtla.2019.100251

J14. **Honorio, T.**; Lemaire, T.; Di Tommaso, D.; Naili, S. (2019) Anomalous water and ion dynamics in hydroxyapatite mesopores. COMPUTATIONAL MATERIALS SCIENCE 156, pp. 26-34, doi: 10.1016/j.commatsci.2018.08.060

2018

J13. **Honorio, T.**; Brochard, L.; Vandamme, M.; Lebée, A. (2018) Flexibility of nanolayers and stacks: implications in the nanostructuration of clays. SOFT MATTER 14, pp. 7354-7367, doi: 10.1039/C8SM01359D

J12. **Honorio, T.**; Brochard, L.; Bary, B. (2018) Statistical variability of mechanical fields in thermo-poro-elasticity: multiscale analytical estimations applied to cement-based materials at early-age. CEMENT AND CONCRETE RESEARCH 110, pp. 24-41, doi: 10.1016/j.cemconres.2018.05.010

J11. **Honorio, T.**; Brochard, L.; Vandamme, M. (2018) Effective stresses and estimations of the apparent Biot coefficient in stacked clay nanolayers. GÉOTECHNIQUE LETTERS 8 (2), pp. 97-101, doi: 10.1680/jgele.17.00170

J10. **Honorio, T.**; Bary, B; Benboudjema, F. (2018) Thermal properties of cement-based materials: multiscale estimations at early-age. CEMENT AND CONCRETE COMPOSITES 87, pp. 205-219, doi: 10.1016/j.cemconcomp.2018.01.003
2017

J9. Wyrzykowski, M.; Knoppik-Wróbel, A.; Benboudjema, F.; Buffo-Lacariere, L.; Sanahuja, J.; Charpin, L.; Königsberger, M.; Hellmich, C.; Pichler, B.; Valentini, L.; **Honorio, T.**; Smilauer, V.; Hajkova, K.G. Ye; Gao, P.; Dunant, C.; Hilaire, A.; Azenha, M. (2017) Numerical benchmark campaign of COST Action TU1404 – microstructural modelling. RILEM TECHNICAL LETTERS (2), pp. 99-107, doi: 10.21809/rilemtechlett.2017.44

J8. **Honorio, T.**; Brochard, L.; Vandamme, M. (2017) Hydration phase diagram of clays from molecular simulations. LANGMUIR 33 (44), pp. 12766-12776, doi: 10.1021/acs.langmuir.7b03198

J7. Brochard, L.; **Honorio, T.**; Vandamme, M.; Bornert, M.; Peigney, M. (2017) Nanoscale origin of the thermomechanical behavior of clays. ACTA GEOTECH-NICA, 12 (6), pp. 1261-1279, doi: 10.1007/s11440-017-0596-3

J6. **Honorio, T.**; Bary, B; Sanahuja, J.; Benboudjema, F. (2017) Effective properties of n-coated composite spheres assemblage in an ageing viscoelastic framework. INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES 124, pp. 1-13, doi: 10.1016/j.ijsolstr.2017.04.028

J5. **Honorio, T.** (2017) Micromechanics of transformation fields in ageing linear viscoelastic composites: effects of phase dissolution or precipitation. MECHANICS OF TIME-DEPENDENT MATERIALS 21 (4), pp. 597-612, doi: 10.1007/s11043-017-9344-1

2014-2016

J4. **Honorio, T.**; Bary, B; Benboudjema, F. (2016) Multiscale estimation of ageing viscoelastic properties of cement-based materials: a combined analytical and numerical approach to estimate the behaviour at early age. CEMENT AND CONCRETE RESEARCH 85, pp. 137-155, doi: 10.1016/j.cemconres.2016.03.010

J3. **Honorio, T.**; Bary, B; Benboudjema, F.; Poyet, S. (2016) Modeling hydration kinetics based on boundary nucleation and space-filling growth in a fixed confined zone. CEMENT AND CONCRETE RESEARCH 83, pp. 31-44, doi: 10.1016/j.cemconres.2016.01.012

J2. **Honorio, T.**; Bary, B; Benboudjema, F. (2016) Factors affecting the thermo-chemo-mechanical behavior of massive concrete structures at early-age: a numerical study. MATERIALS AND STRUCTURES 49. Issue 8, pp. 3055-3073, doi: 10.1617/s11527-015-0704-5

J1. **Honorio, T.**; Bary, B; Benboudjema, F. (2014) Evaluation of the contribution of boundary and initial conditions in the chemo-thermal analysis of a massive concrete structure. ENGINEERING STRUCTURES 80, pp. 173-188, doi: 10.1016/j.engstruct.2014.08.050
**Under Revision**

J43. **Honorio, T.**; **Masara, F.***; Poyet, S.; Benboudjema, F. Surface thermal (de)sorption in C-S-H. Submitted to the CEMENT AND CONCRETE RESEARCH. Preprint available here

**Under Review**

J44. **Honorio, T.** Permeability of C-S-H. Submitted to the CEMENT AND CONCRETE RESEARCH Preprint available here

J45. **Ferhat, M.***; **Honorio, T.**; Bore, T.; Benboudjema, F.; Daout, F.; Vourc'h, E. Monitoring of Mortar Hydration Combining Microwave and Calorimetry Measurements. Submitted to IEEE TRANSACTIONS ON INSTRUMENTATION & MEASUREMENT

J46. **Ait Hamadouche, S.***; **Honorio, T.** Nanomechanics of ASR gels from coarse-grained simulations. Submitted to the JOURNAL OF ENGINEERING MECHANICS

J47. **Ait Hamadouche, S.***; **Honorio, T.**; Bore, T.; Benboudjema, F.; Daout, F.; Vourc'h, E. Dielectric permittivity of C-S-H. Submitted to the CEMENT AND CONCRETE RESEARCH Preprint available here

**In preparation**

J48. Babaei, S.; Benboudjema, F.; **Honorio, T.**; Seetharam, S.C.; Dizier, A.; Crane, B. Micromechanical analysis of thermo-mechanics and hydro-mechanics of hardened cement paste

J49. **Masara, F.***; **Honorio, T.**; Brochard, L; Benboudjema, F. Thermal pressurization in C-S-H

CONFERENCE PROCEEDINGS

2023

C38. Honorio, T.; Masara, F.***; Benboudjema, F. Behaviour of water in C-S-H, ICCC, Bangkok, Thailand, September, 2023

C37. Masara, F.***; Honorio, T.; Benboudjema, F. C-S-H sorption under temperature and relative humidity changes, ICCC, Bangkok, Thailand, September, 2023

C36. Ait Hamadouche, S.***; Honorio, T.; Bore, T.; Benboudjema, F.; Daout, F.; Vourc'h, E. Multiscale modeling of the dielectric response of C-S-H. SynerCrete 2023, Milos, Greece, June, 2023

C35. Masara, F.***; Honorio, T.; Benboudjema, F. Is thermal pressurization in C-S-H relevant for concrete spalling? SynerCrete 2023, Milos, Greece, June, 2023

C34. Saba, P.***; Honorio, T.; Brajer X.; Benboudjema, F. Fiberglass mesh reinforced rendering mortar: Effect of fiberglass reinforcement. SynerCrete 2023, Milos, Greece, June, 2023

C33. Honorio, T. Einstein explains water transport in C-S-H. SynerCrete 2023, Milos, Greece, June, 2023
C32. Sayari, T.*; Honorio, T.; Mohaine, S.; Robert, F.; Adia, J.-L.; Lion, M.; Got-
teland, P.; Clergue, C.; d'Aloia, L.; Benboudjema, F. Concrete drying kinetics:
development of an accelerated drying protocol for fire testing. Fire Spalling – 7th
International Workshop, October, Berlin Germany, 2022

C31. Razafimbelo, M.*; Gatuingt, F.; Hervé-Secourgeon, G.; Bottoni, M.; Pinelli, X.; Honorio, T.; Titirla, M. D. Experimental validation of the strut-and-tie design for reinforced concrete massive structures by deformation flow analysis. fib international congress, Oslo, Norway, June 2022

C30. Sayari, T.*; Honorio, T.; Mohaine, S.; Robert, F.; Adia, J.-L.; Lion, M.; Got-
teland, P.; Clergue, C.; d'Aloia, L.; Benboudjema, F. Concrete drying kinetics:
development of an accelerated drying protocol in fire testing. fib international
congress, Oslo, Norway, June 2022

C29. Sayari, T.*; Honorio, T.; Benboudjema, F.; Tabchoury, R.; Adia, J.-L.; Clergue, C. Numerical and experimental investigation of wall effect in concrete. RILEM international Conference “Numerical Modeling Strategies for Sustainable Concrete Structures” (SSCS 2022), Marseille, France, July 2022.

C28. Masara, F.*; Honorio, T.; Benboudjema, F. Modeling CSH Sorption at the Molec-
ular Scale: Effective Interactions, Stability, and Cavitation. RILEM international
Conference “Numerical Modeling Strategies for Sustainable Concrete Structures”
(SSCS 2022), Marseille, France, July 2022.

C27. Honorio, T.; Masara, F.*; Barbosa, W.; Benboudjema, F. The multi-scale multi-
technique multi-physics framework required to model the thermal properties of
cement-based materials. RILEM international Conference “Numerical Modeling
Strategies for Sustainable Concrete Structures” (SSCS 2022), Marseille, France,
July 2022.
2021

C26. Ait Hamadouche, S.**; Honorio, T. Multiscale modeling of the mesotexture of C-S-H and ASR gels. (EURO-C 2022), Vienna, Austria, May 2022. doi: 10.1201/9781003316404-17

C25. Bourdot, A.; Martin-Cavaillé, C.**; Vacher, M.***; Honorio, T.; Sebaibi, N.; Bennacer, R. Microstructure and durability properties of concretes based on oyster shell co-products. RILEM International Conference; Merida, Mexico, August 2021.

C24. Saba, P.*; Honorio, T.; Mahmood O-A. ; Benboudjema, F. Etude du comportement mécanique d'un mortier de façade dans un système ITE. AFGC, GC'2021, 8-9 June 2021, Cachan, France.

C23. Saba, P.*; Honorio, T.; Mahmood O-A. ; Benboudjema, F. glass fiber reinforced mortars: Crack initiation and propagation study. 13th international symposium on ferrocement and thin fiber reinforced inorganic matrices, Lyon, France, June 21-23, 2021

C22. Saba, P.*; Honorio, T.; Mahmood O-A. ; Benboudjema, F. Crack initiation and propagation in fiber-glass reinforced mortars. CRC2021 : International RILEM Conference on early-age and long-term crack width analysis in RC structures, Gif sur Yvette, April 2021, France.

C21. Honorio, T.; Ait Hamadouche, S.**; Fau, A. CSI (Cement Science Investigation): using machine learning to guess the OPC pastes composition from the elastic response. CRC2021 : International RILEM Conference on early-age and long-term crack width analysis in RC structures, Gif sur Yvette, April 2021, France. doi: 10.1007/978-3-030-72921-9_17

C20. Honorio, T.; Al Dandachli, S.**; Bourdot, A. Reversible order-disorder transition in ettringite-metaettringite conversion? Conference: 14th World Congress on Computational Mechanics (WCCM) and ECCOMAS Congress (2020), Jan 2021, France.

2020

C19. Bourdot, A.; Badreddine, D.; Lackache, Y.; Rateau, O. ; Honorio, T. ; Sebaidi, N. Study of mechanical properties and microstructure of mortars based on oyster shell powder RUGC 2020, May 2020, France.

C18. Honorio, T.; Benboudjema, F.; Bore, T.; Carasek, H.; Cascudo, O.; Ferhat, M.; Vourc'h, E. Electromagnetic properties of concrete: bottom-up modeling from the molecular scale. RILEM International Conference; Guimarães, Portugal, Mars 2020.

2019

C17. Honorio, T.; Bary, B. Numerical and analytical estimation of the ageing linear viscoelastic behavior of a two-phase composite with expansive inclusions. FraMCoS-10, Bayonne, France, 2019.

C16. Honorio, T. Micromecânica aplicada ao estudo de argamassas de revestimento. (in Portuguese), SBTA, Goiânia, Brazil, 2019.

C15. Honorio, T. Mécanique des matériaux nanogranulaires. (in French), CSMA, Giens, France, 2019.
C14. Bary, B., Honorio, T. Numerical and analytical estimation of the ageing linear viscoelastic behavior of a two-phase composite with expansive inclusions. FraMCoS-10, Bayonne, France, 2019.

C13. Honorio, T.; Abahri, K. Non equilibrium molecular dynamics simulation of the hydrodynamics in crystalline calcium silicate hydrates nanopores. RILEM International Conference on Sustainable Materials, Systems and Structures; Rovinj, Croatia, Mars 2019

2018

C12. Honorio, T. Interactions between crystalline calcium silicate hydrates layers: grand canonical simulations of pressure and temperature effects. SynerCrete, Funchal, Portugal, October 2018

C11. Honorio, T. Influence of the flexibility of calcium silicate hydrates layers on the mesotexture: coarse-grained simulations accounting for three-body interactions. SynerCrete, Funchal, Portugal, October 2018

2017

C10. Honorio, T.; Brochard, L. Flexibility of C-S-H sheets and stacks from molecular simulations. 2nd International RILEM/COST Conference on Early Age Cracking and Serviceability in Cement-Based Materials and Structures, EAC-02, Brussels, Belgium, September 2017

C9. Bary, B.; Baestiens, W.; Bernachy-Barbe, F.; Honorio, T.; Imbert, C.; Neji, M.; Poyet, S.; Segarra, C.; Touzé, G. Experimental study and numerical estimation of the early age behavior of a massive concrete structure. 2nd International RILEM/COST Conference on Early Age Cracking and Serviceability in Cement-Based Materials and Structures, EAC-02, Brussels, Belgium, September 2017

C8. Honorio, T.; Brochard, L.; Vandamme, M.; Stefanou, I.; Ghabezloo, S.; Bornert, M. Stability of hydrated clay layers from molecular simulations. 6th Biot Conference on Poromechanics, Champs sur Marne, France, July 2017

C7. Brochard, L.; Honorio, T.; Vandamme, M.; Stefanou, I.; Ghabezloo, S.; Bornert, M. A possible nano-scale origin of the surprising thermal expansion of clays. 6th Biot Conference on Poromechanics, Champs sur Marne, France, July 2017

C6. Honorio, T.; Brochard, L. Fluctuations of mechanical fields in thermo- and poroelasticity: multiscale estimations applied to cement-based composites. 6th Biot Conference on Poromechanics, Champs sur Marne, France, July 2017

2016-2014

C5. Honorio, T., Bary, B., Sanahuja, J., Effective ageing linear viscoelastic properties of composites with phase precipitations: comparison between numerical and analytical homogenization approaches. FraMCoS-9, Berkeley, EUA, 2016.

C4. Honorio, T.; Bary, B.; Benboudjema, F. Multiscale estimation of the viscoelastic properties of cementitious materials at early age: a combined analytical and numerical approach. ConCreep, Wien, Austria, 2015

C3. Honorio, T.; Bary, B.; Benboudjema, F. Estimation of elastic properties of cement based materials at early age based on a combined numerical and analytical multiscale micromechanics approach. CONMOD, Beijing, China, 2014

C2. Honorio, T.; Bary, B.; Benboudjema, F. Influence of the particle size distribution on hydration kinetics: a mechanistic analytical approach. CONMOD, Beijing, China, 2014

C1. Honorio, T.; Bary, B.; Benboudjema, F. Analysis of the thermo-chemomechanical behavior of massive concrete. EURO-C, St Anton am Arlberg, Austria, 2014.
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