*3.3. Compressive Strength Test*

The test was performed at 7, 28, and 90 days as a bending test according to standards EN 196-1 [39] and EN 196-7 [42]. The number of specimens tested was 18 and an average value was calculated. According to Neville [43], the compressive strength of the modified cubic specimen would be 5% higher than the standard cubic specimen. An average value was obtained from this study because only two specimens per flexural strength test were performed.

The test was carried out with the same machine, model ETIMATIC-Proetisa H0224 (Production of Technical and Industrial Equipment, Madrid, Spain). The applied pressure was at an invariant rate of 0.5 MPa/s. The compressive strength is given by the expression:

$$f\_c = \frac{F}{A\_c} \tag{2}$$

where *fc* is the compressive strength in MPa, *F* is the maximum breaking load expressed in N, and *Ac* is the cross-sectional area of the specimen given in mm2.

#### *3.4. Exudation Test*

This test gives the exudation of the grout. It was carried out according to EN 445 [41] (Figure 2). Exudation was measured as the volume of water remaining on the surface of the mix that was kept protected from evaporation. The variation in volume was measured as a difference in percentage of the volume of the grout between the start and the end of the test. The test mainly measured the volume variation caused by sedimentation or expansion. A transparent tube, approximately 60 mm in internal diameter and around 1 m in length, was used. The tube was placed in a vertical position with the top end open. It ensured a rigid fixation that prevented any movement or vibration. The grout was poured into the tube with a constant flow to ensure that no trapped air remained. The tube was filled to a height, ho. The ambient temperature of the laboratory was 18.1 ◦C and the grout acquired a temperature of 18.3 ◦C. The start time t0 and the height h0 were recorded. The height of the cement grout, hg, was recorded at intervals of 15 min during the first hour, and then at 2 h, 3 h, and 4 h. The height of the exuded water, hw, was recorded at the same time as the measurements of the grout were made. Possible heterogeneities that could be seen in its appearance through the transparent tube were recorded. The volume variation was:

$$\text{h}\_{\text{W}}/\text{h}\_{\text{o}} \times 100\% \tag{3}$$

#### **4. Interfacial Transition Zone Review**

Before presenting the data, the basic principles of mixing models based on the interfacial transition zone are reviewed (ITZ) [44]. This model usually applied to concrete assumes that the material is idealized as a composite of mortar and aggregate, where any arbitrarily small volume contains both mortar and aggregate in fixed proportions [45]. The same hypothesis can be applied to the cementitious grout, which properties will be very influenced by the microstructure. This can be classified into three phases: aggregate, cement paste, and the interfacial transition zone (ITZ). ITZ has a critical role. This transition zone has a size comparable with the size of cement grains.

The effects of varying the percentage of slag substitution affects the state of the structure and causes an improvement in fluency. This leads us to expect an increase in the mechanical strength of the hardened grout. There are few studies on this phenomenon, due to it being difficult to find suitable definitions. It is a new diffuse distribution of the particles in the grout. The global grain size does not change, but the permeability evolves. If locally transported particles do not migrate further, an obstruction occurs that accompanies an overpressure. In short, the substitution of cement by slag results in a redistribution of the fine particles without modification of the total solid volume of the specimen.

Below, the formulation of these models are summarized. The partial densities for the three constituents are given by the following expressions:

$$
\mathfrak{p}^{\mathfrak{s}} = \mathfrak{p}\_{\mathfrak{s}} (1 - \mathfrak{q}) \tag{4}
$$

$$
\mathfrak{p}^{\mathbb{W}} = \mathfrak{p}\_{\mathbb{W}} \mathfrak{q} (1 - \mathfrak{c}) \tag{5}
$$

$$
\mathfrak{p}^{\mathfrak{c}} = \mathfrak{p}\_{\mathfrak{c}} \mathfrak{p} \text{ c} \tag{6}
$$

Where ρs, ρw, and ρ<sup>c</sup> are the real densities of the skeleton, water, and fluidized cement paste, respectively. The porosity, ϕ, defines the proportion of the holes in relation to the total volume. "c" is the concentration in the cement paste of the ITZ zone. It represents the total volume of the particles transported from the skeleton by the filtering forces in the void volume. The fraction of the mass of the fluidized solid is:

$$\mathfrak{c}\_{\mathfrak{m}} = \mathfrak{c} \mathfrak{p}\_{\mathfrak{W}} / \left( \mathfrak{c} \mathfrak{p}\_{\mathfrak{W}} + (1 - \mathfrak{c}) \mathfrak{p}\_{\mathfrak{c}} \right) \tag{7}$$

Applying the mass conservation equations to each phase, Equation (8) presents the variation of mass for solid phase, Equation (9) for liquid phase, and Equation (10) for fluidized solid:

$$\frac{\partial \rho^{\rm s}}{\partial t} + \nabla.(\rho^{\rm s} \mathbf{v}^{\rm s}) = \mathbf{m}^{\rm s} \tag{8}$$

$$\frac{\partial \rho^{\rm w}}{\partial t} + \nabla.(\rho^{\rm w} \mathbf{v}^{\rm w}) = 0 \tag{9}$$

$$\frac{\partial \rho^{\circledast}}{\partial t} + \nabla . (\rho^{\circledast} \mathbf{v}^{\circledast}) = \mathbf{m}^{\circledast} \tag{10}$$

where "m" represents the typical variation of the mass of that constituent (mw = 0), "t" is the time and *∂* is the gradient operator. Assuming that all the particles transferred from the skeleton re-enter the fluid, the following mass can be established:

$$\mathbf{m}^c + \mathbf{m}^s = 0\tag{11}$$

It will be assumed, on the other hand, that the slag transported via filtration in the slurry moves with the same speed as the particles near the ITZ zone. This relationship translates the particular nature of the phenomenon that is considered in the framework of this study. There is, for example, no chemical reactions that cause a divergence between the mass transported from the solid skeleton per unit of time and that which is transformed into cement paste at the same time. The previous hypothesis also assumes that the ITZ does not significantly modify the proportions between the different phases that constitute the initial sample. Therefore, the initial variation and the temporal evolution of ρ<sup>s</sup> (density of the solid skeleton) remain negligible. This means, in particular, that this phenomenon does not develop considerably and causes little variation in the initial properties of the fluidized cement paste in, for example, its density.
