1. Introduction
Lime-based grouts have been extensively used for the restoration of heritage structures, both concerning the strengthening of historic masonries and the consolidation of architectural surfaces [
1,
2,
3,
4,
5,
6,
7,
8,
9,
10]. Their type, constituents and properties are usually defined by the characteristics of each case, as well as the restoration requirements. They usually consist of one or more binding agents, whereas additives and admixtures have been applied in order to enhance specific properties [
1,
2,
3,
4,
5]. Regarding the lime type, hydrated lime [
1,
2,
3,
9,
11,
12,
13] or natural hydraulic lime may be used [
4,
5,
6,
7,
8], either solely (especially in the latter case), or mixed with natural and artificial pozzolans.
The water content of grouts is of fundamental importance, since it presupposes the fluidity of the mixtures, directly linked with their applicability and efficacy. On the contrary, it negatively influences their volume stability, both at the fresh (segregation and bleeding) and hardened state (shrinkage deformations) [
10]. Additionally, it inversely affects their mechanical properties, which whatsoever remain at a low level according to their composition [
14]. To this extent, various studies have been performed, introducing admixtures and techniques for decreasing the water demand of the mixtures (superplasticizers, partial substitution of water with other suspensions, etc.) [
1,
10,
13].
Regarding the fresh state properties of grouts, fluidity, injectability and volume stability are usually measured, according to relevant standards and specifications that define their performability during application [
1,
2,
3,
5,
6,
7,
8,
11,
12,
13,
15]. Further testing procedures could be applied, focusing on determining rheological properties, such as plastic viscosity, shear and yield shear stress [
5,
7,
9,
13]. These may characterize the types of mixtures, classifying them as Newtonian (constant viscosity, independent of the stress imposed) and non-Newtonians (alterations of viscosity according to the stress applied) [
16]. In the latter case, shear thinning (viscosity decrease) or shear thickening (viscosity increase) may be displayed according to the shear rate and stress imposed, as well as the consistency and composition of the mixtures [
13,
16]. When the finite stress required in order to deform, known as yield stress, is exceeded, the material flows in a non-linear stress–strain modulus (shear-thickening or shear-thinning behavior) due to the separation of the particles [
17,
18]. Generally, low level values of yield stress and plastic viscosity correspond to a low energy demand for a grout to be flowable and easily injected [
13]. This is related with the minimum stress needed for a suspension to start flowing.
According to the models applied for determining the rheological properties of grouts and slurries, the Newton model mainly concerns Newtonian fluids, while Bingham and Casson models non-Newtonians [
17,
18,
19,
20]. The equations describing these models are as following:
where
τ is shear stress (Pa);
μ is the plastic viscosity (Pa.s);
˙γ is shear rate (s
−1); and
τ0 is yield stress (Pa).
Another classification of fluids is their characterization as viscoplastic or viscoelastic. From a rheological perspective, a viscoplastic material has a yield stress under which it will not deform, whereas a viscoelastic one will deform at any stress application. Natural hydraulic lime grouts could be characterized as viscoplastic, presenting a plastic response up to the yield stress and a viscous performance at higher stress levels [
13]. In the case of air lime grouts, there is limited research on the determination of their rheological properties regarding viscosity, shear and yield stress, which are closely related with their binding system, as well as their water content [
9].
Regarding the hardened state properties of lime-based grouts, they are significantly influenced by their water content, both regarding their physical and mechanical properties. According to former research work and literature [
1,
2,
3,
4,
5], lime-based grouts, such as lime–pozzolan ones, present a very slow strength development rate, attributed to their usually high water content, as well as the characteristics of their binding agents. Generally, the water content increase significantly influences their properties, both regarding shrinkage deformations, absorption and strength [
1,
2,
3,
4,
5,
8,
9,
10].
In the present study, the fresh and hardened state properties of four grout compositions, based on hydrated lime and natural pozzolan, were tested. The studied parameter was the Water/Binder (W/B) ratio, which was gradually decreased from 1 to 0.75. According to the results, the examined properties were significantly influenced by the water content, which was finally the fundamental factor influencing their behavior.
3. Results
3.1. Fresh State Properties
As has been previously stated, the grout mixtures were manufactured with a different W/B ratio, including 1.0 (Comp. 1), 0.9 (Comp. 2), 0.8 (Comp. 3) and 0.75 (Comp. 4) (
Table 2). In
Table 3, the fresh state properties of the compositions are synoptically presented.
Regarding fluidity (
Table 3), recorded by ASTM and EN flow cones at two intervals (immediately after manufacture and 1 h later), the following remarks could be attained. By reducing the W/B ratio from 1 to 0.75, flow time was, as expected, increased in both cases. Immediately after manufacture, ASTM flow time ranged from 9.8 to 16.9 s and 1 h later from 10.23 to 22.47 s, while EN time was 8.1–15 to 8.5–19.3 s, respectively.
At the ASTM cone, the flow time increase varied from 25 to 73% (a 10% decrease in the water content corresponded to a 25% flow time increase). One hour later, the increase rate was higher, ranging from 25 to 120% and being more intense in the lower W/B ratio (0.75). In the case of the EN cone, the time increase ranged from 19 to 85% and 18 to 127% 1 h after manufacture. Generally, compositions 1 and 2 showed the lower flow time increase 1 h after manufacture (~4%), while the highest was given by Comp. 4 (32%).
Figure 3 depicts the influence of the W/B ratio on the flow time of the mixtures. The application of the curve-fitting process on the research data resulted in a high correlation coefficient (R
2 > 0.98) for all cases. Flow time measured immediately after the grouts’ manufacture was increased with the W/B decrease, following a linear function (1
st degree polynomial). One hour after manufacture, values were also increased due to the W/B reduction, presenting, however, a quadratic function (2
nd degree polynomial). It maybe therefore implied that the water content has a linear impact on the initial flow time of the grouts (both measured at ASTM and EN cones) and a quadratic one on the 1 h values. The latter may be directly linked with the applicability of the grouts throughout time, showing that the lower the water content the more difficult or even insufficient would be the grout application at least 1 h after the mixture preparation.
Penetrability (
Table 3,
Figure 4) also had a direct correlation with the W/B ratio, showing a gradual increase from 3 to 7.2 s. The relationship of the values also presented a polynomial function (2
nd degree), showing a high correlation coefficient (R
2 = 0.96). The final increase in the penetration time due to the decrease in W/B ratio from 0.75 to 1 was 130%. Volume reduction and bleeding, on the other hand, were significantly decreased due to the W/B ratio reduction and minimized in the lower W/B ratio (0.75). Volume reduction ranged from 2.2 to 0% and bleeding from 1.0 to 0%.
3.2. Rheological Properties
Figure 5 and
Figure 6 present the rheological properties of the grout mixtures, determined by the Viscometer 10 min after manufacture. According to the results and in line with relevant studies [
5,
9,
13], shear stress (
Figure 5) was almost linearly increased with the shear rate rise, while it varied inversely with the W/B ratio (the lower the W/B ratio the higher the values). Compositions 1 and 2, presenting higher water content (W/B ratio 1 and 0.9, respectively), showed almost similar values and trends, ranging from 14 to 37 Pa. Composition 3 (0.8) and 4 (0.75), on the other hand, showed significantly higher values, intensively increased above 200 s
−1 (25–62 Pa and 46–70 Pa, respectively).
Apparent viscosity (
Figure 6) maintained almost at the same (low) level for Compositions 1 and 2 (W/B > 0.9), showing a slight decrease above 250 s
−1. Values ranged from 0.124 to 0.117 Pa·s for Comp. 1 and 0.138 to 0.125 Pa·s for Comp. 2. In compositions 3 and 4 (W/B: 0.8–0.75), viscosity was decreased with the shear rate rise, with the more intense alterations to be recorded in Comp. 4 (0.462–0.217 Pa·s). According to Jorne et al. [
13], in hydraulic lime grouts, presenting a similar rheological behavior with other cementitious materials, viscosity decreases with the rise of shear rate due to the particles’ dispersion.
3.3. Physical Properties
The shrinkage deformations of the grouts, according to their mass and volume changes, are depicted in
Figure 7. Results show that a decrease in mass and volume was recorded in all cases. Changes were more extreme up to the age of 20 days and were further stabilized (especially mass changes). Generally, the reduction of water led to a reduction both in the weight and volume changes up to 30% and 95%, respectively. Regarding mass changes, a 10% decrease of water in each composition resulted in a proportional reduction in the values (~10%), while volume changes were significantly lower, ranging from 0.12% (Comp. 1) to 0.02% (Comp. 4). The lowest values were recorded for the lower W/B ratio (0.75).
The physical properties of the grouts, concerning porosity, absorption, apparent specific gravity and capillary absorption index, are presented in
Table 4, while in
Figure 8 the correlation of porosity and apparent specific gravity is given. It was observed that porosity and absorption values were slightly increased at 90 d and were further reduced. Apparent specific gravity presented an opposite performance. The decrease in the water quantity greatly influenced these properties, especially in compositions 1, 2 and 3, with a gradual decrease in porosity, absorption and capillary absorption index at all ages, ranging from 4 to 27%. On the other hand, apparent specific gravity increased from 4 to 12%.
Composition 4 showed a slight increase in porosity, absorption and apparent specific gravity (related to Comp. 3), while the capillary absorption index was significantly decreased. However, the 90 d values of porosity and absorption, which are considered to be the more representative in the case of lime-based grouts [
1,
2], followed the trend shown in all compositions.
3.4. Mechanical Properties
The mechanical properties of the grout compositions (dynamic modulus of elasticity, flexural and compressive strength), tested at different ages (28, 90, 180 d), are presented in
Figure 9. From the correlation of the results, it may be firstly concluded that all values significantly increased throughout time, with the highest ones to be recorded at 180 days. Generally, the increase from 28 to 180 d varied from 200 tο 600%, with the highest rise to be seen in the lower W/B ratio and especially in compressive strength. To this extent and according to former research work [
1,
2], it was testified that lime–pozzolan grouts present a very slow strength development rate that should be thoroughly taken into consideration during the design of repair grouts for historic structures.
Dynamic modulus of elasticity ranged from 1 to 4 GPa in Comp. 1, 1.3 to 5.2 GPa in Comp. 2, 1.3 to 5.7 GPa in Comp. 3 and 1.2 to 6.2 GPa in Comp. 4. The water content decrease resulted in a low increase in the 28 d values (~5%) and a significant one further, especially at 180 days (55%).
Flexural strength was mostly influenced by the age of the specimens, especially concerning the 180 days, since the 28 d ones were <0.5 MPa, 90 d 0.7–1 MPa and 180 d 1.5–2.5 MPa. The W/B ratio decrease resulted in strength enhancement, mostly depicted in Comp. 4.
Compressive strength showed the same trend of dynamic modulus of elasticity, with values ranging from 0.5 to 1.5 MPa in Comp. 1, 0.6 to 1.9 MPa in Comp. 2, 0.7 to 2.4 MPa in Comp. 3 and 0.9 to 3 MPa in Comp. 4. The water quantity decrease also resulted in an increase in compressive strength, with a rise of 200% at 180 days.
4. Discussion
Regarding the rheological properties of the grouts, as discussed in
Section 3.1, the applied function fitting method led to identifying the quantitative relationship among flow, penetration time and the W/B ratio of the mixtures (
Figure 3 and
Figure 4). Relevant efforts of quantifying the correlation among properties have been made by other researchers [
6,
18].
As has been already pointed out, the correlation coefficient was high in all cases (R
2 > 0.96), showing a linear correlation of the flow time values and the W/B ratio immediately after the grout preparation and a quadratic one 1 h later (
Table 5). Penetrability presented a quadratic function (2
nd degree polynomial) with the water demand.
According to Larson [
29], in a non-Newtonian fluid, viscosity may be increased or reduced with the shear rate rise, leading to shear thinning or thickening phenomena. On the other hand, in Newtonian fluids, viscosity is constant and independent to the stress imposed [
17]. From the evaluation of the results of this study, it could be asserted that the higher water content of lime–pozzolan grouts (W/B ratio: 0.9–1.0) led to the creation of Newtonian fluids, maintaining their viscosity independently of the stress imposed. At lower W/B ratios (≤0.8), mixtures could be characterized as non-Newtonian, showing a shear thinning behavior, since their viscosity was decreased (
Figure 6). To this direction, it seems than when all other parameters are stable, the water content of lime–pozzolan grouts defines their rheological behavior, as well as their characterization.
The correlation of the apparent viscosity with the shear stress, determines the plastic viscosity of the mixtures, as well as their yield stress [
5,
9,
13,
18]. The Bingham and Casson models (according to Equations (2) and (3)) have been generally applied, while in the case of NHL grouts the Bingham model usually prevails [
5,
9,
13].
In the present study, both equations have been applied, as presented in
Table 6. A wide range of results derived in the case of the Bingham model, varying from −0.0548 to 2.5180 Pa, with a negative value to be detected in Comp. 1 (−0.0548 Pa). In the Casson model, having a more gradual transition between the yield and Newtonian regions, values were near to zero, except for Comp. 4 that exhibited a value of 0.0488 Pa. As expected, Casson values were significantly lower than the Bingham ones, showing an increasing trend with the decrease of the water content.
According to Kelessidis et al. [
30], when applying rheological models (mainly the two-parameter ones), negative values may arise, which is rather controversial, since the condition
τ0 > 0 should always be valid. To this extent, other formulas have been proposed, considering more complex equations (i.e., the Golden Section search method) [
30,
31].
From all the above, it may be concluded that yield stress calculations are difficult to be applied in fluid lime–pozzolan grouts, mixed with a high-speed mixer and exhibiting a flow time below 12 s (measured at ASTM C939_02 flow cone) (W/B ratio: 0.9–1). Considering that yield stress is associated with the minimum stress needed to be applied for a fluid to start flowing, the low values of yield stress and plastic viscosity correspond to a more feasible application (easier injection) [
5,
13,
16]. To this extent, there is an inverse relationship between the flow time and yield stress of the mixtures, mainly defined by their water content. Other parameters related to the type, properties, particle size and geometry of the raw materials, presence of admixtures, mixing procedure (mixing type and time), as well as the accuracy and repeatability of measurements, may play an important role in the research findings. Additionally, the testing and resting time of the grouts are fundamental.
Physical properties, such as porosity, absorption, capillary absorption index and apparent specific gravity were influenced at all ages by the water content decrease. The trend shown at the age of 90 days seems to be more representative, leading to a linear decrease in porosity and increase in ap. specific gravity with water content reduction. In
Figure 10, this correlation is depicted in a linear function, with a relevant high correlation coefficient (R
2 = 0.92–0.94). According to Papayianni and Stefanidou [
32], in lime–pozzolan mortars, the increase in water content results in an increase in open porosity, favoring the development of larger pores. Therefore, the pore size distribution is a crucial parameter influenced by the W/B ratio that should also be further explored in lime-based grouts.
Regarding the mechanical properties of the grouts,
Figure 10 depicts the correlation of the compressive strength with the W/B ratio. As it can be observed, there is an inverse relation of the values, presenting a quadratic function (2
nd degree polynomial). In concrete technology, Abram’s law [
33] depicted the relationship of strength to the Water/Cement (W/C) ratio (Equation (4)).
where
σc is compressive strength,
K1 and
K2 are constants for specific materials and W/C the water/cement ratio. Relevant research has verified the formula in the case of cement-based mortars [
34,
35], whereas there are no relevant findings for lime-based grouts. According to ElNemr [
35], Abram’s law was valid in cement mortars with a W/B ratio above 0.4 and was related to the type and proportion of aggregates, as well as other parameters. In the present study, compressive strength seems to follow a power function related to the W/B ratio, mainly attributed at the age of 180 days (
Figure 11). This may be closely related with the slow strength development rate of lime-based grouts, showing the validation of Abram’s law at 180 d age. Focused experimental research may verify the research findings, identifying the relationship between the strength and water content of lime–pozzolan grouts.