Chopped Basalt Fibers Reinforced Mortar for Strengthening the Architectural Heritage

Abstract

The high seismic vulnerability of unreinforced masonry buildings urgently calls for researchers to develop sustainable reinforcing methods and materials. This paper presents an innovative lime-based mortar reinforced with randomly oriented basalt fibers for the reinforcement of masonry heritage. The main aim of this study is to understand the effect of the content and the length of basalt fibers on the mortar’s mechanical behavior. As a cementitious material made mostly out of lime, the mortar is chemically compatible with the historical substrate and therefore suitable in cases of restoration works on architectural heritage. Moreover, the chopped basalt fibers are randomly oriented, and this characteristic makes the overall layer effective in all directions, as the state of stress induced by seismic action is directionally undetermined. The newly proposed reinforcement system is characterized by a twofold aspect related to sustainability: 30% of the aggregates composing the mortar mix design is a recycled result of the ruins of the 2009 L’Aquila earthquake, and the chopped fibers are made out of basalt, widely known for its environmentally supportable peculiarity. The study consists of testing samples characterized by two fiber lengths and six fiber contents, along with one set of plain mortar samples. Specimens measuring 160 mm × 40 mm × 40 mm are first tested in a three-point bending (TPB) configuration, aiming to determine the flexural strength and the post-peak capacity through the calculation of the fracture energy. Then, the two broken pieces resulting from the TPB tests, each measuring 80 mm × 40 mm × 40 mm, are tested in splitting and compression, respectively, aiming to compute the tensile and compressive strengths. Finally, to provide a trend for the mortar’s mechanical properties, a regression analysis is performed by fitting the experimental data with simple linear, polynomial, and exponential regression models. Results show that: (i) both fiber content and fiber length are responsible for a linear increase of the flexural strength and the fracture energy; (ii) for both short- and long-fiber mortar samples, the tensile strength and the compressive strength parabolically increase with the fiber content; (iii) the increase in fiber content and fiber length always generates a reduction in the conglomerate workability. The fiber content (FC) optimization with respect to the mechanical properties leads to a basalt FC equal to 1.2% for long-fiber samples and an FC equal to 1.9% for short-fiber ones.

1. Introduction

Structures made out of unreinforced masonry are very vulnerable to earthquakes [1,2,3,4,5,6], and their seismic susceptibility augments as structural size increases [7,8]. While developing new materials and seismic strengthening technologies for masonry architectural heritage structures [9], there are several conservation principles to be considered [10,11,12,13,14,15,16,17], including concepts like compatibility and reversibility of repair, minimal intervention, monitorability, structural authenticity, and reliability. Italian codes progressively incorporated these concepts. In particular, first the 2011 Italian Guidelines [18] made an exhaustive list of principles to be observed during the design and execution of restoration works on cultural heritage. Then, the latest version of the Italian building code [19,20] prescribes the adoption of the Italian Guidelines, therefore implying the respect of the aforementioned principles.

Two are the traditional strengthening interventions on existing masonries: the fiber-reinforced polymers (FRP) [21,22,23,24,25,26,27,28] and composites made out of fiber-reinforced cementitious matrix (FRCM) [29,30,31,32,33,34,35,36,37,38,39]. FRPs demonstrated their effectiveness in increasing the load-carrying capacity of masonry elements [40,41], but they are characterized by several drawbacks, such as low fire resistance and permeability. They are not suitable for application on moistened walls and, most importantly, they have a deficient chemical affinity with the historical substrate made out of masonry [42,43]. The alternative use of FRCMs is advantageous because they are easy to place and install, and they have good vapor permeability [44]. FRCMs are generally composed of fiber fabrics embedded in a matrix, which is most often a cement-based mortar [45,46,47,48,49,50]. Many are the materials used for the fibrous component, i.e., steel [51,52], carbon [53,54], glass [55,56], aramid [57,58], and polyvinyl-alcohol (PVA) [59]. During the last few decades, vegetable fibers have shown to be a valid alternative as a fibrous matrix in composite materials [60,61,62,63]. It is undeniable that FRCM is an advantageous technique for strengthening masonry structures, but it is, however, characterized by many drawbacks for interventions on historical heritage. For example, the most widely adopted mortar matrix for FRCM is mostly composed of cement, which does not ensure chemical compatibility with the existing substrate. Moreover, the FRCM fiber textile is made out of fibers disposed of in grids or yarns, which are very weak when solicited out of their axial direction [64]. The two mentioned FRCM drawbacks can be overcome by the adoption of a lime-based mortar [65,66,67,68,69], which allows for chemical affinity with the masonry substrate [19,20,70], and by using chopped short fibers randomly dispersed in the mortar matrix, which offers a multi-directional response to seismic actions. The traditional FRCM technology is characterized by another limitation that appears when the reinforcement is applied at a large scale on masonry structures. The application process is shown in Figure 1 and is composed of three phases, i.e., (i) the inorganic mortar matrix is applied to the historical masonry as a thin layer (see Figure 1b), (ii) the textile fabric is applied to the fresh mortar layer through light pressure (see Figure 1c), (iii) a second and last mortar layer is applied to the fiber grid, which at this stage is completely embedded (see Figure 1d). The mentioned process is totally hand-made and consists of a very time consuming activity.

This study proposes a new material suitable for strengthening existing masonry structures, that is made out of chopped basalt fibers dispersed in a lime-based mortar. The mortar is shown in Figure 1e, and it can be applied all at once on the existing masonry support. The proposed mortar is characterized by high versatility. In fact, it can be used as internal and/or external reinforcement of existing masonry walls, or as an alternative for existing and new masonry joints for irregular and regular masonries. The topic concerning the application of the new basalt mortar at a vast scale on various structural typologies is very interesting, but it is out of the scope of this study. In fact, the goal of this paper is to mechanically characterize the basalt reinforced mortar at the material scale, assessing the effect of both the length and content of basalt fibers on the mortar’s mechanical properties, in perspective of its application to masonry heritage structures. Two are the main features of the newly proposed mortar, aiming to respect a sustainable strategy for the repair works: (i) 30% of the aggregates composing the mortar mix design are recycled, resulting from the ruins of the 2009 L’Aquila earthquake, and (ii) chopped fibers are made out of basalt, a natural material of volcanic origin.

During recent decades, fibers made out of basalt have raised attention while being used in construction engineering [71,72] because of their low cost, non-toxicity, sustainability, and easiness of the production process (for a deeper comparison between basalt and other types of fibers, the reader is referred to [73,74]). Basalt fibers are produced from specific volcanic basalt rocks, namely acidic-type basalts, by means of a thermo-chemical process during which no additives are added. Continuous basalt fibers are then chopped into 12–20 μm diameters and into 3–240 mm lengths depending on the desired composite applications. Basalt fibers proved to be beneficial for enhancing the mechanical properties of several quasi-brittle materials [75,76,77,78]. In particular, several studies demonstrated a good improvement in the concrete mechanical properties when basalt fibers are used, both in cases where they are disposed of as rebars or grids on the external surface of concrete specimens or when the chopped basalt fibers are included within the concrete mix design [79,80,81]. In this latter case, Elshafie and Whittleston [82] showed that the concrete tensile strength significantly enhances by increasing the basalt fiber content or the basalt fiber length. Moreover, in the same study, it was shown that increasing the content or the length of basalt fibers in reinforced concrete improves its flexural strength, elastic modulus, and crack resistance. Other interesting studies pointed out the positive repercussions on the quasi-brittle behavior of cement-based mortar when basalt fibers are included [83,84,85]. Among other results, it was shown that mortar toughness augments when the fiber content grows, thus improving the resistance to deformation property and cracking.

The use of basalt fibers in concrete has already been widely addressed by several studies, but their incorporation within a restoration mortar for masonry architecture seldom appears in the literature. Mostly, a systematic assessment of both the length and content of basalt fibers on the mechanical behavior of restoration mortars remains unexplored, and it will be investigated in this study both experimentally and by means of regression analysis.

2. Materials and Methods

This section illustrates the materials, procedures, and test equipment adopted in the current experimental campaign for the definition of the mechanical properties of the proposed restoration mortar. Aiming to assess the influence of the length of fibers (FL) and content of fibers (FC) on the mechanical performance of the lime mortar strengthened with basalt fibers, two different FLs of 12 mm and 24 mm are used (both lengths are characterized by the same mechanical and geometrical properties), as shown in Figure 2. Nomenclature, geometry (i.e., FL $l_f$, diameter of yarn $d_f$, and strand $d_f^{\ast }$) and mechanical properties (i.e., density ${\rho }_f$, Young’s modulus $E_f$, tensile strength $f_{t,f}$, and ultimate strain ${\epsilon }_{u,f}$) of both basalt FLs are reported in

Table 1. Basalt fibers characterization: geometrical and mechanical properties.

Nomenclature	${\mathit{l}}_{\mathit{f}}$ [mm]	${\mathit{d}}_{\mathit{f}}$ [mm]	${\mathit{d}}_{\mathit{f}}^{\ast }$ [mm]	${\mathit{\rho }}_{\mathit{f}}$ [kg/m3]	${\mathit{E}}_{\mathit{f}}$ [MPa]	${\mathit{f}}_{\mathit{t},\mathit{f}}$ [MPa]	${\mathit{\epsilon }}_{\mathit{u},\mathit{f}}$ [%]
F12	12	0.014	0.030	2700	78,000	1800	4.2
F24	24	0.014	0.030	2700	78,000	1800	4.2

. The basic geometry of both basalt fibers consists of a single yarn, whose average diameter $d_f$ is 0.014 mm. One of the last steps of the manufacturing process provided the application of a thick coating on basalt fibers, which is generally made out of zirconium dioxide (ZrO₂) and titanium dioxide (TiO₂) [83]. The coating process mainly aims to improve fiber durability when exposed to various chemicals, such as Ca(OH)₂ and NaOH. The value of the fiber diameter $d_f^{\ast }$ after coating was not provided by manufacturers, and it was measured by means of an electronic micrometer. Thus, $d_f^{\ast }$ represents an ideal fiber diameter, assuming the fiber cross-section to be perfectly circular.

2.1. Mix Design

With the aim of evaluating the effect of the FL and FC on the mechanical properties of the lime-based mortar, both unreinforced and fiber-reinforced samples were prepared using the same mix design.

Table 2. Mix design composition: the first column indicates the categories, the second column the components, and the third column indicates the percentages in weight.

Category	Component	% [-]
Binders 1	Lime	70
	Portland Cement	30
Aggregates 2	Sand	65
Additives 2	Fluidizer	0.2
	Resin	0.1
-	Water	80 1, 20 2

¹ Compared to the binders weight. ² Compared to the whole product weight.

reports the components and the percentages by weight of the plain mortar conglomerate, consisting of a binder mixture, additives, aggregates, and water. For the mortar application to cultural heritage architectures, the percentage of lime must be a consistent part of the binder. In particular, the proposed mix shows a lime content equal to 70% of the binder weight, while the remaining 30% is Portland cement. The fraction of lime and Portland cement in the total weight of binders defines the mortar as “lime-based mortar”, rather than “pure-lime mortar” [86]. The granular part consists of sand, with diameters ranging between 0.1 mm and 1.2 mm, while the content with respect to the whole weight of the product is equal to 65%. Finally, the water represents the 80% of the binder weight and the 20% of the whole product.

2.2. Sample Preparation and Designation

Operationally, the two additives were first mixed, and then the binders and the sand-aggregate were incorporated into the dried mix, while water at room temperature was included as a last component during the mixing blending phase. After mixing all components in the mortar mixer for about 60 s, the mortar was poured into three molds of $160\times 40\times 40$ mm in length, height, and depth, respectively, and then vibrated according to the standard code EN 1015-11 [87]. Each batch was first subjected to the slump test according to the detailed procedure described in the following section. Once the mortar was poured into molds, specimens were kept in the moist room for 48 h at a temperature of 20 °C (±2 °C) and a moisture content of 95% (±1%). At the end of the treatment in the moist room, samples were moved and kept for 26 days at 20° (room-temperature) and 60% of relative humidity. The testing procedure for the mechanical characterization of the samples took place after 28 days and is detailed in Section 2.4.

Fibers were added during the mixing phase as a second-to-last component, before the water. Since the aim of this study is to investigate the effect of the basalt content (FC) and length (FL) on the mechanical properties of the lime-based mortar, the experimental campaign involves six FC and two FL. In total, 36 strengthened samples are obtained, with a further three non-strengthened samples as a comparison group for a final test sample number equal to 39. For both short (12 mm) and long fibers (24 mm), the following FCs are analyzed: ${\mathrm{FC}}_{B1}$ = 0.50%, ${\mathrm{FC}}_{B2}$ = 0.75%, ${\mathrm{FC}}_{B3}$ = 1.00%, ${\mathrm{FC}}_{B4}$ = 1.50%, ${\mathrm{FC}}_{B5}$ = 2.00%, and ${\mathrm{FC}}_{B6}$ = 2.50%. Note that FC is the ratio of fiber weights to the whole product, so it is expressed as a percentage. Moreover, the highest percentage ${\mathrm{FC}}_{B6}$ = 2.50% is an upper bound for the mortar mixture corresponding to the maximum quantity embeddable in the conglomerate, since a greater percentage does not ensure the mixture’s workability. For practical purposes, the ideal fiber content to be incorporated in mortar mixtures represents a fine balance between the maximization of fiber amount, to maximize the gain in terms of mechanical properties, and the containment of embedded fibers to avoid fiber segregation.

2.3. Workability

The workability is a fundamental characteristic of any cementitious mixtures, especially for industrialized materials to be produced on a large scale and put in place at worksites. Currently, the most common test able to evaluate the rheological properties of mortar and other cementitious materials in the fresh state is the slump test. The workability of the proposed mortar was characterized following the procedure described in EN 1015-3 [87] and ASTM C1437 [88]. In particular, the slump test consists of four phases: (i) casting the mortar in steel molds with a truncated cone shape, (ii) removing the cone in a vertical direction, avoiding rotational movement, straight up to clear the sample, (iii) tamping the mortar with 20 strokes using Hagermann’s table, (iv) using a ruler, measuring the mean diameter of the fresh mortar. Figure 3 shows the slump test procedure.

2.4. Mechanical Characterization

All unreinforced and fiber-reinforced samples were tested after 28 days measured from the casting day [87]. The testing process aims to mechanically characterize the mortar samples in terms of flexural behavior and fracture energy, as well as in tension and in compression. The experimental campaign was carried out at the Laboratorio Prove Materiali e Strutture (LDPM) of the University of L’Aquila (Italy) by using the material testing machine “Zwick Roell”.

2.4.1. Bending Behavior and Post-Peak Capacity

This section illustrates the three-point bending test (3PBT) carried out on the 39 samples, aiming to evaluate the mechanical performances in terms of flexural strength $f_f$ and fracture energy $G_f$. Aiming to address the fracture in the middle of the specimen, before proceeding with the actual tests, a notch was fabricated using a manual precision saw on the entire set of specimens. Each notch has a 2 mm thickness and a 6 mm height, with a ratio between the notch and beam height $a/d$ equal to 0.15 [63]. The testing setup of the notched samples tested in 3PBT is shown in Figure 4a,b. The two sample supports are placed at a distance L of 100 mm and provide constraints against vertical displacements, allowing instead horizontal ones. The test was conducted with a force P applied at the top middle length of the sample under displacement control conditions, with a constant velocity of 0.5 mm/min. The load P on the sample and the vertical displacement $\delta$ corresponding to the same mid-span point were measured and automatically recorded. Once stored, these data are used to compute the flexural stress ${\sigma }_f$ using the following formula based on the theory of elasticity:

$${\sigma }_f={\displaystyle \frac{3PL}{2b{(d-a)}^2}}$$

(1)

where b and d are the width and the height of the specimen cross section, respectively. Once the load P reaches the maximum value ($P=P_{MAX}$), Equation (1) provides the bending resistance $f_f$ supported by the mortar sample.

Aiming to evaluate the property of the tested material on energy dissipation, the fracture energy $G_f$ was also computed. One of the most widely known methods is the ‘work-of-fracture’ method, described in the RILEM recommendations [89,90,91]. The fracture energy $G_f$ can be calculated by resorting to:

$$G_f={\displaystyle \frac{W_0+mg{\delta }_0}{(d-a)b}}$$

(2)

where $W_0$ is the area under the load–deflection curve, m is the weight of the specimen related to the volume included between the two vertical supports, g is the acceleration of gravity, and ${\delta }_0$ is the deformation corresponding to the specimen failure conditions.

After performing the bending test, each of the 39 specimens was bisected and used for the subsequent tests, i.e., for the splitting test and the compression test. Thus, 39 specimens were again tested in tension and compression.

2.4.2. Tensile Behavior

In this section, the splitting tests (ST) are presented. This destructive test (indifferently called the Brazilian test) implies an indirect method of measuring the tensile properties of materials. In comparison with other tensile test procedures, ST is easier to perform, and the data scattering is statistically lower. Moreover, ST does not require the samples to have a unique shape, as most of the testing protocols allow the use of specimens characterized by diversified shapes.

Aiming to measure and compare the tensile resistance in strengthened and non-strengthened configurations, the ST was performed on 40 mm × 40 mm × 80 mm prismatic specimens obtained from the two half specimens representing the broken pieces of the 3PBT, as shown in Figure 4c. ST provides the sample to be subjected to two opposite compressive loads, as depicted in Figure 4d. The application of the two antipodal compressive loads, vertically oriented, generates a tensile force (and thus stresses) in a perpendicular direction, hence horizontally oriented. When the internal tensile stresses exceed the tensile strength of the material, a crack triggers at the geometrical center of the sample, in accordance with Griffith criterion [92]. It should be noticed that when the fracture does not occur in the specimen’s geometrical center, the ST is not valid, and the corresponding results cannot be considered representative of the sample’s tensile resistance. As already performed in 3PBT, the ST was conducted with a force P applied at the top middle length of the sample, imposed with a constant velocity equal to 0.5 mm/min. In the same application point of P, the vertical force F and the vertical displacement $\delta$ are measured and automatically recorded at each iteration time. Therefore, the following equation was used to calculate the tensile stress: ${\sigma }_t$:

$${\sigma }_t={\displaystyle \frac{2F}{\pi bd}}$$

(3)

It is worth observing that when $F=F_{MAX}$, the value of the vertical force F reaches its maximum; therefore, Equation (3) allows us to compute the tensile resistance $f_t$ supported by the prismatic mortar sample.

2.4.3. Compressive Behavior

For the definition of the compressive resistance of the mortar samples, the compressive tests (CT) in unconfined conditions were carried out for both non-strengthened and fiber-strengthened configurations. Each sample measuring 40 mm × 40 mm × 80 mm was obtained from the two broken pieces resulting from the 3PBT (see Figure 4e). The CT were carried out on a total number of 39 specimens, arranged and loaded as shown in Figure 4f. Each specimen was placed with the bottom face on a squared area of 40 mm × 40 mm, while on the top squared area (measuring 40 mm × 40 mm) of the specimen, the distributed load C was applied. As already done for the two previous tests, the CT were carried out in displacement control with a displacement rate equal to 1 mm/min. Finally, the parameters C and $\delta$, i.e., the applied load and the corresponding vertical displacement, were recorded in real time by the dedicated software. After the CT performance, the compressive stress ${\sigma }_c$ was computed based on:

$${\sigma }_c={\displaystyle \frac{C}{b{L}_2}}$$

(4)

When $C=C_{MAX}$, the value of the vertical load C reaches its maximum. Equation (4) allows us to calculate the compressive resistance $f_c$ supported by the prismatic mortar sample. In addition, knowing the vertical displacement at the mid-span point $\delta$, the vertical strain ${\epsilon }_v$ can be computed using the following equation:

$${\epsilon }_v={\displaystyle \frac{\delta }{d}}$$

(5)

3. Experimental Results

The experimental results on both mortars, i.e., non-reinforced and basalt fiber-reinforced, are examined in this section. In particular, the first three sections (namely Section 3.1, Section 3.2, and Section 3.3) report the results for the 3PBT, ST, and CT, respectively. Section 3.4 reports a synthesis of the results and a discussion. Finally, the slump test results are shown in Section 3.5, and the cruciality deriving from the workability of the conglomerate is discussed.

3.1. Flexural Strength and Post-Peak Capacity

The behavior in bending for different contents and lengths of basalt fibers is illustrated in Figure 5, which depicts all the curves on the flexural stress versus displacement plot. From this figure ahead, short and long FRCM samples (named F12 and F24) are marked with red and orange curves, respectively. The unreinforced cases’ results are reported in Figure 5f with gray lines. The analyzed cases characterized by a different fiber content, i.e., ${\mathrm{FC}}_{B1}$ = 0.50%, ${\mathrm{FC}}_{B2}$ = 0.75%, ${\mathrm{FC}}_{B3}$ = 1.00%, ${\mathrm{FC}}_{B4}$ = 1.50%, ${\mathrm{FC}}_{B5}$ = 2.00%, and ${\mathrm{FC}}_{B6}$ = 2.50%, are progressively shown starting from the upper left side of Figure 5.

A general trend can be observed in terms of flexural behavior: The flexural strength $f_f$ rises as the content of fibers is augmented. Figure 5f points out that unreinforced specimens have a flexural strength $f_f$ equal to about 3 MPa, which is much lower than the cases characterized by fibers of long and short lengths at the maximum content, namely F24-${\mathrm{FC}}_{B6}$ and F12-${\mathrm{FC}}_{B6}$, for which $f_f$ turns out to be about 19 MPa and 15 MPa, correspondingly. For fiber contents ranging from ${\mathrm{FC}}_{B1}$ to ${\mathrm{FC}}_{B5}$, the peaks $f_f$ increase monotonically with the FC, and they are bounded between the smaller and the higher values corresponding to the without the fiber case and the ${\mathrm{FC}}_{B6}$ case, respectively. This result is due to the positive correlation between the fiber number encountered during the rupturing process along the fracturing path and the fiber content FC: the higher the fiber number, the higher the sample’s flexural capacity. Also, the fiber length proved to enhance the sample’s bending capacity. In fact, the flexural strength is higher for the long FRCM samples (F24 cases) than for the short ones (F12 cases). This occurs for all the FCs with the exception of the ${\mathrm{FC}}_{B1}$ case. A plausible explanation of this latter exception is that, for a low fiber content, the number of fibers encountered in the fracturing path is very limited and, as a result, the fiber length contributes to the overall flexural capacity in a negligible manner.

Most importantly, the long FRCM samples (F24 cases) exhibit a more pronounced ductility with respect to the F12 cases (the reader can qualitatively compare the areas subtended by the red and orange load-deflection curves in Figure 5a–f). A deeper quantitative discussion is performed in Section 3.4, which physically explains the correlation between the fracture energy $G_f$ and the FL. Unreinforced WF samples are characterized by a purely brittle behavior, as all sample failures occur all at once and very suddenly, generating almost vertical post-peak curves.

3.2. Behavior in Tension

Figure 6 shows the ST results for both the non-reinforced and basalt FRCM cubes. In particular, it illustrates the mortar tensile behavior in terms of tensile stress ${\sigma }_t$ versus displacement $\delta$ curves. The tensile behavior is depicted for all the FC and both the investigated lengths of fibers, marked by red and orange solid lines. Figure 6f also shows the results related to the unreinforced case (WF case), denoted by gray curves in the plot. The WF tensile behavior is very brittle, as samples reach the tensile peak and instantaneously fail with no softening capacity. All six analyzed cases, characterized by a specific content of fibers, i.e., ${\mathrm{FC}}_{B1}$ = 0.50%, ${\mathrm{FC}}_{B2}$ = 0.75%, ${\mathrm{FC}}_{B3}$ = 1.00%, ${\mathrm{FC}}_{B4}$ = 1.50%, ${\mathrm{FC}}_{B5}$ = 2.00%, and ${\mathrm{FC}}_{B6}$ = 2.50%, are shown progressively from the top left corner in Figure 6.

Analogously to 3PBT results, the results related to the ST show that the tensile strength $f_t$ increases when the FC is augmented. In fact, the tensile strength $f_t$ related to the WF sample is equal to about 2 MPa (the reader is referred to Figure 6f), whereas $f_t$ related to the cases reinforced with the maximum fiber content and short fibers is equal to 3.25 MPa (F12-${\mathrm{FC}}_{B6}$ cases), and $f_t$ related to the cases reinforced with the maximum fiber content and long fibers is equal to 4 MPa (F24-${\mathrm{FC}}_{B6}$ cases).

Additionally, the in-between fiber contents (${\mathrm{FC}}_{B1}$ to ${\mathrm{FC}}_{B5}$) are characterized by $f_t$, which progressively increases with the FC. Moreover, the tensile strength $f_t$ increases while augmenting the FL. This result applies to all the FC, except for the ${\mathrm{FC}}_{B1}$ and ${\mathrm{FC}}_{B2}$ cases, with the tensile strength being higher for the long fiber reinforced cases (F24 cases) than for the short fiber reinforced ones (F12 cases).

Plausible reasons for this observation are similar to those drawn in 3PBT: for a low fiber content, the number of fibers involved in the fracture along the ligament is also very low and, thus, the contribution of the fiber length to the overall tensile capacity is not appreciable. Also, in tension and for all the FC, the long FRCM samples (F24 cases) show a greater post-peak capacity when compared with the F12 cases, as shown in Figure 6. Aiming to provide a physical explanation for the increase in post-peak capacity with the FL, one should resort to the fiber-mortar adhesion surface that resists the fracturing process. The adhesion surface is higher for long fiber samples than for small fiber ones, and therefore they better resist the cracking propagation phenomenon, increasing the overall post-peak capacity at all the FC.

3.3. Behavior in Compression

The results related to the mechanical behavior in compression are depicted in Figure 7. The curves are related to different conditions for FC and FL, and they are shown in terms of compressive stress ${\sigma }_c$ versus vertical strain ${\epsilon }_v$ in the various plots. In all figures, the red and orange lines denote the experimental data for small-length and big-length FRCM samples. The bottom right figure, i.e., Figure 7f, additionally shows the experimental data for the non-reinforced cases (WF cases). Once again, the compressive behavior is very brittle, and one assists with a sudden collapse of all the samples once the compressive strength is reached. Also, a positive correlation between compressive strength and fiber content can be pointed out: $f_c$ enhances as the FC augments. This result is very clear if one compares the F24-${\mathrm{FC}}_{B6}$ and F12-${\mathrm{FC}}_{B6}$ cases (enriched by big and small fibers at the highest content) with the plain mortar case (WF case): for the latter cases the average $f_c$ is about 17.5 MPa, whereas for the former ones, it is 30 MPa and 28 MPa, respectively. For median FC, the compressive capacity progressively increases with the FC, going from the WF case up to the ${\mathrm{FC}}_{B6}$ case. The compressive behavior depends on the fiber length in an analogous way to both the flexural and tensile behaviors: the compressive strength $f_c$ rises as the FL is augmented. However, it is worth underlining that the $f_c$ correlates with FL in a milder way when compared to both the tensile and flexural properties. This appears clear if one observes the $f_c$ related to ${\mathrm{FC}}_{B1}$, ${\mathrm{FC}}_{B2}$, and ${\mathrm{FC}}_{B3}$ cases, for which the mean $f_c$ are quite similar, as opposed to the ${\mathrm{FC}}_{B4}$ case and above, for which the dependence of $f_c$ on the FL appears progressively more pronounced. Therefore, the fiber length FL plays a milder role in compression than the fiber content FC; in compression, the fiber number is more important than the fiber length.

3.4. Discussion

The aim of this paper is to understand the effect of basalt fiber content FC and fiber length FL on the mortar’s mechanical properties. Figure 8 and Figure 9 are elaborate to guide the reader in this direction and to summarize the obtained results. In particular, Figure 8 reports four synthetic histograms that clarify how all the mortar’s mechanical properties are enhanced by basalt FC and FL. From top left, Figure 8 shows the trends of the flexural strength, the fracture energy, the tensile strength, and the compressive strength versus the fiber content for different fiber lengths (the reader is referred to Figure 8a, Figure 8b, Figure 8c, and Figure 8d, respectively). It is important to recall that, in order to compute $f_f$, $G_f$, $f_t$, and $f_c$, Equation (1), Equation (2), Equation (3), and Equation (4) are respectively used.

Generally, it is worth underlining that the main basalt fiber effect is to enhance all the analyzed mechanical properties; this occurs for all the contents and lengths of fiber. Analyzing the tensile strength related to the sample reinforced with long fibers and maximum FC (F24-${\mathrm{FC}}_{B6}$ case), one can notice an increase of more than 90% compared with the unreinforced mortar (WF case). In this same case, the flexural strength shows a great enhancement, increasing by more than 690% with respect to the WF case. The enhancement of the mortar’s mechanical properties is very relevant in the perspective of its application at the structural scale. In particular, the enhancement of the tensile strength is important for the seismic retrofitting of heritage buildings, which are prone to show diffuse damage and collapse when subjected to seismic loads [93]. Authors have recently shown the effectiveness of the basalt-enriched mortar applied to one-head and two-head masonry structures [94,95]. One of the mechanical properties that is mostly augmented because of the fiber’s beneficial effects is the fracture energy $G_f$, which exceeds an increment of 2230% for the same mentioned case (F24-${\mathrm{FC}}_{B6}$ case compared with the WF case). The increase in fracture energy is of paramount importance when aiming to reinforce structures located in seismic areas because it increases the structural capacity of dissipating energy in a non-linear regime through extensive fracturing patterns before the partial or overall collapse [96,97,98]. On the contrary, the mechanical parameter less sensitive to fibers, and above all their length, is the compressive strength, which shows a magnification of just about 72% (comparison between the F24-${\mathrm{FC}}_{B6}$ case and WF the case).

Figure 9 shows the role played by the length and the content of basalt fibers on the scattering of experimental results. As a general trend, it can be noticed that the scattering increases as the FC increases. More specifically, the dispersion of flexural strength $s_{f_f}$ increases by increasing both the FC and FL, as shown in Figure 9a. For the tensile behavior, the fact that the FC is responsible for increasing the dispersion of experimental data $s_{f_t}$ can be observed in Figure 9c. In the same plot, one can see that $s_{f_t}$ is higher when mortar samples are enriched by long fibers rather than short ones, and this occurs for all cases except for ${\mathrm{FC}}_{B5}$ = 2.00%. Also in compression, the experimental data scattering $s_{f_c}$ increases with the increment of FC, as shown in Figure 9d. For the compressive behavior, the $s_{f_c}$ is higher for long fiber samples F24 up to ${\mathrm{FC}}_{B2}$ = 0.75%. From ${\mathrm{FC}}_{B3}$ = 1.00% and above, $s_{f_c}$ is greater for mortar test pieces strengthened by small fibers. Finally, Figure 9b shows that there is no dependence of the fracture energy scattering $s_{G_f}$ on both the fiber content and fiber length.

Generally, the presence of basalt fibers increases the overall randomness in the distribution of the mechanical properties of the reinforced mortar compared with the ones related to the non-reinforced case. This is demonstrated by the higher values of data scattering for all the reinforced specimens with respect to the non-fiber ones. This observation applies to all the analyzed fiber contents and fiber lengths and for all the considered behaviors, i.e., flexural, tensile, and compressive behaviors.

3.5. Optimization of the Basalt Reinforced Mortar Based on Its Fresh State Properties

The slump test procedure was described in Section 2.2 and Section 2.3. The results of the slump test performed on all mortar batches are illustrated in Figure 10, which reports the slump versus the fiber content in cases of short and long basalt fiber reinforcement. A univocal trend can be traced: the increase in fiber content generates an almost linear decrease in the slump value. This implies that in both long and short fiber mortars, the fiber’s incorporation within the mortar mixture reduces its workability and therefore negatively affects the conglomerate properties in the fresh state. Also, the slump value is lower for mortar reinforced with long fibers as opposed to short fibers. This demonstrates that mixtures enriched with short fibers are more workable than long fiber mixtures, and therefore the first ones are preferable for practical purposes.

The results obtained in the previous sections are related to mortar specimens in the hardened state. We showed that the main fiber effect is to enhance all the mortar’s mechanical properties. This result wrongly suggests that the best retrofitting mortar is characterized by the highest fiber content and the highest fiber length. In fact, the best engineering solution must satisfy the essential requirement of workability. In this way, the restoration mortar can actually be applied to the existing surfaces on a large scale. In this perspective, it is important to point out several practical considerations that the mortar must satisfy when applied to extensive surfaces: the conglomerate at the fresh state cannot slide when subjected to its own load; the workmanship must have the possibility of applying the mortar mixture not instantaneously but in successive layers; the mortar consistency should allow the mix to be sprayed (and not hand-applied) on the existing surfaces, aiming to reduce the workmanship costs and speed up the construction times. How do we ensure the satisfaction of the workability requirement and, implicitly, of mentioned considerations? The slump value should not be less than about 15.5 mm. Figure 10b shows the two cases for which the aforementioned condition is met: the F24-${\mathrm{FC}}_B$ = 1.2% case, for which the basalt long fibers are at a fiber content equal to 1.2%, and F12-${\mathrm{FC}}_B$ = 1.9% case, which implies the inclusion of basalt short fibers at a fiber content of 1.9%.

4. Regression Analysis

The aim of this section is to derive regression expressions for the four mechanical parameters $f_f$, $G_f$, $f_t$, and $f_c$ calculated by means of the previous tests, for both cases of short and long fibers. This allows us to individuate an average trend for each mechanical property within its observation domain. For all cases, the matching accuracy between experimental data and regression curves is calculated by means of the coefficient of determination $r^2$ [99,100]:

$$r^2={\displaystyle \frac{{\left[{\sum }_{i=1}^n(y_i-\overline{y})(\widehat{y_i}-\overline{\widehat{y}})\right]}^2}{{\sum }_{i=1}^n{(y_i-\overline{y})}^2{\sum }_{i=1}^n{(\widehat{y_i}-\overline{\widehat{y}})}^2}}$$

(6)

In this last equation, n is the specimen number, $y_i$ is the i-th specimen’s experimental parameter, $\widehat{y}$ is the mean value of the experimental parameter, while $\widehat{y_i}$ and $\overline{\widehat{y}}$ are the i-th specimen’s calculated parameter and the mean value of the calculated parameter, respectively. The coefficient $r^2$ provides an estimate of the fitting accuracy, and it ranges between 0 and 1. In this study, we consider one linear and two non-linear regression models for the regression analysis of the experimental data. In particular, we use the function $Y\left(X\right)=AX+B$ for the linear regression (LRL), the exponential function $Y\left(X\right)=C{e}^{DX}$ for the exponential regression (ERL), and the quadratic function $Y\left(X\right)=M{X}^2+N$ for the parabolic regression (PRL). It is worth underlining that regression functions are applicable within the variation domain of experimental data.

4.1. Bending and Post-Peak Behaviors

Two parameters of interest characterizing the mortar bending capacity are considered for the flexural regression analysis, i.e., the flexural strength $f_f$ and fracture energy $G_f$. For both fiber lengths, we first compute the coefficients of determination for the three regression models, i.e., $r_{LRL}^2$, $r_{PRL}^2$, and $r_{ERL}^2$. Therefore, the highest $r^2$ is determined, and the best regression model for each parameter is identified. Figure 11a illustrates the $r^2$ related to the flexural strength $f_f$ for the three different regression models and for short and long fiber mortars (in red and orange colors, respectively). As $r_{LRL}^2$ is the highest for both short and long fibers (equal to 0.993 and 0.997, respectively), the linear regression model provides the best fitting for the parameter $f_f$. A linear regression function $f_f\left(FC\right)=A_{FL}FC+H_{FL}$ is therefore associated with both fiber lengths, where $A_{FL}$ and $H_{FL}$ are the pair of regression constants for each fiber length. Figure 11b shows these equations for the F12 case (red dotted line) and the F24 case (orange dotted line). For the F12 case, the regression constants $A_{12}$ and $H_{12}$ are equal to 4.6 and 2.9 MPa, and for the F24 case $A_{24}$, $H_{24}$ are equal to 5.7 and 2.9 MPa. Therefore, replacing appropriately, for short fibers mortar $f_{f,F12}=4.6FC+2.9$ and for long fibers mortar $f_{f,F24}=5.7FC+2.9$. It is interesting to note that the pair of values $H_{12}$ and $H_{24}$ not only coincide but are also very similar to the value of the average flexural strength of the unreinforced mortar $f_{f,0}$ (see Figure 8a). Moreover, comparing the two angular coefficients $A_{12}$ and $A_{24}$, depicted with red and orange dotted lines in Figure 11b and respectively equal to 4.6 and 5.7, one can notice an additional dependency on the FL. In fact, $A_{FL}$ for long fibers is greater than for short fibers ($A_{24}>A_{12}$), implying a greater flexural strength $f_f$ of the long fiber samples for the entire range of variation of the FC.

The regression analysis for the fracture energy $G_f$ is similar to that performed for the flexural strength. Figure 11c shows the regression coefficients $r_{LRL}^2$, $r_{ERL}^2$, and $r_{PRL}^2$ for the two mortar fiber lengths. With $r_{LRL}^2$ equal to 0.907 and 0.955 for short and long fiber mortars, the linear regression model best describes the mortar behavior, and the function $G_f\left(FC\right)=B_{FL}FC+L_{FL}$ is the fitting function for both lengths. In this equation, $B_{FL}$ and $L_{FL}$ are regression constants for a given FL. Figure 11d shows the linear equations related to F12 (red dotted line) and F24 (orange dotted line) mortar samples. In the first case, the coefficients of regression $B_{12}$ and $L_{12}$ are equal to 2.45 and 0.07 Nmm⁻¹, respectively. For the second case $B_{24}$, $L_{24}$ are equal to 6.75 and 0.07 Nmm⁻¹, respectively. Therefore, replacing appropriately, for the short fibers, the function is $G_{f,F12}=2.45FC+0.07$, while for the long fibers it is $G_{f,F24}=6.75FC+0.07$. It is interesting to point out that the pair of values $H_{12}$ and $H_{24}$ not only coincide but are also very similar to the value of the average flexural strength of the unreinforced mortar $f_{f,0}$ (see Figure 8a). Comparing the two angular coefficients $L_{12}$ and $L_{24}$, they both are small and very close to the fracture energy computed for the case of the plain mortar $G_{f,0}$ (see Figure 8b). From this numerical evidence, the regression coefficient $L_{FL}$ does not depend on FL, and it can be set as null. The latter assumption provides, on one hand, analytical evidence regarding what was already experimentally observed in Section 3.1 about the brittle behavior of the mortar specimen for the not-strengthened configuration; on the other hand, it explains why the fracture energy is often neglected by manufacturers and practitioners engineers. Unlike the case of unreinforced mortar, the fracture energy is one of the main parameters to be considered for fiber-reinforced mortars, as it estimates the mortar capacity of dissipating energy in the post-elastic regime, especially if long fibers are used. In fact, by comparing the two angular coefficients $B_{12}$ and $B_{24}$, depicted with red and orange dotted lines in Figure 11d and respectively equal to 2.45 and 6.75, one can notice a greater value of $B_{FL}$ for long fibers ($B_{24}>B_{12}$), implying a greater fracture energy $G_f$ of the long fibers specimens for the entire range of variation of the FC.

4.2. Tensile Behavior

The regression analysis related to the tensile behavior is performed on the tensile strength $f_t$. Figure 12a shows the three regression coefficients $r_{LRL}^2$, $r_{ERL}^2$, and $r_{PRL}^2$ for F12 and F24 cases. $r_{PRL}^2$ is equal to 0.996 for the short fibers mortar and equal to 0.998 for the long fibers mortar. Being $r_{PRL}^2$ the highest among the regression coefficients, it implies that the parabolic function (described by $f_t\left(FC\right)=C_{FL}F{C}^2+M_{FL}$) provides the best fitting for the experimental data (see Figure 12b). In the expression between parenthesis, $C_{FL}$ and $M_{FL}$ are regression constants peculiar to the specific fiber length. In particular, for the short fibers, the regression coefficients $C_{12}$ and $M_{12}$ are equal to 0.176 and 1.889 MPa, while for the long fibers, $C_{24}$ and $M_{24}$ are equal to 0.246 and 1.895 MPa, respectively. Hence, the equation for short fibers is $f_{t,F12}=0.176F{C}^2+1.889$ and for long fibers $f_{t,F24}=0.264F{C}^2+1.895$. As already previously noticed, the two regression coefficients $M_{12}$ and $M_{24}$ related to both fiber lengths are very similar and almost equal to the average tensile strength value $f_{t,0}$ of the unreinforced mortar samples (see Figure 8c). Based on this observation, we can assume $M_{FL}$ to be length-independent and equal to the average tensile strength for unreinforced mortar samples; that is, $f_{t,0}$ = 1.9 MPa. On the other hand, the two angular coefficients $C_{12}$ and $C_{24}$ are respectively equal to 0.176 and 0.264 MPa, and they are fiber length dependent. In fact $C_{24}>C_{12}$, implying a greater tensile strength $f_t$ of long fiber mortar samples for the entire range of variation of the FC. As already noticed for flexural strength and fracture energy, the results related to the tensile performance of the specimens strengthened with long fibers show a greater tensile strength $f_t$ for all FC.

4.3. Compressive Behavior

The regression analysis of the compressive behavior is performed on the compressive strength $f_c$ as a function of the fiber content and fiber length. Figure 12c shows the regression coefficient values $r_{LRL}^2$, $r_{ERL}^2$, and $r_{PRL}^2$ for the linear, exponential, and parabolic regressions. $r_{PRL}^2$ is the highest for both fiber lengths and equal to 0.997 and to 0.998 for the F24 and F12 case, respectively. Therefore the parabolic function, described by the generic form $f_c\left(FC\right)=D_{FL}F{C}^2+N_{FL}$, provides the best fitting curves for the assigned data. The two equations for short and long fiber length mortars, obtained by replacing the specific regression coefficients $D_{FL}$ and $N_{FL}$ in the generic quadratic function, are depicted in Figure 12d. In particular, for the short fibers the regression coefficients $D_{12}$ and $N_{12}$ are equal to 1.5 and 17.5 MPa, respectively, while for long fibers $D_{24}$ and $N_{24}$ are equal to 2.0 and 17.5 MPa, respectively. Hence, the equation for the short fiber mortar is $f_{c,F12}=1.5F{C}^2+17.5$, while the equation for the long fiber mortar is $f_{c,F24}=2.0F{C}^2+17.5$. As already noticed for the previous mechanical parameters, it is important to underline that ${\mathrm{N}}_{FL}$ is length independent, hence the two regression coefficients values ${\mathrm{N}}_{12}$ and ${\mathrm{N}}_{24}$ coincide; they are also equal to the average compressive strength value of the unreinforced mortar samples $f_{c,0}$ (depicted in Figure 8d). Moreover, by comparing the two angular coefficients $D_{12}$ and $D_{24}$, depicted by red and orange dotted lines in Figure 12d and respectively equal to 1.5 and 2.0 MPa, $D_{FL}$ results are greater for the fiber-strengthened mortar samples ($D_{24}>D_{12}$), implying a better compressive strength of long fiber mortars, although less marked respect to both the tensile and flexural behaviors.

5. Conclusions

This paper aims to characterize a sustainable material to be used for the restoration and strengthening of historical masonry structures: a lime-based mortar reinforced with randomly oriented basalt fibers. More specifically, this study investigates the effect on the mortar’s mechanical properties due to variation in the basalt fiber length (FL) and the basalt fiber content (FC).

The obtained results suggest drawing the following conclusions:

• The basalt fiber reinforced mortar shows a linear increase in its flexural strength while augmenting the content of fibers; this result is valid for both short length (SFL) and long length (LFL) basalt fibers. The flexural strength reaches an increase of 500% for SFL and 590% for LFL when compared to unreinforced prisms.
• The fracture energy linearly increases with increases in fiber content for both short and long fibers. If the fiber content is the maximum, the fracture energy enhances 600% for short fiber mortar and 1590% for long fiber mortar compared with unreinforced prisms.
• The tensile strength of the basalt prisms parabolically enhances while the content of fiber augments, and this increase is larger for high-length fibers than for low-length ones. In correspondence with the largest value of the content of fibers, the tensile strength grows 160% for SFL and 190% for LFL when compared with the unreinforced prisms.
• The basalt fiber reinforced mortar is characterized by a quadratic increase in its compressive strength while the content of fiber increases for both lengths of fiber. In correspondence with the largest value of the content of fibers, the compressive strength reaches an increase of 150% for SFL and 170% for LFL when compared with unreinforced prisms.
• The workability of the basalt-reinforced mortar is affected by both fiber length and fiber content; it always diminishes, as the content and length of fibers increases. As a consequence, considering a specific fiber content, the workability of the basalt conglomerate is always smaller for LFL prisms when compared with SFL ones.

The findings of this study are relevant in the field of civil engineering and architecture, as the newly developed mortar is suitable to be applied to large-scale retrofitting projects. The basalt fiber-enriched mortar stands as an innovative strengthening system that reduces both the costs and the application times when compared to traditional systems, as its workability is optimized to be applied to extensive surfaces.