Study of Bonding between Façade Stones and Substrates with and without Anchorage Using Shear-Splitting Test—Case Study: Travertine, Granite, and Marble

Abstract

This paper presents an investigation into the bond strength of three common façade stones, namely, travertine, granite, and marble, to a concrete substrate using a shear-splitting test. The effects of anchorage, the number of curing days, and the presence of an anti-freezing agent in cement–sand mortar on bond strength were studied. The results show that the number of curing days had a significant impact on the bond strength between the stones and the substrates. The presence of an anti-freezing agent and accelerator increased bonding during the initial days, but this effect gradually decreased. The use of anchorage had a positive effect on the bond strength, particularly with fewer curing days. Granite had the lowest bond strength when no anchorage was used due to its low permeability. Based on the findings, a novel fuzzy logic approach was proposed to predict the bond strength. This study provides valuable insights into improving the bonding of façade stones to substrates and can aid in the safe and efficient use of these materials in construction.

1. Introduction

The aesthetic appeal of building façades has always been an important consideration, in addition to their structural strength. Building façades contribute significantly to the overall visual impact of a city or building. Thus, construction practices around the world use various materials, such as paints, mortar, stones, bricks, and glass, to enhance the attractiveness of façades while also considering the availability and cost of such materials. Stones have long been popular for building façades due to their high durability, affordability, and remarkable aesthetic appeal. However, there is a potential risk associated with using stones for building façades—the possibility of stones falling off after a few years—since, naturally, as time passes, they are subjected to the degradation process. As a result, the bonding of stones to the substrate is paramount to prevent such losses. Various types of igneous, metamorphic, and sedimentary rocks are commonly used in building façades. Granite and marble are two popular sedimentary rocks. Granite, with its high silica content, is highly dense and remarkably resistant to water and impact. However, due to the expensive cost of cutting and polishing, granite is generally more costly. Marble, however, is softer than granite and less resistant to climatic changes and humidity. Another sedimentary rock commonly used in façades is travertine, which is highly porous and, thus, has a high level of water permeability.

Several studies have been conducted on the use of stones in building façades. Tvorra et al. [1] analyzed anchored natural façade stones and studied different types of anchorages applied to façade stones both under laboratory conditions and in the field. Ferreira et al. [2] discussed various maintenance methods for façade stones exposed to diverse environmental conditions. Beak et al. [3] assessed the seismic capacity of anchored stone panels on façades using direct shear and cyclic loading tests. Emidio et al. [4] developed a methodology using the Factor Method to predict the useful life of natural stones used in building façades under various environmental conditions. Pires et al. [5] conducted a study on the effects of high temperatures and thermal shock on anchored granite façades. Pescari et al. [6] used pull-off and porosity tests and morphological and mineralogical analyses, as well as thermography, on the main façade of a historical masonry building, Romanian National Opera Timisoara.

The splitting method was selected to evaluate the strength of the bond between stone and its substrate because this method has been widely used and proven effective in evaluating the strength of concrete-to-concrete bonding [7,8,9,10,11]. However, there are very few or no studies on the use of this method to measure the bond strength between façade stone and its substrate. After conducting many successful tests on old–new concrete composites to determine their bond strength using the splitting method, it was chosen to evaluate the bond between façade stones and their concrete substrates with the help of the splitting method, which is new in this area. This method involves subjecting a square cross-section test specimen to longitudinal shear loading, which causes failure on the plane crossing the axis of the load, separating the specimen into two pieces [12]. Ultimately, the bond strength is calculated by dividing the force by the cross-sectional area.

In building construction, an anchoring system is crucial for attaching stone to mortar due to stones’ relatively smooth surface and low water permeability. This is particularly important for vertically installed stones that must be anchored to prevent them from falling during earthquakes. Different anchorage systems can be applied to façade stones, including wires, bipod scoops, tripod scoops, butterfly scoops, and Z scoops.

Concrete pouring during cold weather is a significant challenge in the construction industry due to the hindrance of the hydration process caused by the freezing of water in concrete, which can disrupt the concrete’s strength gain and even cause the formation of cracks and flaws. Repeated cycles of freezing and thawing have an accumulative effect and can cause the disintegration of concrete, which can be considered a type of fatigue failure [12]. Several studies have investigated the impact of freezing–thawing cycles and the use of admixtures to enhance concrete performance in freezing temperatures [13,14,15,16,17]. The use of anti-freezing agents is a common approach to prevent the freezing of mortar used as an adhesive in cold weather conditions, allowing for a proper stone–substrate bond. Anti-freezing agents speed up the hydration process, which increases the concrete temperature during and after the pouring process and accelerates the hardening process. However, anti-freezing agents reduce water’s freezing point, distinguishing them from admixtures that accelerate the setting time.

In recent decades, numerous studies have applied fuzzy logic systems [18,19,20,21,22,23,24] to predict different properties of concrete. For instance, Silva et al. [25] combined fuzzy logic and genetic algorithms to predict concrete shrinkage. Arslan et al. [26] used a rule-based Mamdani-type fuzzy logic model to predict the bond behavior of lightweight concrete. Najjar et al. [27] predicted the engineering properties of pre-placed aggregate concrete using fuzzy logic systems. Using fuzzy logic systems, Rashid et al. [28] predicted the compressive strength of concrete containing green foundry sand. Beycioglu et al. [29] developed a rule-based Mamdani-type fuzzy logic model to predict the mechanical properties of blended cement at elevated temperatures. Naderi et al. [21] used fuzzy logic to predict the bond strength between self-compacting mortar and concrete and normal vibrated concrete.

However, there is a lack of technical literature on the bonding of façade stone to its substrate and on the factors that affect this bond. Therefore, this research focuses on the bonding of three commonly used façade stones worldwide, namely, travertine, granite, and marble, to a concrete substrate using the splitting method. Three critical factors, including the number of curing days, the use of anti-freezing agents in cement–sand mortar, and the use of anchorage, are considered in this study. Moreover, a Z scoop was used as a common anchorage. As anti-freezing agents are prevalent in the preparation of mortar used for attaching stones to their substrate, this research aimed to evaluate their impact on the bond strength between the stone and substrate. Based on the test results and a fuzzy system with a generalized Mamdani’s interference engine and Yager family of t-norms, this study also proposes a new approach to predict the bond strength between stone façades and their concrete substrates.

2. Materials and Methods

This section describes the experimental and predictive approaches used to investigate the bond strength between three different façade stones and substrates. Laboratory experiments were conducted using the shear-splitting test to determine the bond strength. Additionally, predictive models based on linear regression and a proposed fuzzy system were employed to estimate the experimental results. The methodology used in this study is depicted in Figure 1, which includes two main steps: (1) conducting laboratory experiments to measure the bond strength and (2) using predictive methods to analyze and interpret the experimental data.

2.1. Laboratory Experiments

The laboratory program included cutting stones to the desired dimensions, determining the permeability and density of the stones, preparing the adhesives, constructing cubic concrete specimens with dimensions of 15 cm as substrates (without any treatment or the use of any additional agents to prepare the surface), connecting the anchorages to the stones, preparing the specimens for splitting tests, and conducting splitting tests.

The cement used in this research was Type 2 Portland cement. Its physical and chemical properties are listed in

Table 1. Physical and chemical properties of the used cement.

Physical Properties	Value of Physical Property	Chemical Compound	Amount of Chemical Compound (%)
Initial Setting Time	150 min	SiO2	21.32
Final Setting Time	205 min	Al2O3	4.81
		Fe2O3	3.83
Unit Weight	3.15 gr/cm3	CaO	62.85
		MgO	1.48
Specific Surface Area	2910 cm2/gr	SO3	2.32
		Na2O	0.47
Autoclave Expansion	0.07%	K2O	0.69
		L. O. I	2.04

L. O. I: Loss of Ignition.

.

The anti-freezing agent in the cement–sand mortar had no chloride content. Additionally, it should be noted that the anti-freezing agent was only used in half of the specimens (

Table 2. Mixed proportions of the adhesive mortar.

Anti-Freezing Agent (Cement Weight Based)	Water (kg/m3)	Sand (kg/m3)	Cement (kg/m3)
1%	200	1650	400

). An anti-freezing agent is an accelerator that is used to increase the rate of hydration and then the heat of concrete to stop it from freezing in early stages.

The substrates used were cubic concrete specimens measuring 15 cm on each side. The stones used in the experiment, including travertine, granite, and marble, were cut into pieces measuring 15 × 15 × 2 cm, as depicted in Figure 2. The thickness of the adhesive layers was 3 cm.

After the stone pieces were prepared, half of them were anchored using a Z-type scoop. The direction of the scoop was perpendicular to the loading direction, as shown in Figure 3. Since generally, in practical applications, there is just one anchorage for each piece of stone, even for ones with bigger dimensions, just one scoop was used for each piece in this study. To install the Z-type scoops on each stone, a narrow groove was made at the center of the stones, and then the scoops were locked mechanically in the grooves.

The sand–cement mortar was prepared using the mix design provided in Table 2 to bond the stones to the cube specimens used as substrates. Figure 4 displays a representative sample of each stone piece after being successfully anchored to the substrate using the mortar.

Note that half of the specimens were anchored using scoops, while the other half were left without anchorage to examine the effect of the scoops on the bond strength between the stone and the substrate.

After applying the mortar to attach the stones to their substrates, the specimens were cured in water for 3, 7, and 10 days to investigate the effect of curing time on the bond strength between the stones and their substrates.

The bond strength between the stones and their substrates was evaluated using the splitting method under four different conditions:

(1)

The mortar contained an anti-freezing agent, and the stone was anchored using a scoop, with curing periods of 3, 7, and 10 days;

(2)

The mortar contained an anti-freezing agent, but no anchorage was used, with curing periods of 3, 7, and 10 days;

(3)

The mortar did not contain an anti-freezing agent, and the stone was anchored using a scoop, with curing periods of 3, 7, and 10 days;

(4)

The mortar did not contain an anti-freezing agent, and no anchorage was used, with curing periods of 3, 7, and 10 days.

A schematic and the methodology of the conducted splitting test are presented in Figure 5.

In addition, a permeability test was conducted on the stones according to ASTM C948 [30].

2.2. Background on Generalized Mamdani’s Fuzzy System

A three-step algorithm was used to design the fuzzy system. Suppose that $N$ input–output pairs $\left(x^1,y^1\right)$,$\left(x^2,y^2\right)$, …,$\left(x^N,y^N\right)$ are given, where $x^k=(x_1^k,\dots ,x_n^k)$, $\forall k\in \left\{1,\dots ,N\right\}$, i.e., ${\mathcal{X}}^{\mathcal{K}}\in U=U_{1\times }{U}_{2\times \dots \times }{U}_n\subseteq {ℛ}^n$ and ${\mathsf{\gamma }}^{\mathsf{{\rm K}}} ϵ \mathrm{V}\subseteq ℛ$. The objective is to design a fuzzy system $f\left(x\right)$ based on $M$ input–output pairs (training phase) according to the following steps:

• Step 1. Define fuzzy sets to cover the input and output spaces.

For each $U_j$ ($j=1,\dots ,n$), $M$ fuzzy sets are defined $A_j^l$ ($l=1,\dots ,M$), which are required to be completed in $U_j$. For any $x_j\in U_j$, an $A_j^l$ exists such that ${\mu }_{A_j^l}\left(x_j\right)\ne 0$. For example, by defining ${\mu }_{A_j^l}\left(x_j\right)$ as a Gaussian membership function (Equation (1)), it may be considered that ${\sigma }_j^l=\left|{\overline{x}}_j^{\left(l+1\right)}-{\overline{x}}_j^l\right|/2$ ($l=1,2,\dots ,M$):

$${\mu }_{A_j^l}\left(x_j\right)=e^{-{\left(\frac{x_j-{\overline{x}}_j^l}{{\sigma }_j^l}\right)}^2}$$

(1)

where ${\overline{x}}_j^l$ is the center of the individual fuzzy set $A_{j }^l$, and ${\sigma }_j^l>0$.

• Step 2. Create the fuzzy rule base.

In this step, the algorithm generates one rule from one input–output pair. Specifically, for each input–output pair $\left(x^l,y^l\right)=\left(x_1^l,\dots ,x_n^l,y^l\right)$, $l=1,2,\dots ,M$, the algorithm obtains a fuzzy IF–THEN rule as follows:

$$Rule \left(l\right): IF\left(x_1^l is A_1^l\right) and \left(x_2^l is A_2^l\right) and \dots and \left(x_n^l is A_n^l\right), THEN \left(y^l is B^l\right)$$

(2)

where $A_i^l$ and $B^l$ ($l=1,2,\dots ,M$) are fuzzy sets in $U_i\subseteq ℛ$ ($i=1,2,\dots ,n$), and $V\subseteq ℛ$. Moreover, $x={(x_1,x_2,\dots ,x_n)}^T\in U$ and $y\in V$ are the input and output variables of the fuzzy system, respectively, where $U=U_{1\times }{U}_{2\times \dots \times }{U}_n\subseteq {ℛ}^n$. Fuzzy implications convert a fuzzy IF–THEN rule into a fuzzy relationship in the input–output product space $U\times V$.

• Step 3. Construct the fuzzy system based on the fuzzy rule base.

The algorithm then uses Equation (3) to construct the fuzzy system based on the fuzzy rule base created in Step 2:

$$f\left(x\right)=\frac{{{\displaystyle \sum }}_{l=1}^M{\overline{y}}^l{\phi }_{j=1}^n\left({\mu }_{A_j^l}\left(x_j\right)\right)}{{{\displaystyle \sum }}_{l=1}^M{\phi }_{j=1}^n\left({\mu }_{A_j^l}\left(x_j\right)\right)}$$

(3)

where $x \in U \subseteq {ℛ}^n$ is the input to the fuzzy system, and $ℱ\left(x\right)\in V\subseteq ℛ$ is the output of the fuzzy system (desired approximator).

3. Results and Analyses

3.1. Experimental Results

The water absorption (ASTM C948 [30]) and density values of the stones are displayed in

Table 3. Water absorption and density of the used stones.

Stone Name	Density (kg/m3)	Water Absorption (%)
Travertine	2550	1.33
Granite	2886	0.23
Marble	2806	1.04

. It was found that travertine had the highest water absorption, while granite exhibited the highest density among the tested stones.

Table 4. The bond strength between the façade stones and their substrates using the splitting test (MPa).

Stone Name	Anchored Stone						Unanchored Stone
	With Anti-Freezing Agent			Without Anti-Freezing Agent			With Anti-Freezing Agent			Without Anti-Freezing Agent
	3 Days	7 Days	10 Days	3 Days	7 Days	10 Days	3 Days	7 Days	10 Days	3 Days	7 Days	10 Days
Travertine	0.79	0.96	1.38	0.53	0.73	1.13	0.31	0.50	0.80	0.21	0.36	0.62
Granite	0.73	0.89	1.33	0.48	0.69	1.03	0.26	0.41	0.65	0.15	0.27	0.43
Marble	0.62	0.88	1.23	0.41	0.61	0.83	0.27	0.42	0.68	0.19	0.31	0.52

presents the results of the splitting test conducted to assess the bond strength between the façade stones and concrete substrates. Each number is the average of three experiments. There was no rejected test since, for the all-composite specimens (concrete substrate + adhesive + stone façade), failure occurred precisely at the interface of the façade stone and the adhesive, one of the most significant positive aspects of the splitting method.

To better understand the data presented in the table and to examine the impact of different variables (the number of curing days, stone anchorage, and the presence of an anti-freezing agent), each variable is discussed in detail. The effect of curing days on the bond strength between the stone and substrate was examined by comparing the bond strength values obtained after 7 and 10 days of curing to those obtained after 3 days. The results are presented as a percentage for the conditions in Figure 6.

Based on the diagram, the bond strength of the stones anchored with a scoop and the mortar containing an anti-freezing agent (Condition a) increased by 97% after 10 days of curing compared to that after 3 days. The impact of curing days was the most significant on marble and the least on travertine. However, after 7 days of curing, granite and travertine had a similar bond strength enhancement of about 22%. In Condition b, where the stones were anchored with a scoop, but the mortar did not contain an anti-freezing agent, the impact of 7 and 10 days of curing was more significant than that with the anti-freezing agent. This could be due to the anti-freezing agent reducing the curing time and resulting in a higher primary bond strength. After 10 days of curing, the bond strength doubled compared to that after 3 days of curing. When there was no anchorage and the mortar did not contain an anti-freezing agent (Condition d), the number of curing days had the highest effect on bonding. The highest bond strength improvement was observed in travertine, increasing by about 195% after 10 days of curing compared to that after 3 days. Therefore, the highest effect of the number of curing days on bonding is when there is no scoop and an anti-freezing agent is used in the mortar.

Figure 7 illustrates the influence of the anti-freezing agent on the bond strength under two conditions, namely, when anchorage was used and when it was not, with variations in the number of curing days.

The use of an anti-freezing agent in the mortar led to an acceleration in the hydration temperature during the initial curing days. As the number of curing days increased, the effect of the anti-freezing agent on the bond strength decreased. For instance, in the case of the granite without anchorage, the bond strength increased by 73% after 3 days of curing when the mortar contained an anti-freezing agent compared to the bond strength obtained without the use of an anti-freezing agent. However, the bond strength improvement was 51% after 7 and 10 days of curing.

To better understand the impact of anchorage on bonding between the stones and their substrates, Figure 8 displays the changes in the bond strength under similar conditions.

The impact of anchorage on the bond strength was found to be significant, as evidenced by the results. For example, in the case of the anchored granite with mortar that did not contain an anti-freezing agent, a higher bond strength was observed after 3 days of curing than when no anchorage was used. Additionally, for the same granite with no anti-freezing agent in the mortar, using anchorage resulted in a bond strength that was about 140% higher after 10 days of curing than the bond strength achieved without the use of anchorage. It is worth noting that the results for marble, as seen in both diagrams, showed lower values than those for the other two stones due to its weaker performance after being anchored using the metal piece.

It was observed that granite, due to its low permeability, exhibited a higher bond strength than the other two stones. This emphasizes the significance of anchorage in achieving a stronger bond between stones and their substrates. However, it was also noted that, in many construction workshops, the curing time does not exceed three days, highlighting the importance of considering anchorage to compensate for the shorter curing period and to achieve a better bond strength.

3.2. Prediction of Experimental Results

Linear regression analysis and fuzzy system were used to develop a relationship for predicting the bond strength of each of the three façade stones based on several variables, including the number of curing days, anchorage condition, and presence or absence of an anti-freezing agent in the mortar.

3.2.1. Linear Regression

The resulting equation using linear regression is as follows:

BS = −0.885 + 0.201(AF) + 0.437(AN) + 0.057(ST) + 0.066(CD)

(4)

In this equation, “BS” represents the bond strength (in MPa), “AF” represents the use of an anti-freezing agent (1 if absent, and 2 if present), “AN” represents the use of anchorage (1 if absent, and 2 if present), “ST” represents the type of stone (1 for marble, 2 for granite, and 3 for travertine), and “CD” represents the number of curing days.

Using this equation, the bond strength can be predicted for each stone type based on the various factors considered.

Figure 9 demonstrates the accuracy of the linear regression relationship by plotting a line of best fit alongside the experimental data. The R² coefficient for this relationship was calculated to be 0.935, indicating a high precision.

3.2.2. Proposed Fuzzy System

To predict the bond strength, the fuzzy system (Equation (3)) is applied along with a generalized Mamdani’s inference engine defined by the Yager family of t-norms, as specified in Equation (5):

$$\phi \left(x,y\right)=T_Y^p\left(x,y\right)=\max \{1-{[{(1-x)}^p+{(1-y)}^p]}^{\frac{1}{p}},0\}$$

(5)

where $p>0$. Moreover, a singleton fuzzifier and an average center defuzzifier are used based on Equations (6) and (7), respectively. Gaussian membership functions are also defined for the inputs (i.e., “BS” represents the bond strength (in MPa), “F” represents the use of an anti-freezing agent (1 if absent, and 2 if present), “A” represents the use of anchorage (1 if absent, and 2 if present), “S” represents the type of stone (1 for marble, 2 for granite, and 3 for travertine), and “C” represents the number of curing days), as shown in Figure 10a–d.

$${\mu }_{A^{\prime }}\left(t\right)=\{\begin{array}{cc}1& t=x\\ 0& otherwise\end{array}$$

(6)

$$y^{*}=\frac{{{\displaystyle \sum }}_{l=1}^M{\overline{y}}^l{w}_l}{{{\displaystyle \sum }}_{l=1}^M{w}_l}$$

(7)

where $y^{*}\in U$; ${\overline{y}}^l$ is the center of $l$′s individual output fuzzy set ${\overline{B}}^l$; and $w_l$ is its height.

Figure 11a–h compare the bond strength calculated using each fuzzy method with the test results. The results in Figure 11a–h indicate that the proposed system and the Yager family of t-norms accurately predict the bond strength, with the best results being for R² = 0.98 in Figure 11a, R² = 0.98 in Figure 11b, R² = 0.98 in Figure 11c, R² = 0.98 in Figure 11d, R² = 0.96 in Figure 11e, R² = 0.95 in Figure 11f, R² = 0.91 in Figure 11g, and R² = 0.86 in Figure 11h. Figure 11a–h show that the Yager family of t-norms gives reasonable predictions of the bond strength (R² = 0.98 to 0.86).

Based on the results of this study, it is possible to conclude that the use of fuzzy systems with the generalized Mamdani’s inference engine defined by the Yager family of t-norms is a suitable approach to predict the bond strength of stone façades to their concrete substrates.

4. Conclusions

In conclusion, this research aimed to investigate the impact of the number of curing days, anchorage, and the presence of an anti-freezing agent in the mortar on the bond strength between façade stones and their substrates. The results revealed that the number of curing days and the presence of an anti-freezing agent in the mortar significantly impacted the bond strength. However, this positive effect gradually decreased over time. Anchorage had a positive impact and increased the bond strength, especially when the curing days were few. Moreover, this study found that granite had the lowest bond strength compared to the other two stones when no anchorage was used, while marble had a minor bond strength compared to the other two stones when anchorage was used. Additionally, the novel fuzzy system approach with the Yager family of t-norms predicted the bond strength (R² = 0.98) more accurately than linear regression (R² = 0.93). Accordingly, fuzzy systems can be effectively used to predict the bond strength of stone façades to their substrates, which can help engineers and contractors make informed decisions about the suitability of the type of façade that they use in structures. It is important to note that this research has limitations, including using only three types of stones and a limited number of samples. Nonetheless, these findings provide valuable insights for practitioners in the construction industry to optimize the bonding between façade stones and their substrates.