A Quantitative-Qualitative Classification for Igneous Building Stones Based on Brazilian Tensile Strength: Application to the Stone Durability

Abstract

Building stones are among the most widely used construction materials in building. The Brazilian tensile strength (BTS) is a key indicator for evaluating the durability of building stone against deterioration processes. To date, no quantitative–qualitative classification for the BTS of building stones has been introduced in the literature. This poses a serious challenge for building engineers and architects in selecting the most durable building stone in terms of BTS. In the present study, a novel classification for igneous building stones based on BTS was proposed. In this classification, stones fall into the seven BTS classes: weak (BTS < 1.3 MPa), moderately weak (BTS 1.3–4.2 MPa), strong (BTS 4.2–10.1 MPa), very strong (BTS 10.1–19.3 MPa), and extremely strong (BTS > 19.3 MPa). The applicability of the BTS classification was confirmed using data published on the BTS values of the building stones subjected to deterioration processes. Based on data analysis, it was found that a stone classified into a BTS class with a higher strength can exhibit better quality in terms of its durability against deterioration processes. Consequently, BTS classification has significant advantages as an efficient and practical tool in selecting the most durable building stone for use in a building.

1. Introduction

Building stones are a type of construction material that meets acceptable aesthetic and technical criteria. Currently, building stones are widely used in various places of buildings. Some common applications of building stones, such as cladding, flooring, paving, stairs, and curbs, are shown in Figure 1. Depending on the climatic conditions prevailing where the stone is used in a building, environmental deterioration processes can lead to the loss of stone integrity over its service life. In this context, durability against deterioration processes is a vital technical parameter that requires special attention before a stone is selected for use in a building.

The durability of stone is a function of various factors, including the inherent characteristics of the stone, the location of the stone’s use in the building, and the climatic conditions prevailing in the geographical region [1,2,3,4]. The inherent characteristics (internal factors) are related to the nature of the stone, whereas the location of the stone’s use and climatic conditions, known as external factors, play a noticeable role in the occurrence of the type of environmental deterioration process.

Among the inherent characteristics of a stone, its strength is a critical parameter when it is subjected to stresses induced by deterioration processes such as freezing–thawing, salt crystallization, heating–cooling, or wetting–drying [5,6,7]. When the stresses caused by deterioration processes exceed the tensile strength of the stone, new pore spaces are created, and the existing pores develop. Repeated cycles of the deterioration processes may eventually cause the stone to degrade, resulting in a loss of durability in the long term [8,9].

Considering the tensile nature of stresses resulting from deterioration processes, the tensile strength of a stone will play a decisive role in its durability against the harmful effects of these processes. Therefore, evaluating the tensile strength of various stones can greatly help in choosing the most suitable materials in terms of durability for use in buildings.

According to Table 1, previous studies have used the Brazilian tensile strength (BTS) as a criterion for evaluating the durability of stone exposed to environmental deterioration processes. Altindag et al. [5] evaluated the decay function model (DFM) proposed by Mutluturk et al. [10] for integrity loss of ignimbrite subjected to the freezing–thawing process. The results showed a descending trend in BTS of ignimbrite with increasing cycles of freezing–thawing test. Ghobadi et al. [11] experimentally evaluated the variations of BTS of tuff building stones during cycles of freezing–thawing process. The results revealed the harmful effects of freezing–thawing on the BTS of the samples. The BTS of the samples decreased with an increase in the cycle number of freezing–thawing tests. The BTS of igneous building stones during various cycles of freezing–thawing tests was investigated by Jamshidi et al. [12]. Findings indicated that the BTS of the samples was adversely affected by the freezing–thawing action. Momeni et al. [13] simulated freezing–thawing under laboratory conditions to study the BTS deterioration of three different types of granitic stones including monzogranite, tonalite, and granodiorite. They concluded that BTS decreased linearly with the number of freezing–thawing cycles. The effect of heating–cooling action on the BTS of granites with different textures was studied by Zhao et al. [14]. The results of the data analysis showed a significant decrease in the BTS of the samples after heating–cooling. Qi et al. [15] investigated the deterioration effects of freezing–thawing on the durability of granite using changes in its BTS values during freezing–thawing cycles. According to their results, at the end of freezing–thawing test, the sample experienced considerable changes in its BTS due to the adverse effects of the freezing–thawing process.

Overall, the findings of previous studies have shown that the BTS of stones decreases from low to high degrees, due to the harmful effects of deterioration processes. Generally, a stone with higher BTS exhibits better durability behavior against deterioration processes [16,17,18,19]. Therefore, the BTS can be a good indicator for evaluating the durability of stone subjected to deterioration processes.

Table 1. Some previous studies on the BTS of stones subjected to deterioration processes.

Source	Stone Type	Deterioration Process Type				BTS Changes
		FT	SC	HC	WD
Fener and İnce [1]	Andesitic	×				Decreasing
Altindag et al. [5]	Ignimbrite	×				Decreasing
Torabi-Kaveh et al. [7]	Limestone	×	×	×		Decreasing
Singh et al. [20]	Sandstone				×	Decreasing
Sharma et al. [21]	Limestone				×	Decreasing
Yavuz and Topal [22]	Marble	×		×		Decreasing
Jamshidi et al. [23]	Different stone types		×			Decreasing
Ghobadi and Torabi-Kaveh [24]	Limestone	×				Decreasing
Momeni et al. [25]	Granite	×	×	×		Decreasing
Ghobadi et al. [11]	Tuff	×				Decreasing
Heidari et al. [16]	Limestone	×	×			Decreasing
Fereidooni and Khajevand [26]	Sedimentary stone types				×	Decreasing
Pu et al. [27]	Sandstone	×				Decreasing
Zalooli et al. [28]	Travertine		×			Decreasing
Quan et al. [29]	Sandstone					Decreasing
Seyed Mousavi and Rezaei [30]	Schist	×				Decreasing
Jamshidi [31]	Limestone	×	×	×	×	Decreasing

Table 1. Some previous studies on the BTS of stones subjected to deterioration processes.

Source	Stone Type	Deterioration Process Type				BTS Changes
		FT	SC	HC	WD
Fener and İnce [1]	Andesitic	×				Decreasing
Altindag et al. [5]	Ignimbrite	×				Decreasing
Torabi-Kaveh et al. [7]	Limestone	×	×	×		Decreasing
Singh et al. [20]	Sandstone				×	Decreasing
Sharma et al. [21]	Limestone				×	Decreasing
Yavuz and Topal [22]	Marble	×		×		Decreasing
Jamshidi et al. [23]	Different stone types		×			Decreasing
Ghobadi and Torabi-Kaveh [24]	Limestone	×				Decreasing
Momeni et al. [25]	Granite	×	×	×		Decreasing
Ghobadi et al. [11]	Tuff	×				Decreasing
Heidari et al. [16]	Limestone	×	×			Decreasing
Fereidooni and Khajevand [26]	Sedimentary stone types				×	Decreasing
Pu et al. [27]	Sandstone	×				Decreasing
Zalooli et al. [28]	Travertine		×			Decreasing
Quan et al. [29]	Sandstone					Decreasing
Seyed Mousavi and Rezaei [30]	Schist	×				Decreasing
Jamshidi [31]	Limestone	×	×	×	×	Decreasing

For the strength characteristics of stones, including the uniaxial compressive strength (UCS) and point load index (PLI), several classifications have been proposed by people and institutions. In all these classifications, stones were categorized into several strength classes based on their UCS and PLI values. However, there is no classification for stone BTS in the literature, and this is a critical gap in the previous studies. On the other hand, BTS is an important parameter in assessing the durability of stone, especially in situations where the stone is under tensile stresses caused by some deterioration processes, such as freezing–thawing, salt crystallization, heating–cooling, and wetting–drying. It is evident that under conditions where the stresses governing the stone are predominately tensile, the tensile strength rather than compressive strength can provide a better assessment of the durability behavior of the stone. This can be one of the main reasons why researchers in previous studies have not employed compressive strength classifications, e.g., UCS and PLI classifications, to assess the durability of stone.

The aim of the present study is to provide a quantitative–qualitative classification of igneous building stones based on their BTS so that it can be used as a suitable and practical tool for a quick evaluation of stone durability against deterioration processes under laboratory conditions.

2. Brazilian Tensile Strength

Tensile strength is one of the key parameters for evaluating the durability of the building stones subjected to physical deterioration processes such as freezing–thawing, salt crystallization, heating–cooling, and wetting–drying [7,22,28,30]. There are various methods to measure the tensile strength of stones, among which the BTS is the most common and widely used by researchers [32,33,34,35].

It can be seen from Figure 2 that to perform the BTS test, the cylindrical core specimens with a diameter of 54 mm and a thickness 27–54 mm are placed in a BTS test device [36]. Next, the load is applied on the specimen by two diametrically opposed concave loading jaws. The loading on the specimen is performed continuously at a constant stress rate until failure. At the moment of specimen failure, the load was recorded as the failure load (P_f). Finally, the BTS can determined using Equation (1):

$$\mathrm{B}\mathrm{T}\mathrm{S}={\displaystyle \frac{{2\times \mathrm{P}}_{\mathrm{f}}}{\mathsf{\pi }\times \mathrm{D}\times \mathrm{T}}}$$

(1)

where D and T are diameter and thickness of the specimen, respectively.

3. Materials and Methods

The previous studies conducted on various aspects of building stones with igneous origin were reviewed. These studies were conducted over a period of 52 years, from 1972 to 2024. Next, documents containing the UCS and BTS information were selected. The sources and some of the information regarding the data used in the present study are given in Table 2. The data cover a wide range of igneous stone types, including plutonic, subvolcanic, volcanic (flow), and pyroclastic. Table 3 shows the stone types used for the present study. According to Figure 3, a total of 699 data were collected for igneous stones with plutonic, subvolcanic, volcanic (flow), and pyroclastic origins, with contributions of 412, 35, 112, and 140 data, respectively.

Table 2. Database of the present study.

Source	Stone Type	No of Data	UCS Range (MPa)	BTS Range (MPa)
Fener and İnce [1]	Andesite	6	44.3–60.3	4.0–5.05
Ghobadi et al. [11]	Tuff	48	55.0–245.0	3.7–25.7
Zalooli et al. [28]	Granodiorite, Monzogranite	2	124.3, 145.8	11.1, 13.0
Momeni et al. [13]	Granite	3	90.7–164.0	8.7–14.7
Jamshidi [19]	Granite, Granodiorite, Monzogranite, Syenogranite	16	68.0–123.0	5.3–13.3
Schmidt [37]	Anorthosite, Basalt, Gabbro, Granite	10	89.6–374.7	8.7–28.3
Bilgin [38]	Granite	1	179.1	10.8
Clark [39]	Anorthosite, Basalt, Gabbro, Granite	10	123.2–296.8	7.3–15.4
Howarth [40]	Basalt, Granite, Syenite, Trachyte	4	137.1–234.0	8.0–15.2
Bilgin and Shahriar [41]	Andesite, Tuff	7	27.9–53.0	2.3–6.2
Bilgin et al. [42]	Tuff	1	43.4	4.0
Gupta and Rao [43]	Granite	8	2.5–132.8	0.88–16.1
Bearman [44]	Andesite, Diorite, Granite	4	128.8–274.8	10.6–18.4
Kahraman [45]	Diabase, Tuff	2	10.1, 110.9	0.90, 10.1
Tugrul and Zarif [46]	Granite	19	109.2–193.3	14.9–28.0
Ersoy et al. [47]	Andesite, Dacite, Gabbro, Granite, Syenite, Tuff	10	6.4–168.0	0.50–8.7
Ersoy and Atici [48]	Andesite, Dacite, Tuff	4	6.4–65.3	0.50–4.8
Dwivedi et al. [49]	Granite	5	112.8-133.7	8.9–10.9
Atici and Ersoy [50]	Andesite, Dacite, Diorite, Gabbro, Granite, Syenite, Tuff	12	6.0–375.0	0.50–30.3
Erguler and Ulusay [51]	Tuff	6	1.3–12.9	0.00–1.80
Yagiz [52]	Andesite, Basalt, Diabase, Gabbro, Granite, Granitoid, Syenite	17	47.0–327.0	4.2–17.8
Yilmaz et al. [53]	Granite	3	11.8–131.4	10.4–11.4
Karaca et al. [54]	Granite	2	111.8–131.4	10.4–11.4
Fener [55]	Andesite, Basalt, Granite, Ignimbrite, Tuff	6	3.9–121.8	1.3–9.5
Yarali and Kahraman [56]	Andesite, Basalt, Diabase, Granite, Granodiorite, Syenite	18	28.6–182.1	2.6–16.5
Ghobadi and Rasouli [57]	Granite, Granodiorite, Monzogranite, Tonalite	21	18.6–123.0	3.0–14.6
Kahraman et al. [58]	Andesite, Basalt, Gabbro, Granite, Granodiorite	13	77.5–202.9	7.6–14.8
Khanlari et al. [59]	Granodiorite, Monzogranite	10	12.4–135.7	0.46–11.4
Yavuz [60]	Tuff	2	6.9, 14.9	0.43, 1.4
Basu et al. [61]	Granite	20	91.5–201.7	10.5–19.8
Heidari et al. [62]	Granite, Granodiorite	10	3.8–150.1	0.46–17.6
Karakuş and Akatay [63]	Basalt	18	17.2–145.2	1.1–12.2
Khandelwal [64]	Diabase, Granite	2	89.5, 121.5	6.9, 9.0
Mikaeil et al. [65]	Granite	10	125.0–218.0	7.4–24.6
Heidari et al. [66]	Granite, Tuff	2	122.0–124.3	9.96–11.2
Majeed et al. [67]	Diabase	17	154.6–258.5	15.5–22.2
Sajid and Arif [68]	Granite	21	17.3–63.3	1.2–6.4
İnce and Fener [69]	Tuff	10	7.6–48.6	1.1–4.8
Ribeiro et al. [70]	Andesite, Diabase, Granite, Granodiorite, Monzogranite	8	103.7–223.0	8.9–18.8
Ronmar [71]	Basalt, Tuff	2	212.0, 87.6	14.2, 8.3
Akinbinu [72]	Anorthosite, Granite, Norite, Troctolite	12	129.6–276.3	9.2–16.9
Almasi et al. [73]	Andesite, Diorite, Gabbro, Granite, Syenite	11	91.0–193.0	6.3–15.0
Altindag and Guney [74]	Andesite, Anorthosite, Basalt, Dacite, Diabase, Diorite, Gabbro, Granite, Tuff	39	5.7–375.2	0.20–30.3
Bozdağ and İnce [75]	Andesite, Basalt, Granite, Spilite, Tuff	23	7.6–144.1	1.0–11.5
Jaques et al. [76]	Syenogranite	5	1.2–160.6	0.19–9.7
Teymen and Mengüç [77]	Andesite, Aplite, Basalt, Dacite, Diabase, Dunite, Gabbro, Granite, Granodiorite, Ignimbrite, Rhyolite, Spilite, Syenite, Trachyte, Tuff	52	6.6–330.7	1.1–21.3
Xue et al. [78]	Granite	7	104.0–137.0	4.4–6.4
Akbay and Altindag [79]	Andesite, Diabase, Granite	3	102.4–154.0	10.0–11.6
Hamzaban et al. [80]	Andesite, Basalt, Granite	8	33.8–80.0	2.8–7.5
Wei et al. [81]	Granite	5	88.1–128.7	2.4–5.6
Fereidooni [82]	Diorite, Gabbro, Granite, Granitoid, Monzogranite, Monzonite, Syenite, Tonalite	16	69.7–129.5	2.3–4.3
Pötzl et al. [83]	Tuff	21	4.0–73.7	0.60–6.7
Ajalloeian et al. [84]	Granite, Granodiorite, Monzogranite, Syenogranite	10	67.9–112.3	5.2–12.1
Diamantis et al. [85]	Peridotite	70	52.3–241.6	9.7–24.9
Kahraman et al. [86]	Andesite, Basalt, Diabase, Granite, Granodiorite, Syenite, Tuff	27	3.6–204.9	0.40–13.5

Table 2. Database of the present study.

Source	Stone Type	No of Data	UCS Range (MPa)	BTS Range (MPa)
Fener and İnce [1]	Andesite	6	44.3–60.3	4.0–5.05
Ghobadi et al. [11]	Tuff	48	55.0–245.0	3.7–25.7
Zalooli et al. [28]	Granodiorite, Monzogranite	2	124.3, 145.8	11.1, 13.0
Momeni et al. [13]	Granite	3	90.7–164.0	8.7–14.7
Jamshidi [19]	Granite, Granodiorite, Monzogranite, Syenogranite	16	68.0–123.0	5.3–13.3
Schmidt [37]	Anorthosite, Basalt, Gabbro, Granite	10	89.6–374.7	8.7–28.3
Bilgin [38]	Granite	1	179.1	10.8
Clark [39]	Anorthosite, Basalt, Gabbro, Granite	10	123.2–296.8	7.3–15.4
Howarth [40]	Basalt, Granite, Syenite, Trachyte	4	137.1–234.0	8.0–15.2
Bilgin and Shahriar [41]	Andesite, Tuff	7	27.9–53.0	2.3–6.2
Bilgin et al. [42]	Tuff	1	43.4	4.0
Gupta and Rao [43]	Granite	8	2.5–132.8	0.88–16.1
Bearman [44]	Andesite, Diorite, Granite	4	128.8–274.8	10.6–18.4
Kahraman [45]	Diabase, Tuff	2	10.1, 110.9	0.90, 10.1
Tugrul and Zarif [46]	Granite	19	109.2–193.3	14.9–28.0
Ersoy et al. [47]	Andesite, Dacite, Gabbro, Granite, Syenite, Tuff	10	6.4–168.0	0.50–8.7
Ersoy and Atici [48]	Andesite, Dacite, Tuff	4	6.4–65.3	0.50–4.8
Dwivedi et al. [49]	Granite	5	112.8-133.7	8.9–10.9
Atici and Ersoy [50]	Andesite, Dacite, Diorite, Gabbro, Granite, Syenite, Tuff	12	6.0–375.0	0.50–30.3
Erguler and Ulusay [51]	Tuff	6	1.3–12.9	0.00–1.80
Yagiz [52]	Andesite, Basalt, Diabase, Gabbro, Granite, Granitoid, Syenite	17	47.0–327.0	4.2–17.8
Yilmaz et al. [53]	Granite	3	11.8–131.4	10.4–11.4
Karaca et al. [54]	Granite	2	111.8–131.4	10.4–11.4
Fener [55]	Andesite, Basalt, Granite, Ignimbrite, Tuff	6	3.9–121.8	1.3–9.5
Yarali and Kahraman [56]	Andesite, Basalt, Diabase, Granite, Granodiorite, Syenite	18	28.6–182.1	2.6–16.5
Ghobadi and Rasouli [57]	Granite, Granodiorite, Monzogranite, Tonalite	21	18.6–123.0	3.0–14.6
Kahraman et al. [58]	Andesite, Basalt, Gabbro, Granite, Granodiorite	13	77.5–202.9	7.6–14.8
Khanlari et al. [59]	Granodiorite, Monzogranite	10	12.4–135.7	0.46–11.4
Yavuz [60]	Tuff	2	6.9, 14.9	0.43, 1.4
Basu et al. [61]	Granite	20	91.5–201.7	10.5–19.8
Heidari et al. [62]	Granite, Granodiorite	10	3.8–150.1	0.46–17.6
Karakuş and Akatay [63]	Basalt	18	17.2–145.2	1.1–12.2
Khandelwal [64]	Diabase, Granite	2	89.5, 121.5	6.9, 9.0
Mikaeil et al. [65]	Granite	10	125.0–218.0	7.4–24.6
Heidari et al. [66]	Granite, Tuff	2	122.0–124.3	9.96–11.2
Majeed et al. [67]	Diabase	17	154.6–258.5	15.5–22.2
Sajid and Arif [68]	Granite	21	17.3–63.3	1.2–6.4
İnce and Fener [69]	Tuff	10	7.6–48.6	1.1–4.8
Ribeiro et al. [70]	Andesite, Diabase, Granite, Granodiorite, Monzogranite	8	103.7–223.0	8.9–18.8
Ronmar [71]	Basalt, Tuff	2	212.0, 87.6	14.2, 8.3
Akinbinu [72]	Anorthosite, Granite, Norite, Troctolite	12	129.6–276.3	9.2–16.9
Almasi et al. [73]	Andesite, Diorite, Gabbro, Granite, Syenite	11	91.0–193.0	6.3–15.0
Altindag and Guney [74]	Andesite, Anorthosite, Basalt, Dacite, Diabase, Diorite, Gabbro, Granite, Tuff	39	5.7–375.2	0.20–30.3
Bozdağ and İnce [75]	Andesite, Basalt, Granite, Spilite, Tuff	23	7.6–144.1	1.0–11.5
Jaques et al. [76]	Syenogranite	5	1.2–160.6	0.19–9.7
Teymen and Mengüç [77]	Andesite, Aplite, Basalt, Dacite, Diabase, Dunite, Gabbro, Granite, Granodiorite, Ignimbrite, Rhyolite, Spilite, Syenite, Trachyte, Tuff	52	6.6–330.7	1.1–21.3
Xue et al. [78]	Granite	7	104.0–137.0	4.4–6.4
Akbay and Altindag [79]	Andesite, Diabase, Granite	3	102.4–154.0	10.0–11.6
Hamzaban et al. [80]	Andesite, Basalt, Granite	8	33.8–80.0	2.8–7.5
Wei et al. [81]	Granite	5	88.1–128.7	2.4–5.6
Fereidooni [82]	Diorite, Gabbro, Granite, Granitoid, Monzogranite, Monzonite, Syenite, Tonalite	16	69.7–129.5	2.3–4.3
Pötzl et al. [83]	Tuff	21	4.0–73.7	0.60–6.7
Ajalloeian et al. [84]	Granite, Granodiorite, Monzogranite, Syenogranite	10	67.9–112.3	5.2–12.1
Diamantis et al. [85]	Peridotite	70	52.3–241.6	9.7–24.9
Kahraman et al. [86]	Andesite, Basalt, Diabase, Granite, Granodiorite, Syenite, Tuff	27	3.6–204.9	0.40–13.5

Table 3. Stone types used in the present study.

Stone Class	Stone Subclass	Stone Type
Igneous	Plutonic	Anorthosite, Aplite, Diorite, Dunite, Gabbro, Granite, Granitoid, Granodiorite, Monzogranite, Monzonite, Norite, Peridotite, Syenite, Syenogranite, Tonalite, Troctolite
	Subvolcanic	Diabase, Spilite
	Volcanic (flow)	Andesite, Basalt, Dacite, Rhyolite, Trachyte
	Pyroclastic	Ignimbrite, Tuff

Table 3. Stone types used in the present study.

Stone Class	Stone Subclass	Stone Type
Igneous	Plutonic	Anorthosite, Aplite, Diorite, Dunite, Gabbro, Granite, Granitoid, Granodiorite, Monzogranite, Monzonite, Norite, Peridotite, Syenite, Syenogranite, Tonalite, Troctolite
	Subvolcanic	Diabase, Spilite
	Volcanic (flow)	Andesite, Basalt, Dacite, Rhyolite, Trachyte
	Pyroclastic	Ignimbrite, Tuff

The UCS and BTS data for each type of stone were entered into Microsoft Excel 2019 MSO. Systematically, the data were arranged in Excel spreadsheets. A correlation equation between the UCS and BTS was developed through simple regression analysis. Based on the UCS classification of rocks suggested by the IAEG [87], and the correlation equation established between the UCS and BTS, a quantitative–qualitative classification for igneous building stones considering the BTS was developed.

4. Data Analysis and Results

4.1. Correlation Between UCS and BTS

Various types of curves, including linear (y = ax + b), power (y = ax^b), exponential (y = ae^x), and logarithmic (y = a + ln x), were fitted to the data. The degree of fitting data to a curve can be measured using the value of coefficient of correlation (r). This parameter is one of the most common and widely used statistical criteria to evaluate the accuracy of a regression equation established between two variables [58,85]. For a correlation equation, the r is between 0 and 1, in which a higher r indicates better accuracy for predicting a dependent variable by an independent variable. In the present study, the value of r was used as a comparative measure to select the most appropriate regression curve. Based on which curve had the highest r, the corresponding correlation equation was chosen as the best empirical equation between the UCS and BTS. According to the r values, a linear correlation equation was obtained between UCS and BTS. As shown in Figure 4, there is a good r value equal to 0.81 for the correlation equation between the UCS and BTS as follows:

$$\mathrm{U}\mathrm{C}\mathrm{S}=11.905\times \mathrm{B}\mathrm{T}\mathrm{S} \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\mathrm{r} = 0.81$$

(2)

The correlation equation between UCS and BTS established in the present study was compared with those that were reported in the previous studies. According to the literature, there are many correlation equations to predict UCS of various rocks using their BTS. Some of these equations are presented in Table 4. Tugrul and Zarif [46] developed a linear correlation between the UCS and BTS of igneous rocks with a good r equal to 0.96. Based on the results of Kahraman et al. [58], there is a linear relationship with an r of 0.73 between UCS and BTS for the various rock classes. In another study, Altindag and Guney [74] reported an excellent power correlation between UCS and BTS for various rock classes with an r of 0.95. Teymen and Menguc [77] proposed an excellent power equation (r = 0.95) to predict UCS various rock classes using their BTS. Chatterjee and Mukhopadhyay [88] prepared a power correlation to predict UCS using BTS (r = 0.97) for sedimentary rocks. Gokceoglu and Zorlu [89] established a linear correlation between UCS and BTS (r of 0.81) for sedimentary rocks. According to a study by Tahir et al. [90], a linear equation between UCS and BTS with a moderate r equal to 0.67 was obtained for sedimentary rocks. In another study, Yesiloglu-Gultekin et al. [91] offered a moderate linear correlation (r of 0.78) between UCS and BTS for igneous rocks. In a study by Kallu and Roghanchi [92] on igneous rocks, a power correlation with a good r of 0.89 was obtained between UCS and BTS. Mohamad et al. [93] developed a linear correlation to predict UCS from BTS with a good r equal to 0.91 for sedimentary rocks. Based on their experimental test results on metamorphic rocks, Fereidooni [94] established a linear correlation to express the relationship between UCS and BTS with an excellent r of 0.96. Aliyu et al. [95] determined the UCS and BTS of the sedimentary rocks and results showed a moderate linear correlation between these parameters (r of 0.79). For sedimentary rocks, a linear equation with a r of 0.73 between UCS and BTS was obtained by Arman [96]. Finally, Khajevand [97], using data obtained from the sedimentary rocks, established an excellent logarithmic correlation between UCS and BTS with an r of 0.97. However, in the present study, a linear correlation equation with r equal to 0.81 was obtained between the UCS and BTS of igneous rocks. In this respect, there are differences in equation type and r values of correlations developed between UCS and BTS by various researchers. These differences could be due to differences in the tested rock classes, range of physical characteristics, UCS, and BTS of the samples, mineralogical composition and textural characteristics of the samples, the specimen conditions used to test (i.e., dry or saturation), and number and dimensions of test specimens.

Table 4. Correlation equations between UCS and BTS.

Reference	Rock Class	Correlation Equation	Correlation Type	r
Tugrul and Zarif [46]	Igneous	$\mathrm{U}\mathrm{C}\mathrm{S}=(6.67\times \mathrm{B}\mathrm{T}\mathrm{S})+0.73$	Linear	0.96
Kahraman et al. [58]	Various	$\mathrm{U}\mathrm{C}\mathrm{S}=10.61\times \mathrm{B}\mathrm{T}\mathrm{S}$	Linear	0.73
Altindag and Guney [74]	Various	$\mathrm{U}\mathrm{C}\mathrm{S}=12.308\times {\mathrm{B}\mathrm{T}\mathrm{S}}^{1.0725}$	Power	0.95
Teymen and Menguc [77]	Various	$\mathrm{U}\mathrm{C}\mathrm{S}=7.73\times {\mathrm{B}\mathrm{T}\mathrm{S}}^{1.197}$	Power	0.95
Gunsallus and Kulhawy [98]	Sedimentary	$\mathrm{U}\mathrm{C}\mathrm{S}=(12.4\times \mathrm{B}\mathrm{T}\mathrm{S})-9$	Linear	0.87
Chatterjee and Mukhopadhyay [88]	Sedimentary	$\mathrm{U}\mathrm{C}\mathrm{S}=10.33\times {\mathrm{B}\mathrm{T}\mathrm{S}}^{0.89}$	Power	0.97
Gokceoglu and Zorlu [89]	Sedimentary	$\mathrm{U}\mathrm{C}\mathrm{S}=(6.8\times \mathrm{B}\mathrm{T}\mathrm{S})+13.5$	Linear	0.81
Farah [99]	Sedimentary	$\mathrm{U}\mathrm{C}\mathrm{S}=(7.86\times \mathrm{B}\mathrm{T}\mathrm{S})-447.63$	Linear	0.96
Tahir et al. [90]	Sedimentary	$\mathrm{U}\mathrm{C}\mathrm{S}=7.53\times \mathrm{B}\mathrm{T}\mathrm{S}$	Linear	0.67
Nazir et al. [100]	Sedimentary	$\mathrm{U}\mathrm{C}\mathrm{S}=9.25\times {\mathrm{B}\mathrm{T}\mathrm{S}}^{0.947}$	Power	0.95
Yesiloglu-Gultekin et al. [91]	Igneous	$\mathrm{U}\mathrm{C}\mathrm{S}=(7.22\times \mathrm{B}\mathrm{T}\mathrm{S})+40.08$	Linear	0.78
Kallu and Roghanchi [92]	Igneous	$\mathrm{U}\mathrm{C}\mathrm{S}=6.75\times {\mathrm{B}\mathrm{T}\mathrm{S}}^{1.08}$	Power	0.89
Mohamad et al. [93]	Various	$\mathrm{U}\mathrm{C}\mathrm{S}=(15.361\times \mathrm{B}\mathrm{T}\mathrm{S})-10.303$	Linear	0.91
Fereidooni [94]	Metamorphic	$\mathrm{U}\mathrm{C}\mathrm{S}=(10.03\times \mathrm{B}\mathrm{T}\mathrm{S})+55.19$	Linear	0.96
Aliyu et al. [95]	Sedimentary	$\mathrm{U}\mathrm{C}\mathrm{S}=(10.4\times \mathrm{B}\mathrm{T}\mathrm{S})+18.2$	Linear	0.79
Arman [96]	Sedimentary	$\mathrm{U}\mathrm{C}\mathrm{S}=(4.233\times \mathrm{B}\mathrm{T}\mathrm{S})+13.64$	Linear	0.73
Khajevand [97]	Sedimentary	$\mathrm{U}\mathrm{C}\mathrm{S}=(40.09\times \mathrm{l}\mathrm{n}\mathrm{B}\mathrm{T}\mathrm{S})-36.14$	Logarithmic	0.97
The present study	Igneous	$\mathrm{U}\mathrm{C}\mathrm{S}=11.905\times \mathrm{B}\mathrm{T}\mathrm{S}$	Linear	0.81

Table 4. Correlation equations between UCS and BTS.

Reference	Rock Class	Correlation Equation	Correlation Type	r
Tugrul and Zarif [46]	Igneous	$\mathrm{U}\mathrm{C}\mathrm{S}=(6.67\times \mathrm{B}\mathrm{T}\mathrm{S})+0.73$	Linear	0.96
Kahraman et al. [58]	Various	$\mathrm{U}\mathrm{C}\mathrm{S}=10.61\times \mathrm{B}\mathrm{T}\mathrm{S}$	Linear	0.73
Altindag and Guney [74]	Various	$\mathrm{U}\mathrm{C}\mathrm{S}=12.308\times {\mathrm{B}\mathrm{T}\mathrm{S}}^{1.0725}$	Power	0.95
Teymen and Menguc [77]	Various	$\mathrm{U}\mathrm{C}\mathrm{S}=7.73\times {\mathrm{B}\mathrm{T}\mathrm{S}}^{1.197}$	Power	0.95
Gunsallus and Kulhawy [98]	Sedimentary	$\mathrm{U}\mathrm{C}\mathrm{S}=(12.4\times \mathrm{B}\mathrm{T}\mathrm{S})-9$	Linear	0.87
Chatterjee and Mukhopadhyay [88]	Sedimentary	$\mathrm{U}\mathrm{C}\mathrm{S}=10.33\times {\mathrm{B}\mathrm{T}\mathrm{S}}^{0.89}$	Power	0.97
Gokceoglu and Zorlu [89]	Sedimentary	$\mathrm{U}\mathrm{C}\mathrm{S}=(6.8\times \mathrm{B}\mathrm{T}\mathrm{S})+13.5$	Linear	0.81
Farah [99]	Sedimentary	$\mathrm{U}\mathrm{C}\mathrm{S}=(7.86\times \mathrm{B}\mathrm{T}\mathrm{S})-447.63$	Linear	0.96
Tahir et al. [90]	Sedimentary	$\mathrm{U}\mathrm{C}\mathrm{S}=7.53\times \mathrm{B}\mathrm{T}\mathrm{S}$	Linear	0.67
Nazir et al. [100]	Sedimentary	$\mathrm{U}\mathrm{C}\mathrm{S}=9.25\times {\mathrm{B}\mathrm{T}\mathrm{S}}^{0.947}$	Power	0.95
Yesiloglu-Gultekin et al. [91]	Igneous	$\mathrm{U}\mathrm{C}\mathrm{S}=(7.22\times \mathrm{B}\mathrm{T}\mathrm{S})+40.08$	Linear	0.78
Kallu and Roghanchi [92]	Igneous	$\mathrm{U}\mathrm{C}\mathrm{S}=6.75\times {\mathrm{B}\mathrm{T}\mathrm{S}}^{1.08}$	Power	0.89
Mohamad et al. [93]	Various	$\mathrm{U}\mathrm{C}\mathrm{S}=(15.361\times \mathrm{B}\mathrm{T}\mathrm{S})-10.303$	Linear	0.91
Fereidooni [94]	Metamorphic	$\mathrm{U}\mathrm{C}\mathrm{S}=(10.03\times \mathrm{B}\mathrm{T}\mathrm{S})+55.19$	Linear	0.96
Aliyu et al. [95]	Sedimentary	$\mathrm{U}\mathrm{C}\mathrm{S}=(10.4\times \mathrm{B}\mathrm{T}\mathrm{S})+18.2$	Linear	0.79
Arman [96]	Sedimentary	$\mathrm{U}\mathrm{C}\mathrm{S}=(4.233\times \mathrm{B}\mathrm{T}\mathrm{S})+13.64$	Linear	0.73
Khajevand [97]	Sedimentary	$\mathrm{U}\mathrm{C}\mathrm{S}=(40.09\times \mathrm{l}\mathrm{n}\mathrm{B}\mathrm{T}\mathrm{S})-36.14$	Logarithmic	0.97
The present study	Igneous	$\mathrm{U}\mathrm{C}\mathrm{S}=11.905\times \mathrm{B}\mathrm{T}\mathrm{S}$	Linear	0.81

As two statistical indices, the variance account for (VAF) and mean absolute percentage error (MAPE) were used to assess the validity of the correlation equation between the UCS and BTS.

$$\mathrm{V}\mathrm{A}\mathrm{F}=\left[1-{\displaystyle \frac{\mathrm{v}\mathrm{a}\mathrm{r}\mathrm{}(\mathrm{y}-{\mathrm{y}}^{\prime })}{\mathrm{v}\mathrm{a}\mathrm{r}\mathrm{}\mathrm{y}}}\right]\times 100$$

(3)

$$\mathrm{M}\mathrm{A}\mathrm{P}\mathrm{E}={\displaystyle \frac{\sum _{\mathrm{i}=1}^{\mathrm{N}}\left|\mathrm{y}-{\mathrm{y}}^{\prime }\right|}{\mathrm{N}}}\times 100$$

(4)

where y and y’ are the actual and predicted values of the UCS, respectively, ȳ and ȳ’ are the mean values of the y and y’, respectively, and N is the number of the dataset.

The VAF measures the proportion of the total variance in the actual values that is accounted for by the variance in the predicted values. On the other hand, the MAPE calculates the average percentage difference between the actual and predicted values. A higher VAF, indicates better accuracy of the correlation equation in predicting the unknown parameter. In addition, a lower MAPE indicates higher predictive accuracy. Thus, a correlation equation has excellent performance in predicting the unknown parameter using the one that is known (in the present study: UCS and BTS, respectively) if VAF = 100% and MAPE = 0%. Based on Equations (3) and (4), VAF and MAPE values equal to 62.97 and 29.43%, respectively, were obtained for the correlation equation between the UCS and BTS. These values are in an acceptable level, indicating a meaningful correlation between the UCS and BTS.

4.2. Development of BTS Classification

The UCS classification suggested by the IAEG [87] was used as the base for the BTS classification of igneous stones. As shown in

Table 5. UCS–based classification of rocks suggested by IAEG [87].

Class	UCS (MPa)	UCS Description
I	<15	Weak
II	15–50	Moderately weak
III	50–120	Strong
IV	120–230	Very strong
V	230 <	Extremely strong

, rocks fall into five classes according to their UCS values, namely, weak (UCS < 15 MPa), moderately weak (UCS 15–50 MPa), strong (UCS 50–120 MPa), very strong (UCS 120–230 MPa), and extremely strong (UCS > 230 MPa). For BTS classification, the equation developed between the UCS and BTS [Equation (2)] was rearranged as follows;

$$\mathrm{B}\mathrm{T}\mathrm{S}=0.0840\times \mathrm{U}\mathrm{C}\mathrm{S}$$

(5)

In Equation (5), it is assumed that all the intrinsic characteristics, such as density, porosity, mineralogical composition, and textural parameters, of the studied igneous stone types are different. It can be seen from Equation (5) that there is a conversion factor of 0.0840 between BTS and UCS. In other words, the BTS values of the igneous stones are approximately 0.0840, on average, of the their UCS. Table 5 presents the values of the lower and upper limits of the UCS for each rock class in a UCS-based classification. These values were putted into Equation (5), and their corresponding BTS values were determined. Therefore, a BTS classification for igneous stones was developed. The BTS classification is shown in Figure 5. According to this figure, igneous stones are categorized into five classes: weak (Class I; BTS < 1.3 MPa), moderately weak (Class II; BTS 1.3–4.2 MPa), strong (Class III; BTS 4.2–10.1 MPa), very strong (Class IV; BTS 10.1–19.3 MPa), and extremely strong (Class V; BTS > 19.3 MPa).

In both the UCS- and BTS-based classifications proposed by IAEG [87] and the present study, respectively, igneous stones are classified into five strength classes. These classifications can be used for description of qualitative–quantitative assessment of the igneous stones. However, there are significant differences between the UCS and BTS classifications. In the UCS-based classification, it is essential to prepare stone specimens with standard dimensions, a diameter of 54 mm and a length-to-diameter ratio of 2.5–3.0 [36]. Compared to the specimens required for the UCS test, the BTS test is performed on smaller specimens with a diameter of 54 mm and a thickness-to-diameter ratio of 0.5–1.0, as suggested by ISRM [36]. On the other hand, performing the UCS test is more time-consuming and expensive than the BTS test. Considering the advantages of BTS from the perspectives of the specimen preparation and test performance, BTS classification can be a good alternative for UCS classification for the quantitative–qualitative assessment of stone strength.

Some deterioration processes, such as freezing–thawing, salt crystallization, heating–cooling, and wetting–drying, lead to tensile stresses in the pore space and contact boundaries between the constituent components of the stone [13,30,101]. Schematic illustration of tensile stress induced by the freezing–thawing process is shown in Figure 6. Given that the various stones have different tensile strengths, their durability against deterioration processes will differ. Assuming that all the factors affecting the durability of two stone types are the same, the stone with a higher tensile strength will exhibit better durability against tensile stresses resulting from deterioration processes. The BTS classification developed for stones has two important advantages. One is that by measuring the BTS of various stones and determining their classes according to Figure 5, the BTS can be used as an indicator to select the most suitable stone from a durability perspective. In this context, stones of classes I and V are the least durable and most durable (the lowest and the highest BTS, respectively) against deterioration processes, respectively. Second, conducting the simulation tests of the deterioration processes under laboratory conditions is time-consuming, so it takes weeks or months. In addition, in some cases, the simulation tests require many test specimens, which is costly. Therefore, the BTS-based classification introduced in the present study can be used as a practical tool for a quick evaluation of the durability of building stones against deterioration processes.

4.3. Validity and Applicability of the BTS Classification for Evaluating the Stone Durability

The intensity of the BTS changes after the deterioration process is among the most common criteria for evaluating the durability of a stone. In some previous studies, researchers have used the rate of loss (RL) to investigate the intensity of BTS changes [18,103,104]. The RL is calculated through Equation (6):

$$\mathrm{R}\mathrm{L} \left(\%\right)={\displaystyle \frac{{\mathrm{B}\mathrm{T}\mathrm{S}}_{\mathrm{I}\mathrm{n}\mathrm{i}\mathrm{t}\mathrm{i}\mathrm{a}\mathrm{l}}-{\mathrm{B}\mathrm{T}\mathrm{S}}_{\mathrm{D}\mathrm{e}\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{i}\mathrm{o}\mathrm{r}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{d}}}{{\mathrm{B}\mathrm{T}\mathrm{S}}_{\mathrm{I}\mathrm{n}\mathrm{i}\mathrm{t}\mathrm{i}\mathrm{a}\mathrm{l}}}}\times 100$$

(6)

where BTS_Initial and BTS_Deteriorated are Brazilian tensile strength of the stone sample in initial conditions (i.e., before deterioration process) and after the end of the deterioration process, respectively.

Data published in the previous studies was used for the validity and applicability of the BTS classification for evaluating the durability of stones. Given that the focus of the present study is on the building stones with igneous origin, data related to this class of stones were collected from the previous studies. Based on a literature review, the BTS data of igneous building stones exposed to deterioration processes reported by Altindag et al. [5], Jamshidi et al. [12], Momeni et al. [13], and Zhao et al. [14] were collected. The information extracted from the studies of these researchers are presented in Table 6. Using values of BTS in initial conditions and after the deterioration process, the RL of BTS for stones investigated in the previous studies were calculated using Equation (6). It can be seen from Table 6 that the range of RL values varies from 3.3 to 43.2%. The difference in RL can be attributed to difference in stone type in terms of mineralogical composition and texture, physico-mechanical characteristics of the stone (e.g., porosity, water absorption, BTS), type and cycle number of deterioration process, status of the test specimen (i.e., dry or saturation), etc.

Table 6. Data of previous studies used to validity and applicability of BTS classification in evaluating the stone durability.

Reference	Deterioration Process		Stone Type	BTS (MPa)		* RL (%)
	Type	Cycle Number		Initial Conditions	Deteriorated
Altindag et al. [5]	Freezing–thawing	55	Ignimbrite	1.25	0.71	43.2
Jamshidi et al. [12]	Freezing–thawing	30	Ignimbrite	12.9	10.9	15.5
			Granite	12.1	10.1	16.5
			Granite	14.5	13.9	4.1
			Dacite	18.4	17.8	3.3
			Tuff	11.2	8.8	21.4
Momeni et al. [13]	Freezing–thawing	300	Monzogranite	8.73	5.93	32.1
			Tonalite	11.72	8.6	26.6
			Granodiorite	14.67	12.76	13.0
Zhao et al. [14]	Heating–cooling	1	Granite	14.78	11.81	20.1
			Granite	10.56	7.21	31.7
			Granite	11.83	8.84	25.3

* Calculated using Equation (6).

Table 6. Data of previous studies used to validity and applicability of BTS classification in evaluating the stone durability.

Reference	Deterioration Process		Stone Type	BTS (MPa)		* RL (%)
	Type	Cycle Number		Initial Conditions	Deteriorated
Altindag et al. [5]	Freezing–thawing	55	Ignimbrite	1.25	0.71	43.2
Jamshidi et al. [12]	Freezing–thawing	30	Ignimbrite	12.9	10.9	15.5
			Granite	12.1	10.1	16.5
			Granite	14.5	13.9	4.1
			Dacite	18.4	17.8	3.3
			Tuff	11.2	8.8	21.4
Momeni et al. [13]	Freezing–thawing	300	Monzogranite	8.73	5.93	32.1
			Tonalite	11.72	8.6	26.6
			Granodiorite	14.67	12.76	13.0
Zhao et al. [14]	Heating–cooling	1	Granite	14.78	11.81	20.1
			Granite	10.56	7.21	31.7
			Granite	11.83	8.84	25.3

* Calculated using Equation (6).

In order to investigate the validity and applicability of the BTS classification in evaluating the durability of stones against deterioration process, data of BTS in initial conditions and RL were plotted on the scheme of BTS classification. It can be seen from Figure 7 that there is an acceptable trend between the values of the BTS in initial conditions and RL. A stone with higher BTS in initial conditions experienced a lower RL due to the adverse effects of the deterioration process. In addition, based on the BTS value in initial conditions, a stone can fall into the different BTS classes. According to Figure 7, a stone with a better BTS class showed a lower RL value after the deterioration process. In other words, a shift from BTS class I to V will result in a more durable stone against deterioration processes including freezing–thawing, salt crystallization, heating–cooling, and wetting–drying. Thus, BTS classification can be a quick and low-cost indicator for a preliminary evaluation of durability of igneous building stone before its selection for use in a building. This can lead to the selection of the most durable stone for use in a building exposed to harsh climatic conditions with the possibility of deterioration processes. As a result, the stone can be more resistant to deterioration processes during its service life in a building.

Analysis of the data of previous studies on the changes in the BTS of igneous stones during deterioration processes using the BTS classification revealed the validity and applicability of the BTS classification for evaluating the stone’s durability. However, it should be noted that the BTS classification is only applicable to stones similar to the igneous stone types analyzed in the present study (Table 3) with the UCS and BTS values in the range of 1.18–375.20 and 0.00–30.30 MPa, respectively (Table 2).

5. Conclusions

Data collection was carried out on the uniaxial compressive strength (UCS) and Brazilian tensile strength (BTS) of igneous building stones reported in previous studies. The data were analyzed to introduce a BTS-based classification of these stones. Based on data analyses, igneous stones were categorized into five strength classes: weak (Class I; BTS < 1.3 MPa), moderately weak (Class II; BTS 1.3–4.2 MPa), strong (Class III; BTS 4.2–10.1 MPa), very strong (Class IV; BTS 10.1–19.3 MPa), and extremely strong (Class V; BTS > 19.3 MPa). Since tensile strength is one of the critical technical parameters for evaluating the durability of building stones against deterioration processes (e.g., freezing–thawing, salt crystallization, heating–cooling, and wetting–drying), the BTS-based classification developed in the present study can be used as a quick and low-cost tool for the preliminary evaluation of the durability of igneous building stone before its selection as a building material. In this regard, a shift from BTS class I to V will be accompanied by an increase in the durability of the stone against deterioration processes. The validity and applicability of the BTS classification introduced in the present study were verified using the analysis of data published in previous studies on the BTS changes during deterioration processes. As a suggestion, it is essential to develop the BTS classification for other classes of building stones, including sedimentary and metamorphic, and compare the results with the findings of the present study. This could lead to a more comprehensive understanding regarding the evaluation of the various stones’ durability against the deterioration processes using BTS.