Predicting Unconﬁned Compressive Strength Decrease of Carbonate Building Materials against Frost Attack Using Nondestructive Physical Tests

: Carbonate building materials and engineering constructions are exposed to severe seasonal environmental ﬂuctuations and result in a full or partial disintegration, especially in cold regions, and employment of nondestructive methods for evaluating the durability of building materials subject to frost weathering is gaining great signiﬁcance. This research aims to obtain reliable relationships between unconﬁned compressive strength decrease and nondestructive parameters variations of limestone types under frost conditions and provide useful information regarding their durability in order to ensure the long-term viability or sustainability of these materials used for constructions against frost conditions. In this study, ﬁve important types of Chinese limestone used as construction materials were subjected to 50 frost cycles. Unconﬁned compressive strength, compressional wave velocity and spatial attenuation, and porosity were obtained at the end of every 10 cycles. As a result of progression in frost cycles, the increase and decrease rates were determined at the end of every 10 cycles, and the relationships between them were obtained to predict the loss ratios of unconﬁned compressive strength ( RD σ c ). Results indicated that at the end of 40th cycles, there was a high correlation between RD σ c and spatial attenuation loss with an R 2 of 0.8584. Furthermore, there was also a strong relationship between RD σ c and compressional wave velocity decrease after the end of 20th and 50th cycles with an R 2 of 0.9089 and 0.9025, respectively. Therefore, these relations are reliable to provide useful information for durability and viability of studied samples under frost conditions and support the use of the ultrasonic measurements. It can also be successfully used for pre-estimation of unconﬁned compressive strength loss of studied limestone types against frost weathering without any tests.


Introduction
Degradation of stones used as building and construction materials under severe environmental conditions is very important for many applications such as railroads, roads, and rock slopes, especially in cold areas [1][2][3][4][5][6][7]. Natural rocks are subject to at least one freezing-thawing cycle annually. These repeated cycles lead to rapid changes in engineering characteristics and hence limit rock durability in the course of time [8]. Rock damage in cold regions is influenced by a number of frost weathering cycles, rock types, temperatures, applied pressures, and rock parameters including mineral content, Our current research aims to predict the unconfined compressive strength loss from nondestructive physical tests of some carbonate building materials such as limestone against frost weathering. Specifically, it aims to obtain significant or reliable relationships between unconfined compressive strength decrease and nondestructive parameters variations including compressional wave velocity, spatial attenuation, and porosity of studied materials. It also, aims to provide useful information regarding their durability in order to ensure the long-term viability or sustainability of these materials used for constructions against frost weathering conditions. The remainder of this paper is organized as follows. In Section 2, materials description, and laboratory experiments setup details such as petrographic analysis, frost attack process, unconfined compression test, porosity, water absorption, and ultrasonic detection system are presented. Section 3 presents the results and discussions in addition to evaluation of the relationships between RDσc and some nondestructive properties of studied limestone samples. Finally, conclusions are drawn in Section 4.

Raw Materials
Five different types of limestone used as building and constructions materials in Hubei Province, China, were used in this study. Limestone samples were prepared in a cylindrical shape with a diameter of 50 mm and tested before and after frost attack processes. The studied limestone samples were free from any defects, including bedding planes, fractures, and weathering, in order to eliminate the effect of anisotropy on the measurement. The number of samples used for tests was 180 samples. Two series of specimens were prepared in this study; one set of these specimens was used to determine the initial physical and mechanical characteristics before frost weathering cycles, and the second set of specimens was subjected to frost cycles to determine some nondestructive engineering characteristics including ultrasonic measurements (compressional wave velocity and spatial attenuation), porosity, and unconfined compressive strength.

Petrographic Properties
The X-ray diffraction (XRD) and polarized optical microscope (POM) analysis were used to identify the mineralogical composition and the microstructure characteristics of the different limestone samples. Thin section studies indicated that the studied rocks consist mainly of calcite as major mineral component and represent more than 90%, while some of them have accessory minerals such as talc, magnesite, and quartz in their mineralogical composition. The major petrographic analysis of studied specimens is given in Table 1. As shown in this table, CK-H1 limestone samples consist mainly of calcite as main mineral constituent associated with some rare amounts of opaque minerals. Calcite mineral appears as a fine-grained texture. ZK01-H1 samples have a fine-grained texture and are composed of calcite, an essential component that represents the cement of the rock materials associated with low amounts of opaque minerals. Very fine fossils were presented in this rock. ZK01-H2 samples were coarse grained in texture and were composed mainly of calcite as their major mineral constituent with some traces of opaque and talc minerals (less than 10%). Talc mineral occurs as coarse grains outlined in a matrix of calcite. Few pores and micro-discontinuities were observed in this rock. ZK02-H1 specimens consisted of calcite as a major mineral constituent, with some accessory minerals such as talc and quartz (less than 5%). Talc and quartz are fine-to medium-grained textures. Very few microcracks were observed in this rock. Finally, limestone samples of ZK02-H2 are fine-to medium-grained texture and are composed of calcite as their main mineral constituent, which was associated with some traces of minerals including talc and magnesite. Small amounts of fine fossils were presented in these samples. Table 1. Results of X-ray diffraction (XRD) and petrographic analysis for studied samples.

Rock Type Code Mineralogical Composition Photomicrograph
Limestone.1 CK-H1 Table 1. Results of X-ray diffraction (XRD) and petrographic analysis for studied samples.

Frost Attack Process
Frost action is the atmospheric influence due to seasonal environmental conditions. For this reason, rock materials used for construction partially or completely deteriorate. When the temperature falls below the freezing point, water in the discontinuities and fractures of the rock increases stresses on the surface of these fractures and result in an increase in volume. Repeating this

Frost Attack Process
Frost action is the atmospheric influence due to seasonal environmental conditions. For this reason, rock materials used for construction partially or completely deteriorate. When the temperature falls below the freezing point, water in the discontinuities and fractures of the rock increases stresses on the surface of these fractures and result in an increase in volume. Repeating this

Frost Attack Process
Frost action is the atmospheric influence due to seasonal environmental conditions. For this reason, rock materials used for construction partially or completely deteriorate. When the temperature falls below the freezing point, water in the discontinuities and fractures of the rock increases stresses on the surface of these fractures and result in an increase in volume. Repeating this

Frost Attack Process
Frost action is the atmospheric influence due to seasonal environmental conditions. For this reason, rock materials used for construction partially or completely deteriorate. When the temperature falls below the freezing point, water in the discontinuities and fractures of the rock increases stresses on the surface of these fractures and result in an increase in volume. Repeating this

Frost Attack Process
Frost action is the atmospheric influence due to seasonal environmental conditions. For this reason, rock materials used for construction partially or completely deteriorate. When the temperature falls below the freezing point, water in the discontinuities and fractures of the rock increases stresses on the surface of these fractures and result in an increase in volume. Repeating this

Frost Attack Process
Frost action is the atmospheric influence due to seasonal environmental conditions. For this reason, rock materials used for construction partially or completely deteriorate. When the temperature falls below the freezing point, water in the discontinuities and fractures of the rock increases stresses on the surface of these fractures and result in an increase in volume. Repeating this

Frost Attack Process
Frost action is the atmospheric influence due to seasonal environmental conditions. For this reason, rock materials used for construction partially or completely deteriorate. When the temperature falls below the freezing point, water in the discontinuities and fractures of the rock increases stresses on the surface of these fractures and result in an increase in volume. Repeating this

Frost Attack Process
Frost action is the atmospheric influence due to seasonal environmental conditions. For this reason, rock materials used for construction partially or completely deteriorate. When the temperature falls below the freezing point, water in the discontinuities and fractures of the rock increases stresses on the surface of these fractures and result in an increase in volume. Repeating this

Frost Attack Process
Frost action is the atmospheric influence due to seasonal environmental conditions. For this reason, rock materials used for construction partially or completely deteriorate. When the temperature falls below the freezing point, water in the discontinuities and fractures of the rock increases stresses on the surface of these fractures and result in an increase in volume. Repeating this

Frost Attack Process
Frost action is the atmospheric influence due to seasonal environmental conditions. For this reason, rock materials used for construction partially or completely deteriorate. When the temperature falls below the freezing point, water in the discontinuities and fractures of the rock increases stresses on the surface of these fractures and result in an increase in volume. Repeating this T l Discontinuity Fossils

Frost Attack Process
Frost action is the atmospheric influence due to seasonal environmental conditions. For this reason, rock materials used for construction partially or completely deteriorate. When the temperature falls below the freezing point, water in the discontinuities and fractures of the rock increases stresses on the surface of these fractures and result in an increase in volume. Repeating this process causes degradation of materials [32,33]. An automatic freezing-thawing machine, Wuhan, China was used in this study. Frost attack cycles were carried out according to the test methods procedures outlined by DL/T 5368-2007, the Professional Standard Compilation Group of the People's Republic of China [34]. The rock samples were exposed to cycles of freezing at −20 • C and thawing at 20 • C. Samples were saturated in distilled water beforehand for 48 h and then spent 4 h in a freezing chamber, followed by 4 h in distilled water at 20 • C. This process is named one frost cycle and it was repeated to a total of 50 times. At the end of 10, 20, 30, 40, and 50 cycles, the unconfined compressive strength and some nondestructive engineering parameters (including porosity, compressional wave velocity, and spatial attenuation) were obtained.

Unconfined Compression Test
The unconfined compression strength test was performed on core specimens of 50 mm and a length of 100 cm following the requirements of ISRM outlined methods and some references [35][36][37][38][39][40]. In this study, we used a self-designed TAW-2000 microcomputer electro-hydraulic servo-controlled testing system. The maximum capacity of the system was 2000 kN with loading rate of 0.1kN/s and an accuracy of ±1%. The opposite side surfaces of the rock specimens were ground and flattened so that they were parallel to each other and perpendicular to the specimen axis. Therefore, the load could be applied uniformly. The test was carried out after every 10 cycles of frost. Thirty samples were used in this test, and their mean value and standard deviation were determined.

Porosity and Water Absorption
The porosity and water absorption were measured according to the procedures suggested by ISRM [40] after the end of every 10 frost cycles. The presence of water strongly influences rock materials properties [41]. For this purpose, the porosity and absorption of water was determined using the saturation technique.

Ultrasonic System
Ultrasonic technique was carried out according to the test methods procedures outlined by Martínez-Martínez et al. [15]. In this study, we used a non-metal ultrasonic detector system with two transducers (one was transmitter for launching the ultrasonic wave pulse, and the other was the receiver for receiving the ultrasonic wave). The transducers frequency was centered in 1000 KHz. Ultrasonic tests were carried out on cylindrical samples with a diameter of 50 mm. The faces of specimens were smoothed and flattened, and then end surfaces of the cylindrical samples were covered with grease to achieve a good coupling between the transducer face and the specimen surface in order to maximize accuracy of the travel time measurement. The compressional wave velocity (Vp) and spatial attenuation (αs) were determined from each recorded waveform. This test was performed on 30 samples (six samples for each type of rock). Compressional wave velocity is the most widely used ultrasonic property to evaluate engineering characteristics of the rock samples and it was calculated by using the transit time (µs) from the generator to a receiver at the opposite end and path length of specimen (cm). However, the spatial attenuation (αs) is more critical and sensitive ultrasound properties to detect any degradation processes in materials and it was calculated using (1): where Ae is the maximum amplitude emitted by the transmitter sensor, Amax is the maximum amplitude (in absolute values) recorded by the receptor sensor, and L is the length of the rock sample. This test was performed after the end of every 10 frost attack cycles, and the samples were dried between cycles. The mean values and standard deviation of ultrasonic measurements were obtained.

Results and Discussions
The mean values of the initial physical and mechanical properties of studied fresh limestone specimens (unweathered) are summarized in Table 2. Table 2. Average values of dry bulk density (ρ b ), water absorption (Wa), effective porosity (Pe), compressional wave velocity (Vp), spatial attenuation (αs), and unconfined compressive strength (σ c ) of fresh samples.

Rock Type
Code The unconfined compressive strength, porosity, compressional wave velocity, and spatial attenuation were obtained after the end of each 10 cycles. Thirty samples for each type of rock (Six samples for each 10 cycles), and their mean values and standard deviation are given in Tables 3-6, respectively. As can be seen, the greater the number of cycles, the greater the porosity and spatial attenuation and the lower the unconfined compressive strength and compressional wave velocity of all studied limestone samples. The relation between unconfined compressive strength (σ c ), compression wave velocity (Vp), and the number of cycles for studied samples is presented in Figures 1 and 2.   To indicate the variation in critical parameters, the change ratios of unconfined compressive strength, porosity, compressional wave velocity, and spatial attenuation were obtained. The rate of increase and decrease determines the degree of rock material breakage and it changed between 0 and 1. A rating value of 1 was assigned to rocks that were fully damaged after the end of 50 frost    To indicate the variation in critical parameters, the change ratios of unconfined compressive strength, porosity, compressional wave velocity, and spatial attenuation were obtained. The rate of increase and decrease determines the degree of rock material breakage and it changed between 0 and 1. A rating value of 1 was assigned to rocks that were fully damaged after the end of 50 frost To indicate the variation in critical parameters, the change ratios of unconfined compressive strength, porosity, compressional wave velocity, and spatial attenuation were obtained. The rate of increase and decrease determines the degree of rock material breakage and it changed between 0 and 1. A rating value of 1 was assigned to rocks that were fully damaged after the end of 50 frost cycles. The increase in ratios of an effective porosity and spatial attenuation after the end of every 10 frost cycles was determined using Formula (2) outlined by Khanlari et al. [8]: where RI is the increase ratio of a property (effective porosity, and spatial attenuation), r n is the property after the end of each 10 frost cycles, and r o is the property value of fresh specimens. The relationship between the increase ratio values of effective porosity (RIpe) and the number of frost cycles of studied samples (N) are indicated in Figure 3. As can be observed in this Figure, after 50 cycles of frost action, ZK01-H2 and ZK01-H1 limestone samples indicate the highest increase ratio in porosity (RIpe), with 1.1795 and 1.0983, respectively, in comparison with the other specimens. Limestone samples of ZK02-H1 and ZK02-H2 show slightly higher increased ratio in porosity with 0.9385 and 0.8718, respectively, whereas CK-H1 limestone samples exhibit the lowest increase ratio with 0.6923 in comparison with the other specimens. These variations are considered to be related to the mineralogical composition of these specimens, especially calcium carbonate (calcite) mineral, which exhibits a higher expansion-contraction property in the frost weathering action, and these changes lead to rock breakage or deterioration [42]. According to the degree of variation due to the frost attack process, new cracks or fractures have been observed in limestone samples (namely ZK01-H2). As shown in Figure 1, there were slightly higher changes in the ZK01-H2 specimens after the 10th to 40th cycle, while in other samples, RIpe increased with the increased number of frost cycles. cycles. The increase in ratios of an effective porosity and spatial attenuation after the end of every 10 frost cycles was determined using Formula (2) outlined by Khanlari et al. [8]: where RI is the increase ratio of a property (effective porosity, and spatial attenuation), rn is the property after the end of each 10 frost cycles, and ro is the property value of fresh specimens. The relationship between the increase ratio values of effective porosity (RIpe) and the number of frost cycles of studied samples (N) are indicated in Figure 3. As can be observed in this Figure, after 50 cycles of frost action, ZK01-H2 and ZK01-H1 limestone samples indicate the highest increase ratio in porosity (RIpe), with 1.1795 and 1.0983, respectively, in comparison with the other specimens. Limestone samples of ZK02-H1 and ZK02-H2 show slightly higher increased ratio in porosity with 0.9385 and 0.8718, respectively, whereas CK-H1 limestone samples exhibit the lowest increase ratio with 0.6923 in comparison with the other specimens. These variations are considered to be related to the mineralogical composition of these specimens, especially calcium carbonate (calcite) mineral, which exhibits a higher expansion-contraction property in the frost weathering action, and these changes lead to rock breakage or deterioration [42]. According to the degree of variation due to the frost attack process, new cracks or fractures have been observed in limestone samples (namely ZK01-H2). As shown in Figure 1, there were slightly higher changes in the ZK01-H2 specimens after the 10th to 40th cycle, while in other samples, RIpe increased with the increased number of frost cycles. On the other hand, the relationship between RIαs and number of frost cycles of specimens (N) are illustrated in Figure 4. As can be seen, after 50 cycles of frost, ZK01-H2 samples have the highest increase ratio in spatial attenuation (RIαs), with 0.0630 compared to other samples, while ZK02-H2, ZK01-H1, and ZK02-H1 samples have increased ratios of spatial attenuation with 0.0490, 0.0370, and 0.0340, respectively. Finally, CK-H1 samples have the lowest increase ratio, with 0.0270 compared to other samples. Artificial weathering tests led to internal disintegration of rock materials, which scatters the ultrasound waves and results in increase of spatial attenuation [14]. Therefore, the variation degree of these parameters depends on internal deterioration degree of the rock material [43], which determines the durability of materials. Depending on these results, it can be said that the ZK01-H2 samples have the lowest durability due to having the highest values of RIαs, while CK-H1 samples have the highest durability because RIαs has the lowest values for these samples due to frost process. As shown in Figure 4, RIαs increases with an increased number of frost weathering cycles of studied limestone samples. On the other hand, the relationship between RIαs and number of frost cycles of specimens (N) are illustrated in Figure 4. As can be seen, after 50 cycles of frost, ZK01-H2 samples have the highest increase ratio in spatial attenuation (RIαs), with 0.0630 compared to other samples, while ZK02-H2, ZK01-H1, and ZK02-H1 samples have increased ratios of spatial attenuation with 0.0490, 0.0370, and 0.0340, respectively. Finally, CK-H1 samples have the lowest increase ratio, with 0.0270 compared to other samples. Artificial weathering tests led to internal disintegration of rock materials, which scatters the ultrasound waves and results in increase of spatial attenuation [14]. Therefore, the variation degree of these parameters depends on internal deterioration degree of the rock material [43], which determines the durability of materials. Depending on these results, it can be said that the ZK01-H2 samples have the lowest durability due to having the highest values of RIαs, while CK-H1 samples have the highest durability because RIαs has the lowest values for these samples due to frost process. As shown in Figure 4, RIαs increases with an increased number of frost weathering cycles of studied limestone samples. The high absorption of water, breakage, or disintegration and the weakening and expansion of natural rocks lad to the development and formation of microfractures and cracks due to frost action, and hence, the reduction in the strength of the stones is higher. The decrease in ratios of the unconfined compressive strength and the compressional wave velocity after the end of each 10 cycles of frost were determined using Equation (3), where RD is the decrease ratio of the property (unconfined compressive strength, and compressional wave velocity), rn is the property after the end of each 10 frost cycles, and ro is the initial property of fresh sample. The relationship between the decrease ratios in unconfined compressive strength (RDσc), compressional wave velocity (RDvp) values, and the number of frost cycles of specimens (N) are given in Figures 5 and 6, respectively. It is observed that the progression of the frost cycles caused reduction in unconfined compressive strength and compressional wave velocity. According to Mokhtari and Behnia [44], there are some critical parameters affected on the rock materials strength and elasticity including rock type, mineralogical composition, porosity and water absorption capacity. As can be seen in Figure 5, after 50 cycles of frost action, ZK01-H2 specimens have the highest decrease in unconfined compressive strength value (RDσc) with 0.3903 and hence the highest deterioration because of their higher porosity and water absorption in addition the noticeable presence of talc mineral. Therefore, ZK01-H2 is the most sensitive to frost process in comparison with the other samples. Ruedrich et al. [45] indicated that the water and moisture content of natural rock materials are significant factors during frost action. Wet freezing-thawing process proceedings are considered limited because natural rock materials have to be moistened before frost action. The presence of water in the rocks is an important parameter for the damage action [46]. The high absorption of water, breakage, or disintegration and the weakening and expansion of natural rocks lad to the development and formation of microfractures and cracks due to frost action, and hence, the reduction in the strength of the stones is higher. The decrease in ratios of the unconfined compressive strength and the compressional wave velocity after the end of each 10 cycles of frost were determined using Equation (3), where RD is the decrease ratio of the property (unconfined compressive strength, and compressional wave velocity), r n is the property after the end of each 10 frost cycles, and r o is the initial property of fresh sample. The relationship between the decrease ratios in unconfined compressive strength (RDσc), compressional wave velocity (RDvp) values, and the number of frost cycles of specimens (N) are given in Figures 5 and 6, respectively. It is observed that the progression of the frost cycles caused reduction in unconfined compressive strength and compressional wave velocity. According to Mokhtari and Behnia [44], there are some critical parameters affected on the rock materials strength and elasticity including rock type, mineralogical composition, porosity and water absorption capacity. As can be seen in Figure 5, after 50 cycles of frost action, ZK01-H2 specimens have the highest decrease in unconfined compressive strength value (RDσc) with 0.3903 and hence the highest deterioration because of their higher porosity and water absorption in addition the noticeable presence of talc mineral. Therefore, ZK01-H2 is the most sensitive to frost process in comparison with the other samples. Ruedrich et al. [45] indicated that the water and moisture content of natural rock materials are significant factors during frost action. Wet freezing-thawing process proceedings are considered limited because natural rock materials have to be moistened before frost action. The presence of water in the rocks is an important parameter for the damage action [46].  On the other hand, limestone samples of CK-H1 exhibit the highest resistance to deterioration because these samples have the lowest value of RDσc with 0.0909 due to having the lowest moisture content and porosity under frost weathering action in comparison with the other samples. Erguvan [47] showed that the percentage reduction in uniaxial compressive strength must be less than 20% for rocks used as building materials. If the reduction value of these materials is more than 20%, they should not be used in cold areas. Depending on these results, most studied samples can be used in cold areas as building and construction materials except limestone samples namely ZK01-H2 should not be used in cold areas due to having high percentage reduction in unconfined compressive strength. Figure 6 presents the relationship between the decrease ratio values of compressional wave velocity (RDvp) and the number of frost cycles of specimens (N). After 50 cycles of frost, limestone samples of ZK01-H2 have the highest decrease in compressional wave velocity value (RDvp) with 0.0386, which resulted in the highest internal deterioration in comparison with the other samples while, samples of CK-H1 have the highest resistance to damage due to having the lowest RDvp value with 0.0104 compared to the other samples. The reduction in index properties of rock materials after frost cycles are found to be closely related initial index parameters including porosity, absorption of water, and mineralogical composition. Accelerated weathering processes lead to rock material breakage or degradation and result in variation in the index characteristics of the rocks [42]. According to the present results, it is observed that high porosity, water absorption, and mineralogical composition are critical characteristics for determining the strength loss of studied limestone samples against frost attack processes.  On the other hand, limestone samples of CK-H1 exhibit the highest resistance to deterioration because these samples have the lowest value of RDσc with 0.0909 due to having the lowest moisture content and porosity under frost weathering action in comparison with the other samples. Erguvan [47] showed that the percentage reduction in uniaxial compressive strength must be less than 20% for rocks used as building materials. If the reduction value of these materials is more than 20%, they should not be used in cold areas. Depending on these results, most studied samples can be used in cold areas as building and construction materials except limestone samples namely ZK01-H2 should not be used in cold areas due to having high percentage reduction in unconfined compressive strength. Figure 6 presents the relationship between the decrease ratio values of compressional wave velocity (RDvp) and the number of frost cycles of specimens (N). After 50 cycles of frost, limestone samples of ZK01-H2 have the highest decrease in compressional wave velocity value (RDvp) with 0.0386, which resulted in the highest internal deterioration in comparison with the other samples while, samples of CK-H1 have the highest resistance to damage due to having the lowest RDvp value with 0.0104 compared to the other samples. The reduction in index properties of rock materials after frost cycles are found to be closely related initial index parameters including porosity, absorption of water, and mineralogical composition. Accelerated weathering processes lead to rock material breakage or degradation and result in variation in the index characteristics of the rocks [42]. According to the present results, it is observed that high porosity, water absorption, and mineralogical composition are critical characteristics for determining the strength loss of studied limestone samples against frost attack processes. On the other hand, limestone samples of CK-H1 exhibit the highest resistance to deterioration because these samples have the lowest value of RDσc with 0.0909 due to having the lowest moisture content and porosity under frost weathering action in comparison with the other samples. Erguvan [47] showed that the percentage reduction in uniaxial compressive strength must be less than 20% for rocks used as building materials. If the reduction value of these materials is more than 20%, they should not be used in cold areas. Depending on these results, most studied samples can be used in cold areas as building and construction materials except limestone samples namely ZK01-H2 should not be used in cold areas due to having high percentage reduction in unconfined compressive strength. Figure 6 presents the relationship between the decrease ratio values of compressional wave velocity (RDvp) and the number of frost cycles of specimens (N). After 50 cycles of frost, limestone samples of ZK01-H2 have the highest decrease in compressional wave velocity value (RDvp) with 0.0386, which resulted in the highest internal deterioration in comparison with the other samples while, samples of CK-H1 have the highest resistance to damage due to having the lowest RDvp value with 0.0104 compared to the other samples. The reduction in index properties of rock materials after frost cycles are found to be closely related initial index parameters including porosity, absorption of water, and mineralogical composition. Accelerated weathering processes lead to rock material breakage or degradation and result in variation in the index characteristics of the rocks [42]. According to the present results, it is observed that high porosity, water absorption, and mineralogical composition are critical characteristics for determining the strength loss of studied limestone samples against frost attack processes.

Relationtionships Evolution between RDσc and Limestone Properties Variations
The correlation diagrams were used to investigate the relationships between decrease rate of unconfined compressive strength (RDσc) and other nondestructive physical characteristics variations of studied samples, including the increase ratio in porosity (RIpe) and spatial attenuation (RIαs) and the decrease ratio in compressional wave velocity (RDvp) realized due to frost attack cycles. Moreover, we attempt to find the higher correlation between these parameters. The dataset was analyzed using linear regression analysis and the coefficient of determination (R 2 ) was determined for each regression. Correlation coefficient was determined to assess the strength and direction of the correlations the correlation between RDσc and the other disintegration parameters.

Relationtionships Evolution between RDσc and Limestone Properties Variations
The correlation diagrams were used to investigate the relationships between decrease rate of unconfined compressive strength (RDσc) and other nondestructive physical characteristics variations of studied samples, including the increase ratio in porosity (RIpe) and spatial attenuation (RIαs) and the decrease ratio in compressional wave velocity (RDvp) realized due to frost attack cycles. Moreover, we attempt to find the higher correlation between these parameters. The dataset was analyzed using linear regression analysis and the coefficient of determination (R 2 ) was determined for each regression. Correlation coefficient was determined to assess the strength and direction of the correlations the correlation between RDσc and the other disintegration parameters. Figures 7, 8, 9, 10, and 11 present the relationships between RDσc and RIpe & RIαs at 10, 20, 30, 40, and 50 cycles, respectively, and the relationships between RDσc and RDvp are illustrated in Figures 12, 13, 14, 15, and 16.

Relationtionships Evolution between RDσc and Limestone Properties Variations
The correlation diagrams were used to investigate the relationships between decrease rate of unconfined compressive strength (RDσc) and other nondestructive physical characteristics variations of studied samples, including the increase ratio in porosity (RIpe) and spatial attenuation (RIαs) and the decrease ratio in compressional wave velocity (RDvp) realized due to frost attack cycles. Moreover, we attempt to find the higher correlation between these parameters. The dataset was analyzed using linear regression analysis and the coefficient of determination (R 2 ) was determined for each regression. Correlation coefficient was determined to assess the strength and direction of the correlations the correlation between RDσc and the other disintegration parameters. Figures 7,8,9,10, and 11 present the relationships between RDσc and RIpe & RIαs at 10, 20, 30, 40, and 50 cycles, respectively, and the relationships between RDσc and RDvp are illustrated in Figures 12, 13, 14, 15, and 16.                       As can be observed in Figures 7,8,9,10,and 11,there are no significant correlations between RDσc and RIpe. As these Figures show, the low values of their coefficients of determination (R 2 ) and hence the correlation between them is poor. As shown in these diagrams, depending on the number of cycles, a moderately correlation was observed between RDσc and RIpe after the end of the 10th and 20th cycles of frost. The moderate values of their coefficients of determination with R 2 of 0.58 and 0.61, respectively. In addition, their scatter plots show that some points are close to the regression lines and the others are far and thus the correlation between them are moderate. The progression of frost cycles caused a decrease in relationship between RDσc and RIpe. The greater the number of cycles, the lower the correlation coefficients. Figures 10 and 11 indicate that there is a strong correlation between RDσc and RIαs with large values of R 2 of 0.8584 and 0.8344, respectively, after the end of 40th and 50th frost cycles, and their scatter plots indicate that the stronger the relationship, the closer the data points fall to the regression lines also, which corresponds to the best fitting linear relationship for obtaining the decrease of unconfined compressive strength. It is observed that the progression of frost cycles led to increase in relationship between RDσc and RIαs. These higher relationships indicate that the increase ratio of spatial attenuation (RIαs) is a more sensitive ultrasound parameter for detecting any degradation processes and formation of new microcracks in materials during frost processes (depending on the number of frost cycles). Therefore, the highest relationship between RDσc and RIαs can be used for pre-estimation of unconfined compressive strength loss (RDσc) for studied limestone types.
As can be seen in Figures 12, 13, 14, 15, and 16, the further the progression of frost cycles, the higher the relationship between RDσc and RDvp. Figures 13 and 16 indicate that there is a strong  As can be observed in Figures 7,8,9,10,and 11,there are no significant correlations between RDσc and RIpe. As these Figures show, the low values of their coefficients of determination (R 2 ) and hence the correlation between them is poor. As shown in these diagrams, depending on the number of cycles, a moderately correlation was observed between RDσc and RIpe after the end of the 10th and 20th cycles of frost. The moderate values of their coefficients of determination with R 2 of 0.58 and 0.61, respectively. In addition, their scatter plots show that some points are close to the regression lines and the others are far and thus the correlation between them are moderate. The progression of frost cycles caused a decrease in relationship between RDσc and RIpe. The greater the number of cycles, the lower the correlation coefficients. Figures 10 and 11 indicate that there is a strong correlation between RDσc and RIαs with large values of R 2 of 0.8584 and 0.8344, respectively, after the end of 40th and 50th frost cycles, and their scatter plots indicate that the stronger the relationship, the closer the data points fall to the regression lines also, which corresponds to the best fitting linear relationship for obtaining the decrease of unconfined compressive strength. It is observed that the progression of frost cycles led to increase in relationship between RDσc and RIαs. These higher relationships indicate that the increase ratio of spatial attenuation (RIαs) is a more sensitive ultrasound parameter for detecting any degradation processes and formation of new microcracks in materials during frost processes (depending on the number of frost cycles). Therefore, the highest relationship between RDσc and RIαs can be used for pre-estimation of unconfined compressive strength loss (RDσc) for studied limestone types.
As can be seen in Figures 12, 13, 14, 15, and 16, the further the progression of frost cycles, the higher the relationship between RDσc and RDvp. Figures 13 and 16 indicate that there is a strong As can be observed in Figures 7-11, there are no significant correlations between RDσc and RIpe. As these Figures show, the low values of their coefficients of determination (R 2 ) and hence the correlation between them is poor. As shown in these diagrams, depending on the number of cycles, a moderately correlation was observed between RDσc and RIpe after the end of the 10th and 20th cycles of frost. The moderate values of their coefficients of determination with R 2 of 0.58 and 0.61, respectively. In addition, their scatter plots show that some points are close to the regression lines and the others are far and thus the correlation between them are moderate. The progression of frost cycles caused a decrease in relationship between RDσc and RIpe. The greater the number of cycles, the lower the correlation coefficients. Figures 10 and 11 indicate that there is a strong correlation between RDσc and RIαs with large values of R 2 of 0.8584 and 0.8344, respectively, after the end of 40th and 50th frost cycles, and their scatter plots indicate that the stronger the relationship, the closer the data points fall to the regression lines also, which corresponds to the best fitting linear relationship for obtaining the decrease of unconfined compressive strength. It is observed that the progression of frost cycles led to increase in relationship between RDσc and RIαs. These higher relationships indicate that the increase ratio of spatial attenuation (RIαs) is a more sensitive ultrasound parameter for detecting any degradation processes and formation of new microcracks in materials during frost processes (depending on the number of frost cycles). Therefore, the highest relationship between RDσc and RIαs can be used for pre-estimation of unconfined compressive strength loss (RDσc) for studied limestone types.
As can be seen in Figures 12-16, the further the progression of frost cycles, the higher the relationship between RDσc and RDvp. Figures 13 and 16 indicate that there is a strong correlation between RDσc and RDvp with R 2 of 0.9089 and 0.9025, respectively, at the end of 20th and 50th frost cycles. Consequently, these relations are a strong indicator for pre-determining the unconfined compression strength loss of studied samples.
These correlations also represent a positive and linear relationship. According to the number of cycles, it can be observed that the increase rate of spatial attenuation (RIαs) and the decrease rate of compressional wave velocity (RDvp) are very sensitive for analyzing the fabric deterioration of limestone samples against frost weathering processes.
Therefore, the ultrasonic detection system is a powerful technique for investigating the durability of studied samples during frost attack processes. Overall, it is concluded that the RIαs factor related to spatial attenuation obtained at the end of 40th frost attack cycles can be used to estimate the unconfined compressive strength (RDσc) reduction. Moreover, RDvp parameter related to compressional wave velocity decrease determined at the end of 20th and 50th cycles of frost can be used for pre-estimation of unconfined compressive strength decrease of selected studied samples without tests. These relations may be useful at the preliminary stage of design but should be used with caution and only for the selected samples. The results also support the use of nondestructive tests and provide valuable data when choosing limestone samples.

Conclusions
The employment of nondestructive methods to determine the mechanical strength and durability of carbonate building and construction materials under frost conditions is gaining great significance. For this purpose, the present study aimed to determine the relationships between unconfined compressive strength decrease and some nondestructive physical parameters variations including the increase ratios of porosity and spatial attenuation and the decrease ratios of compressional wave velocity of some limestone types used as building and construction materials and subjected to 50 frost attack cycles. This provided useful information for the assessment of their long-term durability in order to ensure the long-term viability or sustainability of these materials used for constructions under frost action.
The main conclusions drawn from the present study can be summarized as follow: (1) Most of studied limestone samples can be used as building and construction materials for different outdoor applications in severe cold areas, except ZK01-H2.
(2) The high porosity, water absorption capacity, and presence of some accessory minerals such as talc are critical parameters for determining the strength losses of samples from nondestructive physical parameter changes against frost attack processes.
(3) There is a high linear relationship between RDσc and RIαs at 40th frost cycles with R 2 of 0.8584. Moreover, there is also a strong linear correlation between RDσc and RDvp at the end of 20th and 50th frost cycles with R 2 of 0.9089 and 0.9025. Consequently, the ultrasound measurements including compressional wave velocity decrease and spatial attenuation increase factors can be successfully used to pre-determine the unconfined compression strength loss of only the studied limestone types against frost conditions without testing. It also may be useful at the preliminary stage of design but should be used with caution and only for limestone types in many engineering applications in cold regions.
This study also creates a paradigm for future studies for pre-estimation of unconfined compressive strength loss of studied limestone used as building materials subject to frost weathering. However, to evaluate the relations between materials characteristics clearly, future studies need to use different conditions and construction materials in order to obtain more important results.