New methods for assessing brick resistance to freeze-thaw cycles

2.1. Test methods

A series of properties were tested on a total of 16 different brick types (series); 8 brick series originated from controlled production (S1R1030-1.5h; S1R1030-0.5h; S2R1060-1.5h; S2R1060-0.5h; S1S10300-1.5h; S1S1030-0.5h; S2S1060-1.5h; S2S1060-0.5h) and 8 brick series originated from uncontrolled production (S1-S8). Bricks originated from controlled production were bricks produced in local factories under controlled conditions from raw materials whose chemical and mineral composition are presented in (1414. Netinger, I.; Vračević, M.; Ranogajec, J.; Vučetić, S. (2020) Influence of pore-size distribution on the resistance of brick to freeze-thaw cycles. Materials. 13 [10], 2364. https://doi.org/10.3390/ma13102364.
). Bricks originated from uncontrolled production were bricks randomly sampled from building material depots in Croatia, Bosnia and Herzegovina, and Serbia as described in (1515. Netinger, I.; Vračević, M.; Ducman, V.; Marković, B.; Szenti, I.; Kukocz, A. (2020) Influence of the size and type of pores on brick resistance to freeze-thaw cycles. Materials. 13 [17], 3717. https://doi.org/10.3390/ma13173717.
). The dimensions of all bricks were 250/120/65 mm.

Direct brick resistance to freeze-thaw cycles, compressive strength (before and after exposure to freeze-thaw cycles), water absorption, 5 h boiling water absorption, saturation coefficient, initial water absorption, pore distribution, median pore radius, total pore content and total pore volume were tested in all the bricks. Their compressive strength ratios pre- to post-freezing and Maage’s factor were calculated.

Direct brick resistance to freeze-thaw cycles was determined according to the HRN B.D8.011 standard (1616. HRN B.D8.011:1987 Glinene opeke, blokovi i ploče - metode ispitivanja, točka 9. Provjeravanje postojanosti prema mrazu. Croatian Standards Institute. Zagreb, Croatia.
). This standard was chosen for testing brick resistance to freeze-thaw cycles because it requires a smaller number of testing samples in comparison to EN 772-22 (2), which is usually used for testing brick resistance to freeze-thaw cycles. According to this standard, the samples saturated with water were put into a climate chamber and exposed to a temperature of -20±2°C for four hours, after which they were submerged in water at between +15 and 20°C, also for four hours. This cycle was repeated 25 times and samples were checked after each cycle. A brick is considered resistant to freeze-thaw cycles if none of the samples exhibit any signs of damage after 25 freeze-thaw cycles in water. The compressive strengths were determined according to EN 772-1 (1717. EN 772-1:2011+A1:2015 Methods of test for masonry units - Part 1: Determination of compressive strength.
) on a series of each type of brick before and after freezing, and the mean values of compressive strength pre to post freezing were put into a ratio to gain a coefficient as a quantitative indicator of brick resistance to freeze-thaw cycles. The normalised compressive strength was calculated according to Table A.1 of the EN 772-1 standard (1717. EN 772-1:2011+A1:2015 Methods of test for masonry units - Part 1: Determination of compressive strength.
). Water absorption was tested according to EN 772-21 (1818. EN 772-21:2011 Methods of test for masonry units - Part 21: Determination of water absorption of clay and calcium silicate masonry units by cold water absorption.
), and the 5 h boiling water absorption was tested according to EN 772-7 (1919. EN 772-7:1998 Methods of test for masonry units - Part 7: Determination of water absorption of clay masonry damp proof course units by boiling in water.
). The saturation coefficient is defined as the ratio between water absorption and 5 h boiling water absorption. The initial water absorption was determined according to EN 772-11 (2020. EN 772-11:2011 Methods of test for masonry units -Part 11: Determination of water absorption of aggregate concrete, autoclaved aerated concrete, manufactured stone and natural stone masonry units due to capillary action and the initial rate of water absorption of clay masonry units.
). Pore distribution, median pore radius, total pore content and total pore volume were determined by Mercury Intrusion Porosimetry, and Maage’s factor was calculated according to the description in (8-108. Elert, K.; Culturone, G.; Rodríguez, C.; Pardo, E.S. (2003) Durability of bricks used in the conservation of historic buildings-influence of composition and microstructure. J. Cult. Herit. 4[2], 91-99. https://doi.org/10.1016/S1296-2074(03)00020-7.
9. Bracka, A.; Rusin, Z. (2012) Comparison of pore characteristics and water absorption in ceramics materials with frost resistance factor, Fc. Struc. Environ. 3[4], 15-19. Retrieved from http://sae.tu.kielce.pl/12/S&E_NR_12_Art_3.pdf.
10. Korenska, M.; Chobola, Z.; Sokolar R. (2006) Frequency inspection as an assessment tool for the frost resistance of fired roof tiles. Ceram. Silik. 50[3], 185-192. Retrieved from https://www.irsm.cas.cz/materialy/cs_content/2006/Korenska_CS_2006_0000.pdf.
). Pore distribution for bricks from controlled production is shown in (1414. Netinger, I.; Vračević, M.; Ranogajec, J.; Vučetić, S. (2020) Influence of pore-size distribution on the resistance of brick to freeze-thaw cycles. Materials. 13 [10], 2364. https://doi.org/10.3390/ma13102364.
) and pore distribution for bricks from uncontrolled production is shown in (1515. Netinger, I.; Vračević, M.; Ducman, V.; Marković, B.; Szenti, I.; Kukocz, A. (2020) Influence of the size and type of pores on brick resistance to freeze-thaw cycles. Materials. 13 [17], 3717. https://doi.org/10.3390/ma13173717.
). Studies (1414. Netinger, I.; Vračević, M.; Ranogajec, J.; Vučetić, S. (2020) Influence of pore-size distribution on the resistance of brick to freeze-thaw cycles. Materials. 13 [10], 2364. https://doi.org/10.3390/ma13102364.
, 1515. Netinger, I.; Vračević, M.; Ducman, V.; Marković, B.; Szenti, I.; Kukocz, A. (2020) Influence of the size and type of pores on brick resistance to freeze-thaw cycles. Materials. 13 [17], 3717. https://doi.org/10.3390/ma13173717.
) regarded pores larger than 3 µm as large pores, medium-sized pores where those ranging from 0.1 to 3 µm and small pores are smaller than 0.1 µm.

Furthermore, water absorption and desorption were measured in each brick series for a specific time. For the purpose of measuring water absorption, bricks were completely dried, after which they were submerged in water for 10, 20, 30, 40, 50, 100, 150 and 1440 minutes. After taking each brick out of the water, and before it was weighed, the superficial moisture, i.e. water film on the brick’s surface, was eliminated with a cloth. The amount of the absorbed water at the specific moment is given as a percentage for every brick. For the purpose of measuring water desorption, bricks were submerged in water for 24 hours. After 24 hours, they were taken out of the water, their surface was wiped with a dry cloth and they were weighed and put into a drying oven at 105 °C. At 0, 180, 360, 540, 720, 900, 1260, and 1440 minutes, the bricks were taken out of the drying oven, weighed, and their remaining water content percentage was calculated.

2.2. Results of brick property testing

Water absorption and desorption curves at a specific time are shown in Figure 1 for bricks from controlled production and Figure 2 for bricks from uncontrolled production. Every point of the curve is an average value of ten measuring results.

Figures 1 and 2 show that each brick has its water absorption and desorption trend at a time and that the biggest differences between brick series in the absorption curves exist for up to 30 minutes and in desorption curves for up to 540 minutes. Special attention was, therefore, given to water absorption rates at 10, 20 and 30 minutes and desorption rates at 180, 360 and 540 minutes and the following absorption [Equation 1] and desorption [Equation 2] coefficients were defined:

These coefficients were also researched as parameters that describe brick resistance to freeze-thaw cycles.

The testing results given in Section 2.1 and the absorption and desorption coefficients at a given moment are provided in Table 1 for bricks from controlled production, and in Table 2 for bricks from uncontrolled production. Direct resistance to freeze-thaw cycles was determined by observing the damages to the bricks exposed to the freeze-thaw cycles on four sets of bricks (1 set is comprised of 5 bricks), as prescribed by HRN B.D8.011. The compressive strength pre to post freezing given here is the average value of ten individual measured values. The ratio of compressive strengths pre- to post-freezing was determined by putting the average values of compressive strength pre- to post-freezing into a ratio. Water absorption; 5 h boiling water absorption; saturation coefficient; initial water absorption coefficient; water absorption coefficient at 10, 10-20 and 20-30 minutes, and water desorption at 180, 180-360 and 360-540 minutes shown in Tables 1 and 3 are mean values of the ten individual measured values. All the parameters that were determined by Mercury Intrusion Porosimetry (large, medium-sized, and small pore content, medium pore radius and total pore volume) are the result of one measurement. The durability factor was calculated according to Maage, as described in (8-108. Elert, K.; Culturone, G.; Rodríguez, C.; Pardo, E.S. (2003) Durability of bricks used in the conservation of historic buildings-influence of composition and microstructure. J. Cult. Herit. 4[2], 91-99. https://doi.org/10.1016/S1296-2074(03)00020-7.
9. Bracka, A.; Rusin, Z. (2012) Comparison of pore characteristics and water absorption in ceramics materials with frost resistance factor, Fc. Struc. Environ. 3[4], 15-19. Retrieved from http://sae.tu.kielce.pl/12/S&E_NR_12_Art_3.pdf.
10. Korenska, M.; Chobola, Z.; Sokolar R. (2006) Frequency inspection as an assessment tool for the frost resistance of fired roof tiles. Ceram. Silik. 50[3], 185-192. Retrieved from https://www.irsm.cas.cz/materialy/cs_content/2006/Korenska_CS_2006_0000.pdf.
). Proportion of pores of a given size, total porosity, median pore radius and total pore volume in the bricks as well as Maage’s factor are given in Tables 2 and 4.

2.3. Descriptive statistics

Table 5 shows the descriptive statistics for all the tested parameters. The calculation for each parameter was made based on 7 mean values for non-resistant bricks and 9 mean values for resistant bricks.

2.4 The potential of variables for discriminating freeze-thaw cycle resistant from non-resistant bricks

In the course of choosing good classifiers for determining bricks resistant to freeze-thaw cycles, the Mann-Whitney U test and ROC analysis were used (Receiver operating characteristics, cf. e.g. (2121. Fawcett, T. (2006) An introduction to ROC analysis. Pattern Recognit. Lett. 27[8], 861-874. https://doi.org/10.1016/j.patrec.2005.10.010.
)).

The Mann-Whitney U test is employed with rank-order data in a hypothesis testing situation involving a design with two independent samples. If the result of the Mann-Whitney U test is significant, it indicates there is a significant difference between the two sample medians, and it can be concluded that the samples represent populations with different median values. A more-detailed description of this method can be found in (2222. Sheskin, D.J. (2000) Handbook of parametric and nonparametric statistical procedures. Second Edition, Chapman & Hall/CRC, United States of America (2000). Retrieved from https://fmipa.umri.ac.id/wp-content/uploads/2016/03/David_J._Sheskin_David_Sheskin_Handbook_of_ParaBookFi.org_.pdf.
). ROC analysis is a useful tool for classifier evaluation. It is based on an ROC curve (receiver operating characteristic curve) which is a graph showing the performance of a classification model at all classification thresholds. This curve plots “True Positive Rate” versus “False Positive Rate”. Area under the ROC curve (AUC) measures the entire area underneath the entire ROC curve and is used as an aggregate measure of performance across all possible classification thresholds. One way of interpreting AUC is as the probability that the model ranks a random positive example more highly than a random negative example. AUC ranges in value from 0 to 1. A model whose predictions are 100% correct has an AUC of 1. A more-detailed description of this method can be found in (2121. Fawcett, T. (2006) An introduction to ROC analysis. Pattern Recognit. Lett. 27[8], 861-874. https://doi.org/10.1016/j.patrec.2005.10.010.
).

The results of the Mann-Whitney U test, which tested the existence of a difference between variable distributions in resistant and non-resistant bricks, are given in Table 6.

Since variables that have a p-value lower than 0.05 in Table 6 show the potential for classifying resistant and non-resistant bricks, the following variables can be included in the group of potentially good classifiers: median pore radius, water desorption coefficient at 180-360 minutes, compressive strength ratio pre- to post-freezing, large pore content, total pore volume, water absorption coefficient at 10-20 and 20-30 minutes, total pore content and Maage’s coefficient.

At this level, the following were observed:

As mentioned in the introductory part, American and Canadian regulations prescribe cut-off values for a set of parameters that have to be met by the brick to be regarded as resistant to freeze-thaw cycles due to harsh exposure conditions (33. Straube, J.; Schumacher, C.; Mensinga, P. (2010) CP-1013: Assessing the freeze-thaw resistance of clay brick for interior insulation retrofit project. Building Science Corporation. Retrieved from https://www.buildingscience.com/documents/reports/rr-1013-freeze-thaw-resistance-clay-brick-interior-insulation-retrofits.
) in the sense of the minimum required compressive strength, the maximum allowed water absorption, maximum 5 h boiling water absorption, and the maximum allowed saturation coefficient that the brick must meet. Three out of four parameters were not proven statistically significant in this research. Water absorption was proven as statistically significant, and the upper threshold of this parameter at which a brick can be regarded resistant to freeze-thaw cycles is 12.6%, whereas the upper threshold of this parameter is 8% according to Canadian and American regulations.

2.5. ROC analysis for potential classifiers

A ROC analysis was carried out for each variable that proved to be a potential classifier in Table 6. AUC (area under the curve, cf. e.g. (2424. Pouillot, R.; Delignette-Muller, M.L. (2010) Evaluating variability and uncertainty in microbial quantitative risk assessment using two R packages. Int. J. Food Microbiol. 142[3], 330-340. https://doi.org/10.1016/j.ijfoodmicro.2010.07.011.
)) values were calculated and are shown in Table 7. The calculations were carried out using the R software package ROCR.

According to the results shown in Table 7, the same variables proved again to be the best classifiers (a very high AUC value), water absorption, median pore radius, desorption coefficient and the compressive strength ratio pre- to post-freezing.

To enable the use of these variables for brick classification into resistant and non-resistant, it is very important to define a cut-off for each chosen classifier and estimate the risk of a wrong decision. Due to the relatively small sample size, a Monte Carlo study was carried out for this purpose. The values of the selected variable from the estimated distributions were simulated separately for the resistant and non-resistant bricks, assuming normality for each.

Two-dimensional simulations were used in the sense that the expectation and the standard deviation of normal distributions were also simulated from the distributions of the parameter estimators. The simulations and analysis of the results were carried out using the R software package mc2d (2525. Sing, T.; Sander, O.; Beerenwinkel, N.; Lengauer, T. (2005) ROCR: visualizing classifier performance in R. Bioinformatics. 21 [20], 3940-3941. https://doi.org/10.1093/bioinformatics/bti623.
).

The study showed that the median pore radius is a reliable classifier. The cut-off that separates resistant from non-resistant bricks can be set to 1.2 µm. Bricks with a median pore radius lower than 1.2 µm can be classified as non-resistant and those with a median pore radius higher than 1.2 µm as resistant. The probability of a wrong decision is lower than 1% if the median pore radius is lower than 1.2 µm, and the probability of a wrong decision is lower than 10E-6 if the median pore radius is higher than 1.2 µm.

Water desorption coefficient in 180-360 minutes is also a reliable classifier. The separation cut-off can be set to 1.019 %/min. Bricks with a water desorption coefficient in 180-360 minutes lower than 1.019 %/min can be regarded as resistant to freeze-thaw cycles and bricks with higher values of this coefficient can be regarded as non-resistant. The probability of a wrong decision is lower than 3% if the coefficient is lower than 1.019 %/min, and the probability of a wrong decision is lower than 1% if the coefficient is higher than 1.019 %/min.

Monte Carlo simulations applied to the variable of compressive strength ratio pre- to post-freezing suggest a cut-off of 0.72 for classification into resistant and non-resistant bricks. For that cut-off, the probability of a wrong decision is lower than 5% if the brick, whose value of the ratio variable is greater than or equal to 0.72, is designated as resistant to freeze-thaw cycles and the probability of a wrong decision is lower than 9% if the brick, whose value of the ratio variable is lower than 0.72, is designated as non-resistant to freeze-thaw cycles.

Even though literature sources do not explicitly state it, in practice, it is usually believed that bricks with high water absorption are not resistant to freeze-thaw cycles. This study confirmed that, and it is clear that all resistant bricks in the sample have water absorption values between 10 and 12.6%, whereas all non-resistant bricks have higher values, between 13.4 and 24.2%. However, results that could clearly define a water absorption cut-off for separating resistant from non-resistant bricks with an acceptable risk of the wrong decision were not achieved. The standard deviation of water absorption in bricks that are non-resistant to freeze-thaw cycles is high, which, under the assumption of normality of water absorption distribution, allows for low values of water absorption in non-resistant bricks with a not so low probability. Therefore, based on this sample, a reliable cut-off cannot be set for the water absorption value with the aim of classifying bricks according to their resistance to freeze-thaw cycles.

2.6. Description of reliable classifiers for assessing brick resistance to freeze-thaw cycles by the pore system

The median pore radius proved to be an excellent classifier for assessing brick resistance to freeze-thaw cycles, which is in line with Franke and Bentrup’s results (2626. Raimondo, M.; Ceroni, C.; Dondi, M.; Guarini, G.; Marsigli, M.; Venturi, I.; Zanelli, C. (2009) Durability of clay roofing tiles: the influence of microstructural and compositional variables. J. Eur. Ceram. Soc. 29 [15], 3121-3128. https://doi.org/10.1016/j.jeurceramsoc.2009.06.004.
). Franke and Bentrup report 1.65 μm as the median pore radius cut-off that separates resistant from non-resistant bricks, and bricks with a median pore radius equal to or higher than 1.65 μm are resistant to freeze-thaw cycles. However, no risk assessment for the wrong decision was made for that cut-off. Our research showed that the cut-off can be set to 1.2 μm with an extremely low risk of a wrong decision.

Since the pore system is regarded as responsible for brick resistance to freeze-thaw cycles in literature sources (5-75. Kung, J.H. (1985) Frost durability of canadian clay bricks. Proceedings of the 7th International Brick Masonry Conference, Melbourne, Australia.[1], 245-251. Retrieved from https://nrc-publications.canada.ca/eng/view/ft/?id=85a8f3ac-6e9e-43a4-aad1-51c6288e929b.
6. Hansen, W.; Kung, J.H. (1988) Pore structure and frost durability of clay bricks. Mater Struct. 21, 443-447. https://doi.org/10.1007/BF02472325.
7. Perrin, B.; Vu, N.A.; Multon, S.; Voland, T.; Ducroquetz, C. (2011) Mechanical behaviour of fired clay materials subjected to freeze-thaw cycles. Constr Build Mater. 25[2], 1056-1064. https://doi.org/10.1016/j.conbuildmat.2010.06.072.
), this section provides a description of reliable classifiers from section 2.5 by means of the pore system (large, medium-sized, and small pore content; total pore content; median pore radius; and total pore volume). As the median pore radius itself is one of the parameters in the pore system, the other two reliable classifiers from Section 2.5, the brick’s compressive strength ratio pre- to post-freezing and the water desorption coefficient in 180-360 minutes, were described using pore system as quantitative indicators of brick resistance to freezing cycles.

2.6.1. Modelling pre- to post-freezing compressive strengths ratio of the brick

 ⌅

Spearman’s rank correlation coefficient is used here as a measure of association between two variables. It is based on an analysis of two sets of ranks and determines the degree to which a monotonic relationship exists between two variables. A more-detailed description of this method can be found in (2222. Sheskin, D.J. (2000) Handbook of parametric and nonparametric statistical procedures. Second Edition, Chapman & Hall/CRC, United States of America (2000). Retrieved from https://fmipa.umri.ac.id/wp-content/uploads/2016/03/David_J._Sheskin_David_Sheskin_Handbook_of_ParaBookFi.org_.pdf.
). As the initial indicator for the existence of a monotonic relationship between compressive strength ratio pre- to post-freezing and the variables from the pore system, the value of Spearman’s rank correlation and the pertaining p-value for testing the hypothesis on the non-existence of a monotonic relationship are shown in Table 8.

Table 8.  Spearman’s rank correlation of compressive strengths ratio pre- to post-freezing and variables of the pore system.

Property	Spearman’s rank correlation	p-value
Large pore content	0.7354476	0.0011674
Medium-sized pore content	-0.3036116	0.2529648
Small pore content	-0.4369005	0.0906236
Total pore content	-0.6543863	0.0059524
Median pore radius	0.9344164	1.18E-07
Total pore volume	-0.6234356	0.0098700

It can be seen here that there is a statistically significant increasing relationship between the compressive strength ratio and large pore content as well as between the compressive strength ratio and the median pore radius. A significant decreasing relationship was proven between the compressive strength ratio and total pore content and between the compressive strength ratio and total pore volume.

In the course of choosing a model that describes the compressive strength ratio using the pore system, classical methods of regression analysis were used. The aim was to establish a model that maximizes the adjusted R², minimizes the Akaike information criterion and exhibits a stable behaviour during the bootstrap method. The R software package car (2727. Fox, J.; Weisberg, S. (2019) An R companion to applied regression. Third Edition. Sage, Thousand Oaks CA (2019).
) was used for model building, and the R software package boot (2828. Davison, A.C.; Hinkley, D.V. (1997) Bootstrap methods and their applications. Cambridge series in statistical and probabilistic mathematics. Cambridge University Press, Cambridge (1997). https://doi.org/10.1017/CBO9780511802843.
, 2929. Canty, A.; Ripley, B.D. (2019) Boot: Bootstrap R (S-plus) functions. R package version 1.3-24, (2019).
) was used for bootstrapping.

The best model achieved in the aforementioned sense is gained using the large pore content and median pore radius variables. The median pore radius does not enter the model linearly, but a piecewise linear function was used. The model coefficients are shown in Table 9.

Table 9.  Coefficients of the model for variable description by large pore content and the median pore radius.

Regressor	Estimate	Std. error	p-value of t-test
Free member	0.2970001	0.0604426	0.000461
Large pore content	0.0024181	0.0003549	2.90e-05
Median pore radius	0.3046612	0.0414089	1.43e-05
I (median radius ≤ 1.2)	0.3878672	0.0610214	5.40e-05
median pore radius* I (median radius ≤ 1.2)	-0.3199488	0.0445659	1.80e-05

This model shows that the relationship between variables and compressive strength ratio is described in different ways for bricks with a median pore size of ≤1.2 μm than for bricks with a median pore size of >1.2 μm.

Namely,

• for median pore radius ≤1.2 μm, the relationship can be described as:

  compressive strength ratio =0.6849+0.0024*large pore content-0.0153*median pore radius

• for median pore radius >1.2 µm, the relationship can be described as:

  compressive strength ratio =0.297+0.0024*large pore content+0.3047*median pore radius

Even though the assumption of normality and homoscedasticity of the residual in the achieved model is supported (the Shapiro-Wilk test yields a p-value of 0.834, the Non-Constant Variance Score Test yields a p-value of 0.831), due to the relatively small data set, a bootstrap analysis of the suggested model was carried out as well, which shows that the key conclusions are stable. Table 10 provides bootstrapped confidence intervals for the adjusted R² model and the model’s coefficients.

Table 10.  Bootstrapped confidence intervals for the adjusted R² and the coefficients of the presented model.

Coefficient	Estimate	Percentile bootstrap confidence interval
Adjusted R 2	0.9519899	0.9305, 0.9957
Intercept	0.2970001	0.1374, 0.4485
Large pore content	0.0024181	0.0001, 0.0030
Median pore radius	0.3046612	0.2084, 0.4174
I (median pore radius <= 1.2)	0.3878672	0.2279, 0.5472
Median pore radius* I (median pore radius <=1.2)	-0.3199488	-0.4453, -0.1843

Based on the obtained model, it is clear that high values of the median pore radius (higher than 1.2μm) contribute much more to the description of the variable ratio than in the case of values lower than 1.2 μm. Spearman’s rank correlation coefficient for ratio and median pore radius, on the data subset for which median pore radius ≤ 1.2 μm, do not point towards the existence of a monotonic relationship (the p-value is 0.17) in that part. The aforementioned is shown in Figure 3.

Figure 3.  The dependence of compressive strengths pre- to post-brick freezing and the median pore radius for the estimated large pore content.

If compressive strength ratio pre- to post-freezing is accepted as a quantitative indicator of brick resistance to freeze-thaw cycles, this model suggests that the median pore radius value, as long as it is lower than 1.2μm, does not significantly contribute to the resistance to freeze-thaw cycles but classifies bricks as non-resistant. As opposed to that, median pore radius values higher than 1.2 μm significantly contribute to resistance to freeze-thaw cycles. This fact is in line with the theory set forth in (55. Kung, J.H. (1985) Frost durability of canadian clay bricks. Proceedings of the 7th International Brick Masonry Conference, Melbourne, Australia.[1], 245-251. Retrieved from https://nrc-publications.canada.ca/eng/view/ft/?id=85a8f3ac-6e9e-43a4-aad1-51c6288e929b.
), according to which small pores have little influence on the brick’s resistance to freeze-thaw cycles. The model also confirms that the information on the large pore content, along with a known median pore radius value, is important for the description of brick resistance to cycles and that bricks with a higher large pore content have a better resistance to freeze-thaw cycles, which is, again, in line with the facts provided in literature sources (55. Kung, J.H. (1985) Frost durability of canadian clay bricks. Proceedings of the 7th International Brick Masonry Conference, Melbourne, Australia.[1], 245-251. Retrieved from https://nrc-publications.canada.ca/eng/view/ft/?id=85a8f3ac-6e9e-43a4-aad1-51c6288e929b.
, 77. Perrin, B.; Vu, N.A.; Multon, S.; Voland, T.; Ducroquetz, C. (2011) Mechanical behaviour of fired clay materials subjected to freeze-thaw cycles. Constr Build Mater. 25[2], 1056-1064. https://doi.org/10.1016/j.conbuildmat.2010.06.072.
).