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FILE ON HEAVY CLAY ROOFING TILE IMPERMEABILITY TEST: A MATERIAL INTRINSIC WATER PERMEABILITY MEASUREMENT By G. Laurent (2), B. Perrin (1), F. Poeydemenge(2), G. Wardeh(1). The European Committee for standardisation advocates that there should be only one testing method for any one given mandated requirements for the CE marking of a product. Yet at this time the European impermeability testing standard for clay roofing tiles (NF EN 539-1) includes two methods which characterize only one physical property, the intrinsic permeability of the material. The comparison between both methods should enable to lay the foundations of a single standard. This work is driven by the fact that the European Committee for standardization advocates that there should be only one testing method for any one given mandated requirement for the CE marking of a product. Yet at this time the European impermeability testing standard for clay roof tiles includes two methods: - the first method consists in measuring the time it takes for the first drop of water, formed on the surface of the underside of an initially dry tile, to fall down when a 6 cm head of water is applied on the top side of the tile. The test is carried out at an ambient temperature of 20°C ±2°C and 60 % ±5% relative humidity; - the second method consists in measuring the water volume that has permeated through the saturated material over a 24 hour period per cm 2 of sample surface area whilst maintaining a 10 cm head of water on the surface of the tile. The aim of the study is to demonstrate, through the use of the single method described hereunder, that there is a correlation between the two test methods and to understand the relationship that exists between the time a drop of water is formed on the underside of the clay roofing tile and the amount of water that has permeated through the saturated material over a 24 hour period when a head of water is maintained on the surface of the tile. To do this, we have numerically simulated the behaviour of a clay roofing tile of known physical properties, whilst conducting the two previously described tests, in order to determine what material properties have an influence on the time taken for a drop of water to appear and the volume of water. The results from the numerical simulation were then compared to a whole series of experimental values taken at the CTTB from testing different products. Firstly, we will introduce the project of standardization and the experimental device used, then the numerical computing, the results obtained, and the conclusions that can be drawn from it. (1) LMDC : Laboratoire matériaux et durabilité des constructions INSA-UPS Toulouse (2) CTTB : Centre technique des tuiles et briques 1/13 FILE ON HEAVY CLAY THE EUROPEAN SINGLE STANDARD TEST PROJECT Principle It involves testing the impermeability to water of a clay roofing tile or of a clay fittings by determining the time it takes, from the moment that a head of water is applied on the surface of a tile under normal weather stress conditions and the first drop of water to fall down. This single method consists in measuring the time it takes for the first drop of water, formed on the surface of the underside of an initially dry tile, to fall down when a 10 cm head of water is applied on the top side of the tile. The test is carried out at an ambient temperature of 20 °C ±2 °C and 75% ±5% relative humidity. Fig. 1 shows the device that has been implemented at the CTTB and that has allowed us to test the different products, which we will introduce later on. Figure 1 – Example of an experimental device allowing the measurement of the time taken for the formation of a water drop 2/13 FILE ON HEAVY CLAY NUMERICAL MODELLING Modelling of the first test method and of the single test method (time taken for the formation of the drop) Two phases can be observed in the drop testing experiment. The first involves the water imbibition of the clay roofing tile, which is initially dry and thus becomes progressively water saturated. It is when the underside of the roofing tile under controlled ambient conditions becomes water saturated that the second phase is initiated. The phenomenon of water percolation is a specific feature of the second phase. During this phase the flow of water vapours that escapes from the underside surface of the tile to the atmosphere and the flow of liquid that comes to the underside surface are in competition. It is all of these phenomena as a whole that condition the time that it takes for a drop of water to form. Application of the numerical model The numerical code requires: - environmental conditions, as shown in fig. 2; - material properties. We have used our database involving a body used on a previous project. First phasis Ambient conditions at controlled temperature and moisture 20°C , 75% RH Figure 2 - Ambient conditions of the basic configuration As the numerical code does not make it possible to describe the kinetics involved in producing the water drops, we have resorted to consecutively establish a model for the two phases mentioned earlier. First phase We started with a dry material, with its underside exposed to predetermined ambient conditions whilst submitting its top side under a head of water of 6 cm (see fig. 2). The numerical computing has described the capillary intrusion up to the moment when the underside becomes saturated. Beyond this point of time the code reveals a permanent state due to the equilibrium that takes place between the flow of liquid arriving at the surface of the 3/13 FILE ON HEAVY CLAY underside and the rate at which the water vapour escapes due to evaporation. The flow of liquid permeating through the material is therefore limited by the rate at which the water vapour escapes from the underside. The time T1 that results from this calculation corresponds to the diffusion phase of the material. Second phase As the time thus obtained is still less than the actual time taken for the drop of water to appear, we then measure the flow rate of liquid permeating through the saturated medium by applying a 6 cm water head to one of the surfaces (see fig. 3). We then compare this water flow and the evaporation rate from the saturated medium that corresponds to the end of the first phase. The time taken to form a drop of water corresponds to the time T 2, where the difference between the two flow rates is likely to form a drop. It will be generally recognised that for a drop of water to form and to drop off, it has to reach a volume of 6.54/10-2 cm3 (size of a spherical drop with a diameter of 0.5 cm). Furthermore we reckon that a drop of water is formed per each 4 cm². Second phasis Figure 3 - Liquid flow permeating through the saturated medium The behaviour of the material during this second phase is solely due to the phenomenon of percolation. 4/13 FILE ON HEAVY CLAY Modelling the second test method: volume of water percolating through a 24 hour period This model corresponds exactly to phase 2 of the previous model. Given that the only difference is that the water head applied on the surface of the roof tile is not 6 cm but 10 cm thick, there is no need to specially describe it. NUMERICAL RESULTS The figures 4 and 5 show the changes in water content profiles during the saturation phase of the body and the densities of the liquid flow passing through to the underside of the disc during the first and second phases. 0 mn 30 1 2 3 25 4 5 Water volume content [%] 20 6 7 15 8 10 11 10 12 14 5 16 19 0 20 0 2 4 6 8 10 12 21 -5 22 23 mm 24 Figure 4 - Water concentration profile during phase 1 7,00E-01 6,00E-01 Density of flow rate[g/m2.s] 5,00E-01 4,00E-01 3,00E-01 2,00E-01 1,00E-01 0,00E+00 0 10 20 30 40 50 60 -1,00E-01 Tim e [m in] Figure 5 - Water flow rate evolution across the underside profile during phase 1 5/13 FILE ON HEAVY CLAY The material used for the calculations shown in the above figures is a body having an intrinsic permeability of k = 2.10-17.m2. We can observe (see fig. 4) the moisture content profile against time, showing the obvious progressive water logging of the material. The water flow rate to the underside (see fig. 5) does not increase until after about ten minutes, which corresponds to the time it takes for the water to permeate through the surface. This rate of liquid flow corresponds to phase 1 of the model, it progressively decreases (see fig. 6), as previously explained, because that it is limited by the rate at which the water vapour escapes from the underside. On fig. 6, we have also plotted out the change in the rate of liquid flow that corresponds to phase 2, i.e. the percolation phase that occurs through the saturated material. For that configuration, the rate of percolation exceeds the previous rate after about thirty minutes. The time is defined as time T1. The rate of flow at this point remains at a constant value of 0.0012 g/m2.s. 5,00E-03 Flow rate phase 1 4,00E-03 Flow rate phase 2 Flow rate [g/m2.s] 3,00E-03 2,00E-03 1,00E-03 0,00E+00 0 10 20 30 40 50 60 70 80 90 100 110 120 -1,00E-03 Time [min] Figure 6 - Water flow rate evolution across the underside profile during phases 1 and 2 Consequently this last value allows to calculate the time T2 required to form a drop of water of 6.54/10-2g over an area of 2.5 cm2. Thus: T2=6.54.10-2/(0.0012659x2.5/10,000)=206,651s=3,444.2min.=57.4h This time is far greater than time T 1, which is typical of the first phase, and as recalled, is about of 30 min. We have repeated the same type of calculation by simply changing the intrinsic permeability value of the clay product. To do this, we have multiplied the k values by 5, 10, 20, and 40. Table 1 gives the values obtained for the formation of a drop of water for the different permeabilities. These results clearly show that the time required for the appearance of a drop of water remains very much greater than time T 1 at the end of phase 1. 6/13 FILE ON HEAVY CLAY Table 1 - Results of the numerical calculation Permeability Duration of the first Time taken for drop phase t1 (min.) to appear t2 (min.) Clay 1 k 30 3444,2 Clay 2 kx5 7 707 Clay 3 k x 10 1 365,6 Clay 4 k x 20 - 194,6 Clay 5 k x 40 - 109 Therefore the dominant phenomena that conditions the physical behaviour is the filtration phenomena as described by Darcy's law. This law describes the macroscopic transfer of the liquid through the porous body, links the macroscopic filtration velocity ul and the density of the water flow mass jl, that can be inferred with the pressure gradient of the liquid phase due to the 6 cm water head. Hereafter the relationships that can be stated: K lapp pl ul l x with K lapp hydraulic conductivity: k .k rl pl p jl l K lapp l l x x with k, k rl intrinsic and relative permeability, l , l dynamic viscosity and volumetric mass of water. The density of the liquid flow is, as shown by the previous relationships, directly proportional to the pressure gradient of the liquid phase and therefore, for the same thickness of material, is directly proportional to the head of water placed on top of the piece of clay product. Indeed, because the body in the modelled experiments is water saturated, the effective hydraulic conductivity in this case is equal to the unit. 7/13 FILE ON HEAVY CLAY Thus, given that we know the density of the liquid flow that was numerically obtained during phase two, as previously described, we can infer the density of the liquid flow for a 10 cm water head as opposed to only 6 cm on the one hand, as well as the volume of water percolating through the material during a 24 hour period. We then carried over all of the results obtained from the numerical computing exercise in table 2, using the time that it takes for a drop of water to appear in the different clay tiles as well as the volumes of water that correspond to a 24 hour percolation period under 10 cm thick water head. Furthermore, given that time T2 of the water drop appearance is essentially driven by phase 2, i.e. that it is also driven by Darcy's law, it is virtually inversely proportional to the density of the liquid flow (for the 6 cm thick water head). Table 2: Evolution of the T 2 time and of the water volume for the various clay roofing tiles Permeability Time taken for a drop Volume of water percolating to appear T2 (min) through a 24 hour period 3 2 10 cm water film cm / c m . 2 4 h Clay 1 k 3444,2 0,0172 Clay 2 kx5 707 0,084 Clay 3 k x 10 365,6 0,162 Clay 4 k x 20 194,6 0,304 Clay 5 k x 40 109 0,544 We can therefore assume that the volume of water V, that percolates through the material over a 24 hour period which is also virtually inversely proportional to time T2 of the water drop appearance, is therefore in relation with form: a V T2 8/13 FILE ON HEAVY CLAY COMPARISON BETWEEN NUMERICAL AND EXPERIMENTAL RESULTS Table 3 shows the results supplied by the CTTB for the testing on a set of tiles from various origins. Table 3 - CTTB measures on various tiles Water volume Time 3 2 crn lcm .24h in min. 0,019 2023 0,020 2 880 0,110 1 002 0,126 1 757,67 0,134 333,70 0,146 1 308 0,147 508,89 0,160 224,78 0,200 750,00 0,231 205 0,290 92 0,294 420,65 0,313 248 0,430 26,75 0,476 39,20 0,900 1,70 We have carried over on fig. 7 the values of the table 3 as well as the results obtained from our numerical simulations (see table 2). 4000 Time taken for a drop to appear 3500 CTTB measures 3000 Numerical values 2500 2000 [min] 1500 1000 500 0 -500 0 0,2 0,4 0,6 0,8 1 Volume of water percolating in 24 hour[cm3/cm2.24h] Figure 7 - Experimental and numerical values 9/13 FILE ON HEAVY CLAY We note that the numerical values, in spite of the numerous assumptions made to arrive to these results, such as for instance the size of the water drop and the number of drops formed per cm2, are relatively in agreement with all of the experimental results. Nevertheless, in order to refine our calculations and conclusions, we have tried to smooth out the points of the experimental curve with an equation as a function of : y a x b We note that: - the smoothing function gives an exponent of 0.8185. Therefore, experimentally there isn't necessarily a correlation between the time t and the volume V of the function: t = a/V. However, the coefficient is sufficiently close to 1 to consider the relationship as acceptable. This experimental difference may be due to the heterogeneity of the materials used in these experiments; - two points appear to move away a little more from the green curve of fig.8 than the others. These points on the curve correspond to the materials marked in red in Table 3. Smoothing the curve without including these two points produce the result shown on fig 9. We observe a far better correlation and the influence that prospectively poorer readings can have; - the results obtained from the digital simulations are almost in perfect agreement with the experimental curve once the points have been smoothed out. This, with hindsight, justifies the assumptions that were made in formulating the calculations. 5000 4500 CTTB measures 4000 Numerical values 3500 Smouthed out curve 3000 2500 Equation y=(a/x) b 2000 a=291.97 b=0.8185 1500 Correlation coefficient :r=0.84 1000 500 0 -500 0 0,2 0,4 0,6 0,8 1 1,2 Volume of water percolating in 24 hour[cm3/cm²/24h] Figure 8 - Rational smoothing function 10/13 FILE ON HEAVY CLAY 6000 5000 Numerical values Time taken for a drop to Smoothed out curve 4000 CTTB measures appear(min) 3000 Equation y=(a/x) b 2000 a=28.62 b=1.07 Correlation coefficient:r=0.93 1000 0 0 0,2 0,4 0,6 0,8 1 1,2 -1000 Volume of water percolating in 24 hour [cm3/cm2.24h] Figure 9: Influence of the experimental points on the appearance of the smoothed out curve 11/13 FILE ON HEAVY CLAY E V AL U AT I N G T H E I N T R I N S I C P E R M E AB I L I T Y O F T H E M AT E R I AL S As previously stated, using Darcy's law allows us to go back to the hydraulic conductivity value (s) and knowing the physical properties of water we can infer the intrinsic permeability (m2) of the clay roofing tiles. We have carried out these calculations using the two types of testing, knowing that the time taken for a drop of water to appear affected by assuming the size of the drop of water per unit of surface area. The results are given in Table 4. Obviously, we note differences between the permeabilities obtained for both tests. Although the tests, as we have just seen, are very close in terms of materials properties, it nevertheless seems to us that the test whose implementation allows for a better evaluation of the intrinsic permeability is permeability test number 2 on account of the unique physical phenomena that it displayed whilst it was carried out. We have indeed observed that test number 1 involved several phases and that its use was subject to a number of assumptions for instance as regards the formation of the water drop. Table 4 - Determination of intrinsic permeability from the two tests Water volume Intrinsic permeability Permeability relation Time in min. Intrinsic permeability 2 cm3/cm2.24 h 2 test 2 (m ) Trial 1 / Trial 2 test 1 (m ) 0,019 2023 2,770 E-17 2,550 E-17 0,92 0,020 2 880 7,960 E-17 1,400 E-16 1,76 0,110 1 002 1,060 E-16 2,550 E-16 2,39 0,126 1 757,67 2,980 E-15 5,470 E-16 0,18 0,134 333,7 8,670 E-16 3,690 E-16 0,43 0.146 1 308 4,690 E-14 1,146 E-15 0,02 0,147 508,89 3,549 E-16 2,037 E-16 0,57 0,160 224,78 2,39 E-16 1,706 E-16 0,71 0,200 750 3,944 E-17 2,419 E-17 0,61 0,231 205 3,891E-16 2,940E-16 0,76 0,290 92 3,217 E-16 3,980 E-16 1,24 0,294 420,65 6,100 E-17 1,859 E-16 3,05 0,313 248 1,568 E-16 1,870 E-16 1,19 0,430 26,75 2,035 E-15 6,060 E-16 0,30 0,476 39,2 1,897 E-16 3,740 E-16 1,97 0,900 1,7 4,540 E-17 1,600 E-16 3,53 12/13 FILE ON HEAVY CLAY CONCLUSIONS We have tried, through the course of this work, to establish a correlation between two clay roofing tile permeability test results. The first test consists in measuring the time taken for a drop of water to appear on the underside of the roofing tile when a 6 cm thick water head is applied on the opposite side, the second test consists in measuring the volume of water that passes through a saturated roofing tile under a 10 cm thick water head. To achieve this, we have carried out a number of numerical simulations intended to reproduce the behaviour of the roofing tile during the two tests. These simulations have shown that the time that the drop of water takes to appear is largely dependant on the phenomenon of percolation through the material, this phenomenon of percolation is the only contributing factor in the second test. Thus, the flow of liquid passing through the material during the two tests differs only by the hydraulic head applied. The volume of water percolating in a 24 h period is proportional to the rate of flow of the liquid, the time it takes for a drop of water to appear is inversely proportional to, it. Apart from the differences in hydraulic heads applied in each case, we can assume that the relationship between time and volume is inversely proportional. Using the results obtained by the CTTB on a number of products positively confirms, given the accuracy of the experiments, the anticipated results. The tests features only one physical property, which is the intrinsic permeability of the material. We have simulated these permeabilities starting with the two tests. The average of the ratios for both tests remains close to 1. However, in terms of the physical conditions for implementing the tests, test number two, which is based on a simple percolation experiment appears to be the best suited for determining the intrinsic permeability of the media. Test number one which is based on the time taken for a water drop to appear, seems nevertheless to be a very good means for carrying out a comparative classification of the different products, given that the saturation phase is relatively short in comparison to the percolation phase. References J.P. Monlouis-Bonnaire. Modélisation numérique des transferts couplés air-eau-sel dans les matériaux cimentaires et les terres cuites. Thèse université Paul-Sabatier, mai 2003. J.P Monlouis-Bonnaire, J. Verdier, B. Perrin, Prediction of the relative permeability to gas flow of cement based materials, C.C.R (2003). M. Diaw, B. Perrin, J.P Monlouis-Bonnaire. Limit of validity of the moisture diffusivity for the study of moisture transfer inside terracotta, Materials and Structures/ Matériaux et Constructions, Vol.35, January-February 2002, pp. 42-49. Norme NF EN 539-1. The digital simulations were made thanks to the DELPHIN code of the Technical University of Dresde (John Grunewald). 13/13

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