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ROOF TILE IMPERMEABILITY TEST A MATERIAL INTRINSIC

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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




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               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




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                                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



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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.




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                       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



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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.




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                                  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.




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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




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     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




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                                                                                      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




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                                             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




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                               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




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                                      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).




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