Proceedings of the American Association of Radon Scientists and Technologists 2008 International Symposium
Las Vegas NV, September 14-17, 2008. AARST © 2008
RADON DIFFUSION COPEFFICIENT – A MATERIAL PROPERTY
DETERMINING THE APPLICABILITY OF WATERPROOF
MEMBRANES AS RADON BARRIERS
Martin Jiránek1, Kateřina Rovenská2,3 and Aleš Froňka3
Czech Technical University, Faculty of Civil Engineering, Thákurova 7, 166 29 Praha 6,
Czech Republic
2
Czech Technical University, Faculty of Nuclear Sciences and Physical Engineering. Břehová
7, 115 19 Praha 1, Czech Republic
3
National Radiation Protection Institute, Bartoškova 28, 140 00 Praha 4, Czech Republic
1
ABSTRACT
Barrier properties of various waterproofing materials against radon were studied by means of
the radon diffusion coefficient. Method for the determination of this material property used in
the Czech Republic is presented. Results of radon diffusion coefficients measurements in
more than 300 insulating materials are summarized. We have found out that great differences
exist in diffusion properties because the diffusion coefficients vary within eight orders from
10-15 m2/s to 10-8 m2/s. Various possibilities of application of the radon diffusion coefficient
for the design of radon barrier materials are discussed. Setting strict limits for maximal radon
diffusion coefficient or minimal thickness of membranes results in significant reduction of the
amount of materials that can be used for protection against radon. Calculation of the
membrane thickness based on the radon diffusion coefficient and particular soil conditions
and building characteristics seems to be the most effective and convenient approach.
INTRODUCTION
Some damp-proof or waterproof membranes placed over the entire surface of the house
substructure can prevent radon from entering buildings from the soil. However the selection
of effective radon barriers from the total amount of tanking materials is very difficult due to
the lack of information about radon diffusion through these materials. Radon diffusion
coefficient is a material property that determines this transport and therefore it can be used for
the proper selection of radon-proof membranes based on a quantitative parameter assessment.
Testing of barrier properties of tanking materials against radon by means of the radon
diffusion coefficient started in the Czech Republic in 1995 according to the method
introduced by the Faculty of Civil Engineering of the Czech Technical University in Prague in
cooperation with the National Radiation Protection Institute in Prague. Up to now a quite
excellent database of results is available (more than 300 materials obtained throughout Europe
and Canada, have been measured). This enables to make some general requirements
considering the applicability of the radon diffusion coefficient for the design of radon-proof
membranes.
DETERMINATION OF THE RADON DIFFUSION COEFFICIENT
The Czech test method, which is accredited by the Czech Accreditation Institute, is based on
the determination of the radon flux through the tested material placed between two cylindrical
containers. Radon diffuses from the lower container, which is connected to the radon source,
through the sample to the upper container. From the known time dependent curves of the
radon concentration in both containers the radon diffusion coefficient can be calculated.
Radon concentration in both containers that serve as ionisation chambers operating in current
mode is measured continuously by fully automatic measuring device enabling monitoring in
Proceedings of the American Association of Radon Scientists and Technologists 2008 International Symposium
Las Vegas NV, September 14-17, 2008. AARST © 2008
very short time intervals (from 1 minute). Detailed description of the measuring technique,
which schematic drawing is presented in Fig. 1, can be found in (Jiránek, 2008).
Figure 1: Schematic drawing of the new device (1.1, 1.2 – upper (receiver) containers, 2 – lower (source)
container, 3 - pressure difference sensor, 4 - pump, 5 – control and operation unit, 6 – radon source, 7 – tested
sample).
In order to obtain reliable values of the radon diffusion coefficient from the measured data,
the calculation must be based on an appropriate mathematical model reflecting the time
dependent radon concentration curves not only in the source and receiver containers, but also
in the membrane itself. For the analysis of the radon concentration curve measured in the
upper container we use the time dependent numerical modelling of the non-steady state radon
diffusion through the membrane. Applied numerical model simulating the whole measuring
process solves the one-dimensional diffusion equation:
#C (x,t)
#t
= D.
# 2C (x,t)
#x2
" !.C (x,t)
(1)
where D is the radon diffusion coefficient [m2/s], λ is the radon decay constant (2.1 X 10-6 s-1 )
and C(x,t) is the radon concentration [Bq/m3].
Proceedings of the American Association of Radon Scientists and Technologists 2008 International Symposium
Las Vegas NV, September 14-17, 2008. AARST © 2008
Figure 2: Fitting the numerical solution to the measured concentration in the receiver container.
Radon diffusion coefficient is derived from the process of fitting the numerical solution to the
measured curve of radon concentration in the receiver container (Fig. 2). The great advantage
of the applied mathematical solution is that it enables to determine the radon diffusion
coefficient from data obtained by all known measuring modes used throughout Europe. This
is very helpful, especially in the situation when no uniform measuring method exists within
Europe.
VALUES OF THE RADON DIFFUSION COEFFICIENT
7.3E-09
2.5E-10
8.1E-11
3.6E-11
2.3E-11
Na bentonite
paper/geotextile
EPDM
polymer cement
coatings
PO
recycled PVC-P
polymer midified
bitumen
compositions
LDPE
modified bitumen
ECB
PVC-P
PP
HDPE
chlorinated PE
PU coatings
1.0E-14
1.0E-15
2.2E-11
1.9E-11
1.5E-11
1.4E-11
1.3E-11
1.0E-11
Measured by the
Czech Technical University and National
Radiation Protection Institute
1.0E-13
oxidised bitumen
1.0E-12
3.9E-14
1.0E-11
5.8E-12
2.3E-12
1.0E-10
3.5E-12
1.0E-09
oxidised/modified
bitumen with Al
sheet
)
Radon diffusion coefficient D2/ s(m
1.0E-08
1.2E-10
Results of the radon diffusion coefficient measurements are summarized in Fig. 3. On x-axis
materials are grouped into categories according to the chemical composition.
Fig. 3: Summary of the radon diffusion coefficient measurements realized in various waterproofing materials. On x-axis
materials are registered with respect to rising order of their diffusion coefficients (HDPE - high density polyethylene, LDPE low density polyethylene, PVC-P - flexible polyvinyl chloride, PP - polypropylene, PO – polyolefin, PU – polyurethane, ECB ethylene copolymer bitumen, EPDM - ethylene propylene dien monomer).
Proceedings of the American Association of Radon Scientists and Technologists 2008 International Symposium
Las Vegas NV, September 14-17, 2008. AARST © 2008
Fig. 3 shows very clearly that in common insulating materials used for protection of houses
against radon the diffusion coefficients vary within eight orders from 10-15 m2/s to 10-8 m2/s.
The lowest values were obtained for bitumen membranes with Al foils no matter whether the
bitumen was modified or not. On the other hand the highest values of the radon diffusion
coefficient were discovered for sodium bentonite placed between paper or geotextile sheets,
rubber membranes made of EPDM, polymer cement coatings and polyolefin membranes.
Radon diffusion coefficient for the majority of materials varies in the range 3 X 10-12 and 3 X
10-11 m2/s.
From Fig.3 it is also evident that relatively long scatter lines were obtained for two material
categories – for bitumen membranes with Al foils and for polymer modified bitumen
compositions. In case of membranes with Al foils it is caused by different thickness of Al
foils. However in the category of bitumen compositions it is a result of different chemical
composition of each material. It means that on the lower end of the scatter line materials with
very good barrier properties can be found, but on the upper end there are materials, which
could be hardly considered as radon-proof. Since the mean value lies close to the upper end,
we can assume that majority of these materials will not work satisfactorily.
DESIGN OF RADON-PROOF MEMBRANES
Radon diffusion coefficient has been adopted in several countries (Czech Republic, Germany,
Spain, Netherlands, Ireland, etc.) as a suitable parameter for the design of radon-proof
membranes. However the application of this parameter differs from country to country. In
general we can find three different approaches how to use the diffusion coefficient for the
design of membranes:
1.
the radon diffusion coefficient D of the radon-proof membrane must be below the strict
limit value,
2.
the thickness d of the radon-proof membrane must be at least three times greater than the
radon diffusion length l (Keller) calculated as l = (D/λ)1/2,
3.
the thickness of the membrane is calculated for each house (Jiránek, Hůlka, 2000,
Jiránek, Hůlka, 2001, Jiránek, 2004, CTS, 2006) according to the radon diffusion
coefficient in the membrane, radon concentration in the soil on the building site and
house parameters (ventilation rate, area in contact with the soil).
Limit for the maximal value of the radon diffusion coefficient
The main problem connected with this approach is how to choose correctly the limit value.
To be safe and reliable under all circumstances (for all types of houses and radon
concentrations in the soil) it should be rather lower than higher. However the lower the limit
will be, the more materials will be of no use. For a typical single-family house, typical soil
gas radon concentration and typical thickness of the membrane the maximum value of the
radon diffusion coefficient should be 1 X 10-11 m2/s. As a consequence of this the protection
against radon will be solved preferably by materials with Al foils, which is from the technical
point of view meaningless, because membranes with Al foils feature very low elongation and
therefore they can very easily loose their barrier properties by destroying of the Al foil.
Limit for the minimal thickness of the membrane
Limits for the minimal thickness of membranes are derived from the assumption that most
radon atoms will decay before they pass through the insulation, if the thickness of the
insulation is greater than the diffusion length. However the condition that the insulation
thickness should be at least three times greater than the diffusion length that is applied in
Proceedings of the American Association of Radon Scientists and Technologists 2008 International Symposium
Las Vegas NV, September 14-17, 2008. AARST © 2008
some countries (Keller) leads to the enormous thickness of membranes. The required
thickness exceeds the production thickness, if the radon diffusion coefficient is higher than 1
X 10-12 m2/s in case of plastic membranes or 4 X10-12 m2/s in case of bitumen membranes.
This simply leads to the conclusion that the requirement d ≥ 3l is stricter than the previously
described limit for D and will be met by a considerably smaller group of materials.
CALCULATION OF THE MEMBRANE THICKNESS
Under the conditions that the insulation is placed over the entire area of structures in direct
contact with the soil, all joints between sheets are airtight and any penetration of utility entries
through the insulation is properly sealed, we can consider the convective transport of radon to
be negligible. Therefore it is possible to assume that the radon supply rate into the house with
continuous tanking is created only by the diffusion through the insulation. Based on this
simplification the highest permissible radon exhalation rate into the house, Elim, can be
expressed by equation (2):
Elim =
Cdif .V . n
A f + Aw
(Bq/m2h)
(2)
where V is the interior air volume (m3), n is the air exchange rate (h-1), Af is the floor area in
direct contact with the soil (m2), Aw is the area of the basement walls in direct contact with the
soil (m2) and Cdif is a fraction of the reference level for indoor radon concentration Cref caused
by diffusion. The value of Cdif can be estimated, for example according to the Czech standard
ČSN 730601 as 10% (CTS, 2006). This means that the importance of the diffusion is reduced
to 10 % of Cref and the remaining 90 % of Cref is reserved for the accidentally occurring
convection.
In this context, the thickness of the radon-proof insulation can be derived with respect to real
geological and building characteristics from the condition that the radon exhalation rate E
from the real insulation in a real house calculated according to equation (3) must be less or
equal to the highest permissible radon exhalation rate Elim calculated for that house, i.e. E ≤
Elim.
E = !1 . l . ". CS
1
sinh( d / l )
(Bq/m2h)
(3)
where Cs is the radon concentration in the soil gas (Bq/m3) measured on the building site, λ is
the radon decay constant (0,00756 h-1), d is the thickness of the radon-proof insulation (m), l
is the radon diffusion length in the insulation l = (D/λ)1/2 (m), D is the radon diffusion
coefficient in the insulation (m2/h) and α1 is the safety factor that should eliminate the
inaccuracies arising during the soil gas radon concentration measurements. Values of α1 can
be estimated according to the soil permeability (for highly permeable soils α1 = 7, for soils
with medium permeability α1 = 3 and for low permeable soils α1 = 2,1).
On the assumption that the insulation is homogeneous, its minimal thickness can be calculated
from equation (4) obtained after the replacement of E in the equation (3) by Elim from equation
(2).
# 1.l .".C s .(Af + Aw )
d ! l .arcsinh
C dif .n.V
(m)
(4)
The great advantage of this approach is that the design of the radon-proof membrane can be
fitted according to particular conditions (soil and building characteristics). The possibility of
Proceedings of the American Association of Radon Scientists and Technologists 2008 International Symposium
Las Vegas NV, September 14-17, 2008. AARST © 2008
Thickness of insulation (mm)
under- or over-dimensioning is thus strongly reduced. This method of the radon-proof
insulation design was thoroughly verified in practice because it has been used in the Czech
Republic since 1996.
100
3
Cs = 200 kBq/m
+ low permeability or
3
Cs = 60 kBq/m
+ high permeability
10
1
0,1
3
Cs = 100 kBq/m
+ low permeability or
3
Cs = 30 kBq/m
+ high permeability
0,01
3
Cs = 30 kBq/m
+ low permeability or
3
Cs = 10 kBq/m
+ high permeability
0,001
1,00E-13
1,00E-12
1,00E-11
1,00E-10
1,00E-09
2
Radon diffusion coefficient / D
s ) (m
Fig. 4; Thickness of the insulation calculated according to the equation (6) for different values of D and various
combinations of soil gas radon concentration and soil permeability. The influence of the soil permeability is
introduced by the safety factor α1 that increases proportionally with the permeability. Chart is valid for the
house with habitable rooms in the basement.
The principle of designing according to this method can be identified from Fig. 4 in which the
thickness of the insulation is plotted as a function of the radon diffusion coefficient and
various combinations of soil gas radon concentration and soil permeability. It is clear that the
thickness of the insulation with D lower than 10-12 m2/s can be only several tenths of one
millimetre, even in the areas with high radon concentration in the soil. Such small thickness
is hardly producible and applicable due to sensitivity to puncturing and thus thicker insulation
must be in practice used. On the other hand, the applicability of the insulation with D of order
of 10-10 m2/s will be very strongly dependent on building characteristics and the radon
concentration in the soil. Membranes with D above 1.10-10 m2/s are too permeable to be used
for radon-proof insulation.
This clearly leads to the conclusion that the optimal value of the diffusion coefficient can be
found within the interval 5.10-12 to 5.10-11 m2/s. This interval corresponds with the production
thickness of the most frequently used insulating materials, that is 1 or 2 mm for plastic foils
and 3 or 4 mm for bitumen membranes (which in addition can be applied in two or three
layers).
CONCLUSIONS
Radon diffusion coefficient seems to be a convenient parameter for testing of radon-proof
membranes and thus measurement of this parameter should be required for all insulating
materials designated as a radon barrier.
Proceedings of the American Association of Radon Scientists and Technologists 2008 International Symposium
Las Vegas NV, September 14-17, 2008. AARST © 2008
Time dependent numerical modelling of the radon diffusion through membranes under the
non-steady state conditions that simulates the whole measuring process provides evaluation of
the radon diffusion coefficient with the highest accuracy.
Based on the experience from the Czech Republic controlling applicability of membranes by
setting strict limits for the maximal value of the radon diffusion coefficient or the minimal
thickness of the membrane is not a convenient approach. It seems to be reasonable to replace
strict limits by the real design of the insulation in dependence on particular building and soil
characteristics. Radon diffusion coefficient plays a crucial role in this design, because it
enables to calculate the membrane thickness and the radon exhalation rate from the
membrane.
In countries, where radon prone areas are classified according to indoor radon data and where
measurements of the radon concentration in the soil gas are not so common, evaluation of Cs
can be a problem. However it can be overcome, if we realize that in fact radon prone areas
substitute real soil gas concentrations. Therefore an appropriate value of the radon
concentration in the soil can be added to the each type of the radon prone area. The
uncertainty of this procedure can be covered by the safety factor α1.
Design of radon resisting membranes should be more complex. It should be stressed that
barrier properties of membranes should be in balance with other very important properties
such as durability, flexibility, buildability, chemical resistance, etc.
ACKNOWLEDGEMENT
Presented work has been supported by the research project MSM 6840770005.
Proceedings of the American Association of Radon Scientists and Technologists 2008 International Symposium
Las Vegas NV, September 14-17, 2008. AARST © 2008
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