Building and Environment 65 (2013) 18e25

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Building and Environment

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Mould resistance design (MRD) model for evaluation of risk for

microbial growth under varying climate conditions
Sven Thelandersson, Tord Isaksson*
Division of Structural Engineering, Lund University, PO Box 118, SE-221 00 Lund, Sweden

a r t i c l e i n f o a b s t r a c t

Article history: The risk for microbial growth depends on the microclimatic conditions at material surfaces. In the
Received 24 December 2012 building envelope the microclimate will vary significantly with time. Whether microbial growth will
Received in revised form occur or not, depends on humidity, temperature, duration of exposure and type of material (substrate). A
22 March 2013
limit state for onset of mould growth is here defined as a prescribed level observed by microscopy (40
)
Accepted 23 March 2013
in laboratory tests. In this paper, a mould resistance design (MRD) model is proposed by which onset of
growth can be predicted for an arbitrary climate history of combined relative humidity f and temper-
Keywords:
ature T. The model is calibrated and verified against a comprehensive set of new experimental data
Mould growth
Limit state
describing mould development on wood specimens (spruce and pine) as a function of exposure of
Doseeresponse relative humidity and temperature and material and surface characteristics. The exposure in the tests
Relative humidity comprised both steady and time-variable conditions.
Temperature Application of the MRD-model is demonstrated by assessment of mould risk based on results from
Varying climate simulations of an external wall design with hygro-thermal computer software (WUFI). The results show
that a generally applicable, quantitative model together with building physics software can be used as a
powerful tool for moisture safety design in practice.
The model is designed to facilitate continuous improvement by further laboratory testing of various
materials under specified climate conditions. The MRD-model is controlled by a basic parameter in the form
of a critical dose Dcrit, which depends on the substrate or material surface on which growth may take place.
Ó 2013 Elsevier Ltd. All rights reserved.

1. Introduction material properties, ventilation conditions in air gaps etc. All these
are normally associated with significant variability, which some-
For components in the building envelope an important how must be taken into account in any risk assessment. It is here
requirement is to limit the risk for microbial growth under the assumed that acceptability of the performance is based on a clearly
intended service life of the building. In general, this risk depends on defined limit state, which in this context could be onset of mould
humidity, temperature, duration of exposure and type of material growth. An operational performance model for unique verification
(substrate) on which the growth may take place [1e7]. Hygro- of such a limit state requires, however, a mathematical formulation,
thermal computer software is nowadays available to predict con- by which the onset of mould growth can be evaluated for a general
ditions in the form of time series for relative humidity and tem- climate history [f(t), T(t)] of combined relative humidity f(t) and
perature at different locations in building components, see e.g. temperature T(t), where t is the time.
WUFI [8]. The issue is then to interpret these results in terms of risk A mathematical model of mould growth on wooden material
for microbial growth, which is normally not accepted in building was proposed by Huuka & Viitanen [9] and Viitanen & Ojanen [6].
components in contact with indoor environment. Fig. 1 gives an The model is directly based on the comprehensive tests of condi-
illustration of the parameters and factors affecting moisture safety tions for mould growth presented by Viitanen and others [4,6,10,11]
design of the building envelope with respect to microbial growth. and it was shown that their model gives good predictions also
The result from the hygro-thermal analysis is a function of a large under variable moisture conditions. Isaksson et al. [3] proposed a
number of input parameters related to outdoor and indoor climate, similar model based on doseeresponse relationships, which in its
original form was calibrated against Viitanens data [4]. The purpose
with the present paper is to develop the model presented in [3] into
* Corresponding author. Tel.: þ46 46 222 4885. a more general form and verify it against new laboratory tests
E-mail address: tord.isaksson@kstr.lth.se (T. Isaksson). performed for various wood materials [13]. Another purpose is to

0360-1323/$ e see front matter Ó 2013 Elsevier Ltd. All rights reserved.
http://dx.doi.org/10.1016/j.buildenv.2013.03.016
 S. Thelandersson, T. Isaksson / Building and Environment 65 (2013) 18e25 19

Table 2
Properties of material surfaces tested.

Identifier Species Surface characteristics Thickness Widtha Comment

(mm) (mm)
SO1 Norway Original, planed in 12 90
Spruce sawmill
SO2 (picea Original, sawn in 18 95
abies) sawmill
SP1 Planed in laboratory 10 90
SP2 Planed in laboratory 17 95
PO1 Pine (pinus Original, sawn in 25 150 Rough
silvestris) sawmill sawn
PO2 Original, sawn in 18 75
sawmill
PP1 Planed in laboratory 21 150
PP2 Planed in laboratory 18 75
a
Width of original board. Length of specimen w0.5e1 times the width.

Fig. 1. Illustration of principle for moisture safety design. units for relative humidity and 0.5  C for temperature. Further
details on the test procedure are given in references [12] and [13].
estimate the variability in the response, which is an essential aspect
in risk assessment. 3. Critical time to onset of mould growth

2. Experimental investigation of mould growth on material For the purpose of modelling, the limit state “onset of mould
surfaces growth” is defined as rating 2 on the scale in Table 1. The suscep-
tibility of mould growth for a specific material surface can then be
The extent of mould growth is usually determined by observa- characterised by the time tcrit to reach this level under a specified
tions in microscope. In the new tests described in this paper the reference climate with temperature Tref and relative humidity fref
scale presented in Table 1 has been used. If mould is detected at all, (both constant in time). The critical time tcrit depends on Tref and
the extent of it is subjectively classified on 5 levels by an experi- fref, but also in general on the availability of nutrition on the ma-
enced analyst. Clearly this method is associated with some uncer- terial surface, the type and extent of spore exposure and the surface
tainty due to the subjective assessment involved, but its reliability texture. In laboratory tests, when standardised spore exposure can
can be improved by using a number of test specimens, Johansson be realised, this critical time can be seen as a characteristic and
[12]. It should also be noted that the scale in Table 1 differs from measurable property for a specific material surface.
that used by Viitanen [4], who made his classification on 6 levels, As an example, the response of planed spruce from one sawmill is
and where the ratings are described in a different way representing shown in Fig. 2 for tests 1 and 2 according to Table 2. Each point in the
different extent of growth. diagram is the average rating of six nominally identical specimens. If
In the new tests referred to in this paper, board specimens of the reference conditions are chosen as fref ¼ 90% and Tref ¼ 22  C, the
wood were sprayed with a spore suspension on one of its surfaces. critical time tcrit to onset of mould growth is of the order 30 days
The materials investigated in this test series are described in Table 2. based on this particular test. As can be seen in Fig. 2 the variation of
For some specimens the test surface was directly used (denoted the average rating is not monotonously increasing as would be ex-
original) as it was delivered from the sawmill, while in other tests pected. This reflects the uncertainty in the subjective rating of mould.
1e4 mm was cut away from the surface in the laboratory one day For the case T ¼ 22  C in Fig. 2 the rating was performed by the same
prior to the test (denoted planed). The original surface of the wood person at each particular time, but two different persons alternated
coming from the sawmill could be planed (SO1), fine sawn (SO2 and at different rating occasions. No systematic difference depending on
PO2) or more roughly sawn (PO1). The specimens were sprayed the individual analyst could be seen from the results.
with a spore suspension in a standardised way, Johansson [12], and The effect of temperature is also clearly seen in Fig. 2. If the
then incubated in climate chambers under specified conditions of temperature is changed from 22  C to 10  C while keeping the
relative humidity and temperature. The species used in the spore relative humidity constant at 90%, mould growth is not initiated
suspension are listed in Table 3 [12]. The samples were inspected even after 4 months exposure.
twice a week in microscope (40
magnification). Six nominally
identical specimens were used for each type of material. Each 4. Response under time-variable climate conditions
specimen was evaluated individually according to the scale in
Table 1. The test program is summarised in Table 4, from which it Test results from wood specimens exposed to cyclic relative
can be seen that test series with constant climate, cyclic relative humidity (RH) at temperature T ¼ 22  C are shown in Fig. 3. Each
humidity as well as cyclic temperature were included. The vari- cycle starts at f ¼ 90% during either one week or 12 h, followed by
ability relative the nominal values was of the order 2 percentage f ¼ 60% with the same duration. The results are compared with the

Table 1 Table 3
Evaluation scale of mould growth. Mould species used in the spore suspension[12].

Rating Description of extent of growth Species CBS number

0 No mould growth Eurotium herbariorum 115,808

1 Initial growth, one or a few hyphae and no conidiophores Aspergillus versicolor 117,286
2 Sparse but clearly established growth; often conidiophores Penicillium chrysogenum 401.92
are beginning to develop Aureobasidium pullulans 101,160
3 Patchy, heavy growth with many well-developed conidiophores Cladosporium sphaerospermum 122.63
4 Heavy growth over more or less the entire surface Stachybotrys chartarum 109.292
20 S. Thelandersson, T. Isaksson / Building and Environment 65 (2013) 18e25

Table 4 4
Laboratory test program for mould growth on wood specimens.
SP1
3.5
Test Climate Nominal relative Nominal temperature Length of Test SP1, 2 week cycle
no. type humidity (%) ( C) cycle duration SP1, 24h cycle
3
(days) limit state
1 Constant 90 22 e 49 2.5

Mould rating
2 Constant 90 10 e 115
3 Cyclic 90-60-90-60- etc. 22 2
7 days 112 2
4 Cyclic 90-60-90-60- etc. 22 2
12 h 91
5 Cyclic 90 22a-5-22-5b-22-5etc. 2
7 days 115
1.5
a
The first period at 22  C was only 3 days.
b
The second period at 5  C lasted 14 days instead of 7 days as intended. 1

0.5
case for steady exposure at f ¼ 90%. The figure displays mould
rating as a function of the accumulated time at f ¼ 90%, i.e. periods 0
0 10 20 30 40 50 60
at f ¼ 60% are not included. It is obvious that intermediate periods Accumulated time at RH=90% (days)
with dry climate have a very strong inhibiting effect on the po-
tential for microbial growth even when the total accumulated time Fig. 3. Mould development under cyclic and constant relative humidity at temperature
T ¼ 22  C. Cycling always started at f ¼ 90% followed by an equally long period at f ¼ 60%
of exposure at high humidity is the same. The inhibiting effect is
and so on. Length of a complete cycle was either 24 h or 2 weeks. Test specimens type SP1,
slightly less for daily moisture cycles than for cycles with longer see Table 2.
duration but still very significant. The shorter cycles may be rele-
vant for material in e.g. attics, where strong variations in humidity
in indoor room climate which will influence the conditions for
may occur between day and night.
mould growth.
Results from tests with constant f ¼ 90%, but with cyclic tem-
Define the half day dose D12 as the product of a component Df
perature are shown in Fig. 4. The development of mould is signif-
dependent on 12 h average of relative humidity f12 and a compo-
icantly delayed also in this case, but to a lesser degree than for the
nent DT dependent on 12 h average of temperature T12, i.e.
case of cyclic humidity. Further test results and a more detailed
description of methodology for the experimental investigation can D12 ¼ Df ðf12 Þ$DT ðT12 Þ (1)
be found in Johansson [13].
For exposure during the time t ¼ 0,5,n12 days, the total dose is
given by
5. MRD-model for prediction of onset of mould under general
climate conditions X
n12 X
n12
DðtÞ ¼ Dð0; 5n12 Þ ¼ D12i ¼ Df ðf12i Þ$DT ðT12i Þ (2)
As mentioned above, it is necessary to have a mathematical 1 1
model, by which the limit state “onset of mould growth” can be
evaluated for a general climate history [f(t), T(t)]. A doseeresponse where f12i is average relative humidity and T12i is average tem-
model was presented in [3], based on daily averages of f and T. It perature for 12 h period number i and n12 is the total number of
has been argued, however, that using daily averages will not ac- 12 h periods within the time period t (days). The dose can be
count for the sometimes rather strong variations in temperature defined in relation to a specified reference climate (fref, Tref). For a
and humidity between day and night. Therefore, a modified and material surface under constant exposure to this reference climate
more generalized MRD-model based on 12 h averages is presented onset of mould takes place after tcrit days. The critical dose is
below and verified against the new tests described in Sections 2e4. defined so that
Using shorter periods than 12 h cannot be verified against the test
X
2t crit    
data. Also, shorter test cycles are difficult to control, e.g. when Dcrit ¼ Dðtcrit Þ ¼ Df fref;i $DT Tref;i ¼ tcrit (3)
evaluating the mould rating the specimens are stored for some time 1

4
4 2
Cyclic Tmax=22, Tmin=5 ˚C
3.6 1.8 3.5
Constant T=22 ˚C
3.2 1.6 limit state
3
2.8 1.4
2.5
Mould rating
MRD index

2.4 1.2
Mould rating

2
2 1
SP1(10˚C) (test results)
1.6 0.8 1.5
SP1 (22˚C) (test results)
1.2 SP1 (10˚C) (model) 0.6
1
SP1 (22˚C) (model)
0.8 limit state 0.4
0.5
0.4 0.2

0 0 0
0 20 40 60 80 100 120 140 0 20 40 60 80 100 120
Time (days) Time (days)

Fig. 2. Mould development under constant climate with relative humidity 90% and Fig. 4. Mould development under cyclic temperature for constant f ¼ 90%. Cycling of
temperatures 22 or 10  C. Test specimens type SP1, see Table 2. temperature between 22 and 5  C, see Table 3. Test specimens type SP1, see Table 2.
 S. Thelandersson, T. Isaksson / Building and Environment 65 (2013) 18e25 21

100 8   
> T
Days < exp 2; 0$ln 12 if 0; 1 < T  30+ C and Df > 0
DT ðT12 Þ ¼ 20
7
95 >
: if Df > 0
1; 0
Relative humidity (%)

14
90 (4b)
28
85 35 with f12 in % and T12 in  C. Eqs. (6a) and (b) can be illustrated in the
56
form of isopleths as shown in Fig. 5, which is valid for the case with
84 Dcrit ¼ 39 days at fref ¼ 90% and Tref ¼ 20  C (planed spruce). The
80
curves represent different times for onset of mould growth (rating
2) according to the definition given in Section 3.
75 Under dry conditions and at low temperatures some recovery or
set back for the germination/growth process can be expected. This
70 can be described as a negative daily dose, i.e. D < 0. A “safe” region
0 5 10 15 20 25 30 35
Temperature (˚C)
with dry conditions and/or low temperatures with unfavourable
conditions for germination and mould growth is also defined in the
Fig. 5. Isopleths illustrating the MDR-model expressed by Eq. (6) and Dcrit ¼ 39 days at model, as all states where f < 75% or T < 0.1  C. The safe region is
fref ¼ 90% and Tref ¼ 20  C. illustrated in Fig. 5. For conditions in the safe region the following
“negative” doses are assumed.
This means that the dose is expressed in days and is equal to 1.0
Df ðf12 Þ ¼ 2:118 þ 0:0286f12 for 60 < f12  75% (5a)
for a day with constant reference climate (fref, Tref). For other relative
humidities and temperatures than the reference values the dose per
day will be less than 1.0 if growth conditions are more unfavourable Df ðf12 Þ ¼ 0:4 for f12  60% (5b)
for the mould and greater than 1.0 if conditions are more favourable
than the reference conditions. Mould growth is assumed to be with f in %.
initiated when the accumulated dose becomes equal to Dcrit ¼ tcrit. As Likewise, when the temperature is below 0.1  C the total dose D
described in Section 3 above the critical time tcrit and thus the critical is given by
dose Dcrit can be seen as a property characterizing the substrate or
material surface. Dcrit can be determined by laboratory testing. Dðf12 ; T12 Þ ¼ 0:4 for T12 < 0:1+ C (6)
The structure of the model described in [3] was based on The dose factors Df and DT in the model are graphically dis-
comprehensive experimental data presented by Viitanen [10,11], who played in Figs. 6 and 7. Note that Df has the dimension days, while
derived expressions for response time as a function of relative hu- DT is a dimensionless factor. Also, note that the total accumulated
midity f and temperature T by statistical fitting against test results. dose can never be negative, which is an important condition in the
Evaluation of the results from the new tests presented here algorithm.
revealed, however, that the relative effect of temperature and The interpretation of a negative value 0.4 of D is that a total
relative humidity derived from the tests in [10] had to be modified recovery from a situation where onset of mould growth is imme-
to match the data. Using the reference conditions fref ¼ 90% and diately imminent will be achieved after 1.25,Dcrit (90%; 20  C) days
Tref ¼ 20  C, the following relations were derived based on the in a climate with f < 60% and/or T < 0  C. The estimated recovery
experimental evidence from the present tests and in a qualitative behaviour here is based on examination of the new test results
sense from the tests by Viitanen [10,11]. under variable climate conditions.
The MRD-model may now be used for general climatic expo-
sures with arbitrary variations of f(t) and T(t). It may also be used
  
f for prediction of mould on other substrates if test data are available
Df ðf12 Þ ¼ 0; 5exp 15; 5$ln 12 for 75 < f  100% (4a) to predict the value of Dcrit (90%; 20  C) for a given substrate ma-
90
terial. If other constant values for f and/or T are used in a test the
critical time has to be recalculated on the basis of Eq. (6) to be valid
3
for 90% and 20  C.
The basic feature of the MRD-model is to transform dynamic
2.5 climate variations to a time dependent dose D[f(t), T(t)] which can
be compared to a critical dose Dcrit for onset of mould growth. The
2 limit state function g(f, T) can thus be formulated as
Dose factor DΦ (days)

D½fðtÞ; TðtÞ
1.5
g½fðtÞ; TðtÞ ¼ 1  drel ¼ 1  (7)
1 Dcrit

0.5 defined so that g() 0 or drel  1 corresponds to an acceptable

exposure and g() < 0 or drel > 1 implies violation of the limit state.
0
The quantity drel can be seen as an index describing the risk of
mould and will in the following be called MRD-index. Note that the
-0.5
critical dose Dcrit must be related to the reference conditions
-1 f ¼ 90% and T ¼ 20  C since the numerical values in Eqs. (4)e(6) are
20 30 40 50 60 70 80 90 100
based on this. The model is in principle only valid for a relative dose
Relative humidity, 12 hour average (%)
drel < 1, i.e. a mould rating less than 2. However, in the results
Fig. 6. Dose function Df assuming fref ¼ 90%. shown below, higher levels are still displayed to visualize the
22 S. Thelandersson, T. Isaksson / Building and Environment 65 (2013) 18e25

2.5 materials. One possibility could have been to adjust the model to
better account for the observed behaviour at lower temperature,
but it was decided not to manipulate the model further to avoid
2
added complexity in its structure.
The case with 2
1 week cycling of relative humidity between
)

1.5
90% and 60% is shown in Fig. 9a and b for planed spruce and planed
Dose DT (

pine respectively. The critical dose Dcrit for each type of material is
based on (fref, Tref) ¼ (90%, 20  C) and was determined from test 1 in
1 Table 4 at constant climate conditions for the same material. The
difference between the temperature in the test (22  C) and Tref was
taken into account by adjustment of Dcrit based on Eq. (6b).
0.5 It can be seen in Fig. 9 that the modelled response agrees quite
well but is slightly on the conservative side compared to the tests. A
similar comparison with other tested materials also gives a con-
0
0 5 10 15 20 25 30 servative model response. From Fig. 9b it can also be seen that the
Temperature (˚C) test results for planed pine are unstable in the final period of the
Fig. 7. Dose factor DT related to temperature given that Df > 0 and Tref ¼ 20  C.
test series. This illustrates the difficulties associated with the sub-
jective rating, which are especially significant for mould ratings
around 1.
performance of the model and provide a measure of to what extent Comparisons against tests performed with 2
12 h cycling of
the limit state is exceeded. But comparison with the observed relative humidity between 90 and 60% (test 4 in Table 4) are shown in
mould index above level 2 should be made with care. Fig. 10a for planed spruce and in Fig. 10b for pine with the “original”
surface from the sawmill. From Fig. 10a it can be seen that the model
agrees reasonably well with the tests for spruce type SP1 and test
6. Verification of the MDR-model for varying climate conditions type 4 in Table 4. Fig. 10b shows the results for pine type PO1 with
significantly different susceptibility to mould growth. In this case the
To verify the model presented in Section 5 above it has been model is clearly non-conservative. The material surface in this case
applied for the laboratory tests performed under controlled
climate conditions. First consider the case with constant climate
(Tests 1 and 2 in Table 4). The response of the proposed model for
these two tests is shown in Fig. 2 and compared with the test a2 4
results. The critical dose Dcrit for this particular material (planed 1.8 3.6
spruce) is determined from the test at T ¼ 22  C and f ¼ 90% (by
Limit state

adjustment from 22  C to 20  C based on Eq. (6b)). It is then 1.6 MRD index SP1 (model) 3.2

applied for the test performed at 10  C and the result is shown in 1.4 Mould rating SP1 (test results)
2.8
Fig. 2. It can be seen that the model response is clearly conser-

Mould rating
MRD index

1.2 2.4
vative compared to the test result at 10  C. Comparisons for other
tested materials show similar results with the model generally 1 2

giving conservative results, i.e. predicting onset of mould earlier 0.8 1.6
than observed in the test.
0.6 1.2
In Fig. 8 the model is compared with test results for the case with
cyclic temperature for spruce specimens of type SP1 (see Table 2). 0.4 0.8
Fig. 8 shows that also for this case the model is slightly con-
0.2 0.4
servative underestimating the suppression of mould growth due to
lower temperature. Similar results are obtained for other tested 0 0
0 20 40 60 80 100 120 140
Time (days)

2 4
b 2 4

1.8 Limit state 3.6

1.8 3.6 MRD index PP1 (model)
Limit state
1.6 3.2
1.6 MRD index SP1 (model) 3.2 Mould rating PP1 (test results)
1.4 2.8
1.4 Mould rating SP1 (test results) 2.8
Mould rating
MRD index

1.2 2.4
Mould rating
MRD index

1.2 2.4
1 2
1 2
0.8 1.6
0.8 1.6
0.6 1.2
0.6 1.2
0.4 0.8
0.4 0.8
0.2 0.4
0.2 0.4
0 0
0 20 40 60 80 100 120 140
0 0
0 20 40 60 80 100 120 140 Time (days)
Time (days)
Fig. 9. Model response compared to results from tests with 2 week cycles of relative
Fig. 8. Model response vs. test response for cyclic temperature with weekly change humidity between 90% and 60% (test 3, Table 3). a) Planed spruce (SP1), with Dcrit ¼ 39
between 22 and 5  C and with constant relative humidity 90% (Test 5 in Table 3). days b) Planed pine (PP1) with Dcrit ¼ 22 days.
 S. Thelandersson, T. Isaksson / Building and Environment 65 (2013) 18e25 23

4
a 2 4
Limit state 3.5
1.8 3.6
MRD index SP1 (model)
1.6 3.2 3
Mould rating SP1 (test data)
1.4 2.8

Mould rating
2.5

Mould rating
MRD index

1.2 2.4
2
1 2
PO1
0.8 1.6 1.5
PO2
0.6 1.2 1 PP1
PP2
0.4 0.8
0.5 Limit state
0.2 0.4
0
0 0 0 10 20 30 40 50 60
0 10 20 30 40 50 60 70 80 90 100
Time (days)
Time (days)

b 2 4 Fig. 12. Results from tests of mould development for different types of pine specimens,
see also Table 2.
1.8 3.6

1.6 3.2 increase and decrease of the mould index each day has been
omitted in the graphical presentations.
1.4 2.8 Mould rating
MRD index

1.2 2.4
7. Influence of material quality
1 2

0.8 1.6 The most important parameter in the MDR-model is the critical
Limit state dose Dcrit for onset of mould growth which describes the influence
0.6 1.2
MRD index PO1 (model) of the material surface or substrate where mould growth may take
0.4 Mould rating PO1 (test data) 0.8 place. It can, as mentioned above, be determined from a laboratory
0.2 0.4
test where the material is exposed to constant relative humidity
and temperature and where the level of mould growth is observed
0 0 as a function of exposure time. Results from tests of this type
0 10 20 30 40 50 60 70 80 90 100
Time (days) are shown in Fig. 11 for the different types of spruce described in
Table 2.
Fig. 10. Model response compared to results from tests with daily cycles of relative
It is obvious from Fig. 11 that there can be a great variation
humidity between 90% and 60% (test 4, Table 3). a) Planed spruce, with Dcrit ¼ 39 days
b) “Original” pine with Dcrit ¼ 8,5 days. within the same wood species depending on surface structure and
treatment. The critical time to reach the limit state at (f,
T) ¼ (90,22) for the four types of spruce varies from 7 to 32 days
was roughly sawn, i.e. not planed at all showing that surface char- (8,5e39 days if adjusted to 20  C). The worst case is found for SO2,
acteristics and production conditions have significant influence on with original sawn surface. If the surface has been planed after
the biological process. Values for the “material property” Dcrit kiln drying in the sawmill (SO1) the performance is improved
correspond to fref ¼ 90% and Tref ¼ 20  C, i.e. the same as in Fig. 9. and even more so if planing was done just before the test (SP1 and
The model response shown in Fig. 10 is somewhat simplified SP2).
since the actual response with small perturbations due to regular Similar results for the tested pine specimens are shown in
Fig. 12. Comparison with Fig. 11 shows that the susceptibility for
mould growth is somewhat higher for pine than for spruce. These
results also confirm that mould grows very fast on original sawn
4
surfaces. A possible explanation is that nutrition substances are
3.5
present on the surface after kiln drying. Similar observations were
made by Viitanen, see e.g [4].
3
Mould rating

2.5

1.5 SO1
SO2
1 SP1
SP2
0.5 Limit state

0
0 10 20 30 40 50 60
Time (days)

Fig. 11. Results from tests of mould development for different types of spruce speci- Fig. 13. Design of timber framed wall with brick facade. Monitoring point indicated by
mens, see also Table 2. arrow.
24 S. Thelandersson, T. Isaksson / Building and Environment 65 (2013) 18e25

2 2

1.5 10 ACH 1.5 Lund

100 ACH Stockholm

Limit state

MRD index
MRD index

Limit state

1 1

0.5 0.5

0 0
0 200 400 600 800 1000 1200 1400 1600 1800 2000 0 200 400 600 800 1000 1200 1400 1600 1800 2000
Time (days) Time (days)

Fig. 14. Results from mould risk analysis for the wall shown in Fig. 13. Fig. 16. Results from mould risk analysis for the wall shown in Fig. 15. 30 ACH assumed
in air gap.

8. Application of the model for assessing risk for onset of Fig. 14 shows that for the assumption of 10 ACH the limit state is
mould growth clearly exceeded already during the first year, while the assumption of
the high ventilation of 100 ACH means that the relative dose always
One of the main applications of the proposed MRD-model is to remains below the limit. A number of other analyses with varying
evaluate the output from hygro-thermal analyses of different de- assumptions concerning parameters like radiation absorptivity,
signs of the building envelope. A few examples of this will be effectiveness of the vapour retarder, wall orientation, climate input
shown in this section. First a typical external timber frame wall in etc. generally show that the limit state is exceeded. Only if a very high
Sweden from the period 1970e1990 is investigated, see Fig. 13. ventilation rate in the air gap is assumed, the wall solution can be
The wall solution shown in Fig. 13 has been used in practice in a regarded as safe. From a practical point of view, it is not realistic to
large number of houses in the region of Lund, Sweden. It was assume 100 ACH for a wall like this [14]. Therefore, the conclusion
analysed with the software WUFI [8] using climate data for a must be that the wall shown in Fig.13 can not be accepted if one wants
normal year in Lund and with all necessary input parameters to avoid the risk of mould growth in the monitoring position at the
chosen according to the best available knowledge today. The wall outer edge of the wood studs. However, the wall solution considered
was analysed with a one-dimensional model since this is often here is used in a great number of houses in the actual region. The
done by practitioners. Moreover, the effect of some important pa- general experience from practice is that no significant moisture
rameters was investigated in a parameter study. To assure the problems related to the wall design has been identified in the build-
stability in the simulation all analyses were performed for five ings which are of the order 20e40 years old. This may indicate either
consecutive years, with the same external climate data applied that the model is conservative or that mould growth inside the walls is
each year. Due to lack of space all details of the simulations are not often present, but creates no problems for the occupants. Another
presented, since the purpose here is only to illustrate the applica- explanation could be that the one-dimensional WUFI analysis can not
tion of the MRD-model. The output from each analysis in terms of capture the thermal bridge caused by the timber studs. This will
coupled time series of relative humidity f(t) and temperature T(t) significantly reduce the relative humidity and the dose at the wood
in a monitoring point in the wall (see Fig. 13) was fed into the MRD- surface compared to that predicted by the one-dimensional analysis,
model. It is then assumed that the wood studs installed in the wall which was demonstrated clearly in experiments performed on
has a value of Dcrit ¼ 17 days (at fref ¼ 90%, Tref ¼ 20  C) corre- different types of timber framed walls, see [15].
sponding to spruce planed in a sawmill, see Fig. 11. The output from A timber framed wall with external wood panel and with higher
this gives the MRD-index as a function of time as shown in Fig. 14 energy performance is shown in Fig. 15.
for two different assumptions about ventilation of the air gap in the This wall was analysed with WUFI in a similar manner as the
wall, either 10 or 100 air changes per hour (ACH). previous wall using reasonable assumptions for input data, per-
forming parameter studies and with external climate for different
sites in Sweden. One example of results is shown in Fig. 16 for the
two sites Lund and Stockholm with their respective climate.
Obviously, the analysis gives the answer that this wall solution is
safe at both sites. The MRD-index is somewhat lower for Stockholm
reflecting the fact that the climate generally is cooler and drier at
that site. The same result was found for different variations of input
parameters as well as for a number of other sites in Sweden. The
general engineering conclusion from the analyses is that the wall
solution can be used safely in the whole country.

9. Discussion and conclusions

A moisture resistance design (MRD) model is presented for pre-

dicting onset of mould growth when material surfaces are exposed to
Fig. 15. Design of highly insulated timber framed wall with wooden facade. Moni- a dynamic and arbitrary climate exposure described in terms of time
toring point indicated by arrow. variation of coupled relative humidity f and temperature T. The
 S. Thelandersson, T. Isaksson / Building and Environment 65 (2013) 18e25 25

MRD-model is quantified on the basis of new test results for various In summary, the following main conclusions can be drawn from
wood qualities published by Johansson [13]. Tests were made under the present study:
conditions constant in time as well as for exposure with cyclic vari-
ations in both relative humidity and temperature. To be able to  It is possible to predict onset of mould growth for arbitrary climate
describe the response when the exposure fluctuates in time between exposure with reasonable reliability based on the MRD-model.
conditions favourable for mould and dry and/or cold conditions  The MRD-model can in general be quantified on the basis of
unfavourable for mould the model operates with “recovery”, i.e. it is laboratory tests on different substrate materials under speci-
assumed that conditions unfavourable for mould germination and fied climate conditions.
growth will disturb and set back the biological process. This type of  The critical dose Dcrit, which is the governing parameter in the
behaviour is clearly confirmed by the results from the tests per- MRD-model, can be determined from tests.
formed under cyclic conditions. The existence of this type of recovery  The susceptibility of different materials to mould growth
can also be deduced from qualitative experience. Without “recovery” shows a very large variability.
during dry periods, the model would predict initiation of mould  The risk associated with this can be handled by appropriate
almost everywhere sooner or later because each period in the unsafe choice of the parameter Dcrit.
area would give an accumulated effect which inevitably would lead  The MRD-model is a powerful tool for evaluation of the effect of
to mould growth also in e.g. heated indoor environments. This is in various assumptions in the analysis with respect to risk for
clear contradiction to what is generally known. mould growth. Hygor-thermal analysis performed for walls in
It should be noted that the MRD-model is conceptually intended existing buildings shows that the results are very sensitive to
to simulate the process up to the limit state “onset of mould growth”. many input parameters.
The model response above this level can however be seen as a  The MRD-model is a powerful tool to compare different design
measure of to what extent the limit state is exceeded and should not solutions for elements in the building envelope with respect to
be compared to the actual mould development when mould is risk for mould growth
already established. Clearly, mould which is already established  The model is also useful as a tool for probability based evaluation
cannot disappear in reality in periods of dry and/or cold conditions. of safety against non-performance defined by a limit state.
The limit state “onset of mould growth” was defined as rating 2
on the scale used for the laboratory tests. It is defined as “Sparse but
Acknowledgements
clearly established growth” which can be observed in microscope.
This definition is to a certain degree pragmatic for two reasons.
The present research is a part of the research programme
Woodbuild co-ordinated by SP Technical Research Institute of
 Rating 2 is easier to identify during testing than rating 1, which
Sweden. The research is financed by Vinnova, the Swedish Feder-
is associated with higher uncertainty.
ation of Forest Industries and a number of companies in the forest
 It is to a certain extent based on engineering judgement and
and building sector.
regarded as accurate enough compared to other uncertainties
in moisture resistance design. References

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