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A mathematical model of mould growth on wooden material


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A mathematical model for the simulation of mould fungi growth on wooden material is presented, based on previous regression models for mould growth on sapwood of pine and spruce. Quantification of mould growth in the model is based on the mould index used in the experiments for visual inspection. The model consists of differential equations describing the growth rate of the mould index in different fluctuating conditions including the effect of exposure time, temperature, relative humidity and dry periods. Temperature and humidity conditions favourable for mould growth are presented as a mathematical model. The mould index has an upper limit which depends on temperature and relative humidity. This limiting value can also be interpreted as the critical relative humidity needed for mould growth depending also on the mould growth itself. The model enables to calculate the development of mould growth on the surface of small wooden samples exposed to arbitrary fluctuating temperature and humidity conditions including dry periods. The numerical values of the parameters included in the model are fitted for pine and spruce sapwood, but the functional form of the model can be reasoned to be valid also for other wood-based materials.
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A mathematical model of mould growth
on wooden material
A. Hukka, H. A. Viitanen
Summary A mathematical model for the simulation of mould fungi growth on
wooden material is presented, based on previous regression models for mould
growth on sapwood of pine and spruce. Quanti®cation of mould growth in the
model is based on the mould index used in the experiments for visual inspection.
The model consists of differential equations describing the growth rate of the
mould index in different ¯uctuating conditions including the effect of exposure
time, temperature, relative humidity and dry periods. Temperature and humidity
conditions favourable for mould growth are presented as a mathematical model.
The mould index has an upper limit which depends on temperature and relative
humidity. This limiting value can also be interpreted as the critical relative
humidity needed for mould growth depending also on the mould growth itself.
The model enables to calculate the development of mould growth on the surface
of small wooden samples exposed to arbitrary ¯uctuating temperature and
humidity conditions including dry periods. The numerical values of the
parameters included in the model are ®tted for pine and spruce sapwood, but
the functional form of the model can be reasoned to be valid also for other
wood-based materials.
List of symbols
M mould index [)]
T temperature [°C]
SQ surface quality (0 = resawn, 1 = original kiln-dried)
t time [d]
correction coef®cients [)]
W wood species (0 = pine, 1 = spruce)
RH relative humidity [%]
Wood Science and Technology 33 (1999) 475±485 ÓSpringer-Verlag 1999
Received 18 May 1997
A. Hukka, H. A. Viitanen (&)
VTT Building Technology, Wood Technology,
P.O. Box 1806, FIN-02044 VTT, Finland
Present addresses:
A. Hukka
Valmet-Utec Oy,
P.O. Box 43, FIN-20251, Turku, Finland
H. A. Viitanen
FFRI Joensuu Research Station,
P.O. Box 68, FIN-80101 Joensuu, Finland
Mould fungi is a heterogeneous and not a particularly well de®ned group of fungi.
Most of the mould fungi, as also the blue-stain and soft rot fungi, belong to Asco-
mycotina-(Ascomycetes) fungi. Mould and bluestain fungi are often both called
discolouring fungi. Discolouring fungi are often the initial microbial colonisers of
wood: logs can be infected in forests and in storage, sawn goods can be contami-
nated before and during drying, at storage or at the building site if the conditions for
fungal growth are favourable. In buildings, mould fungi cause problems in different
structures and materials: roofs, basements, ¯oors and walls. Except of wooden
substrates, surfaces of many other materials support growth of microbes and mould
problems are more common than decay damages. Typical mould fungi found in
moisture damaged wood are Alternaria alternata,Aspergillus species, Aur-
eobasidium pullullans,Cladosporium cladosporioides,Chaetomium globosum,
Paecilomyces variotii,Penicillium species and Trichoderma viride.
The growth of mould fungi on wooden material has been the subject of ex-
perimental research for a long time, but the knowledge thus gathered has been
mostly qualitative in nature (Henningsson 1980; Block 1953; Park 1982). The aim
has been to describe the material response and ®nd the critical conditions for
mould growth on surfaces of different materials with different treatments. Most of
this previous extensive research has been carried out in constant temperature and
humidity conditions but even such models are usually not applicable in arbi-
trarily varying conditions. Concerning ¯uctuating conditions, no mathematical
models seem to be available at all in the literature.
Especially dry periods have posed a problem in the published regression
models, as experimental knowledge concerning the effect of non-favourable
conditions for mould growth has been very limited. The few results published on
this subject are not applicable to humidity histories other than those used in the
experiments. From a practical point of view, it has not been possible to analyse
real building structures in actual varying climatic conditions.
Recently, Viitanen (1997a) has published comprehensive regression models for
mould growth in constant humidity and temperature conditions for pure pine
and spruce sapwood. Those regression models along with the experiments in
¯uctuating conditions are the basis for the present mathematical model. It is a
material model describing the response of pure wooden material to arbitrary
temperature and humidity conditions and will form an essential part of a more
complete structural model simulating the moisture behaviour of building struc-
tures in actual measured weather conditions.
Experimental material
The experimental material consisted of small samples (7 ´15 ´50 mm) of pure
kiln dried pine and spruce sapwood. Two different surface qualities differing in
nutrient content were studied: original kiln-dried and resawn. The experimental
results have been presented in detail by Viitanen and Ritschkoff (1991), Viitanen
and Bjurman (1995) and Viitanen (1997a).
Certain preconditions must be assumed concerning these experiments:
The small samples used do describe the mould growth on wooden material
reaching the equilibrium moisture content without delay. The ®nite size of the
samples may thus be neglected as well as the delay in the wood cell wall
attaining the equilibrium moisture content prescribed by the surrounding
relative humidity.
The growth of mould fungi takes place only on the material surface and it may
thus be modelled using only surface temperature and moisture content as input
The existence of mould fungi on the material surface does not in¯uence the
moisture behaviour of the material, e.g. sorption properties.
The mould was measured applying an existing standard index based on the visual
appearance of the surface under study. Some re®nement has been made concerning
the scale and as a result this mould index assumes following integer values:
0 no growth
1 some growth detected only with microscopy
2 moderate growth detected with microscopy (coverage more than 10%)
3 some growth detected visually
4 visually detected coverage more than 10%
5 visually detected coverage more than 50%
6 visually detected coverage 100%
The same scale is applied in the present mathematical model, but the index is not
limited to integer values.
Model development
Conditions favourable to initiation of mould growth
Moisture content of wood depends on ambient humidity, temperature, exposure
time, dimensions and moisture absorption capacity of wood; water can also exist
in wood as free water in cavities or bound water within cell walls (Siau 1981;
Cloutier and Fortin 1991; Hartley et al. 1992). Being a hygroscopic material, the
equilibrium moisture content of wood is easily affected by the ambient humidity.
At low moisture content, the most direct measure of water availability is water
potential (w) de®ned as the free energy of water in a system relative to that of a
reference pool of pure water (Schniewind 1980). Water activity (a
) is, like water
potential, related to actual availability of water and it is determined by both matric
and osmotic components. Relative humidity (RH) is a percentage relation of
actual vapour pressure (p) and saturated vapour pressure (p
). The a
can also be
de®ned as the relative humidity at equilibrium (ERH) divided by 100, i.e. rela-
tive vapour pressure (p/p
) of the atmosphere in equilibrium with the substratum.
The water activity in the ambient air or in the cavities of the material is critical
for active stages of mould growth. Growth of mould fungi and time period needed
for the initiation of mould growth is mainly regulated by water activity, tem-
perature, exposure time and surface quality of the substrate. The experiments
suggest that the possible temperature and relative humidity conditions favouring
initiation of mould growth on wooden material can be described as a mathe-
matical diagram in Fig. 1. The favourable temperature range is 0±50 °C, and the
critical relative humidity required for initiation of mould growth is a function of
temperature. Based on experiments covering the temperature range 5±40 °C this
boundary curve can be described using a polynomial function
RHcrit ÿ0:00267T30:160T2ÿ3:13T 100:0 when T 20
80% when T >20
The behaviour of RH
in the vicinity of the upper end of the temperature range
is only an approximation, but it is of only very little importance in practical
The largest possible mould growth
As known from experience, mould growth once initiated does not necessarily lead
to visually detectable mould (Viitanen and Bjurman 1995). Also, the ®nal coverage
of mould fungi on a surface is dependent on the temperature and humidity con-
ditions suggesting that a certain limiting value exists above which the mould index
does not rise irrespective of time available in basically favourable conditions. To
construct this limit, it is natural to assume that in conditions critical for the ini-
tiation of mould growth, Eq. (1), this upper limit for growth is 1, i.e. just some
growth can be detected microscopically no matter how much time passes. In the
other extreme it may be concluded that at 100% relative humidity the mould will
eventually cover the whole surface regardless of temperature (in the range 0±50 °C)
and M thus reaches a value of 6. In between these two ®xed points the experiments
suggest that the largest possible value of the mould index assumes a parabolic form:
Mmax 17RHcrit ÿRH
RHcrit ÿ100 ÿ2RHcrit ÿRH
RHcrit ÿ100
 2
The contents of Eq. (2) may also be interpreted by stating that the critical RH
needed for mould growth does not only depend on temperature but also on the
Fig. 1. Conditions favourable for
initiation of mould growth on wooden
material as a mathematical model
Fig. 2. Temperature-
dependent critical relative
humidity needed for mould
growth at different values of
mould index
stage of mould development, i.e. the mould index itself. This result is arrived at by
solving Eq. (2) for RH, which now represents the temperature-dependent RH
needed for mould index reaching a value of M
. This result is depicted in Fig. 2.
Growth rate in favourable conditions
The present model is based on mathematical relations for the growth rate of
mould index in different conditions. The model is purely mathematical in nature
and as mould growth is only investigated by visual inspection, so it does not have
any connection to biology in the form of modelling the number of live cells. Also,
the mould index resulting from computation with the model does not re¯ect the
visual appearance of the surface under study, because traces of mould growth
remain on wood surfaces for a long time. The correct way to interpret the results
is that the mould index represents the possible activity of the mould fungi on the
wood surface.
As a basis for the growth model, Viitanen (1997a) presents a regression
equation for the response time (weeks) needed for the initiation of mould growth
on wooden material in constant temperature and humidity conditions:
tmexpÿ0:68 ln T ÿ13:9 ln RH 0:14W ÿ0:33SQ 66:02 3
If the mould index M is presumed to increase linearly in time and time is mea-
sured in days, Eq. (3) may be interpreted as a differential relation
dt 1
7 expÿ0:68 ln T ÿ13:9 ln RH 0:14W ÿ0:33SQ 66:02;M<1
This conversion extends the applicability of Eq. (3) into variable conditions such
that the relative humidity is constantly above the critical value de®ned by Eq. (1)
and the temperature is in the range 0±50 °C. Linear growth in the range M < 1 is
only a mathematical description and in principle any other growth model could
be utilised. When interpreting the results of the model all values of M below 1
indicate no growth.
As the growth proceeds above the initial stage (M = 1), Eq. (4) is no longer
valid. For a larger growth Viitanen (1997a) presents another regression model
describing the response time needed for the ®rst visual appearance of mould
growth (M = 3):
tvexpÿ0:74 ln T ÿ12:72 ln RH 0:06W 61:50:5
If growth of the mould index is presumed to proceed from M = 1 to M = 3 on
a constant rate in constant conditions, Eqs. (3) and (5) can be combined to
give the growth rate on that range. The result is a correction coef®cient if
Eq. (4) is used as a basis:
k11 when M<1
tv=tmÿ1when M >1
Although based on constant conditions, the experiments suggest that Eq. (6) is
valid also for mould growth in ¯uctuating conditions as long as the conditions are
continually favourable to growth. Based on data from growth after the visual
appearance of mould fungi it may be concluded that the same correction for
growth rate applies for the entire range M > 1.
Taking into account the upper limit for mould growth de®ned by Eq. (2) may
also be accomplished by using a correction coef®cient. Assuming the delay to
affect the growth rate by 10% at 1 unit below the maximum value of the index
gives this coef®cient to the following form
k21ÿexp2:3MÿMmax 7
The complete model in conditions favourable for mould growth consists of
Eqs. (4), (6) and (7):
dt 1
7 expÿ0:68 ln T ÿ13:9 ln RH 0:14W ÿ0:33SQ 66:02k1k28
As an initial condition M must be a known value, usually equal to zero imme-
diately after arti®cial drying of wood in a kiln with wood temperature exceeding
50 °C.
Model during non-favourable conditions
In ¯uctuating humidity conditions Viitanen (1997a) states that the cumulative
time in high-humidity conditions can be used to a limited extent to quantify the
response time needed for the initiation of mould growth. This simpli®cation,
however, eventually always leads to a large mould activity as humidity cycles are
repeated. Instead of remaining on a constant level the activity of mould can be
thus regarded as decreasing during dry periods. Of course, the visual appearance
of the surface does not necessarily change during the dry period, but a ®nite delay
in growth after the dry period can be clearly observed. This delay does exist as
soon as after 6 h in dry conditions, but extending the dry period to 24 h does not
seem to signi®cantly affect the delay, if growth will initiate at all. After that the
delay is again prolonged. A mathematical description of the delay can be written
by using the time passed from the beginning of the dry period (t )t
ÿ0:032 when t ÿt16 h
0 when 6 h tÿt124 h
ÿ0:016 when t ÿt1>24 h
The experimental data behind this equation cover dry periods between 6 h and 14
days, but the functional form of expression (9) is based only on a small number of
experiments and thus must not be seen as the best possible one. Knowledge of the
in¯uence of longer dry periods on mould growth is very limited as is the data
concerning the effect of temperatures below 0 °C. In lack of better information
Eq. (9) may be applied also for such situations, although the validity of such an
application must be questioned.
Comparing the model results against experimental data
The largest possible value of the mould index, Eq. (2), is based on 12-week ex-
periments in constant conditions. Figure 3 presents the values calculated using
Eq. (2) versus the experimental observations. Only points showing a clear limit of
mould index have been taken into account. It can be seen that the largest error in
the maximum value of mould index is 1.2 and that only one point includes an
error larger than 0.5 in value.
To compare the model results to the original experimental data, Figs. 4 and 5
present the experimental and simulated response times needed for the initiation
and the ®rst visual appearance of mould growth on the surface of resawn pine
sapwood. Similar results for spruce are presented in Figs. 6 and 7. The experi-
mental results represent the average of 6 parallel samples. It can be seen that there
are no major systematic errors in the model and that in all cases most of the
errors in response time are smaller than 25% in numerical value. However, also
some points with very large errors can be detected, indicating that a model with
only a very few numerical parameters may not be suf®cient for describing the
phenomenon of mould growth in the whole temperature and RH range, especially
in higher temperatures.
Figure 8 presents the results obtained when using the model to predict the
response time needed for the initiation of mould growth on pine sapwood in
Fig. 3. Comparison of the largest
possible value of mould index
produced by Eq. (2) against the
Fig. 4. Comparison of
simulated and experimental
response times needed for
initiation of mould growth on
pine sapwood in constant
¯uctuating humidity conditions. The relative humidity has been kept at two
constant values, 75% and 95%, the period in each condition varying between
6 and 196 h. The temperature has been constant at 20 °C. It can be seen that
most of the simulated points (80%) are such that the error in response time is less
than 25%. The average error in simulated response time is only 1%, indicating
that there is essentially no systematic error in the model.
Discussion and conclusion
The mathematical model presented is throughout formulated in a differential
form. As such it allows to calculate the development of mould growth on a
wooden surface exposed to arbitrary temperature and humidity histories in-
cluding also dry periods. The numerical values of the parameters in the model
apply only for pure pine and spruce sapwood and aim at describing the average
response of the material based on a small number of parallel samples. The
Fig. 5. Comparison of
simulated and experimental
response times needed for
visual appearance of mould
growth on pine sapwood in
constant conditions
Fig. 6. Comparison of
simulated and experimental
response times needed for
initiation of mould growth on
spruce sapwood in constant
response does, however, exhibit a very large variation between samples origi-
nating from different stems of the same wood species. This variation is of the
same order in magnitude as is the variation in results between samples repre-
senting different species of wood. Based on this it may be reasoned that the same
functional form of the model could be utilised also for prediction of mould
growth on other wood-based materials, only the numerical values of the coef®-
cients must be re-evaluated.
The experimental data behind the model covers temperatures between 5 and
40 °C and relative humidities between 75 and 100%. The exposure time in con-
stant conditions has been at least 12 weeks and the time in ¯uctuating conditions
has varied between 6 and 24 weeks. This temporal scale is clearly shorter than will
be the application area of the model. This requires an extrapolation of experi-
mental results and causes an uncertainty in the results produced by the model in
such situations. Also the nature and range of the experiments conducted in
¯uctuating conditions will certainly need some revision as the numerical result
proposed by Eq. (9) is not totally satisfactory.
Fig. 7. Comparison of
simulated and experimental
response times needed for
visual appearance of mould
growth on spruce sapwood in
constant conditions
Fig. 8. Comparison of
simulated and experimental
response times needed for
initiation of mould growth on
pine sapwood in ¯uctuating
humidity conditions. Values of
surface quality SQ correspond
to original kiln-dried (1) and
resawn (0) surfaces
The maximum value of the mould index used in the model, Eq. (2), has been
deduced from experiments conducted in constant humidity conditions. It is
known that this parameter is lower in ¯uctuating humidity conditions, but the
numerical value of the maximum growth in such situations on a general level is
not comprehensively known. In this sense the present model obviously needs
further development. The same applies for ¯uctuating temperature conditions
with constant RH.
The present model describes mould growth on wooden material surfaces. It is a
pure material model trying to quantify the experimental results of mould expo-
sures conducted on small samples. The next natural step in the evolution of the
model is to insert the mathematical equations into a simulation program for
calculation of mould growth on an actual wooden structure. This would create a
new tool for prediction of the service life of a certain structural design in critical
temperature and humidity conditions. Another possible direction of further de-
velopment is to apply the model for quanti®cation of mould growth in materials
other than pure wood, which combined to a moisture simulation program would
give a powerful tool for analysing the moisture behaviour of a very wide range of
It has been found in laboratory studies and in practice that mould fungi are
more rapid invaders than decay fungi in wooden structures subjected to excess
moisture stresses (Viitanen 1997a, b). Also, the minimum humidity and tem-
perature requirements are in general lower for mould fungi than for brown rot
fungi. Growth of mould fungi and time period needed for the initiation of mould
growth are mainly regulated by water activity, temperature, exposure time and
surface quality of the substrate. Especially at low water activity and low tem-
perature, the latent period preceding the initial stages of mould growth and the
appearance of mould fungi on wood have been found to be several weeks al-
though the equilibrium moisture content of the small samples used was reached
in two weeks (Viitanen 1997a). However, Viitanen and Paajanen (1986) found no
mould growth at RH 75% and according to recent studies, the lowest humidity
condition allowing mould growth is RH 80±85% (i.e. water activity 0.80±0.85)
providing that the temperature is above 5 °C (Bjurman 1989; Park 1982; Wang
1992; Adan 1994; Hocking et al. 1994; Viitanen 1997a). Modeling of the critical
humidity and temperature conditions, and especially of the critical time required
for spore germination and the growth of mould fungi mycelium on pine and
spruce sapwood was presented by Viitanen (1997a). Temperature conditions
have a minor effect on the water activity and the main effect is concerned with
the growth and metabolic activity of the fungi. Often the selection of mould
species at high temperatures (above +30 to +35 °C) consists mainly in thermo-
tolerant or thermophilic mould fungi (Henningsson 1980). At ¯uctuating hu-
midity conditions, the growth of mould fungi is clearly retarded and latent period
is even longer than at constant favourable conditions (Adan 1994; Viitanen
In general, the higher the temperature and the more favourable the nutrition at
a given relative humidity, the less time is required for spore germination. After
kiln drying, the concentration of nitrogen and low-molecular hydrocarbon
compounds on the surface layers of sawn timber are often higher than inside the
wood (Boutleje 1990; Theander et al. 1993). Terziev et al. (1994) and Viitanen and
Bjurman (1995) showed, that the growth of mould is clearly more rapid and
vigorous on the original kiln dried wood surface than on a resawn surface.
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Boutelje J (1990) Increase in the content of nitrogenous compounds at lumber surfaces
during drying and possible biological effects. Wood Sci. Technol. 24: 191±200
Cloutier A, Fortin Y (1991) Moisture content ± water potential relationship of wood from
saturated to dry conditions. Wood Sci. Technol. 25: 263±280
Hartley ID, Kamke FA, Peemoeller H (1992) Cluster theory for water sorption on wood.
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... WUFI ® hygrothermal simulations were performed to measure the hygrothermal performance and the risk of mold growth in cold and subarctic climate zones. The water content, as well as the mold growth index (which was developed by Hukka and Viitanen [35] and was also more recently enhanced by Ojanen et al. [36]), were both used as indicators to compare the mold proliferation potential and drying capacity of the assemblies. ...
... The mathematical mold growth model that was developed by Hukka and Viitanen [35] and was more recently improved by Ojanen et al. [36] was used in this study to evaluate the risk of mold growth. The model, which is available via the WUFI Mold Index VTT add-ons, was developed according to the researchers' work and led to the recent addition of Addendum E to the ASHRAE 160 standard [43]. ...
... The mold growth model, on the other hand, provides an assessment of the risk of mold growth within a component of an assembly by considering the material's sensitivity to mold, its RH and its temperature. The mold growth index was thoroughly explained by Hukka and Viitanen [35]. ...
Full-text available
While externally insulated wall assemblies are widely recognized for their hygrothermal performance, few research projects have focused on the impact of shifting the entire wall insulation to the exterior side of a structural cavity in cold or subarctic climates or its effectiveness in terms of acoustic performance and airtightness. The objective of this study was to propose fully externally insulated assemblies that could be used in cold and subarctic climates by assessing the benefits of the hygrothermal performance of these assemblies and by achieving a comparable airtightness and sound transmission performance to the modern assemblies that are currently built in North America. The results suggested that the externally insulated assemblies limited the risk of condensation occurring inside structural cavities and allowed for faster drying than the modern assemblies when exposed to water infiltration or high water contents in all climates that were tested. The assemblies with external airtight insulation boards were more airtight than assemblies with air barrier membranes and, in addition, assemblies with external soundproof insulation were shown to be necessary to achieve a comparable sound transmission loss to that of a modern assembly.
... The resulting models (IEA 1991, Hukka and Viitanen 1999, Krus et al. 2007) are being used for new architectural design and concomitant standards development will have an impact on the buildings made for storage of cultural property and even retrofits to historic structures themselves. ...
... LIM models from graphs in Krus et al. (2007). VTT limit function (Hukka and Viitanen 1999) plotted as solid grey line `e'. Outliers are not overly suspicious given evidence in figures 3 through 8 and indicates long term studies at marginal RH may not be well represented in temperature tolerance studies. ...
... See Figure 5 for the IEA threshold comparison to collated mould data in the humidity/time domain. Vereecken et al. (2011) reviewed current mould prediction models for structures: Temperature ratio (IEA 1991), VTT versions (Hukka and Viitanen 1999) and Isopleth 2 models (Sedlbauer 2001) for dynamic conditions. However, the very sensitive class used in the VTT model is untreated pine lumber with a stipulated minimum 80 %RH as does the IEA Annex 2 Isopleths of mould response as germination time or growth rate on RH/temperature plots. ...
Conference Paper
Full-text available
The interplay of environmental conditions which contribute to the support of mould growth has had scientific study for a century. The recognition of moisture as the primary factor by which to control fungi is common knowledge. How both moisture and temperature combine to delay or accelerate growth is also well represented in the literature. The earliest studies looked quite carefully at growth rates while many later ones relied more on categorized impressions. Unfortunately, what is often absent from these studies are measures which we can translate directly as harms to cultural property. We do infer there will be harms by fungi to a variety of objects we care for from mustiness through obscuration to digestion, but we cannot predict their severity with any confidence from the studies which define under which conditions fungi will start to grow. At best for us, the worst case likelihood of mould onset can be proposed, but that has to be recognized as quite subject to modification by the species and substrate actually present. For prevention, two possibly safe paths are now used within the building science community: the avoidance of risk by controlling for a threshold of abiotic `dryness'; or allowing timed residence inside growth encouraging conditions but with subsequent timed drying conditions to prevent it. The former is a simple threshold which imposes on performance of the building construction to withstand moisture movement. The latter is predicated on knowing the dynamic behaviour of moisture within the layers of structures and room contents. Both have inherent uncertainties in their biological risk models, and both can run up against what people feel objects require for their preservation.
... Three different performance indicators related to degradation were considered in this study: first, the formation of mold on the inner contact surface was predicted with the updated VTT model by Hukka and Viitanen (1999). Mold endangers the occupants' health by introducing respiratory complaints, headaches, allergenic nausea and should be controlled in a correct fashion (ASHREA, 2009;Hukka and Viitanen, 1999;Vereecken and Roels, 2012;Viitanen et al., 2010). ...
... Three different performance indicators related to degradation were considered in this study: first, the formation of mold on the inner contact surface was predicted with the updated VTT model by Hukka and Viitanen (1999). Mold endangers the occupants' health by introducing respiratory complaints, headaches, allergenic nausea and should be controlled in a correct fashion (ASHREA, 2009;Hukka and Viitanen, 1999;Vereecken and Roels, 2012;Viitanen et al., 2010). Secondly, historic masonry facades often provide a load bearing support for wooden beams which are vital as structural support in the flooring system (Krzˇisˇnik et al., 2019; Vereecken and Roels, 2019). ...
... There are different mold prediction models, the authors refer to Vereecken and Roels (2012) for an overview and evaluation of these models. In this study, the mold growth on the inner surface of the wall structure was predicted by the updated VTT model by Hukka and Viitanen (1999), Viitanen and Ojanen (2007) as it considers mold initiation, growth rate as well as decline during dryer periods. It comprises a dynamic model related to two time-depending variables: relative humidity and the temperature on the surface. ...
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Historic masonry has a rich and colorful history making it a treasured part in our society. To preserve and protect this heritage, adequate moisture control, retrofit, and res-tauration strategies are required. However, due to the large range of material properties inherent to historic brickwork, a single uniform renovation strategy appears impossible. To describe similarity in brickwork, the existing clustering approach developed by Zhao was evaluated. The idea is that different types of bricks with similar properties can be represented by a single representative brick for that cluster, for example, when conducting hygrothermal simulations. It could help improve existing retrofit practice by reducing characterization processes and minimizing time-consuming laboratory measuring tests. However, in this paper the approach presented by Zhao is questioned since the clustering is solely based on an equal impact of the material properties and the response behavior and associated degradation risks are neglected. The aim of this paper was twofold. Firstly, similarity in brickwork obtained by clustering according to Zhao was evaluated by means of hygrothermal simulations to see whether bricks in the same cluster show similar degradation risks. Zhao's clustering provides homogenous clusters regarding physical material properties, but significant variation was found in degradation risks for different bricks within the same cluster. Secondly, a methodology is presented to translate similarities in degradation profiles toward similarities in material properties. Sensitivity analyses were used to study the response behavior based on three degradations risks: mold growth, wood rot, and frost damage. Finally, an overall clustering scheme was generated for brickwork, based on classification trees for different degradation phenomena.
... Insulation is also considered to be the first element of defence for mould prevention and its effectiveness is determined by thickness, type, Table 1. Table showing the mould-growth index and its corresponding physical characteristics [11]. Additionally, mould growth is a function of three primary variables: water activity (A w ), equilibrium relative humidity (ERH), and moisture content (MC), which are discussed further. ...
... A numerical mould-growth model was used to evaluate the response of humidity, temperature, and exposure duration for mould growth on wood material [11,25,26]. This was based on extensive research with Northern wood species in the lab [26]. ...
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Commercial energy consumption currently accounts for 8.6% of the total national energy consumption in India and it is predicted to surge in upcoming years. To tackle this issue, building envelope insulation is being promoted through codes and standards to reduce the cooling and heating demand and hence reduce the overall energy demand. However, with prolonged exposure to humid ambient conditions in warm-humid locations, building materials undergo decay in their hygrothermal properties, which induces mould growth and increases the energy that is needed to tackle the latent cooling load. Mould growth, in turn, harms the occupant and building health. Therefore, this study attempts to evaluate the mould-growth index (MGI) in the coastal city of Mangalore, Karnataka, India using the heat and mass transfer (HAMT) model. The MGI for one autoclaved aerated concrete (AAC) wall assembly in a representative commercial building has been studied by integrating EnergyPlus through the Python plugin. The simulated results suggest that the annual mean MGI for the AAC assembly is 3.5 and that mould growth will cover about 30–70% of the surface area. Furthermore, it was concluded that surface temperature, surface humidity, and solar radiation are key parameters for mould growth on the surface of a material.
... Several approaches for modeling service life of timber structures are summarized by (van Niekerk et al., 2021). Most of those approaches rely on dose-response models, which confront the time-wise integrated deterioration dose with the intrinsic material resistance (Hukka and Viitanen, 1999;Thelandersson and Isaksson, 2013). The "critical dose" is reached when the exposure of the material equals or exceeds its resistance. ...
... Preliminary findings show the effectiveness of avatars in using different hygrothermal parameters to apply alternative mold growth prediction models. As shown in Figure 2, reconstructed RH data were used by Avatars 2 and 3 to apply models developed by (Hukka and Viitanen, 1999;Viitanen et al., 2000;and Thelandersson et al., 2011). At the same time, "Avatar 4" used MC values from location 2 for mold risk prediction according to the serviceability limit state (SLS) model (Lepage et al., 2022). ...
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Mass timber construction systems, incorporating engineered wood products as structural elements, are gaining acceptance as a sustainable alternative to multi-story concrete or steel-frame structures. The relative novelty of these systems brings uncertainties on whether these buildings perform long-term as expected. Consequently, several structural health monitoring (SHM) projects have recently emerged to document their behavior. A wide and systematic use of this data by the mass timber industry is currently hindered by limitations of SHM programs. These limitations include scalability, difficulty of data integration, diverse strategies for data collection, scarcity of relevant data, complexity of data analysis, and limited usability of predictive tools. This perspective paper envisions the use of avatars as a Web-based layer on top of sensing devices to support SHM data and protocol interoperability, analysis, and reasoning capability and to improve life cycle management of mass timber buildings. The proposed approach supports robustness, high level and large-scale interoperability and data processing by leveraging the Web protocol stack, overcoming many limitations of conventional centralized SHM systems. The design of avatars is applied in an exemplary scenario of hygrothermal data reconstruction, and use of this data to compare different mold growth prediction models. The proposed approach demonstrates the ability of avatars to efficiently filter and enrich data from heterogeneous sensors, thus overcoming problems due to data gaps or insufficient spatial distribution of sensors. In addition, the designed avatars can provide prediction or reasoning capability about the building, thus acting as a digital twin solution to support building lifecycle management.
... Additional experiments showed that microclimatic conditions affect survival of Ixodes ticks, although questing behavior depends largely on geographic origin of populations, suggesting local ecological adaptation [43,49]. Another limitation may be the possibility of developing mold growth on the wooden skewers, especially at high humidities >80% RH [50]. We did not observe any evidence of mold growth on the skewers or on the ticks during the 30-day experiment, but users of this protocol should inspect all surfaces frequently for mold contamination when working with a high RH. ...
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Ticks are the most important vectors of zoonotic disease-causing pathogens in North America and Europe. Many tick species are expanding their geographic range. Although correlational evidence suggests that climate change is driving the range expansion of ticks, experimental evidence is necessary to develop a mechanistic understanding of ticks’ response to a range of climatic conditions. Previous experiments used simulated microclimates, but these protocols require hazardous salts or expensive laboratory equipment to manipulate humidity. We developed a novel, safe, stable, convenient, and economical method to isolate individual ticks and manipulate their microclimates. The protocol involves placing individual ticks in plastic tubes, and placing six tubes along with a commercial two-way humidity control pack in an airtight container. We successfully used this method to investigate how humidity affects survival and host-seeking (questing) behavior of three tick species: the lone star tick ( Amblyomma americanum ), American dog tick ( Dermacentor variabilis ), and black-legged tick ( Ixodes scapularis ). We placed 72 adult females of each species individually into plastic tubes and separated them into three experimental relative humidity (RH) treatments representing distinct climates: 32% RH, 58% RH, and 84% RH. We assessed the survival and questing behavior of each tick for 30 days. In all three species, survivorship significantly declined in drier conditions. Questing height was negatively associated with RH in Amblyomma , positively associated with RH in Dermacentor , and not associated with RH in Ixodes . The frequency of questing behavior increased significantly with drier conditions for Dermacentor but not for Amblyomma or Ixodes . This report demonstrates an effective method for assessing the viability and host-seeking behavior of tick vectors of zoonotic diseases under different climatic conditions.
... The results of the WUFI 2D simulation were controlled for mould growth risk, using the accessory plugin WUFI Mould Index VTT. The plugin is based on a mould growth model described by Viitanen et al. [33,34], outputting a mould growth index from 0 to 6. The model takes into account the relative humidity, temperature, time, and type of material. ...
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Due to increasingly stringent requirements, tapes and adhesive joints are a commonly used method to ensure tightness and energy efficiency in modern building envelopes. Previous studies have researched and tested properties such as the strength and tightness of adhesive joints. So far, water vapour resistance has been neglected. This article aims to determine the vapour resistance and shed light on possible consequences of vapour-tight adhesive joints in breather membranes used in roof assemblies. Laboratory measurements of vapour resistance were conducted according to NS-EN ISO 12572:2016, known as the cup method. Eleven products of breather membranes were tested. Results from the laboratory measurements were used to evaluate the impact of vapour-resistant adhesive joints related to the drying of built-in moisture. The simulation programs WUFI 2D and WUFI Mould Index VTT were used to model scenarios for moisture transport and risk for mould growth. Laboratory results show that the vapour resistance of breather membrane adhesive joints varies from 1.1 to 32 m in sd-value. Three of the tested products have a vapour resistance larger than 10 m, while four products have an sd-value less than 2.0 m. The sd-values of the membranes themselves range between 0.027 and 0.20 m. All tested adhesive joints are considerably more vapour tight than the Norwegian recommended value for breather membranes (<0.5 m). However, the mould growth analysis shows that the risk of mould growth is low in most practical cases, except when using adhesive joints with the highest vapour resistance in roofs assembled during autumn.
... Please refer to Refs. [26,27] for a complete description of the mould model. The calculation of M air is based on the daily average temperature and relative humidity of the outdoor air. ...
The dominant degradation agent in facades is exposure to moisture. Damages resulting from long-term moisture exposure are typically evaluated through hygrothermal simulations. These simulations are computationally expensive. Therefore, a Moisture Reference Year (MRY), i.e. one year representing the moisture stress of the climate, is often used instead of simulating damages with the long-term climate itself. Usually, the methods to select MRYs were developed for specific wall types and damages. Up to now, no guideline exists to select one of these methods for particular cases. Therefore, we evaluated 21 existing MRY methods, and we developed a decision framework on how to select appropriate climate data for hygrothermal simulations. This paper presents the comparison between long-term simulations and simulations using MRYs for solid masonry walls in Brussels. The wall assemblies are analysed with and without interior insulation for 16 parameter variations each. A number of MRYs are able to represent the risk on freeze-thaw damage and wood decay, but the best performing MRYs vary between the different damages. Further, the decision framework consists of 5 levels, with each level requiring less computational power at the cost of its precision. It is recommended to perform long-term simulations whenever possible. Second best is to select an MRY with respect to a long-term simulation for a reference case. For large studies, a climate-based MRY accounting for the expected damage mechanisms could be considered as a first estimate of the results. In this study, the decision framework was successfully tested for solid masonry walls in Brussels.
The study comprises three laboratory tests in which typical Finnish highly insulated (HI) walls were exposed to concentrated leakages of indoor air under steady outdoor temperatures of 1–5°C. Airflows with a relative humidity of 50% and at rates of 1–3 L/min were directed close to the wooden frames inside the walls. The thermal resistance ratios between the exterior sheathing(s) and the whole wall (Γ) were 20%–22% and 1%–10% for the HI and baseline (BL) walls. The HI walls that presented Γ values of at least 20% were observed to be resistant to air exfiltration, and their durability was not affected by the addition of a gypsum sheathing outside the wooden frame or a more permeable vapor retarder. This is related to the negative linear correlation that exists between the moisture accumulation rate in wood-based material and the dew point depression (DPD) value. The developed approach, called the DPD method, shows that a significant degree of moisture accumulation does not occur even for DPD values of as low as −2°C if the exterior sheathing is vapor permeable. The airflow does not penetrate into the rigid mineral wool sheathing, which helps to avoid interstitial condensation. Regardless of thermal transmittance, the HI and BL walls with maximum Γ values of 1% were exposed to a high relative humidity and even interstitial condensation because the DPD values were often below −2°C. For these walls, the mold index analysis and visual observations confirmed the local risk for mold growth on the opposite side of the leakage point. In practice, long-term mold growth may be limited if the seasonal periods during which the outdoor temperature is 1–5°C last for a maximum of about 1 month every year.
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The IPCC 2021 report predicts rising global temperatures and more frequent extreme weather events in the future, which will have different effects on the regional climate and concentrations of ambient air pollutants. Consequently, changes in heat and mass transfer between the inside and outside of buildings will also have an increasing impact on indoor air quality. It is therefore surprising that indoor spaces and occupant well‐being still play a subordinate role in the studies of climate change. To increase awareness for this topic, the Indoor Air Quality Climate Change (IAQCC) model system was developed, which allows short and long‐term predictions of the indoor climate with respect to outdoor conditions. The IAQCC is a holistic model that combines different scenarios in the form of submodels: building physics, indoor emissions, chemical–physical reaction and transformation, mold growth, and indoor exposure. IAQCC allows simulation of indoor gas and particle concentrations with outdoor influences, indoor materials and activity emissions, particle deposition and coagulation, gas reactions, and SVOC partitioning. These key processes are fundamentally linked to temperature and relative humidity. With the aid of the building physics model, the indoor temperature and humidity, and pollutant transport in building zones can be simulated. The exposure model refers to the calculated concentrations and provides evaluations of indoor thermal comfort and exposure to gaseous, particulate, and microbial pollutants.
In this study, three groups of models based on regression analyses of the critical time required for the growth of mould fungi on pine and spruce sapwood are presented. The first group of models describe the response time needed for development of the initial stages of mould growth on wood and the second group of models describe the response time needed for visual appearance of mould fungi. The models are based on the results of exposing wood to different mould fungi in static humidity and temperature conditions. The third group of models implicate the fluctuation of humidity conditions in the initial stages of mould growth based on the mould exposures in limited number of fluctuating or alternating humidity conditions. An aspect of surface quality (kiln dried surface, normal sawn surface) and wood species (pine, spruce) are included in the models. In continual humidity exposures at RH above 80% (water activity above 0.8) for several weeks/months, the risk for mould growth in pine and spruce sapwood exists when the temperature is between 5 and 5O °C. Between 0 and 5 °C, the growth of mould fungi is slow and expected only when the water activity is above 0.9. At RH above 95% (water activity above 0.95), the critical time reeded for the visual appearance of mould fungi in wood is only a few days, when temperature is between 25 and 4O °C, and approximately 4 to 8 weeks, when temperature is between 10 and 2O °C. Within the same temperature and humidity conditions, the critical response time for mould growth on the original yellow surfaces which had been exposed to the atmosphere during kiln drying of wood is shorter than on samples taken at 7mm below the original surface. In fluctuating humidity conditions, when favourable and unfavourable conditions are alternating, the cumulative time of high humidity needed for the development of mould fungi is longer and the final rate of mould growth is lower as compared to the same total time in constant favourable condition.
Ln this study, models based on the regression analyses of the critical exposure time periods of humidity and temperature conditions needed for the development of brown rot decay in pine and spruce sapwood are presented. The growth conditions and decay development of a typical brown rot fungus Coniophoia puteana (Schum. ex Fr.) P. Karsten (BAM Ebw. 15) was studied in Scots pine (Pinus sylvestris L.) and Norway spruce (Picea abies Karst.) by exposures at 0, 5, 15, 20 and 30 degrees C using RH of 86-88, 90-92%, 96-98% and 99-100% under laboratory conditions. A regression model is presented for the critical response time periods of temperature and humidity conditions allowing the initiation and development of decay as expressed by the mass loss of wood. The response time for decay development in wood is strongly dependent on the temperature: after 3 months' exposure at RH of 96 and 100% and at 30 degrees C, the wood was heavily attacked and decayed by C. puteana, but after one year exposure in different humidity conditions, no decay was detected at 0 degrees C. According to the present model: the lowest humidity conditions for decay development must lie above RH of 90-92% during 60 month exposure time at 30 degrees C. Between 0 and 5 degrees C, the lowest humidity conditions for decay development lie around RH of 97% and the wood moisture content around the fibre saturation point.
Changes in ergosterol content in cultures of Penicillium brevicompactum and Aspergillus versicolor on wood with time, changes in humidity or addition of glucose solutions to wood were studied with HPLC. Lowering of the humidity level caused a very large decline in ergosterol content of cultures of P. brevicompactum on wood over a 10 day period, although small amounts remained after this time. After an initial increase, up to an inoculation time of 45 days, reductions were also observed in control samples maintained at 100% RH, but these were smaller. The amount of ergosterol decreased to very low levels in wood impregnated with low levels of glucose during a 93 day incubation period. Ergosterol concentration in hyphae produced in surface liquid cultures was shown to be higher in mycelia growing on media enriched with nitrogen or with more available nutrients. The concentration of ergosterol in the mycelia of P. brevicompactum in surface liquid cultures varied by a factor of 5 from 2 to 10 mg g−. The results clearly show that ergosterol present in solid materials in mainly related to active biomass. With certain prerequisites, ergosterol determinations could also be used for total fungal biomass estimations on wood.
Nitrogen contents have been determined at different depths from the surface of dried pine (Pinus sylvestris) and spruce (Picea abies) lumber. The effects of factors such as time of felling, storage of the timber, and drying process for the lumber, have been studied. Part of the selected lumber was characterized by surfaces which were yellowish after drying. At such surfaces, to a depth of about 2 mm, a high accumulation of nitrogen was always found. Yellowing is enhanced in lumber from wet-stored timber but also occurs in other lumber. Some possible contributive factors are suggested. More research in this field is proposed. The nitrogen gradients in outer sapwood without a yellow surface and in inner sapwood and in heartwood were much weaker. The effect which enrichment of nitrogenous compounds at surfaces may have on timber with regard to its disposition towards moulding is discussed. Although attention is drawn to the fact that strong nutrient gradients may occur, it must be emphasised that in most lumber nutrient gradients are weak and probably without practical consequence for its susceptibility towards fungal attack.
In this study a quantitative analysis of the low molecular carbohydrates (predominantly sucrose, fructose and glucose) in a series of lumber samples of Pinus sylvestris and Picea abies taken at various distances from the surface has been made. The increase of nitrogenous compounds towards the surface had been shown in a previous study. Several of the lumber samples showed a marked sugar accumulation at the surface, which correlated quite well with a corresponding nitrogen accumulation. In one case, the total amount of the three sugars was as high as 4.9% of the dry matter content in the 0–1 mm layer. It was of special interest to note that samples with high nitrogen and sugar contents also had a yellow surface colour, which probably formed during the drying process by the well-known Maillard reaction — a complex of reactions occurring when sugars and amino acids, peptides and proteins are heat-treated together. Growth of the mould fungus Penicillium brevicompactum was well correlated with the content of nitrogen and low molecular carbohydrates in adjacent samples. The initial colonization was somewhat delayed in material from the outermost sapwood zone despite high nutrient contents indicating effects of antifungal compounds from the bark or toxic Maillard reaction products effective against germination. Growth of Aspergillus versicolor was likewise most elaborate on samples with the highest nitrogen and soluble carbohydrate content but the results also indicate a sensitivity to antifungal compounds present.
A review of water interaction in cellulosic-systems, particularly wood, is presented. Discussed are the different states of water in these systems according to Nuclear Magnetic Resonance results, the BET, Dent, and Hailwood and Horrobin sorption isotherm models. The discussion includes details of water structure, and, conformational analysis of cellulose crystals and amorphous cellulose. The water cluster theory is used to more adequately explain the sigmoid curve of the wood isotherm.
The water potential concept as applied to wood-water relations is presented. The gradient in water potential can be used as the driving force of moisture in wood in a model of drying in isothermal conditions provided the moisture content — water potential relationship is known. This relationship is established for aspen sapwood in desorption from saturated to dry conditions at 20, 35 and 50 C for two specimen orientations. The tension plate, pressure plate and pressure membrane methods were used at high moisture contents and equilibration over saturated salt solutions was used at low moisture contents. The results obtained demonstrate that these methods can be used in combination in order to establish the relationship within the whole range of moisture contents. The equilibrium moisture contents obtained by the tension plate, the pressure plate and the pressure membrane methods for tangential desorption were slightly higher than those measured for radial desorption. The water potential increased with temperature at a given moisture content. This effect cannot be solely explained by the variation of surface tension of water with temperature.
The effects of water activity (aw) on the growth rates of two isolates of Alternaria alternata and a single isolate each of Cladosporium cladosporioides, Clad. sphaerospermum, Curvularia lunata and Curv. pallescens were examined at 25 °C. The aw of the growth media was controlled by glucose/fructose. The minimum aw for germination of A. alternata, Curvularia lunata and Curv. pallescens was 0·855. Cladosporium cladosporioides and Clad. sphaerospermum germinated at a minimum aw of 0·815. Clad. sphaerospermum also grew at this aw, but germinating conidia of Clad. cladosporioides did not produce microcolonies.