**3.1 Mould growth on building materials**

Modelling of mould growth and decay development based on humidity, temperature, exposure time and material will give tools for the evaluation of durability of different building materials and structures. The models make it possible to evaluate the risk and development of mould growth and to analyse the critical conditions needed for the start of growth of microbes and fungi. The model is also a tool to simulate the progress of mould and decay development under different conditions on the structure surfaces. This requires that the moisture capacity and moisture transport properties in the material and at the surface layer have been taken into account in the simulations. In practice there are even more parameters affecting mould growth, e.g. thickness of the material layers combined with the local surface heat and mass transfer coefficients. Therefore, the outcome of the simulations and in-situ observations of biological deterioration may not agree. One of the results of a newly finished large Finnish research project "Modelling of mould growth" is an improved and extended mathematical model for mould growth based on development of mould index in different materials under different exposure conditions (table 2).

Hukka and Viitanen (1999) and Viitanen et al. (2000) presented a model of mould growth which is based on duration of suitable exposure conditions required before microbial growth will start or the damage will reach a certain degree. Particular emphasis is focused on this time period, the so-called response time or response duration, in different humidity and temperature conditions for the start of mould growth (Figure 1). The model is based on the large laboratory studies on Scots pine and Norway spruce sapwood.

Moisture and Bio-Deterioration Risk of Building Materials and Structures 583

<sup>1</sup>Small amounts of mould on surface (microscope), initial stages of

2 Several local mould growth colonies on surface (microscope) <sup>3</sup>Visual findings of mould on surface, < 10 % coverage, or,

<sup>4</sup>Visual findings of mould on surface, 10 - 50 % coverage, or,

5 Plenty of growth on surface, > 50 % coverage (visual) 6 Heavy and tight growth, coverage about 100 % Table 2. Mould index for experiments and modeling of mould growth on building materials Sedlbauer (2001) studied different models to evaluate spore germination and growth of different mould species on different types of materials. He found, that the isopleths developed by growth of mould on an artificial medium can be used to evaluate the growth rate of different fungi. He used a hygrothermal model based on the relative humidity, temperature and exposure time needed for the spore germination of mould fungi based on the osmotic potential of spores. He analysed the effect of different climatic conditions on the spore moisture content and germination. He also evaluated the spore moisture content and germination time based on calculated time courses of temperature and relative humidity in various positions of the exterior plaster of an external wall using WUFI program (Sedbauer and Krus 2003). In Figure 3, a comparison of the critical conditions for mould growth assumed by some of mould growth models is shown. These curves represent lower limiting

Fig. 3. Comparison of the LIM's of substrate class 1 (LIM I, biodegradable materials) and substrate class 2 (LIM II, porous materials) after Sedlbauer (2001) with data from results of

building materials after Viitanen et al. (2000), Clarke et al. (1998) and Hens (1999)

local growth

**< 50 % coverage of mould (microscope)** 

**>50 % coverage of mould (microscope)** 

**Index Description of the growth rate** 

0 No growth

isopleths (humidity levels) for mould growth.

Fig. 1. Critical humidity (RH %), time (weeks) and temperature needed to start mould growth on pine sapwood (Viitanen 1996)

The growth of mould in this model was evaluated using the "mould index" scale shown in Table 2. The model can be used to evaluate the mould growth in different exposure conditions, and it can be introduced to building physic modeling to evaluate the performance of different structure. The model is not suitable for evaluate the development of decay, for which different models exist (Viitanen 1996, Viitanen et al. 2000).

The model describes also the dynamic nature of mould growth under varying temperature and humidity conditions as it gives the predicted mould index as a function of time. Simulation results with the model show that under fluctuating humidity, the mould index will decrease during low humidity or temperature periods, depending on the time periods (Figure 2). This kind of behaviour can also be found in the "Modelling of mould growth" study (Viitanen et al 2010).

Fig. 2. Modelling the effect of varied fluctuating humidity conditions on the development of mould index in pine sapwood (Viitanen et al. 2000)

The original index is based on wood materials (Viitanen and Ritschkoff 1991a). New determinations for index levels 3 and 4 for other materials are presented using bold fonts and has been presented by Viitanen et al (2011a).

1 °C 5 °C 10 °C 20 °C

0 5 10 15 20 25 30 **Time (weeks)**

Fig. 1. Critical humidity (RH %), time (weeks) and temperature needed to start mould

of decay, for which different models exist (Viitanen 1996, Viitanen et al. 2000).

The growth of mould in this model was evaluated using the "mould index" scale shown in Table 2. The model can be used to evaluate the mould growth in different exposure conditions, and it can be introduced to building physic modeling to evaluate the performance of different structure. The model is not suitable for evaluate the development

The model describes also the dynamic nature of mould growth under varying temperature and humidity conditions as it gives the predicted mould index as a function of time. Simulation results with the model show that under fluctuating humidity, the mould index will decrease during low humidity or temperature periods, depending on the time periods (Figure 2). This kind of behaviour can also be found in the "Modelling of mould growth"

**B**

**3/4 d 97/75 RH**

**Mould index** 

Fig. 2. Modelling the effect of varied fluctuating humidity conditions on the development of

The original index is based on wood materials (Viitanen and Ritschkoff 1991a). New determinations for index levels 3 and 4 for other materials are presented using bold fonts

0 28 56 84 112 140 168 196 **Time (days)**

**6/42 h 97/75 RH**

**7/14 d 97/75 RH**

**7/23 d 97/75 RH 1/6 d 97/75 RH**

growth on pine sapwood (Viitanen 1996)

0 28 56 84 112 140 168 196 **Time (days)**

mould index in pine sapwood (Viitanen et al. 2000)

and has been presented by Viitanen et al (2011a).

**12/12 h 97/75 RH**

**6/12 h 97/75 RH**

**3 / 21 h 97/75 RH**

study (Viitanen et al 2010).

**A Constant RH**

**Mould index** 

**RH (%)**


Table 2. Mould index for experiments and modeling of mould growth on building materials

Sedlbauer (2001) studied different models to evaluate spore germination and growth of different mould species on different types of materials. He found, that the isopleths developed by growth of mould on an artificial medium can be used to evaluate the growth rate of different fungi. He used a hygrothermal model based on the relative humidity, temperature and exposure time needed for the spore germination of mould fungi based on the osmotic potential of spores. He analysed the effect of different climatic conditions on the spore moisture content and germination. He also evaluated the spore moisture content and germination time based on calculated time courses of temperature and relative humidity in various positions of the exterior plaster of an external wall using WUFI program (Sedbauer and Krus 2003). In Figure 3, a comparison of the critical conditions for mould growth assumed by some of mould growth models is shown. These curves represent lower limiting isopleths (humidity levels) for mould growth.

Fig. 3. Comparison of the LIM's of substrate class 1 (LIM I, biodegradable materials) and substrate class 2 (LIM II, porous materials) after Sedlbauer (2001) with data from results of building materials after Viitanen et al. (2000), Clarke et al. (1998) and Hens (1999)

Moisture and Bio-Deterioration Risk of Building Materials and Structures 585

The mould growth maximum values set restrictions for the growth and limit the index to realistic levels. For the new set of materials the equation of the maximum mould index level

max 100 100

In this equation the coefficients A, B and C can have values that depend on the material class. The new Mmax has an effect on the factor k2 (Equation 3) and it contributes to the simulation results. Table 4 presents the maximum levels of mould index values for different materials under different conditions. These results were classified to material sensitivity groups, presented both for growth intensities and maximum mould index levels. Table 3 gives the values for the growth intensity parameter k1 classes and for the coefficients of the maximum mould index factors Mmax and k2. The factor RHmin represents the minimum

= +⋅ −⋅⎜ ⎟ − − ⎝ ⎠

*RH RH RH RH M AB <sup>C</sup> RH RH*

*crit crit crit crit*

 **k1 k2 (Mmax) RHmin**

**Sensitivity class M<1 M≥1 A B C %**  very sensitive, vs 1 2 1 7 2 80 sensitive, s 0.578 0.386 0.3 6 1 80 medium resistant, mr 0.072 0.097 0 5 1.5 85 resistant, r 0.033 0.014 0 3 1 85

Table 3. Parameters for the sensitivity classes of the updated mould model (Ojanen et al

Table 4. Mould growth sensitivity classes and some corresponding materials in the research. The figure in table illustrates the predicted mould growth for the established sensitivity

13

20

26

33

40

46

53

59

Time [weeks]

66

73

79

86

92

99

very sensitive sensitive medium resistant resistant

106

112

119

classes for constant conditions at 97 % RH and 22 C (Viitanen et al 2011)

0

0

7

1

2

3

Mould Index

4

5

6

− − ⎛ ⎞

2

(7)

was written in form shown in equation 7 (Ojanen et al 2010, Viitanen et al 2011a):

humidity level for starting mould growth for each material group.

2010, Viitanen et al 2011a)

**class Materials** 

sensitive Pine sapwood

Resistant PUR polished

Glued wooden boards, PUR (paper surface), spruce

Concrete, aerated and cellular concrete, glass wool, polyester wool

surface

**Sensitivity** 

Very

Sensitive

Medium resistant

The first version of the mould growth model was based on large laboratory studies with pine sapwood (Viitanen and Ritschkoff 1989). The mould growth intensities were determined at the constant conditions. In the later stages, studies in varied and fluctuated humidity conditions were performed and based on these studies, mould growth model (equation 1) was presented by Hukka and Viitanen 1999.

$$\frac{dM}{dt} = \frac{1}{7 \cdot \exp(-0.68 \ln T - 13.9 \ln RH + 0.14W - 0.33SQ + 66.02)} k\_1 k\_2 \tag{1}$$

where the factor *k1* represents the intensity of growth (Equation 3), W is the timber species (0 = pine and 1 = spruce) and SQ is the term for surface quality (SQ = 0 for sawn surface, SQ = 1 for kiln dried quality) based on Hukka and Viitanen (1999).

For other materials than wood the value SQ = 0 is used, which omits this factor. Numerical simulation is typically carried out using one hour time steps (climate data intervals) and hours are used in the equations instead of days.

$$k\_1 = \begin{cases} 1 & \text{when } M \le 1\\ \frac{2}{t\_{M=3} \sqrt{\frac{t\_{M=1} - 1}{t\_{M=1} - 1}}} & \text{when } M > 1 \end{cases} \tag{2}$$

In the equation, the factor tM=1 is the time needed to start of the growth (M = 1, Table 2), and tM=3 the time needed to reach the level M =3. The factor k2 (Equation 3) represents the moderation of the growth intensity when the mould index (M) level approaches the maximum peak value in the range of 4 < M < 6.

$$k\_2 = \max\left[1 - \exp\left[2.3 \cdot \left(M - M\_{\text{max}}\right)\right], 0\right] \tag{3}$$

where the maximum mould index Mmax level depends on the current conditions (Equation 4):

$$M\_{\text{max}} = 1 + 7 \cdot \frac{RH\_{crit} - RH}{RH\_{crit} - 100} - 2 \cdot \left(\frac{RH\_{crit} - RH}{RH\_{crit} - 100}\right)^2 \tag{4}$$

In Equation 4 RHcrit is the limit RH level to start the mould growth (Viitanen et al 2011a). For other materials than wood, the model has to be modified. The new mould growth intensity factors are presented as relative values compared to those of the reference material pine by using Equations (5) and (6).

$$k\_1 = \frac{t\_{M=1, prime}}{t\_{M=1}} \text{ when } \mathbf{M} \le \mathbf{1} \tag{5}$$

$$k\_1 = 2 \cdot \frac{\left(t\_{M=3, prime} - t\_{M=1, prime}\right)}{t\_{M=3} - t\_{M=1}} \text{ when } \mathbf{M} \ge 1 \tag{6}$$

where tM=1 is the time needed for the material to start the growth (Mould index reaches level M = 1), and tM=3 the time needed for the material to reach level M =3. The subscript pine refers to the value with the reference material pine.

The first version of the mould growth model was based on large laboratory studies with pine sapwood (Viitanen and Ritschkoff 1989). The mould growth intensities were determined at the constant conditions. In the later stages, studies in varied and fluctuated humidity conditions were performed and based on these studies, mould growth model

> 1 7 exp( 0.68ln 13.9ln 0.14 0.33 66.02) *dM k k*

where the factor *k1* represents the intensity of growth (Equation 3), W is the timber species (0 = pine and 1 = spruce) and SQ is the term for surface quality (SQ = 0 for sawn surface, SQ =

For other materials than wood the value SQ = 0 is used, which omits this factor. Numerical simulation is typically carried out using one hour time steps (climate data intervals) and

1 when 1

⎪⎪ <sup>=</sup> <sup>⎨</sup> <sup>&</sup>gt; <sup>⎪</sup> <sup>−</sup> ⎪⎩

In the equation, the factor tM=1 is the time needed to start of the growth (M = 1, Table 2), and tM=3 the time needed to reach the level M =3. The factor k2 (Equation 3) represents the moderation of the growth intensity when the mould index (M) level approaches the

where the maximum mould index Mmax level depends on the current conditions (Equation

*RH RH RH RH <sup>M</sup> RH RH*

In Equation 4 RHcrit is the limit RH level to start the mould growth (Viitanen et al 2011a). For other materials than wood, the model has to be modified. The new mould growth intensity factors are presented as relative values compared to those of the reference material

1,

*t k*

*t* = =

*t t*

*t t* = = = =

1 *M pine M*

( 3, 1, )

3 1 <sup>2</sup> *M pine M pine M M*

where tM=1 is the time needed for the material to start the growth (Mould index reaches level M = 1), and tM=3 the time needed for the material to reach level M =3. The subscript pine refers

1

1

*k*

to the value with the reference material pine.

2 when 1

*M*

2 m max 1 exp 2.3 ( ) ax *k M* = − ⋅− <sup>⎡</sup> ⎡ ⎤ *<sup>M</sup>* ,0<sup>⎤</sup> <sup>⎣</sup> ⎣ ⎦ <sup>⎦</sup> (3)

100 100

− − ⎛ ⎞

*crit crit crit crit*

=+⋅ −⋅⎜ ⎟ − − ⎝ ⎠

2

= when M < 1 (5)

<sup>−</sup> = ⋅ <sup>−</sup> when M ≥ 1 (6)

*dt T RH W SQ* <sup>=</sup> ⋅− − + − +

1 2

(2)

(4)

(1)

(equation 1) was presented by Hukka and Viitanen 1999.

1 for kiln dried quality) based on Hukka and Viitanen (1999).

1

3

*t* = =

max 1 7 2

1

*<sup>k</sup> <sup>M</sup> <sup>t</sup>*

⎧ ≤

*<sup>M</sup>* 1 *M*

hours are used in the equations instead of days.

maximum peak value in the range of 4 < M < 6.

pine by using Equations (5) and (6).

4):

The mould growth maximum values set restrictions for the growth and limit the index to realistic levels. For the new set of materials the equation of the maximum mould index level was written in form shown in equation 7 (Ojanen et al 2010, Viitanen et al 2011a):

$$M\_{\text{max}} = A + B \cdot \frac{RH\_{crit} - RH}{RH\_{crit} - 100} - C \cdot \left(\frac{RH\_{crit} - RH}{RH\_{crit} - 100}\right)^2 \tag{7}$$

In this equation the coefficients A, B and C can have values that depend on the material class. The new Mmax has an effect on the factor k2 (Equation 3) and it contributes to the simulation results. Table 4 presents the maximum levels of mould index values for different materials under different conditions. These results were classified to material sensitivity groups, presented both for growth intensities and maximum mould index levels. Table 3 gives the values for the growth intensity parameter k1 classes and for the coefficients of the maximum mould index factors Mmax and k2. The factor RHmin represents the minimum humidity level for starting mould growth for each material group.


Table 3. Parameters for the sensitivity classes of the updated mould model (Ojanen et al 2010, Viitanen et al 2011a)

Table 4. Mould growth sensitivity classes and some corresponding materials in the research. The figure in table illustrates the predicted mould growth for the established sensitivity classes for constant conditions at 97 % RH and 22 C (Viitanen et al 2011)

Moisture and Bio-Deterioration Risk of Building Materials and Structures 587

on the decline process. The decline of mould index for other materials was presented using a

<sup>0</sup> *mat mat dM dM <sup>C</sup>*

where (dM/dt)mat is the mould decline intensity for each material, (dM/dt)0 is that for pine in the original model (Equation 9), and Cmat is the relative coefficient for mould index decline used in the simulation model. The original decline model for wood could be applied

The relative decline of mould for different materials was determined using laboratory experiments with walls (Ojanen et al 2010). The temperature and relative humidity conditions on the critical boundary layer between two different materials were monitored continuously. The mould index level of the material surfaces was determined with suitable intervals by opening the structure from three different parts. The experimental target

These experimental walls had mould growth after the first warm and humid period ('Summer/autumn'). The mould decline was determined by the change of the mould index during the second period, a four month long 'Winter' period causing freezing temperatures at the critical boundary. The mould index values were determined for both material surfaces on each critical interface. Figure 11 presents the relative mould decline values (Cmat) solved from the observations in the experiments. The results include the detected mean, minimum

Stage **1 2 3 4** 

Time, months 7 4 6 12

Temperature °C 27 … 18 -5 … +3 2 … 10 20 … 24

The decline of mould intensity on different materials under unfavourable mould growth conditions could be presented as decline classes (Table 6). This classification is based on few measurements with relatively large scattering and it should be considered as the first approximation of these classes. It was found, that the decline was larger within wood

> 1.0 Pine in original model, short periods 0.5 Significant Relevant decline 0.25 Relatively low decline 0.1 Almost no decline

Table 5. Exposure conditions during the wall assemble test (Ojanen et al 2010)

**Ceff Description** 

Table 6. Classification of relative mould index decline (Ojanen et al 2010)

Season Summer/autumn Winter Spring High exposure

RH % 80 … 100 92 … 100 60 … 95 94 … 100

*dt dt* = ⋅ (9)

constant, relative coefficient for each material (Equation 9).

using these additional factors (Ojanen et al 2010, Viitanen et al 2011a).

conditions at the interface of the two materials are presented in Table 5.

and maximum mould index values.

The factors presented in Table 3 form the new basis for numerical simulation of mould growth on different material surfaces. These values will be applied in the following studies where the model performance will be evaluated.

Table 4 represents the tested materials, whose resulting mould indexes were used for the determination of k1 for the respective classes. The k1 classes were determined by using expert estimation for most suitable values.

#### **3.2 Decline of the mould growth and mould index caused by frost or dry condition**

As living organisms mould fungi need water and suitable temperature to grow. When conditions are unfavourable for fungi, activity of mould fungi will be inactivated depending on the extent of the frost or dryness and the time periods of unfavourable conditions. In Figure 4, the humidity and temperature conditions of microclimate for the favourable and unfavourable conditions for mould growth is shown. The rate of humidity and temperature and the time periods in favourable and unfavourable conditions will affect on the growth rate of mould. Especially the longer periods in low humidity or temperature will cause decline of the mould growth and development and even the decline of mould index.

Fig. 4. Illustration of the regimes for the favourable and unfavourable conditions for mould growth (Viitanen et al 2011a)

The decline of mould growth on wooden surface has been modelled based on cyclic changes between two humidity conditions (Equation 8). The decline of mould index under different fluctuating conditions is modelled and shown in the figure 2.

$$\frac{dM}{dt} = \begin{cases} -0.00133, \text{when } t \cdot t\_1 \le 6 \text{ h} \\ 0, \text{when } 6 \text{ h} \le t - t\_1 \le 24 \text{ h} \\ -0.000667, \text{when } t \text{-} t\_1 > 24 \text{ h} \end{cases} \tag{8}$$

where M is the mould index and t is the time (h) from the moment *t1* when the conditions on the critical surface changed from growth to outside growth conditions (Hukka and Viitanen 1999).

Under long period seasonal variations of humidity conditions the decline of mould index may differ from that presented in Equation 8. Also the material may have a significant effect

The factors presented in Table 3 form the new basis for numerical simulation of mould growth on different material surfaces. These values will be applied in the following studies

Table 4 represents the tested materials, whose resulting mould indexes were used for the determination of k1 for the respective classes. The k1 classes were determined by using

**3.2 Decline of the mould growth and mould index caused by frost or dry condition**  As living organisms mould fungi need water and suitable temperature to grow. When conditions are unfavourable for fungi, activity of mould fungi will be inactivated depending on the extent of the frost or dryness and the time periods of unfavourable conditions. In Figure 4, the humidity and temperature conditions of microclimate for the favourable and unfavourable conditions for mould growth is shown. The rate of humidity and temperature and the time periods in favourable and unfavourable conditions will affect on the growth rate of mould. Especially the longer periods in low humidity or temperature will cause

decline of the mould growth and development and even the decline of mould index.

Fig. 4. Illustration of the regimes for the favourable and unfavourable conditions for mould

**-15 -10 -5 0 5 10 15 20 25 30 35 T, <sup>o</sup> C**

**-15 -10 -5 0 5 10 15 20 25 30 35 T, <sup>o</sup> C**

The decline of mould growth on wooden surface has been modelled based on cyclic changes between two humidity conditions (Equation 8). The decline of mould index under different

> ⎧− ≤ <sup>⎪</sup> <sup>=</sup> <sup>⎨</sup> <sup>≤</sup> − ≤ ⎪− > <sup>⎩</sup>

where M is the mould index and t is the time (h) from the moment *t1* when the conditions on the critical surface changed from growth to outside growth conditions (Hukka and

Under long period seasonal variations of humidity conditions the decline of mould index may differ from that presented in Equation 8. Also the material may have a significant effect

*dM hen t t*

0.00133,when - 6 h 0,w 6 h 24 h 0.000667,when - 24 h

1 1 1

**Mould growth conditions**

*Critical RH curve*

(8)

*t t*

*t t*

fluctuating conditions is modelled and shown in the figure 2.

**No mould growth Decline of mould index**

*dt*

where the model performance will be evaluated.

expert estimation for most suitable values.

growth (Viitanen et al 2011a)

**70**

**90 95 100**

**% RH**

**% RH**

Viitanen 1999).

on the decline process. The decline of mould index for other materials was presented using a constant, relative coefficient for each material (Equation 9).

$$\frac{dM}{dt}\_{\text{mat}} = \mathbb{C}\_{\text{mat}} \cdot \frac{dM}{dt}\_{\text{oc}} \tag{9}$$

where (dM/dt)mat is the mould decline intensity for each material, (dM/dt)0 is that for pine in the original model (Equation 9), and Cmat is the relative coefficient for mould index decline used in the simulation model. The original decline model for wood could be applied using these additional factors (Ojanen et al 2010, Viitanen et al 2011a).

The relative decline of mould for different materials was determined using laboratory experiments with walls (Ojanen et al 2010). The temperature and relative humidity conditions on the critical boundary layer between two different materials were monitored continuously. The mould index level of the material surfaces was determined with suitable intervals by opening the structure from three different parts. The experimental target conditions at the interface of the two materials are presented in Table 5.

These experimental walls had mould growth after the first warm and humid period ('Summer/autumn'). The mould decline was determined by the change of the mould index during the second period, a four month long 'Winter' period causing freezing temperatures at the critical boundary. The mould index values were determined for both material surfaces on each critical interface. Figure 11 presents the relative mould decline values (Cmat) solved from the observations in the experiments. The results include the detected mean, minimum and maximum mould index values.


Table 5. Exposure conditions during the wall assemble test (Ojanen et al 2010)

The decline of mould intensity on different materials under unfavourable mould growth conditions could be presented as decline classes (Table 6). This classification is based on few measurements with relatively large scattering and it should be considered as the first approximation of these classes. It was found, that the decline was larger within wood


Table 6. Classification of relative mould index decline (Ojanen et al 2010)

Moisture and Bio-Deterioration Risk of Building Materials and Structures 589

This is termed as α parameter, which is initially 0 and gradually grows depending on the air conditions to a limit value of 1. This process is able to recover in favourable conditions (dry

This occurs when the activation process has fully developed (α=1) otherwise it does not

These processes only occur when the temperature is 0..30 °C and the relative humidity is 95% or above. Outside these condition bounds, the activation process may recover, but the mass loss process is simply stopped. The activation process is as given in Equation 2. The recovery time (i.e. α recovers from a value of 1 back to 0) is assumed to be 17520 hours (2 years). Recovery takes place when the conditions are outside the bounds of the decay

The model can be used for evaluation the exposure condition for the eventual risk of decay to develop. For example, recorded temperatures and relative humidity are given for the Helsinki area. This climate is shown in the figure 1 for a one year period. According to the model, this climate seems to induce a low mass loss of 1.1 % in 4 years (Figures 4 and 5). During the first year, no decay development will occur in untreated pine sapwood. After 3 and 4 years exposure, decay is expected to occur only to a very limited extent in the surface of unprotected pine sapwood. Under normal use conditions, the cladding is protected by paints or other coatings. The direct influence of water on the wood surface is very small, and

or (in favorable conditions of decay) ( ,)

2.3 0.035 0.024 ( ,) 30 24 [hours] 42.0 0.14 0.45

⎡ ⎤ + −× <sup>=</sup> <sup>×</sup> <sup>×</sup> ⎢ ⎥ ⎣ ⎦ −+ +

The mass loss process proceeds the activation process, when α has reached 1(Eq. 11).

*T RH*

24 4

−− −

( ,) 5.96 10 1.96 10 6.25 10 [% / ]

*ML RH T T RH hour*

For advanced decay to develop, a significantly longer period is needed, and after a 10 years period, severe decay in unprotected and uncovered pine sapwood can be expected in the Helsinki area. The design of details has a strongly marked effect on the durability and

*dt dt*

⎛ ⎞ ′ <sup>=</sup> <sup>=</sup> ⎜ ⎟ × Δ ⎝ ⎠

=− × + × + ×

α

(10)

(11)

air) at a given rate (although no experimental evidence of recovery is available).

decay development will be significantly retarded or even negligible.

α

=

*T RH T RH t RH T*

1 1

= =

α

*t t*

′ ′

∫ ∑

*t at t at*

( ,) ( ,) ( )

*ML RH T ML RH T ML t dt <sup>t</sup>*

≥

0 0

*t t RH T*

Massloss process when 1

α

*crit*

*t d*

<sup>Δ</sup> Δ =

*crit*

*dt*

α

*t t*

= = Δ

∫ ∑

ααα

Activation process 0..1

( ) ( ) , where

*a) Activation process:* 

*b) Mass loss process:* 

growth.

occur. This process is naturally irrecoverable.
