Research Article

Building Thermal, Lighting,

and Acoustics Modeling

E-mail: hsaito@ashitech.ac.jp

Integration model of hygrothermal analysis with decay process for durability assessment of building envelopes

Hiroaki Saito1 (), Kiyoharu Fukuda2, Takao Sawachi3

1. Ashikaga Institute of Technology, Division of Architecture and Civil Engineering, 268-1, Ohmae-Cho Ashikaga-City Tochigi-Pre. 326-8558, Japan 2. Tokyo University of Agriculture and Technology, Faculty of Agriculture, 3-5-8 Saiwaicho, Fuchu, Tokyo, 183-8509, Japan 3. Building Research Institute, Department of Environmental Engineering, 1 Tachihara, Tsukuba, Ibaraki, 305-0802, Japan Abstract In this study a numerical simulation model that integrates hygrothermal analysis with the decaying process of wood structures caused by moisture accumulation is presented. This simulation model can quantitatively predict both hygrothermal conditions within the building envelopes and the progress of decay in wood structures under variable conditions. The following are characteristics of the simulation model used in this study: (1) the development of wood decay represented by a differential equation with a variable of mass loss of wood substance and (2) the addition into moisture balance equations of biochemical reactions within wood decay. Hence, the simulation model enables assessment of the long-term performance of building envelopes with regard to both durability and drying potential. Rate constants of the wood decay and a coefficient of the moisture production for the model were determined by the mass loss data of small wood samples in decay tests using Fomitopsis palustris, a brown rot fungus. Additionally, numerical simulations using the model were implemented to understand both the decaying process and moisture accumulation within building envelopes. The results numerically demonstrated important phenomenon that the moisture production by biochemical reactions of wood decay helps to maintain the decaying process.

Keywords building envelope,

hygrothermal analysis,

durability assessment,

wood decay,

biochemical reaction Article History Received: 29 June 2011

Revised: 7 March 2012

Accepted: 26 March 2012 © Tsinghua University Press and

Springer-Verlag Berlin Heidelberg

2012

1 Introduction

Moisture accumulation within the building envelopes of wood-frame construction significantly affects problems related to durability such as decay, mould, and termites. To avoid these types of moisture-related damage, various building components and wood preservatives have recently been developed and applied in the construction process. However, corrosion of metal fasteners embedded in preservative-treated wood is a significant durability problem in terms of assurance of structural resistance (Zelinka et al. 2011). It follows therefore, that appropriate moisture control design in building envelopes is desirable to better ensure durable structures and to extend the service life of wooden products.

To ensure the appropriate moisture control design, advanced hygrothermal analysis models that can accurately

predict temperature and moisture behavior within building envelopes have been developed (Hens 1996). Nofal and Kumaran (1999, 2011) proposed a unique durability assessment system that links the hygrothermal analysis model with biological damage models. Viitanen et al. (2010) also proposed an empirical model for wood decay development incorporated into the hygrothermal analysis. These models can also calculate the extent of long-term deterioration of material properties caused by wood rot fungi and/or mould fungi under various climate conditions. Similarly, Krus and Sedlbauer (2005) implemented damage analysis and linked the hygrothermal model with the damage predictions. In these models, the calculated temperature and moisture profiles are applied to a prediction of the extent of biological damage.

However, these studies did not completely simulate the decaying process of wood in terms of the moisture balance.

BUILD SIMUL (2012) 5: 315–324 DOI 10.1007/s12273-012-0081-8

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Wood rot fungi that can degrade cellulose (e.g., Sepula lacrymans and Coniophora puteana) generally produce non- negligible moisture through the decaying process. Hence decay persists even though the relative humidity of the surrounding air may be below the saturation point (Zabel and Morrell 1992; Hannu and Viitanen 1997). The impact of this moisture production on the decaying process needs to be verified to enhance the relative safety of wood construction. With these considerations in mind, the current study proposes a durability assessment model that integrates hygrothermal analysis with biochemical reactions related to the moisture production on the decaying process.

The first part of this study focuses on modeling the progression of wood decay and describes the governing equations associated with the moisture production. Coefficients related to the progression of the wood decay and the moisture production are defined. In the second part, wood decay tests with small wood samples are conducted in a laboratory. The coefficients for the wood decay model are determined by the experimental data of the decay tests. Finally, in the third part, numerical simulations using the wood decay model are implemented to assess the impact of the moisture production on the decaying process.

2 Modeling of the wood decay process with moisture transfer

2.1 Assumption of the proposed model

Wood rot fungi degrade cellulose within the wood through enzymatic reactions, and produce both H2O and CO2 through this degradation. This process consists of two biochemical reactions, hydrolysis and aerobic degradation. Both the biochemical reactions and moisture transfer occur simultaneously within the decayed wood, as shown in Fig. 1. In this study, these phenomena are expressed as a numerical simulation model relating to mass loss and moisture content of the wood. Additionally, we define a rate constant

determined by experiments in order to predict the mass loss on the basis of a deterministic non-structural model. In this study, the wood decay model is developed under the following assumptions: (1) The hygrothermal properties such as moisture con-

ductivity are stable before and after the wood decays. (2) The extent of mass loss is directly correlated with the

amount of moisture produced by biochemical reactions. (3) The impacts of both O2 and CO2 concentrations on wood

decay can be neglected. (4) The impacts of different types of wood and fungus species

are presented using experimental coefficients. (5) Wood rot fungus does not conduct liquid water from

other sources over long distances (e.g., soil of crawl space), and does not control actively the microclimate.

(6) Initial response time for decay to begin after critical relative humidity has been exceeded is neglected.

2.2 Progression of wood decay

The proposed wood decay model supposes that the pro- gression of mass loss is determined by hygrothermal conditions such as temperature and relative humidity at a control volume for finite difference analysis. Mass loss by wood decay is defined as follows:

n d

n

m mLm-

= (1)

where L is the mass loss by wood decay (—), mn is the mass of the wood before the decay process begins (kg), and md is the mass of the wood after the decay process (kg).

Wood rot fungi need liquid water to effect mass loss through biochemical reactions. Thus, mass loss on the surface node of the wood occurs where the relative humidity is above the critical relative humidity c (%RH) in Eq. (2). Furthermore, Eq. (3) is applied to the progression of mass loss at the inner node because grown hypha needs to reach

Fig. 1 Scheme for wood decay and moisture transfer within the wood substance

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this node for the decaying process to begin:

m c0

d ( ) ( )d i

x

L k θ φ φt =

= ≥ (2)

≥m 1 1 c0

d ( ) ( or 0, )d i i i

x

L k θ L L φ φt - +>

= > (3)

where t is the time (s), i is the relative humidity (% RH) at node i,c is the critical relative humidity for the beginning of the wood decay (% RH), km is the rate constant for mass loss to determine decaying rate (1/s). Since Zabel and Morrell (1992) and Hannu and Viitanen (1997) indicated that temperature significantly affects the decaying rate, the rate constant is defined as a function of temperature (℃). Several factors such as wood species, fiber directions and hygrothermal conditions might similarly have impacts on the decaying rate. Hence the rate constants in this model should be determined by decay tests in various conditions.

The concentration of the hyphae in each node may affect the rate constant for mass loss. Gooding et al. (1966) pointed out that the growth rate of the hyphae within the wood material is several millimeters per day. Thus, this model assumes that the hyphae concentration has already been uniformed within node i when the mass loss of node i+1 or i–1 begins.

2.3 Heat and moisture balance in decayed wood material

Heat and moisture balance coupling the moisture production by the biochemical reactions are presented by Eqs. (4) and (5). The heat of the biochemical reactions is neglected in Eq. (4), and the third term on the right side of Eq. (5) corresponds to the moisture production:

( ){ } m Tg μgTρ c r T r μt= + + ' (4)

( ) w μ T L

μρ μ T Wμ t

= + +' ' (5)

where mis the material density (kg/m3), T is the Kelvin temperature (K), c is the material specific heat (J/kg), is the thermal conductivity (W/(m·K)), r is the latent heat of moisture (J/kg), Tg is the moisture conductivity in the gaseous phase related to temperature gradient (kg/(m·s·K)), g is the moisture conductivity in the gaseous phase related to the water chemical potential gradient (kg/(m·s·(J/kg))), wis the density of liquid water (kg/m3), is the moisture content per volume of material (m3/m3), is the water chemical potential (J/kg), is the moisture conductivity in the gaseous and liquid phase related to the water chemical potential gradient (kg/(m·s·(J/kg))), T is the moisture

conductivity in the gaseous and liquid phase related to temperature gradient (kg/(m·s·K)), and WL is the decay moisture production rate (kg/(s·m3)).

Since this model assumes that the extent of mass loss is directly correlated with the amount of moisture produced, the moisture product ratio h (—) that corresponds to the relation between the mass loss and the moisture produced can be defined as follows:

dd

hL

= (6)

The moisture product ratio h cannot be determined from the reaction formulae of the biochemical reactions for the decaying process because the quantitative details of the metabolism of wood rot fungi within the wood substance are uncertain. However, the decay moisture production rate is expressed as Eq. (7), where the moisture product ratio can be determined experimentally:

L wddLW hρt

= (7)

3 Determination of coefficients for the model

Wood decay tests under sterile conditions in a laboratory were conducted to determine the rate constants for mass loss and the moisture product ratio. In general standardized wood decay tests such as EN 113 (1991) and JIS K 1571 (2004), the test samples are exposed on the surface of active agar colony of a fungus. However, consideration of the moisture balance in the test samples is difficult when employing these standardized test methods because the mycelium of the fungus keeps supplying moisture and nutrition to the test samples through the agar medium. Therefore, the decay tests in this study were conducted in plastic dishes without agar medium. Additionally, the relative humidity levels in the plastic dishes were adjusted by saturated salt solutions.

3.1 Outline of experiments

The test samples for the decay tests (40 mm × 20 mm × 5 mm) were cut from the outer part of the sapwood of Pinus densiflora (wood species: Japanese red pine), which is classified as a non-durable species with regard to fungus attack. A brown rot fungus, Fomitopsis palustris, was used as a test fungus because it showed less dispersion in the decay tests and is also employed as a test fungus in JIS K 1571 (2004). Before the start of the decay tests, dry weights of the test samples were measured at 105℃. After the test fungus was grown on the agar medium for 2 weeks, inoculations of the test fungus were made through resin mesh on the mycelium (Fig. 2). The resin mesh was used to ensure that

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Fig. 2 Inoculation of fungus to test samples on mycelium

there was no direct contact between the test samples and the agar medium. The inoculated test samples were transferred to the plastic dishes after the mycelium on the surface of the samples was observed through a microscope. Furthermore, the plastic dishes with the test samples were incubated at temperatures between 5 and 40℃.

During incubation, the relative humidity in the plastic dishes was controlled by the saturated salt solutions (Fig. 3). These inoculation processes were performed under sterile conditions. Exposure conditions for the decay tests are shown in Table 1. The mass loss and the moisture contents of the test samples were determined by weighting and drying after the exposure times specified in Table 1.

Fig. 3 Test samples in plastic dish in which relative humidity levels were adjusted by saturated salt solutions

Table 1 The exposure conditions and details regarding the decay tests

Temperature (℃) Humidity (%RH) Exposure time (month) Number of replications Initial moisture contents

(kg/kg)

5, 10, 20, 30, 40 93[KNO3]*, 97[K2SO4], 100[distilled water] 1, 2, 3, 6, 9, 12 (12 is only 100%RH) 5 (summation of samples: 475) 0.25 (average of 10 replications after

inoculation)

*[ ] means employed saturated salt solutions.

3.2 Time-dependent change of mass loss and moisture content

According to the results of the decay tests at 100%RH (Fig. 4(a)), the mass loss reached approximately 0.4 by 12 months at 20 and 30℃. Although the extent of the mass loss at 5 and 15℃ was less than at 20℃, the activity of the fungus

and the mass loss could be clearly detected after 6 months. On the other hand, no decay was detected at 97%RH or below at any temperature (Fig. 4 (b)). The initial moisture contents of the test samples after the inoculation were approximately 0.25 kg/kg. These results indicate that the decaying process does not progress without liquid water within the micro-pore of the wood (i.e., the moisture content reaches fiber saturation point).

Figure 5 shows the comparison of other tests with regard to the temperature dependence of the mass loss after 2 months exposure. Although the temperature dependence in this experiment is similar those of other tests performed at 28℃ (Suzuki 1994; Fukuda et al. 1981), Suzuki’s results using test samples that were exposed on agar medium show values that are three times greater than in this study. It is conceivable that differences between Suzuki’s and our results were caused by the agar medium supplying nutrition to the test samples. However, the mycelium on wood structures of current dwelling houses cannot get such nutrition if it cannot reach the soil around the foundation. Hence, it can be asserted that the results obtained without the agar medium more accurately reflect actual exposure conditions within building envelopes.

Fig. 4 Time-dependent change of mass loss of test samples in (a) 100%RH and (b) 97%RH (average and standard deviation)

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Fig. 5 Comparison of temperature dependence of the mass loss after 2 months exposure in 100%RH (white dots are the quoted value from references)

3.3 Determination of the moisture product ratio

The moisture product ratio was determined by the relation between the mass loss and the moisture contents of the test samples. Figure 6 shows the time-dependent change of

Fig. 6 Time-dependent change of moisture contents of test samples in (a) 100%RH and (b) 97%RH (average and standard deviation)

moisture contents at 100%RH and 97%RH. The gradients of the moisture contents in Fig. 6(a) are similar to those of the mass loss in Fig. 4(a). The differences in the gradients can be regarded as the amount of moisture produced by biochemical reactions, where the moisture evaporation from the test samples is neglected at 100%RH. Consequently, the moisture product ratio h could be determined to be 0.319 by considering the relationship between the mass loss and the moisture content by volume (Fig. 7). The coefficient of determination of regression analysis (R2) was larger than 0.7.

Fig. 7 Relation between mass loss and moisture contents for all test samples in 100%RH

3.4 Determination of the rate constant for mass loss

The rate constant for mass loss was determined by linear regression analysis of the time-dependent change of the mass loss in each temperature condition shown in Fig. 4(a). A regression curve (Fig. 8) shows the relation between the determined rate constants for mass loss and the temperature at 100%RH. The empirical formula for the rate constants for mass loss is given by Eq. (8). The mass loss was predicted using this equation and experimental conditions. Figure 9 shows a good correlation between the predicted values

Fig. 8 Relation between the determined rate constants and temperature at 100%RH

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Fig. 9 Relation between measured and predicted value in 100%RH

and the measured values of the mass loss against all the test samples. The coefficient of determination of the regression analysis (R2) was larger than 0.85.

2 3m ( ) 2.77 3.23 0.865 0.0189k θ θ θ θ= - + - (8)

4 Analysis for wood decay process considering moisture balance

4.1 Outline of the analysis

To better understand the wood decay process, numerical simulations under stable and dynamic conditions with climate data were performed. The wood decay model was applied to a wood structural board (Pinus densiflora) and an multi- layer wall, as shown in Fig. 10. The numerical simulations employed Eqs. (2) through (7) assumed one-dimensional heat and moisture flows in finite differential approximations. The initial response time, or the time taken for the wood decay

to begin after reaching the critical relative humidity (Nofal and kumaran 1999), was neglected.

Viitanen (1997) indicated that wood decay can progress even under fiber saturation point, and that the decay rate depends on moisture content on the basis of decay tests with Coniophora puteana. However, our experimental results with Fomitopsis palustris at 97%RH in Fig. 4(b) could not provide enough evidence for the decay rate and the critical relative humidity under fiber saturation point. Although the reason for differences between these results was supposed to be experimental methods such as inoculation procedure and fungus species, this issue is not discussed in this paper as it is the subject of the future study. Thus the critical relative humidity in the following analyses was set at 98%RH equivalent to the fiber saturation point, on the basis of conventional knowledge that the enzyme process needs free water (Zebel and Morrell 1992). Also Eq. (8) was applied to the decay rate as a function of temperature when relative humidity of a calculation node exceeds the critical relative humidity.

Table 2 shows the calculation conditions. In Cases 1 and 2, wood structural board with a thickness of 50 mm was used under stable boundary conditions. In addition, both condensation and evaporation processes were set in train to clarify the impact of moisture production on moisture accumulation. The initial moisture content of the wood structural board was set at 0.2 kg/kg (Case 1) and 0.3 kg/kg (Case 2) respectively. Although the surface coefficient of moisture transfer at the indoor side was kept constant at 1.54´10–7 kg/(m2·s·Pa), the coefficient at the outdoor side was assumed impermeable.

In Case 3, a multilayer wall was used to examine long- term variations in wood decay using climate data of Osaka (Latitude: 34°41' , Longitude: 135°31' ) and Sapporo (Latitude: 43°02' , Longitude: 135°10' ) of Japan as boundary conditions. While the R-value of this wall complies with current energy guidelines in Japan, the vapor retarder for the multi-layer

Fig. 10 Cross-section of (a) wood structural board and (b) multi-layer wall

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wall was removed intentionally so as to ensure continuing decay by moisture condensation. Similarly, the initial moisture content of the wood structural board was set at 0.66 kg/kg. The moisture properties of the building components (Kumaran et al. 2002) are shown in Fig. 11. Equation (9) shows the indoor temperature for Case 3:

[ ]r 25.0 5.0cos 2π(DAY 212)/365θ = + - (9)

where r is the indoor temperature (℃) and DAY is the number of days from January 1.

Fig. 11 (a) Moisture diffusivity and (b) sorption curve of building materials (Kumaran et al. 2002)

4.2 Results and discussion

4.2.1 Sensitivity analysis (Cases 1 and 2)

The distribution of moisture contents within the wood structural board are shown in Fig. 12. The impact of moisture production on the moisture accumulation and mass loss can be observed from the internal layer of Case 1. According to the sorption curve of Pinus densiflora in Fig. 11, the moisture content never exceeds approximately 0.3 kg/kg, even though an equilibrium state was reached at 98.5%RH. However, the moisture content reached 0.37 kg/kg after 12 months because of the moisture produced by the biochemical reactions.

It should also be noted that significant differences of the moisture contents at the internal layer can be observed on the evaporation process (Case 2). These results suggest that the quantity of moisture produced within the wood exceeded the quantity of moisture evaporated on the surface. In this case, the decay process at the internal layer can be continued even if relative humidity of the surrounding air decreases below the critical relative humidity. Therefore, the addition of the decay moisture production rate WL to the moisture balance equations is significant in terms of predicting the extent of the wood decay.

4.2.2 Long-term variation (Case 3)

In order to understand the long-term decaying process, the long-term variations in the mass loss and the moisture contents are presented in Fig. 13 and Fig. 14, respectively. While the mass loss at the surface node of the wood structural board (i.e., 0 mm) slightly increased in the mid winter of Osaka (Fig. 13(a)), those in Sapporo (Fig. 13(b)) seem to hardly increase in this period. The mass loss in Osaka was accelerated in the spring rather than in the mid winter because of the temperature dependence of the rate constant for mass loss (see Eq. (8) and Fig. 8). Significance in these results is that the wood decay at the inner node of the wood structural board progressed for a few months, after the moisture contents at the surface node decreased. Hence, in order to avoid serious damage of the wood decay, the

Table 2 Calculation conditions for wood decay analyses

Indoor Outdoor

Case T(℃) RH(%) T(℃) RH(%) Initial moisture content

w (kg/kg) Rate constant

km(1/s) Process

Case 1 98.5 — 0.2 Condensation

Case 2 20

75.0

20

20 — 0.3

1.30×10–8

1.30×10–8 Evaporation

Case 3 Eq. (9) 60 Climate data in Osaka and Sapporo, Japan

0.66 (= 99%RH) Eq. (8) Evaporation

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Fig. 12 Distributions of ((a) and (b)) the moisture content and ((c) and (d)) the mass loss under stable boundary conditions (Cases 1 and 2)

Fig. 13 Long-term variation for the mass loss of wood structural board in each depth at (a) Osaka and (b) Sapporo (Case 3)

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moisture contents of wood products need to be decreased below the critical relative humidity by the early spring.

As for the impact of moisture production on mass loss and moisture contents, the differences in the calculation condition against the moisture product appeared at the inner node of the wood structural board (e.g., 4 mm or 10 mm) rather than at the surface node (Fig. 13 and Fig. 14). Differences of the moisture contents reaches 0.1 kg/kg in the September at the depth of 4 mm (Fig. 14(a)). This result suggests that the quantity of moisture produced at the internal layer is greater than that removed by moisture diffusion.

5 Conclusions

A durability assessment model that integrates hygrothermal analysis with biochemical reactions related to the moisture production on the decaying process has been presented in detail. Moisture accumulation and the decaying process on wall assemblies considering climate data as boundary conditions were also analyzed.

The first part of this paper described modeling the progression of the wood decay associated with the moisture production in the decayed wood. The quantity of the moisture due to the biochemical reactions of wood decay was added into moisture balance equations. Two coefficients that were rate constant and moisture product ratio were defined for the differential equations: the rate constant corresponds to a time factor for decay development, and the moisture product ratio corresponds to the relation between the mass loss and the quantity of the moisture product. Secondly, these coefficients were determined by the wood decay tests under sterile conditions in a laboratory, with adequate correlation coefficient. Finally, in order to better

understand the impact of the production of moisture on the decaying process, numerical simulations for wood materials using the durability assessment model were performed and some important phenomena of the decayed wood were numerically demonstrated: the moisture content at the internal layer of the decayed

wood exceeds an equilibrium state of the surrounding air despite isothermal conditions;

the moisture production by biochemical reactions of the wood decay prolongs the decay process when the quantity of moisture evaporation on the surface is less than the production of moisture at the internal layer;

the wood decay caused by the internal condensation of an multi-layer wall is accelerated in the spring rather than in the mid winter because of the temperature’s dependence on the rate constant for mass loss.

This model should be experimentally verified under various conditions to further enhance its reliability. In particular, the impact of wood decay on hygrothermal properties should be experimentally verified, and further detailed information on growth conditions of wood rot fungi carried out to more accurately enhance durability assessment.

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Fig. 14 Long-term variation of the moisture contents of wood structural board in each depth (lines) and daily summation of decay moisture product (bars) at (a) Osaka and (b) Sapporo (Case 3)

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