The Significance of Using Temperature-Dependent Material Properties in Hygrothermal Performance Assessment of Exterior Wall Systems

Abstract

The reliability of hygrothermal models depends on the quality of their inputs. Conventionally, thermal and moisture properties are treated as temperature-independent, yet previous studies have shown that many of these properties are temperature-dependent. This paper investigates the impact of using temperature-dependent material properties on hygrothermal simulation results compared to standard temperature-independent properties at the building envelope level. A representative exterior wood-frame wall assembly is modelled with constant material properties, including water vapour permeability, sorption isotherm, and water absorption coefficient corresponding to values measured at 3 °C, 21 °C, and 45 °C, as well as a case in which the properties vary with temperature. The variation in hygrothermal response is evaluated under several scenarios, including different climates (Toronto and Vancouver, Canada), cladding types (fibre cement and stucco), sheathing materials (oriented strand board (OSB) and plywood), and with and without rain-penetration load. Results indicate that the variation attributed to temperature-dependent material properties was greater for Vancouver than for Toronto and increased with rain penetration. In particular, the choice of cladding seemed to have a greater impact than the choice of sheathing material, with stucco showing greater differences than fibre cement. Overall, however, the temperature at which material properties are defined has a minimal impact on hygrothermal simulation results and wall performance assessments, with maximum hourly differences in sheathing moisture content (MC) differences ranging from 1.18 to 4.32 wt% without rain penetration. These findings demonstrate that the use of temperature-dependent material properties does not have a significant impact on the hygrothermal simulation results or the performance assessment of exterior wood-frame wall assemblies.

1. Introduction

Buildings are exposed to randomly varying outdoor climatic conditions on the exterior and a relatively stable indoor climate in the interior. The building enclosure separating the outdoor and indoor environments is referred to as the building envelope. While the thermal load on the building envelope is determined by the combined effects of outdoor temperature, solar radiation, and long-wave radiation exchange between the surface, the surroundings, and the sky, the moisture load is related to the outdoor vapour pressure and the wind-driven rain on the surface. The difference in exterior and interior thermal and moisture loads (hygrothermal load) creates driving forces for heat and moisture transfer through the building envelope. The rate of heat and moisture transfer and storage in the building envelope, however, is dictated by the thermal and moisture transport and storage properties of the envelope materials. Researchers and industry practitioners utilize hygrothermal models (WUFI [1], HygIRC [2], DELPHIN [3], HAMFit [4], etc.) to simulate heat and moisture transfer and assess the durability and energy performance of the envelope system [5,6,7]. In these analyses, hourly varying interior and exterior hygrothermal loads and material properties measured at standard temperature (21–23 °C) are commonly used. In reality, however, the temperature of the materials changes with the thermal load, reaching its highest value at peak solar radiation and its lowest in the early morning. For example, the cladding temperature on the southeast-facing wall in Vancouver ranges from −5 °C to 40 °C in winter and from 7 °C to 55 °C in summer [8]. Laboratory measurements of material thermal conductivities across a wide mean temperature range have shown the dependency of thermal conductivity of materials on temperature [9,10,11,12,13,14]. For example, Yousefi and Tariku [13,15] reported 29% and 103% increases in the thermal conductivity of open-cell spray polyurethane foam (SPF) insulation and fibre cement cladding, respectively, as the mean temperature increased from 5 °C to 60 °C. These measurements suggest that the use of the same thermal conductivity value for hygrothermal performance assessments of envelope systems for both winter and summer conditions may lead to errors, and researchers call for the use of variable thermal conductivity, adjusted according to prevailing temperatures, to improve predictions of building envelope durability and building energy performance [3,16,17,18,19]. Similarly, the temperature dependency of other hygrothermal properties of materials, including vapour permeability, sorption isotherm, and water absorption coefficients, was demonstrated in several studies [13,15,20,21,22,23,24,25,26]. As part of their extensive measurement campaign, Yousefi and Tariku [13,15,25,26] characterized the temperature-dependent hygrothermal properties of 18 different building materials, including claddings, sheathing membranes, sheathing boards, insulation materials, and wood (spruce and Douglas fir). They found that the properties of all materials are affected by temperature to varying degrees. For example, for stucco, the thermal conductivity increased by about 35% as the mean temperature increased from 5 to 60 °C, the vapour permeability at 70% RH increased by four times as the temperature increased from 3 °C to 45 °C; at the same relative humidity and temperature differences, the water absorption coefficient value increased by two times while the sorption isotherm measurements decreased by 38%.

The aforementioned discussions, however, are at a material level and require verification at the building envelope level, where materials are layered to form an assembly. Moreover, the extrapolation of observations from static laboratory measurements to real-world, dynamically changing environmental conditions with randomly varying temperature and humidity levels requires assessment. In this paper, a multi-layered building envelope system is considered, and its hygrothermal responses to seasonally varying weather conditions and material properties are simulated and studied. The primary objective of this study is to investigate variations in hygrothermal responses that may arise from employing temperature-dependent properties in hygrothermal simulations and performance analysis. In addition to assessing the impact of using temperature-dependent material properties across different climates, this research aims to identify which material properties and layers are most temperature-sensitive and should be treated as temperature-dependent inputs to hygrothermal models.

2. Methods

This study constitutes the second phase of a broader research project investigating the influence of temperature on the hygrothermal properties of building materials and the resulting implications at the building envelope scale. Building on the material-level findings previously reported [13,15,25,26,27], the present work extends the analysis to evaluate the effects of temperature-dependent properties at the assembly (building envelope) level.

2.1. Approach

To study the sensitivity and level of discrepancy in simulation results obtained from using material properties determined at different temperatures, an exterior wood-frame wall is considered. Four base cases with material properties at 3 °C, 21 °C, 45 °C (referred to as the “constant-temperature” cases), as well as a case where the properties varied with temperature (referred to as the “variable temperature” (VT) case), are created. The material properties of the wall layers, including water vapour permeability, sorption isotherm, and water absorption coefficients at these three temperatures, as well as thermal conductivity and heat capacity at various temperatures, were derived from experimental measurements previously reported by the authors and implemented to establish the material database for the hygrothermal model. The wall is oriented south to allow for higher temperature fluctuations in winter and the shoulder season, and to examine its hygrothermal responses across a wider temperature range. Materials outboard of the insulation layer exhibit greater daily temperature fluctuations. Therefore, two commonly used cladding types and sheathing boards are considered to allow assessment of more wall assemblies and variations in material properties. Stucco and fibre cement are chosen as cladding materials, while plywood and OSB are chosen as sheathing materials in this study. The hygrothermal responses of the different wall configurations are assessed in two climates: Toronto and Vancouver, characterized by cold winters and hot summers, and wet mild climates, respectively. Additional simulation test cases with rain penetration are included in the study to assess how material properties, defined at different temperatures, differently affect cases with and without rain penetration. The hygrothermal simulations are conducted using COMSOL Multiphysics 6.1, and the results are analyzed using moisture content, RHT index [6], and mould index [28] as performance indicators.

2.2. Hygrothermal Model

COMSOL Multiphysics 6.1, specifically the heat and moisture transfer module, is capable of simulating the coupled heat and moisture transport through wall systems. The transport processes are formulated using temperature and moisture content as the driving potentials, with the governing equations comprising coupled energy and moisture conservation equations.

The energy balance is expressed as:

$$\rho C_{eff}{\displaystyle \frac{\partial T}{\partial t}}=\nabla \cdot ({\lambda }_{eff}\nabla T)+L_v\nabla \cdot {\mathrm{g}}_w$$

(1)

where $T$ is temperature, $\rho C_{eff}$ is the effective volumetric heat capacity, ${\lambda }_{eff}$ is the effective thermal conductivity, $L_v$ is the latent heat of vaporization, and ${\mathrm{g}}_w$ is the total moisture flux.

Moisture transport is described by:

$${\displaystyle \frac{\partial w}{\partial t}}=-\nabla \cdot {\mathrm{g}}_w$$

(2)

with the total moisture flux defined as:

$${\mathrm{g}}_w=-{\delta }_p\nabla p_v-D_w\nabla w$$

(3)

where ${\delta }_p$ is the vapour permeability, $D_w$ is the liquid transport coefficient, and $p_v=RH.{ p}_{sat}\left(T\right)$ is the vapour pressure, expressed as a function of relative humidity $RH$ and saturation vapour pressure $p_{sat}\left(T\right)$.

Model implementation was validated against analytical solutions for one-dimensional transient diffusion and against standardized benchmark cases, including EN 15026 [29] and HAMSTAD project benchmarks [30], demonstrating strong agreement in the evolution of temperature and relative humidity under transient boundary conditions. It is assumed that there is no airflow across the material layers (no convective heat and mass transfer across the layers) and contact between the material layers is perfect (no thermal or moisture resistances at material interfaces).

2.3. Wall Composition

In this study, a representative wood-frame exterior wall assembly typical in North America is considered. Figure 1 shows the cross-section of the wall systems, materials, and their configuration. It consists of cladding, a weather-resistant barrier (WRB), sheathing, insulation, and interior finish layers. The interior layer is finished with a 60 ng/(Pa.s.m²) vapour permeance paint that serves as a vapour barrier according to the Canadian national building code [31]. Two cladding materials, fibre cement and stucco, and two exterior sheathings, plywood and OSB, are included in the simulation matrix to examine the sensitivity of the wall system’s moisture performance to different cladding and sheathing layers. These layers are identified as important because they experience high diurnal and seasonal temperature fluctuations, and to account for variations in water absorption characteristics of claddings and the sheathing, which is the moisture-sensitive layer in the wood-frame exterior wall system. As such, two claddings and two exterior sheathing wall systems, a total of four exterior wall systems, are studied. The physical characteristics of the layers are given in Table 1.

Figure 1. Wall assembly diagram.

Table 1. Wall assembly layers and materials.

Wall Component	Materials	Thickness [mm]	Density [kg/m3]	Capillary Saturation [kg/m3]
Cladding	Fibre Cement (FC)	6	1358	399.08
	Stucco (St)	19	2399	305.88
WRB	Building Paper 60 min	0.34	-	-
Exterior sheathing	Plywood (PW)	12.7	461	358.31
	OSB	12.7	620	651.75
Insulation	Fibreglass Batt	140	12	-
Interior sheathing	Interior Gypsum Board	12.7	1380	-
Interior finish	Vapour Retarder Paint	-	-	-

3. Temperature-Dependent Material Properties

The temperature-dependent hygrothermal properties of the materials used for the simulation were generated from measurements conducted at the BCIT Hygrothermal Property Measurement Laboratory and reported in Yousefi [27] and Yousefi and Tariku [13,15,25,26]. In this section, the measurements and the corresponding continuous-function equations established for the various properties and materials used in the simulation are presented. For layers with minimal temperature fluctuations (interior gypsum sheathing) and low moisture storage capacity (fibreglass batt insulation), hygrothermal property measurements at 21 °C are used. Apart from density and capillary saturation, the other material properties required for hygrothermal modelling include the sorption isotherm, vapour permeability, liquid diffusivity, thermal conductivity, and the specific heat capacity.

3.1. Moisture Storage Function

The fibre cement, stucco, OSB, and plywood sorption isotherm measurements at 3 °C, 21 °C, and 45 °C, and 50%, 70% and 90% relative humidity are presented in Figure 2. The Guggenheim–Anderson–de Boer (GAB) model [32,33,34,35], given by Equation (4), is used to fit the measurements and create continuous sorption isotherm curves for each temperature and material. The values of the GAB model coefficients, a, b, and c, found to represent the sorption isotherms of the four materials at 3 °C, 21 °C, and 45 °C, are given in Table 2. In all 12 cases (sorption isotherms of four materials at three temperatures), the R² values of the curve fittings fall within the range between 0.970 and 0.999 (Table 2), and as such, the use of the GAB model in this work is deemed acceptable. As hysteresis effects are not typically included in standard hygrothermal simulation tools, hysteresis effects were not considered in this study. COMSOL allows material property data as input in a table format and linearly interpolates between the listed values. Using the fitted functions, the moisture content was calculated over the full RH range (e.g., 0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.55, 0.6, 0.65, 0.7, 0.75, 0.8, 0.85, 0.903, 0.908, 0.913, 0.918, 0.923, 0.928, 0.933, 0.938, 0.943, 0.948, 0.953, 0.958, 0.963, 0.968, 0.973, 0.978, 0.98, 0.983, 0.988, 0.993, 0.994, 0.995, 0.996, 0.997, 0.998, 0.9985, 0.999, 0.9991, 0.9992, 0.9993, 0.9994, 0.9995, 0.9996, 0.9997, 0.9998, 0.999, 1) and input as discrete values into a lookup table. For the VT case, the same values were input with an added temperature argument, ensuring that the variable-temperature case has the same sorption isotherm as the constant-temperature cases if the temperatures are the same.

$$wc\left(\varphi [-]\right)={\displaystyle \frac{a·\varphi }{(1-b·\varphi )(1-b·\varphi +c·\varphi )}} \left[{\displaystyle \frac{\mathrm{k}\mathrm{g}}{\mathrm{k}\mathrm{g}}}\right]$$

(4)

Figure 2. Sorption curves for (a) fibre cement, (b) stucco, (c) OSB, and (d) plywood measured at 3 °C (blue circles), 21 °C (orange diamonds), and 45 °C (grey triangles), respectively [26].

Table 2. Curve-fitting coefficients for sorption data measured at 3 °C, 21 °C, and 45 °C.

Material	3 °C				21 °C				45 °C
	a	b	c	R2	a	b	c	R2	a	b	c	R2
Fibre Cement	1.39 × 105	9.41 × 10−1	7.16 × 106	0.996	1.11 × 105	9.48 × 10−1	6.47 × 106	0.997	1.02 × 105	9.49 × 10−1	6.06 × 106	0.998
Stucco	4.93 × 104	8.65 × 10−1	2.83 × 106	0.970	5.67 × 104	9.13 × 10−1	4.95 × 106	0.988	5.03 × 104	9.25 × 10−1	5.12 × 106	0.987
OSB	6.03 × 104	0.9817	2.62 × 106	0.997	8.70 × 104	9.84 × 10−1	4.44 × 106	0.999	8.38 × 104	9.85 × 10−1	4.37 × 106	0.999
Plywood	1.12 × 105	9.76 × 10−1	4.99 × 106	0.997	4.93 × 104	9.77 × 10−1	2.28 × 106	0.998	9.38 × 104	9.78 × 10−1	4.50 × 106	0.999

3.2. Vapour Permeability

Similar to the sorption isotherms, the vapour permeability of the materials measured following the ASTM E96 [36] wet-cup and dry-cup methods and previously reported at mean relative humidities of 25%, 35%, 45%, 75%, 85%, and 95% was used. The measurements at the three temperatures, 3 °C, 21 °C, and 45 °C, are presented in Figure 3. An exponential function, Equation (5) with coefficients j and k, represents the vapour permeability of the materials as a function of relative humidity [37]. Table 3 lists the curve-fitting coefficients for the fitted vapour permeability curves at each temperature. The R² values for the 12 curve-fitting equations (four materials and three temperatures) range from 0.837 to 0.997. The RH values used to calculate the vapour permeabilities for the lookup tables range from zero to 100% with intervals of 2% RH.

$$\mathsf{\delta }p\left(\varphi \left[-\right]\right)=j·{\mathrm{e}\mathrm{x}\mathrm{p}}^{k·\varphi } \left[{\displaystyle \frac{\mathrm{k}\mathrm{g}}{\mathrm{P}\mathrm{a}.\mathrm{m}.\mathrm{s}}}\right]$$

(5)

Figure 3. Vapour permeability curves for (a) fibre cement, (b) stucco, (c) OSB, (d) plywood, and (e) 60 min building paper measured at 3 °C (blue circles), 21 °C (orange diamonds), and 45 °C (grey triangles), respectively [15,25].

Table 3. Curve-fitting coefficients for vapour permeability data measured at 3 °C, 21 °C, and 45 °C.

Material	3 °C			21 °C			45 °C
	j	k	R2	j	k	R2	j	k	R2
Fibre cement	2.216 × 10−13	3.5072	0.995	2.171 × 10−13	3.8700	0.977	1.838 × 10−13	4.7025	0.992
Stucco	5.971 × 10−13	1.5369	0.957	2.078 × 10−12	1.0259	0.912	3.704 × 10−12	1.3620	0.837
OSB	4.104 × 10−13	1.9551	0.983	3.600 × 10−13	2.8149	0.982	5.092 × 10−13	2.5909	0.954
Plywood	2.687 × 10−13	3.1952	0.982	2.460 × 10−13	3.8765	0.992	2.747 × 10−13	4.0798	0.980

3.3. Liquid Diffusivity

The average liquid diffusivity was estimated from the water absorption coefficient (WAC) using Equation (6) as described by Kumaran [38].

$$D_w\left[{\displaystyle \frac{{\mathrm{m}}^2}{\mathrm{s}}}\right]~{\left({\displaystyle \frac{A_W\left[\frac{\mathrm{k}\mathrm{g}}{{\mathrm{m}}^2.\sqrt{s}}\right]}{w_c\left[\frac{\mathrm{k}\mathrm{g}}{{\mathrm{m}}^3}\right]}}\right)}^2$$

(6)

For each temperature, the diffusion coefficient Dw [m²/s] is calculated using the WAC measured from samples at 50% RH and the saturated moisture content w_c [kg/m³] determined from water immersion tests. Liquid transport is assumed to be active in the free capillary region above 95% RH. Therefore, below 95% RH, the diffusion coefficient is 1 × 10⁻¹⁶ m²/s, indicating negligible liquid transport. Between 95 and 97% RH, the diffusion coefficient is assumed to increase linearly to the values calculated by Equation (6) and listed in Table 4. Above 97% RH, the diffusion coefficient equals the values listed in Table 4. The 95% RH threshold follows the conventional separation between hygroscopic and capillary moisture regimes [1,4,39]. However, in reality, some degree of liquid transport may occur below this threshold, particularly in fine-pore hygroscopic materials. As a result, moisture redistribution may be slightly underestimated under sub-saturation conditions, resulting in increased moisture content gradients. Nevertheless, the assumption is applied to both the constant-temperature and variable-temperature cases. Therefore, the relative differences are not expected to differ significantly based on the selected activation threshold. Similar to the sorption isotherm and vapour permeability, the moisture diffusivity was input as a table with one argument (RH) for the constant-temperature cases and two arguments (RH and temperature) for the variable-temperature case.

Table 4. Diffusion coefficients (RH > 97%) at 3 °C, 21 °C, and 45 °C.

Material	Diffusion Coefficient [m2/s]
	Temperature: 3 °C	Temperature: 21 °C	Temperature: 45 °C
Fibre Cement	2.25 × 10−12	3.10 × 10−12	3.51 × 10−12
Stucco	6.30 × 10−10	9.00 × 10−10	1.26 × 10−9
OSB	3.04 × 10−12	9.04 × 10−12	4.90 × 10−10
Plywood	1.03 × 10−11	4.05 × 10−11	7.48 × 10−11

3.4. Thermal Conductivity and Specific Heat Capacity

The thermal conductivity and heat capacity measurements conducted at different temperatures and reported in Yousefi [27] are used in this study. The thermal conductivity and heat capacity of the materials are linearly dependent on temperature (Figure 4). The relationships between temperature and thermal conductivity and specific heat capacity of the materials are defined by the linear Equations (7) and (8), respectively. Unlike the previous material properties, the thermal conductivity and specific heat capacity were entered as analytical functions for the variable-temperature case, and the values were calculated at 3 °C, 21 °C, and 45 °C for input to the constant-temperature cases. Table 5 presents the slopes ($m_1 \mathrm{a}\mathrm{n}\mathrm{d} m_2)$ and intercepts ($n_{1 }\mathrm{a}\mathrm{n}\mathrm{d} n_2)$ of the linear thermal conductivity and heat capacity equations, along with the calculated constant-temperature values. Thermal conductivity and/or specific heat capacity data for the gypsum board and fibreglass insulation were assumed to have constant values corresponding to those in ASHRAE Fundamentals [40].

$$k\left(\mathrm{T}[°\mathrm{C}]\right)=m_1·\mathrm{T}+n_1 \left[{\displaystyle \frac{\mathrm{W}}{\mathrm{m}.\mathrm{K}}}\right]$$

(7)

$$c_p\left(\mathrm{T}[°\mathrm{C}]\right)=m_2·\mathrm{T}+n_2 \left[{\displaystyle \frac{\mathrm{J}}{\mathrm{k}\mathrm{g}.\mathrm{K}}}\right]$$

(8)

Figure 4. Thermal conductivity and heat capacity as a function of temperature for fibre cement (blue circles), stucco (orange diamonds), OSB (grey triangles), and plywood (yellow stars) and their linear relationships [27].

Table 5. Thermal conductivity and specific heat capacity as a function of temperature.

Material	m	n	R2	Value at T = 3 °C	Value at T = 21 °C	Value at T = 45 °C
Thermal Conductivity [W/(m.K)]
Fibre Cement	1.75 × 10−3	0.103	0.97	0.108	0.140	0.182
Stucco	1.901 × 10−3	0.4299	1.00	0.436	0.470	0.515
OSB	2.04 × 10−4	0.0794	0.99	0.080	0.084	0.089
Plywood	2.604 × 10−4	0.0842	1.00	0.085	0.090	0.096
Specific Heat Capacity [J/(kg.K)]
Fibre Cement	2.1533	974.9	0.93	981	1020	1072
Stucco	-	-	-	840	840	840
OSB	6.400	1219	0.99	1238	1353	1507
Plywood	6.087	1210	0.99	1228	1338	1484

4. Hygrothermal Performance Assessment

4.1. Boundary Conditions

To investigate the effect of temperature-dependent material properties on the hygrothermal performance of exterior walls, the study considers two Canadian locations with different climates, Toronto and Vancouver. While weather data for Toronto is taken from the Environment Canada website, for Vancouver, measurements at the BCIT Building Science Centre of Excellence are used. The outdoor temperature and RH on an hourly and daily basis are shown in Figure 5(a1,a2). In order to examine the temperature-dependent effect, the south façade, which experiences the highest temperature variations due to its greater sun exposure, was selected for simulation.

Figure 5. Outdoor hourly and daily average temperature and RH (a1,a2) and solar flux and rain flux incident on the south wall (b1,b2) for Toronto and Vancouver.

The weather in Toronto is generally characterized as a semi-continental climate, with warm, humid summers and cold winters. For the year shown, the daily average temperatures range from −20.2 °C to 25.1 °C, and the total annual rainfall is 474 kg/m² (mm). The weather in Vancouver is generally characterized as mild and humid. Compared with Toronto, Vancouver experiences warmer winters and more rainfall. For the year shown, the daily average temperatures range from −3.8 °C to 24.9 °C, and the total annual rainfall is 1771 kg/m² (mm). Figure 5(b1,b2) shows the solar flux and rain flux incident on the south façade. The hygrothermal responses of the wall assemblies were investigated with and without rain-penetration load. For cases with rain penetration, the moisture load was represented by defining a moisture source equal to 1% of the wind-driven rain applied to the exterior 1/3rd of the sheathing layer. The wind-driven rain was calculated from horizontal rain flux, wind speed, and wind direction data according to ASHRAE 160, assuming a rain exposure factor of 0.5 and a rain deposition factor of one. Each simulation case was run for two years, starting in January, and using the boundary conditions presented in the previous section. The first year is considered a conditioning year, and results from the second year are used for analysis. At the beginning of the two-year simulation period, the material layers in the wall assemblies are assumed to be at 22 °C and 80% RH. The heat and moisture transfer coefficients are assumed to be 25 W/(m².K) and 8.3 W/(m².K), and 25 × 10⁻⁸ and 6.0 × 10⁻¹¹ kg/(Pa.m².s) for the exterior and interior surfaces, respectively. The indoor temperature and relative humidity boundary conditions are maintained at 22 °C and 50% RH, respectively.

4.2. Test Cases

Table 6 summarizes the test cases considered in this study. It shows the combinations of cladding and sheathing materials, consideration of rain-penetration load, and the climate for each case. For each simulation case, the temperature at which the materials’ properties are determined is varied between 3 °C, 21 °C, 45 °C, and VT. Additional simulation test cases are included to identify the prominent temperature-dependent properties of stucco and building paper that influence the results.

Table 6. Base simulation cases.

Cladding	Sheathing	Rain Load?	T-Dependent WRB?	Climate
Fibre Cement	OSB	No	No	Toronto/Vancouver
	OSB	Yes	No	Toronto/Vancouver
	OSB	No	Yes	Toronto
	PW	No	No	Toronto/Vancouver
	PW	Yes	No	Toronto/Vancouver
Stucco	OSB	No	No	Toronto/Vancouver
	OSB	Yes	No	Toronto/Vancouver
	OSB	No	Yes	Toronto
	PW	No	No	Toronto/Vancouver
	PW	Yes	No	Toronto/Vancouver
Stucco parametric analysis	OSB	No	No	Toronto

4.3. Performance Indicators

Regarding moisture durability, the sheathing layer is generally the critical layer because it is a moisture-sensitive material affected by exterior weather conditions and by possible condensation from moist warm air touching the cold interior surface. Therefore, the simulation cases are compared based on the moisture content (MC) of the sheathing boards. The relative humidity at the exterior surface of the gypsum board is also examined to assess the risk of summer condensation driven by solar-driven vapour diffusion and cooler indoor temperature. Moreover, the moisture damage risk potential of the different simulation cases is compared using RHT [6] and mould growth index [28] values. The RHT index captures the cumulative co-existence of temperature (T) and relative humidity (RH) above threshold levels in a moisture-sensitive layer. It is calculated from the RH and T outputs on the interior side of the sheathing from the numerical simulations. A threshold RH of 80% and a threshold temperature of 0 °C, as suggested by Mukhopadhyaya et al. [6], were used; therefore, the RHT index is indicated as RHT80. Higher RHT index values generally indicate a greater risk of moisture-related deterioration [6,41]. Furthermore, the risk of mould growth on the interior side of the sheathing is assessed using the mould growth index, calculated assuming a sensitivity class ‘Sensitive’ according to ASHRAE 160 [28]. The results of the 3 °C, 45 °C, and VT cases are compared against the 21 °C case, which is the standard temperature around which most material properties are measured.

5. Results and Discussion

In the following sections, the simulation test cases will be grouped and presented by cladding type. In the first two sections, the two cladding types are examined with OSB sheathing. The moisture response of the sheathing is examined both with and without direct rain leakage onto the sheathing layer, in both Toronto, which is humid in the summer, and Vancouver, which has high rain load during the winter. A total of 1% of the wind-driven rain is assumed to be deposited onto the exterior 1/3rd of the sheathing layer. The third section compares the temperature-dependent moisture performance of a stucco-clad wood-frame wall with plywood sheathing against OSB sheathing in Toronto. The fourth section is a parametric analysis for a case with stucco cladding where a single material property is defined to be temperature-dependent at a time. Lastly, the effect of defining the vapour permeability of the WRB to be temperature-dependent is analyzed.

5.1. Fibre Cement Cladding with OSB Sheathing

The moisture content of the OSB sheathing layer and the RH on the exterior side of the gypsum board are presented in Figure 6 for cases with and without rain penetration in Toronto and Vancouver for fibre cement cladding. In both climates, the 3 °C case generally produces the highest sheathing MC throughout the year, whereas the other three temperature cases produce relatively similar results. The 21 °C and 45 °C cases produce MC results that are more similar to each other, with each case having higher MC during different times of the year. The 21 °C case tends to produce higher MC during the spring and summer, whereas the 45 °C case tends to produce higher MC during the fall and winter. The VT case generally produces MC results similar to or lower than the 21 °C and 45 °C cases; however, it never produces the highest MC across all temperature cases. During winter, the VT case tends to exhibit slightly higher MC than the 21 °C and 45 °C cases, particularly for the colder Toronto climate. On the other hand, the VT case tends to exhibit the lowest MC among all temperature cases during the summer, indicating that it adjusts to the winter and summer temperature conditions. As for the RH of the gypsum board, the difference between the temperature cases appears to be relatively minor. Similar to the sheathing MC, the VT case tends to produce the least conservative results with the lowest RH.

Figure 6. Fibre cement cladding in Toronto and Vancouver: (a1,a2) Moisture content of the OSB sheathing without rain; (b1,b2) moisture content of the OSB sheathing with rain; (c1,c2) RH at the exterior surface of the gypsum board without rain; (d1,d2) RH at the exterior surface of the gypsum board with rain.

A summary of the maximum moisture content by weight, RHT index, maximum mould growth index, and maximum RH for the exterior side of the gypsum board for the 3 °C, 21 °C, 45 °C, and VT cases is presented in Table 7. The 3 °C, 45 °C, and VT cases are compared with the 21 °C standard case in order to examine how the use of different temperature-dependent material properties can affect moisture performance results. In general, the 3 °C case produces an increased maximum MC and RHT index, the VT case produces an increased maximum MC and a reduced RHT index and maximum RH, and the 45 °C case produces a less consistent pattern (both increases and decreases are observed). In all cases, the mould growth index is very low and poses no concern, regardless of temperature dependency.

Table 7. Summary of maximum sheathing MC, RHT index, maximum mould growth index, and maximum gypsum RH for each temperature case for fibre cement cladding with variations in climate and rain penetration.

Case	Indicator	Temperature Case				Difference
		3 °C	21 °C	45 °C	VT	3 °C vs. 21 °C	45 °C vs. 21 °C	VT vs. 21 °C
TOR (no rain)	Max sheathing MC [wt%]	13.4	12.1	12.0	12.7	10.8%	−0.5%	5.3%
	RHT80	154,192	100,204	91,375	86,734	53.9%	−8.8%	−13.4%
	Max MI	0.45	0.20	0.16	0.18	124.4%	−18.5%	−11.5%
	Max gypsum RH [%]	86.3	83.7	83.1	79.9	3.1%	−0.7%	−4.6%
TOR with Rain	Max MC [wt%]	16.6	14.8	14.6	15.6	12.5%	−1.4%	5.4%
	RHT80	271,691	197,049	176,132	164,087	37.9%	−10.6%	−16.7%
	Max MI	0.92	0.57	0.47	0.49	62.9%	−17.6%	−13.1%
	Max gypsum RH [%]	91.5	90.8	89.4	87.0	0.9%	−1.5%	−4.1%
VAN (no rain)	Max MC [wt%]	13.8	13.1	13.6	13.5	4.9%	3.3%	2.6%
	RHT80	152,772	145,875	157,864	98,980	4.7%	8.2%	−32.1%
	Max MI	0.37	0.35	0.40	0.18	6.2%	12.5%	−50.1%
	Max gypsum RH [%]	85.0	86.1	86.6	82.8	−1.2%	0.6%	−3.8%
VAN with Rain	Max MC [wt%]	18.6	17.2	17.2	17.4	8.1%	−0.2%	1.0%
	RHT80	289,454	285,537	284,621	204,415	1.4%	−0.3%	−28.4%
	Max MI	0.89	0.90	0.92	0.59	−1.2%	2.3%	−35.0%
	Max gypsum RH [%]	89.3	90.8	91.0	89.3	−1.7%	0.2%	−1.7%

Overall, the fibre cement cladding shows relatively small differences between the 21 °C and VT cases. For OSB sheathing without rain penetration, the average absolute difference is 0.41 wt% and the maximum hourly difference is 1.18 wt% in Toronto. For Vancouver, the average difference is 0.40 wt% and the maximum hourly difference is 1.59 wt%. The addition of rain leakage does not appear to significantly affect the behaviour of the different temperature cases. As expected, the MC and RH are higher when rain leakage is included. The overall difference between the 21 °C and VT cases is slightly higher than the case without rain leakage, with an average absolute difference of 0.55 wt% and a maximum hourly difference of 1.39 wt% for Toronto. For Vancouver, the average difference is 0.55 wt%, and the maximum hourly difference is 2.09 wt% with rain leakage.

5.2. Stucco Cladding with OSB Sheathing

Figure 7 shows the sheathing MC and RH on the exterior side of the gypsum board with stucco cladding for Toronto and Vancouver. Similar to the fibre cement cladding, for both climates, the 3 °C case produces much higher sheathing MC throughout the year, whereas the other three temperature cases produce relatively similar results. Again, the 21 °C cases tend to produce higher MC during the spring and summer, whereas the 45 °C cases tend to produce higher MC during the fall and winter. During the summer, the VT cases tend to follow the 45 °C case; however, during the rest of the year, the VT case produces lower MC than all other temperature cases. As for the RH of the gypsum board, the difference between the temperature cases is more substantial than for the fibre cement cladding, with up to 9% difference in RH between the VT and 3 °C cases. Furthermore, the differences mainly occur during peak summer periods, which can affect the amount of time the gypsum experiences RH above 80% and, therefore, the mould growth risk. However, similar to the sheathing MC, the VT case tends to produce the least conservative results with the lowest RH.

Figure 7. Stucco cladding in Toronto and Vancouver: (a1,a2) Moisture content of the OSB sheathing without rain; (b1,b2) moisture content of the OSB sheathing with rain; (c1,c2) RH at the exterior surface of the gypsum board without rain; (d1,d2) RH at the exterior surface of the gypsum board with rain.

A summary of the maximum moisture content by weight, RHT index, maximum mould growth index, and maximum RH for the exterior side of the gypsum board for the 3 °C, 21 °C, 45 °C, and VT cases is presented in Table 8. Compared to the fibre cement cladding, the stucco cladding shows that the 3 °C and 45 °C cases consistently produce higher maximum MC than the 21 °C case. The maximum RH of the gypsum board is also consistently higher for the 3 °C case and lower for the 45 °C and VT cases. The 3 °C case in particular shows a large deviation compared to the other temperature cases for the stucco cladding to the point where the maximum mould index for the Vancouver case with rain leakage reaches as high as 2.10 for a one-year calculation, and the RHT index for the Toronto case with rain leakage is up to 92.1% higher than the 21 °C case.

Table 8. Summary of maximum sheathing MC, RHT index, maximum mould growth index, and maximum gypsum RH for each temperature case for stucco cladding with variations in climate and rain penetration.

Case	Indicator	Temperature Case				Difference
		3 °C	21 °C	45 °C	VT	3 °C vs. 21 °C	45 °C vs. 21 °C	VT vs. 21 °C
TOR (no rain)	Max sheathing MC [wt%]	14.4	13.4	14.7	12.7	7.9%	9.5%	−5.2%
	RHT80	205,066	145,753	150,600	82,815	40.7%	3.3%	−43.2%
	Max MI	0.60	0.38	0.42	0.14	58.1%	10.3%	−63.2%
	Max gypsum RH [%]	91.1	90.6	88.3	82.9	0.5%	−2.6%	−8.5%
TOR with Rain	Max MC [wt%]	20.7	17.2	17.7	16.3	20.1%	3.0%	−5.1%
	RHT80	607,426	316,209	253,180	190,717	92.1%	−19.9%	−39.7%
	Max MI	1.59	0.96	0.84	0.59	66.0%	−12.2%	−38.4%
	Max gypsum RH [%]	93.5	92.8	92.1	91.5	0.8%	−0.7%	−1.4%
VAN (no rain)	Max MC [wt%]	18.0	16.3	17.1	14.7	10.0%	4.8%	−9.9%
	RHT80	498,730	325,063	296,067	116,803	53.4%	−8.9%	−64.1%
	Max MI	1.16	0.94	0.91	0.29	23.2%	−2.9%	−69.1%
	Max gypsum RH [%]	93.3	92.9	91.2	90.0	0.4%	−1.9%	−3.2%
VAN with Rain	Max MC [wt%]	25.2	21.4	22.2	19.9	17.7%	3.5%	−7.4%
	RHT80	845,174	565,608	460,219	294,974	49.4%	−18.6%	−47.8%
	Max MI	2.10	1.50	1.39	0.85	40.0%	−6.9%	−43.1%
	Max gypsum RH [%]	94.3	94.3	92.5	92.0	0.0%	−1.8%	−2.3%

In general, compared to fibre cement cladding, stucco cladding shows relatively large differences between the 21 °C and VT cases. The average absolute difference is 0.96 wt% and 1.59 wt% without and with rain penetration, respectively, and the maximum hourly difference is 2.58 wt% and 3.43 wt%, respectively. It is important to note that, though the difference is relatively large, the 21 °C case generally predicts conservative results compared to the VT case. With the addition of rain leakage, the 3 °C case appears to separate itself further from the other temperature cases and maintains a higher MC throughout the year. Otherwise, the moisture response is similar to the case with no rain leakage.

Compared to Toronto, the moisture content in the sheathing is higher in Vancouver, and the separation between the temperature cases is also greater. As a result, compared to the 21 °C standard case, the difference between the 21 °C and VT cases is large with an average absolute difference of 2.18 wt% and a maximum hourly difference of 4.32 wt% for the case without rain. The addition of rain leakage increases this difference as the average absolute difference is 2.80 wt% and the maximum hourly difference is 5.03 wt%. Once again, the 21 °C case produces conservative results compared to the VT case.

5.3. Temperature-Dependent Plywood and OSB Sheathings: Comparison

In this section, the temperature-dependent moisture response of OSB and plywood sheathing materials in Toronto is compared. The MC for the OSB and plywood layers is shown for the two cladding materials in Figure 8. Compared to the OSB sheathing, the plywood sheathing appears to experience less spread between the different temperature cases. In particular, the MC of the 3 °C case is more in line with the other temperature cases. The general trend, however, is similar between the two sheathing materials, with the 3 °C case producing the highest MC throughout the year, while (with the exception of stucco during the winter), the 21 °C case produces higher MC during the spring and summer compared to the 45 °C case, and the 45 °C case produces higher MC during the fall and winter. While the behaviour of the VT case changes slightly depending on the cladding type, it is consistent between both sheathing types. In all scenarios, the VT case never produces the highest MC results out of all temperature cases. The main difference appears to be a reduction in MC observed in the 3 °C case during winter for stucco-clad walls with plywood sheathing compared to the OSB sheathing. During the winter, the 3 °C case produces lower MC than both the 45 °C and 21 °C cases for the plywood sheathing, whereas the 3 °C case sits between the 45 °C and 21 °C cases for the OSB sheathing.

Figure 8. Moisture content of plywood and OSB sheathing layers for fibre cement and stucco cladding in Toronto.

Summaries of the maximum moisture content by weight, RHT index, maximum mould growth index, and maximum RH for the exterior side of the gypsum board for the 3 °C, 21 °C, 45 °C, and VT cases are presented in Table 9 for each cladding. The table presents the differences between OSB and plywood sheathing results for each indicator. For the fibre cement cladding, while the plywood sheathing produces a higher maximum MC, the RHT index and mould growth index are reduced across all temperature cases. In fact, the RHT index is reduced for the plywood in all cases except for the stucco VT case. The maximum gypsum RH for the plywood sheathing was also lower than for the OSB sheathing for all temperature cases except for a slight increase in the VT case. Since rain leakage was not considered, the maximum mould growth index is low in all cases, indicating a low risk of mould growth. The change in maximum RH for gypsum is relatively moderate in most cases, indicating a minor influence of sheathing material on gypsum performance.

Table 9. Summary of maximum sheathing MC, RHT index, maximum mould growth index, and maximum gypsum RH for each temperature case for fibre cement and stucco cladding with variations in sheathing material (OSB vs. plywood).

Case	Indicator	Temperature Case				Difference
		3 °C	21 °C	45 °C	VT	3 °C vs. 21 °C	45 °C vs. 21 °C	VT vs. 21 °C
FC-OSB	Max Sheathing MC [wt%]	13.4	12.1	12.0	12.7	10.8%	−0.5%	5.3%
	RHT80	154,192	100,204	91,375	86,734	53.9%	−8.8%	−13.4%
	Max MI	0.4	0.2	0.2	0.2	124.4%	−18.5%	−11.5%
	Max Gypsum RH [%]	86.3	83.7	83.1	79.9	3.1%	−0.7%	−4.6%
FC-PW	Max Sheathing MC [wt%]	14.2	13.6	13.3	13.8	4.5%	−2.2%	1.3%
	RHT80	107,936	69,735	55,539	83,291	54.8%	−20.4%	19.4%
	Max MI	0.24	0.10	0.04	0.16	149.5%	−57.8%	61.7%
	Max Gypsum RH [%]	81.5	80.1	80.9	80.2	1.6%	0.9%	0.1%
Stucco-OSB	Max Sheathing MC [wt%]	14.4	13.4	14.7	12.7	7.9%	9.5%	−5.2%
	RHT80	205,066	145,753	150,600	82,815	40.7%	3.3%	−43.2%
	Max MI	0.6	0.4	0.4	0.1	58.1%	10.3%	−63.2%
	Max Gypsum RH [%]	91.1	90.6	88.3	82.9	0.5%	−2.6%	−8.5%
Stucco-PW	Max Sheathing MC [wt%]	15.0	15.7	17.1	14.1	−4.3%	9.2%	−9.9%
	RHT80	173,748	138,424	126,506	102,223	25.5%	−8.6%	−26.2%
	Max MI	0.46	0.35	0.32	0.22	32.0%	−9.6%	−36.9%
	Max Gypsum RH [%]	91.3	90.5	84.3	85.1	0.9%	−6.9%	−5.9%

When comparing the 3 °C, 45 °C, and VT cases against the 21 °C standard case, the choice of sheathing material produces similar results in terms of increasing or decreasing maximum MC. As mentioned, the 3 °C stucco case produced much lower MC during winter than the plywood case compared to the OSB case. As a result, the maximum MC for the 3 °C case is lower than the 21 °C case for the plywood sheathing with stucco, whereas the opposite is true for the OSB sheathing. In four out of six cases, the relative difference between the maximum MC of the 21 °C case and other temperature cases is smaller for the plywood sheathing compared to the OSB sheathing.

Overall, the plywood sheathing appears slightly less temperature-sensitive than OSB, as the difference between the 21 °C and VT cases is reduced in most plywood scenarios. For fibre cement and stucco cladding, the average absolute differences in MC are 0.23 wt% and 1.21 wt%, respectively, while the maximum absolute differences are 0.64 wt% and 2.10 wt%, respectively. In comparison, the average differences mentioned previously for the OSB scenarios are 0.41 wt% and 0.96 wt% for the fibre cement and stucco claddings, respectively, and the maximum differences are 1.18 wt% and 2.58 wt%, respectively.

Based on the results for the various combinations of fibre cement cladding, stucco cladding, OSB sheathing, and plywood sheathing summarized in Table 7, Table 8 and Table 9, in comparison to the standard 21 °C cases, the VT cases indicate that the use of temperature-dependent material properties may systematically lead to an estimation of higher hygrothermal risk in the studied conditions. In particular, apart from the fibre cement cladding with plywood sheathing scenario, the RHT index, maximum mould growth index, and maximum gypsum RH are reduced for all other scenarios.

In order to quantitively define the relative importance of cladding and sheathing layers in relation to temperature-dependency, an Analysis of Variance (ANOVA) was used as a sensitivity analysis to decompose the total variance (sum of squares) of the different data sources, which include cladding type (fibre cement and stucco), sheathing type (OSB and plywood), and temperature model (21 °C and VT). Figure 9 shows the variance contribution of each source on the performance indicators for the case in Toronto without rain penetration. Results indicate that the sheathing type is the dominant factor affecting the maximum moisture content of the sheathing layer. On the other hand, cladding type plays a more important role for RHT index, maximum mould growth index, and maximum gypsum RH. Furthermore, the interaction between the temperature model and the cladding has a greater effect on all performance indicators compared to the sheathing-temperature model relationship.

Figure 9. Variance contribution of cladding type, sheathing type, and temperature model for each performance indicator.

5.4. Stucco Cladding Parametric Analysis

To investigate the cause of the relatively large MC discrepancy between the temperature cases for the stucco cladding, test cases were run where one moisture property was varied at a time for a stucco wall. In other words, including the base case where all properties are maintained at 21 °C, four cases were investigated. For each case, one of the diffusion coefficient (21C w/DwVT), sorption isotherm (21C w/wcVT), or vapour permeability (21C w/vpVT) is set to the VT case values, while all other properties are maintained as the 21 °C values. To isolate and investigate the effect of changes in stucco properties with temperature on wall performance, these simulations use the plywood sheathing properties determined at 21 °C in all cases.

The MC results for sheathing are presented in Figure 10. Based on the results, the difference in vapour permeability appears to cause the greatest moisture variations. Figure 3b shows the vapour permeability curves for the stucco cladding at three different temperatures of 3 °C, 21 °C, and 45 °C. The figure shows that vapour permeability increases with temperature. As shown in Figure 10, the temperature-dependent vapour permeability of the stucco cladding produces lower sheathing MC throughout the year compared to constant 21 °C values. The corresponding average temperature-independent and temperature-dependent vapour permeabilities for the stucco cladding are presented in Figure 11. During cold periods, the vapour permeability of the vpVT case is lower than the 21 °C case, reducing the amount of moisture absorbed by the cladding. During warmer periods, the vapour permeability of the vpVT case increases above the 21 °C case during the daytime when the wall heats up due to solar energy, while nighttime vapour permeability is similar to or lower than the 21 °C case (Figure 11b). As a result, the wall is likely able to dry more effectively during the daytime and thereby maintain a lower overall moisture content.

Figure 10. MC of plywood sheathing for parametric analysis.

Figure 11. Average vapour permeability of stucco cladding layer for temperature-independent case (21 °C) and temperature-dependent vapour permeability case (21 °C w/vpVT) for (a) whole year and (b) one week in summer.

5.5. Temperature-Dependent WRB

Based on the parametric analysis in the previous section, the temperature-dependence of the cladding’s vapour permeability appears to be an important property to consider when evaluating moisture response. Therefore, as an essential layer for moisture control, the impact of temperature-dependent vapour permeability of the WRB (Figure 3e) was examined. Previous simulations used a constant vapour permeability value of 3.305 × 10⁻¹³ kg/(Pa.m.s) for the 60 min building paper (BP) WRB. For the temperature-dependent simulations, the BP and OSB sheathing are simulated with both cladding materials.

Figure 12 shows the MC of the sheathing board for the VT case for fibre cement and stucco cladding materials with OSB sheathing and 60 min building paper in between in Toronto. Based on the figures, defining the BP’s vapour permeability as temperature-dependent did not produce significant differences in the results. Similar results were obtained for the Vancouver climate and have therefore not been presented here.

Figure 12. MC of OSB sheathing with and without temperature-dependent building paper for fibre cement cladding and stucco cladding.

6. Conclusions

In this paper, the significance of using temperature-dependent material properties in hygrothermal performance assessment of exterior wall systems is studied. Material properties measurements at 3 °C, 21 °C, and 45 °C, conducted by the authors in previous work, are used as input to the hygrothermal model. Various combinations of wall configurations and climate loads were examined to identify wall assemblies whose hygrothermal responses are highly sensitive to variation in material properties defined at different temperatures.

Hygrothermal simulation results for the exterior wall system with fibre cement cladding showed that the moisture content (MC) of the sheathing showed minor differences between the different temperature cases for each sheathing material, with maximum hourly differences between the 21 °C and variable-temperature (VT) cases less than 1.18 wt% for OSB sheathing in Toronto. On the other hand, the stucco cladding showed the greatest differences, up to 2.58 wt% under the same conditions. In comparison, the fibre cement and stucco claddings produced maximum hourly differences of 1.59 wt% and 4.32 wt%, respectively, for the OSB sheathing in Vancouver. The plywood sheathing followed a similar trend, with stucco showing the highest differences between the temperature cases; however, the magnitude of the differences was slightly smaller than that of the OSB sheathing. In general, the choice of cladding type appears to dominate the moisture behaviour of the wall, as changing the cladding type produced large variations in sheathing MC, whereas varying the sheathing type yielded more moderate variations. The addition of rain leakage did not seem to significantly alter the differences in the moisture response of the walls (with material properties of different temperatures). The magnitude of the differences was similar between Toronto and Vancouver; however, Vancouver tended to have higher maximum differences, even though the outdoor temperature in Toronto varies over a greater range than in Vancouver. A parametric analysis where one of the diffusion coefficient, sorption isotherm, or vapour permeability was set to the VT case values, while all other properties were maintained as the 21 °C values, showed that the temperature-dependent vapour permeability of the stucco cladding produces lower sheathing MC throughout the year compared to constant 21 °C values. Therefore, it appears that the vapour permeability was the major factor influencing the moisture behaviour. However, the temperature-dependency of the 60 min building paper’s vapour permeability was not a significant factor.

In general, the results of this study confirm that although material properties vary with temperature, their influence on the hygrothermal simulation results was low. This observation remained valid across cases with different sheathing board materials (plywood and OSB), climatic conditions (Vancouver and Toronto), and consideration of additional hygrothermal loads resulting from rain penetration. These findings demonstrate that the use of temperature-dependent material properties does not significantly affect hygrothermal simulation results or the performance assessment of exterior wood-frame wall assemblies for the studied cases. For practical modelling purposes, simulations using material properties data at the standard 21–23 °C provide conservative and acceptable results.