Assessing the Moisture Resilience of Wood Frame Wall Assemblies

Abstract

Resilience has been used as a building performance metric that measures the building’s capability of absorption, response, and recovery from one or a series of disruptive events, e.g., extreme weather events or power outage events. With respect to resilience, in relation to the moisture performance of the building envelope (moisture resilience), this aspect has not yet been thoroughly explored nor defined. Given the expected increase in annual precipitation in certain regions of Canada as induced by climate change effects occurring both currently and in the future, the moisture resilience of building envelops will require immediate attention given that wall assemblies of buildings are predicted to be subjected to excessive moisture loads in the coming years. In this study, the moisture resilience of wood frame wall assemblies to mould growth was described from three aspects: (i) absorption—the ability of the wall to maintain a low level of relative humidity on the OSB; (ii) response—the fluctuation of the relative humidity on the OSB; and (iii) recovery—the rate at which the relative humidity recovers to an acceptable level. The metrics used to demonstrate the relative impact of these factors on moisture performance were also developed. The results have revealed a robust correlation between moisture performance and the relative influence of various newly defined aspects of moisture resilience.

1. Introduction

Climate change has brought new challenges to the design of performance-based buildings, for which measurable and predictable building performance metrics are required to permit assessing the climate resilience of new building designs or the retrofitting of existing buildings. As defined by IPCC [1], climate resilience refers to “the capacity of social, economic and ecosystems to cope with a hazardous event or trend or disturbance, responding or reorganizing in ways that maintain their essential function, identity and structure … …while also maintaining the capacity for adaptation, learning and transformation”. Attia et al. [2] identified nine types of hazardous events or disturbances that affect buildings or the built environment that might be exacerbated by climate change, including outdoor air pollution, wildfires, earthquakes, windstorms, flooding, heat waves, power outages, water shortages, and pandemics. To cope with these hazardous events or disturbances, many studies have been carried out to quantify and improve the climate resilience of buildings or the built environment. Burton et al. [3] proposed a framework to assess community resilience to earthquakes. This framework has incorporated probabilistic building performance limit states that can be used to assess the ability to recover functionality at a building level for a given seismic magnitude. Wildfires can lead to two types of consequences: power outages in communities at wildland–urban interfaces (WUIs) and air pollution that could affect a much larger scale of regions [4,5]. The climate resilience of a community to wildfire could be improved by introducing a microgrid system to support the areas surrounded by wildfires [6,7] and improving mechanical ventilation systems to minimize their exposure to PM2.5 within indoor environments during the wildfire season [8]. As regards resilience to heatwaves, Ji et al. [9] proposed a resilience framework to describe a building’s resilience to heatwaves. This framework can be used to measure zone-level and building-level thermal resilience to heatwave events, and it has been successfully used to evaluate the thermal resilience of different retrofitting strategies. Siu et al. [10] reviewed different heat stress and resilience metrics and proposed a framework for building performance simulation-aided resilience quantification to evaluate the thermal resilience of building designs. Studies focused on the climate resilience of the built environment with regard to other aspects, such as flooding, windstorms, water quality, and air quality, can also be found in the literature [11,12,13,14].

Numerous studies have demonstrated that climate change will worsen the moisture-related degradation of building envelope components, especially for wood frame systems. A summary of the different types of moisture-related problems affecting wood materials, which negatively impact the serviceability of the building envelope and which are categorized in the CAS standard [15], is shown in

Table 1. Moisture-related problems that affect the serviceability of wood materials in wall assemblies [15].

Mechanism	Failure	Condition for Process
Fungal decay	Loss of material; strength; appearance	Sustained moisture content (MC) > 26%; temperature 0–40 °C; oxygen > 0.25%; pH < 2.2 or >9.6
Mould growth	Appearance; potential health impacts	Sustained high relative humidity (>80%); temperature 0–40 °C; oxygen > 0.25%; pH < 2.2 or >9.6
Subterranean termites	Loss of material; strength	Access from ground; sustained moisture and oxygen; temperature ≥ 5 °C
Drying-induced shrinkage perpendicular to grain	Splitting or checking; damage to other components; floor misalignment; nail popping	High initial moisture content used in a dry environment; seasonal moisture content changes; inappropriate fastening that restricts drying; shrinkage movement of members; accumulated thicknesses perpendicular to grain (beams, stringers, plates)

. Lacasse et al. [16] conducted a comprehensive review of the impact of climate change on the durability performance of building envelope materials, including masonry materials, wooden materials, concrete, and metals. It was concluded that a change in key climate parameters such as temperature, relative humidity, and wind-driven rain could significantly influence the durability performance of building components. Defo et al. [17] performed hygrothermal simulations for the typical brick-veneer wood frame walls of buildings located in different cities based on a set of historical and projected future climate data considering a global warming increase by 3.5 °C scenario. It was determined that the risk of moisture-related degradation (i.e., the risk of mould growth in wood sheathing panels) in wood frame wall assemblies in coastal cities would increase in the future. Xiao et al. [18] assessed the changes in moisture load acting on two types of wood frame wall assemblies: vinyl-clad and brick veneer-clad wall assemblies located in different cities in Canada for both historical and future climate conditions. It was found that the moisture loads increased for most cities in Canada.

While many studies have investigated the performance of built environments in respective hazardous climate events, there remains a lack of research on using resilience to describe the long-term durability of building envelopes exposed to a changing climate. According to the definition, resilience should be based on specific capabilities, with better capabilities leading to improved performance. If the given requirements are met by the performance, a resilient performance can be concluded. The objective of this study is to define resilience capabilities that are related to moisture performance, establish metrics that can be used to quantify these capabilities, as well as investigate the correlation between these metrics and moisture performance. In this context, the moisture resilience of wood frame wall assemblies was established by considering three aspects of capability that hinge on its short-term-response atmospheric moisture. These aspects of moisture resilience were measured using mathematical-based metrics, where the values obtained were indicative of the respective performance levels. Performance rankings were applied to each metric within every aspect, and these rankings were then summarized for each individual wall assembly. Subsequently, the performance of the wall assembly with respect to the risk of formation of mould growth over the longer term was assessed through simulations utilizing 31-year climate data. The ranking for moisture resilience was linked to the long-term mould growth performance of the wall assembly, illustrating the correlation between moisture resilience and the moisture performance of the wall assembly.

2. Climate Data and Hygrothermal Simulation

2.1. Climate Data

The moisture performance of a wood frame wall assembly is typically assessed through hygrothermal simulations. To ensure unbiased and generalizable conclusions, climate data for historical and projected future time periods for various Canadian cities, each with distinct atmospheric humidity levels throughout the year, were randomly selected. These data were derived from the Canadian Regional Climate Model (CanRCM4) by Environment and Climate Change Canada (ECCC), which predicted future climate data for seven global warming scenarios, with each scenario encompassing 15 realizations based on the uncertainties of initial conditions starting in January 1950 during the climate modelling process. Details regarding the cases used in this study are specified in the subsequent discussions.

2.2. Hygrothermal Simulation

The hygrothermal simulations in this study were conducted using Delphin 5.9.6. This software was also used in numerous other research studies to investigate the performance of building envelopes [19,20,21,22,23]. Simulations were carried out on 1-D models of three types of wood frame wall assemblies: a brick-clad wall assembly, a stucco-clad wall assembly, and a vinyl-clad wall assembly. These wall assemblies were exposed to the aforementioned 31-year climate conditions. Moisture performance indicators and metrics for quantifying moisture resilience were derived from the simulation outputs. The configurations and cross-sections of each wall assembly are presented in Figure 1, Figure 2 and Figure 3, respectively. Material properties of wall components were obtained from Kumaran et al. [24]; the thermal and moisture transport property database for common building and insulation materials given in ASHRAE Transactions [25] are illustrated in

Table 2. Overview of the dynamic weather data parameters for the full heating period.

Components/Material	e (mm)	Density (kg/m3)	kt (W/mk)	CE (J/kg K)	Porosity (m3/m3)	vper (s)	vperm (ng/m2sPa)	A (kg/m2s0.5)	DL (m2/s)
Red matt clay	90.0	1900	0.500	800	0.21	1.5 × 10−12	16.2	0.0268	5.01 × 10−8
Vinyl	1.10	1500	0.160	1260	0.00	1.0 × 10−16	0.1	-	1.00 × 10−16
Stucco	10	1960	0.407	840	0.235	2.7 × 10−13	14.1	0.0123	6.34 × 10−15
Weather-Resistive Barrier	0.24	909	0.159	1256	0.97	9.7 × 10−14	404.2	0.00093	3.72 × 10−12
OSB	11.0	600	0.094	1880	0.96	2.5 × 10−13	22.6	0.0022	2.11 × 10−11
Gypsum	13.0	700	0.150	870	0.40	5.8 × 10−11	4430.0	0.001	6.35 × 10−11
Mineral fibre	140.0	37	0.032	670	0.66	1.3 × 10−10	928.6	-	1.00 × 10−18

e: thickness; kt: thermal conductivity (at 0% RH); CE: specific heat capacity (at 0% RH); vper: vapour permeability (at 0% RH); veperm: vapour permeance (at 0% RH); A: water absorption coefficient; DL: liquid diffusivity (at maximum MC); RH: relative humidity; MC: moisture content.

.

The moisture load in the simulation was considered to be 1% of the wind-driven rain (WDR) load, as specified in the ASHRAE standard 160 [26]. The air change rate for the brick wall and the stucco wall was set at 5 ACH and 2 ACH, respectively. Two different air change rates, namely 50 ACH and 200 ACH, were applied to the vinyl wall. The orientation of the wall in the simulation was chosen to face the direction with the highest WDR load for the 31-year time period. Indoor temperature and relative humidity were held constant at 21 °C and 50%, respectively. The initial temperature and relative humidity of all wall components were set at 21 °C and 80%, respectively.

2.3. Performance Indicator—Mould Growth Index

The mould growth index was selected as the criterion for evaluating the moisture performance of wall assemblies. This index, developed by Ojanen et al. [27], measures the severity of mould growth through visual inspection, assigning values that range from 0 (indicating no growth) to 6 (indicating significant and dense growth, with almost 100% coverage). The ASHRAE 160 standard [26] outlines the procedures for calculating the mould growth index. This index is influenced by factors such as relative humidity, temperature, and the duration of exposure to favourable conditions for mould growth. The sensitivity class of the material is also taken into account when calculating mould growth. The mould growth index starts at an initial value of 0, and this value accumulates over time, as specified in Equation (1).

M_t = M_(t−1) + ∆M

(1)

where Mt is the mould growth index for the current hour; M_(t−1) is the mould growth index for the previous hour; and ∆M is the change in mould growth index for each hour calculated using Equation (2) or Equation (4) based on the values of temperature and relative humidity. When the relative humidity (RH_s) at the surface of the materials is greater than the critical relative humidity (RH_crit, Equation (6)), an increment in the mould growth index is calculated using Equation (5). If surface temperature T_s ≤ 0 °C or RH_s ≤ RH_crit, a reduction in the value of the mould growth index is calculated using Equation (5).

$$∆M={\displaystyle \frac{k_1{k}_2}{168\times \exp \left(-0.68\ln T_s-13.9\ln {RH}_s+0.14W+66.02\right)}}$$

(2)

where k₁ represents the mould growth intensity factor, which is determined according to the sensitivity level of materials as indicated in

Table 3. Parameters for mould growth index calculation.

Sensitivity Class	k1
	(If M < 1)	(If M ≥ 1)	W	A	B	C
Very sensitive	1	2	0	1	7	2
Sensitive	0.578	0.386	1	0.3	6	1
Medium-resistant	0.072	0.097	1	0	5	1.5
Resistant	0.033	0.014	1	0	3	1

, k₂ is the mould growth index attenuation factor calculated using Equation (3), and W is also chosen from Table 3 according to the sensitivity level of the materials.

$$k_2=\mathrm{m}\mathrm{a}\mathrm{x}\left\{1-\exp \left[2.3\left(M-M_{max}\right)\right], 0\right\}$$

(3)

where M_max is the maximum mould growth index as relates to the surface temperature and relative humidity calculated using Equation (4).

$$M_{max}=\mathrm{A}+\mathrm{B}\left({\displaystyle \frac{{RH}_{crit}-{RH}_s}{{RH}_{crit}-100}}\right)-{C\left({\displaystyle \frac{{RH}_{crit}-{RH}_s}{{RH}_{crit}-100}}\right)}^2$$

(4)

where A, B, and C are coefficients selected from Table 3.

$$∆M=\left\{\begin{array}{c}-0.00133\times k_3 when t_{decl}\le 6\\ 0 when 6<t_{decl}\le 24\\ -0.000667\times k_3 when t_{decl}>24\end{array}\right.$$

(5)

where k₃ is the mould growth index decline coefficient; the recommended value is 0.1; and t_decl represents the number of hours from the moment conditions for mould growth shift from favourable (Ts > 0 °C and RH_s > RH_crit) to unfavourable ((Ts ≤ 0 °C or RH_s ≤ RH_crit).

The critical relative humidity for materials with different sensitivity classes is given in Equation (6):

$$\left\{\begin{array}{c}{RH}_{crit}=-0.00267T_s^3+0.16T_s^2-3.13T_s+100 when T_s\le 20 °C \\ {RH}_{crit}=80 when T_s>20 °C\end{array}\right.$$

(6)

The OSB is classified as a sensitive material according to the ASHRAE standard [26]. The corresponding coefficients given in Table 3 were selected to complete the calculations. The relative humidity and temperature on the material surface for each hour were obtained from the results of hygrothermal simulations.

3. Definition of Moisture Resilience

As per the Canadian Standard CSA S473 [15] on durability in buildings, the degradation mechanisms caused by moisture in wood components of the wood frame wall assemblies are related to fungal decay and the growth of mould. Fungal decay leads to material loss and loss in strength, posing risks to the structural integrity and safety of buildings. It is crucial to acknowledge that any compromise in materials and their strength should be regarded as a risk to the safety of the structure. Furthermore, it is important to note that the occurrence of decay is an irreversible process; this contradicts the concept of “resilience”, which involves the ability of materials to absorb, respond, and recover from climate-related stresses. Whereas mould growth can be reversed by addressing climate conditions, it serves as an indicator of long-term moisture performance and reflects the cumulative effects of prolonged exposure to excessive relative humidity levels within a specific temperature range. In other words, the severity of mould growth on the surface of wood sheathing boards reflects a wall’s capability to maintain a relatively low level of relative humidity throughout a resilience cycle, where the increases in relative humidity due to climate loading events are kept at an elevated level for a specific period of time, and ultimately recovers from the impact of the climate load event. The moisture content, which is associated with the occurrence of decay, is also influenced by the relative humidity of the material. Moreover, the exposure of the material to lower relative humidity levels decreases the likelihood of decay, whereas exposure to higher levels of relative humidity increases the risk of decay. This reduction in risk can be regarded as an improvement in the moisture performance of the material, or conversely, higher relative humidity levels can be seen as being detrimental to the material’s long-term moisture performance.

Therefore, the relative humidity should be used as the key parameter for assessing the moisture resilience of the wall assembly. In line with the definition of resilience in other aspects related to building performance, and since the growth of mould hinges on the relative humidity attaining a specific level at a given temperature, the evaluation of the moisture resilience of a wall assembly, considering that OSB is a critical component of the assembly, should encompass three essential aspects: (i) absorption—the ability of the wall to maintain a lower level of relative humidity on the OSB due to the climate impact; (ii) response—the degree of fluctuation of relative humidity on the OSB; and, (iii) recovery—the rate at which the relative humidity decreases and recovers from a critical level after a WDR event has occurred. A diagram depicting different aspects of moisture resilience is shown in Figure 4. These aspects reflect the risk as determined by the duration in time of the relative humidity, surpassing a critical threshold level.

3.1. Characteristics of Relative Humidity in the Wall Assembly

To provide a more comprehensive depiction of the meaning of the aforementioned variations in relative humidity, a hygrothermal simulation was performed for the typical wood frame walls located in Ottawa. The plots showing the relative humidity and temperature profiles on the Oriented Strand Board (OSB) of various wall assemblies obtained from hygrothermal simulations are presented in Figure 1, Figure 2 and Figure 3. These assemblies consist of a brick-clad wall with a ventilation rate of five air changes per hour (ACH), a vinyl-clad wall with 50 ACH, and a vinyl-clad wall with 200 ACH. The depicted plots encompass the simulation results obtained for a wall assembly located in Ottawa from the 14,000th to the 15,000th hour for the time period of 2034 to 2064 (the second realization), specifically within the temporal span of July 2035 to August 2035. The moisture load considered, assumed as 1% of the WDR load, was rainwater that had penetrated into the wall assembly and deposited onto the building paper.

For the brick-clad wall assembly, as shown in Figure 5, between the initial 0th and 700th hours, the relative humidity on the OSB displayed higher values in comparison to the relative humidity recorded between the 700th and 1000th hour. This difference was attributed to the frequent WDR events within the first 700 h. The relative humidity variation during the initial 700 h ranged from 85.2% to 94.5%, and the variation during the last 300 h ranged between 80.8% and 88.9%. Under stable climate conditions, the relative humidity in the brick-clad wall assembly displayed a variation of less than 10%. This variation was not sensitive to individual WDR events, possibly due to the relatively high level of relative humidity maintained in the brick masonry assembly. This high level of relative humidity was a result of the combined effects of continuous climate loads, i.e., elevated temperatures (i.e., >x °C), frequent rain events, as well as the configuration of the wall assembly. The fluctuation in relative humidity generally aligned with the daily fluctuations observed in atmospheric relative humidity. Furthermore, the temperature on the OSB also followed the variations in atmospheric temperature, albeit with a smaller magnitude of variation.

The relative humidity and temperature profiles on the OSB of the vinyl-clad wall assembly with a 50 ACH are shown in Figure 6. Similarly to the brick-clad wall assembly, the daily variation in relative humidity on the OSB of the vinyl-clad wall assembly followed the daily fluctuation in atmospheric relative humidity. However, the average level of relative humidity in the vinyl-clad wall assembly (75.6%) was lower compared to the brick-clad wall assembly (88.2%). During the initial 700 h, the relative humidity on the OSB of the vinyl-clad wall assembly was significantly influenced by the occurrence of WDR events. The relative humidity variation during this time period ranged from 59.3% to 91.6%. Subsequently, between the 700th and 1000th hour, the relative humidity gradually decreased due to a series of WDR events around the 670th hour. The relative humidity in this period ranged from 74.3% to 90.7%. The temperature profiles on the OSB of the vinyl-clad wall assembly followed the fluctuations observed in the daily atmospheric temperature profiles but with a greater extent of fluctuation compared to the brick-clad wall assembly. This difference can be attributed to the thermal storage property of exterior cladding: vinyl cladding has reduced thermal capacitance compared to brick cladding, and accordingly, the temperature within the OSB is more sensitive to short-term variations in ambient thermal loads, i.e., temperature and solar radiation.

The relative humidity and temperature profiles on the OSB of the vinyl-clad wall assembly with 200 ACH are shown in Figure 7. The daily fluctuation in relative humidity on the OSB in this particular wall assembly was significantly higher compared to both the brick-clad wall assembly with 5 ACH and the vinyl-clad wall assembly with 50 ACH. Furthermore, the average relative humidity level in this wall assembly was 73.5%, which is lower than any of the previously analyzed wall assemblies, which were 74.3% and 90.7%, respectively. During the initial 700 h, the relative humidity variation in the OSB of this wall assembly ranged from 50.4% to 90.8%, whereas for the last 300 h, it ranged from 63.2% to 89.5%. Notably, the variation in relative humidity over a relatively long time period for this wall assembly was also greater than that observed for the other two wall assemblies analyzed. As for the temperature profile, it followed the variations observed in the daily atmospheric temperature profiles, although with a relatively smaller fluctuation when compared to the vinyl-clad wall assembly with 50 ACH. This difference was attributed to the higher values of ACH, which facilitate faster heat dissipation within the wall assembly.

3.2. Moisture Resilience and Corresponding Relative Humidity Behaviours

In terms of the three aspects of resilience: absorption, response and recovery, the aspect related to absorption can be described by the average relative humidity at the exterior surface of the OSB. Given that the wall itself does not generate moisture, all moisture in a wall assembly is obtained from the atmosphere or through WDR events. A higher average relative humidity within the wall represents a greater amount of absorbed moisture. Recorded values in the previous analysis for the brick wall with 5 ACH, the vinyl wall with 50 ACH, and the vinyl wall with 200 ACH were 90.7%, 74.3%, and 73.5%, respectively. These values indicate that, when exposed to the same climate, more moisture is absorbed from the surrounding environment by the brick wall compared to the other two walls.

Regarding the aspect of resilience related to response, the brick-clad wall assembly consistently maintained a high level of relative humidity when exposed to a series of WDR events due to a low level of fluctuation in the relative humidity. In contrast, the vinyl-clad wall assembly exhibited a more rapid dissipation of the effects of WDR events on relative humidity, leading to a relatively lower level of relative humidity throughout the time period analyzed. Furthermore, the increased daily fluctuation in relative humidity observed in the vinyl-clad wall assembly with 200 ACH reduced the exposure time to critical levels of relative humidity compared to the other two wall assemblies.

The recovery aspect of resilience should be characterized by the negative change rate of the relative humidity over a certain time window. A higher negative change rate represents a greater recovery capability of a wall. This parameter for these three wall assemblies is discussed in the following section.

The relative humidity profiles at the surface of the OSB when exposed to climate loads over a colder time period are presented in Appendix A for the three wall assemblies, respectively, in Figure A1, Figure A2 and Figure A3. These profiles exhibit similarities with respect to the three aspects of resilience when compared to those observed in Figure 5, Figure 6 and Figure 7, respectively, showcasing the consistent relative humidity pattern for the same type of wall assembly. A scheme to demonstrate the meaning and implication of each aspect of moisture resilience is shown in Figure 8.

3.3. Quantification of Aspects of Moisture Resilience

The three dimensions of resilience can be articulated using corresponding mathematical measures. The relative humidity level, which pertains to the absorptive aspect of resilience, can be captured through the mean value. A lower mean value suggests reduced moisture absorption from climate impacts, indicating better resilience, whereas a higher mean value implies the opposite. The extent of fluctuation in relative humidity, associated with the response aspect of resilience, can be depicted by the standard deviation—a metric that assesses the dispersion among data points. A higher fluctuation in relative humidity, reflected by a larger standard deviation, may lead to a shorter duration in which relative humidity remains above a critical level. Furthermore, the negative rate of change in relative humidity, as related to the recovery aspect of resilience, can be illustrated by subtracting relative humidity values across specific time intervals. A higher rate indicates that there is less time required for relative humidity to return to a lower level following the climate impact. It is important to mention that the influence of the climate load on the moisture response of the wall assembly typically extends over a span of several days. In other words, the wall’s recovery process in response to the climate load can also persist for several days. Consequently, when conducting calculations for those metrics, it is necessary to test various time spans or intervals, as these can significantly influence the resulting resilience metric values.

In relation to the information provided by Figure 5, Figure 6 and Figure 7, the duration required for the relative humidity level to recover from the effect of WDR around the 673rd hour was approximately within the range of 200 to 400 h. Similarly, as shown in

Table 4. Summary of mathematical resilience metrics of different wall assemblies.

Categories	Time Spans and Intervals	Brick 5 ACH	Vinyl 50 ACH	Vinyl 200 ACH
Standard Deviation (Response)	384 h (16 Days)	2.36	3.29	5.73
	288 h (12 Days)	2.21	2.95	5.47
	192 h (8 Days)	2	2.48	5.1
Mean Value (Absorption)	384 h (16 Days)	86	81.1	71.3
	288 h (12 Days)	86	81.1	71.3
	192 h (8 Days)	86	81.1	71.3
Differences (Recovery)	384 h (16 Days)	−3.74	−5.52	−7.42
	288 h (12 Days)	−3.46	−4.92	−7.09
	192 h (8 Days)	−3.14	−4.19	−6.59

, the time spans or intervals tested for determining the value of the three resilience metrics were 192, 288, and 384 h (equivalent to 8, 12, and 16 days). The values presented in the table represent the mean values for each time interval over a duration of 31 years. For instance, the value of standard deviation established for the 384 h time span, as shown in Table 4, reflects the averaged values for standard deviation from the 1st hour to the 384th hour, the 2nd hour to the 385th hour, the 3rd hour to the 386th hour, continuing until the 271,536th hour to the 271,560th hour (to the end of the 31st year). A similar calculation was also conducted for the mean value. Regarding the differences, only negative changes were taken into account in the analysis, as they represent recovery from the impact of the climate load. The differences were calculated considering the time interval, and the length of the time interval was the same as the three values of the time span under consideration.

All three metrics presented in Table 4 align with observations derived from the preceding analysis for Figure 5, Figure 6 and Figure 7. A higher standard deviation indicates a more significant level of fluctuation in the relative humidity during those specific time spans. The vinyl wall assembly displayed the highest standard deviation, showcasing the most significant relative humidity fluctuation. Similarly, the vinyl wall assembly with 50 ACH exhibited a greater standard deviation than the brick wall assembly with 5 ACH, indicating a more substantial fluctuation. The choice of time spans for calculating standard deviations significantly influenced the values obtained; as the time span increased, more substantial differences were observed between the values of the standard deviation of distinct wall assemblies. The mean relative humidity value was not (indeed, should not be) affected by the time spans selected. The average relative humidity levels for each wall assembly, as shown in Table 4, aligned with the findings outlined in the previous analysis. Specifically, the brick wall with 5 ACH exhibited a relatively higher average relative humidity compared to the other two vinyl wall assemblies. Additionally, the vinyl wall assembly with 50 ACH had a greater average relative humidity level than the one with 200 ACH. The most significant difference in the recovery of relative humidity occurred with the vinyl wall assembly with 200 ACH, showcasing a superior rate of recuperation from the climate load’s influence in comparison to the other two wall assemblies. Likewise, the vinyl wall assembly with 50 ACH exhibited a more rapid rate of recovery than the brick wall assembly at 5 ACH. These findings are also consistent with the conclusions drawn in the preceding analysis. Importantly, while the duration of the time span, or interval length, does indeed influence the values for the resilience metric, the relative distinctions between various wall assemblies persist, reflecting their specific moisture resilience attributes.

Considering the potential for a broader application of these resilience metrics to different wall assemblies, a greater discrepancy in these metrics between each assembly will help accurately differentiate their relative performance. Thus, for the subsequent sections of analysis, a 384 h time span, or interval, was employed to compute the resilience metrics.

An overview is presented in

Table 5. Summary of characteristics for each wall assembly related to the different aspects of moisture resilience.

Wall Types	Resilience				31-Year Averaged Mould Growth Index
	Response	Absorption	Recovery	Overall Ranking
Brick 5 ACH	3	3	3	3	4.54
Vinyl 50 ACH	2	2	2	2	0.02
Vinyl 200 ACH	1	1	1	1	0.001

, in which the characteristics of each wall assembly are given that pertain to the diverse facets of moisture resilience. It is worth noting that the mould growth index and the relative humidity at the surface of the OSB in the previous analysis were derived from the same set of simulation results. To facilitate a comparative analysis of the moisture performance of the various wall assemblies across each aspect, ranking was employed for the three cases analyzed based on the metrics presented in Table 4, with a higher ranking indicating a superior performance. The overall score serves as a qualitative indicator of the overall resilience defined by the three resilience aspects. The evidence suggests that a higher overall resilience ranking is indicative of better moisture performance, as reflected by the mould growth index over a 31-year simulation period. This observation further implies that the variations in relative humidity, as defined by the three aspects of absorption, response, and recovery, can effectively serve as indicators of moisture resilience in wall assemblies.

The three facets of moisture resilience are influenced either individually or as a whole by varying configurations of the wall assembly. Altering these assembly configurations to enhance these resilience aspects is expected to lead to an overall improvement in moisture performance.

4. Moisture Resilience of Different Wood Frame Wall Assemblies Under Different Climate Conditions

The assessment of moisture resilience for the analyzed wall assemblies, as presented in Table 5, was conducted under a specific climate condition. Further exploration was required to determine whether comparable findings or the correlation between the newly defined moisture resilience and the moisture performance hold true for different types of wall assemblies exposed to diverse climatic conditions. In this section, the moisture resilience and moisture performance of a stucco-clad wall assembly, as well as additional climate conditions, will be discussed, together with the three previously mentioned wall assemblies. The influence of various aspects of moisture resilience on moisture performance is demonstrated by discussing two separate scenarios: one involving the same type of wall assemblies exposed to different climates and another involving different wall assemblies exposed to the same climate. Using this approach, the influence of a variation in wall configuration and that of different climate conditions will thereby be excluded from the assessment of moisture performance. Metrics describing the relative capabilities of the three aspects of moisture resilience will be employed to explain the variations in moisture performance for the different assessment scenarios considered.

Metrics that describe different aspects of moisture resilience for the same type of wall assembly exposed to different climate conditions are listed in

Table 6. Summary of mathematical metrics of different wall assemblies subjected to different climates.

Wall Assemblies	Cities and Climate Scenarios	Standard Deviation: Response (Ranking)	Mean Value: Absorption (Ranking)	Differences: Recovery (Ranking)	31-Year Averaged Mould Growth Index
Brick 5 ACH	Calgary F7 (R8) *	2.39 (2)	81.8 (1)	−3.43 (2)	3.38
	Halifax F0 (R11)	2.96 (1)	88.7 (3)	−4.4 (1)	4.38
	Toronto F4 (R3)	1.72 (3)	87.8 (2)	−2.41 (3)	4.4
Vinyl 50 ACH	Saskatoon F0 (R13)	2.37 (3)	71.2 (1)	−4.11 (3)	0.0268
	Montreal F4 (R10)	3.24 (2)	76.4 (2)	−4.73 (2)	0.0652
	Vancouver F7 (R7)	3.4 (1)	84.1 (3)	−6.03 (1)	4.92
Vinyl 200 ACH	Winnipeg F0 (R6)	4.03 (2)	71.9 (1)	−5.29 (2)	0.0006
	Moncton F4 (R3)	5.53 (1)	77.1 (2)	−6.82 (1)	0.0158
	St. John’s F7 (R6)	3.72 (3)	85.7 (3)	−5 (3)	0.863
Stucco 2 ACH	Calgary F7 (R3)	1.78 (1)	86.6 (1)	−3.48 (1)	3.5
	Toronto F4 (R2)	1.43 (2)	92.3 (2)	−2.99 (2)	4.32
	Halifax F0 (R1)	0.745 (3)	97.1 (3)	−1.34 (3)	4.76

F0, F4, and F7 represent the following time periods: 1986–2016, 2034–2064, and 2062–2092, respectively. * R8 represents the 8th realization of the climate data generated from the climate model.

. Hygrothermal simulations were conducted for each wall assembly using randomly selected climate data from three cities with varying degrees of atmospheric humidity throughout the year. Ranking numbers were assigned to each aspect of moisture resilience for the three climate scenarios to which the brick-clad wall assembly was exposed. As was discussed on the basis of information provided in Table 5, a higher ranking indicates better resilience.

For the brick-clad wall assembly, the overall ranking of different aspects of moisture resilience is higher in Calgary, and the corresponding mould growth index (MGI) is also smaller, which reflects a better moisture performance. The MGI for the brick-clad wall assembly in Halifax and Toronto was nearly identical. Despite the fact that the ranking of the response in Halifax was lower than that in Toronto, the discrepancy in the values of the metric describing the response was very small. The rankings for the absorption and recovery in Halifax were higher than those in Toronto. This could explain why the MGI in Halifax was slightly smaller than that in Toronto, even though the response for the brick wall assembly in Toronto was slightly better.

In the case of the vinyl wall assembly with 50 ACH, the ranking of response was determined by the magnitude of the MGI. This phenomenon is reasonable, given that the MGI is directly influenced by the magnitude of relative humidity. According to the ASHRAE standard 160, a minimum relative humidity of 85% is required for mould growth to occur. The mean relative humidity values in Saskatoon and Montreal were both lower than the threshold value. The variation in relative humidity, as represented by response and recovery aspects of the moisture resilience, was deemed insignificant in terms of its impact on the MGI in these cases. Similar observations were also applied to the vinyl wall with 200 ACH and the stucco wall with 2 ACH. In the case of the stucco wall, the ranks of all three metrics were in descending order, indicating a higher MGI and reflecting a poorer moisture performance.

In

Table 7. Summary of mathematical metrics of different wall assemblies subjected to the same climate.

Cities and Climate Scenarios	Wall Assemblies	Standard Deviation: Response (Ranking)	Mean Value: Absorption (Ranking)	Differences: Recovery (Ranking)	31-Year Averaged Mould Growth Index
Calgary F7 (R3) *	Vinyl 200 ACH	5.35 (1)	63.8 (1)	−6.96 (1)	0.00293
	Vinyl 50 ACH	3.42 (2)	67.2 (2)	−5.54 (2)	0.0812
	Brick 5 ACH	2.26 (3)	83.4 (3)	−3.27 (4)	3.78
	Stucco 2 ACH	1.78 (4)	86.6 (4)	−3.48 (3)	3.5
Toronto F4 (R2)	Vinyl 200 ACH	5.12 (1)	70.3 (1)	−6.06 (1)	0.0022
	Vinyl 50 ACH	3.22 (2)	75.9 (2)	−4.98 (2)	0.182
	Brick 5 ACH	1.7 (3)	87.5 (3)	−2.35 (4)	4.2
	Stucco 2 ACH	1.43 (4)	92.3 (4)	−2.99 (3)	4.32
Halifax F0 (R1)	Vinyl 200 ACH	5.2 (1)	80.9 (1)	−6.95 (1)	0.213
	Brick 5 ACH	3.03 (2)	88.5 (2)	−4.38 (2)	4.34
	Stucco 2 ACH	0.745 (4)	97 (3)	−1.34 (4)	4.76
	Vinyl 50 ACH	0.759 (3)	97.2 (4)	−1.41 (3)	4.92

F0, F4, and F7 represent the following time periods: 1986–2016, 2034–2064, and 2062–2092, respectively. * R3 represents the 3rd realization of the climate data generated from the climate model.

, resilience metrics for different wall assemblies exposed to identical climate conditions are presented. In this section, climate scenarios for three cities are included, and rankings are applied to the metrics for different wall assemblies subjected to the same climate. The rankings for absorption and response displayed a consistent correlation with the MGI level, where a higher ranking consistently indicated a lower MGI across various wall assemblies for all climate scenarios analyzed. The recovery performance of the brick wall with 5 ACH was slightly better than that of the stucco wall with 2 ACH in Calgary and Toronto. However, given the notable discrepancies in response between the two walls in these two cities, the limited differences in the recovery metric did not significantly affect the relative MGI level. In Halifax, the rankings for the absorption and recovery of the vinyl wall with 50 ACH were higher than those of the stucco wall with 2 ACH. Nonetheless, the MGI of the vinyl wall was slightly greater than that of the stucco wall. This can be attributed to the stucco wall having a higher response ranking and the relatively small magnitude of discrepancies between the other two metrics.

Based on the analysis presented in this section, it can be further inferred that the ranking of absorption is of greater significance in determining the MGI level, as the MGI directly correlates with the magnitude of relative humidity. Response and recovery, on the other hand, contribute to assessing the relative fluctuations in relative humidity around its mean value. When there is a substantial discrepancy in mean values among the different cases, the impact of response and recovery capabilities on the MGI level is relatively minor.

5. Conclusions and Future Work

In this study, the moisture resilience of wood frame wall assemblies was defined by three aspects: absorption, response, and recovery. These aspects were used to represent the wall’s capability to maintain a low level of relative humidity on the OSB, the degree of relative humidity fluctuation on the OSB, and the rate at which relative humidity decreases and recovers from a critical level, respectively. Each of these aspects related to the moisture resilience, was quantified by three metrics, respectively: the mean value, standard deviation, and negative differences in relative humidity at the surface of OSB within a wall assembly. Relative humidity data were obtained from hygrothermal simulations conducted on four wood frame wall assemblies using climate data from randomly selected Canadian cities. Rankings were subsequently assigned to these metrics, and the overall ranking of a wall assembly was then associated with its corresponding MGI level.

It is evident that the assessment of moisture performance in different wall assemblies under different climatic conditions can be facilitated through an examination of the relative performance of these three aspects of moisture resilience. In particular, an inference can be drawn regarding the pronounced importance when ranking moisture performance using the absorption metric in influencing the MGI due to its direct association with the degree of relative humidity. In contrast, response and recovery metrics contribute to the assessment of fluctuations in relative humidity around its mean value. In cases where significant differences in mean values were observed among different scenarios, it became evident that the impact of response and recovery metrics on the MGI level was relatively limited as compared to that of the absorption metric.

Future endeavours will involve identifying factors, including environmental conditions and wall assembly configurations, that affect different aspects of resilience. These factors will be examined to evaluate their relative influence on moisture performance. Measures will be considered for the promotion of enhancements to specific aspects of moisture resilience, thus contributing to an overall improvement in the moisture performance of wall assembly types. Additionally, expanding the study to encompass additional wall assembly types and a broader spectrum of climate conditions will also be considered. Simultaneously, criteria associated with the moisture resilience that can be employed to determine whether a wall assembly is resilient or not will be investigated.