1 Introduction

A building is a complicated system that needs to have various performance objectives, such as a comfortable indoor environment (thermal, acoustic, air quality, and light), structural stability, accessibility, aesthetics, security, and information technology. Now, due to concerns over global warming and high energy costs, buildings are required to meet a sustainability goal as well. To maximize or optimize these various characteristics, architects and building designers have started to pursue a whole building design approach, in which building systems are designed as interdependent parts of the entire system rather than focusing on individual characteristics [1]. A building can be optimized to satisfy various design needs through this approach.

The International FORUM of Fire Research Directors suggested that “(in sustainable building design), optimizing a product or system without fire performance as one of the parameters can lead to an increase in the risk of fire with serious consequences on human health, the environment, and economic investment [2].” It is necessary to consider fire performance as well as other design objectives when a sub-system or system in a building is optimized. While meeting codes and standards for fire safety is important, it is essential to note that safety regulations often represent the minimum requirement for fire safety that a society expects. Merely meeting these regulations may not necessarily optimize fire performance in a building. By considering fire performance as part of the building optimization process, which includes optimizing building materials and their fire performance as variables, there is potential not only to enhance fire safety beyond regulatory compliance, but also to use materials more efficiently and improve overall building performance. This approach allows for a more comprehensive and holistic consideration of fire performance in building design, leading to optimized solutions that go beyond meeting minimum regulatory requirements. It is challenging, however, for a designer to consider all design objectives and options without the help of an assistant design tool due to the characteristics of the design objectives being different and the various design factors that must be considered. A design tool that can help to consider these objectives can be beneficial for this complex decision problem.

Thermal insulation is one of the key materials in modern buildings, as it is related to critical building performance such as energy consumption, fire safety, soundproofing, human health, environmental impact, and sustainability. There are a few studies to develop methodologies to help choose the right insulation materials while considering fire safety performance. The works by Hidalgo [3] and Roberts [4] are two of the most recent examples of this tool. Hidalgo developed a methodology to determine failure criteria of each type of insulation material, and it focuses on fire performance without considering other types of performance. Roberts developed a methodology to consider various performances as well as fire safety performance. This methodology focuses on fire safety performance, sustainability, thermal resistance, cost, acoustic damping, and durability of insulation materials, but not the entire wall systems that contain the insulation materials [4]. For example, for fire safety performance, the methodology considers Flame Spread Index (FSI), Smoke Development Index (SDI), and the heat release rate per unit area of each insulation material. These are the burning characteristics related to the material when they are exposed to a fire.

Relying solely on the fire performance of insulation material, however, can be problematic because it may differ from the real fire performance of the system that includes the insulation material in a fire. For example, FSI and SDI are tested using ASTM E84 [5], or UL 723 [6], in which the samples are exposed to the fire source and also measure the flame spread and smoke development. In real life, the insulation material is normally protected by sheathing material. Also, the fire performance of the wall system (which consists of insulation material and sheathing layer) is significantly different from the fire performance of the insulation material only. Thus, it is crucial to consider the fire performance of wall systems as it provides a more realistic demonstration of a wall on fire, rather than solely focusing on the fire performance of individual materials, such as ASTM E84, in order to fully understand their behavior in a fire event.

Lightweight construction is one of the most widely used construction styles in the United States. In this construction, a wall system normally consists of two sheathing layers and one insulation layer between them. To differentiate from other wall assemblies, let’s call this the wall-insulation system hereinafter. This research aims to develop a methodology to optimize the elements of the wall insulation systems in lightweight construction buildings while considering the essential building performances as well as fire safety performance. Note that structural elements such as steel studs and wood studs are normally used in wall assemblies, and the effects of these elements are often not negligible, such as thermal bridging effect in energy performance and thermal bowing effects of steel studs in post flashover fire. For the simplistic approach, the effects of the structural elements are not included in this study. And a box-type building is assumed as a prototype building for this tool development. When the methodology was developed, several issues related to the current wall-insulation system design approaches were considered.

  1. 1.

    Current regulations indirectly require putting flame retardant materials into foam plastic insulation, even in the case where there might be no additional fire safety benefits. This is problematic because flame retardant materials have environmental and health issues. In addition to this, adding flame retardant materials would increase the cost of foam plastic insulations that usually have higher R-values. This would eventually limit the customer's options to build better energy-efficient buildings.

  2. 2.

    Using ½ inch gypsum boards for a thermal barrier without consideration of specific building conditions could create fire safety issues when a compartment has a worse fire condition than the standard fire condition. In addition, installing a proper thermal barrier is an essential prerequisite for not using flame retardants in foam plastic insulations. A tool to design proper thermal barriers should be included in the proposed design approach.

  3. 3.

    For the whole building design, which is a more suitable approach for sustainable design, it is important to estimate how each design factor affects the whole system performance. The performance-based design method is appropriate for this purpose because this method allows consideration of the design effects on various performances.

To reflect these issues, a new performance-based, multi-characteristics tool for wall-insulation systems was developed. The next section of this paper provides a background study including the issues of current insulation system design approaches. Following that, a new design approach is introduced, and details are explained. Lastly, the design tool is applied to specific cases.

2 Background

2.1 Multiple Objects of the Methodology: Energy Performance, Sound Performance, Fire Safety Performance, Sustainability, and Cost

In this method, five performance characteristics were selected—energy performance, soundproofing performance, fire safety performance, sustainability, and cost. It is well known that energy performance and soundproofing performance are two of the most important performance characteristics of a wall-insulation system. Approximately 10–45% of total heat loss from a building is through the wall-insulation system, i.e., a critical factor to determine the heating and cooling cost [7]. Sound can be “a very real form of pollution” [8] and it is important to reduce the transmission of sound through the wall-insulation systems. This performance is closely related to the privacy of people, and poor performance may cause discomfort or even pain; pain often occurs from a high level of noise around 130 dB. Interestingly, heat transfer phenomena in solid materials and sound transmission can both be explained as “mechanical vibrations transmitted through the atomic lattice [9],” which is evident with the research efforts to develop new materials to control heat and sound together [9, 10]. One of the most widely quoted definitions of sustainability is from the concept of sustainable development, articulated by the Brundtland Commission of the United Nations on March 20, 1987: "sustainable development is a development that meets the needs of the present without compromising the ability of future generations to meet their own needs" [10, 11]. The metrics to represent sustainability for buildings are often about the consumption of resources such as water or electricity and emission of gasses against the environment such as carbon dioxide. Buildings account for 39% of total U.S. energy consumption and 72% of total U.S. electricity consumption [12] and about 40% of the nation’s total carbon dioxide emission [13]. The metrics are often based on the life cycle assessment (LCA) [14]. Cost as a universal motivation for any engineering decision may sometimes be the most important factor in selecting the wall-insulation system. The current study includes both product and installation costs.

2.2 Current Insulation System Design Approach in the Building Codes and Challenges Related to Fire Safety Performance

The fire safety performance of a wall-insulation system is influenced mainly by two components: the external sheathing layer and the internal insulation layer. When a foam plastic material is used in the insulation layer, it is crucial to provide enough thermal protection by a sheathing layer as they often generate severely hazardous gas products when they burn [15]. Due to this, the 2018 International Building Code (IBC) prescribes two protection measures when foam plastic insulation materials are used: surface burning characteristics and thermal barrier. For the former one, foam plastic insulations shall have a flame spread index of not more than 75 and a smoke-developed index of not more than 450 per ASTM E84 [5]. For the latter, IBC requires a thermal barrier such as a ½ inch gypsum board or other materials meeting the acceptance criteria based on two standard tests in NFPA 275 [16]: the temperature transmission fire test and the integrity fire test. The temperature transmission fire test is based on the ASTM E119 [17], or UL 263 [18] which is about the fire-resistant performance of building components in the post-flashover fire condition, and the integrity fire test is about how an insulation system reacts to a pre-flashover fire.

While IBC refers to two standardized fire tests: ASTM E84 and ASTM E119, there are criticisms for each of these fire tests. A previous study by Babrauskas [19] argued that ASTM E84 requirements on plastic foam insulation materials are not necessary when a thermal barrier is installed because a thermal barrier is enough to protect the foam plastic insulation material. It may even be problematic because of the flame retardant's health and sustainability issues [10, 19]. Flame retardants often are applied to insulation materials to meet ASTM E84 requirements. In addition, many studies and literature argue that ASTM E84 is “unreliable in assessing the hazards of plastic foam [19],” and “should be disregarded for foam plastics” [20]. One of the main reasons for this is related to the mounting geometry of specimens. Per ASTM E84, the specimen is mounted on the ceiling facing downward in a tunnel-shape furnace with a burner located at one end of the tunnel. Soon after ignition, thermoplastic foam insulation tends to melt and drip onto the furnace floor, which can render the result inaccurate.

The performance of thermal barriers is tested in a furnace against the standard time–temperature curve specified in the ASTM E119 shown per NFPA275. The time–temperature curve was developed more than a century ago and thus does not capture improved understandings of modern fire characteristics [21]. In Fig. 1, the two temperature curves other than the standard time–temperature curve were obtained from actual compartment fire tests [22]. The fire intensity in the initial phase becomes more severe than that represented by the time–temperature curve. This discrepancy in an early fire development period can be especially problematic for the thermal barrier design because the role of thermal barriers is mainly to protect the insulation for the initial 15 min of fire [16]. Testing a thermal barrier against lower temperature could lead to a low-quality wall-insulation system that could fail earlier in a real fire situation. Note that in real fire situations, the time–temperature curves may be lower than the standard curves depending on the types and amounts of materials inside the room.

Figure 1
figure 1

Comparison of temperature–time curves in natural fires with standard temperature–time curves (Figure is modified from reference [22])

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3 Introduction to the Proposed Design Tool

3.1 Structure of the Design Tool

The workflow of the proposed tool is presented in Fig. 2, which consists of the following five main steps:

  1. (1)

    User inputs of building characteristics, environmental temperature data, and material information;

  2. (2)

    Quantification of performance levels of wall-insulation systems for each design objective;

  3. (3)

    Normalization of the quantified performance;

  4. (4)

    Calculation of total performance scores taking into account the priorities of objectives;

  5. (5)

    Selection of optimum insulation systems.

Figure 2
figure 2

Design flow of the proposed tool

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First, the user should define building information (compartment and opening dimensions), materials information for insulation and sheathings of wall-insulation systems, and climate information. Second, the performance levels of the wall-insulation systems are estimated for the following five sub-models: energy-consumption performance (EP), soundproofing performance (SP), fire safety performance (FP), sustainability performance (SuP), and cost performance (CoP). Further details of each sub-model are included in the next section. Third, the estimated performance levels in the sub-models are normalized for the comparison of parameters having different units and priorities. Fourth, the decision analysis model integrates all performance levels of the wall-insulation systems and provides a quantified score for each system. Then lastly, the optimal wall-insulation system is recommended to the user.

3.2 Details of Sub-models

3.2.1 Energy-Consumption Performance (EP) Sub-model

The EP sub-model estimates how much energy is consumed in a building. An energy balance approach is applied with the following assumptions:

  • The temperature in the room \(({T}_{g})\) is uniform (one zone assumption).

  • Outdoor temperature is uniform, and the average monthly temperatures are used for each month’s temperature.

  • The thermal mass in the wall over a sufficiently long period has no significant impact on total heat flow and the main solar heat gain occurs through fenestration such as windows and glass doors.

  • Heat is transferred one-dimensionally.

The control volume for a simple building is illustrated in Fig. 3.

Figure 3
figure 3

The schematic diagram for energy balance in the energy-consumption performance sub-model

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Energy balance for the control volume and the conditions in Fig. 3 is expressed as

$${\dot{q}}_{st}=({\dot{q}}_{rad}+{\dot{q}}_{occu}+{\dot{q}}_{elec})-\left({\dot{q}}_{cond}+{\dot{q}}_{vent}+{\dot{q}}_{infil}\right)+{\dot{q}}_{HVAC}$$
(1)

where \({\dot{q}}_{rad}\) is the solar radiation gain, \({\dot{q}}_{occu}\) is the heat gain by occupants, \({\dot{q}}_{elec}\) is the heat gain by using electrical devices, \({\dot{q}}_{cond}\) is the conduction heat loss, \({\dot{q}}_{vent}\) is the ventilation heat loss with heat recovery, \({\dot{q}}_{infil}\) is the infiltration heat loss through leakages in a building, and \({\dot{q}}_{HVAC}\) is the heat gain by the HVAC system. The unit for these terms is [W].

The solar radiation gain is calculated based on Eq. (2).

$${\dot{q}}_{rad}=\chi {A}_{fen}G$$
(2)

where \(\chi\) is the solar heat gain coefficient, i.e., the fraction of solar radiation that results in heat gain to space (= 0.75 [23]), \({A}_{fen}\) is the area of building fenestration [m2], and G is the irradiation of the sun to the building fenestration [W/m2].

Based on the assumption of the quasi-steady-state condition, the heat loss through the wall is as below,

$${\dot{q}}_{cond}=\frac{{A}_{w}}{R}\left({T}_{g}-{T}_{\infty }\right)$$
(3)

where \({A}_{w}\) is the wall surface area [m2], \({T}_{g}\) is the indoor air temperature [K], \({T}_{\infty }\) is the outdoor temperature [K], and R is the thermal resistance [m2 K/W] and written as Eq. (4).

$$R=\left(\frac{1}{{h}_{ext}}\right)+\sum \left(\frac{{L}_{n}}{{k}_{n}}\right)+\left(\frac{1}{{h}_{int}}\right)$$
(4)

where \({h}_{ext}\) and \({h}_{int}\) are exterior and interior convective transfer coefficient (W/m2 K), \({k}_{n}\) is thermal conductivity (W/m2 K), and \({L}_{n}\) is the thickness [m].

The ventilation heat loss is presented in Eq. (5).

$${\dot{q}}_{vent}= \left(1-\frac{\beta }{100} \right){c}_{p,0}{\rho }_{0}\dot{V}{A}_{f}({T}_{g}-{T}_{\infty })$$
(5)

where \(\beta\) is heat recovery efficiency (%), \({c}_{p,0}\) is the specific heat of air (J/kg K), \({\rho }_{0}\) is the density of ambient air [kg/m3], \(\dot{V}\) is ventilation rate per floor area (m3/m2 s), and \({A}_{f}\) is the area of floor (m2).

The net heat loss by air infiltration [Eq. (6)] is,

$${\dot{q}}_{infil}={c}_{p,0}{\rho }_{0}nV({T}_{g}-{T}_{\infty })$$
(6)

where \(n\) is air replacement per second (1/s), and \(V\) is building volume (m3)\(.\) With this approach, the heating and cooling energy to maintain the comfort temperature can be calculated. Refer to a previous study [10] for further information.

3.2.2 Fire Safety Performance (FP) Sub-model

The FP sub-model calculates the temperature profiles of the insulation systems and also estimates its failure times. It consists of both a fire severity model and a heat transfer model. Based on the fuel load, the compartment’s size and its lining materials, and the ventilation condition, the fire severity model generates a probable time–temperature curve. The heat transfer model then calculates the temperature profile of the wall-insulation system subjected to the time–temperature curve from the fire severity model. The performance is quantified in terms of the failure time of the insulation layer.

The parametric time–temperature curve adopted in the Eurocode [24] is used for the fire severity model. For further details, please refer to the previous study [25].

The heat transfer model uses the one-dimensional transient heat diffusion equation without heat generation; the governing equation and boundary conditions are presented in Eq. (7). BC1 and BC2 refer to the exposed and unexposed boundaries to fire, respectively.

$$\frac{\partial }{\partial x}\left(k\frac{\partial T}{\partial x}\right)=\rho c\frac{\partial T}{\partial t}$$
(7)

BC1: at x = 0, \(k\frac{\partial T}{\partial x}={h}_{c-in}\left({T}_{g}-T\right)+\varepsilon \sigma ({T}_{g}^{4}-{T}^{4})\).

BC2: at x = L, \(k\frac{\partial T}{\partial x}={h}_{c-out}\left(T-{T}_{\infty }\right)\).

where T is the temperature of the sheathing or insulation layers at different locations, \(k\) is thermal conductivity (W/m K), \(\rho\) is density (kg/m3), and \(c\) is specific heat (J/kg K). \({h}_{c-in}\) and \({h}_{c-out}\) are the convective heat transfer coefficients for the inside (assumed to be 25 W/m2) and outside (assumed to be 10 W/m2) compartment, respectively. L is the total thickness of the wall-insulation system (m). Note that the convective heat transfer coefficients were assumed above for general applications, but they can be changed when special situations should be considered.

This partial differential equation is solved numerically using the Finite Difference Method (FDM) assuming the boundary surfaces are met perfectly. The failure time is defined to be the moment at which the first node of the insulation layer reaches its failure temperature (or minimum ignition surface temperature) in this study.

3.2.3 Soundproofing Performance (SP) Sub-model

The SP sub-model estimates the sound transmission loss through an insulation system. Figure 4 presents a schematic diagram of the one-dimensional sound model for the wall-insulation system.

Figure 4
figure 4

Schematic diagram of one-dimensional soundproofing performance sub-model: x is the sound source; \({\Omega }_{i}\) is the acoustic domain, i (e.g. rooms); \(k\) is the material propagation constant; A is admittance (m3/Ns) (Figure is modified from reference [26])

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The propagation of a sound wave through a stationary medium can be modeled by a one-dimensional Helmholtz equation as Eq. (8).

$$\frac{{d}^{2}{p}_{i}}{d{x}^{2}}+{k}^{2}{p}_{i}=0$$
(8)

where k is the wavenumber (\(k=\omega /c\)), \(\omega =2\pi f\) (the angular frequency), c is the speed of sound (m/s), \(f\) is frequency (Hz), and p is the sound pressure (Pa).

The analytical solution provided by Poblet–Puig [26] is used for the soundproofing performance sub-model.

3.2.4 Sustainability (SuP) Sub-model

The three key factors identified by Roberts [4] was used to assess sustainability: carbon dioxide equivalent (CO2e) (kg), total energy usage (MJ), and water consumption (kg). For the sustainability values, Life Cycle Assessment (LCA) [4, 14, 27] was used. Note that cradle-to-grave assessment is the full life cycle assessment that considers the effects of a product from obtaining of natural resources (cradle) to disposal phase (grave). However, it is challenging to get the data of all materials based on the cradle-to-grave assessment. Many manufactures provide environmental product declarations, and they are usually based on cradle-to-gate assessment which consider the effects from obtaining of natural resources (cradle) to the factory gate (gate). The database in this study is based on cradle-to-gate assessment.

The functional unit is defined as the amount of usage that corresponds to one R-value (m2K/W) per one square meter of the wall-insulation components. The carbon dioxide equivalent of a wall-insulation system is calculated as shown in Eq. (9).

$${x}_{{co}_{2e}}={x}_{{co}_{2e}, SH1}+{x}_{{co}_{2e}, IN}+{x}_{{co}_{2e}, SH2}$$
(9)

where \({x}_{{co}_{2e}, SH1}\), \({x}_{{co}_{2e}, IN}\) and \({x}_{{co}_{2e}, SH2}\) is the carbon dioxide equivalent values for sheathing layer 1 (SH1), insulation material (IN), and sheathing layer 2 (SH2), respectively.

Note that carbon footprint is one of the widely used terms for environmental impacts by human activities, and it is defined as “a measure of the exclusive total amount of carbon dioxide emissions that are directly and indirectly caused by an activity or is accumulated over the life stages of a product [28].” Other greenhouse gases such as methane (CH4) or nitrous oxide (N2O) can be converted to CO2e. For example, the global warming potential for methane over 100 years is 21 tons of CO2e and it means one ton of methane emissions is equivalent to 21 tons of carbon dioxide emission [29].

The total energy usage of an insulation system is estimated using Eq. (10).

$${x}_{eu}={x}_{eu, SH1}+{x}_{eu, IN}+{x}_{eu, SH2}$$
(10)

where \({x}_{eu, SH1}\), \({x}_{eu, IN}\) and \({x}_{eu, SH2}\) are the total energy usage (MJ) for interior sheathing (SH1), insulation material (IN), and exterior sheathing (SH2), respectively.

The total water consumption of an insulation system is estimated as shown in Eq. (11).

$${x}_{wc}={x}_{wc, SH1}+{x}_{wc, IN}+{x}_{wc, SH2}$$
(11)

where \({x}_{wc, SH1}\), \({x}_{wc, IN}\) and \({x}_{wc, SH2}\) are the water consumption [kg] for interior sheathing (SH1), insulation material (IN), and exterior sheathing (SH2), respectively.

Due to the discrepancy of concepts and units, each term is normalized first; and the total sustainability performance value is determined to be the sum of each normalized term divided by three.

3.2.5 Cost (CP) Sub-model

The cost of insulation includes the cost of materials, labor, and equipment that the contractor might pay [30]. The cost of insulation is based on per unit area of insulation \(\left[{m}^{2}\right]\). The total cost of an insulation system is estimated as shown in Eq. (12).

$${x}_{co}={x}_{co, SH1}+{x}_{co, IN}+{x}_{co, SH2}$$
(12)

where \({x}_{co, SH1}\), \({x}_{co, IN}\) and \({x}_{co, SH2}\) are the cost values [$] for interior sheathing (SH1), insulation material (IN), and exterior sheathing (SH2), respectively. Various sources such as reference [30] can be used to estimate the cost performance. Note that the cost of energy consumption is not included in this section.

3.2.6 Normalization and Decision Analysis Model

A multi-attribute decision analysis model helps to compare and evaluate various attributes and alternatives systematically [31]. Equation (13) is an additive form of multi-attribute evaluation. The performance score, \(v\), is defined as a parameter that represents the total performance level of the five attributes:

$$v\left({x}_{1}, {x}_{2}, \ldots , {x}_{n}\right)={\sum }_{i=1}^{n}{{w}_{i}r}_{i}({x}_{i})$$
(13)

where \({w}_{i}\) is the weight and \({r}_{i}\) is the normalized performance value. Note that each performance model has different levels of detail and importance. As a result, all categories are separately normalized based on the minimum and maximum values of each performance. Additionally, each category has its own weights. To compare the physical outputs of each sub-model and parameters from manufacturers, data transformation techniques are necessary because they have different units of measurement [32]. To convert the data into a homogenous data type, the linear normalization function is used [32]. For the beneficial attributes for soundproofing and fire safety performance, i.e., the higher the value, the better the performance, the normalization function can be expressed as

$${r}_{i}=\frac{{x}_{i}-{x}_{min}}{{x}_{max}-{x}_{min}}$$
(14)

where \({x}_{max}\) and \({x}_{min}\) are the maximum and minimum values of an attribute, i.

For the detrimental attributes for energy-consumption, sustainability, cost performance, the normalization function can be expressed as

$${r}_{i}=\frac{{x}_{max}-{x}_{i}}{{x}_{max}-{x}_{min}}$$
(15)

One of the important steps for the weighted-sum method in Eq. (13) is to decide weights for the attributes. For an important attribute, a higher weight should be assigned while lower weights should be used for less important attributes. If a decision-maker has specific weights for each attribute in mind, those should be used. In case it is difficult to decide the appropriate weights, a tool such as the Analytical Hierarchy Process (AHP) [33] may be useful, which has been widely reviewed and applied in many fields [10, 22].

3.3 Wall-Insulation System Options

The proposed tool includes a material database for 17 sheathing materials and 7 insulation materials by default. Users can add more materials.

3.3.1 Sheathing Materials

A total of 17 materials, gypsum boards (1–7), plywood (8–12), and oriented strand boards (OSBs) (13–17) are included in the list of sheathing layers as shown in Table 1. Note that reference [14] provides values for 5/8″ gypsum board, and values for other thicknesses were extrapolated based on the assumption that the values increase as the thickness of the gypsum board increases.

Table 1 Thermal and Sustainable Properties of Sheathing Materials
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When inert and non-foam plastic insulation is used for the insulation layer, a thermal barrier is not required per IBC. However, when a foam plastic insulation material is used, the exposed sheathing layer to fire should work as a thermal barrier.

3.3.2 Insulation Materials

Table 2 includes the thermal and sustainability properties of the insulation materials. Note that the insulation material selection and main property data are based on Roberts [4]. Among these, INS No. 5, 6, and 7 are foam plastic insulation materials, and IBC requires a 15 min thermal barrier for these.

Table 2 Thermal and Sustainable Properties of Insulations
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3.3.3 Wall-Insulation System Options

As mentioned previously, a wall-insulation system in this research is defined as a composite system that includes a sheathing layer (SH1), an insulation layer (IN), and another sheathing layer (SH2). With 17 types of SH1, 7 types of IN, and 17 types of SH2, a total of 2023 combinations are available. Table 3 shows some of them as examples. The naming convention for the sheathing is ‘material type-thickness’, e.g., ‘GB-0.0064’ means a 0.0064 m thick gypsum board.

Table 3 Examples of Configurations of Insulation Systems
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4 Application of the Design/Analysis Tool

To demonstrate how to use the proposed tool, a prototype building is selected as below.

  • A box-shape building is located in the Boston area, MA, USA.

  • The building has a dimension of 4.5 m (W) × 4.5 m (L) × 2.7 m (H) with fenestration of a 1.5 m (W) × 1.5 m (H) glass window which becomes an opening in the event of a fire.

  • All external walls are constructed with a wall-insulation system that consists of three layers: interior sheathing (SH1), insulation (IN), and exterior sheathing (SH2).

  • The insulation layer is 10.2 cm (4″) thick, which is generally used in lightweight construction.

  • For the fire safety sub-model, the fire load density in the space is 780 MJ/m2.

  • The indoor temperature for the energy-consumption model is 20 °C.

  • Climate information is from the National Centers for Environmental Information [41].

This prototype building is subjected to the following three types of performance priorities:

  • Type I: the building focused on sustainability performance,

  • Type II: the building focused on energy-consumption and sustainability, and

  • Type III: the building focused on fire safety performance.

The weights for each type are assumed as presented in Table 4. In an actual application of the tool, these values can be determined by the stakeholders (knowledgeable designer, authority having jurisdiction (AHJ), etc.). For the latter, the Analytical Hierarchy Process (AHP) method may be used [25].

Table 4 An Example of Weights for the Selected Space Uses [wi in Eq. (13)]
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4.1 Estimation of Performance Value [r i in Eq. (13)]

4.1.1 Energy-Consumption Performance

The EP sub-model simulates the monthly energy consumption of the prototype compartment with various insulation system options. Figure 5 shows six examples of the simulation results listed in Table 3. Positive energy consumptions indicate that energy is used to heat the compartment, and negative numbers indicate that energy is used to cool the compartment. Since the six examples have the same sheathing layers, the energy-consumption of each system is proportional to the conductivity of the insulation layer. System #103 using spray polyurethane foam with the lowest thermal conductivity consumed the lowest energy, while system #35 using cellulose blown with the highest conductivity consumed the highest energy. The energy-consumption performance is calculated by adding the absolute values of energy-consumption over 12 months for each system.

Figure 5
figure 5

Monthly energy consumptions estimated by the energy-consumption performance sub-model

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4.1.2 Fire Safety Performance

When foam plastic insulation is used (IN 5, 6, and 7), it is crucial to have an appropriate thermal barrier to prevent any thermal failure of the insulation layer, at least for the first 15 min of a fire. Those systems having failure times less than 15 min are not deemed to be appropriate for SH1. The parametric time–temperature curve is generated based on the given compartment and opening configuration (Fig. 6). This curve serves as an example of a more severe fire than the ASTM E119 time–temperature curve during the initial period. It should be also noted that the parametric time–temperature is a function of the thermal inertia of the enclosure surface material such that it varies depending on the type of SH1. Figure 7 shows the failure times of all 2023 systems with the failure criterion of the insulation layer presented in Table 2. The blue data points indicate the foam plastic insulation (IN 5, 6, and 7), which also means that only those two groups (1) above 15 min failure time are qualified. It should be noted that non-foam plastic insulations indicated by the red data points do not have to satisfy the 15 min requirement per IBC.

Figure 6
figure 6

Parametric time–temperature curve generated using material properties of gypsum board sheathing layer

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Figure 7
figure 7

Fire safety performance (indicated by failure time) for the 2023 wall-insulation systems

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4.1.3 Soundproofing Performance

The soundproofing performance sub-model simulates the sound transmission loss (dB) through an insulation system between two compartments. Figure 8 shows the sound transmission loss between 0 and 4000 Hz of the six examples in Table 3. This frequency range is based on the Sound Transmission Class (STC) rating system which is one of the widely used sound classification rating systems in the U.S. to characterize the effectiveness of interior partitions, ceiling/floors, doors, windows, and exterior walls in isolating airborne noise. As a median value, the sound transmission loss value at 2000 Hz is selected to represent the soundproofing performance of each insulation system.

Figure 8
figure 8

Sound transmission losses of the six wall-insulation systems estimated by soundproofing performance sub-model

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4.1.4 Sustainability Performance

Sustainability performance is calculated by adding one-third of the normalized values of carbon dioxide equivalent, water consumption, and energy-consumption, discussed in Eqs. (9), (10) and (11) respectively, for two sheathing layers and an insulation layer. Based on Tables 1 and 2, the sustainability performance values for all systems are presented as shown in Fig. 9.

Figure 9
figure 9

Sustainability performance values for all 2023 wall-insulation systems

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4.1.5 Cost Performance

The cost performance of a wall-insulation system is estimated by adding the cost of each layer following Eq. (12). Based on the cost data in Tables 1 and 2, the cost performance is presented in Fig. 10.

Figure 10
figure 10

Cost performance values for all 2023 wall-insulation systems

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4.1.6 Decision Making

The first step for decision-making is the normalization of all the performance values using Eqs. (14) and (15). With the estimated weights in Table 4, the performance scores, \(\upsilon\), of each wall-insulation system for the three types are obtained. Figure 11 shows the performance scores of all 2023 insulation systems with the Type II weights as an example. It should be noted that the Type II weights emphasize the energy-consumption and sustainability performance. The wall-insulation systems in group (2) in Fig. 11 are the foam plastic insulations having a failure time of less than 15 min and should not be qualified regardless of the other performance values. For this reason, their scores are marked as zero. The system 800 presents the best performance, the highest dot in Fig. 11, which consists of 0.0254 m gypsum board (SH1 #7), SPF-OC (INS #6), and 0.0064 m gypsum board (SH2 #1).

Figure 11
figure 11

Normalized total performance scores of the systems with the Type II weights

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Even though system #800 has the highest performance score, the other systems (#801–#816) marked in group (1) of Fig. 11 also have relatively high-performance scores (0.72–0.80). Most of them may be considered as appropriate candidates for the optimum wall-insulation system with Type II weights. Among this group, if the user wanted to choose better soundproofing performance, comparative soundproofing performance numbers need to be further checked. Figure 12 shows the soundproofing performance of the systems from 800 to 816 and system 806 shows the best sound performance in group (1). Similarly, other performances can be checked for further refined decisions.

Figure 12
figure 12

Soundproofing performance of the wall-insulation systems from 800 to 816

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Although a wall-insulation system is selected based on the analysis above, it is not clear how good it is compared to other systems. To understand the relative performance of the selected system, a reference wall-insulation system is defined: a ½ inch thick gypsum board for SH1, a 4-inch thick fiberglass batt for the insulation, and a 3/8 inch OSB for SH2. Each of these is the most widely used component for SH1, insulation, and SH2 layers in the U.S. [42].

For the same compartment and opening condition discussed above, the performance values for the reference system (#370) and the best-scored systems for Type I, II, and III are provided in Table 5. In the case of Type I, when sustainability was the most important value, the design tool recommended system #749. Sustainability performance (SuP) increased by 24%. EP and FP increased by 6.8% and 296%, respectively. However, SP and CP decreased by 35% and 32%, respectively. In the case of Type II, when energy-consumption was the most important value, system #800 was recommended and EP increased by 24%. And, FP and SP also increased by 122% and 4.2%, respectively. However, CP decreased by 69%. For Type III, when FP was the most important value, the model recommended system #751, and FP increased to 296%. EP and SuP also rose to 7.1% and 23%, respectively. However, SP and CP were reduced to 34% and 30%, respectively. Interestingly enough, the reference system, which is the most widely used, has relatively lower performances in the four objectives but it has the highest performance in cost. It may show that currently, cost is the most important performance for many people.

Table 5 Performance of Reference Insulation System and Optimum Insulation Systems for Type I, II, and III Cases
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5 Discussion and Future Work

A performance-based, multi-characteristic optimization tool for wall-insulation systems is developed. This tool incorporates various building performance models, offering a systematic understanding of how material selection impacts each performance aspect. This knowledge aids building designers in making informed material selection decisions. Additionally, the optimization method recommends the best suitable selection for each project.

Despite its advantages, several limitations of this tool must be acknowledged. Firstly, it should be noted that the tool primarily focuses on the thermal performance of wall systems and does not specifically address the mechanical and structural effects during a fire, such as loose cross-sections, opening joints, and deflection of wall systems. These factors have the potential to significantly impact the performance of the wall system during a fire event and may not be fully accounted for in the tool's simulations, leading to potential limitations in its predictions. Secondly, the tool utilizes thermal properties at ambient temperature only, except for gypsum boards, although materials' thermal properties may change when exposed to higher temperatures, which may impact the tool's prediction accuracy. This limitation can be easily addressed by incorporating temperature-dependent property data into the tool, if available. Furthermore, the potential economic benefits of improved fire safety, such as reduced fire suppression time and economic loss caused by fire, are not considered in the tool. If these economic factors were included in the tool's calculations, it could potentially decrease the overall cost of the system. Additionally, in the event of a fire, the spread of CO2, which can greatly affect sustainability, cannot be avoided [43]. Although the tool can help improve the thermal barrier performance to prevent the spread of fire and the potential reduction in CO2 emissions resulting from improved fire safety is not currently included in the tool. This aspect could be considered in future upgrades of the tool to better evaluate the sustainability performance of the wall-insulation system. Lastly, the proposed design tool is currently only applicable to buildings with a three-layer wall-insulation system: two sheathing layers with one insulation layer between them. The tool does not account for the effects of wood or metal studs on the performance, and future development should consider more sophisticated models to incorporate these factors.

In summary, while the tool provides valuable insights into wall-insulation system performance and aids in more systematic material selection, these limitations must be kept in mind when interpreting results and making design decisions.