A Design Methodology Incorporating a Sound Insulation Prediction Model, Life Cycle Assessment (LCA), and Thermal Insulation: A Comparative Study of Various Cross-Laminated Timber (CLT) and Ribbed CLT-Based Floor Assemblies

Abstract

Mass timber is increasingly being employed in constructing low- and mid-rise buildings. One of the primary reasons for using mass timber structures is their sustainability and ability to reduce environmental consequences in the building sector. One criticism of these structures is their lower subjective sound insulation quality. Therefore, acoustic treatments should be considered. However, acoustic solutions do not necessarily contribute to lower environmental impacts or improved thermal insulation performance. This paper discusses a design methodology that incorporates the development of a sound insulation prediction tool (using an artificial neural networks approach), life cycle assessment analysis, and thermal insulation study. A total of 112 sound insulation measurements (in one-third octave bands from 50 to 5000 Hz) are utilized to develop the network model and are also used for the LCA and thermal insulation study. They are lab-based measurements and are performed on 45 various CLT- and ribbed CLT-based assemblies. The acoustic model demonstrates satisfactory results with 1 dB differences in the prediction of airborne and impact sound indices ($R_w$ and $L_{n,w}$). An acoustic sensitivity study and a statistical analysis are then conducted to validate the model’s results. Additionally, an LCA analysis is performed on the floor assemblies to calculate their environmental footprints. LCA categories are plotted against the acoustic performance of floors. No correlations are found, and the results emphasize that a wide range of sound insulation can be achieved with similar environmental impacts. Within each acoustic performance tier, the LCA results can be optimized for a floor assembly by selecting appropriate materials. The thermal insulation of floors is then calculated. Overall, a strong positive correlation is found between the total thermal resistance and heat loss against acoustic performance. Designers should be cognizant of the trade-offs between acoustic, thermal insulation, and environmental performance when choosing assemblies with favorable environmental impacts relative to acoustic and thermal insulation ratios.

1. Introduction

The environmental and energetic crises have resulted in a new interest in using renewable and sustainable materials in the building sector. In 2015, it was documented that the construction and infrastructure sectors emitted 7 ${GTCO}_2$ eq and 4 ${GTCO}_2$ eq, respectively, both related to construction materials [1]. Moreover, the global demand for housing each year is five million units, indicating a significant need for constructing new dwellings [2]. Between 2011 and 2017, the growth rate of the North American housing construction market was reported at 75% [3]. Engineered wood products (EWPs) are considered one of the best building materials due to their lower environmental impacts and their energy efficiency [4]. EWPs are increasingly being employed in construction as building materials. The expanded use of timber panel construction began to rise at the end of the 1980s in Western European countries such as Germany, the UK, and Austria. Cross-laminated timber (CLT), a type of EWP developed in Austria in the 1990s [5], can be directly used for floors, walls, and roofs. In 2022, it was reported that around 31 and 13 million $m^3$ of structural panels were produced in North America and Europe, respectively [6]. Additionally, technological innovations in EWPs products and their production process enable compliance with building regulations, such as fire resistance requirements, thereby facilitating the growth of the mass timber market in construction.

However, maintaining a satisfactory indoor environment is an essential need in residential buildings to ensure comfort for occupants. The COVID-19 pandemic reshaped work globally, leading many people to prefer working remotely. Therefore, the demand for indoor environmental comfort has abruptly increased. The indoor environment is primarily characterized by, but not limited to, acoustic and thermal comfort. Human dwellings must serve various purposes to meet the broad needs of inhabitants. Protection, safety, and technical quality are important for a shelter, while thermal and acoustic comfort are crucial for a dwelling.

Acoustic comfort is a term that can be simply defined as the absence of unwanted sound and having the opportunity to perform acoustic activities without disturbing others [7]. Being exposed to noise from neighbors can be disturbing, but it can also be annoying to know that your acoustic activities can be heard by others. Mass timber floors are often governed by serviceability needs, such as sound insulation requirements as outlined by the international building code (IBC) [8]. The sound insulation performance of an element is usually expressed in one-third frequency bands from 100 to 3150 Hz or in an extended range from 50 to 5000 Hz [9]. In Scandinavian countries, the latter is extended down to 20 Hz. There are two sound insulation indices that describe acoustic floor performance. $R_w$ is the weighted sound reduction index, which measures the assembly’s ability to prevent the transmission of airborne sound between spaces. The second index is $L_{n,w}$, the weighted impact sound pressure level, which represents the impact noise transmitted through an assembly [9]. Inadequate sound insulation in dwellings can lead to conflicts between occupants. In 1995, an investigation study using 2322 questionnaires in Sweden was conducted to assess the level of sound insulation in new buildings [10]. It was concluded that around 60% of residents were willing to pay an average of 10% more in rent if the sound insulation in their dwellings could be improved. However, a challenge that arises when dealing with mass timber constructions is that their subjective sound insulation is often rated lower than that of traditional concrete structures with the same objective sound insulation level [11]. Bare CLT panels cannot meet the sound insulation requirements due to their relatively low stiffness and mass. Therefore, it is unavoidable to add additional layers/elements to enhance acoustic performance [12]. To this end, numerous commercial materials are available on the market, each with its own acoustic properties. Quantifying the acoustic performance of an assembly needs to be carried out in the laboratory or in the field, which can be time and cost demanding.

ISO standard 12354 Part 1 [13] provides a straightforward prediction tool based on a heavy monolithic panel, which is not currently applicable to lightweight elements (such as CLT panels). While the latter may yield approximate results at high frequencies, it does not necessarily perform well at low frequencies. Developing a reliable sound insulation estimation tool is an essential need for building constructors during project decision-making to meet the sound insulation requirements. Several estimation tools have been employed to assess sound insulation, including theoretical methods [14,15,16,17], numerical approaches [18,19,20,21], and artificial intelligence models [22,23]. However, these tools often lack accuracy [19,24,25]. To enhance reliability, specific details must be incorporated into simulations, including the mechanical properties of the elements, connections between layers, and indirect paths [26,27,28]. Furthermore, the variety of acoustic materials on the market complicates the development of a prediction tool that encompasses a wide range of solutions. Additionally, airborne insulation treatments do not necessarily improve the attenuation of impact noise. Consequently, the absence of a universal estimation tool that addresses various scenarios underscores the importance of developing a suitable prediction tool.

Recently, artificial intelligence algorithms have been used in diverse domains that were considered challenging tasks in the past, such as speech and image recognition [29,30], language translation [31,32], and a few in building acoustics [23,28]. This approach enables the algorithm to learn from samples, improving its prediction capability across various tasks. Providing large and diverse data samples can significantly enhance predictions, particularly for artificial neural network (ANN) models. Thus, this approach can yield reliable results in building acoustics if large and varied data sets are employed.

However, acoustic solutions can be environmentally costly. Various acoustic materials are available on the market, but they are not necessarily eco-friendly. Given that the primary motivation for using engineered wood products (EWPs), such as cross-laminated timber (CLT), is environmental concerns, improving the acoustic performance of wood structures should not come at the expense of sustainability. In a previous study by the authors [33], it was found that increasing sound insulation correlates with heightened environmental impacts. However, this study utilized a limited number of assemblies. Another investigation on the same topic reached a similar conclusion regarding embodied carbon emissions [34]. Both studies confirmed that sufficient sound attenuation can be achieved by selecting appropriate acoustic solutions [33,34]. For instance, a bare CLT panel can readily meet the airborne sound insulation requirements by using environmentally friendly materials, but this does not necessarily correlate with improved impact noise attenuation or reduction heating energy demand, particularly in cold climate countries. Given that the primary motivation for utilizing wood-based materials in construction revolves around environmental and energy concerns, a large-scale comparative study addressing sound insulation, environmental impacts, and thermal performance is essential. Few studies addressing this triple bottom line have been identified in the literature.

Life cycle assessment has been universally employed to quantify the environmental impacts of a product across various domains [35,36]. It has been applied to mass timber constructions [37,38] and has been utilized in the building context since the early 1990s [39,40,41]. It is a method that addresses the potential environmental impact throughout the life cycle of a product [42]. A clear and standardized methodological framework is established in ISO 14040 [43] and ISO 14044 [44], which comprises goal and scope definitions, life cycle inventory analysis, impact assessment, and interpretation.

It is well known that wood has superior thermal insulation performance compared to concrete, with thermal conductivity for wood ranging from 0.09 to 0.197 W/(m.K) and from 0.08 to 3.63 W/(m.K) for concrete, depending on its density [45,46]. Thus, this reduces the energy consumption then decreases carbon emissions. The indoor thermal comfort of occupants directly impacts building energy consumption [47,48]. Estimating energy performance is a crucial step during the design phase of buildings, not only to ensure occupant comfort and compliance with regulations but also to optimize the design concerning the life cycle of buildings [49,50].

The aim of this research is to develop an acoustic design methodology utilizing artificial neural networks (ANN) approach by integrating life cycle analysis (LCA) and thermal insulation analysis. A total of 112 lab-based sound insulation measurements (airborne and impact measurements) are employed to develop the ANN model, which relates to 45 CLT- and ribbed CLT-based assemblies. Subsequently, an LCA study and thermal insulation analysis are carried out.

2. Materials and Methods

2.1. Floor Assemblies

For this study, 45 wooden assemblies are utilized to conduct the research. These floors are constructed in order to carry out sound insulation measurements (airborne and impact) in laboratory. Following this, a life cycle assessment and thermal insulation study are carried out on the floors. Two types of base floor are used: CLT and ribbed CLT panels (open ribbed panels).

The data include four CLT thicknesses: 140, 160, 200, and 240 mm. Ribbed CLT panels have an 80 mm thickness with Glulam ribs, primarily designed for long-span structural applications as shown in Figure 1. Figure 2 illustrates the general trends in floor compositions. The floor dimensions for both types are 4.2 m × 3.6 m. Furthermore, since the aim of the paper is to explore the overall relationship among the three topics (acoustics, thermal insulation, and LCA), floor compositions are presented for clarification purposes.

2.2. Acoustic Insulation Data

In this research, 112 lab-based sound insulation measurements are used. Of them, 48 pertain to airborne sound insulation and 64 to impact insulation measurements. The tests are conducted on 45 ribbed CLT and CLT-based floor assemblies across one-third octave bands (50–5000 Hz), adhering to ISO standards 10140 (Parts 2 and 3) [51,52]. Single number quantities ($R_w$ and $L_{n,w}$) are calculated in accordance with ISO 717 (Parts 1 and 2) [53,54]. Acoustic measurements are shared by Atelier Indépendant D’Acoustique (Aïda) in France. These measurements are confidential and intended to be shared for the purpose of conducting this research. However, acoustic measurements are conducted in the same laboratory and by the same company, which helps to reduce the uncertainties related to the measurements.

For a better overview of the acoustic data,

Table 1. The general trends of the acoustic sound insulation performance of floor assemblies used in the study. Maximum, minimum, standard deviation, and median values of SNQs are calculated.

Floor Type	Max. ${\mathit{R}}_{\mathit{w}}$	Min. ${\mathit{R}}_{\mathit{w}}$	Mdn * (${\mathit{R}}_{\mathit{w}}$)	SD ** (${\mathit{R}}_{\mathit{w}}$)	Max. ${\mathit{L}}_{\mathit{n},\mathit{w}}$	Min. ${\mathit{L}}_{\mathit{n},\mathit{w}}$	Mdn * (${\mathit{L}}_{\mathit{n},\mathit{w}}$)	SD ** (${\mathit{L}}_{\mathit{n},\mathit{w}}$)
CLT based	81	36	61	14.1	89	35	56	15.5
Ribbed CLT based	73	34	69	14.4	91	44	50	14.3

* Mdn: Median value. ** SD: standard deviation value.

illustrates the maximum and minimum SNQs of CLT- and ribbed CLT-based floors. Additionally, standard deviations and medians are calculated. It can be observed that the standard deviation values are closely aligned, and the minimum acoustic performance value consistently corresponds to the bare CLT and ribbed CLT slab.

To organize the database for developing the ANN model and to maintain a uniform style, each floor is divided into three parts: topping, base, and ceiling (see Figure 2). The data are organized using MySQL software (version 8.4) [55] to identify various parameters. Each floor component has a categorical variable value [56], which serves as inputs for ANN modeling. The thickness and density of each floor composition are considered, along with resilient channels, hangers, floor type (CLT based or ribbed CLT based), and the installation order of the elements.

Table 2. List of structural parameters that are identified to organize the acoustic data.

Parameter	Unit	Class
− Floor type	—	CLT based/ribbed CLT based
− Floor part	—	topping/base/ceiling
− components	—	i.e., CLT panel and insulation materials
− Plies number of a CLT	—	1/2/3/…
− Material order	—	1st/2nd/…
− Material thickness	mm	—
− Material density	${kg/m}^3$	—
− Presence of ceiling	—	Yes/No
− Air gap	mm	—
− Acoustic hangers type	—	depending on the product
− Resilient channel thickness	mm	—

illustrates the structural parameters used to organize the acoustic data. It is important to note that all the measurements are conducted in the same laboratory; consequently, the area of the test floor and the volume of the receiving room remain consistent. The latter are not considered in the modeling, as the ANN approach is a statistical approach and the diversity of the data (with a large number) is important. Furthermore, if a certain parameter is missing, a null value is assigned; however, this situation is rare in this study.

2.3. Sound Insulation Modeling Using ANN Approach

The artificial neural network approach enables algorithms to recognize patterns and solve complex tasks. It is a relatively new computational tool that is extensively applied to intricate real-world problems [57]. A simple structure of an ANN model consists of layers, including an input layer, hidden layer(s), and output layer. These layers are densely interconnected by processing computational units known as artificial neurons [58,59]. Each neuron represents a specific output function, referred to as an activation or transfer function [60].

Before the simulation begins, the database is divided into three sets: training, validation, and testing sets. The network model propagates the training data from the input layer to the output layer, where the prediction values are presented [57]. This process is known as training the ANN model. The validation and testing sets are then used to validate and test the model, respectively.

In each neuron, the input values are weighted, meaning they are multiplied by values known as weights. At the beginning of the training phase, these weights are initialized arbitrarily. They are then adjusted to achieve good accuracy based on the predicted values (outputs). Activation functions are employed to propagate the input values to adjacent layers, controlling the amplitude of the neurons [61]. The most common activation functions include tangent, sigmoid, ReLU, and LeakyReLU [62].

This paper develops a multi-layered perceptron ANN model consisting of two hidden layers, containing 30 and 25 neurons, respectively. Cross-over and dropout techniques are employed to address overfitting and validate the network model [63,64]. The Adam optimizer algorithm [65] is used to train the model. Leaky ReLU (Leaky Rectified Linear Unit) [66] is utilized as the activation function for the two hidden layers. The model is developed using Python and the PyTorch machine learning library [67].

Structural parameters listed in Table 2 are used as input parameters. The acoustic performance of floor assemblies in one-third-octave bands from 50 to 5000 Hz serves as the output values. The database is divided into training (80%), validation (10%), and testing (10%) sets, respectively. A root-mean-square error (RMSE) is utilized as a cost function to evaluate the network’s accuracy (differences between measured and predicted values).

2.4. Acoustic Sensitivity Analysis

ANN models are often regarded as black box prediction tools, as explaining their mechanisms can be quite cumbersome [68]. It is essential to determine which parameters the model relies on during prediction. Therefore, the attribution power of an ANN network to its input features must be assessed. A challenge in attribution methods is distinguishing between errors stemming from the model’s misbehavior and those arising from the method itself. The attribution problem has been formally investigated in several studies [69,70,71]. To address these limitations, an axiomatic approach known as integrated gradients (IG) has been proposed [72].

Using a function F:$R^n\to [0,1]$ that represents a neural network, an input $x=(x^1,\dots ,x^n)$∈$R^n$, and a baseline z∈$R^n$. Then, an attribution of the prediction at the input x that corresponds to a baseline is a vector $A_F(x,z)$$=(a^1,\dots ,a^n)$∈$R^n$, where $a^i$ is the attribution of $x^i$ to the prediction function $F\left(x\right)$. Therefore, the integrated gradients can be defined as the integral of the gradients through a straight path from the baseline z to the input x. For the $i^{th}$ dimension between a baseline and an input, the integrated gradient is donated as [72]

$$\begin{array}{c}\hfill I{G}_i\left(x\right)=(x_i-z_i)\ast {\int }_{\alpha =0}^1{\displaystyle \frac{\partial F(z+\alpha \ast (x-z\left)\right)}{\partial x_i}}d\alpha \end{array}$$

(1)

2.5. Life Cycle Assessment Simulation

For this study, OpenLCA software [73] is utilized to conduct a life cycle assessment (LCA). It is open source and supports coding languages such as Python, providing a feasible interactive tool for developers. This software offers an API (application programming interface) for interprocess communication with OpenLCA. Consequently, the Olca-ipc package [74] is employed as a connection between the developed ANN model and OpenLCA. The European Reference Life Cycle Database (ELCD) V3.2 [75] is used for the analysis. For life cycle impact assessment (LCIA), the IMPACT World+ method [76] is applied. To highlight the general trends between sound insulation and the environmental impacts of our case study, an LCA study is performed on all assemblies in the database.

2.6. Thermal Analysis

The thermal performance simulation of floor assemblies is conducted using the Ubakus online calculator [77]. This calculator provides the heat transfer coefficient, total thermal resistance, components’ heat storage capacity, and heat loss of elements. In this research, the thermal performance of each assembly is calculated and plotted against its sound insulation performance (both airborne and impact attenuations). The simulation is performed between two heated rooms (with an ambient temperature of −${5.0 }^{\circ }$C to ${20.0 }^{\circ }$C and a relative humidity of 50%) since the study focuses on the inner floors of residential buildings. Consequently, the climate details are set to France, Nouvelle Aquitaine, to ensure consistency in the data, as the LCA database is European based, the floor reports present acoustic solutions in France, and the thermal performance calculator (German based) includes most structural components used in Europe. However, this does not imply that the practical applications of engineering in this study are limited to Europe.

3. Results and Discussion

3.1. Sound Insulation Predictions

The ANN model is trained and validated using 80% and 10% of the database, respectively. The remaining data are employed to test the accuracy of the network model. Twelve acoustic measurements (six airborne and six impact) are selected for the testing step, corresponding to six different floors (four CLT-based and two ribbed CLT floors). These measurements represent the general trend of the floor assemblies in the database. However, neither the training phase nor the validation step utilizes these test floors.

Figure 3 illustrates the measured and predicted airborne sound insulation curves in the 50–5000 Hz range. It also displays the RMSE for each predicted and measured curve across the entire spectrum. The components of each floor are presented in Figure A1 in Appendix A. The highest RMSE is 6.34 dB, associated with floor assembly #5, while the lowest is 2.16 dB for floor #2. The absolute residuals between the measured and predicted curves in each one-third octave band can be seen in Figure 3. There are minor discrepancies between measurements and predictions for assemblies #2, #3, and #5. These deviations are particularly noticeable near dips in the measured curves, which represent the coupling response between floor compositions [9]. The latter can be particularly observed below 200 Hz (where the first eigenfrequencies or fundamental resonances occur) or above 1000 Hz (where the coincidence frequencies of mass timber structures typically exist [9,78].

Coincidence frequency exists when the wavelength of the bending wave of a plate matches or couples with the projected incident acoustic wavelength [9]. Good coupling or matching indicates that effective sound radiation occurs at and above this frequency [7]. However, most fluctuations in the measured curves are captured by the ANN model. Such limitations have also been highlighted in previous studies [22,26,27,28].

Figure 4 displays the normalized impact sound pressure levels for measured and predicted curves from 50 to 5000 Hz. Floor configurations are also shown in Figure A1 in Appendix A. There is a good correlation with small deviations at low frequencies (below 200 Hz), where the first eigenfrequencies or fundamental resonances occur [9]. Moreover, significant uncertainties at low frequencies due to receiving room effects may be present. This is related to the Schr$\ddot{o}$der frequency, where the diffuse sound field does not hold below that frequency [79,80]. Overall, the model demonstrates a strong ability to predict the general trends of the insulation curves, with small deviations that do not significantly affect the accuracy.

For a better evaluation of the model performance, root-mean-square errors are calculated for the predicted airborne and impact values across four frequency ranges: low (50–200 Hz), middle (250–1000 Hz), high (1250–5000 Hz), and the entire range (50–5000 Hz). The bar chart in Figure 5 displays the RMSE values for airborne and impact sound predictions. It can be noted that airborne sound predictions exhibit lower accuracy than impact predictions in the aforementioned frequency ranges.

Higher deviations can be observed for low and high frequencies (both airborne and impact), where eigenfrequencies and coincidence frequencies occur, respectively. The model shows a limited ability to detect fluctuations in these areas as illustrated in Figure 3 and Figure 4. Nevertheless, acoustic performance highly depends on physical and mechanical material properties, such as elastic modulus and dynamic stiffness, which are not available in the database. These missing data can negatively affect accuracy. However, middle frequencies demonstrate better accuracy, as they are governed by the mass law [7,9,78]. This is a straightforward calculation that depends on the assembly’s mass, a known parameter in our case study.

However, the ANN is a statistical approach that does not rely on physical and mechanical calculations related to sound insulation theories. Including these parameters would help enhance the reliability of the network model. Additionally, prediction accuracy highly depends on the quantity and quality of the training data. Furthermore, the ANN approach does not account for uncertainties in the measurements, which could negatively impact accuracy. Therefore, high-quality measurements are essential when developing such models.

Table 3. SNQs, $R_w$, and $L_{n,w}$ in dB for test assemblies calculated based on measured and predicted curves in Figure 3 and Figure 4.

Floor Assembly	${\mathit{R}}_{\mathit{w}}$	${\mathit{R}}_{\mathit{w}},\mathit{predicted}$	${\mathit{L}}_{\mathit{n},\mathit{w}}$	${\mathit{L}}_{\mathit{n},\mathit{w}},\mathit{predicted}$
#1	35	36	88	88
#2	57	57	65	65
#3	61	61	56	56
#4	63	64	56	57
#5	69	70	54	53
#6	70	70	46	46

presents the calculated single number quantities (SNQs), including the weighted airborne sound reduction index $R_w$ and the weighted normalized impact sound pressure level $L_{n,w}$ for the test assemblies. The model demonstrates very good accuracy, with a 1 dB difference in the prediction of airborne and impact sound indices. This indicates better results than the authors’ previous work on the development of an ANN model for joists and mass timber floors using lab-based measurements [27]. Deviations reach up to 2 dB in the prediction of $R_w$, while they are 5 dB for $L_{n,w}$ [27]. One reason for this could be that all sound insulation measurements are conducted in the same laboratory, thereby reducing uncertainties related to different labs and the people performing the measurements. Another reason might be the consistency of the data, as no varied floor systems are used compared to the total number of assemblies.

3.2. Acoustic Sensitivity and Statistical Analysis

A feature attribution analysis is conducted to explore which parameters the network model relies on during the prediction process (the parameters are summarized in Table 2). This step is essential as a double check of the model’s performance. Since the ANN is a statistical approach, analyzing the results of the attribution method to see if they align with theoretical expectations can serve as an additional validation step for the model. Another advantage of the attribution method is that it provides the contribution of each parameter in each frequency band. In this attribution study, the total thickness and density of CLT and ribbed CLT assemblies are considered.

Figure 6 illustrates the normalized (to 1) feature attribution of the total thickness and density to the airborne sound predictions. It indicates that the total thickness and density of CLT and ribbed CLT floors contribute across all frequency bands, with greater attribution at higher frequencies. This is likely due to mass control in the middle frequency range (250–1250 Hz), where mass plays a significant role [9]. However, the attribution spectrum of total density shows fluctuations near 250 Hz and dips between 1.25 and 5 kHz, which are probably due to the effects of fundamental and coincidence frequencies, respectively. The latter is likely a result of the coupling between floor components that facilitates energy transfer between elements. This phenomenon was also highlighted in previous work by the authors [28].

A statistical study is conducted on the 45 floors used in the research to gain insight into sound insulation performance in relation to thicknesses and densities. Additionally, this allows for a comparison of the sensitivity analysis outcomes and serves to validate the network model. Figure 7 illustrates the Pearson correlation coefficients of the weighted sound reduction index $R_w$ versus the total thicknesses and densities of CLT and ribbed CLT floors. Figure 7a shows a positive correlation between $R_w$ and the total thickness of CLT- and ribbed CLT-based floors, with $R^2$ values of 0.77 and 0.96, respectively. This indicates a strong positive linear relationship supported by a firm linear trend and aligns with the results of the sensitivity analysis presented in Figure 6. Figure 6 and Figure 7 can generally be compared, as the former presents the attribution in one-third-octave bands (in the range of 50–5000 Hz), while the latter shows the overall weighted performance ($R_w$) from 100 to 3150 Hz (according to the ISO reference curve for sound insulation rating calculation [53,54]).

Figure 7b shows a moderate positive relationship for CLT-based assemblies with $R^2$ = 0.65, while a strong positive correlation is indicated for ribbed CLT ($R^2$ = 0.83). It is noteworthy that ribbed CLT floors exhibit a stronger correlation between thickness and density versus $R_w$ compared to CLT assemblies. One reason for this could be that the number of CLT assemblies is greater than that of ribbed CLT-based ones, contributing to greater heterogeneity in the results and affecting the correlation. Another reason is that ribbed CLT assemblies have a thickness of 80 mm, where adding additional elements could significantly enhance insulation performance.

Figure 8 illustrates feature attributions of total thicknesses and densities of CLT and ribbed CLT floor assemblies to the impact sound predictions. Around 50 Hz, thickness has a significant effect on impact sound insulation, where stiffness plays a crucial role (stiffness control region) [78]. However, some dips and peaks between 50 and 250 Hz are likely due to resonance coupling effects (for both airborne and impact) as reported in previous works [26,27,28]. In the middle frequencies, there is a notable increase in attributions until a peak is reached, where coincidence effects are likely influenced near 1.25–5 kHz. This analysis is essential to uncover the general trends of the model and to assess whether the results align with the theoretical expectations. However, these findings represent approximate trends rather than precise analyses, as some critical parameters, such as dynamic stiffness and the connection types between layers, are missing.

Following the same approach for airborne sound, a statistical study is conducted for the weighted normalized impact sound pressure level ($L_{n,w}$) versus the total thicknesses and densities of floor assemblies (see Figure 9). Since $L_{n,w}$ represents the sound pressure, while $R_w$ indicates sound attenuation, a negative relationship in the results for impact sound would suggest that thickness and density are positively attributed to sound insulation. In Figure 9a,b, a strong negative correlation is found for impact insulation versus the thickness and density of ribbed CLT-based floors ($R^2$ = 0.93, $R^2$ = 0.71, respectively). However, a moderate negative relationship is indicated for CLT assemblies.

The results in Figure 6 and Figure 8 provide an overview of how the prediction values are generated by the network model. While these predictions may be approximations, as they are based on statistical values that contain uncertainties and lack some vital parameters, they still yield good results when compared to the data trends shown in Figure 7 and Figure 9.

Another validation step for the developed ANN model can be demonstrated through standardized residual analysis. Residuals are defined as the differences between the actual dependent variable values (in this case, insulation measurement curves) and their predicted values [56]. Figure 10a presents the standardized predicted values against studentized residuals (for both airborne and impact cases) across frequencies from 50 to 5000 Hz. This is the most basic type of residual plot. It can be noted that the residuals generally fall within a random pattern and resemble a null plot [56]. In addition, no outlier values are observed in the plot. This indicates the validity of the model, suggesting that there is no bias in the predicted values and that the errors are not autocorrelated. Figure 10b illustrates the probability density function of error distributions for airborne and impact predictions in the frequency range of 50–5000 Hz. It is evident that the errors are densely concentrated around zero and are normally distributed, further verifying the model’s accuracy.

3.3. Life Cycle Assessment Outcomes

A life cycle assessment (LCA) analysis is conducted for the 45 assemblies to calculate their environmental impacts. Six impact categories are considered in the LCA study: climate change (long term), freshwater acidification and eutrophication, ionizing radiation, ozone layer depletion, and particulate matter formation. To explore how acoustic performance affects a mass timber floor system’s energy use during manufacturing, a comparison between the single-number quantities (SNQs) of $R_w$ and $L_{n,w}$ and the environmental footprints of the floors is performed.

Table 4. Pearson correlation coefficients between acoustic and LCA results for ribbed and CLT floors. Max. and min. values are presented, corresponding to each environmental impact category unit.

	$R_{\mathit{w}}$	$L_{\mathit{n},\mathit{w}}$	Assembly Max. Value *	Assembly Min. Value *
Climate change long term
(kg ${CO}_2$ eq)
CLT based	0.1018	0.0.0562	214,531.565	32.577
Ribbed CLT	0.3123	0.2066	120,250.702	26.193
Freshwater acidification
(kg ${SO}_2$ eq)
CLT based	0.1218	0.0696	7.29345 × ${10}^{-09}$	8.82938 × ${10}^{-13}$
Ribbed CLT	0.3112	0.2057	4.08185 × ${10}^{-09}$	7.09897 × ${10}^{-13}$
Freshwater eutrophication
(kg PO4 P-lim eq)
CLT based	0.1232	0.0709	0.283	2.01 × ${10}^{-01}$
Ribbed CLT	0.3282	0.2182	0.162	1.62 × ${10}^{-05}$
Ionizing radiation
(Bq C-14 eq)
CLT based	0.1232	0.0709	1,721,280.663	322.724
Ribbed CLT	0.3282	0.2182	980,501.772	259.476
Ozone layer depletion
(kg CFC-11 eq)
CLT based	0.0854	0.0445	0.0120	2.2444 × ${10}^{-06}$
Ribbed CLT	0.3252	0.2129	0.007	1.8045 × ${10}^{-06}$
Particulate matter formation
(kg PM2.5 eq)
CLT based	0.0854	0.0446	56.53	0.005
Ribbed CLT	0.3252	0.2085	31.770	0.004

* Corresponding assemblies are visualized in Table 5.

summarizes the Pearson correlation coefficients for the acoustic and LCA results for CLT- and ribbed CLT-based assemblies. In addition, the maximum and minimum values for each LCA category are presented. The correlation plots are shown in Appendix B in Figure A2 and Figure A3. Table 4 indicates that there is no correlation between the sound insulation performance and CLT-based assemblies.

However, a weak positive correlation is noted between airborne and impact sound insulation for ribbed CLT floors and their environmental impacts. This weaker relationship can be attributed to the fact that ribbed CLT slabs have a thickness of 80 mm, and adding acoustic treatments (such as a concrete slab) can initially enhance sound attenuation while also increasing environmental impacts. Nonetheless, the relationship is not linear; improving sound insulation can be achieved by selecting materials that have relatively low environmental impacts.

Appendix B illustrates that each impact category tier exhibits different acoustic performance. For instance, Figure A2a shows the trade-offs between climate change and $R_w$, indicating that at around the 100,000 kg ${CO}_2$ eq tier and lower, the range of $R_w$ is between 48 and 82 dB (a difference of about 32 dB), with a broader insulation range for impact attenuations within the same impact category tier (Figure A3a). This trend is also observed for impact sound insulation and all other environmental impacts. This highlights that effective sound insulation can be achieved by using materials with favorable LCA results in relation to acoustic insulation ratios.

Table 5. Schematics represent the component of each floor assembly (CLT or ribbed CLT) in the context of their maximum and minimum thermal insulation performance. Component abbreviations are explained in the table footnote.

	CLT Max. Value	CLT Min. Value	Ribbed Max. Value	Ribbed Min. Value
Environmental impacts *
Components **	FF, 60 mm CS, 30 mm RW, 60 mm GV, 140 mm CLT	140 mm bare CLT panel	FF, 50 mm CS, 13 mm HGW, 80 mm ribbed CLT, 2 × 18 mm HGB, 135 mm GW, Acoustic ceiling, 90 mm AG, 18 mm GB, 20 mm WP	80 mm ribbed CLT panel
Acoustic performance	$R_w$ = 58 dB $L_{n,w}$ = 59 dB	$R_w$ = 35 dB $L_{n,w}$ = 88 dB	$R_w$ = 69 dB $L_{n,w}$ = 47 dB	$R_w$ = 34 dB $L_{n,w}$ = 91 dB

* The environmental impacts represent the categories that are mentioned in Table 4. ** FF: floor finishing; CS: concrete slab; RW: rock wool; GV; gravels; CLT: cross-laminated timber; HGW: high-density glass wool; HGB: high-density gypsum board; GW: glass wool; AG: air gap; GB: gypsum board; WP: wood panel.

presents the schematics of the highest and lowest environmental footprints of floors (CLT and ribbed CLT) alongside their SNQs. It is evident that a bare CLT or ribbed CLT floor results in the lowest environmental impacts. Generally, increasing acoustic attenuation corresponds to higher environmental impacts. However, the highest values in Table 4 do not correlate with the highest sound insulation performance (as seen in the data used in this study; Table 1). In other words, enhanced acoustic performance can be achieved by selecting appropriate materials that yield favorable LCA results.

3.4. Thermal Insulation Performance

A thermal insulation analysis is conducted to identify trends that could inform decision-making in design by considering acoustic insulation and LCA trade-offs. To achieve this, each floor in the database is modeled using the Ubakus calculator [77].

Table 6. Pearson correlation coefficients between acoustic and thermal performance for CLT- and ribbed CLT-based assemblies. Max. and min. values are presented corresponding to the unit of each thermal performance category.

	$R_{\mathit{w}}$	$L_{\mathit{n},\mathit{w}}$	Assembly Max. Value *	Assembly Min. Value *
Total thermal resistance
($m^{\mathbf{2}}$K/W)
CLT based	0.7912	0.7266	6.934	1.42
Ribbed CLT	0.9601	0.945	4.745	0.956
Heat storage capacity
(${kJ/m}^{\mathbf{2}}$K)
CLT based	0.3288	0.2166	397	112
Ribbed CLT	0.6469	0.5472	280	64
Heat loss
(${kWh/m}^{\mathbf{2}}$)
CLT based	0.829	0.7873	41	8
Ribbed CLT	0.9806	0.9616	60	12

* Related assemblies are visualized in Table 7.

presents the Pearson correlation coefficients between the total thermal resistance, heat storage capacity, and heat loss versus acoustic insulation indices ($R_w$ and $L_{n,w}$). Correlation plots can be found in Appendix C in Figure A4 and Figure A5.

Generally, the results illustrate a strong positive relationship between total thermal resistance and sound insulation performance for CLT- and ribbed CLT-based floors. This correlation also applies to heat loss versus acoustic indices. However, ribbed CLT-based assemblies exhibit a stronger correlation than CLT floors. This can be attributed to the thin thickness (80 mm) of the ribbed CLT in the database, where a bare panel provides insufficient thermal and acoustic performance. Meeting the acoustic requirements positively contributes to improved overall thermal properties. In general, timber mass structures offer better thermal insulation than traditional construction elements. Enhancing their sound attenuation could involve adding materials such as glass or rock wool, which also contribute to thermal improvements. However, no correlation is found for heat storage capacity. The heat storage of a material is defined as the amount of heat energy supplied by the corresponding change in temperature, depending on the physical properties of the materials. In general, the heavier the material (such as concrete topping), the more heat it stores, contributing to higher sound attenuation. However, the results show that greater heat storage capacity does not necessarily correlate with improvements in sound attenuation. Sound insulation performance can be achieved using various materials (not solely relying on a heavy concrete slab), and it depends on the interaction between materials and how much sound energy can be dissipated.

Table 7. Schematics represent the component of each floor assembly (CLT or ribbed CLT) in the context of their maximum and minimum thermal insulation performance. Component abbreviations are explained in the table footnote.

	CLT Max. Value	CLT Min. Value	Ribbed Max. Value	Ribbed Min. Value
Total thermal resistance *
Components **	50 mm CS, 13 mm HGW, 240 mm CLT panel, Acoustic ceiling, 20 mm AG, 2 × 18 mm GB	140 mm bare CLT panel	22 mm OSB, 13 mm HGW, 80 mm ribbed CLT panel, 2 × 18 mm HGB, 135 mm GW, 90 mm AG, Acoustic ceiling, 18 mm GB	80 mm ribbed CLT panel
Acoustic performance	$R_w$ = 81 dB $L_{n,w}$ = 39 dB	$R_w$ = 35 dB $L_{n,w}$ = 88 dB	$R_w$ = 68 dB $L_{n,w}$ = 48 dB	$R_w$ = 34 dB $L_{n,w}$ = 91 dB
Heat storage capacity *
Components **	FF, 60 mm CS, 30 mm RW, 60 mm GV, 140 mm CLT	140 mm bare CLT panel	FF, 50 mm CS, 13 mm HGW, 80 mm ribbed CLT, 2 × 18 mm HGB, 135 mm GW, Acoustic ceiling, 90 mm AG, 18 mm GB, 20 mm WP	80 mm ribbed CLT panel
Acoustic performance	$R_w$ = 58 dB $L_{n,w}$ = 59 dB	$R_w$ = 35 dB $L_{n,w}$ = 88 dB	$R_w$ = 69 dB $L_{n,w}$ = 47 dB	$R_w$ = 34 dB $L_{n,w}$ = 91 dB
Heat loss *
Components**	140 mm bare CLT panel	50 mm CS, 13 mm HGW, 240 mm CLT panel, Acoustic ceiling, 20 mm AG, 2 × 18 mm GB	80 mm ribbed CLT panel	FF, 50 mm CS, 13 mm HGW, 80 mm ribbed CLT, 2 × 18 mm HGB, 135 mm GW, Acoustic ceiling, 90 mm AG, 18 mm GB, 20 mm WP
Acoustic performance	$R_w$ = 35 dB $L_{n,w}$ = 88 dB	$R_w$ = 81 dB $L_{n,w}$ = 39 dB	$R_w$ = 34 dB $L_{n,w}$ = 91 dB	$R_w$ = 69 dB $L_{n,w}$ = 47 dB

* Thermal performance values are presented in Table 6. ** CS: concrete slab; HGW: high-density glass wool; CLT: cross-laminated timber; GW: glass wool; AG: air gap; HGB: high-density gypsum board; GB: gypsum board; FF: floor finishing; RW: rock wool; GV; gravels; WP: wood panel.

lists and sketches the maximum and minimum thermal performance values for floors in the database. It is evident that the bare rib/CLT panel has the lowest thermal performance. A floor assembly with gravels has the highest heat storage capacity; however, this is associated with higher environmental footprints as shown in Table 5. Other floor treatments could perform better acoustically and thermally while maintaining lower environmental impacts. CLT and ribbed CLT configurations in Table 7 demonstrate high sound insulation performance along with the highest thermal insulation (among the measurements in the database). Furthermore, they are not linked to the highest environmental impacts presented in Table 5 or the highest sound insulation values (Table 1). This further illustrates that thermal and acoustic insulation can be achieved with lower LCA results. Wood-based top-finishing materials can offer favorable thermal and sound insulation performance with commendable LCA results.

3.5. Triple Bottom Line Trends

Results have shown that increasing the sound insulation performance of a bare mass timber floor initially increases both the environmental footprints and thermal performance. A strong positive relationship is found between sound and thermal insulation, while a weak correlation is observed for heat storage capacity and SNQs. However, a weak or no correlation is highlighted between sound insulation and LCA outcomes. This indicates that sound and thermal insulation can be achieved with different environmental impacts, suggesting that designers should prioritize assemblies with favorable LCA results.

The results in this study emphasize that an optimized floor system offering good sound attenuation, thermal insulation, and favorable environmental impacts can be achieved through informed decision-making during the design phase by considering their trade-offs. Bare floors have favorable environmental emissions, but indoor spaces require more heating energy to meet occupant thermal comfort. Additionally, this energy is often produced from sources that can have significant environmental footprints. However, different floor assemblies exhibit roughly similar environmental impacts while presenting a wide range of acoustic performance (see Figure A2 and Figure A3). In addition, acoustic and thermal insulations are strongly correlated. Appropriate materials that have commendable environmental consequences and provide indoor acoustic and thermal comfort should be chosen. Concrete floor finishes may enhance airborne and impact sound insulation, but they come with high environmental impacts. In contrast, wood-based finishes can offer favorable acoustic and thermal insulation along with positive LCA results. Using a suspended ceiling can also be associated with agreeable outcomes.

4. Conclusions

This paper reveals a potential approach for predicting the sound insulation performance of mass timber floors by integrating LCA and thermal insulation analysis. Three key aspects are investigated—acoustic performance, LCA, and thermal insulation—of CLT- and ribbed CLT-based assemblies. Various sound insulation measurements are employed to develop the artificial neural network model, which relates to different CLT and ribbed CLT floors. Following this, a life cycle assessment study is conducted to evaluate the environmental impacts of the floors using OpenLCA software. Finally, the thermal insulation performance of the assemblies is calculated using the Ubakus online calculator.

A sound insulation prediction model using artificial neural networks is developed based on laboratory measurements from 45 CLT-based floor assemblies. Airborne and impact sound insulation curves, across frequencies of 50–5000 Hz, are predicted with satisfactory results. Weighted sound reduction indices ($R_w$) and weighted normalized impact sound pressure levels ($L_{n,w}$) are estimated with an error of 1 dB. Differences of 1 dB to 3 dB are perceptible from a human perspective. Acoustic sensitivity and statistical analyses are conducted to explore the structural parameters on which the model most relies. Results indicate a strong correlation between the airborne sound insulation and both the total thickness and density of the floor. However, a moderate correlation is found for impact sound. The sound attenuation can be compromised due to the influence of resonance and coincidence coupling between the assembly’s components, which may negatively affect the accuracy of the model. Certain mechanical properties should be considered in the modeling, such as dynamic stiffness, elastic modulus, measurement uncertainties, and the connection between floor components. Addressing these factors could lead to improved accuracy near resonance and coincidence frequencies. The results encourage designers to integrate the developed model into practical engineering applications, particularly in decision-making. It serves as a cost- and time-saving prediction tool that gives reliable results across a wide frequency range (50–5000 Hz).

A life cycle assessment analysis is conducted on the studied assemblies, examining six impact categories: climate change (long term), freshwater acidification and eutrophication, ionizing radiation, ozone layer depletion, and particulate matter formation. Following this, a correlation study is performed between each category and the single number quantities (SNQs) $R_w$ and ${\mathrm{L}}_{n,w}$. No correlation is found between the acoustic performance of CLT-based assemblies and their environmental impacts. However, a weak relationship is observed for ribbed CLT floors. The results emphasize that satisfactory noise attenuation can be achieved by selecting materials with favorable LCA results.

Total thermal resistance, heat storage capacity, and heat loss are calculated for each floor assembly to determine their thermal insulation performance. These metrics are plotted against the sound insulation indices to explore the relationship between acoustic and thermal insulation. Airborne and impact sound insulations show a strong correlation with total thermal resistance and heat loss. However, the correlation is weaker for heat storage capacity. It appears that addressing acoustic requirements can positively contribute to improved thermal insulation. The heat storage capacity is not necessarily linked to acoustic performance, as it depends on the amount of heat energy required for the corresponding change in temperature.

The results reveal that enhancing the sound insulation initially increases the environmental impacts while positively contributing to thermal insulation. However, a wide range of airborne and impact sound insulation can be associated with similar environmental impacts and thermal performance. In other words, environmental footprints and thermal insulation can be optimized by using appropriate acoustic solutions, such as avoiding gravel layers and using wood-based finishing materials.

Further research would benefit from considering a larger number of floor assemblies and more information about floor components. Details such as elastic modulus, dynamic stiffness, interconnections between elements, and uncertainties in the measurements could enhance accuracy. Additionally, extending the study to include low-frequency impact insulation is essential, as most indoor annoyances in mass timber residential buildings arise from these frequencies. An optimization study would provide valuable insights for designers, and aid in decision-making during the design phase.