Building Retrofit Measures and Design: A Probabilistic Approach for LCA

Abstract

Green building design and architecture have become widespread tenets in the development of sustainable buildings. In this context, the use of sustainable materials and the awareness of resource/energy consumption are strategic aspects to consider for the improvement of building performances. This paper presents a new and structured approach to address uncertainty and sensitivity analysis in Life Cycle Assessment (LCA) to support the decision-making process in building renovation. This “probabilistic” approach to LCA allows for the obtaining of results expressed as ranges of environmental impacts and for alternative solutions, offering an idea of the meaning of input parameters’ uncertainties and their influence on the result. The approach includes (i) the assessment of inputs’ uncertainties (represented by Probability Density Functions—PDF); (ii) the data sampling; and (iii) the uncertainty propagation (Monte Carlo method). Variance decomposition techniques have been used to sample inputs’ PDFs and assess their impact on the LCA result distribution (sensitivity analysis). The methodology application is illustrated through a case study where three building retrofit measures were assessed. Results provide an insight about the uncertainties of LCA indicators in terms of climate change and nonrenewable energy. The input parameters related to the use phase are confirmed as the most influential in building LCA.

1. Introduction

In recent years, sustainability as a concept has become a popular subject in the context of buildings and architecture science. In particular, the sector has started to look at energy efficient components and equipment for energy use savings as well as sustainable materials, with the aim to improve building performance and comply with certain policies and energy targets (e.g., EU targets for 2020 [1]). Buildings are responsible for approximately 40% of the total energy use within Europe, where more than 30% of actual buildings are historic buildings that ought to last for decades. In this context, new EU directives have been issued (e.g., Energy Performance of Buildings Directive [2]) aiming to significantly reduce greenhouse gas emissions and energy consumption related to the use phase [3,4]. New buildings are designed to fulfill this existing regulatory framework; these projects involve all the building items (e.g., external walls, windows, heating system, lighting, etc.). On the other hand, existing buildings need to be upgraded to meet the requirements of “green” buildings and only few items are usually involved in renovation activities (e.g., internal insulation). On 19 June 2018 Directive (2018/844/EU) amending the Energy Performance of Buildings Directive was published and entered into force on 9 July 2018 [1]. This revision introduces targeted amendments to the current Directive and is aimed at accelerating the cost-effective renovation of existing buildings, with the vision of a decarbonized building stock by 2050 and the mobilization of investments. Cost therefore represents an important metric to assess the improvement and overall building performances reached by the adoption of renovation measures [5]. In addition, environmental aspects (e.g., greenhouse gas emissions) are also strictly related to building performances and drive design choices during renovation projects [6].

Since the useful life of buildings is particularly long, the assessment of economic and environmental performances requires an analysis from a life cycle perspective. A life cycle assessment (LCA) allows for the consideration of energy needs as well as the issues related to renovation design choices (type of renovation strategy, replacement and maintenance needs, building components embedded energy and costs, their service life, etc.) [6]. A considerable amount of research refers to “standardized” LCA methods to assess the environmental impacts of energy efficiency measures for building design and renovation, with notable simplifications related to the data input selection and quantification. Unfortunately, useful information necessary for the creation of a life cycle inventory may suffer from many sources of uncertainty and variability. These uncertainties are rarely considered and even more rarely quantified, even if they can be relevant in the final assessment, especially in a long-term perspective. Uncertainty and variability in LCA is an important issue to be addressed in order to improve the reliability of LCA-based decision making.

The paper aims at the definition of a novel “probabilistic” LCA approach, which includes Uncertainty (UA) and Sensitivity Analysis (SA) through variance-based decomposition techniques. The innovative aspect of the probabilistic LCA methodology proposed herein is the possibility to couple the calculation of the environmental indicators following “traditional” consolidated LCA methods with the Monte Carlo calculations, which are effective ways to build the entire output probability distribution and assess global uncertainty and sensitivity. The method wants to overcome two main limitations observed in the literature for the environmental assessment of building retrofitting: (i) the characterization of input uncertainties and (ii) the propagation of input uncertainties in LCA outcomes. Indeed, “standard” LCA procedures applied to energy renovation measures of existing buildings may suffer from several intrinsic problems of data knowledge and quality and, for this reason, the development of a “probabilistic” LCA approach is considered a novelty in this sector, in particular for historic buildings. A “probabilistic” approach underlines how uncertainty sources of input data may affect the LCA results hence making the user aware of the inherent limitations of the analysis. As a result of the probabilistic LCA, the user can obtain: (i) A comparison of the environmental performance of several building design options expressed by probability density functions (PDFs); (ii) the assessment of the results’ robustness under different scenarios, for instance different reference study periods (RSP); and (iii) identification of the most influencing input parameters on the outcome uncertainty.

Within this work, a simplified case study of building energy renovation has been reported to demonstrate the applicability of the “probabilistic” LCA method. For a historic building case study, alternative envelope insulation solutions are proposed as retrofit measures and a probabilistic LCA, where input parameters have been characterized in terms of PDFs and carried out considering two RSPs, 30 and 45 years.

Considering the limited extent of the proposed case study, a general conclusion beyond the specific context of analysis is related to the potential of the “probabilistic” LCA approach in amending the reliability of building design decision-making, where common “deterministic” approaches do not properly address the topic of inputs’ inherent uncertainties.

2. State of the Art

Life Cycle Assessment (LCA) is a consolidated approach to assess environmental performances of products and services aiming to identify potential issues by having a cradle-to-grave perspective [7,8]. LCA has a long history in the field of buildings and this approach has been applied for decades in this context to evaluate environmental performances [9,10]. However, practical limitations in the adoption of this method in building assessment have often been addressed in the literature. In particular, two concerns related to LCA result robustness have been debated by several authors: (i) data inputs’ uncertainties and (ii) data forecast in a long term perspective [11,12,13].

Concerning the data inputs’ uncertainties, different works have been issued with the aim to characterize the uncertainties in LCA. Roughly, uncertainties can be classified as aleatory and epistemic. Epistemic uncertainty is the scientific uncertainty in the model of the process and it is related to the limited data availability and knowledge. Aleatory variability is the natural randomness in a process that cannot be reduced by model/data refinement [14]. From an engineering point of view, the way to reduce uncertainties in LCA data inputs is to act on the epistemic sources. According to Chouquet et al., the sources of uncertainty for the characterization of building parameters in LCA are (i) environmental data quality (incomplete, inaccurate, or obsolete); (ii) building description (incomplete or inaccurate); (iii) building lifespan and materials/components’ service life (assumptions on lifespan and degree of refurbishment); and (iv) building operation (performance of heating equipment, long term evolution of costs, resource depletion, etc.) [15].

Looking at the environmental data quality uncertainties, the use of pedigree matrix has been used to account uncertainties in data collection and to create LCA datasets and databases (e.g., Ecoinvent) [11,16,17]. Other researchers have tried to adopt statistical methods to characterize input data quality in LCA [18,19,20].

Looking at the building description uncertainties, data quality is referred to as the available project design documentation and the level of detail reported within this. This type of uncertainty can be easily managed and reduced by the project engineers of new buildings; however, for historical buildings or renovation activities data quality can be affected by a higher degree of uncertainty [21].

Materials’ service life used to manufacture building components is strongly affected by several factors such as environmental/climate conditions (e.g., humidity, UV, temperature, etc.), building use, etc., that strongly affect the components service life. Usually this results in a service life shorter than the building life, thus maintenance or replacement activities are required [22,23]. An estimation of data uncertainty related to the lifespan of building materials and components has been proposed by different works [21,24].

Another important uncertainty source in life cycle building analysis is related to the building operations. This is affected by a large variability which is difficult to quantify. The use of building performance simulation tools could allow to estimate the range or the distribution of primary energy consumptions, taking into account the use behaviors [25,26]. Despite these tools are able to manage problem complexity and a large number of parameters, they often do not consider important factors, as new technologies, new material formulations, changes in the composition of energy carriers, etc. [27,28]. This is a relevant topic in the environmental assessment of existing buildings, where energy consumption can drastically change from one technology to another.

All the described uncertainty sources can affect, in different ways, the LCA results. A sound method to assess the contribution of each parameter to the final result uncertainty is the Sensitivity Analysis (SA) [29,30]. To date, SA has been adopted in LCA to a limited extent and only few examples are available in the literature [31]. This research moves a step forward on this topic proposing a novel approach to include uncertainty and sensitivity analysis in building LCA.

3. Materials and Methods

3.1. The Building Case Study

The case study investigated in this work is a single-family house of early ‘900, with a ground floor, a first floor, and an attic (Figure 1). The building is located in the Mediterranean coast of Italy (Cattolica, RN—average heating degree days: 2165).

The external original walls (before building renovation) are made from plastered brick masonry with variable thicknesses from 29 cm (U = 1.76 W/m²K) to 16 cm (U = 2.58 W/m²K). The material layers of the original walls are a 2 cm external plaster (lime and cement based plaster), 12 to 25 cm brick masonry, and 2 cm internal plaster (lime and gypsum-based plaster). The original floors and roof, before renovation, consisted of wooden slabs without insulation, with floor tiles (U = 1.29 W/m²K-first floor slab) and clay tiles (U = 1.68 W/m²K), respectively.

The house is designed in the Art Nouveau style (Modern Style). It is not a nationally listed building but shows interesting architectural elements. For this reason, with the aim of improving the building heating energy performance and the indoor thermal comfort, interior insulation was selected as a renovation solution for improving the envelope performance. In this exemplary case, three alternative internal insulation solutions are identified for LCA prior to the renovation intervention, as the most widespread in Italy for this kind of application:

• Design option A (

  Table 1. Design option A (EPS), U-value: 0.34 W/m²K.

  Materials	Thickness (m)	Density (kg/m3)	Thermal Conductivity (W/mK)
  Adhesive mortar	0.006	1400	0.540
  EPS	0.100	18	0.035
  Adhesive mortar	0.006	1400	0.540
  Plasterboard	0.013	680	0.200
  Skimcoat	0.004	1200	-
  Primer + Paint	0.0002	1670	-

  ): 10 cm Expanded Polystyrene insulating material (EPS) coupled with plasterboard, without vapor barrier, directly fixed to the wall with a specific mortar.
• Design option B (

  Table 2. Design option B (Cork), U-value: 0.33 W/m²K.

  Materials	Thickness (m)	Density (kg/m3)	Thermal Conductivity (W/mK)
  Adhesive mortar	0.007	950	0.310
  Cork	0.120	120	0.040
  Surface rendering	0.007	950	0.310
  Primer + Paint	0.0002	1670	-

  ): 12 cm Cork finished with a mortar as surface rendering (similar to ETICS—External Thermal Insulation Composite Systems used in building facades) and directly fixed to the wall with a specific mortar.
• Design option C (

  Table 3. Design option C (Rockwool), U-value: 0.34 W/m²K.

  Materials	Thickness (m)	Density (kg/m3)	Thermal Conductivity (W/mK)
  Rockwool	0.1	70	0.035
  Vapor barrier	0.002	2700	-
  Metallic frame	-	7800	-
  Plasterboard	0.013	680	0.200
  Skimcoat	0.004	1200	-
  Primer + Paint	0.0002	1670	-

  ): 10 cm Rockwool coupled with plasterboard and a vapor barrier fixed to the wall by a metallic frame.

The three design options reach approximately the same wall U-value (thermal transmittance) required by current Italian legislation (U ≤ 0.364 W/m²K) [2]. The insulation systems U-values are 0.33 W/m²K for system B and 0.34 W/m²K for systems A and C. The slight U-value difference results from the thickness of insulation panels which are commercially available for the proposed materials.

The needed energy for building heating (Q_h) has been calculated through a simplified approach, considering that the assessment focuses on the only internal insulation as an energy retrofit measure. Hence the heat transmission losses through the walls before and after the internal insulation application are calculated with the annual Heating Degree Days method (HDD), Equation (1):

$${\mathrm{Q}}_{\mathrm{h}}=\frac{\mathrm{U}}{1000}\times \mathrm{HDD}\times \mathrm{HH}[\mathrm{kWh}/{\mathrm{m}}^2]$$

(1)

where,

• Q_h is the heat loss through the wall (kWh/m²)
• U is the wall U-value (W/m²K)
• HH is the heating hours a day (h) (set at 24 h)
• HDD are the annual heating degree-days (K)

Then the primary energy for heating (Q_P) can be calculated based on the Equation (2).

$${\mathrm{Q}}_{\mathrm{P}}=\frac{{\mathrm{Q}}_{\mathrm{h}}}{{\mathrm{ETA}}_{\mathrm{h}}}\times \mathrm{EnFc}[\mathrm{kWh}/{\mathrm{m}}^2]$$

(2)

where,

• ETA_h is the overall system efficiency for heating (-)
• EnFc is the conversion factor from delivered to primary energy (-)

3.2. The LCA Model

UNI EN ISO 14040 [8] has been used as a reference standard for the definition of the LCA model. In addition, the terminology proposed by the EN 15978 [7] standard has been adopted for the sake of consistency with LCA in the building sector.

The functional unit is defined as: “the insulation intervention (realized with insulation systems A, B, or C) needed to cover a wall area of 1 m², providing an average thermal resistance U ≤ 0.364 W/m²K (based on Italian Ministerial Decree 26/06/2015) for a building reference study period of 30 (or 45) years”.

In particular, the comparison, in terms of LCA, is made between the three design options able to achieve the same function (what), for the same time period (when), for the same thermal resistance (how much), and in the same context (Italian Ministerial Decree 26/06/2015). The reference flows are therefore the design options which allow us to carry out the defined functional unit, i.e., the three insulation systems analyzed. The wall is not included in the environmental analysis, due to the fact that it remains the same in all simulated cases. It has been instead considered for the calculation of the Q_h, i.e., the heat loss through the wall.

In agreement with the EN 15978 [7] standard, the system boundaries encompass (i) the production stage (modules A1–A3); (ii) the use stage (with modules B2 maintenance, B4 replacement, and B6 operational energy use) and; (iii) the End of Life stage (EoL, modules C1–C4). Aspects that are outside the limits of the system include the construction–installation process (A5) and transportation. The literature highlights how both the construction–installation and transportation processes can be neglected from the analysis [13].

At the aim of the “probabilistic” LCA of internal insulation on historic building, maintenance is considered as the need of periodic replacement of the internal finishing material, i.e., the internal painting, which depends on the paints’ estimated service lives. Instead, replacement involves the whole insulation system, according to its estimated service life [32].

Concerning the LCI (Life Cycle Inventory), all the data related to components, materials, and manufacturing processes of the three design options have been retrieved by direct interviews with the producers. Data on energy consumption have been derived by calculation. Starting from all the collected data, EcoInvent v.3.1 has been used as commercial database to realize the design options’ modeling. In particular, the following datasets have been selected to model materials that constitute the insulation interventions and the gas energy vector:

• EPS: Polystyrene foam slab (RER)| production | Alloc Rec, U
• Cork. Cork slab (RER) | production | Alloc Rec, U
• Rockwool: Rockwool, packed (RER)| production | Alloc Rec, U
• Mortar and Surface rendering: Adhesive mortar (RoW)| production | Alloc Rec, U
• Plasterboard: Gypsum plasterboard (RoW)| production | Alloc Rec, U
• Metallic frame and fixing screw: Steel, low-alloyed, hot rolled (RER)| production | Alloc Rec, U
• Vapour barrier: Aluminium alloy, AlMg3 (RER) | production | Alloc Rec,
• Primer + paint: Alkyd paint, white, without solvent, in 60% solution state (RER)| alkyd paint production, white, solvent-based, product in 60% solution state | Alloc Rec, U
• Skimcoat; Stucco (RoW)| production | Alloc Rec, U
• Gas: Heat, central or small-scale, natural gas (Europe without Switzerland)| heat production, natural gas, at boiler atm. low-NOx condensing non-modulating <100 kW | Alloc Rec, U;

The following dataset has been selected from EcoInvent v3.1 to model the EoL phase for all the materials used.

• Municipal solid waste (waste scenario) (RoW)| Treatment of municipal solid waste and landfill | Alloc Rec, U.

Each process of each life cycle phase has been included in the LCA model in terms of input and output. The cut-off criterion for inclusion was set at 5%, assuming a very minor effect on the results under this level. In relation to data quality, the energy consumption data were based on calculation, data related to components, and materials; production processes were derived from producers’; the EoL scenario was supposed on the basis of the waste typology. The study refers to the year 2017 and data used in the model cover the same geographical area of the study.

The environmental impacts have been calculated according to the following life cycle impact assessment (LCIA) methods.

• ReCiPe midpoint, Hierarchist (H) version—Europe [33].
• Cumulative Energy Demand (CED) [34].

Since this study is focused on building retrofit measures, energy and natural resources are of primary importance. For this reason, this study uses midpoint impact categories from the ReCiPe (H) method [33] and, in particular, climate change has been chosen as a reference indicator [35]. The default ReCiPe midpoint method perspective used is the Hierarchist (H) version referred to the normalization values of Europe. Perspective H is based on the most common policy principles with regards to the 100 year timeframe. The cumulative energy demand (CED) method [34] is used, and in particular, the nonrenewable fossil indicator (CED-NRE) is considered in the analysis as a single-issue indicator to evaluate energy demand associated with a product’s life cycle.

In the probabilistic LCA approach, the following four steps are covered. (i) Identification of PDF for each LCA input parameter affected by uncertainty; (ii) input parameters sampling and propagation by the Monte Carlo (MC) method; (iii) uncertainty analysis (UA); and (iv) global sensitivity analysis (SA) based on variance decomposition.

Monte Carlo methods are used to run the LCA model N-times, where N is the dimension of the vectors obtained by drawing samples from the LCA inputs’ distributions. The outcome of the probabilistic LCA approach is then a certain PDF for each environmental indicator. SA is able to demonstrate the effect of each input’s uncertainty in the final result and, in particular, which one has the highest influence to the model output variance.

The LCA has been performed for the three insulation measures A, B, and C under two reference study periods (30 and 45 years).

3.3. Characterization of Probabilistic Input Parameters

As mentioned above, the development of a LCA model based on UA and SA requires the definition of inputs’ PDFs, which will be propagated to achieve the output variable (environmental indicator) PDF [24]. Within this work, input parameter PDFs have been assumed independent. The PDFs characterization has been performed based on literature investigation, analysis of time series from different repositories and organizations, consultation of the existing database in the field, etc.

Concerning the production stage (A1–3) the following input parameters have been considered stochastic and characterized by distributions.

• The mass of the materials used in the insulation measures;
• the unitary environmental impacts for each material.

For the material mass, based on the literature, a triangular (tri) PDF with a min = −5% and a max = +10% has been adopted [13]. In this case, the distribution refers to the primary data used within the LCA model. For the unitary environmental impacts (materials, transport, and natural gas energy), based on a data quality assessment developed by the use of pedigree matrix for each specific dataset of Ecoinvent DB 3.1, a normal (nor) PDF has been adopted [36]. Then, considering the proposed LCA model, for each dataset a MC analysis, performed by the adoption of ReCiPe LCIA method and 500 iterations, has been run for the definition of each PDF. In this case, the distribution is referred to secondary data used within the LCA model.

Concerning the use stage (B6), the following parameters for the calculation of Q_P have considered stochastic and characterized by distributions.

• HDD of the Emilia Romagna Region, climatic zone E (Italy), where the building is located. Eurostat HDD data were processed, considering the spatial variability in the whole region and the time variability (data are available from 2000 to 2009), obtaining normal distributions;
• Thermal resistance of structural existing wall: 0.22 to 0.40 m²K/W (based on the wall thickness variation), defined by a normal distribution;
• The heating equipment efficiency. A uniform distribution was assigned, considering natural gas as heating source, based on authors’ judgment: 0.6–1.
• The environmental impact (both CC and CED-NRE) related to the Italian energy grid mix (primary energy) represented by a normal distribution (according with Eco-Invent 3.1 and MC analysis).

The conversion factor for natural gas has been fixed at the deterministic value established by Italian law 26/06/2015: 1.05.

Concerning the use stage (B4—replacement), a reference service life of 30 years has been considered for the insulation systems, and then the estimated service life has calculated based on the probabilistic factorial method (ISO 15686-8) assuming a uniform distribution (0.9; 1.1) for all factors.

Finally, concerning the use stage (B2—maintenance), a deterministic value of 10 years has been assumed for the service life of internal painting.

Looking at the system of interest (building case study),

Table 4. Probabilistic input parameters (for phases A1 to A3 and C1 to C4).

LCA Parameter	Design Option A	Design Option B	Design Option C	Mass Quantity (kg)		Unitary Impact for Material CC—(kg CO2 eq/kg)
				PDF *	Reference for PDF	PDF for Phases A1–A3	PDF for Phases C1–C4	Reference for PDF
Adhesive mortar and surface rendering	X			Tri (6.38; 7.39; 6.72)	[11]	Nor (1.376;0.366)	Nor (0.515;0.220)	Eco-Invent DB3.1 with MC analysis
		X		Tri (9.48; 10.97; 9.98)	[11]	Nor (1.376;0.366)	Nor (0.515;0.220)	Eco-Invent DB3.1 with MC analysis
Plasterboard	X		X	Tri (8.08; 9.35; 8.50)	[11]	Nor (0.399;0.055)	Nor (0.518;0.223)	Eco-Invent DB3.1 with MC analysis
EPS	X			Tri (1.71; 1.98; 1.80)	[11]	Nor (4.46; 0.344)	Nor (0.118;0.064)	Eco-Invent DB3.1 with MC analysis
Cork		X		Tri (13.68; 15.84;14.40)	[11]	Nor (1.58; 0.163)	Nor (0.502;0.202)	Eco-Invent DB3.1 with MC analysis
Rockwool			X	Tri (6.65; 7.70; 7.00)	[11]	Nor (1.45; 0.142)	Nor (0.496;0.208)	Eco-Invent DB3.1 with MC analysis
Vapor barriers			X	Tri (0.38; 0.45; 0.41)	[11]	Nor (4.96; 0.946)	Nor (0.505;0.212)	Eco-Invent DB3.1 with MC analysis
Fixing screw (carbon steel)			X	Tri (0.13; 0.15; 0.14)	[11]	Nor (2.03; 0.446)	Nor (0.005;0.002)	Eco-Invent DB3.1 with MC analysis
C-shape frame (carbon steel)			X	Tri (0.72; 0.83; 0.75)	[11]	Nor (2.03;0.446)	Nor (0.005;0.002)	Eco-Invent DB3.1 with MC analysis
U-shape frame (carbon steel)			X	Tri (0.19; 0.22; 0.20)	[11]	Nor (2.03;0.446)	Nor (0.005;0.002)	Eco-Invent DB3.1 with MC analysis
Skim coat	X		X	Tri (0.23; 0.26; 0.24)	[11]	Nor (0.103; 0.012)	Nor (0.504;0.220)	Eco-Invent DB3.1 with MC analysis
Primer and paint	X	X	X	Tri (0.32, 0.37; 0.33)	[11]	Nor (5.26; 8.93)	Nor (0.089;0.049)	Eco-Invent DB3.1 with MC analysis

* Uni (a, b): uniform distribution where a and b are the extreme values. Nor (μ, σ): normal distribution with mean value μ and standard deviation σ. Tri (a, b, c): triangular distribution mode c and a and b are the extreme values, a ≤ c ≤ b. Det (a): deterministic value a.

reports input parameters and related PDFs for phases A1–A3 and C1–C4 and

Table 5. Probabilistic input parameters (for phase B6).

LCA Parameter	Design Option A	Design Option B	Design Option C	Quantity	Unitary Impact for Material
				PDF *	PDF for Phase B6	Reference for PDF
Energy needs for heating (natural gas)	X			Nor (14.12; 2.35) [kWh]	Nor (0.26; 0.04) (kg CO2 eq/kWh)	Eco-Invent DB3.1 with MC analysis
		X		Nor (13.79; 2.34) [kWh]	Nor (0.26; 0.04) (kg CO2 eq/kWh)	Eco-Invent DB3.1 with MC analysis
			X	Nor (14.21; 2.35) [kWh]	Nor (0.26; 0.04) (kg CO2 eq/kWh)	Eco-Invent DB3.1 with MC analysis
Overall system efficiency for heating	X	X	X	Uni (0.6; 1)	-	-

* Uni (a, b): uniform distribution where a and b are the extreme values. Nor (μ, σ): normal distribution with mean value μ and standard deviation σ.

reports input parameters and related PDFs for phases B6. For the sake of comprehension, only the climate change indicator (kg CO₂ eq.) has been reported as unitary impact.

3.4. Uncertainty and Sensitivity Analysis

After the uncertainty characterization of input parameters, their distributions are propagated by the MC method in accordance with the proposed LCA model. The outcome of this step is the environmental impact assessment with its probability distribution. In this study, Sobol’s sequences are used as quasirandom sampling technique in order to generate samples from input distributions as uniformly as possible and then perform the sensitivity analysis through variance-based decomposition techniques.

The size of sample needed for the analysis is dependent on the number of input variables and has been calculated as n(2k + 2) [37], where n takes the value of 16, 32, 64, etc…; k is the number of variables. In order to have robust results and an efficient method of sampling, calculating residuals of the outcome at increasing runs have been compared with a reference solution (MC Basic Random samples—BRS) at 10,000 runs. Given low normalized mean and standard deviation obtained with 8192 runs (less than 0.0005 and 0.002, respectively), this sample size has been selected to run all the simulations and obtain the probability distributions of the resulting environmental impacts.

Finally, sensitivity indices have been assessed with the Sobol’s method to establish which input parameter’s uncertainty is more significant on the result outcome and how this affects the output distribution. Sobol’s “first-order” (Si) and “total-order” (STi) sensitivity indices are calculated. Si provides the main impact of each data input to the variance of the output. STi represents the influence of each input, also considering the variance caused by its interactions with the other inputs’ factors. Higher indices values (nearer to 1) are reached by the most influential input parameters. In this way, SA is useful for establishing which parameter uncertainty can be neglected.

R software has been used as computational tool for the Monte Carlo procedure including SA.

4. Results and Discussion

Figure 2 shows the distribution of the environmental impacts for the selected indicators (climate change and CED-NRE) of the three insulation systems for a reference study period of 30 years. As is observed from the box–whisker plots, results are associated with considerable uncertainty: Blue box plots represent the 50% probability that impact values are contained within the ranges identified by the box, while the red points represent the results obtained from a deterministic LCA assessment performed on the same solutions. The inclusion in the graphs of the deterministic results allows confirming the validity of the probabilistic approach used, while highlighting how the results are affected by the inputs uncertainties.

Looking at the graphs reported in Figure 2 a slight difference on the environmental impact distributions for the three design options is noticed. Solution C (Rockwool) is able to guarantee minor median values of the impacts according to both indicators, followed by Solution A (EPS) and B (cork). In particular, median values and standard deviations for the environmental impacts considered are summarized in the following

Table 6. Median value and standard deviation for climate change and CED-NRE indicators for Systems A, B, and C.

Design Options	Climate Change Indicator		CED-NRE Indicator
	Median Value	Standard Deviation	Median Value	Standard Deviation
A (EPS)	193.05 kg of CO2 eq	43.90	2932.20 MJ	831.30
B (cork)	217.85 kg of CO2 eq	47.90	3138.80 MJ	841.20
C (Rockwool)	190.52 kg of CO2 eq	43.47	2750.40 MJ	818.80

.

This outcome can be further analyzed considering the environmental impacts related to each phase of the entire life cycle. Environmental impacts related to the use phase are almost the same for all the insulation measures due to the same average thermal resistance they guarantee. Environmental impacts related to EoL are quite similar for all the insulation measures, as well as the impact related to maintenance phase. For those two life cycle stages, results are mainly dependent on the involved materials.

Impacts related to production phase are instead different for each solution (they depend on the typology of material used and their mass) and consequently they are responsible for the differences on the total impacts among the three insulation solutions. Unitary environmental impacts of Rockwool and cork are quite similar in number (both for climate change and CED-NRE indicators), but lower than EPS. However, the mass of insulation materials is quite different for the three systems, respectively: 14 kg for cork, 7 kg for Rockwool, and 1.8 kg for EPS. This leads to a higher impact related to the production phase for Solution B (cork), followed by Solution A (EPS) and C (Rockwool). Despite the fact that cork has the lowest unitary environmental impact and is therefore usually considered an ecofriendly product, its thermal performance relies heavily on its mass to apply the insulation intervention and reach the desired thermal resistance.

Considering a global life cycle perspective, for all of the analyzed solutions, the impact related to the use phase is predominant in respect to those of the other life cycle phases, as shown in

Table 7. Impact related to each phase of the solution’s life cycle.

Phase	Climate Change Indicator			CED-NRE Indicator
	A (EPS)	B (Cork)	C (Rockwool)	A (EPS)	B (Cork)	C (Rockwool)
Production + Maintenance	13.65%	20.63%	12.16%	14.48%	20.36%	9.83%
Use	81.71%	72.97%	83.14%	85.29%	79.33%	89.94%
End of Life	4.64%	6.40%	4.70%	0.22%	0.30%	0.23%

. It accounts for approximately 80% of the total impact; this is due to high consumption of gases that are consumed during the entire reference study period considered (30 years).

In order to understand how much the uncertainties of the inputs’ impact on the outputs’ variance, a sensitivity analysis, based on Sobol’s method, is realized. Figure 3 and Figure 4 report the outcomes of the sensitivity analysis performed by Sobol’s method in two different RSP: 30 years vs. 45 years. In particular, looking at the graphs reported in Figure 3, they represent the total-order indices for both environmental indicators (a—CC and b—CED-NRE) for a RSP of 30 years. The following labels have been used in the graphs.

• sI: insulation system environmental impact related to production phase
• smI: insulation system environmental impact related to maintenance phase
• EoLI: insulation system environmental impact related to end of life phase
• Qhpost: heat transmission losses through the wall after renovation
• ETAh: overall system efficiency for heating
• SL: insulation system service life
• EI: unitary impact of the energy vector

For all the three options, the ranking of inputs’ uncertainties is similar. Four inputs account for almost the whole output uncertainty: (i) Qhpost; (ii) ETAh; (iii) EI; and (iv) SL. The first three are related to the system energy performance and to the energy career impact. Mainly, their influence on output variance is due to the importance of the operational energy use phase in the whole LCA results and to the inputs’ inherent uncertainties. On the other hand, the SL parameter requires a specific analysis. The mean value of insulation systems SL is set to 30 years, as well as the RSP during the Monte Carlo sampling procedure. In this case, some draws occur before 30 years, thereby inducing the replacement of the whole insulation system thus affecting the outcome uncertainty. This outcome is also demonstrated when the RSP is set to 45 years, far from the insulation system SL (30 years), in order to include at least one insulation replacement during the assessment. In this case, the SL uncertainty has a very low impact on the final results; as demonstrated by the STi provided in Figure 4 for both environmental indicators.

By analyzing the outcomes of Figure 3 and Figure 4, system production (sI), system maintenance (smI), and end-of-life (EoLI) uncertainties have a limited impact on result variance. It is worth noticing that if the user is interested in assessing the LCA of an insulation solution in a specific building scenario (with an accurate heat loss calculation through specific simulation tools) some of the uncertainties related to ETAh and/or Qhpost parameters can be strongly reduced in favor of other inputs.

5. Conclusions

The paper proposes a probabilistic LCA approach for building retrofit measures and illustrates its effectiveness through a simplified case study of building renovation, involving interior insulation as retrofit measures.

Despite LCA can be considered a consolidated tool to evaluate environmental performances and, in the case of building refurbishments, assumptions and simplifications can generate unforeseen consequences on the result. This aspect is not easily identifiable within the result which is usually represented as a deterministic value. In order to make LCA a robust support in the building design decision-making process, the user (engineer, architect, etc.) needs to be aware of the inherent limitations of the method itself and require the right tools to address all these aspects.

To this aim, a “probabilistic” LCA approach is proposed in this work, coupling Monte Carlo calculation with building renovation LCA. The novel approach includes several aspects such as (i) suggestions for the identification of PDF for each input parameter affected by uncertainty; (ii) input parameters sampling and propagation by the adoption of Monte Carlo method; and (iii) uncertainty and global sensitivity analysis, based on variance decomposition. One of the main outcomes of the LCA probabilistic approach is the possibility to establish the impact of input data uncertainties on the output distribution.

An illustrative case study of the methodology application has been carried out to test the feasibility and the robustness of the proposed approach. Three alternative internal insulation measures (EPS, Cork, and Rockwool) for building renovation, under different reference study periods, have been accounted for the assessment.

Results obtained highlighted a small difference in the median values of the environmental impacts of the design options considered, mainly because the impact of the use phase is the same for the two measures and this phase is the most relevant to the overall impact result. Nevertheless, the study outcomes and the results of the SA pointed out how the model inputs influence the output variance depending on the specific assumptions made on their PDFs and on the reference study period considered.

The performed probabilistic LCA analysis limits the system boundaries until the production, use, and EoL phases and excluded the transport phase and all the building in situ processes.

Future works will focus on the study of other renovation measures, using the proposed approach. The possibility to perform SA on a wider range of solutions and building case studies will provide a clearer picture of the input parameters that require more attention by the building designer/consultants. All these studies will support practitioners working in this field to judge, with a proper decision-making tool, which design solutions are more sustainable in a certain environment (boundary conditions) knowing the level of uncertainty related to his/her choice. By coupling probabilistic LCA and LCC (Life Cycle Costing) approaches, practitioners are driven towards the selection of the most affordable design solutions in building retrofit, properly taking into account the inherent risks associated.