#### 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/m^{2}K) to 16 cm (U = 2.58 W/m^{2}K). 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/m^{2}K-first floor slab) and clay tiles (U = 1.68 W/m^{2}K), 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): 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): 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): 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/m

^{2}K) [

2]. The insulation systems U-values are 0.33 W/m

^{2}K for system B and 0.34 W/m

^{2}K 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):

where,

Q_{h} is the heat loss through the wall (kWh/m^{2})

U is the wall U-value (W/m^{2}K)

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).

where,

#### 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 m^{2}, providing an average thermal resistance U ≤ 0.364 W/m^{2}K (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.

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.

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 m^{2}K/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 reports input parameters and related PDFs for phases A1–A3 and C1–C4 and

Table 5 reports input parameters and related PDFs for phases B6. For the sake of comprehension, only the climate change indicator (kg CO

_{2} 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.