*5.3. Simulation*

Ideal data for the model calibration of this study would be the actual repair or replacement details, collected for the apartment building. In particular, information, such as the repair time, type of repair activity, and quantity of repair, is required for each object. However, there is still a lack of data accumulation on the repair content of buildings. Therefore, the guidelines in the Housing Act is applied, instead of the real-world value for the calibration of the model. Despite the fact that the guidelines of the Housing Act do not match the real world, calibration based on this reference means reflecting a long-term repair documentary plan in Korean apartment housing.

Comparing carbon emissions and cumulative carbon emissions during the building service life, based on the repairing time and rate from the Housing Act guidelines, λ, ρ, and the required performance parameters are optimized. Initial running with an initial λ = 0.9, the initial performance = 4 is simulated for the model variables for the 50-year study period. Optimized λ, ρ, and the required performance value from the calibration, with a payoff, is displayed in Table 3.



M = plastering; T = tile; S = stone; I = interior finishing; P = painting; D = decoration; RO = roof; EW = exterior wall; IC = interior ceiling; IW = interior wall; IF = interior floor; ST = stair.

A base run with the parameters' input value from the calibration results is simulated. The total embodied GHG emissions are 1.97 million kgCO2eq in the dynamic model (Base run), whereas they are 1.528 million kgCO2eq in the static calculation from the Housing Act guidelines (Figure 6).

**Figure 6.** Comparison of the base run and Housing Act in the Greenhouse Gases of the usage stage.

Despite the optimization, the difference between the model and the guidelines is considerable. The dynamic model tends to have a lower intervention than the guideline value, at the beginning of the building service life, and this becomes more frequent as the building ages. Additionally, the intervention quantity is small at the beginning and grows larger at the end of the building's life in the dynamic model. While the static calculation shows a periodic value, ignoring the building condition, the dynamic model can describe the changing period and quantity of the intervention. Regardless of the benchmark data reality, this conceptual method presents the specific tool for dynamic LCA. It also shows the possibility of anticipating a realistic intervention and its environmental impact in advance.

#### *5.4. Sensitivity Analysis*

Using the developed dynamic model with a calibrated base run allows for an analysis of the variability involved in the environmental impact of construction activity in the usage stage. In this study, sensitivity analysis is performed on the variability of environmental impacts using two parameters. First, we analyzed the λ, which shows the intensity of the maintenance strategy. The λ variability of the sensitivity analysis was set to ±10% of the values derived from each trade and object in the calibration (Table 4). Sensitivity analysis applies the Monte Carlo simulation method, which generates random numbers, according to the probability distribution. Since we do not know about the specific probability distributions for λ, a simply uniform distribution was assumed. The analysis results are shown in Figure 7. With λ changes, the total embodied emissions in the usage stage from the base run of 1970 tCO2eq could range from at least 1930 tCO2eq to 2140 tCO2eq.


**Table 4.** Sensitivity analysis results concerning the maintenance strategy intensity (λ).

**Figure 7.** Sensitivity analysis results on maintenance strategy intensity (λ).

In other words, each λ variation of 20% resulted in a total embodied emissions value, in the usage stage variation, of approximately 10.6%. The variation ratio of the embodied emissions for each trade and object in accordance with the λ variation is described in Table 4. There were several components that did not change, regardless of the λ variation, tile work in the interior wall, interior finishing work in the interior ceiling and wall, painting work in every object, and decoration work in the interior wall. Stone work is the most sensitive work affected by λ, even if it occupies a small percentage in the total emissions. Tile work in the interior floor, tile work in the roof, decoration work in the interior floor, plastering work in the interior floor, and plastering work in the roof were found to have a high sensitivity in sequence.

Next, the sensitivity is analyzed for the required performance of the building users. The required performance variation was ±10% of the values derived from each trade and object in the calibration in the sensitivity analysis (Table 5). The specific probability distribution of the required performance is also unknown, so a uniform distribution is assumed for the Monte Carlo simulation. The analysis results are shown in Figure 8. As the required performance changes, the total embodied emissions in the usage stage, from 1970 tCO2eq in the base run, can vary from at least 1848 tCO2eq to 2111 tCO2eq.


**Table 5.** Sensitivity analysis results concerning the required performance.

**Figure 8.** Sensitivity analysis results concerning the required performance.

Each required performance variation of 20% resulted in the embodied emission variation of approximately 13.4% during the usage stage. The variation ratio of the embodied emissions for each trade and object, in accordance with the required performance variation, is described in Table 5. There were several components that did not change, regardless of the required performance, stone work, interior finishing work in the interior ceiling and wall, painting work in every object, and decoration work in the interior wall. Tile work in the interior floor is the most sensitive work affected by the required performance, even if it occupies a small percentage of the total emissions. Tile work in the interior wall, tile work in the roof, decoration work in the interior floor, plastering work in the interior floor, and plastering work in the roof were found to have a high sensitivity in sequence.

Under the same conditions, the required performance was found to be more sensitive to changes in emissions for the components and total value than λ. The rate of change in tile work tends to have the largest ratio, and the painting work shows no change for both λ and the required performance. Stone work was the most sensitive work in terms of λ but did not show any variation in the required performance.

Adding a larger amount of data accumulation and elaborate assumptions, this analysis can be a useful tool for preliminarily verifying the variability of the repair scenarios for each trade and object. In addition, the evaluation of the life cycle environmental impacts, taking into account the variability of the intervention scenarios, could be useful for risk analysis in building environmental management.

#### **6. Conclusions**

Maintenance activities mainly depend on changes in building performance over time, but the static methodology of traditional LCA does not take this variability into account. Besides, current embodied environmental impact assessment has tended to focus on the structural materials, and decorating materials used in M&R are overlooked. This study combines system dynamics with LCA to assess the recurrent embodied carbon emissions. It visualizes the long-term behavior of the environmental impacts caused by the feedback structure between the building performance and intervention. Additionally, the variability of the environmental impacts, from the changes in users' required performance and maintenance strategy intensity, is analyzed.

The results of this study show the possibility of acquiring a great amount of important information that could not be captured by the traditional LCA methodology. It shows how the estimates of environmental impacts, assuming the application of fixed repair cycles and ratios, differ from the actual performance-based maintenance concept. This implies that it is possible to provide statistical information on the uncertainty of the forecast when estimating the emissions, and it can support the reliability of the environmental impact estimation of buildings.

This study has some limitations in terms of data collection and utilization. First, because the site of the case building was closed, it was impossible to collect activity data on the building. A simulation was performed using assumptions and data from the literature, and analysis based on the measured data should be performed in the next study. A lot of activity data, generated in M&R work during the usage stage, are not accessible and difficult to measure. Nevertheless, data acquisition for several sample works would be a meaningful starting place, before considering whole buildings.

Additionally, because of the lack of available information about performance degradation, it was replaced with data from the existing study. While the main interest of this study is the relationship between the building performance and the environmental impact, the accuracy of the deterioration data is important in the model, since performance is a major variable determining the timing of M&R. It is necessary to explore the performance deterioration, which is suitable for the LCA target building, through the accumulation of performance evaluation for representative buildings.

**Author Contributions:** Conceptualization, G.K.; methodology, G.K.; validation, G.K., H.C. and D.L.; formal analysis, G.K. and H.C.; investigation, G.K., H.C., and D.L.; data curation, G.K. and D.L.; writing—original draft preparation, G.K.; writing—review and editing, H.C. and D.L.; visualization, G.K. and D.L.; supervision, G.K.; project administration, H.C.; funding acquisition, H.C.

**Funding:** This research was funded by National Research Foundation of Korea grant number 2016R1A2B3015348 and Korea Institute of Civil Engineering and Building Technology grant number 20180543-001.

**Conflicts of Interest:** The authors declare no conflict of interest.
