intervention = initial construction × repairing rate

As the repair time varies according to the supplied performance and the required performance of the building, the repairing quantity will also be variably determined, depending on the performance of the period. In this study, the repairing rate is defined as the ratio of the required performance to the gap between the repairing performance and the supplied performance, as shown in the following. Combined with the definitions mentioned above, the final repairing time and quantity are defined as follows.

> repairing rate = (RP − SP)/RP IF THEN ELSE ("SP/RP" < λ, initial construction × repairing rate, 0))

(3) The extent to which the performance will be improved by intervention activities: ratio of intervention quantity to initial construction.

When intervention activities are performed, performance is improved. Performance improvement will increase the supplied performance of buildings and meet the required performance. The question is the extent to which the performance improvement is created by the intervention activity. As a result of investigating the asset management tools of the US federal agencies [22], indices are developed to accumulate and predict information about the supplied performance, the amount of intervention, and the timing of intervention. However, quantitative indicators of performance improvement by intervention are not found. This may be because the asset management or facility management deals with the building condition, focusing on the budget expenditure.

Quantitative indicators representing the degree of performance improvement are not utilized in the present asset management and facility management fields. It could be intuitively deduced that the performance improvement due to intervention is proportional to the amount of intervention. In this study, it is intended to quantify the performance improvement by introducing a coefficient (ρ) that can represent a proportional relationship according to this intuition.

performance improvement = (intervention/initial construction) × ρ

The above definition is based on the assumption that the performance improvement is simply proportional to only the intervention ratio, compared to the initial construction quantity. ρ is a coefficient indicating the relation between intervention quantity ratio and function improvement. Here, ρ is a coefficient, with a yet unknown value. This value could be found through a model calibration in a further case study.

The SFD was created by adding the introduced variables, described above, and setting the stock and flow variable. The supplied performance is determined according to the stock variable, where the performance deterioration is the outflow variable, and the performance improvement is the inflow variable. In addition, the cumulative recurrent environmental impact is added as a stock variable to identify the total amount of recurrent environmental impacts during the building service life. The model includes the required service life parameter of the building, so that there is no intervention activity when the required service life is reached. The reference variable is a parameter generated for the calculation to refer to the initial construction value throughout the analysis period and does not affect the relationship between the variables in the environmental impact system of the usage stage. The SFD is shown in Figure 3. The bold arrows represent the feedback loop, analyzed in the causal map.

**Figure 3.** Stock and Flow Diagram of environmental impact in building usage stage.

## **5. Case Study**

#### *5.1. Data Information*

The case building is a 30-story apartment building, with a reinforced concrete structure. This building consists of five types of floor plans, with a floor area of 146.48 m2, 158.89 m2, 161.25 m2, 161.75 m2, and 272.8 m2, accommodating 117 generations. A summary of the building construction and the bill of quantity (BoQ) were collected for the building.

Referencing the existing research [31,32] that thoroughly analyzed the target materials of the Korean apartment building for LCA, this study determines the main materials for the case study: Rebar, ready-mixed concrete, concrete brick, cement, insulations, and paints are selected. However, existing studies tend to overlook the materials that are used in the finishing work, probably because of their lightweight and fewer emissions, comparing the structural components by cut-off rules. Since this study focuses on the intervention activities, some non-structural materials, which are repaired or replaced during the building usage, need to be considered. In this context, board, tile, granite, wallpaper, and flooring are also selected.

Using the National lifecycle inventory database by KEITI [33] and KICT [34], Greenhouse Gases (GHGs) emission factors are calculated. Three types of GHGs, carbon dioxide, methane, and nitrous oxide are considered among the lots of GHGs, considering the GWP and its importance, according to the IPCC report. Table 1 below shows the selected main materials and respective emission factors used in the case study.


**Table 1.** Main materials and emission factors.

EA (each) = 1.2 × 0.19 × 0.01 m<sup>3</sup> (size of one MDF flooring panel).

#### *5.2. Assumptions in the Case Study*

In EN 15978 [35], the system boundary for assessment is described, and the assessment modules in the building lifecycle are defined, as shown in Figure 4. Among the assessment modules, A1–A3 in the product stage, A4 and A5 in the construction process stage, B2–B5 in the usage stage, and C1–C4 in the end-of-life stage are relevant to the embodied impact (faded part in Figure 4). Since the DLCA model is focused on the recurrent EC, the case study is performed within modules B2–B5. The carbon emissions in modules A1–A5 were also calculated ahead of the simulation, because several variables in the DLCA model refer to initial construction information.

This study introduced several assumptions in the case study due to the availability of data. Table 2 shows the assumptions applied in the emissions calculation, with an LCA and Dynamic simulation.

**Figure 4.** System boundary and assessment modules in building lifecycle assessment.

Building embodied emissions are caused by two factors, material use (the energy consumption in production) and construction activities (the energy consumption by transportation and execution). Material type and quantity data are quite well found in BoQ or the standard unit cost book. However, activity data, such as transportation or carriage-on-site, are not easy to obtain, since they are not well documented during construction. Moreover, M&R activity data, such as the type of repair machinery, work time, and productivity, are even harder to acquire, compared with new construction. Consequently, even if several activities cause carbon emissions, they are excluded from the calculation.

Meanwhile, several variables applied in SFD for dynamic simulation do not allow the real data to be acquired. M&R history data, such as the repair method, time, and quantity in relation to private buildings, are not yet recorded and organized in a database. Accordingly, the guidelines from Enforcement Decree of the Multi-Family Housing Management Act in Korea are assumed. Performance is quantified in a five-point scale, based on the condition grading system for building assets in the International Infrastructure Management Manual [36]. Additionally, there is no system for the performance assessment of private buildings, so deterioration (performance history) data are virtually assumed, referencing the existing study [37].


**Table 2.** Assumptions of the case study.

Keshavarzrad et al. [37] presented deterioration curves using the National Asset Management Support data. They used the Markov model for the prediction of the deterioration trend. A Markov chain has been used in deterioration prediction in relation to bridges [38] and sewers [39]. Sharabah [40] introduced a weighting model for building assemblies using Markov process data, collected from Victorian city councils. Edirisinghe et al. [41] also applied the Markov model for building deterioration prediction.

The state transition probabilities and deterioration curves might be different for each building component. Components using materials with short service lives will have a high probability of transitioning to the next state (curve 2), and components using durable materials will have a significantly higher probability of staying current than transitioning to the next state (curve 1). Since a well-founded transition matrix that can be referred to in the literature is limited, two types of condition curves are virtually adopted. Figure 5 shows the two types of condition curves, resulting from the Markov model calculation. Stone work and interior finishing work, which recommend a repair time of more than 25 years in the guidelines, are applied to deterioration data form curve 1, assuming their performance is relatively slowly degraded. The plastering, tiling, painting and decoration works are applied data from curve 2.

**Figure 5.** Condition curve of reference and discretion.
