# Method of Planning Repairs of the Installation including Building Waste
## 2 Materials and Methods
### Main Principles of the Method
The prediction of the change in performance, \(R_{M}(t)\), of a repaired building, where \(t_{pi}\) is the date of repair, is expressed by the formula [51; 52]:  
\[R_{M}(t)=\left\{ \begin{array}{ll}\sum\limits_{i=1}^{m-r}A_{i}\exp\left(- \left(\frac{t}{T_{Ri}}\right)^{2}\right)&if\;t\in\left(0,\;t_{pi}\right)\\ \sum\limits_{i=1}^{r}A_{i}\exp\left(-\left(\frac{t-t_{pi}}{T_{Ri}}\right)^{2} \right)&if\;t\in\left(t_{pi},\;T\right)\end{array} \right. \tag{3}\]  
where  
\(r\)--the number of refurbished components in a given inter-repair cycle;  
\(m\)--number of all elements;  
\(A_{i}\)--weight of \(i\)-th element;  
\(t_{pi}\)--time of carrying out refurbishment on element, \(i\);  
\(T_{Ri}\)--life cycle of \(i\)-th element. The proposed repair works aim to maintain the building in good, satisfactory or average technical condition and rely on prophylactic action and preventing the premature emergence of unfavorable changes. Modeling various possible usage scenarios of a building according to the proposed method will allow for the optimal planning of building maintenance works' undertakings. The material and construction solutions for the analyzed building were chosen based on traditional technology: e.g., walls and foundations are made of brick, ceilings, stairs and roof trusses are made of wood and covered with ceramic tiles. Each building material has a specific life span. Estimating the life span of both the material itself and the product made from it is not possible in a clear and universal way. An identical product may have a radically different lifetime after taking into account the location and local conditions (geological, hydrological and climatic) [53], environmental pollution, including air pollution [54], as well as the impact of climate change [55]. Depending on local conditions, even the number of building elements indicated in the literature may vary [56; 57]. For example, the central heating system can be considered as a single system or divided into pipe system and radiators. The situation becomes more complicated with the spread of new techniques such as heat pumps or surface heating. Table 2 presents the division of the building into 25 elements, the material solutions of these elements and their lifetimes. The data included are based on an analysis of literature data [53; 54; 55; 56; 57; 58; 59; 60; 61; 62]. All the refurbishment strategies proposed are associated with refurbishment costs. In this paper, the main focus is on the improvement of technical condition and environmental protection, while cost is also an important topic that will be addressed in future research. \begin{table}
\begin{tabular}{c c c} \hline \hline
**No.** & **Element Name \(i\)** & \(\mathbf{T_{Ri\,SR}}\) \\ \hline
1 & brick foundations & 110 \\
2 & masonry walls made of solid bricks & 140 \\
3 & separating walls made of brick & 100 \\
4 & wooden beam ceilings & 70 \\
5 & wooden stairs & 35 \\
6 & rafter framing & 80 \\
7 & ceramic roofing tiles & 70 \\
8 & gutters and downpipes made of galvanized steel sheet & 17.5 \\
9 & internal plasters & 55 \\
10 & external plasters & 45 \\
11 & window joinery & 50 \\
12 & door joinery & 90 \\
13 & glazing & 40 \\
14 & wooden floors (coniferous timber) & 50 \\
15 & painting of walls and ceilings & 4 \\
16 & oil paintings of woodwork & 5 \\
17 & ceramic kitchen stoves & 35 \\
18 & tile cookers & 45 \\
19 & heating pipes (steel) & 35 \\
20 & central heating boilers and radiators & 50 \\
21 & water and sewage pipes (galvanized steel) & 37.5 \\
22 & water and sewage pipes & 30 \\
23 & gas pipes (galvanized steel) & 37.5 \\
24 & wiring for electrical installations (flush mounted) & 60 \\
25 & fittings for electrical installations & 22.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Service life of building elements with a specific material and construction system. The method also neglects the problem of dwelling use during the repair work carried out. The more often a refurbishment is carried out, the more difficulties in use occur.