Structural Analysis of Factors Inﬂuencing the Costs of Facade System Implementation

: External facades of buildings and other structures shape the image of every building, creating the architecture of cities. Traditional concrete forms, as a symbol of durability and stability, have been replaced by lightweight enclosures—for example, in the form of aluminium–glass facades and ventilated facades. In this paper, the authors attempt to verify the strength of inﬂuence and relations between the identiﬁed factors shaping the costs of facade system implementation using structural analysis. On the basis of the collected quantitative and qualitative data obtained as a result of research on design documentation and cost estimates of implemented public buildings, as well as on the basis of interviews conducted among experts, factors which have a real impact on the costs of facade systems in the form of aluminium and glass facades and ventilated facades were identiﬁed. The indicated factors were analysed and classiﬁed using the method of structural analysis, namely the MICMAC method (refers to the French acronym for Cross-Impact Matrix Multiplication Applied to Classiﬁcation). Particular inﬂuences and relations between factors were examined. Finally, six groups of factors inﬂuencing the costs of facade systems were identiﬁed, including regulatory factors that do not have a very strong impact on the level of costs, but which show a strong correlation with other factors; determinants that have a very strong impact on the costs; and a group of external factors that show the smallest inﬂuence on the estimation of façade cost.


Introduction
External facades of buildings and other structures shape the image of every building, creating the architecture of cities. The dynamic development of technology, the discovery of new innovative building materials [1], as well as the ever-increasing technical, production, and execution capabilities have resulted in exterior walls with complex shapes and forms. Traditional concrete forms as a symbol of durability and stability have been replaced by lightweight enclosures-for example, in the form of aluminium-glass facades and ventilated facades [2]. Aluminium and glass facades are built from aluminium sections, and the spaces between the aluminium construction is filled with glass. Glass that is used in construction should meet the requirements of thermal protection, fire protection, burglary protection, protection against noise, and safety of use [3]. A solid building made in the form of aluminium-glass facades is an indispensable element of architecture for a modern city [4]. Also, ventilated facade systems have gained much attention. It is a cladding system, which incorporates the insulation layer, positioned usually on the external surface of the wall, the air cavity and the outer skin [5]. The air gap allows air to enter and flow through the facade. The external part of the ventilated façade is a panel suspended, glued, or screwed to the substructure. Ventilated facades allow for shaping external claddings from various materials, structures, textures, or colours. The panels can be made of many materials, including wood, fiber concrete, aluminium and ceramics. Due to their high aesthetics, ventilated facades are increasingly often used as external parts of newly built buildings, Figure 1. Type of aluminium-glass facades. Own study based on [26].
The first type of structure consists of mullion-transom, and the inner space is filled with glass. On the outside of the mullion-transom system are termination bars and masking strips. A semistructural façade is smooth. Glass is fixed directly to the construction, and the gap is filled with a special weather silicone. The structural system is characterized by the possibility of obtaining an external glass faced without visible elements. This effect can be achieved by gluing the glass directly to the aluminium structure. The other facade system frequently used for public buildings in combination with aluminium and glass facades is a ventilated facade [18]. This solution is based on leaving a ventilation gap between the external cladding and the thermal insulation layer. A ventilated facade is defined as a set of elements for enclosing external walls, consisting of the following [2]: • external panels (for instance, cement, stone, wood-based, plastic, metal, or laminate) attached to the grate (suspended, glued, or screwed to the grate); • grate (made of metal or wood) attached-suspended, glued, or screwed-to the external wall; • fastening elements; • insulating material.
Due to the variety of materials used for the external panel and the substructure used (grate), it is possible to present the classification of ventilated facades, as shown in Figure 2.
Type of aluminum-glass facade mullion-transom system Facade system with post and transom construction. The filling is a glass package. Clamping and masking strips are mounted from the outside.

semistructural system
The structure is based on a post and transom system, with no masking strips from the outside.
The glass is attached directly to the structure, and the gaps are filled with weather silicones structural system Fully glazed outer surface. Glass glued to the structure with structural silicone Figure 1. Type of aluminium-glass facades. Own study based on [26].
The first type of structure consists of mullion-transom, and the inner space is filled with glass. On the outside of the mullion-transom system are termination bars and masking strips. A semistructural façade is smooth. Glass is fixed directly to the construction, and the gap is filled with a special weather silicone. The structural system is characterized by the possibility of obtaining an external glass faced without visible elements. This effect can be achieved by gluing the glass directly to the aluminium structure. The other facade system frequently used for public buildings in combination with aluminium and glass facades is a ventilated facade [18]. This solution is based on leaving a ventilation gap between the external cladding and the thermal insulation layer. A ventilated facade is defined as a set of elements for enclosing external walls, consisting of the following [  Ventilated facades should meet all the requirements for technical assessment, and above all, should be tested for fire safety, namely, reaction to fire, resistance to fire, and ability to continuously smoulder [27]. Ventilated fire facade elements should be tested, and their fire class should be equal to class "A". Aluminium and steel grates, which are substructures of ventilated facades, are classified as non-combustible in class A1, and they are most often used for fire-rated ventilated facades. On the other hand, the external lining itself, whether in the form of composite panels or HPL (High Pressure Ventilated facades should meet all the requirements for technical assessment, and above all, should be tested for fire safety, namely, reaction to fire, resistance to fire, and ability to continuously smoulder [27]. Ventilated fire facade elements should be tested, and their fire class should be equal to class "A". Aluminium and steel grates, which are substructures of ventilated facades, are classified as non-combustible in class A1, and they are most often used for fire-rated ventilated facades. On the other hand, the external lining itself, whether in the form of composite panels or HPL (High Pressure Laminate) panels, should have a fire-resistant core, which gives the fire-resistant characteristics to the element in question.

The Structural Analysis: Methodology
Structural analysis, namely the MICMAC method (refers to the French acronym Matrice d'Impacts Croisés Multiplication Appliquée á un Classement/Cross-Impact Matrix Multiplication Applied to Classification), allows us to examine particular influences and relations between specific variables or factors. The MICMAC method examines direct influences, but also analyses indirect relationships that are not always noticed by experts and analysts [28]. The input element of the analysis is the evaluation and description of direct impacts made by the experts, and then indirect impacts that may occur between factors are additionally examined. As a result of the application of this method, it is possible to separate those factors which are the most decisive and crucial for the examined area from the set of variables. The method also makes it possible to prioritize and organize the variables that seemingly do not influence each other, but thanks to cross analysis, it is possible to show their mutual interactions [29,30]. The individual steps of the structural analysis are depicted in Figure 3.

The Structural Analysis: Methodology
Structural analysis, namely the MICMAC method (refers to the French acronym Matrice d'Impacts Croisés Multiplication Appliquée á un Classement/Cross-Impact Matrix Multiplication Applied to Classification), allows us to examine particular influences and relations between specific variables or factors. The MICMAC method examines direct influences, but also analyses indirect relationships that are not always noticed by experts and analysts [28]. The input element of the analysis is the evaluation and description of direct impacts made by the experts, and then indirect impacts that may occur between factors are additionally examined. As a result of the application of this method, it is possible to separate those factors which are the most decisive and crucial for the examined area from the set of variables. The method also makes it possible to prioritize and organize the variables that seemingly do not influence each other, but thanks to cross analysis, it is possible to show their mutual interactions [29,30]. The individual steps of the structural analysis are depicted in Figure 3.

The First Stage: Identfication of Factors
The basis for structural analysis is the identification of the variables/factors that influence and shape a given research area. This is the first and most time-consuming stage. The collected research materials, documentation, literature studies, expert surveys, and face-to-face interviews allow us to distinguish a group of factors that have a decisive influence on the analysed problem.

The Second Stage: Description of Factor Relationships
The second stage of the analysis involves a description of mutual relationships between individual factors by coding the relationships. Mutual relations are defined as follows [28]: 0 = no influence, 1 = weak influence, 2 = medium influence (significant but not decisive), 3 = big influence (decisive), and P = potential influence. This step is usually performed by experts.

Identification of Factors
Literature analysis Analysis of documentation Analiza tekstów źródlowych Ankieta ekspercka expert-based survey Face-to-face interviews

Evaluation of Factors' Impacts
Evaluation of direct and indirect impacts between factors using the MICMAC method

Identification of Factor Groups
The possible group: -key factors -target factors -result factors -determining factors -regulatory factors -ancillary factors -autonomous factors -external factors

The First Stage: Identfication of Factors
The basis for structural analysis is the identification of the variables/factors that influence and shape a given research area. This is the first and most time-consuming stage. The collected research materials, documentation, literature studies, expert surveys, and face-to-face interviews allow us to distinguish a group of factors that have a decisive influence on the analysed problem.

The Second Stage: Description of Factor Relationships
The second stage of the analysis involves a description of mutual relationships between individual factors by coding the relationships. Mutual relations are defined as follows [28]: 0 = no influence, 1 = weak influence, 2 = medium influence (significant but not decisive), 3 = big influence (decisive), and P = potential influence. This step is usually performed by experts.

The Third Stage: Examination of Factors' Impacts
The next step examines the direct and indirect impacts that may occur between factors. To evaluate and describe the direct and indirect factor relationships, the authors used the MICMAC free online software developed by French Computer Innovation Institute 3IE and LIPSOR Prospective (foresight) Strategic and Organisational Research Laboratory [25]. The software allows for a quick calculation. Its operation is based on the algebraic principle of Boolle's logic, which is usually used to build scenarios at the initial stage of describing future trends.
On the basis of the experts' assessment, a direct impact matrix and a graph are built, the vertices of which represent the factors. In order to calculate the strength of each factor's influence on another factor, the number of paths (relationships) between them and their length is then determined as the strength of the relationship. Indirect relationships between the factors are obtained by successive exponentiation of the direct influence matrix. The total strength of influence is the sum of all elements of the matrix row of direct influence for a given factor, while the total strength of dependence is the sum of elements in the matrix column.
As a result, two matrices are built out of direct and indirect interactions, as well as two graphs of the direct and indirect impact strength of the variables.

The Fourth Stage: Identification of Factor Groups
A comparison of the results of different classifications of variables as direct (dependent), indirect, or potential impacts enables an in-depth analysis of the subject under consideration.
Additionally, the analysis allows us to distinguish the following in the structure of the research area [31]: • Key factors, which are characterized by a very high impact on other factors; • Target factors, which involve variables that change themselves to a large extent under the influence of factors other than those that affect them; • Result factors, which have a low impact on the structure of the research area, but are very dependent on other factors; • Determining factors (mainspring and barrier), which describe, characterize, and control the structure of the research topic. These have a real impact on the whole system, either driving it or being a barrier to the whole operation; • Regulatory factors and ancillary factors, which do not affect the structure and do not have any strong dependencies on other factors, but help to define the strategic objective; • Autonomous and external factors, which include secondary factors that have very little influence on the system and its forecasts.
The result of the MICMAC method is ordered variables, where one can distinguish such factors that have the greatest real impact on the examined system [32]. The system of influence-dependence factors within MICMAC method is shown in Figure 4.

Results and Discussion
The methods used and the results obtained through the successive stages of the research procedure are presented in Figure 5. A detailed description is provided in the subchapters below.

Identified Cost Factors
The cost of the construction of elevations of public facilities using facade systems is influenced by many factors. The authors identified cost factors with the analysis of project and cost documentation and as-built settlements for cases, as well as direct interviews with contractors and investors. The factor identification studies presented in this paper constitute an extension of the preliminary studies, the results of which have been previously presented [18]. Finally, the completed study included 80 cases of public buildings constructed in the years 2013-2019 in Poland. The characteristics of the analysed buildings due to their different parameters are presented in Table 1.

Stage of structural analysis
The method / techinque used Results The

Results and Discussion
The methods used and the results obtained through the successive stages of the research procedure are presented in Figure 5. A detailed description is provided in the subchapters below.

Results and Discussion
The methods used and the results obtained through the successive stages of the research procedure are presented in Figure 5. A detailed description is provided in the subchapters below.

Identified Cost Factors
The cost of the construction of elevations of public facilities using facade systems is influenced by many factors. The authors identified cost factors with the analysis of project and cost documentation and as-built settlements for cases, as well as direct interviews with contractors and investors. The factor identification studies presented in this paper constitute an extension of the preliminary studies, the results of which have been previously presented [18]. Finally, the completed study included 80 cases of public buildings constructed in the years 2013-2019 in Poland. The characteristics of the analysed buildings due to their different parameters are presented in Table 1.

Stage of structural analysis
The method / techinque used Results The

Identified Cost Factors
The cost of the construction of elevations of public facilities using facade systems is influenced by many factors. The authors identified cost factors with the analysis of project and cost documentation and as-built settlements for cases, as well as direct interviews with contractors and investors. The factor identification studies presented in this paper constitute an extension of the preliminary studies, the results of which have been previously presented [18]. Finally, the completed study included  Table 1. The conducted research identified 15 factors. Fourteen of them were proposed by the authors, while the remaining one, the availability of subcontractors, was proposed by the contractors participating in direct interviews. The factors were then assigned to five groups. The number and type of groups were intuitively proposed by the authors, based on the studies of literature on factors in the construction industry and on experience from engineering practice. The proposed division of factors is illustrated in Figure 6. The factors were additionally given letter symbols to facilitate further analysis. The conducted research identified 15 factors. Fourteen of them were proposed by the authors, while the remaining one, the availability of subcontractors, was proposed by the contractors participating in direct interviews. The factors were then assigned to five groups. The number and type of groups were intuitively proposed by the authors, based on the studies of literature on factors in the construction industry and on experience from engineering practice. The proposed division of factors is illustrated in Figure 6. The factors were additionally given letter symbols to facilitate further analysis.   Group 1-materials-contains the following factors: type of aluminium-glass façade, type of glass used, and type of external cladding used for ventilated facades. These are the main parameters directly influencing implementation costs.
Group 2-facility characteristics-includes the height of the facility, facade surface, complexity of the building body, and number of window and door frames. The factors of this group describe the characteristics of the building body. Not only does the size of the area have an impact on costs, but its height is also important. High buildings generate additional costs due to the employment of building scaffolding and a crane, the method of transporting facade elements inside the facility, and the need to use specialised equipment dedicated to the assembly of glass panels. Complication of the building body, such as inclined surfaces in combination with straight surfaces, will generate additional costs related to difficult installation. The factor "the number of window and door frames" concerns the surfaces of windows and doors (in m 2 ) and their condition. High functionality of the windows and doors requires the use of appropriate accessories, such as anti-panic hardware, actuators, automatic sliding door machines, or access control accessories.
Group 3 is contractual conditions. These factors have an indirect impact on the cost of the facade. The location of construction site (in or outside the city centre) has a significant impact on the costs of transporting and unloading large facade elements, e.g., aluminium sections or glass panes. Implementation time-duration is a factor that generates both labour costs (shorter implementation times will increase them) and indirect costs (such as construction site organisation). Implementation deadline (season), together with adverse weather conditions, can cause delays in facade installation.
Group 4-aesthetics-includes only one factor: quality of execution. It is expressed by the proper selection of materials, technology, and above all, by the correct execution of construction works. Its assessment can be obtained by performing a number of tests, including checking the facade planes and testing the tightness of a given building.
Group 5-macroeconomic factors-includes company size, specialisation of subcontractors, inflation, and availability of subcontractors. The factors listed in this group have an indirect impact on the cost of facade systems. Large companies have greater opportunities to access specialised machinery and equipment, which affects the time of assembly and prefabrication, and thus the cost of implementation. In addition, companies making facade systems use subcontractors, who support both the assembly and prefabrication process. Therefore, well-specialized subcontractors with large machine parks, experience, and highly qualified staff are valued companies, which results in their limited availability on the market. All these parameters describing subcontracting companies influence the price of their service, which additionally influences the final cost of the facade systems. Moreover, inflation and the related change in means of production-that is, the prices of materials and services-may determine the change of costs of facade execution in the form of lightweight casing.

Conduct and Results of Factor Analysis
The expert research was performed with 10 Polish companies dealing with and specialising in the implementation of external facades. In 2019, 15 experts were invited (including works managers, production managers, and bid managers) to describe the relationships between the identified factors. According to the principle of factor interdependence, one of the factors (X) may have a very strong influence on the other factor (Y), while the Y factor itself does not have to influence the X factor or the influence may be very weak. The evaluation involved a five-stage scale, where 0 = no impact, 1 = weak impact, 2 = medium impact (significant but not decisive), 3 = large impact (decisive), and P = potential impact.
On the basis of the results obtained, matrix A (direct influence) was constructed.
Using the example of the first row of the A matrix, the following interpretation of the influence of factor A on other factors can be made: • Factor A affects on average factors B, I, and K, which is why the matrix was assigned a grade 2 according to a five-degree scale; • Factor A does not affect factors C, D, E, F, H, J, L, M, N, and O-therefore, a degree of 0 is assigned in the matrix; • Factor A potentially affects factor G; therefore, a grade P is assigned in the matrix. Table 2 presents the results of the structural analysis as the total strength of influences and direct relationships for the analysed factors. The calculated values of the influence strength and dependencies are the dominants of the influence force of the factors on each other. The following variables reveal the greatest strength of direct influence on other factors: height of the facility (D), complexity of the building body (F), and specialisation of subcontractors (M). On the other hand, the variable showing the greatest dependence on other factors and the subsequent impact on the costs of facade systems is implementation time-duration (I), while the following revealed less dependence on other factors, but also at a high level: type of aluminium-glass façade (A), type of glass used (B), and quality of execution (K).
The direct impact strength of the individual variables is illustrated in Figure 7.
Appl. Sci. 2020, 10, x; doi: www.mdpi.com/journal/applsci The following variables reveal the greatest strength of direct influence on other factors: height of the facility (D), complexity of the building body (F), and specialisation of subcontractors (M). On the other hand, the variable showing the greatest dependence on other factors and the subsequent impact on the costs of facade systems is implementation time-duration (I), while the following revealed less dependence on other factors, but also at a high level: type of aluminium-glass façade (A), type of glass used (B), and quality of execution (K).
The direct impact strength of the individual variables is illustrated in Figure 7. The next stage of structural analysis of the identified variables was the analysis of impacts and indirect relationships between the identified variables. The MICMAC method allows us to analyse the spread of interactions through connections and feedback loops coming in and out of particular factors, which in turn extracts hidden relationships between variables, which are often not directly visible for experts or analysts. Using the MICMAC software [25], matrix B-indirect influence-was calculated.
The interactions between variables are shown in Figure 8. The next stage of structural analysis of the identified variables was the analysis of impacts and indirect relationships between the identified variables. The MICMAC method allows us to analyse the spread of interactions through connections and feedback loops coming in and out of particular factors, which in turn extracts hidden relationships between variables, which are often not directly visible for experts or analysts. Using the MICMAC software [25], matrix B-indirect influence-was calculated.
The interactions between variables are shown in Figure 8. The next stage of the research is to separate the structure of factors in the research area. Figure 9 presents the groups of factors that influence and describe the research problem of estimating the costs of facade systems.  The next stage of the research is to separate the structure of factors in the research area. Figure 9 presents the groups of factors that influence and describe the research problem of estimating the costs of facade systems.  The next stage of the research is to separate the structure of factors in the research area. Figure 9 presents the groups of factors that influence and describe the research problem of estimating the costs of facade systems.

Conclusions
The paper presents a structural analysis of mutual influences and relationships between factors identified on the basis of quantitative and qualitative studies of project documentation and cost estimates. This was done using the MICMAC free online software which, by means of cross-analysis of the interactions between variables, helped to determine the six groups of factors influencing the research area, being the estimation of costs of facade systems. The largest and strongest group of factors were determinants and regulatory factors. Determinants, also known as mainsprings and barriers, are factors that have a very strong influence on the cost estimation of the building facades under consideration, which include height of the facility, facade surface, complexity of the building body, and degree of specialisation of assembly companies. Another important group for the research problem are regulatory factors. They do not have a strong influence on the whole cost structure, but by interacting with each other and with other variables, they provide a basis for achieving the goal of estimating facade costs. The regulatory factors were the type of aluminium-glass facade, the type of glass used, and the external cladding for ventilated facades. During the analysis, a goal factor has also been identified, which is the implementation time. Limiting the assumptions for the isolated parameters may cause the implementation time to be shorter or longer. Such an effect makes the factor a goal in the time-and-cost relationship. The factors per group are presented in Table 3. Additionally, the analysis of direct and indirect influence matrices and relationships between the variables revealed which interactions occur between individual variables. The direct relationships were a reflection of experts' opinions, which indicated that the strongest influence was shown by the following variables: height of the facility, complexity of the building body, and the level of specialisation of contractors. The analysis of the indirect influence matrix showed hidden relationships and interactions between the variables. The strongest influence on the quality of execution was exerted by the variable height of the facility and company (contractor) size.