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==Abstract==

The design of all spatial scales in a manufactured environment is part of the architectural skills and knowledge. Therefore, an architectural design should be drafted to reduce the vulnerability of humans and buildings against unexpected events, such as terrorist attacks and bombardments. Human casualties and equipment destruction inside the buildings could be prevented by designing a suitable architectural space. This study addresses the absence of a codified and detailed criterion to evaluate architectural spaces and their design. Hence, all proposed indices for architectural spaces have been extracted using the ideas of experts in the field of architecture and explosives.

Questionnaires were presented to 25 experts to weigh the effective indices using the analytic hierarchy process method. The human-oriented (ergonomic) characteristics of the building space is found to be the most important factor in facilitating crisis management, followed by the location of critical spaces.

==Keywords==

Architectural space ; Building ; Explosion ; Index

==1. Introduction==

Huge budget is spent annually worldwide in constructing public and private buildings using various architectural designs. At the same time, the destruction of resources, assets, and national infrastructures of countries are seen daily in every corner worldwide because of bombardments or terrorist attacks. These activities have not yet ceased and are currently unfolding. Thus, all military and non-military buildings should be designed with less vulnerability against these threats. A design should be drafted for buildings exposed to such threats. Architectural space is an important part in building design, which prevents human casualties and destruction of equipment inside the buildings. In the design of architectural spaces, the necessity of people to evacuate and their ability to leave the building after an explosion is crucial. Easy access paths all over the building should also be provided for rescue teams.

Therefore, this study primarily addresses the absence of a codified and detailed criterion in the evaluation and design of architectural spaces. Numerous studies on building structures that are resistant against threats have been conducted. [[#bib1|Khairodin et al. (2007)]] focused on the impact of architectural elements on the vulnerability of structures against earthquake hazards. [[#bib2|Fesharaki et al. (2011)]] investigated the importance of space organization in architecture as a passive defense and its variants.

[[#bib3|Gebbeken and Döge (2010)]] examined the geometry of buildings and the effects of the environment to prevent blast waves from reaching the building. Essentially, the peak pressures and maximum impulses were found to depend on the distance from the blast center, angle of reflected blast wave, and resistance against the waves. They also found that the structural elements of a building can also reduce the explosive charges. [[#bib4|Barakat and Hetherington (1998)]] studied the blast effects on various building forms, such as cubic, cylindrical, hemisphere, and prismatic forms, and concluded that in addition to the structural components of the buildings, architectural forms can be effective in reducing the effects of explosion on buildings.

[[#bib5|Araghizadeh (2011)]] investigated blast-resistant office buildings in 2011 and presented 11 indices to evaluate these buildings. This study showed that the location of a building with respect to the ground level is one of the most important factors in reducing the impact of explosion.

Numerous studies have been conducted on blast-resistant buildings without considering the role of architectural space. However, structural factors or architectural forms are very important, particularly after the blast waves reach the interior of the building. Moreover, people should have access to shelters in buildings especially at the time of aerial bombardment. Therefore, some architectural space factors, such as ergonomics, can facilitate access to secure spaces.

Thus, this research aims to determine the position of architectural space on blast-resistant buildings and its effective indicators.

The methodology of this study was created, and effective indicators were proposed by considering several factors to achieve appropriate architectural spaces against explosion.

==2. Methodology==

Basic indicators for evaluating the blast-resistant architectural spaces were identified in this study using library resources. The proposed indices were extracted from interviews with experts in the field of architecture and explosives ([[#t0005|Table 1]] ). A questionnaire was presented to 15 experts to acquire ideas for determining the effective indicators. The degree of each index was determined in a frame of the nine-point Likert scale by applying the group decision-making method based on a pairwise comparison model. Finally, the preferences and ultimate weights of the indices were determined. Moreover, the Cronbachs Alpha test and the analytic hierarchy process (AHP) were used to evaluate the validity of the questionnaires ([[#bib6|Carver and Nash, 2009]] ).



{| class="wikitable" style="min-width: 60%;margin-left: auto; margin-right: auto;"
|+

Table 1.

Pairwise comparison matrix of the architectural indicators compatible with the purposes and principles of passive defense.

|-

!
! ''X''1
! ''X''2
! ''X''3
! ''X''4
! ''X''5
|-

| ''X''1
| 1
| 0.444
| 0.537
| 3.383
| 3.384
|-

| ''X''2
|
| 1
| 1.038
| 5.491
| 5.491
|-

| ''X''3
|
|
| 1
| 4.877
| 4.877
|-

| ''X''4
|
|
|
| 1
| 1
|-

| ''X''5
|
|
|
|
| 1
|}

===2.1. AHP method===

The AHP method developed by [[#bib7|Saaty (1980)]] aims to determine the relative importance of a set of activities in a multi-criteria decision problem. According to this method, the decision maker could incorporate and translate judgments on intangible qualitative criteria alongside tangible quantitative criteria ([[#bib8|Badri, 2001]] ). The AHP method is based on three steps, namely, the structure of the model, comparative judgment of the alternatives and criteria, and finally, the synthesis of the priorities ([[#bib9|Da˘gdeviren, 2008]] ). The recent developments in the decision-making models based on the AHP method are listed below:
* [[#bib10|Medineckiene et al. (2010)]] applied AHP in a sustainable construction;
* [[#bib11|Podvezko et al. (2010)]] used AHP in the evaluation of contracts;
* [[#bib12|Sivilevicius (2011a)]] applied AHP in modeling a transport system;
* [[#bib13|Sivilevicius (2011b)]] used AHP to determine the quality of technology; and
* [[#bib14|Fouladgar et al. (2011)]] applied AHP in prioritizing strategies.

During the first step, a sophisticated decision problem is structured in a hierarchy. This method breaks down a sophisticated decision-making problem into hierarchies, such as objectives, criteria, and alternatives.

These decision elements comprise the hierarchy of a structure such that the goal of the problem is at the top of the hierarchy, criterion is at the middle, and all the alternatives are at the bottom.

During the second step, alternatives and criteria are compared. In AHP, comparisons were performed based on a standard nine-point scale ([[#t0010|Table 2]] ).



{| class="wikitable" style="min-width: 60%;margin-left: auto; margin-right: auto;"
|+

Table 2.

Nine-point intensity of importance scale and its description.

|-

! '''Definition'''
! '''Degree of importance'''
|-

| Equally important
| 1
|-

| Moderately more important
| 3
|-

| Strongly more important
| 5
|-

| Very strongly more important
| 7
|-

| Extremely more important
| 9
|-

| Intermediate values
| 2, 4, 6, 8
|}

Let <math display="inline">C=\lbrace C_j\vert j=1,2,\ldots ,n\rbrace </math> be the set of criteria. The result of the pairwise comparison on <math display="inline">n</math> criteria can be summarized in an <math display="inline">(n\times n)</math> evaluation of matrix <math display="inline">A</math> in which every element <math display="inline">a_{ij}\left(i,j=1,2,...,n\right)</math> is the quotient of weights of the criteria, as shown in Eq. [[#eq0005|(1)]] :


{| class="formulaSCP" style="width: 100%; text-align: center;"
|-
|
{| style="text-align: center; margin:auto;"
|-
| <math>A=\left[\begin{array}{cccc}
a_{11} & a_{12} & ... & a_{1n}\\
a_{21} & a_{22} & ... & a_{2n}\\
\vdots & \vdots & \ddots & \vdots \\
a_{n1} & a_{n2} & ... & a_{nn}
\end{array}\right],\quad a_{ii}=1,\quad a_{ji}=1/a_{ij},\quad a_{ij}\not =</math><math>0</math>
|}
| style="width: 5px;text-align: right;white-space: nowrap;" | ( 1)
|}

During the third step, the mathematical process commences to normalize and find the relative weights for each matrix. The relative weights are given by the right eigenvector (''w '' ) corresponding to the largest eigenvalue <math display="inline">({\lambda }_{max})</math> , as

{| class="formulaSCP" style="width: 100%; text-align: center;"
|-
|
{| style="text-align: center; margin:auto;"
|-
| <math>Aw={\lambda }_{max}w.</math>
|}
| style="width: 5px;text-align: right;white-space: nowrap;" | ( 2)
|}

If the pairwise comparisons are completely consistent, then matrix ''A '' has a rank of 1 and <math display="inline">{\lambda }_{max}=n</math> .

In this case, weights can be obtained by normalizing any of the rows or columns of ''A'' ( [[#bib15|Wang and Yang, 2007]] ). The quality of the AHP output is strictly related to the consistency of the pair-wise comparison judgments ([[#bib9|Da˘gdeviren, 2008]] ). Consistency is defined by the relation between the entries of <math display="inline">A</math> :<math display="inline">a_{ij}\times a_{jk}=a_{ik}</math> . The consistency index (CI) is

{| class="formulaSCP" style="width: 100%; text-align: center;"
|-
|
{| style="text-align: center; margin:auto;"
|-
| <math>\mbox{CI}=({\lambda }_{max}-n)/(n-1)</math>
|}
| style="width: 5px;text-align: right;white-space: nowrap;" | ( 3)
|}

as presented in Eq. [[#eq0020|(4)]] . The final consistency ratio (CR) is used to determine whether the evaluations are sufficiently consistent and is calculated as the ratio of (CI) and the random index (RI),


{| class="formulaSCP" style="width: 100%; text-align: center;"
|-
|
{| style="text-align: center; margin:auto;"
|-
| <math>\mbox{CR}=\mbox{CI}/RI</math>
|}
| style="width: 5px;text-align: right;white-space: nowrap;" | ( 4)
|}

The (CR) index should be lower than 0.10 to be considered consistent in the AHP results ([[#bib16|Işıklar and Büyüközkan, 2007]] ). If the final consistency ratio exceeds this value, then the evaluation process has to be repeated to improve its consistency ([[#bib9|Da˘gdeviren, 2008]] ). The <math display="inline">CR</math> index could be used to calculate the consistency of decision makers and that of the hierarchy ([[#bib15|Wang and Yang, 2007]] ).

===2.2. Data collection===

During the first step, a group that consists of experts in the fields of explosives, architects, and top managers with sufficient experience in architectural design participated in a conference meeting to perform the decision-making process. In the preliminary work of the decision-making team, five important criteria were determined on the role of architectural space in blast-resistant buildings. The background information of the experts is given in [[#t0015|Table 3]] .



{| class="wikitable" style="min-width: 60%;margin-left: auto; margin-right: auto;"
|+

Table 3.

Background information of experts.

|-

! Variable
! Items
! No.
! Variable
! Items
! No.
|-

| 1)Architecture
| Bachelor
| 0
| 3) Explosion
| Bachelor
| 0
|-

| Experts
| Master
| 2
| Experts
| Master
| 4
|-

|
| Ph.D.
| 4
|
| Ph.D.
| 2
|-

|
|
|
| 4) Top
| Bachelor
| 0
|-

|
|
|
| Managers
| Master
| 1
|-

|
|
|
|
| Ph.D.
| 2
|}

==3. Associated indicators with the architectural space of the buildings==

Architectural space is another effective topic on explosion-resistant architecture. According to the views of expert on the community, architecture styles, and information from the book, “Form, Space, and Discipline” of [[#bib17|D.K.Ching (2007)]] , the indicators affecting architectural space include the following:
* Function of architectural spaces at different times (''X''1 );
* Amount of human-oriented (ergonomics) characteristics of the building space (''X''2 );
* Method of locating the vital and critical areas in the buildings (''X''3 );
* Independency of the building spaces (''X''4 ); and
* Density of the building spaces (''X''5 ).

A pairwise comparison matrix was considered for these indices to determine the weight and the effect of each factor in the explosion-resistant architecture.

The final weight is given in [[#t0005|Table 1]] from the analysis of the questionnaire results.

In the next part, each of these items, their sub-indices, and their importance will be considered.

===3.1. Function of architectural spaces at different times===

A multi-functional space that can function differently during peace and war times is very important economically and in terms of viability of space dynamics. In this regard, the performance of the architectural spaces was examined at different times using the following aspects:
* Flexible spaces: spaces that can be considered for another function (performance) with no modifications.
* Adaptive spaces: spaces that can be considered for another function (performance) with slight modifications.
* Single functional spaces: spaces that can only have one function.

According to the surveys, the first option is “very compatible”, the second option is “compatible”, and the third option is “highly incompatible”.

===3.2. Amount of human-oriented (ergonomics) characteristics of building spaces===

Ergonomics provide great importance to the human understanding of the environment and its objectives that include motivation, satisfaction, creativity, and enjoyable working and living environment. To achieve these goals, principles such as flexibility, efficiency, beauty, and human error prevention are carefully considered in the process of designing. One of the goals of ergonomics is the appropriate use of interior design, equipment, and facilities in the building for human comfort. The goal of ergonomics in interior design is to improve the physical and mental performance of the internal building spaces to facilitate daily activities. Moreover, this science also attempts to fit the environment with human life instead of fitting human life to its environment.

The following options were considered in this category:
* Ability to reduce blast effects;
* Ability to facilitate crisis management (emergency evacuation of the building);
* Ability to continue operations in crisis situations; and
* Immunization to reduce human casualties.

The results of the questionnaire indicated that the abilities to facilitate both crisis management (emergency evacuation of the building) and continue the operations during crisis are very significant. However, immunization to reduce human casualties was considered a lesser priority. The ability to reduce the explosion effect also had little significance.

In this section, the experts discussed the ergonomic level in the physical and psychological factors in architectural spaces. Based on the results, the ergonomic level in the physical factors obtained higher scores than those in the psychological factors. The psychological factors only influence the continuity of essential functions, whereas physical factors influence all four factors.

Human-oriented characteristics in architectural spaces depend on the following proportionate factors: dimensions, material, internal furniture, light, temperature and humidity, and color according to the building operation. Among these factors, only the dimensions, materials, and internal furniture are effective in the reduction or amplification of the effect of explosion. Other factors are ineffective in reducing the effect of explosion. As seen in the following table, four factors, namely, dimensions, interior furniture, materials, and lighting, influence the feasibility of crisis management. The proportionate dimension factor is highly important in facilitating crisis management because of its significant role in the emergency evacuation of occupants in the building [[#t0020|Table 4]] , [[#t0025|Table 5]] , [[#t0030|Table 6]] , [[#t0035|Table 7]] , [[#t0040|Table 8]] , [[#t0045|Table 9]] , [[#t0050|Table 10]] , [[#t0055|Table 11]] , [[#t0060|Table 12]] , [[#t0065|Table 13]] ; [[#t0070|Table 14]] .



{| class="wikitable" style="min-width: 60%;margin-left: auto; margin-right: auto;"
|+

Table 4.

Weights and effectiveness of each architectural indicator compatible with the purposes and principles of passive defense.

|-

! '''Architectural indicators compatible with the purposes and principles of passive defense'''
! '''Weight and influence of each indicator (Total weighted of indicators is equal to 100.)'''
|-

| Function of architectural spaces at different times
| 18.9
|-

| The humanist (ergonomics) of building space
| 36.1
|-

| Method of locating the vital and critical areas in the buildings
| 32.6
|-

| Independence of the building spaces
| 6.2
|-

| Density of the building spaces
| 6.2
|}



{| class="wikitable" style="min-width: 60%;margin-left: auto; margin-right: auto;"
|+

Table 5.

Importance of each passive defense related to the function of architectural spaces at different times.

|-

! '''Single functional spaces'''
! '''Adaptive spaces'''
! '''Flexible spaces'''
|-

| 2.92
| 6.96
| 8.66
|-

| Highly incompatible
| Compatible
| Very compatible
|}



{| class="wikitable" style="min-width: 60%;margin-left: auto; margin-right: auto;"
|+

Table 6.

Importance of passive defense purposes on the human-oriented indicator (ergonomics) of a building space.

|-

! '''Immunization to reduce human casualties'''
! '''Ability to continue operations in crisis situations'''
! '''Ability to facilitate the crisis management (emergency evacuation of the building)'''
! '''Ability to reduce blast effects'''
|-

| 6.85
| 7.03
| 7.14
| 4.62
|-

| Important
| Very important
| Very important
| Less important
|}



{| class="wikitable" style="min-width: 60%;margin-left: auto; margin-right: auto;"
|+

Table 7.

Results of sub-indicators related to human-oriented (ergonomics) characteristics of a building space.

|-

! rowspan="2" | '''Passive defense objectives in buildings'''
! colspan="2" | '''Ergonomic level of building space'''
|-

! '''Humanist level in the psychological factors'''
! '''Humanist level in the physical factors'''
|-

| '''Ability to reduce blast effects'''
| 4.66
| 5.18
|-

| '''Ability to facilitate the crisis management'''
| 5.85
| 7.92
|-

| '''Ability to continue operations in crisis situations'''
| 6.62
| 6.81
|-

| '''Immunization to reduce human casualties'''
| 5.44
| 7.063
|-

| '''Final Score'''
| 5.73
| 6.88
|-

| '''Compatibility'''
| Incompatible
| Compatible
|}



{| class="wikitable" style="min-width: 60%;margin-left: auto; margin-right: auto;"
|+

Table 8.

Results of the questionnaire related to the amount of human-oriented characteristics of the physical factors of building spaces.

|-

! rowspan="2" | '''Passive defense objectives in buildings'''
! colspan="6" | '''Humanist level in the physical factors'''
|-

! '''Appropriate color with building performance'''
! '''Appropriate temperature and humidity with building performance'''
! '''Appropriate light with building performance'''
! '''Appropriate internal furniture with building performance'''
! '''Appropriate materials with building performance'''
! '''Appropriate dimensions with building performance'''
|-

| '''Ability to reduce blast effects'''
| 4.7
| 4.96
| 4.70
| 5.25
| 6.22
| 6.11
|-

| '''Ability to facilitate the crisis management'''
| 4.77
| 5.7
| 6.4
| 7
| 6.33
| 8.25
|-

| '''Ability to continue operations in crisis situations'''
| 5.44
| 6.66
| 6.48
| 6.96
| 6.51
| 7.59
|-

| '''Immunization to reduce human casualties'''
| 4.77
| 4.96
| 5.29
| 7.11
| 7.66
| 6.62
|-

| '''Final Score'''
| 4.94
| 5.63
| 5.82
| 6.7
| 6.71
| 7.25
|-

| '''Compatibility'''
| Incompatible
| Compatible
| Compatible
| Compatible
| Compatible
| Very compatible
|}



{| class="wikitable" style="min-width: 60%;margin-left: auto; margin-right: auto;"
|+

Table 9.

Degree of importance of passive defense purposes on the location of critical and sensitive spaces in the building.

|-

! '''Ability to continue operations in crisis situations'''
! '''Ability to reduce blast effects'''
|-

| 8.11
| 7.22
|-

| Very important
| Very important
|}



{| class="wikitable" style="min-width: 60%;margin-left: auto; margin-right: auto;"
|+

Table 10.

Results from the questionnaire related to locating the critical and sensitive spaces of the building.

|-

! rowspan="2" | '''Locating the critical and sensitive spaces of the building'''
! colspan="3" | '''Passive defense objectives in buildings'''
|-

! '''Located in the wall plan'''
! '''Main spaces located in the middle of the floor plan of the building'''
! '''Sensitive areas located in the basement of the building'''
|-

| '''Ability to reduce blast effects'''
| 2.55
| 7.11
| 8.33
|-

| '''Ability to continue operations in crisis situations'''
| 3.35
| 6.29
| 7.77
|-

| '''Final Score'''
| 2.97
| 6.67
| 8.03
|-

| '''Compatibility'''
| Very incompatible
| Compatible
| Very compatible
|}



{| class="wikitable" style="min-width: 60%;margin-left: auto; margin-right: auto;"
|+

Table 11.

Importance of the amount of passive defense purposes with the independence of building spaces.

|-

! '''Ability to continue operations in crisis situations'''
! '''Ability to reduce blast effects'''
|-

| 6.62
| 6.70
|-

| Very important
| Very important
|}



{| class="wikitable" style="min-width: 60%;margin-left: auto; margin-right: auto;"
|+

Table 12.

Results of the questionnaire related to the independence of building spaces.

|-

! rowspan="2" | '''Passie defense objectives in buildings'''
! colspan="2" | '''Independence of building spaces'''
|-

! '''Relatively open spaces and associated to other spaces (open design – intrusion spaces)'''
! '''Relatively closed spaces and apart from the other spaces (cell design – adjacency spaces)'''
|-

| '''Ability to reduce blast effects'''
| 3.29
| 7.44
|-

| '''Ability to continue operations in crisis situations'''
| 5.88
| 5.14
|-

| '''Final Score'''
| 4.37
| 5.56
|-

| '''Compatibility'''
| Incompatible
| Compatible
|}



{| class="wikitable" style="min-width: 60%;margin-left: auto; margin-right: auto;"
|+

Table 13.

Degree of importance of passive defense purposes related to the density of building spaces.

|-

! '''Facilitate the crisis management'''
! '''Reducing the blast wave driven'''
|-

| 4.22
| 7.29
|-

| Less important
| Very important
|}



{| class="wikitable" style="min-width: 60%;margin-left: auto; margin-right: auto;"
|+

Table 14.

Results of the questionnaire related to the density of building spaces.

|-

! rowspan="3" | '''Passive defense objectives in buildings'''
! colspan="2" | '''Density of building spaces'''
|-

! '''High-density areas'''
! '''Low-density areas'''
|-

!
[[Image:draft_Content_804169043-1-s2.0-S2095263512000799-fx1.jpg|center|209px|Full-size image (14 K)]]

!
[[Image:draft_Content_804169043-1-s2.0-S2095263512000799-fx2.jpg|center|200px|Full-size image (9 K)]]

|-

| '''Reducing the blast wave driven'''
| 6.85
| 2.29
|-

| '''Facilitate the crisis management'''
| 3.33
| 6.85
|-

| '''Final Score'''
| 5.56
| 3.28
|-

| '''Compatibility'''
| Compatible
| Incompatible
|}

===3.3. Location of critical and sensitive spaces in the building===

The locations of critical and sensitive spaces, as well as their distances from the external walls and exit accesses ways, were evaluated in this study. The location of these spaces was determined in terms of the ability to reduce the blast effects and sustain activities that are highly important in times of crisis. The spaces in the building, regardless of the floor or level, should be designed with easy access to exits to achieve the intended goals of this study.

===3.4. Independence of building spaces===

The independence of building spaces is highly important, as determined in this study, in terms of the ability to reduce the effects of explosion and in sustaining activities at the time of crisis. In this regard, spaces that are closed and separate from the other spaces (cellular design—adjacency of spaces) are compatible solutions. Relatively open spaces and spaces associated with other spaces (open-designed spaces) are considered incompatible.

===3.5. Density of building spaces===

The density of building spaces is highly important in terms of the ability to reduce the explosion wave conduction. However, this factor does not play a significant role in facilitating crisis management.

The density of an architectural space indicates the amount of architectural elements in a specific space (amount of open or closed spaces). In low-density spaces (open spaces), the movement of explosion waves travels easily and human casualties increase in these spaces. Therefore, low-density spaces are incompatible and high-density spaces are compatible in terms of passive defense. Human casualties are greatly reduced in high-density architectural spaces because of the existence of obstacles on the path of explosion waves.

==4. Conclusion==

Based on the opinions of contemporary architectural theorists, the design of all spatial scales in a manufactured environment should be part of the architectural skills and knowledge. Thus, an architectural design should be drafted to reduce the vulnerability of humans and buildings against threats. Previous studies have shown that the focus of blast-resistant design is on the basic forms of architecture and the impact of explosion on these forms. However, the role of architectural space has received little attention. Delphi method was used to evaluate the architectural space of blast-resistant buildings, whereas AHP method was used to analyze the results. AHP method is an efficient, low cost, and highly accurate method in the determination of the best and appropriate decision-making choice. This method can be a good model as a management tool with minimal time and cost that provides the best choice among the available options.

With the use of the AHP method, this study determined that the amount of human-oriented (ergonomics) characteristics of building spaces is the most important factor among other indicators, and that the location of critical and sensitive spaces in the building is the next priority. The selected architectural mode should also coincide with the building performance.

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