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Comprehensive appraisal of the safety of hidden frame glass curtain wall based on fuzzy theory
Journal of Building Engineering 26 (2019) 100863
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Comprehensive appraisal of the safety of hidden frame glass curtain wall based on fuzzy theory
T
Huang Teng-tenga, Zhang Da-weia,*, Zhao Yu-xia, Liu Jun-jinb, Li Jian-huib a b
College of Architecture and Civil Engineering, Zhejiang University, Hangzhou, 310058, China China Academy of Building Research, Beijing, 100013, China
ARTICLE INFO
ABSTRACT
Keywords: Hidden frame glass curtain wall Analytic hierarchy process Fuzzy theory Safety appraisal
The falling accident of a building's curtain wall may bring adverse social impact and economic loss. It is therefore of great importance to efficiently and reliably identify the security status of existing curtain walls. Current safety appraisal methods for glass curtain walls are facing the adverse effect of a large amount of imperfect information and subjective indicators. There are shortcomings of these methods, such as: i) The appraisal rank is easily affected by subjective judging, ii) The key appraisal indicators are not clear, and iii) The top-level indicators are not scientifically determined and systematically evaluated through the lower-level indicators. This paper takes existing hidden frame glass curtain wall as the research object, divides the safety grade of curtain walls into four fuzzy ranks (fine, good, poor and dangerous) and establishes five levels of appraisal hierarchy for components. An appraisal weight determination system is established for existing hidden frame glass curtain walls in three aspects (appearance, material testing and bearing capacity testing) based on a survey among experienced curtain wall experts from diverse areas and professions. The frequency statistics method is used to determine the weights of the indicators. The ranks of quantitative and qualitative indicators are quantified using fuzzy theory. Finally, applicability of the proposed safety appraisal model is verified with a real project. The appraisal result obtained through the proposed models is consistent with the actual situation on a real project.
1. Introduction The hidden frame glass curtain wall has been widely applied by the architects and owners because of the clean and tidy outer surface of the building. During its service life, the hidden frame glass curtain wall is usually subjected to gravity load, wind load, temperature variation and various environmental erosion effects, together with design defects, material erosion, corrosion and aging, etc. Its performance deteriorates with time, causing potential danger to its safety [1–8]. Although the damage of the glass curtain wall generally does not threaten the safety of the main structure, its fall is unpredictable and can cause serious safety accidents and arise adverse social impacts. In 2018 alone, there have been many reports, e.g. in Shiyan City, Hubei Province, China, the curtain wall glass of an existing building fell off, which smashed the head of a 3-year-old child, causing his unfortunate death [9]. In the UK, a man died after reportedly being hit by a windowpane that fell around 76 m from the top of a block of flats in Albert Embankment of London [10]. Similar incidents have aroused great concern from the society and the government, and it is imperative to ensure the safety of existing glass curtain walls. Establishing a comprehensive safety appraisal *
system for existing glass curtain walls and regularly assessing the safety of existing curtain walls may allow us to keep abreast of the state of the existing curtain wall and take appropriate protective measures in a timely manner. Due to objective factors such as unclear construction situation, uncertainty of material properties, and complexity of service load and environment, etc., most current safety appraisal of glass curtain wall uses multi-indicators appraisal methods based on a large number of unclear information and subjective indicators [3,6–8,11]. Most of existing safety appraisal methods are essentially analytic hierarchy processes, and their core issues include the division of ranks, the determination of weights and ranks. At present, codes for inspection of bearing capacity and performance of glass curtain wall are available in United States [12], Europe [13], Japan [14] and Australia [15], where there are still no relevant provisions for the overall appraisal of the safety of existing curtain wall. In China, specifications for appraisal of curtain wall include local standards and national standards, of which national standards [16] are based on the hierarchy of overall curtain walls, appraisal units, subunits, a kind of component or connection, a single component or connection. Local standards [17–20] mostly divide
Corresponding author. E-mail address: [email protected] (Z. Da-wei).
https://doi.org/10.1016/j.jobe.2019.100863 Received 29 March 2019; Received in revised form 6 July 2019; Accepted 7 July 2019 Available online 08 July 2019 2352-7102/ © 2019 Elsevier Ltd. All rights reserved.
Journal of Building Engineering 26 (2019) 100863
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the bearing capacity and performance of existing glass curtain walls into three hierarchy levels: component (including connection), subunit, and appraisal unit. Through the appraisal of three aspects: appearance, structure and bearing capacity, the ranks of each hierarchy level (au, bu, cu, du) are identified. The above-mentioned local and national standards determine the rank of the higher level indicators according to the quantitative proportional relation of the lower level indicators. In terms of rank determination, the four-level absolute interval is adopted, while the effect of uncertainty is not considered, and the weight relationship between different indicators is not considered, neither. Generally speaking, the current appraisal method has following shortcomings: 1. the result is susceptible to subjective judgement, 2. the key assessment indicators are not clear, and 3. the appraisal of higher-level indicators through lower-level indicators lacks scientific and systemic foundation. Fuzzy theory is a method of strictly quantifying the concept of fuzzy uncertainty into information that can be processed by computer. It does not advocate the use of complicated mathematical analysis or model to solve the model. Fuzzy theory is applicable to the appraisal system combining quantitative indicators and qualitative indicators. Structural performance appraisal method based on fuzzy theory has been widely studied in the field of bridges, tunnels, etc [21–23]. Due to insufficient research on related mechanisms, the safety appraisal of curtain wall structure has more subjective and qualitative indicators than the main structure of buildings and infrastructures such as bridges and highways, and is more susceptible to subjective judgment. Therefore, the fuzzy appraisal method is regarded more suitable to the safety appraisal of the existing hidden frame glass curtain wall. Some scholars have conducted research on the application of fuzzy evaluation methods in the curtain wall. Zhang et al. [6] proposed an appraisal method for comprehensively evaluating the safety of glass curtain wall structure by using area method combined with uncertain analytical hierarchy process. Zhao et al. [3] proposed the fuzzy comprehensive appraisal method to evaluate the safety performance of glass curtain wall. Wu and Wu et al. [7,8] established a set pair analysis appraisal method and interval fuzzy comprehensive method in the glass curtain wall safety appraisal. However, the existing research lacks the overall performance evaluation of the curtain wall corresponding to the quantitative measurement of the detection indicators and it is difficult to be used in engineering practice. Therefore, it is necessary to establish a safety performance appraisal indicator system and appraisal method for curtain wall structure with on-site engineering operability and verification. It is worth noting that the structural performance assessment is divided into three stages: “structural inspection”, “analytical appraisal” and “decision management”. In this paper, the hidden frame glass curtain wall is taken as the research object only on the “analytical appraisal” process. With reference to the existing curtain wall appraisal specifications [16–20,24], a five-level comprehensive appraisal system for hidden frame glass curtain wall as shown in Table 1 is established based on the multi-indicator analytic hierarchy process and fuzzy appraisal theory.
wherein v1-v4 indicates respectively the degree to which the indicator matches the rank 1–4. When the indicator in the appraisal set is a fuzzy indicator, the value of v1-v4 is between 0 and 1, in which 1 means complete coincidence and 0 means complete non-conformity. 3. Fuzzy comprehensive appraisal method Referring to the existing curtain wall appraisal specifications [16–20], the building curtain wall is divided according to panel materials and curtain wall types, and the curtain wall area that can independently perform safety appraisal is used as an appraisal unit. Taking the three component subunits of the curtain wall appraisal unit n as input indicators, the component setUn = [glass panel un1, metal frame un2, structural glue u n3]. For the glass panel, there has un1 = [appearance un11, material un12, bearing capacity un13], whereinu n11, u n12 and u n13 can be set by several specific appraisal indicators. The set of factors of other appraisal units and subunits can be obtained in the same ways. Considering the bearing capacity factor set of glass panel u n13 = [un131, u n132, u n133], where u n131 indicates impact resistance capacity, u n132 indicates recheck of design bearing capacity and u n133 indicates wind pressure resistance capacity. Define the single factor appraisal matrix as: 1 2 3 4 rn13y1 rn13y1 rn13y1 rn13y1
Rn13y =
1 2 3 4 rn13y2 rn13y2 rn13y2 rn13y2
(y = 1,2,3)
1 2 3 4 rn13y m rn13ym rn13ym rn13ym
x Where rn13y i represents the degree to which the y-th appraisal indicator of the i-th glass panel component matches the rankx (x = 1,2,3,4; i = 1,2, …, m) , and m is the total number of components of the glass panel in the appraisal unit n. The weight distribution of each Wn13y = component constitutes the weight matrix [wn13y1, wn13y2, …, wn13ym]. The set of factors of other subunits can obtain the corresponding appraisal matrix and weight matrix according to the above definition. Define Bn13y as the comprehensive appraisal matrix of indicator , Bn13y is a 4 × 1 matrix, and have: 1 2 3 4 Bn13y = Wn13y ORn13y = [bn13 y , bn13y , bn13y , bn13y ] (y = 1,2,3)
x where O represents the fuzzy operator, bn13y represents the degree to which the performance of indicator matches the rank-x (x = 1,2,3,4). While there is no single predominant appraisal factor in the hidden frame curtain wall structure, the appraisal of its safety needs to comprehensively consider all aspects of performance indicators. Referring to the application of multi-level fuzzy comprehensive appraisal in other fields [25–29], this study uses the average weighted operator, that is: m x x Bn13y = Wn13y *Rn13y , bn13 (wn13yi *rn13y y = i). i=1 The result of normalizing Bn13y is still recorded as Bn13y . The appraisal results of various appraisal indicators of the bearing capacity factors together constitute the appraisal matrix of the bearing capacity of the glass panel, that is: Rn13 = [Bn131, Bn132 , Bn133]T . The weight distribution of each appraisal indicator constitutes the weight matrix, that Wn13 = [wn131, wn132, wn133]. is: Then there have: 1 2 3 4 Bn13 = Wn13 ORn13 = [bn13 , bn13 , bn13 , bn13 ], where the result of normalizing Bn13 is the appraisal result of the bearing capacity of the glass panel subunit. The same method can be used to evaluate the appearance and material property of the glass panel subunit. By analogy, after the same method is used to determine the judgment results and weights of each indicator, the overall safety appraisal result of the hidden frame glass curtain wall is finally obtained B = WOR .
2. Division of ranks Referring to the current curtain wall appraisal specification [19], the safety status is divided into four fuzzy ranks of good, general, poor and dangerous, and classified according to Table 2. For quantitative indicators, the slight deviation of the test results will directly lead to different appraisal results at the boundary level; for qualitative indicators, different engineers have deviate understanding of the fuzzy evaluation language such as “good” and “poor”. The fuzzy appraisal results in matrix form can not only describe the gradual transition of appraisal ranks well, but also describe the ambiguity in natural language well. Thus, unlike the deterministic ranking of existing specifications, the appraisal set V = {v1, v2, v3, v4} is defined,
4. Weight determination The weight matrix is an important computational component that 2
Journal of Building Engineering 26 (2019) 100863
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Table 1 Appraisal model for the safety of existing hidden frame curtain wall. Level 1
Level 2
Level 3
Level 4
Level 5
Overall appraisal of building curtain wall safety
appraisal unit (1,2, …,n)
Glass panel
Appearance
Panel type Panel size Defects on the surface Warping deformation of the panel Panel material color change Laminating, blistering, degumming Foaming, condensation, water ingress Mechanical edging around the glass Glass panel tempering, surface stress Impact resistance capacity Review of design bearing capacity Wind pressure resistance capacity Metal frame size Defects on the surface Corrosion of metal components The structure of connections Vickers hardness Review of design bearing capacity Wind pressure resistance capacity Structural adhesive size Colloid discoloration, chalking Colloidal blistering, defect Partial failure of bonding Bonding of the outer surface of the insulating glass Tensile bond strength Shore hardness of structural adhesive Shear strength of structural adhesive Colloidal bond failure area ratio
Material test Bearing capacity Metal frame
Appearance
Material test Bearing capacity Structural adhesive
Appearance
Material test
is adopted. The surveyed experts should judge the degree of influence of the appraisal results of the indicator on the overall safety of the existing glass curtain wall. 0 means no effect at all, and 10 means heavy effect, as an example shown in Table 3. For the weight of each indicator, the magnitude of the weight value is not a key factor, while the relative difference between the different indicators will have a direct impact on the judgment result. Each expert's score is homogenized by the average of the scores as the relative weights, which are used as a direct statistical result. Frequency statistics is performed on the relative weights of the experts and distribution map is given. A scoring value that considers the relative weights of different experts may have a normal distribution, and a corresponding normal distribution curve is drawn. Taking the glass panel component indicator (shown in Table 4) as an example, the frequency distribution map is shown in Fig. 3, and other indicators are deduced by analogy. It can be seen from the frequency distribution map of each indicator that the frequency distribution maps of different indicators have large differences. A normal D test is used for each set of data to test the goodness-of-fit of the frequency distribution of the data for the normal distribution. Getting Y ≤ Y0.05 of indicator 1-1 means that fitting the frequency distribution to a normal distribution does not have sufficient reliability. The goodness-of-fit test of the normal distribution of the other indicators of the panel shows that only some of the indicators, like 1–4, 1–5, 1–7, 1–8, have sufficient credibility that the frequency distribution is fitted to a normal distribution, while the others are not. The results of the goodness-of-fit test for the structural adhesive and the metal frame are similar. Therefore, the statistical operation using the normal distribution is not universal for each indicator, and the statistical calculation of the weight is obtained by direct frequency statistics. Using the frequency statistics method, the weight calculation of the underlying indicators is firstly performed. For the i th appraisal indicator (ui), the questionnaire results of its weights (wij , j = 1,2, , k ) from k (k ≥ 30) individuals (respondents) are divided into p groups (p generally is taken 5–10), whose class interval is h = (max {wij} min {wij})/p , and then calculate the frequency ki and wk = ki /k , the weight corresponding to the appraisal indicator ui is min {wij} + kh p wi = k = 1 wk . Finally wi is normalized to obtain the required 2
transforms the lower-rank indicator appraisal matrix into the upperrank indicator appraisal matrix. The assignment of weights must be scientific and objective, which requires appropriate weight determination methods. The objective weighting method is relatively shortlived and still not perfect. It has a strong mathematical theoretical basis, but the determined weight may be inconsistent with people's subjective wishes or actual conditions. The subjective weighting method is an early and mature method. The survey results often directly reflect the actual situation of the project, and there is no contradiction between the attribute weight and the actual importance of the attribute. Therefore, this paper chooses the subjective weighting method after comprehensive comparison. The frequency statistics method [30] is a questionnaire survey method. The respondents can express their opinions without interference. After the data screening and statistical analysis, the results are more objective and easy to operate. Therefore, we use this method to determine the weight of the appraisal indicator in this study. In the process of issuing and counting the questionnaire data, some factors that have little effect on the safety of the glass curtain wall are added as trap questions. If the score of the factor is too high, the questionnaire is considered invalid. Through this process, the professionalism of the experts surveyed has been verified and screened. The survey collected questionnaires from experts from Beijing, Shanghai, Hangzhou, Guangzhou, etc., involving 22 provinces or municipalities and 42 different cities in China. A total of 231 responses were collected. The composition of the experts is shown in Fig. 1 to Fig. 2. The respondents include curtain wall engineering experts with many years of engineering experience in design, construction, supervision, testing and other types of work. Among them, curtain wall experts in design, construction and inspection with rich firsthand engineering experience accounted for 82%, curtain wall experts with no less than 6 years working experience accounted for 73%, and senior curtain wall experts with no less than 10 years engineering experience accounted for 48%. In the questionnaire, the 5 content sections of glass panel, metal frame, structural adhesive, material properties and bearing capacity are surveyed. For each appraisal indicator, the ten-grade appraisal standard 3
Journal of Building Engineering 26 (2019) 100863
Poor The curtain wall has defects, and it has a significant impact on the bearing capacity. The curtain wall is in a poor state of safety. General The curtain wall has defects, but it does not significantly affect the bearing capacity. The curtain wall is in a general state of safety. Good The curtain wall has few defects, and has sufficient bearing capacity. The curtain wall is in a good state of safety. Condition Safety performance status
Dangerous The curtain wall has defects, and it has seriously impact on the bearing capacity. The curtain wall is in a dangerous state of safety.
3rd rank 2nd rank 1st rank Safety rank
Table 2 Safety rank classification of building curtain wall.
4th rank
H. Teng-teng, et al.
Fig. 1. Distribution of expert's career field.
Fig. 2. Distribution of expert's career experience. Table 3 Example of questionnaire survey on weights of appraisal indicator.
a) The dimensions of the panel do not match the design.
0
1
2
3
4
5
6
7
8
9
10
○
○
○
○
○
○
○
○
○
○
○
lower-rank indicator weight wi . For each component in the same component subunit, the weights can be considered equal. For upperrank indicator including n lower-rank indicators, the statistical data is the statistical result of all n indicators that all experts include. Therefore, by replacing the statistical data, the same calculation method can be used to obtain the weight values of all upper-rank indicators. The weight values of the various indicators calculated according to the above-mentioned frequency statistical processing method are shown in Table 5. It is worth noting that not all indicators in the table can get the corresponding inspection results. For example, for a singlelayer ordinary glass, there is no detection indicator of ‘Foaming, condensation, water ingress’. In such case, this indicator and its weight should be deleted, and the remaining indicators should be renormalized. 5. Rank determination Based on the Chinese glass curtain wall inspection standard [31], the current Chinese curtain wall appraisal specifications [19] gives rank intervals of quantitative indicators and qualitative indicators or its method of class interval determination. For example, for Shore hardness, the rank intervals of 1–4 ranks are divided into [20, 60), [60, 70), [67, 75), [0, 20) U [75, + ∞). By using fuzzy theory, the rank determination of quantitative and qualitative indicators can be given as 4
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Table 4 Glass panel component indicator. number
1–1
1–2
1–3
1–4
1–5
1–6
1–7
1–8
content
Panel type
Panel size
Defects on the surface
Warping deformation of the panel
Panel material color change
Laminating, blistering, degumming
Foaming, condensation, water ingress
Mechanical edging around the glass
below.
matching in the matched interval is 1. But for other ranks, the change of degree of rank matching should be gradual rather than abrupt. The common linear rank determination considers that the change rate of the degree of rank matching is the same, but usually the same change in the indicator value near the boundary of the interval has different influence on rank determination; therefore, the optimal interval type rank
5.1. Quantitative indicators For quantitative indicators, the rank can be determined according to the relevant provisions in the specification, and the degree of rank
Fig. 3. Glass panel component indicator. 5
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Table 5 Calculation results of appraisal indicator weights of hidden frame glass curtain wall. Level 3
Level 4
Level 5
Indicator
Weight
Indicator
Weight
Indicator
Weight
Glass panel
0.334
Appearance
0.315
Material test Bearing capacity
0.315 0.370
Appearance
0.325
Material test Bearing capacity
0.314 0.361
Appearance
0.506
Material test
0.494
Panel type Panel size Defects on the surface Warping deformation of the panel Panel material color change Laminating, blistering, degumming Foaming, condensation, water ingress Mechanical edging around the glass Glass panel tempering, surface stress Curtain wall impact resistance test Review of design bearing capacity Wind pressure resistance test Metal frame size Defects on the surface Corrosion of metal components The structure of connections Vickers hardness Review of design bearing capacity Wind pressure resistance test Structural adhesive size Colloid discoloration, chalking Colloidal blistering, defect Partial failure of bonding Bonding of the outer surface of the insulating glass Tensile bond strength Shore hardness of structural adhesive Shear strength of structural adhesive Colloidal bond failure area ratio
0.187 0.130 0.144 0.154 0.114 0.134 0.136 0.187 1.000 0.355 0.369 0.275 0.242 0.227 0.260 0.271 1.000 0.490 0.510 0.199 0.204 0.187 0.222 0.188 0.257 0.256 0.233 0.253
Metal frame
0.298
Structural adhesive
0.368
determining formula [15] is developed as:
1+ rcd =
( ) s b
d 2 d
3(s b) b d
1
( ) s c
a 2 a
3(s c ) c a
s b
d d
c
a a
rcd = 0 for the remaining ranks.
d
5.2. Qualitative indicators
b
d a
c
For the qualitative indicators of the appearance observation, the rank determination matrix of the four appraisal ranks is considered, and the matrix of the subjective appraisal indicator is assumed in Table 7. In order to compare the difference of result between the fuzzy appraisal method proposed in this study and the absolute appraisal method based on the current specification [19], define the equivalent 4 appraisal rankH = j = 1 jbj , where j refer to the safety rank (j = 1,2,3,4). For the consideration of field engineering operability and verifiability, this paper makes the assumption that the appraisal result of the qualitative indicators are consistent with the equivalent appraisal rank of the hypothesis value matrix. The equivalent result of the fuzzy appraisal set should be the same as the evaluation result of the absolute method after considering the approximation principle of rounding. Therefore, the assumed value should satisfy the following relationship: ①For the subjective appraisal indicator uij , if the appraisal result of 100% component is rank i (i =1,2,3,4), the appraisal result of the component uij of the component subunit must be the same rank. Then there has:
(1)
where: s is the actual measured value of the quantitative indicator, the lower bound is a, the upper bound is b; The values of the upper and lower bounds [a, b] are referred to Table 6; [c, d] is the optimal interval corresponding to a certain rank, the value of which is determined by the current specification; And rcd is the degree of rank matching of the given quantitative indicator. The interval division and upper/lower bounds of each appraisal indicator are taken according to relevant specifications; if the appraisal indicator follows hard and fast rules, it should be converted into a performance degradation degree (percentage) compared with the standard performance and substituted into Eq. (1). For the case where the actual value of the indicator exceeds the upper and lower bounds, the following is processed: For the indicators the smaller whose value the better, if the actual value of the indicator is lower than the lower bound, rcd = 1 for rank-1, rcd = 0 for the remaining ranks; if the actual value of the indicator exceeds the upper bound, rcd = 1 for rank-4, rcd = 0 for the remaining ranks. For the indicators the bigger whose value the better, the actual value of the index is lower than the lower bound, rcd = 1 for rank-4, rcd = 0 for the remaining ranks; if the actual value of the indicator exceeds the upper bound, rcd = 1 for rank-1,
x11 + 2x12 < 1.5 x11 + x12 = 1 1.5 x21 + 2x22 + 3x23 < 2.5 x21 + x22 + x23 = 1 2.5 2x32 + 3x33 + 4x34 < 3.5 x32 + x33 + x34 = 1 3.5 3x 43 + 4x 44 x 43 + x 44 = 1
(2)
Table 6 Value table of upper and lower bounds [a, b] of indicators. optimal interval Indicator type
Rank-1 [c1,d1]
Rank-2 [c2,d2]
Rank-3 [c3,d3]
Rank-4 [c4,d4]
For those indicators whose value is larger, the safer For those indicators whose value is smaller, the safer
[c2,d1] [c1,d2]
[c3,d1] [c1,d3]
[c4,d2] [c2,d4]
[c4,d3] [c3,d4]
6
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Table 7 Rank determination hypothesis of subjective appraisal indicator. Judging result
v1
v2
v3
v4
1st rank 2nd rank 3rd rank 4th rank
x11 x21 0 0
x12 x22 x32 0
0 x23 x33 x 43
0 0 x34 x 44
②Referring to the current curtain wall appraisal code [19], when the third- and fourth-rank components are not included, and the secondary component is ≤ 30%, the component sub-unit is ranked as 1st. The first-rank judging rules are:
[0.7 0.3]
x11 x12 0 0 = x21 x22 x23 0
Fig. 4. H–R/γS function image.
(3)
and issued corresponding test reports. The engineers selected two different typical areas of hidden glass curtain wall, as two appraisal units for the appraisal of hidden frame curtain walls, namely I and II. According to the relevant test report, the curtain wall was evaluated from three aspects: the metal frame, the glass panel and the silicone structural adhesive. Due to the space limitation, only partial appraisal results are given below. In order to verify the rationality of this appraisal method and to reveal the difference with the existing curtain wall appraisal specifications, the appraisal results of hidden frame glass curtain wall of the office building following the existing curtain wall appraisal specification were compared [19].
The second, third and fourth ranks of judgment rules can obtain similar inequality relations. On the basis of satisfying all the above inequality relations, the inequality group can obtain a set of solutions of Table 7, and the table of subjective appraisal indicators can be obtained, as shown in Table 8. For the qualitative indicators of the appearance observation, the appraisal matrix can be determined according to Table 8. Taking the indicator of bearing capacity recheck R/γS as an example, the functional relationship between the value of R/γS and its equivalent appraisal rank H is established, as shown in Fig. 4. It can be verified that the equivalent appraisal rank H is a continuous and differentiable value (marked in black solid lines in Fig. 4) with the change of R/γS, so as to provide more elaborate appraisal results than the fourrank absolute appraisal results (marked in red solid lines in Fig. 4), which is discrete and suddenly changed at given boundaries from Equation (4) (marked in red dashed lines in Fig. 4). At present, the rank decision of qualitative indicators such as “defects” is judged by field engineers according to the requirements of existing curtain wall inspection specifications. More refined interval division and more accurate rank decision are also the prospects of this study. It is worth noting that the safety appraisal model established in this paper is only applicable to the existing hidden frame glass curtain wall. The research on the safety appraisal of other types of glass curtain wall and stone curtain wall still has extensive significance and deserves further study. In addition, the rapid appraisal system based on on-site engineering inspection can give engineers a grasp of the overall structural safety of the curtain wall in a short time. The proposal of the rapid appraisal system of the hidden frame curtain wall and the accuracy of its appraisal results are still to be further studied.
6.1. The appraisal process using fuzzy rank matching method Indicator appraisal of level-5 indicators. The initial appraisal of each appraisal indicator of the level 5 of the appraisal unit I is carried out, taking the qualitative indicator ‘panel type’ and the quantitative indicator ‘short hardness of the structural adhesive’ as an example. ‘Panel type’: After spot check on the curtain wall of the appraisal unit I, it is found that the outer sheets of the 5 examined hollow glass plates are all tempered glass that meets the safety specification, and the inner pieces are ordinary float glass. The safety is slightly lower than the requirements of the existing curtain wall specifications, and the bearing capacity is not significantly affected, the curtain wall safety status is General. All five components were rated rank-2. The appraisal matrix is given according to Table 7. For the same component of the same appraisal unit, the weights are equal. Then the appraisal matrix R1111 of the indicator is
R1111 = [0.08 0.54 0.38 0]
6. Examples
‘Shore hardness of surface structural adhesive’: A sample of the silicone rubber of the appraisal unit I was selected for laboratory testing. The test results showed that the silicone structural adhesive used in the glass curtain wall was aging, and the actual measured value of Shore hardness was s1322 = 47 , thus the performance do not meet the requirements of the specification. According to the current specification [19], for Shore hardness, the 1–4 ranks are divided into [20, 60), [60, 70), [67, 75), [0, 20) U [75, +∞). According to Eq. (1), x r1322 (x = 1,2,3,4) corresponding to each level division interval is calculated, and the final result is normalized. Then the appraisal matrix R1322 of the indicator is
Taking an office building in Shanghai, China as an example, the building uses curtain wall compositing glass and stone as an external enclosure structure with a total height of about 132 m and a curtain wall area of about 19,500 square meters. In order to know the safety status of the building curtain wall at the present stage, the engineers carried out safety appraisal of the building curtain wall in April 2013 Table 8 Subjective appraisal indicator rank matching suggestion. Judging result
v1
v2
v3
v4
1st rank 2nd rank 3rd rank 4th rank
0.82 0.08 0 0
0.18 0.54 0.08 0
0 0.38 0.48 0.08
0 0 0.44 0.92
(4)
1 2 3 4 B1322 = [r1322 r1322 r1322 r1322 ] = [0.571 0.429 0.000 0.000]
(5)
For the other bottom-layer indicators of the appraisal units I and II, the initial appraisal may be performed by referring to the above method, and details are not described herein again. 7
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6.2. Appraisal of other levels After the initial appraisal of the bottom-layer indicators, the weight matrix of each level of indicators can be established according to the weights of the indicators in Table 5, and the final appraisal results are obtained recursively. Partial results are shown in Table 9, and their comprehensive score is calculated as H = 1.254. According to the final appraisal result and the appraisal result of the bottom layer index, the safety appraisal result of the curtain wall project can be obtained as follows: the curtain wall structure has sufficient carrying capacity, and the curtain wall safety status is good. However, the inner glass sheet of the empty glass panel is ordinary float glass. The safety is slightly lower than that of the existing curtain wall specification. It is recommended to take appropriate measures to rectify the inner glass sheet. The silicone structural adhesive used in the glass curtain wall of the project has an aging phenomenon, and some performance indicators do not meet the requirements of the specification, and appropriate measures should be taken for rectification. 6.3. The appraisal process using the current curtain wall appraisal specification [19] (referred to as current specification) is as follows The two appraisal units of the curtain wall were evaluated by the appraisal method of the current specification [19], and part of the appraisal results are shown in Table 10. Finally, the appraisal result of the curtain wall is rank-2, the safety is slightly lower than the requirements of the existing curtain wall specifications, and the bearing capacity is not significantly affected. In fact, from the inspection report and subunit appraisal results of the curtain wall project, the metal frame part of the curtain wall project is in a rank-1 state. Though the glass panel and the structural adhesive are flawed, they have a good ability to resist loads. Therefore, the comprehensive comparison shows that the appraisal results of the curtain wall using the proposed method are more consistent with the actual situation, and the appraisal results using the current specification [19] are more conservative.
Metal frame [0.970 0.030 0.000 0.000] Structural adhesive [0.775 0.098 0.082 0.046] Appraisal unit II [0.862 0.067 0.047 0.024]
Bearing capacity [1.000 0.000 0.000 0.000]
Panel type [0.080 0.540 0.380 0.000] Defects on the surface [0.000 0.080 0.480 0.440 ] Glass panel tempering, surface stress [1.000 0.000 0.000 0.000] Wind pressure resistance test [1.000 0.000 0.000 0.000] Review of design bearing capacity [1.000 0.000 0.000 0.000] Appearance [0.318 0.246 0.302 0.134]
Glass panel [0.787 0.077 0.094 0.042] Appraisal unit I [0.843 0.069 0.058 0.029] Overall appraisal of hidden frame glass curtain wall safety [0.852 0.068 0.053 0.027] H = 1.254
Material test [1.000 0.000 0.000 0.000]
Level 5 Level 4 Level 3 Level 2 Level 1
Table 9 Appraisal result of fuzzy appraisal method.
H. Teng-teng, et al.
7. Summary The safety of building facades can cause undesirable social impacts. Taking the hidden glass curtain wall as research target, this paper refers to the hierarchical system of the existing appraisal codes, and establishes the five-level appraisal hierarchy system. For each component or connection, multiple indicators are evaluated for individual components or connections from three aspects: appearance and construction, material testing, and bearing capacity testing, thereby establishing a five-level appraisal model for the hidden glass curtain wall. Some of the characteristics of the proposed appraisal methods are as follows: (1) With reference to the relevant specifications of the current curtain wall, the safety rank of the hidden frame glass curtain wall is divided into four fuzzy ranks of good, general, poor and dangerous, and the degree of rank matching are continuously changed, which is in line with the current curtain wall specification and avoids the adverse effects of mutations. The fuzzy comprehensive appraisal method is used to judge the safety rank of the existing hidden frame glass curtain wall, and the optimal interval rank determination criterion is adopted for both quantitative and qualitative indicators. (2) We surveyed the opinions of curtain wall experts from many fields, and the curtain wall experts with 10 years or more of curtain wall engineering experience accounted for 48%. The frequency statistics method is used to determine the weight of each appraisal indicator, and the expert engineering experience is transformed into data, which reduces the subjective influence to some extent. (3) The comprehensive appraisal method parameterizes the quantitative and qualitative indicators, which matches the existing codes as well. It has the characteristics of solid engineering base, more 8
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Table 10 Curtain wall appraisal results of specification appraisal methods. Overall curtain wall
Appraisal unit
Component subunit
Kindred Component
Single indicator
Overall appraisal of hidden frame glass curtain wall safety: Rank-2
Appraisal unit I: IIu
Panel: Bu
Glass panel: Bu'
Connection: Bu
Metal frame: Au' Structural adhesive:u′
Panel type: Bu'′ Defects on the surface: Bu'′ Glass panel tempering, surface stress: Au'′ Wind pressure resistance test: Au'′ Review of design bearing capacity: Au'′
Appraisal unit II: Iu
consistent with the actual situation, programmable, easy to operate, etc. However, due to the complexity of the actual curtain wall engineering environment, the curtain wall appraisal method proposed in this paper is not universal to other types of glass curtain wall, and the rapid appraisal method for various curtain wall forms still has great research value.
curtain walls of China and America, Construction Technology (22) (2014) 68–72. [12] A.S.T.M. ASTMCOMPASS, E283—04 Standard Test Method for Determining Rate of Air Leakage through Exterior Windows,curtain Walls,and Doors under Specified Pressure Differences across the Specimen, (2013). [13] C. CENELEC, BS EN 12153—2000 Curtain Walling Air Permeability Test Method, BSI, 2000. [14] J.A.I.M. Subcommittee, JASS14 Curtain Wall Construction, (2011). [15] J.T.C. BD, AS/NZS 4284—2008 Testing of Building Facades, (2008). [16] M.O.C. China, GB/T 21086—2007, Curtain Wall for Building, China Standard Press, 2007. [17] Sichuan Province, D.O.C., DB51/T 5068—2010 Technical Specification for Safety Performance Testing and Appraisal of Existing Glass Curtain Walls, China Standard Press, 2010. [18] Guangdong Province, D.O.C., DBJ/T15—88—2011 Technical Specification for Appraisal of Reliability of Curtain Wall, China Standard Press, 2011. [19] D.O.C. Shanghai, DG/TJ08—803—2005 Testing and Evaluating Technical Code for Glass Curtain Wall Safety Performance, China Standard Press, 2005. [20] D.O.C. Jiangsu Province, DGJ32/J63—2008 Technical Specification for Inspection and Evaluation of Reliability of Existing Glass Curtain Walls, China Standard Press, 2008. [21] W. Fangwen, Y. Caofang, X. Chengfeng, Durability evaluation of reinforced concrete arch bridge based on fuzzy analytic hierarchy process method, Open Civ. Eng. J. 9 (1) (2015) 888–895. [22] W. Zhang, et al., Fuzzy analytic hierarchy process synthetic evaluation models for the health monitoring of shield tunnels, Comput. Aided Civ. Infrastruct. Eng. 29 (9) (2014) 676–688. [23] M.B. Anoop, B.K. Raghuprasad, K. Balaji Rao, A refined methodology for durabilitybased service life estimation of reinforced concrete structural elements considering fuzzy and random uncertainties, Comput. Aided Civ. Infrastruct. Eng. 27 (3) (2012) 170–186. [24] M.O.C. China, JGJ/T324-2014 Standard for Test Method of Building Curtain Wall Engineering, China Building Industry Press, 2014. [25] W. Zhang, et al., Fuzzy analytic hierarchy process synthetic evaluation models for the health monitoring of shield tunnels, Comput. Aided Civ. Infrastruct. Eng. 29 (9) (2014) 676–688. [26] W. Fangwen, Y. Caofang, X. Chengfeng, Durability evaluation of reinforced concrete arch bridge based on fuzzy analytic hierarchy process method, Open Civ. Eng. J. 9 (1) (2015) 888–895. [27] Y.C. Fang, N. Di Tao, Durability assessment of RFC bridges based on the analytic hierarchy process and fuzzy synthetic evaluation, J Xi an Univ of Arch & Tech. (Natural Science Edition) (06) (2010) 829–834. [28] J. Jixiao, W. Fumin, L. Qi, Bridge construction risk assessment based on analytic hierarchy process and grey fuzzy theory, Journal of Xihua University( Natural Science) (05) (2016) 58–63. [29] Y. Guangqiang, Research on Durability Assessment of Bridge Based on the Fuzzy Theory, Southwest Jiaotong University, 2005, p. 64. [30] N. Guorong, Probability Prediction and Evaluation Method of Durability of Reinforced Concrete Highway Bridges and Corresponding Program System, Zhejiang University, 2006, p. 91. [31] M.O.C. China, JGJ/T 139-2001 Standard for Testing of Engineering Quality of Glass Curtain Walls, China Standard Press, 2001.
Acknowledgments The financial support from the National Key Research and Development Program (2017YFC0806100), the self-funded research project of China Academy of Building Research (20160122330730017) and the Fundamental Research Funds for the Central Universities in China (2019FZA4017) are greatly appreciated. Appendix A. Supplementary data Supplementary data to this article can be found online at https:// doi.org/10.1016/j.jobe.2019.100863. References [1] Q. Xu, H. Wang, Comparative Study on Safety Indexes of Structural Silicone Sealant for Glass Curtain Wall, China Building Waterproofing, 2013. [2] H. Wang, Z. Yu, Q. Xu, Discussion on On-Site Inspection Techniques for Adhesive Safety Performance of Existing Glass Curtain Wall, China Building Waterproofing, 2013. [3] M. Zhao, L. Sun, H. Zhao, Fuzzy comprehensive evaluation method for structural safety performance of existed glass curtain wall, Sichuan Building Science 34 (5) (2008) 80–84. [4] Z. Huang, et al., Rapid evaluation of safety-state in hidden-frame supported glass curtain walls using remote vibration measurement, Journal of Building Engineering 19 (2018) 91–97. [5] X.G. Liu, Y.W. Bao, Reliability evaluation of glass curtain wall via vibration detection, Key Eng. Mater. 492 (2011) 410–414. [6] S.S. Zhang, et al., Safety evaluation of existed glass curtain wall, Earthq. Resist. Eng. Retrofit. (04) (2010) 94–99. [7] W. Hong-Hua, Study on safety evaluation method of glass curtain wall, J. Nat. Disasters (5) (2010) 96–100. [8] W. Hong-Hua, W. Jie, Safety evaluation method of glass curtain wall based on set pair analysis, J. Nat. Disasters 20 (4) (2011) 66–70. [9] C.C.W. Web, Warning! the Glass Fell and the Child Died! Pay Close Attention to the Safety of Existing Curtain Wall, (2018). [10] T. Batchelor, Pedestrian Killed after ‘glass Windowpane Falls 250ft from Top Floor of London Tower Block’, (2018). [11] W. Zuohu, P. Jie, L. Jianhui, The differences of safe inspection for existing building
9
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Journal of Building Engineering journal homepage: www.elsevier.com/locate/jobe
Comprehensive appraisal of the safety of hidden frame glass curtain wall based on fuzzy theory
T
Huang Teng-tenga, Zhang Da-weia,*, Zhao Yu-xia, Liu Jun-jinb, Li Jian-huib a b
College of Architecture and Civil Engineering, Zhejiang University, Hangzhou, 310058, China China Academy of Building Research, Beijing, 100013, China
ARTICLE INFO
ABSTRACT
Keywords: Hidden frame glass curtain wall Analytic hierarchy process Fuzzy theory Safety appraisal
The falling accident of a building's curtain wall may bring adverse social impact and economic loss. It is therefore of great importance to efficiently and reliably identify the security status of existing curtain walls. Current safety appraisal methods for glass curtain walls are facing the adverse effect of a large amount of imperfect information and subjective indicators. There are shortcomings of these methods, such as: i) The appraisal rank is easily affected by subjective judging, ii) The key appraisal indicators are not clear, and iii) The top-level indicators are not scientifically determined and systematically evaluated through the lower-level indicators. This paper takes existing hidden frame glass curtain wall as the research object, divides the safety grade of curtain walls into four fuzzy ranks (fine, good, poor and dangerous) and establishes five levels of appraisal hierarchy for components. An appraisal weight determination system is established for existing hidden frame glass curtain walls in three aspects (appearance, material testing and bearing capacity testing) based on a survey among experienced curtain wall experts from diverse areas and professions. The frequency statistics method is used to determine the weights of the indicators. The ranks of quantitative and qualitative indicators are quantified using fuzzy theory. Finally, applicability of the proposed safety appraisal model is verified with a real project. The appraisal result obtained through the proposed models is consistent with the actual situation on a real project.
1. Introduction The hidden frame glass curtain wall has been widely applied by the architects and owners because of the clean and tidy outer surface of the building. During its service life, the hidden frame glass curtain wall is usually subjected to gravity load, wind load, temperature variation and various environmental erosion effects, together with design defects, material erosion, corrosion and aging, etc. Its performance deteriorates with time, causing potential danger to its safety [1–8]. Although the damage of the glass curtain wall generally does not threaten the safety of the main structure, its fall is unpredictable and can cause serious safety accidents and arise adverse social impacts. In 2018 alone, there have been many reports, e.g. in Shiyan City, Hubei Province, China, the curtain wall glass of an existing building fell off, which smashed the head of a 3-year-old child, causing his unfortunate death [9]. In the UK, a man died after reportedly being hit by a windowpane that fell around 76 m from the top of a block of flats in Albert Embankment of London [10]. Similar incidents have aroused great concern from the society and the government, and it is imperative to ensure the safety of existing glass curtain walls. Establishing a comprehensive safety appraisal *
system for existing glass curtain walls and regularly assessing the safety of existing curtain walls may allow us to keep abreast of the state of the existing curtain wall and take appropriate protective measures in a timely manner. Due to objective factors such as unclear construction situation, uncertainty of material properties, and complexity of service load and environment, etc., most current safety appraisal of glass curtain wall uses multi-indicators appraisal methods based on a large number of unclear information and subjective indicators [3,6–8,11]. Most of existing safety appraisal methods are essentially analytic hierarchy processes, and their core issues include the division of ranks, the determination of weights and ranks. At present, codes for inspection of bearing capacity and performance of glass curtain wall are available in United States [12], Europe [13], Japan [14] and Australia [15], where there are still no relevant provisions for the overall appraisal of the safety of existing curtain wall. In China, specifications for appraisal of curtain wall include local standards and national standards, of which national standards [16] are based on the hierarchy of overall curtain walls, appraisal units, subunits, a kind of component or connection, a single component or connection. Local standards [17–20] mostly divide
Corresponding author. E-mail address: [email protected] (Z. Da-wei).
https://doi.org/10.1016/j.jobe.2019.100863 Received 29 March 2019; Received in revised form 6 July 2019; Accepted 7 July 2019 Available online 08 July 2019 2352-7102/ © 2019 Elsevier Ltd. All rights reserved.
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the bearing capacity and performance of existing glass curtain walls into three hierarchy levels: component (including connection), subunit, and appraisal unit. Through the appraisal of three aspects: appearance, structure and bearing capacity, the ranks of each hierarchy level (au, bu, cu, du) are identified. The above-mentioned local and national standards determine the rank of the higher level indicators according to the quantitative proportional relation of the lower level indicators. In terms of rank determination, the four-level absolute interval is adopted, while the effect of uncertainty is not considered, and the weight relationship between different indicators is not considered, neither. Generally speaking, the current appraisal method has following shortcomings: 1. the result is susceptible to subjective judgement, 2. the key assessment indicators are not clear, and 3. the appraisal of higher-level indicators through lower-level indicators lacks scientific and systemic foundation. Fuzzy theory is a method of strictly quantifying the concept of fuzzy uncertainty into information that can be processed by computer. It does not advocate the use of complicated mathematical analysis or model to solve the model. Fuzzy theory is applicable to the appraisal system combining quantitative indicators and qualitative indicators. Structural performance appraisal method based on fuzzy theory has been widely studied in the field of bridges, tunnels, etc [21–23]. Due to insufficient research on related mechanisms, the safety appraisal of curtain wall structure has more subjective and qualitative indicators than the main structure of buildings and infrastructures such as bridges and highways, and is more susceptible to subjective judgment. Therefore, the fuzzy appraisal method is regarded more suitable to the safety appraisal of the existing hidden frame glass curtain wall. Some scholars have conducted research on the application of fuzzy evaluation methods in the curtain wall. Zhang et al. [6] proposed an appraisal method for comprehensively evaluating the safety of glass curtain wall structure by using area method combined with uncertain analytical hierarchy process. Zhao et al. [3] proposed the fuzzy comprehensive appraisal method to evaluate the safety performance of glass curtain wall. Wu and Wu et al. [7,8] established a set pair analysis appraisal method and interval fuzzy comprehensive method in the glass curtain wall safety appraisal. However, the existing research lacks the overall performance evaluation of the curtain wall corresponding to the quantitative measurement of the detection indicators and it is difficult to be used in engineering practice. Therefore, it is necessary to establish a safety performance appraisal indicator system and appraisal method for curtain wall structure with on-site engineering operability and verification. It is worth noting that the structural performance assessment is divided into three stages: “structural inspection”, “analytical appraisal” and “decision management”. In this paper, the hidden frame glass curtain wall is taken as the research object only on the “analytical appraisal” process. With reference to the existing curtain wall appraisal specifications [16–20,24], a five-level comprehensive appraisal system for hidden frame glass curtain wall as shown in Table 1 is established based on the multi-indicator analytic hierarchy process and fuzzy appraisal theory.
wherein v1-v4 indicates respectively the degree to which the indicator matches the rank 1–4. When the indicator in the appraisal set is a fuzzy indicator, the value of v1-v4 is between 0 and 1, in which 1 means complete coincidence and 0 means complete non-conformity. 3. Fuzzy comprehensive appraisal method Referring to the existing curtain wall appraisal specifications [16–20], the building curtain wall is divided according to panel materials and curtain wall types, and the curtain wall area that can independently perform safety appraisal is used as an appraisal unit. Taking the three component subunits of the curtain wall appraisal unit n as input indicators, the component setUn = [glass panel un1, metal frame un2, structural glue u n3]. For the glass panel, there has un1 = [appearance un11, material un12, bearing capacity un13], whereinu n11, u n12 and u n13 can be set by several specific appraisal indicators. The set of factors of other appraisal units and subunits can be obtained in the same ways. Considering the bearing capacity factor set of glass panel u n13 = [un131, u n132, u n133], where u n131 indicates impact resistance capacity, u n132 indicates recheck of design bearing capacity and u n133 indicates wind pressure resistance capacity. Define the single factor appraisal matrix as: 1 2 3 4 rn13y1 rn13y1 rn13y1 rn13y1
Rn13y =
1 2 3 4 rn13y2 rn13y2 rn13y2 rn13y2
(y = 1,2,3)
1 2 3 4 rn13y m rn13ym rn13ym rn13ym
x Where rn13y i represents the degree to which the y-th appraisal indicator of the i-th glass panel component matches the rankx (x = 1,2,3,4; i = 1,2, …, m) , and m is the total number of components of the glass panel in the appraisal unit n. The weight distribution of each Wn13y = component constitutes the weight matrix [wn13y1, wn13y2, …, wn13ym]. The set of factors of other subunits can obtain the corresponding appraisal matrix and weight matrix according to the above definition. Define Bn13y as the comprehensive appraisal matrix of indicator , Bn13y is a 4 × 1 matrix, and have: 1 2 3 4 Bn13y = Wn13y ORn13y = [bn13 y , bn13y , bn13y , bn13y ] (y = 1,2,3)
x where O represents the fuzzy operator, bn13y represents the degree to which the performance of indicator matches the rank-x (x = 1,2,3,4). While there is no single predominant appraisal factor in the hidden frame curtain wall structure, the appraisal of its safety needs to comprehensively consider all aspects of performance indicators. Referring to the application of multi-level fuzzy comprehensive appraisal in other fields [25–29], this study uses the average weighted operator, that is: m x x Bn13y = Wn13y *Rn13y , bn13 (wn13yi *rn13y y = i). i=1 The result of normalizing Bn13y is still recorded as Bn13y . The appraisal results of various appraisal indicators of the bearing capacity factors together constitute the appraisal matrix of the bearing capacity of the glass panel, that is: Rn13 = [Bn131, Bn132 , Bn133]T . The weight distribution of each appraisal indicator constitutes the weight matrix, that Wn13 = [wn131, wn132, wn133]. is: Then there have: 1 2 3 4 Bn13 = Wn13 ORn13 = [bn13 , bn13 , bn13 , bn13 ], where the result of normalizing Bn13 is the appraisal result of the bearing capacity of the glass panel subunit. The same method can be used to evaluate the appearance and material property of the glass panel subunit. By analogy, after the same method is used to determine the judgment results and weights of each indicator, the overall safety appraisal result of the hidden frame glass curtain wall is finally obtained B = WOR .
2. Division of ranks Referring to the current curtain wall appraisal specification [19], the safety status is divided into four fuzzy ranks of good, general, poor and dangerous, and classified according to Table 2. For quantitative indicators, the slight deviation of the test results will directly lead to different appraisal results at the boundary level; for qualitative indicators, different engineers have deviate understanding of the fuzzy evaluation language such as “good” and “poor”. The fuzzy appraisal results in matrix form can not only describe the gradual transition of appraisal ranks well, but also describe the ambiguity in natural language well. Thus, unlike the deterministic ranking of existing specifications, the appraisal set V = {v1, v2, v3, v4} is defined,
4. Weight determination The weight matrix is an important computational component that 2
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Table 1 Appraisal model for the safety of existing hidden frame curtain wall. Level 1
Level 2
Level 3
Level 4
Level 5
Overall appraisal of building curtain wall safety
appraisal unit (1,2, …,n)
Glass panel
Appearance
Panel type Panel size Defects on the surface Warping deformation of the panel Panel material color change Laminating, blistering, degumming Foaming, condensation, water ingress Mechanical edging around the glass Glass panel tempering, surface stress Impact resistance capacity Review of design bearing capacity Wind pressure resistance capacity Metal frame size Defects on the surface Corrosion of metal components The structure of connections Vickers hardness Review of design bearing capacity Wind pressure resistance capacity Structural adhesive size Colloid discoloration, chalking Colloidal blistering, defect Partial failure of bonding Bonding of the outer surface of the insulating glass Tensile bond strength Shore hardness of structural adhesive Shear strength of structural adhesive Colloidal bond failure area ratio
Material test Bearing capacity Metal frame
Appearance
Material test Bearing capacity Structural adhesive
Appearance
Material test
is adopted. The surveyed experts should judge the degree of influence of the appraisal results of the indicator on the overall safety of the existing glass curtain wall. 0 means no effect at all, and 10 means heavy effect, as an example shown in Table 3. For the weight of each indicator, the magnitude of the weight value is not a key factor, while the relative difference between the different indicators will have a direct impact on the judgment result. Each expert's score is homogenized by the average of the scores as the relative weights, which are used as a direct statistical result. Frequency statistics is performed on the relative weights of the experts and distribution map is given. A scoring value that considers the relative weights of different experts may have a normal distribution, and a corresponding normal distribution curve is drawn. Taking the glass panel component indicator (shown in Table 4) as an example, the frequency distribution map is shown in Fig. 3, and other indicators are deduced by analogy. It can be seen from the frequency distribution map of each indicator that the frequency distribution maps of different indicators have large differences. A normal D test is used for each set of data to test the goodness-of-fit of the frequency distribution of the data for the normal distribution. Getting Y ≤ Y0.05 of indicator 1-1 means that fitting the frequency distribution to a normal distribution does not have sufficient reliability. The goodness-of-fit test of the normal distribution of the other indicators of the panel shows that only some of the indicators, like 1–4, 1–5, 1–7, 1–8, have sufficient credibility that the frequency distribution is fitted to a normal distribution, while the others are not. The results of the goodness-of-fit test for the structural adhesive and the metal frame are similar. Therefore, the statistical operation using the normal distribution is not universal for each indicator, and the statistical calculation of the weight is obtained by direct frequency statistics. Using the frequency statistics method, the weight calculation of the underlying indicators is firstly performed. For the i th appraisal indicator (ui), the questionnaire results of its weights (wij , j = 1,2, , k ) from k (k ≥ 30) individuals (respondents) are divided into p groups (p generally is taken 5–10), whose class interval is h = (max {wij} min {wij})/p , and then calculate the frequency ki and wk = ki /k , the weight corresponding to the appraisal indicator ui is min {wij} + kh p wi = k = 1 wk . Finally wi is normalized to obtain the required 2
transforms the lower-rank indicator appraisal matrix into the upperrank indicator appraisal matrix. The assignment of weights must be scientific and objective, which requires appropriate weight determination methods. The objective weighting method is relatively shortlived and still not perfect. It has a strong mathematical theoretical basis, but the determined weight may be inconsistent with people's subjective wishes or actual conditions. The subjective weighting method is an early and mature method. The survey results often directly reflect the actual situation of the project, and there is no contradiction between the attribute weight and the actual importance of the attribute. Therefore, this paper chooses the subjective weighting method after comprehensive comparison. The frequency statistics method [30] is a questionnaire survey method. The respondents can express their opinions without interference. After the data screening and statistical analysis, the results are more objective and easy to operate. Therefore, we use this method to determine the weight of the appraisal indicator in this study. In the process of issuing and counting the questionnaire data, some factors that have little effect on the safety of the glass curtain wall are added as trap questions. If the score of the factor is too high, the questionnaire is considered invalid. Through this process, the professionalism of the experts surveyed has been verified and screened. The survey collected questionnaires from experts from Beijing, Shanghai, Hangzhou, Guangzhou, etc., involving 22 provinces or municipalities and 42 different cities in China. A total of 231 responses were collected. The composition of the experts is shown in Fig. 1 to Fig. 2. The respondents include curtain wall engineering experts with many years of engineering experience in design, construction, supervision, testing and other types of work. Among them, curtain wall experts in design, construction and inspection with rich firsthand engineering experience accounted for 82%, curtain wall experts with no less than 6 years working experience accounted for 73%, and senior curtain wall experts with no less than 10 years engineering experience accounted for 48%. In the questionnaire, the 5 content sections of glass panel, metal frame, structural adhesive, material properties and bearing capacity are surveyed. For each appraisal indicator, the ten-grade appraisal standard 3
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Poor The curtain wall has defects, and it has a significant impact on the bearing capacity. The curtain wall is in a poor state of safety. General The curtain wall has defects, but it does not significantly affect the bearing capacity. The curtain wall is in a general state of safety. Good The curtain wall has few defects, and has sufficient bearing capacity. The curtain wall is in a good state of safety. Condition Safety performance status
Dangerous The curtain wall has defects, and it has seriously impact on the bearing capacity. The curtain wall is in a dangerous state of safety.
3rd rank 2nd rank 1st rank Safety rank
Table 2 Safety rank classification of building curtain wall.
4th rank
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Fig. 1. Distribution of expert's career field.
Fig. 2. Distribution of expert's career experience. Table 3 Example of questionnaire survey on weights of appraisal indicator.
a) The dimensions of the panel do not match the design.
0
1
2
3
4
5
6
7
8
9
10
○
○
○
○
○
○
○
○
○
○
○
lower-rank indicator weight wi . For each component in the same component subunit, the weights can be considered equal. For upperrank indicator including n lower-rank indicators, the statistical data is the statistical result of all n indicators that all experts include. Therefore, by replacing the statistical data, the same calculation method can be used to obtain the weight values of all upper-rank indicators. The weight values of the various indicators calculated according to the above-mentioned frequency statistical processing method are shown in Table 5. It is worth noting that not all indicators in the table can get the corresponding inspection results. For example, for a singlelayer ordinary glass, there is no detection indicator of ‘Foaming, condensation, water ingress’. In such case, this indicator and its weight should be deleted, and the remaining indicators should be renormalized. 5. Rank determination Based on the Chinese glass curtain wall inspection standard [31], the current Chinese curtain wall appraisal specifications [19] gives rank intervals of quantitative indicators and qualitative indicators or its method of class interval determination. For example, for Shore hardness, the rank intervals of 1–4 ranks are divided into [20, 60), [60, 70), [67, 75), [0, 20) U [75, + ∞). By using fuzzy theory, the rank determination of quantitative and qualitative indicators can be given as 4
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Table 4 Glass panel component indicator. number
1–1
1–2
1–3
1–4
1–5
1–6
1–7
1–8
content
Panel type
Panel size
Defects on the surface
Warping deformation of the panel
Panel material color change
Laminating, blistering, degumming
Foaming, condensation, water ingress
Mechanical edging around the glass
below.
matching in the matched interval is 1. But for other ranks, the change of degree of rank matching should be gradual rather than abrupt. The common linear rank determination considers that the change rate of the degree of rank matching is the same, but usually the same change in the indicator value near the boundary of the interval has different influence on rank determination; therefore, the optimal interval type rank
5.1. Quantitative indicators For quantitative indicators, the rank can be determined according to the relevant provisions in the specification, and the degree of rank
Fig. 3. Glass panel component indicator. 5
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Table 5 Calculation results of appraisal indicator weights of hidden frame glass curtain wall. Level 3
Level 4
Level 5
Indicator
Weight
Indicator
Weight
Indicator
Weight
Glass panel
0.334
Appearance
0.315
Material test Bearing capacity
0.315 0.370
Appearance
0.325
Material test Bearing capacity
0.314 0.361
Appearance
0.506
Material test
0.494
Panel type Panel size Defects on the surface Warping deformation of the panel Panel material color change Laminating, blistering, degumming Foaming, condensation, water ingress Mechanical edging around the glass Glass panel tempering, surface stress Curtain wall impact resistance test Review of design bearing capacity Wind pressure resistance test Metal frame size Defects on the surface Corrosion of metal components The structure of connections Vickers hardness Review of design bearing capacity Wind pressure resistance test Structural adhesive size Colloid discoloration, chalking Colloidal blistering, defect Partial failure of bonding Bonding of the outer surface of the insulating glass Tensile bond strength Shore hardness of structural adhesive Shear strength of structural adhesive Colloidal bond failure area ratio
0.187 0.130 0.144 0.154 0.114 0.134 0.136 0.187 1.000 0.355 0.369 0.275 0.242 0.227 0.260 0.271 1.000 0.490 0.510 0.199 0.204 0.187 0.222 0.188 0.257 0.256 0.233 0.253
Metal frame
0.298
Structural adhesive
0.368
determining formula [15] is developed as:
1+ rcd =
( ) s b
d 2 d
3(s b) b d
1
( ) s c
a 2 a
3(s c ) c a
s b
d d
c
a a
rcd = 0 for the remaining ranks.
d
5.2. Qualitative indicators
b
d a
c
For the qualitative indicators of the appearance observation, the rank determination matrix of the four appraisal ranks is considered, and the matrix of the subjective appraisal indicator is assumed in Table 7. In order to compare the difference of result between the fuzzy appraisal method proposed in this study and the absolute appraisal method based on the current specification [19], define the equivalent 4 appraisal rankH = j = 1 jbj , where j refer to the safety rank (j = 1,2,3,4). For the consideration of field engineering operability and verifiability, this paper makes the assumption that the appraisal result of the qualitative indicators are consistent with the equivalent appraisal rank of the hypothesis value matrix. The equivalent result of the fuzzy appraisal set should be the same as the evaluation result of the absolute method after considering the approximation principle of rounding. Therefore, the assumed value should satisfy the following relationship: ①For the subjective appraisal indicator uij , if the appraisal result of 100% component is rank i (i =1,2,3,4), the appraisal result of the component uij of the component subunit must be the same rank. Then there has:
(1)
where: s is the actual measured value of the quantitative indicator, the lower bound is a, the upper bound is b; The values of the upper and lower bounds [a, b] are referred to Table 6; [c, d] is the optimal interval corresponding to a certain rank, the value of which is determined by the current specification; And rcd is the degree of rank matching of the given quantitative indicator. The interval division and upper/lower bounds of each appraisal indicator are taken according to relevant specifications; if the appraisal indicator follows hard and fast rules, it should be converted into a performance degradation degree (percentage) compared with the standard performance and substituted into Eq. (1). For the case where the actual value of the indicator exceeds the upper and lower bounds, the following is processed: For the indicators the smaller whose value the better, if the actual value of the indicator is lower than the lower bound, rcd = 1 for rank-1, rcd = 0 for the remaining ranks; if the actual value of the indicator exceeds the upper bound, rcd = 1 for rank-4, rcd = 0 for the remaining ranks. For the indicators the bigger whose value the better, the actual value of the index is lower than the lower bound, rcd = 1 for rank-4, rcd = 0 for the remaining ranks; if the actual value of the indicator exceeds the upper bound, rcd = 1 for rank-1,
x11 + 2x12 < 1.5 x11 + x12 = 1 1.5 x21 + 2x22 + 3x23 < 2.5 x21 + x22 + x23 = 1 2.5 2x32 + 3x33 + 4x34 < 3.5 x32 + x33 + x34 = 1 3.5 3x 43 + 4x 44 x 43 + x 44 = 1
(2)
Table 6 Value table of upper and lower bounds [a, b] of indicators. optimal interval Indicator type
Rank-1 [c1,d1]
Rank-2 [c2,d2]
Rank-3 [c3,d3]
Rank-4 [c4,d4]
For those indicators whose value is larger, the safer For those indicators whose value is smaller, the safer
[c2,d1] [c1,d2]
[c3,d1] [c1,d3]
[c4,d2] [c2,d4]
[c4,d3] [c3,d4]
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Table 7 Rank determination hypothesis of subjective appraisal indicator. Judging result
v1
v2
v3
v4
1st rank 2nd rank 3rd rank 4th rank
x11 x21 0 0
x12 x22 x32 0
0 x23 x33 x 43
0 0 x34 x 44
②Referring to the current curtain wall appraisal code [19], when the third- and fourth-rank components are not included, and the secondary component is ≤ 30%, the component sub-unit is ranked as 1st. The first-rank judging rules are:
[0.7 0.3]
x11 x12 0 0 = x21 x22 x23 0
Fig. 4. H–R/γS function image.
(3)
and issued corresponding test reports. The engineers selected two different typical areas of hidden glass curtain wall, as two appraisal units for the appraisal of hidden frame curtain walls, namely I and II. According to the relevant test report, the curtain wall was evaluated from three aspects: the metal frame, the glass panel and the silicone structural adhesive. Due to the space limitation, only partial appraisal results are given below. In order to verify the rationality of this appraisal method and to reveal the difference with the existing curtain wall appraisal specifications, the appraisal results of hidden frame glass curtain wall of the office building following the existing curtain wall appraisal specification were compared [19].
The second, third and fourth ranks of judgment rules can obtain similar inequality relations. On the basis of satisfying all the above inequality relations, the inequality group can obtain a set of solutions of Table 7, and the table of subjective appraisal indicators can be obtained, as shown in Table 8. For the qualitative indicators of the appearance observation, the appraisal matrix can be determined according to Table 8. Taking the indicator of bearing capacity recheck R/γS as an example, the functional relationship between the value of R/γS and its equivalent appraisal rank H is established, as shown in Fig. 4. It can be verified that the equivalent appraisal rank H is a continuous and differentiable value (marked in black solid lines in Fig. 4) with the change of R/γS, so as to provide more elaborate appraisal results than the fourrank absolute appraisal results (marked in red solid lines in Fig. 4), which is discrete and suddenly changed at given boundaries from Equation (4) (marked in red dashed lines in Fig. 4). At present, the rank decision of qualitative indicators such as “defects” is judged by field engineers according to the requirements of existing curtain wall inspection specifications. More refined interval division and more accurate rank decision are also the prospects of this study. It is worth noting that the safety appraisal model established in this paper is only applicable to the existing hidden frame glass curtain wall. The research on the safety appraisal of other types of glass curtain wall and stone curtain wall still has extensive significance and deserves further study. In addition, the rapid appraisal system based on on-site engineering inspection can give engineers a grasp of the overall structural safety of the curtain wall in a short time. The proposal of the rapid appraisal system of the hidden frame curtain wall and the accuracy of its appraisal results are still to be further studied.
6.1. The appraisal process using fuzzy rank matching method Indicator appraisal of level-5 indicators. The initial appraisal of each appraisal indicator of the level 5 of the appraisal unit I is carried out, taking the qualitative indicator ‘panel type’ and the quantitative indicator ‘short hardness of the structural adhesive’ as an example. ‘Panel type’: After spot check on the curtain wall of the appraisal unit I, it is found that the outer sheets of the 5 examined hollow glass plates are all tempered glass that meets the safety specification, and the inner pieces are ordinary float glass. The safety is slightly lower than the requirements of the existing curtain wall specifications, and the bearing capacity is not significantly affected, the curtain wall safety status is General. All five components were rated rank-2. The appraisal matrix is given according to Table 7. For the same component of the same appraisal unit, the weights are equal. Then the appraisal matrix R1111 of the indicator is
R1111 = [0.08 0.54 0.38 0]
6. Examples
‘Shore hardness of surface structural adhesive’: A sample of the silicone rubber of the appraisal unit I was selected for laboratory testing. The test results showed that the silicone structural adhesive used in the glass curtain wall was aging, and the actual measured value of Shore hardness was s1322 = 47 , thus the performance do not meet the requirements of the specification. According to the current specification [19], for Shore hardness, the 1–4 ranks are divided into [20, 60), [60, 70), [67, 75), [0, 20) U [75, +∞). According to Eq. (1), x r1322 (x = 1,2,3,4) corresponding to each level division interval is calculated, and the final result is normalized. Then the appraisal matrix R1322 of the indicator is
Taking an office building in Shanghai, China as an example, the building uses curtain wall compositing glass and stone as an external enclosure structure with a total height of about 132 m and a curtain wall area of about 19,500 square meters. In order to know the safety status of the building curtain wall at the present stage, the engineers carried out safety appraisal of the building curtain wall in April 2013 Table 8 Subjective appraisal indicator rank matching suggestion. Judging result
v1
v2
v3
v4
1st rank 2nd rank 3rd rank 4th rank
0.82 0.08 0 0
0.18 0.54 0.08 0
0 0.38 0.48 0.08
0 0 0.44 0.92
(4)
1 2 3 4 B1322 = [r1322 r1322 r1322 r1322 ] = [0.571 0.429 0.000 0.000]
(5)
For the other bottom-layer indicators of the appraisal units I and II, the initial appraisal may be performed by referring to the above method, and details are not described herein again. 7
Journal of Building Engineering 26 (2019) 100863
6.2. Appraisal of other levels After the initial appraisal of the bottom-layer indicators, the weight matrix of each level of indicators can be established according to the weights of the indicators in Table 5, and the final appraisal results are obtained recursively. Partial results are shown in Table 9, and their comprehensive score is calculated as H = 1.254. According to the final appraisal result and the appraisal result of the bottom layer index, the safety appraisal result of the curtain wall project can be obtained as follows: the curtain wall structure has sufficient carrying capacity, and the curtain wall safety status is good. However, the inner glass sheet of the empty glass panel is ordinary float glass. The safety is slightly lower than that of the existing curtain wall specification. It is recommended to take appropriate measures to rectify the inner glass sheet. The silicone structural adhesive used in the glass curtain wall of the project has an aging phenomenon, and some performance indicators do not meet the requirements of the specification, and appropriate measures should be taken for rectification. 6.3. The appraisal process using the current curtain wall appraisal specification [19] (referred to as current specification) is as follows The two appraisal units of the curtain wall were evaluated by the appraisal method of the current specification [19], and part of the appraisal results are shown in Table 10. Finally, the appraisal result of the curtain wall is rank-2, the safety is slightly lower than the requirements of the existing curtain wall specifications, and the bearing capacity is not significantly affected. In fact, from the inspection report and subunit appraisal results of the curtain wall project, the metal frame part of the curtain wall project is in a rank-1 state. Though the glass panel and the structural adhesive are flawed, they have a good ability to resist loads. Therefore, the comprehensive comparison shows that the appraisal results of the curtain wall using the proposed method are more consistent with the actual situation, and the appraisal results using the current specification [19] are more conservative.
Metal frame [0.970 0.030 0.000 0.000] Structural adhesive [0.775 0.098 0.082 0.046] Appraisal unit II [0.862 0.067 0.047 0.024]
Bearing capacity [1.000 0.000 0.000 0.000]
Panel type [0.080 0.540 0.380 0.000] Defects on the surface [0.000 0.080 0.480 0.440 ] Glass panel tempering, surface stress [1.000 0.000 0.000 0.000] Wind pressure resistance test [1.000 0.000 0.000 0.000] Review of design bearing capacity [1.000 0.000 0.000 0.000] Appearance [0.318 0.246 0.302 0.134]
Glass panel [0.787 0.077 0.094 0.042] Appraisal unit I [0.843 0.069 0.058 0.029] Overall appraisal of hidden frame glass curtain wall safety [0.852 0.068 0.053 0.027] H = 1.254
Material test [1.000 0.000 0.000 0.000]
Level 5 Level 4 Level 3 Level 2 Level 1
Table 9 Appraisal result of fuzzy appraisal method.
H. Teng-teng, et al.
7. Summary The safety of building facades can cause undesirable social impacts. Taking the hidden glass curtain wall as research target, this paper refers to the hierarchical system of the existing appraisal codes, and establishes the five-level appraisal hierarchy system. For each component or connection, multiple indicators are evaluated for individual components or connections from three aspects: appearance and construction, material testing, and bearing capacity testing, thereby establishing a five-level appraisal model for the hidden glass curtain wall. Some of the characteristics of the proposed appraisal methods are as follows: (1) With reference to the relevant specifications of the current curtain wall, the safety rank of the hidden frame glass curtain wall is divided into four fuzzy ranks of good, general, poor and dangerous, and the degree of rank matching are continuously changed, which is in line with the current curtain wall specification and avoids the adverse effects of mutations. The fuzzy comprehensive appraisal method is used to judge the safety rank of the existing hidden frame glass curtain wall, and the optimal interval rank determination criterion is adopted for both quantitative and qualitative indicators. (2) We surveyed the opinions of curtain wall experts from many fields, and the curtain wall experts with 10 years or more of curtain wall engineering experience accounted for 48%. The frequency statistics method is used to determine the weight of each appraisal indicator, and the expert engineering experience is transformed into data, which reduces the subjective influence to some extent. (3) The comprehensive appraisal method parameterizes the quantitative and qualitative indicators, which matches the existing codes as well. It has the characteristics of solid engineering base, more 8
Journal of Building Engineering 26 (2019) 100863
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Table 10 Curtain wall appraisal results of specification appraisal methods. Overall curtain wall
Appraisal unit
Component subunit
Kindred Component
Single indicator
Overall appraisal of hidden frame glass curtain wall safety: Rank-2
Appraisal unit I: IIu
Panel: Bu
Glass panel: Bu'
Connection: Bu
Metal frame: Au' Structural adhesive:u′
Panel type: Bu'′ Defects on the surface: Bu'′ Glass panel tempering, surface stress: Au'′ Wind pressure resistance test: Au'′ Review of design bearing capacity: Au'′
Appraisal unit II: Iu
consistent with the actual situation, programmable, easy to operate, etc. However, due to the complexity of the actual curtain wall engineering environment, the curtain wall appraisal method proposed in this paper is not universal to other types of glass curtain wall, and the rapid appraisal method for various curtain wall forms still has great research value.
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Acknowledgments The financial support from the National Key Research and Development Program (2017YFC0806100), the self-funded research project of China Academy of Building Research (20160122330730017) and the Fundamental Research Funds for the Central Universities in China (2019FZA4017) are greatly appreciated. Appendix A. Supplementary data Supplementary data to this article can be found online at https:// doi.org/10.1016/j.jobe.2019.100863. References [1] Q. Xu, H. Wang, Comparative Study on Safety Indexes of Structural Silicone Sealant for Glass Curtain Wall, China Building Waterproofing, 2013. [2] H. Wang, Z. Yu, Q. Xu, Discussion on On-Site Inspection Techniques for Adhesive Safety Performance of Existing Glass Curtain Wall, China Building Waterproofing, 2013. [3] M. Zhao, L. Sun, H. Zhao, Fuzzy comprehensive evaluation method for structural safety performance of existed glass curtain wall, Sichuan Building Science 34 (5) (2008) 80–84. [4] Z. Huang, et al., Rapid evaluation of safety-state in hidden-frame supported glass curtain walls using remote vibration measurement, Journal of Building Engineering 19 (2018) 91–97. [5] X.G. Liu, Y.W. Bao, Reliability evaluation of glass curtain wall via vibration detection, Key Eng. Mater. 492 (2011) 410–414. [6] S.S. Zhang, et al., Safety evaluation of existed glass curtain wall, Earthq. Resist. Eng. Retrofit. (04) (2010) 94–99. [7] W. Hong-Hua, Study on safety evaluation method of glass curtain wall, J. Nat. Disasters (5) (2010) 96–100. [8] W. Hong-Hua, W. Jie, Safety evaluation method of glass curtain wall based on set pair analysis, J. Nat. Disasters 20 (4) (2011) 66–70. [9] C.C.W. Web, Warning! the Glass Fell and the Child Died! Pay Close Attention to the Safety of Existing Curtain Wall, (2018). [10] T. Batchelor, Pedestrian Killed after ‘glass Windowpane Falls 250ft from Top Floor of London Tower Block’, (2018). [11] W. Zuohu, P. Jie, L. Jianhui, The differences of safe inspection for existing building
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