A Novel Approach for Risk Assessment of Building Damage via Metro Tunnel Construction

. Te impact of shield construction on the surrounding buildings involves numerous factors, and the factors are uncertain and ambiguous, which have a great impact on the progress and safety of the project. Terefore, this paper developed a systematic approach for the risk assessment of existing buildings adjacent to tunneling excavation. Firstly, a risk assessment system for adjacent buildings in shield tunneling environments was proposed. Secondly, the weighting of factors was calculated by Py-thagorean fuzzy AHP. Ten, the VIKOR method was used to divide the risk of existing buildings adjacent to tunneling excavation into fve uneven levels. Finally, the extended VIKOR with interval numbers was frst introduced in risk assessment of building adjacent to tunneling environment to determine a specifc building risk level. Te proposed approach was successfully applied to the risk assessment of several buildings adjacent to tunnel construction of Metro Line 4 of Changsha. Te accuracy and effectiveness of the constructed new approach were verifed by comparing the obtained evaluation results with the actual situation on-site. Tis work provides a new method for similar engineering risk assessment.


Introduction
Due to an increase in urbanization all over the world, urban population density increases and road trafc pressure becomes severe, a large number of metro tunnels are being constructed or planned in urban areas, especially in China [1]. Many subway tunnels in China have been constructed using the shield tunneling technique because of their distinct advantages over other conventional methods [2][3][4]. However, shield tunneling excavation through soft soils are tend to produce surface settlements due to disturbance to the soil layers around tunnels and the volume loss of the tail void, which may cause adjacent buildings deformation, and then threaten the safety and security of urban inhabitants [5][6][7][8][9][10][11][12][13][14]. Terefore, to reduce the impact of subway shield construction on surrounding buildings, it is very important to analyze and evaluate the safety of existing buildings and to perceive and anticipate the potential safety risks in tunnel-induced building damages.
Numerous studies have been conducted for risk assessment of adjacent buildings around the tunnel and can be categorized into the following methods: empirical formula method [15,16], analytical theoretical method [17,18], and numerical analysis method [19,20]. Tese methods have several advantages in analyzing tunnel-soil-building interaction, however, some limits have been found in application. Te empirical formula method and analytical theoretical method are based on greenfeld scenarios, the efect of surface buildings has been mostly neglected in these previous studies. Meanwhile, many parameters in the empirical formula method and the theoretical analysis method are more difcult to obtain accurate values, so the calculation results have certain deviations. Te numerical analysis method can fully consider the building-tunnel-soil interaction and save time and efort through computer calculations, but diferent parameter settings can lead to excessive diferences in the fnal results due to model construction. To address those issues, multicriteria decision making (MCDM) approaches, which is capable of taking all relevant information into account, are presented to facilitate risk assessment in a complex project environment.
MCDM provides a broad range of methodologies to decision-makers and experts that can work out the complexity of risk assessment problems. Te commonly used MCDM methods include analytical hierarchy process (AHP) [21,22], analytical network process (ANP) [23], technique for order preference by similarity to an ideal solution (TOPSIS) [24,25], VlseKriterijuska Optimizacija I Komoromisno Resenje (VIKOR) [26,27], and multiplicative form of multiobjective optimization by ratio analysis (MULTIMOORA) [28]. AHP is one of the most important methods in MCDM, which can transform uncertain information or concepts into quantitative expressions and is often used to determine indicator weights. However, the criteria of hierarchical analysis are too fxed when calculating the weights, which cannot refect the experts' ideas well and are infuenced by the subjective factors of the researcher. Pythagorean fuzzy sets are extensions of intuitionistic fuzzy sets that can better deal with ambiguity and uncertainty in decision making. Terefore, this paper combines Pythagorean fuzzy sets with hierarchical analysis and transforms them into Pythagorean fuzzy hierarchical analysis (PFAHP). PFAHP converts the linguistic descriptions of experts into fuzzy numbers better and refects the opinions of experts more accurately, which in turn makes up for the shortcomings of traditional hierarchical analysis and makes the obtained index weights more reasonable and reliable. Te VIKOR method is developed to solve the discrete multicriteria problem with conficting criteria, and aims to determine a compromise ranking and selection scheme taking into account conficting criteria. Te interval number improvement VIKOR method is based on the VIKOR method by replacing specifc values with interval numbers. Due to the complexity of underground engineering and the uncertainty of factor values, the interval number is used to improve the VIKOR method, which can better refect the actual engineering situation, and thus improve the accuracy and objectivity of risk assessment.
In this paper, we combine PFAHP and interval number improved VIKOR method for the frst time and applied it to the risk assessment of shield tunnel in the engineering feld. Firstly, based on relevant literature and expert experience, this paper proposed a risk assessment system for adjacent buildings in shield tunneling environments. Secondly, according to experts' judgments and in-site geological conditions, the weighting of factors was calculated by PFAHP. Ten, the VIKOR method was used to divide the risk of existing buildings adjacent to tunneling excavation into fve uneven levels. Meanwhile, the extended VIKOR with interval numbers was frst introduced in the risk assessment of building adjacent to tunneling environment to determine a specifc building risk level. Finally, the proposed approach was applied to the risk assessment of several buildings adjacent to tunnel construction of Metro Line 4 of Changsha. Te accuracy and efectiveness of the constructed new approach were verifed by comparing the obtained evaluation results with the actual situation on-site. Tis work provides a new method for similar engineering risk assessment.
Te paper is organized as follows: in section 2, we describe the methodology used in this paper, including PFAHP method, VIKOR method, and extended VIKOR method with interval number. In section 3, we introduce the construction process of risk assessment of adjacent buildings in shield tunneling environment. In section 4, the proposed approach is applied to a case study. In section 5, we discuss the results and provide some managerial comments. In section 6, conclusions are drawn.

PFAHP Method
2.1.1. Pythagorean Fuzzy Sets. Ever since Zadeh frst introduced the concept of fuzzy sets, these sets have been used by many researchers in various felds to express uncertainty. Fuzzy sets have developed into a variety of forms. Intuitionistic fuzzy sets are one of these that was proposed. In intuitionistic fuzzy sets, membership function, nonmembership function, and hesitancy degree can be determined by decision-makers. However, in some cases, it cannot express the accuracy of membership and nonmembership function. For example, the sum of membership and nonmembership degrees is over 1, which dissatisfes the requirement of intuitionistic fuzzy sets. As a result, Yager [29] proposed Pythagorean fuzzy sets. Tese sets are the generalization of intuitionistic fuzzy sets in some conditions. Pythagorean fuzzy sets can address uncertainty and reduce vagueness. Tese achievements make Pythagorean fuzzy sets a powerful and fexible tool to solve problems about uncertainty.

Notations of Pythagorean Fuzzy Sets. In Pythagorean
Fuzzy sets, the sum of membership and nonmembership degrees can exceed 1, but the sum of squares cannot. Tis situation is described below in Defnition 1.
Defnition 1. Let a set X be a universe of discourse. A Pythagorean fuzzy set P is an object having the form [30].

Steps of PFAHP.
In this section, the steps of the PFAHP method will be introduced [31,32].
Step 1. Construct the compromised pairwise comparison matrix R � (r ik ) m×m based on the linguistic evaluation of experts using the scale in Table 1.
Step 2. Calculate the diference matrix D � (d ik ) m×m between the lower and upper values of the membership and nonmembership functions using the following equations: Step 3. Calculate the interval multiplicative matrix S � (s ik ) m×m using the following equations: Step 4. Calculate the determinacy value τ � (τ ik ) m×m using the following equation: Step 5. Multiply the determinacy value τ � (τ ik ) m×m and the interval multiplicative matrix for obtaining the matrix of weights, obtain T � (t ik ) m×m before normalization using the following equation: Step 6. Calculate the normalized weights w i using the following equation:

VIKOR Method.
Te VlseKriterijumska Optimizacija I Kompro-misno Resenje (VIKOR) is an efective method in MCDM. Tis method focuses on solving discrete decision problems with conficting criteria and determining a compromise solution for a problem with conficting criteria, which can help the decision-makers to optimize complex systems to get a fnal solution. In this article, the VIKOR method is used for determining risk levels based on the value of Q i . Te VIKOR method started with the following form of L p -metric [33,34]: where f ij means the value of j-th criterion function for the alternative A i , n is the number of criteria, f * j is the best value of criterion j, f − j is the worst value of criterion j, and w j means the weight of criterion j.
Te procedure of the VIKOR method is described as follows: Step 1. Normalize quantities by using the following equation: Step 2. Determine the best value f * j and the worst value f − j of each criterion. If the j-th function represents a beneft then: f * j � max i f ij and f − j � min i f ij . If the jth function represents a cost then: Step 3. Calculate the values S i and R i by using the following equations: Step 4. Calculate the value Q i by using the following equation: where and v represents the weight of the strategy of "the majority of Criteria" (or "the maximum group utility"), usually v = 0.5.
Step 5. Rank the value Q i by increasing order, the minimum Q i is the best option.

Extended VIKOR Method with Interval Number.
In some cases, due to incomplete and uncertain data, it is difcult to obtain accurate values, and the interval numbers are more Advances in Civil Engineering 3 probable to deal with problems. Using interval numbers can make decision-makers make a better judgment. In the risk assessment area, VIKOR with interval number is frst used for determining the specifc building risk level. Te procedure of the extended VIKOR method is described as follows [35]: Step 1. Construct a decision matrix M using the interval numbers: where i � 1,2, . . ., n; j � 1,2, . . ., m.
Step 2. Determine the best value f * j and the worst value f − j for each criterion using the following equations: where I is associated with the beneft criterion and J is associated with the cost criterion.
Step 3. Calculate the values [S L i , S U i ] and [R L i , R U i ] by using the following equations: Step 4. Calculate the value [Q L i , Q U i ] by using the following equations: an d v is the weight of "the majority of criteria" (or "the maximum group utility"), usually v � 0.5.

Risk Assessment of Adjacent Buildings in Shield Tunneling Environments
According to the PFAHP method, VIKOR method, and extended VIKOR method with interval number mentioned in section 2, the new method of risk assessment of adjacent buildings in the tunnel environment is established in this section.

Te Process of Risk Assessment of Adjacent Buildings.
Te process of risk assessment of adjacent buildings can be divided into four phases. Firstly, a risk assessment system for adjacent buildings in shield tunneling environments is constructed by referring to relevant literature and code for risk management of underground engineering construction of urban rail transit. Secondly, the PFAHP method is used to transfer the expert's linguistic judgment into quantitative numbers, then factors weighting is determined. Tirdly, a risk level classifcation standard is constructed using the VIKOR method. Finally, the extended VIKOR method is used to determine a specifc building risk level. Te full fowchart of the process is given in Figure 1.

Infuence Variables.
Risk factor identifcation is crucial for risk assessment. Shield tunneling is a very complicated process where various factors are involved. Tunnel-induced building damage happens more and more frequently. Based on relevant literature [36][37][38][39][40][41] and code for risk management of underground engineering construction of urban rail transit, four types of variables are proposed, and a risk assessment system for adjacent buildings in shield tunneling environments was established, as shown in Figure 2.

Case Study
Tis paper takes the tunnel construction on Metro Line 4 of Changsha as an example and applies the new approach constructed in Section 3 to this actual project, which efectively verifes the scientifc and practicality of the new approach.

Background.
In this study, tunnel construction on Metro Line 4 of Changsha, China, was investigated. Te buildings along the tunnel route are dense, and the geological environment is complicated. It is necessary to carry out risk assessment for the buildings. Among hundreds of buildings around tunnels, fve buildings were randomly selected for the case study. Figure 3 shows the layout of fve buildings adjacent to tunnels, denoted by 1 # , 2 # , 3 # , 4 # , and 5 # . Te whole geological profle along these fve buildings is shown in Figure 4. In this tunnel section, the cover depth of the tunnel ranges from 16 m to 22 m. On top of the ground is a backfll layer with a thickness of about 1.3 to 2 m. Under the backfll layer is a silt clay layer, to the depth of about 5 m. Te following is the sandstone layer, with a thickness of 6 to 25 m, and a marlite layer mixed with mudstone and carbonaceous mudstone.
Te tunnel was constructed by the Earth pressure balanced (EPB) shield-driven method. Te cutter head diameter and length of EPB shields used in this project are 6.28 Based on geological information and integrate with the expert judgments, values of 19 evaluation factors were obtained for those fve adjacent buildings, as presented in Table 3. In this paper, the 3 # building was taken as an example to show the procedure of the new method based on PFAHP and extended VIKOR.

Weighting Calculation Using
PFAHP. An expert group of ten members participated in the risk assessment process. Restricted to space, the main criteria is an example to show the process of PFAHP. First, the pairwise comparison matrix R � (r ik ) m×m is constructed based on the experts' opinions given in Table 4. Te experts' opinions are obtained using the scale from Table 1. Te diference matrix D � (d ik ) m×m between the lower and upper values of the membership and nonmembership functions using equations (4) and (5) are shown in Table 5. Ten, the interval multiplicative matrix S � (s ik ) m×m is presented in Table 6 using equations (6) and (7). Subsequently, the determinacy value τ � (τ ik ) m×m shown in Table 7 is calculated using equation (8). Te matrix of unnormalized weights T � (t ik ) m×m given in Table 8 is calculated using equation (9). Finally, the normalized weights w i are presented in Table 9 using equation (10).
Since how to obtain the weights is already explained in the main criteria, the other infuence variables' calculation steps are omitted. Te normalized weight of each infuence variable is presented in Table 10.

Determining Risk Rating Classifcation Based on VIKOR.
After identifying the infuence variable's weights, the VIKOR method is applied for determining risk rating classifcation. According to the risk level classifcation of infuence variables, six typical samples were selected from the best to worst values of variables. Ten, the matrix R was formed.

Advances in Civil Engineering
Te normalized data using equations (11)- (12) are given in matrix V.
Te best value f * j and the worst value f − j for all infuence variables are shown in Table 11.
Te R i and S i values of each sample are calculated in Table 12.
Te value Q i with v � 0.5 is calculated by using equation (15). Ten, the risk level classifcation is presented in Table 13 based on the value Q i .

Determine Building Risk Level Using Extended VIKOR.
Te 3 # building was taken as an example to illustrate the reliability of the extended VIKOR method with interval numbers. Table 3 shows the values of 19 evaluation factors that were obtained for the 3# building. Te decision matrix M with the interval numbers is constructed using equation (16).
Te best value f * j and the worst value f − j for buildings are presented in Table 14 using equations (17)- (18).  (23) and (24) are 0.576 and 0.648, respectively. In accordance with the risk level classifcation (Table 13), the 3 # building's risk level is III, which is medium risk situation.
Te same risk assessment procedures are also applied to 1 # , 2 # , 4 # , and 5 # buildings. Te overall values [Q L i , Q U i ] and risk level classifcation are shown in Figure 5. Te 1 # building's risk level is IV, which means in a high risk situation. Te 1 # and 5 # buildings are both in the situation between II to III risk level and the 3 # and 4 # buildings are both in the medium risk level.

Discussion
Te accuracy of the results calculated by the model is verifed by the actual situation of the damage degree of 1-5 # buildings during the shield tunneling process. Among them, no signifcant settlement occurred in buildings 2-5 # during the shield tunneling process, and there were no obvious cracks in the building walls. For building # 1, the maximum settlement of the building was 9.2 mm when the right line passed through building # 1, and at this time the appearance of the building did not show any cracks or plaster peeling of. When the left line went down through building # 1, the alternating interface of fully weathered sandstone and medium weathered sandstone in the stratum caused the shield machine to stop for more than 32 hours, at which time large settlement occurred in the stratum. When the left line crossed the building, the maximum settlement of the building was nearly 37 mm. Te building wall showed signifcant cracks with lengths of 0.6∼7.6 m and widths of 0.5∼5.0 mm. According to the damage assessment based on damage phenomena, the building is in the "minor damage" to "moderate damage" category. In summary, the accuracy and efectiveness of the constructed new approach in the risk assessment of shield underpass existing buildings are verifed by comparing the obtained evaluation results with the actual situation on-site. At the same time, this study contributes to future construction studies, as this work provides a new method for similar engineering risk assessment.
To reduce the impact of shield construction on existing buildings, measures need to be taken to control the risk as much as possible. In the design stage, the tunnel should be placed in the deep soil and the soil layer with good mechanical properties. Keep the tunnel as far away from the Advances in Civil Engineering 11 buildings as possible in the horizontal direction. In the construction process, the relevant parameters of the shield tunneling machine should be well controlled, and the tunneling should not be completed too quickly and too aggressively. Make all relevant factors as close as possible to the level of risk level I in Table 2.
Tere are also some limitations to the method. Despite plenty of infuence variables that have been considered, there are still many factors that have not been taken into account. Te weightings and ratings of the criteria and variables by the experts could have been subjective and their personal opinions and perspectives might have been infuenced by their expertise and knowledge. Terefore, the subjectivity and the personal prejudice of the experts of the study might have afected the results. To generalize the risk assessment to building adjacent tunneling, further investigations and studies should be conducted.

Conclusion
To assess adjacent buildings' potential risk, a novel risk assessment method with detailed step-by-step procedures has been proposed. It merges the PFAHP method, VIKOR method, and extended VIKOR method with interval numbers to support the construction safety risk perception. A case study was presented to analyze the buildings' safety performance adjacent to the Changsha Metro Line 4 construction in China. Te results       demonstrated the feasibility of the proposed method and its application potential. Te following conclusions can be drawn: (1) Based on engineering practice and expert estimates regarding tunnel-soil-building interaction, a risk assessment system for adjacent buildings in shield tunneling environments was proposed, including four types of variables: geotechnical variables, building-related variables, tunnel related variables, and machine-related variables. Tese infuence variables can be assessed within fve diferent risk levels, namely, "I (safe), II (low risk), III (medium risk), IV (high risk), and V (extreme risk)," with the building health condition and the environmental condition.
(2) Tis approach provides a more powerful tool for knowledge representation and reasoning under vagueness and uncertainty compared to traditional risk assessment method. Experts can feel free while assigning variables weightings when lacking sufcient pieces of information. Using the PFAHP method can easily change expert linguistical opinion to fuzzy sets, as well as maintain accuracy. Compared to traditional risk level classifcation, in this article, the risk level is unevenly classifed by using VIKOR method, which is more accurate and reasonable. (3) For the frst time, the extended VIKOR method with interval number was introduced in risk assessment to determine specifc building risk levels. Due to the complexity of the geological condition and tunneling condition, using interval values instead of crisp values can be reliable, which also guarantees that the interval numbers refect the actual knowledge of domain experts. (4) Te proposed approach was used to evaluate the risk assessment of several buildings adjacent to tunnel construction of Metro Line 4 of Changsha. Te accuracy and efectiveness of the constructed new approach were verifed by comparing the obtained evaluation results with the actual situation on-site. Te evaluation case verifed that the new approach is highly operational when applied to evaluate the risk assessment of several buildings adjacent to tunnel construction.

Data Availability
Te data used to support the fndings of this study are included within the article.

Conflicts of Interest
Te authors declare that they have no conficts of interest.