# Safety Assessment of Ancient Buildings under Adjacent Subway Blasting Construction Based on the Optimized Fuzzy Optimal Method

Authors: Bo Wu; Pingting Liu; Wei Huang; Guowang Meng
Journal: Shock and Vibration
 (2021)

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## Abstract

Fragile ancient buildings are recognized as an eloquent testimony to human civilization, and their safety should arouse more attention. According to the special case of adjacent blasting construction, the assessment model should be essentially built to assess the effect of tunnel blasting on the safety of the ancient buildings. To analyze the structural safety of ancient buildings under blasting vibration and to protect the precious ancient buildings, a risk assessment model of ancient buildings with 20 relevant assessment indexes was initiatively built in this study. To be specific, the relative factors of blasting, the factors of ancient buildings, and other factors (e.g., religion) were comprehensively considered in the model. Subsequently, the risk level and weight were calculated more systematically and quantitatively by adopting the optimized optimal comprehensive method integrating the G1 method and the entropy method. Lastly, the overall risk value was determined by applying the fuzzy gray method. Afterward, the value was adopted to assess the safety of the Asoka Temple, the only existing temple named after the Indian King Asoka in China, as an attempt to verify the feasibility of this model. Besides, the Asoka tunnel was around it. As demonstrated from the results, the age of the buildings maximally impacted the safety of ancient buildings, and the safety level of the Asoka Temple was “relatively safe.” The present study built an effective model to assess the safety of ancient buildings under adjacent subway blasting construction, which could help improve the efficiency and accuracy of assessments.


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## Body

## 1. Introduction

Ancient buildings are an eloquent testimony to the countries’ history and the embodiment of the countries’ culture. However, the safety and durability of the structures as well as the sensitivity to blasting of tunnel construction are decreasing with the aging of the buildings [1–3]. A reasonable safety assessment model should be built to assess the safety of ancient buildings and protect the ancient buildings from destruction. In this study, its own factors, the effect of vibration, and other factors (e.g., religion) were all considered to define the safety of ancient buildings to be no longer limited to safety of the structure, whereas a comprehensive safety assessment was conducted.Over the past few years, the analysis of ancient building structures has aroused huge attention from numerous researchers. Structural damage correlated with ancient buildings [4–10] has been extensively investigated, and ancient buildings [11–13] have been monitored and measured. Moreover, Xue et al. built an earthquake damage assessment model for Chinese ancient wooden structures to reveal the influences exerted by the vibration on the ancient building [14]. Qiu et al. examined the effect of vibration attributed to Xi’an subway during the tunnel excavation on Xi’an ancient circumvallation [15]. Thus, the architectural factor should be considered in the risk assessment. Wang et al. built a prioritization model for historic building conservation by complying with object element theory and then proposed a novel assessment decision method for subsequent heritage impacts following the metro lines [4]. Though the building structure has been extensively studied, most of the existing studies had certain limitations. To be specific, the safety of ancient buildings was only studied from a single perspective (e.g., vibration or structure). As indicated from the literature review, other factors (e.g., the public religious sentiment) should be considered when assessing the safety of ancient buildings [16]. Accordingly, a novel and comprehensive assessment model should be built given the factors of ancient buildings and the effect of other disciplines.According to engineering, risks are estimated by adopting some methods. Lu et al. [17] exploited the fuzzy COPRAS (complex proportional assessment) method to select the optimal green suppliers. Besides, the cross-entropy optimization model was adopted to objectively determine the weight vector, and a mathematical programming model of dual-objective probabilistic neural network was built to obtain the comprehensive attribute weights of two inconsistent indicators. The model was verified to be effective by conducting an example study. The entropy method was generally adopted for decision making. Furthermore, the G1 method is considered an optimized AHP method without the requirement for a consistency test. Though various studies have long been conducted on the risk analysis of ancient buildings, few researchers have comprehensively considered the factors and built an assessment model in numerous aspects. Accordingly, the optimal combination weighting method of entropy value method integrated with the G1 method could make the assessment more accurate and more effectively control the risk of ancient buildings as a whole.It is noteworthy that the Asoka Temple was taken as an example to verify and practically implement the model built by using the optimal weighting method, and the results were consistent with the relevant engineering practice. The mentioned assessment system based on the optimized fuzzy optimal method could effectively identify and reasonably assess the safety of ancient buildings, which showed the guiding significance to the subsequent protection of the ancient buildings.


## 2. Methodology

The steps shown in Figure1 were followed to assess the safety of the ancient building and optimize the risk assessment [18].Figure 1
Risk management steps.According to the mentioned steps, the safety assessment can be presented in Figure2. The specific risk assessment is illustrated in Figure 3.Figure 2
Safety assessment process.Figure 3
Specific process.


### 2.1. Basic Principle

#### 2.1.1. G1 Method and Its Improvement

In fact, the G1 method (order relation analysis method) [19] refers to a type of order relation analysis method without the requirement for a consistency test, thereby leading to a decrease in the computational complexity and an increase in the computation efficiency. The steps of the G1method (Figure 2) are as follows [19]:(1)
Determine the order relationship between the assessment indexesXm:(1)X1>X2>⋯>Xk−1>Xk>⋯>Xm.(2)
Judge the relative significance between the adjacent index:(2)rk=wk−1wk,k=m,m−1,m−2,…,3,2,whererk denotes the coefficient of significance of Xk−1 to Xk.(3)
The calculation of the weighting number:(3)wn=1+∑k=2n∏j=knrj−1.The weight matrix of the indexX=X1,X2,…,Xm:(4)W=w1w2⋯wnT.As impacted by the limitation of human cognition and the complexity of the risk problem, experts failed to accurately determine the specific order of the weight while providing the exact degree of the significance coefficient. Thus, the redefinition of the weight calculation coefficient was adopted during the calculation. Since the significance score recommended in the Guidelines [20] optimizes the significance comparison method, a significance assessment standard for the G1 method was proposed in this study, and experts were invited to compare the materiality of the respective risk indicator on a case-by-case basis. The novel expert scoring criteria [21] are listed in Table 1.Table 1
Expert scoring criteria of the significance.
The degree of significanceScoreParticularly important9-10Comparatively important6–8Important4-5Unimportant1–3


#### 2.1.2. Entropy Weight Method

To avoid the subjectivity of the results, an objective weighting method should be comprehensively selected. The entropy weight method [22, 23] has been extensively applied in problem decision making and exhibits strong objectivity. The entropy weight method was applied to the weight calculation to reduce the subjectivity brought by expert grading according to the G1 method. It could determine the weight of relevant factors by analyzing the amount of the information entropy of the respective indicator value [24, 25]. The smaller the information entropy is, the greater the weight of the indicator would be. However, the subjective intention of the decision maker could be easy to ignore. The risk fell to five levels based on ISO 31000 [20]. The risk scale is illustrated in Figure 4.Figure 4
Risk scales.Risk assessment criteria were formulated in accordance with the relevant codes [20, 26–31] and in consultation with experts in special fields. The experts invited consisted of researchers in the protection of ancient buildings, architectural protection engineers, government regulators, tunnel engineers, and tunnel technicians, who had high professional levels and huge engineering experiences and were in expert assessment teams. Subsequently, experts rated risk factors by complying with the criteria and actual situation of ancient buildings. The resulting risk scores were regarded as the entropy of each factor. In this study, the node value of risk classification and the data under the assessment of object indicators could jointly constitute the original indicator data. Afterward, the entropy value method could process the data to determine the ranking of the significance of the indicators. The specific steps are illustrated in Figure 2.


### 2.2. Assessment System Establishment

#### 2.2.1. Establishment of the System

In the present study, the factors (e.g., ancient buildings and blasting vibration) were considered with the references of Chinese regulations on ancient buildings and relevant literature to build the safety and risk assessment system of ancient buildings. To be specific, the developed risk system consisted of three floors. The first floor was the risk of ancient buildingsU. The second target floor was composed of the building factors U1, blasting vibration factors U2, and other factors U3.Given the literature review [5, 7, 11–13], this study subdivided the risk of ancient buildings into three target floors. U1 contained nine subfactors, U2 consisted of seven subfactors, and U3 covered four subfactors. The system is presented in Figure 5.Figure 5
The risk assessment system.Table2 lists the risk assessment criteria of the ancient buildings corresponding to risk factors in Figure 5. U11 (foundation type), U12 (age of the buildings), U13 (significance), and U14 (materials) represent the durability of the foundation of ancient buildings, the time of building the buildings, the protection level of the buildings in accordance with the national cultural relic classification standard, and the materials adopted to construct ancient buildings, respectively. U15 (durability), U16 (height), and U17 (size), respectively, denote the durability of ancient buildings, the height of the buildings, and the floor space of the ancient buildings. U18 (structure safety level) refers to the safety level of the ancient buildings assessed by the code [29]. Besides, U19 (velocity response) represents the gap between the velocity response and permissible velocity of vibration [30]. U21 (vibration source type), U22 (frequency range), U23 (source distribution), U24 (blasting methods), U25 (propagation velocity of an elastic wave), U26 (position between buildings and source), and U27 (distance between buildings and source), respectively, denote the cause of the vibration, the frequency exhibited by the blast, the type of blasting source distribution, the method rationality, the propagation velocity of an elastic wave, the position between buildings and source, and the distance between buildings and source. Furthermore, U31 (construction personnel management), U32 (public religious sentiment), U33 (engineering geological condition), and U34 (engineering hydrologic condition), respectively, represent the management during the construction, the public awareness and the degree of piety, the engineering geological condition, and the engineering hydrologic condition. A hierarchical assessment system was established, and the model fell to three levels. The correlation between the upper and lower levels was summarized and listed.Table 2
The score criteria of the risk.
0∼2 (V)2∼4 (IV)4∼6 (III)6∼8 (II)8∼10 (I)U11StableRelatively stableRelatively fragileFragileExtremely fragileU12The Old Stone AgeThe Neolithic AgeAncient timesModern timesU13National levelProvincial levelCity levelCounty levelTownship levelU14Grotto structureBrick masonry structureMasonry-timber structureStone structureTimber structureU15Good durabilityRelatively good durabilityRelatively bad durabilityBad durabilityExtremely bad durabilityU16>25 m20–25 m15–20 m10–15 m<10 mU17>100000 m210000–100000 m21000–10000 m2100–1000 m2<100 m2U184th level3rd level2nd level1st levelU19Much largerLargerApproximately equalLessMuch lessU21Dynamic compactionPilingCars, city trainsSubwayTrainU22<4 Hz4-7 Hz7–110 Hz10–13 Hz>13 HzU23ConcentratedRelatively concentratedRelatively sporadicSporadicExtremely sporadicU24ReasonableRelatively reasonableRelatively unreasonableUnreasonableExtremely unreasonableU251500 m/s2100–1500 m/s2900–2100 m/s5600–2900 m/s>5600 m/sU26UndergroundOvergroundU27<100 m100–400 m400–700 m700–1000 m>1000 mU31StrictRelatively strictGeneralRelatively freeFreeU32StrongRelatively strongGeneralRelatively weakWeakU33StrongRelatively strongGeneralRelatively weakWeakU34StrongRelatively strongGeneralRelatively weakWeak


### 2.3. Weight Setting

#### 2.3.1. Combination Weighting Method

The combined weighting method [32] could indicate the opinions and preferences of decision makers, as well as the laws of objective data. Besides, the difference between subjective weight and objective weight complied with the difference between their corresponding distribution coefficients. The combination coefficient of subjective factors and objective factors was determined by equations (5)–(10) to yield the combination weight. Subjective weighting was determined by consulting the opinions of relevant experts, followed by the entropy according to statistics. The optimal combination weighting model was built to address the unreasonable weight problem of single weighting. The steps to obtain the combined weight are illustrated in Figure 6.Figure 6
Combined weight steps.The combination weight method should determine the combination weight coefficient in accordance with the following two factors.The first was to ensure the minimum distance between the weighted score of each assessment object and the ideal generalized point in the following formula.(5)min∑i=1nli=∑i=1n∑j=1m∑c=1sαcwjc1−vij.The second was Jaynes maximum entropy principle [7], capable of avoiding the contribution error of various weighting results to the combined weighting results to the maximal extent.The objective function built by the idea of minimizing the difference of the respective weighting result could simplify the calculation:(6)maxZ=−∑c=1sαclnαc,(7)minθ∑i=1n∑j=1m∑c=1sαcwjc1−vij+1−θ∑c=1sαclnαc,s.t.∑c=1sαc=1,vc≥0,where α denotes the balance coefficient between the two targets, 0≤θ≤1, θ=0.5. Given the mentioned two factors, the Lagrange function could yield the combination weight coefficient and the value of αc:(8)αc=exp−1+θ∑i=1n∑j=1mwjc1−vij/1−θ∑i=1sexp−1+θ∑i=1n∑j=1mwjc1−vij/1−θ.The combination weightw [32]:(9)w=∑c=1sαcwc,where wc represents the weight of the index obtained by a single method.(10)∑c=1sαc=1.


### 2.4. Comprehensive Safety Assessment

#### 2.4.1. Gray Fuzzy Analysis Method

By using the gray fuzzy assessment method to the risk assessment of ancient buildings, the cognitive differences attributed to evaluators could be avoided to a certain extent, and the scientific nature of the assessment results could be improved. The process of the gray theory [33, 34] calculation (sample assessment matrix construction ⟶ determination of the whitening weight function ⟶ construction of gray assessment matrix), the whitening weight function, and gray assessment matrix were acquired by the following equations [35].(1) Sample Assessment Matrix Construction. The risk assessment level vector can be acquired based on the established risk assessment indicators system:(11)V=v1,v2,v3,…,vt,where t represents the number of risk levels. By using the Delphi method [21], p experts invited independently scored the respective indicator with the consideration of the assessment level vector V. Set the jth expert’s assessment value of the jth secondary indicator of the first-level indicator Ui of the criterion level as dijq. The final sample assessment matrix D obtained is written as(12)D=d111d121⋯dij1⋯dnni1d112d122⋯dij2⋯dmni2⋮⋮⋮⋮d11qd12q⋯dijq⋯dmniq⋮⋮⋮⋮d11pd12p⋯dijp⋯dmnip,where i = 1, 2, 3, …, n; j = 1, 2, 3, …, n; i, q = 1, 2, …, p;(2) Determination of the Whitening Weight Function. The determination of the whitening function was different due to the different assessment objects. The function used in the gray assessment method was determined abiding by the literature and the practical assessment of this study. In the present study, the risk fell to five levels. Thus, we chose the five gray assessment model [36]. The functions that can be used to construct the gray assessment matrix in the gray statistical method are listed in Table 3.Table 3
Gray whitening weight function.
The gray classLeveleFunctionThe first gray classSafe1fe=1vij=vij/9vij∈0,91vij∈9,10The second gray classRelatively safe2fe=2vij=vij/7vij∈0,72−vij/7vij∈7,10The third gray classRelatively dangerous3fe=3vij=vij/5vij∈0,52−vij/5vij∈5,100vij∉5,10The fourth gray classDangerous4fe=4vij=vij/3vij∈0,32−vij/3vij∈5,60vij∉5,6The fifth gray classExtremely dangerous5fe=5vij=1vij∈0,12−vijvij∈1,20vij∉2,10(3) Construction of Gray Assessment Matrix. It can be assumed that there are E gray classes. The whitening weight functions fe were determined by the gray statistics method. Subsequently, the whitening weights of the assessment sample dijq pertaining to the e (e = 1, 2, 3, …, E) gray classes were calculated. E of the gray class of the whitening weights was fe (dijq).The following equations represent the gray statisticsnije of the index Uij pertaining to the eth gray class and the total gray statistics nij, respectively [36]:(13)nije=∑q=1pfedijq,nij=∑e=1Enije.Based on the gray statistics and the total gray statistics, the gray assessment weightzije could be calculated by(14)zije=nijenij.In the above equation, the value ofzije indicates how strongly all experts advocate that Uij belongs to the eth gray class. The gray assessment weight vector Zi=zij1,zij2,…,zije,…,zijE of Uij for each assessment gray class can be obtained from zije. In turn, the gray assessment matrix Z of indicator Uij on each assessment gray class is expressed as(15)Z=Z1Z2⋮Zi⋮Zn=z111z112⋯z11e⋯z11Ez121z122⋯z12e⋯z12E⋮⋮⋮⋮⋮⋮zij1zij2⋯zije⋯zijE⋮⋮⋮⋮⋮⋮znni1znni2⋯znnie⋯znniEi=1,2,…,E.


#### 2.4.2. Gray Relation Sensitivity Analysis

The advantage of gray relational degree analysis is that it can be easy to calculate, and there will be no inconsistency between the quantitative results and the qualitative results. The calculated steps are represented as follows.(1)
Prioritization:m represents the number of assessment samples; n represents risk assessment index;xi¯ is the mean value of the index set; and x0 is the reference sample. We set it as the final risk in the gray fuzzy method in this article. The original assessment matrix xi′ is [37](16)xi′=x′1,x′2,…,x′m,xi=xi1xi¯,xi2xi¯,…,ximxi¯,wherei=0,1,2,…,n.(2)
Absolute differenceΔik calculation:(17)Δik=x0k−xik,wherek=0,1,2,…,m.(3)
Calculation of correlation coefficientζik:(18)ζik=Δmin+ρΔmaxΔik+ρΔmax,whereρ=0.5.(4)
Gray correlationri calculation:(19)ri=1m∑k=1mζik.The greater the correlation is, the weaker the uncertainty and the less the sensitivity would be.


#### 2.4.3. Comprehensive Assessment

Based on the weight vectorW and the gray assessment matrix Z obtained by the optimized combination method and the gray statistical method, respectively, their product was the comprehensive assessment vector H [24]:(20)H=W∗Z.Under the combination of the integrated assessment vectorH and the risk level vector V, the overall structural safety assessment value risk of the system was the product of the H and the risk level vector V:(21)Risk=H∗VT.During the practical assessment process, the most intuitive way was to express the risk status of the system as quantitative assessment values.Risk denotes the final risk assessment value of the system. The safety risk level of the system could be determined through the combination with the risk assessment level vector V. It laid a scientific and effective reference basis for assessing the safety of ancient building structures.


## 2.1. Basic Principle

### 2.1.1. G1 Method and Its Improvement

In fact, the G1 method (order relation analysis method) [19] refers to a type of order relation analysis method without the requirement for a consistency test, thereby leading to a decrease in the computational complexity and an increase in the computation efficiency. The steps of the G1method (Figure 2) are as follows [19]:(1)
Determine the order relationship between the assessment indexesXm:(1)X1>X2>⋯>Xk−1>Xk>⋯>Xm.(2)
Judge the relative significance between the adjacent index:(2)rk=wk−1wk,k=m,m−1,m−2,…,3,2,whererk denotes the coefficient of significance of Xk−1 to Xk.(3)
The calculation of the weighting number:(3)wn=1+∑k=2n∏j=knrj−1.The weight matrix of the indexX=X1,X2,…,Xm:(4)W=w1w2⋯wnT.As impacted by the limitation of human cognition and the complexity of the risk problem, experts failed to accurately determine the specific order of the weight while providing the exact degree of the significance coefficient. Thus, the redefinition of the weight calculation coefficient was adopted during the calculation. Since the significance score recommended in the Guidelines [20] optimizes the significance comparison method, a significance assessment standard for the G1 method was proposed in this study, and experts were invited to compare the materiality of the respective risk indicator on a case-by-case basis. The novel expert scoring criteria [21] are listed in Table 1.Table 1
Expert scoring criteria of the significance.
The degree of significanceScoreParticularly important9-10Comparatively important6–8Important4-5Unimportant1–3


### 2.1.2. Entropy Weight Method

To avoid the subjectivity of the results, an objective weighting method should be comprehensively selected. The entropy weight method [22, 23] has been extensively applied in problem decision making and exhibits strong objectivity. The entropy weight method was applied to the weight calculation to reduce the subjectivity brought by expert grading according to the G1 method. It could determine the weight of relevant factors by analyzing the amount of the information entropy of the respective indicator value [24, 25]. The smaller the information entropy is, the greater the weight of the indicator would be. However, the subjective intention of the decision maker could be easy to ignore. The risk fell to five levels based on ISO 31000 [20]. The risk scale is illustrated in Figure 4.Figure 4
Risk scales.Risk assessment criteria were formulated in accordance with the relevant codes [20, 26–31] and in consultation with experts in special fields. The experts invited consisted of researchers in the protection of ancient buildings, architectural protection engineers, government regulators, tunnel engineers, and tunnel technicians, who had high professional levels and huge engineering experiences and were in expert assessment teams. Subsequently, experts rated risk factors by complying with the criteria and actual situation of ancient buildings. The resulting risk scores were regarded as the entropy of each factor. In this study, the node value of risk classification and the data under the assessment of object indicators could jointly constitute the original indicator data. Afterward, the entropy value method could process the data to determine the ranking of the significance of the indicators. The specific steps are illustrated in Figure 2.


## 2.1.1. G1 Method and Its Improvement

In fact, the G1 method (order relation analysis method) [19] refers to a type of order relation analysis method without the requirement for a consistency test, thereby leading to a decrease in the computational complexity and an increase in the computation efficiency. The steps of the G1method (Figure 2) are as follows [19]:(1)
Determine the order relationship between the assessment indexesXm:(1)X1>X2>⋯>Xk−1>Xk>⋯>Xm.(2)
Judge the relative significance between the adjacent index:(2)rk=wk−1wk,k=m,m−1,m−2,…,3,2,whererk denotes the coefficient of significance of Xk−1 to Xk.(3)
The calculation of the weighting number:(3)wn=1+∑k=2n∏j=knrj−1.The weight matrix of the indexX=X1,X2,…,Xm:(4)W=w1w2⋯wnT.As impacted by the limitation of human cognition and the complexity of the risk problem, experts failed to accurately determine the specific order of the weight while providing the exact degree of the significance coefficient. Thus, the redefinition of the weight calculation coefficient was adopted during the calculation. Since the significance score recommended in the Guidelines [20] optimizes the significance comparison method, a significance assessment standard for the G1 method was proposed in this study, and experts were invited to compare the materiality of the respective risk indicator on a case-by-case basis. The novel expert scoring criteria [21] are listed in Table 1.Table 1
Expert scoring criteria of the significance.
The degree of significanceScoreParticularly important9-10Comparatively important6–8Important4-5Unimportant1–3


## 2.1.2. Entropy Weight Method

To avoid the subjectivity of the results, an objective weighting method should be comprehensively selected. The entropy weight method [22, 23] has been extensively applied in problem decision making and exhibits strong objectivity. The entropy weight method was applied to the weight calculation to reduce the subjectivity brought by expert grading according to the G1 method. It could determine the weight of relevant factors by analyzing the amount of the information entropy of the respective indicator value [24, 25]. The smaller the information entropy is, the greater the weight of the indicator would be. However, the subjective intention of the decision maker could be easy to ignore. The risk fell to five levels based on ISO 31000 [20]. The risk scale is illustrated in Figure 4.Figure 4
Risk scales.Risk assessment criteria were formulated in accordance with the relevant codes [20, 26–31] and in consultation with experts in special fields. The experts invited consisted of researchers in the protection of ancient buildings, architectural protection engineers, government regulators, tunnel engineers, and tunnel technicians, who had high professional levels and huge engineering experiences and were in expert assessment teams. Subsequently, experts rated risk factors by complying with the criteria and actual situation of ancient buildings. The resulting risk scores were regarded as the entropy of each factor. In this study, the node value of risk classification and the data under the assessment of object indicators could jointly constitute the original indicator data. Afterward, the entropy value method could process the data to determine the ranking of the significance of the indicators. The specific steps are illustrated in Figure 2.


## 2.2. Assessment System Establishment

### 2.2.1. Establishment of the System

In the present study, the factors (e.g., ancient buildings and blasting vibration) were considered with the references of Chinese regulations on ancient buildings and relevant literature to build the safety and risk assessment system of ancient buildings. To be specific, the developed risk system consisted of three floors. The first floor was the risk of ancient buildingsU. The second target floor was composed of the building factors U1, blasting vibration factors U2, and other factors U3.Given the literature review [5, 7, 11–13], this study subdivided the risk of ancient buildings into three target floors. U1 contained nine subfactors, U2 consisted of seven subfactors, and U3 covered four subfactors. The system is presented in Figure 5.Figure 5
The risk assessment system.Table2 lists the risk assessment criteria of the ancient buildings corresponding to risk factors in Figure 5. U11 (foundation type), U12 (age of the buildings), U13 (significance), and U14 (materials) represent the durability of the foundation of ancient buildings, the time of building the buildings, the protection level of the buildings in accordance with the national cultural relic classification standard, and the materials adopted to construct ancient buildings, respectively. U15 (durability), U16 (height), and U17 (size), respectively, denote the durability of ancient buildings, the height of the buildings, and the floor space of the ancient buildings. U18 (structure safety level) refers to the safety level of the ancient buildings assessed by the code [29]. Besides, U19 (velocity response) represents the gap between the velocity response and permissible velocity of vibration [30]. U21 (vibration source type), U22 (frequency range), U23 (source distribution), U24 (blasting methods), U25 (propagation velocity of an elastic wave), U26 (position between buildings and source), and U27 (distance between buildings and source), respectively, denote the cause of the vibration, the frequency exhibited by the blast, the type of blasting source distribution, the method rationality, the propagation velocity of an elastic wave, the position between buildings and source, and the distance between buildings and source. Furthermore, U31 (construction personnel management), U32 (public religious sentiment), U33 (engineering geological condition), and U34 (engineering hydrologic condition), respectively, represent the management during the construction, the public awareness and the degree of piety, the engineering geological condition, and the engineering hydrologic condition. A hierarchical assessment system was established, and the model fell to three levels. The correlation between the upper and lower levels was summarized and listed.Table 2
The score criteria of the risk.
0∼2 (V)2∼4 (IV)4∼6 (III)6∼8 (II)8∼10 (I)U11StableRelatively stableRelatively fragileFragileExtremely fragileU12The Old Stone AgeThe Neolithic AgeAncient timesModern timesU13National levelProvincial levelCity levelCounty levelTownship levelU14Grotto structureBrick masonry structureMasonry-timber structureStone structureTimber structureU15Good durabilityRelatively good durabilityRelatively bad durabilityBad durabilityExtremely bad durabilityU16>25 m20–25 m15–20 m10–15 m<10 mU17>100000 m210000–100000 m21000–10000 m2100–1000 m2<100 m2U184th level3rd level2nd level1st levelU19Much largerLargerApproximately equalLessMuch lessU21Dynamic compactionPilingCars, city trainsSubwayTrainU22<4 Hz4-7 Hz7–110 Hz10–13 Hz>13 HzU23ConcentratedRelatively concentratedRelatively sporadicSporadicExtremely sporadicU24ReasonableRelatively reasonableRelatively unreasonableUnreasonableExtremely unreasonableU251500 m/s2100–1500 m/s2900–2100 m/s5600–2900 m/s>5600 m/sU26UndergroundOvergroundU27<100 m100–400 m400–700 m700–1000 m>1000 mU31StrictRelatively strictGeneralRelatively freeFreeU32StrongRelatively strongGeneralRelatively weakWeakU33StrongRelatively strongGeneralRelatively weakWeakU34StrongRelatively strongGeneralRelatively weakWeak


## 2.2.1. Establishment of the System

In the present study, the factors (e.g., ancient buildings and blasting vibration) were considered with the references of Chinese regulations on ancient buildings and relevant literature to build the safety and risk assessment system of ancient buildings. To be specific, the developed risk system consisted of three floors. The first floor was the risk of ancient buildingsU. The second target floor was composed of the building factors U1, blasting vibration factors U2, and other factors U3.Given the literature review [5, 7, 11–13], this study subdivided the risk of ancient buildings into three target floors. U1 contained nine subfactors, U2 consisted of seven subfactors, and U3 covered four subfactors. The system is presented in Figure 5.Figure 5
The risk assessment system.Table2 lists the risk assessment criteria of the ancient buildings corresponding to risk factors in Figure 5. U11 (foundation type), U12 (age of the buildings), U13 (significance), and U14 (materials) represent the durability of the foundation of ancient buildings, the time of building the buildings, the protection level of the buildings in accordance with the national cultural relic classification standard, and the materials adopted to construct ancient buildings, respectively. U15 (durability), U16 (height), and U17 (size), respectively, denote the durability of ancient buildings, the height of the buildings, and the floor space of the ancient buildings. U18 (structure safety level) refers to the safety level of the ancient buildings assessed by the code [29]. Besides, U19 (velocity response) represents the gap between the velocity response and permissible velocity of vibration [30]. U21 (vibration source type), U22 (frequency range), U23 (source distribution), U24 (blasting methods), U25 (propagation velocity of an elastic wave), U26 (position between buildings and source), and U27 (distance between buildings and source), respectively, denote the cause of the vibration, the frequency exhibited by the blast, the type of blasting source distribution, the method rationality, the propagation velocity of an elastic wave, the position between buildings and source, and the distance between buildings and source. Furthermore, U31 (construction personnel management), U32 (public religious sentiment), U33 (engineering geological condition), and U34 (engineering hydrologic condition), respectively, represent the management during the construction, the public awareness and the degree of piety, the engineering geological condition, and the engineering hydrologic condition. A hierarchical assessment system was established, and the model fell to three levels. The correlation between the upper and lower levels was summarized and listed.Table 2
The score criteria of the risk.
0∼2 (V)2∼4 (IV)4∼6 (III)6∼8 (II)8∼10 (I)U11StableRelatively stableRelatively fragileFragileExtremely fragileU12The Old Stone AgeThe Neolithic AgeAncient timesModern timesU13National levelProvincial levelCity levelCounty levelTownship levelU14Grotto structureBrick masonry structureMasonry-timber structureStone structureTimber structureU15Good durabilityRelatively good durabilityRelatively bad durabilityBad durabilityExtremely bad durabilityU16>25 m20–25 m15–20 m10–15 m<10 mU17>100000 m210000–100000 m21000–10000 m2100–1000 m2<100 m2U184th level3rd level2nd level1st levelU19Much largerLargerApproximately equalLessMuch lessU21Dynamic compactionPilingCars, city trainsSubwayTrainU22<4 Hz4-7 Hz7–110 Hz10–13 Hz>13 HzU23ConcentratedRelatively concentratedRelatively sporadicSporadicExtremely sporadicU24ReasonableRelatively reasonableRelatively unreasonableUnreasonableExtremely unreasonableU251500 m/s2100–1500 m/s2900–2100 m/s5600–2900 m/s>5600 m/sU26UndergroundOvergroundU27<100 m100–400 m400–700 m700–1000 m>1000 mU31StrictRelatively strictGeneralRelatively freeFreeU32StrongRelatively strongGeneralRelatively weakWeakU33StrongRelatively strongGeneralRelatively weakWeakU34StrongRelatively strongGeneralRelatively weakWeak


## 2.3. Weight Setting

### 2.3.1. Combination Weighting Method

The combined weighting method [32] could indicate the opinions and preferences of decision makers, as well as the laws of objective data. Besides, the difference between subjective weight and objective weight complied with the difference between their corresponding distribution coefficients. The combination coefficient of subjective factors and objective factors was determined by equations (5)–(10) to yield the combination weight. Subjective weighting was determined by consulting the opinions of relevant experts, followed by the entropy according to statistics. The optimal combination weighting model was built to address the unreasonable weight problem of single weighting. The steps to obtain the combined weight are illustrated in Figure 6.Figure 6
Combined weight steps.The combination weight method should determine the combination weight coefficient in accordance with the following two factors.The first was to ensure the minimum distance between the weighted score of each assessment object and the ideal generalized point in the following formula.(5)min∑i=1nli=∑i=1n∑j=1m∑c=1sαcwjc1−vij.The second was Jaynes maximum entropy principle [7], capable of avoiding the contribution error of various weighting results to the combined weighting results to the maximal extent.The objective function built by the idea of minimizing the difference of the respective weighting result could simplify the calculation:(6)maxZ=−∑c=1sαclnαc,(7)minθ∑i=1n∑j=1m∑c=1sαcwjc1−vij+1−θ∑c=1sαclnαc,s.t.∑c=1sαc=1,vc≥0,where α denotes the balance coefficient between the two targets, 0≤θ≤1, θ=0.5. Given the mentioned two factors, the Lagrange function could yield the combination weight coefficient and the value of αc:(8)αc=exp−1+θ∑i=1n∑j=1mwjc1−vij/1−θ∑i=1sexp−1+θ∑i=1n∑j=1mwjc1−vij/1−θ.The combination weightw [32]:(9)w=∑c=1sαcwc,where wc represents the weight of the index obtained by a single method.(10)∑c=1sαc=1.


## 2.3.1. Combination Weighting Method

The combined weighting method [32] could indicate the opinions and preferences of decision makers, as well as the laws of objective data. Besides, the difference between subjective weight and objective weight complied with the difference between their corresponding distribution coefficients. The combination coefficient of subjective factors and objective factors was determined by equations (5)–(10) to yield the combination weight. Subjective weighting was determined by consulting the opinions of relevant experts, followed by the entropy according to statistics. The optimal combination weighting model was built to address the unreasonable weight problem of single weighting. The steps to obtain the combined weight are illustrated in Figure 6.Figure 6
Combined weight steps.The combination weight method should determine the combination weight coefficient in accordance with the following two factors.The first was to ensure the minimum distance between the weighted score of each assessment object and the ideal generalized point in the following formula.(5)min∑i=1nli=∑i=1n∑j=1m∑c=1sαcwjc1−vij.The second was Jaynes maximum entropy principle [7], capable of avoiding the contribution error of various weighting results to the combined weighting results to the maximal extent.The objective function built by the idea of minimizing the difference of the respective weighting result could simplify the calculation:(6)maxZ=−∑c=1sαclnαc,(7)minθ∑i=1n∑j=1m∑c=1sαcwjc1−vij+1−θ∑c=1sαclnαc,s.t.∑c=1sαc=1,vc≥0,where α denotes the balance coefficient between the two targets, 0≤θ≤1, θ=0.5. Given the mentioned two factors, the Lagrange function could yield the combination weight coefficient and the value of αc:(8)αc=exp−1+θ∑i=1n∑j=1mwjc1−vij/1−θ∑i=1sexp−1+θ∑i=1n∑j=1mwjc1−vij/1−θ.The combination weightw [32]:(9)w=∑c=1sαcwc,where wc represents the weight of the index obtained by a single method.(10)∑c=1sαc=1.


## 2.4. Comprehensive Safety Assessment

### 2.4.1. Gray Fuzzy Analysis Method

By using the gray fuzzy assessment method to the risk assessment of ancient buildings, the cognitive differences attributed to evaluators could be avoided to a certain extent, and the scientific nature of the assessment results could be improved. The process of the gray theory [33, 34] calculation (sample assessment matrix construction ⟶ determination of the whitening weight function ⟶ construction of gray assessment matrix), the whitening weight function, and gray assessment matrix were acquired by the following equations [35].(1) Sample Assessment Matrix Construction. The risk assessment level vector can be acquired based on the established risk assessment indicators system:(11)V=v1,v2,v3,…,vt,where t represents the number of risk levels. By using the Delphi method [21], p experts invited independently scored the respective indicator with the consideration of the assessment level vector V. Set the jth expert’s assessment value of the jth secondary indicator of the first-level indicator Ui of the criterion level as dijq. The final sample assessment matrix D obtained is written as(12)D=d111d121⋯dij1⋯dnni1d112d122⋯dij2⋯dmni2⋮⋮⋮⋮d11qd12q⋯dijq⋯dmniq⋮⋮⋮⋮d11pd12p⋯dijp⋯dmnip,where i = 1, 2, 3, …, n; j = 1, 2, 3, …, n; i, q = 1, 2, …, p;(2) Determination of the Whitening Weight Function. The determination of the whitening function was different due to the different assessment objects. The function used in the gray assessment method was determined abiding by the literature and the practical assessment of this study. In the present study, the risk fell to five levels. Thus, we chose the five gray assessment model [36]. The functions that can be used to construct the gray assessment matrix in the gray statistical method are listed in Table 3.Table 3
Gray whitening weight function.
The gray classLeveleFunctionThe first gray classSafe1fe=1vij=vij/9vij∈0,91vij∈9,10The second gray classRelatively safe2fe=2vij=vij/7vij∈0,72−vij/7vij∈7,10The third gray classRelatively dangerous3fe=3vij=vij/5vij∈0,52−vij/5vij∈5,100vij∉5,10The fourth gray classDangerous4fe=4vij=vij/3vij∈0,32−vij/3vij∈5,60vij∉5,6The fifth gray classExtremely dangerous5fe=5vij=1vij∈0,12−vijvij∈1,20vij∉2,10(3) Construction of Gray Assessment Matrix. It can be assumed that there are E gray classes. The whitening weight functions fe were determined by the gray statistics method. Subsequently, the whitening weights of the assessment sample dijq pertaining to the e (e = 1, 2, 3, …, E) gray classes were calculated. E of the gray class of the whitening weights was fe (dijq).The following equations represent the gray statisticsnije of the index Uij pertaining to the eth gray class and the total gray statistics nij, respectively [36]:(13)nije=∑q=1pfedijq,nij=∑e=1Enije.Based on the gray statistics and the total gray statistics, the gray assessment weightzije could be calculated by(14)zije=nijenij.In the above equation, the value ofzije indicates how strongly all experts advocate that Uij belongs to the eth gray class. The gray assessment weight vector Zi=zij1,zij2,…,zije,…,zijE of Uij for each assessment gray class can be obtained from zije. In turn, the gray assessment matrix Z of indicator Uij on each assessment gray class is expressed as(15)Z=Z1Z2⋮Zi⋮Zn=z111z112⋯z11e⋯z11Ez121z122⋯z12e⋯z12E⋮⋮⋮⋮⋮⋮zij1zij2⋯zije⋯zijE⋮⋮⋮⋮⋮⋮znni1znni2⋯znnie⋯znniEi=1,2,…,E.


### 2.4.2. Gray Relation Sensitivity Analysis

The advantage of gray relational degree analysis is that it can be easy to calculate, and there will be no inconsistency between the quantitative results and the qualitative results. The calculated steps are represented as follows.(1)
Prioritization:m represents the number of assessment samples; n represents risk assessment index;xi¯ is the mean value of the index set; and x0 is the reference sample. We set it as the final risk in the gray fuzzy method in this article. The original assessment matrix xi′ is [37](16)xi′=x′1,x′2,…,x′m,xi=xi1xi¯,xi2xi¯,…,ximxi¯,wherei=0,1,2,…,n.(2)
Absolute differenceΔik calculation:(17)Δik=x0k−xik,wherek=0,1,2,…,m.(3)
Calculation of correlation coefficientζik:(18)ζik=Δmin+ρΔmaxΔik+ρΔmax,whereρ=0.5.(4)
Gray correlationri calculation:(19)ri=1m∑k=1mζik.The greater the correlation is, the weaker the uncertainty and the less the sensitivity would be.


### 2.4.3. Comprehensive Assessment

Based on the weight vectorW and the gray assessment matrix Z obtained by the optimized combination method and the gray statistical method, respectively, their product was the comprehensive assessment vector H [24]:(20)H=W∗Z.Under the combination of the integrated assessment vectorH and the risk level vector V, the overall structural safety assessment value risk of the system was the product of the H and the risk level vector V:(21)Risk=H∗VT.During the practical assessment process, the most intuitive way was to express the risk status of the system as quantitative assessment values.Risk denotes the final risk assessment value of the system. The safety risk level of the system could be determined through the combination with the risk assessment level vector V. It laid a scientific and effective reference basis for assessing the safety of ancient building structures.


## 2.4.1. Gray Fuzzy Analysis Method

By using the gray fuzzy assessment method to the risk assessment of ancient buildings, the cognitive differences attributed to evaluators could be avoided to a certain extent, and the scientific nature of the assessment results could be improved. The process of the gray theory [33, 34] calculation (sample assessment matrix construction ⟶ determination of the whitening weight function ⟶ construction of gray assessment matrix), the whitening weight function, and gray assessment matrix were acquired by the following equations [35].(1) Sample Assessment Matrix Construction. The risk assessment level vector can be acquired based on the established risk assessment indicators system:(11)V=v1,v2,v3,…,vt,where t represents the number of risk levels. By using the Delphi method [21], p experts invited independently scored the respective indicator with the consideration of the assessment level vector V. Set the jth expert’s assessment value of the jth secondary indicator of the first-level indicator Ui of the criterion level as dijq. The final sample assessment matrix D obtained is written as(12)D=d111d121⋯dij1⋯dnni1d112d122⋯dij2⋯dmni2⋮⋮⋮⋮d11qd12q⋯dijq⋯dmniq⋮⋮⋮⋮d11pd12p⋯dijp⋯dmnip,where i = 1, 2, 3, …, n; j = 1, 2, 3, …, n; i, q = 1, 2, …, p;(2) Determination of the Whitening Weight Function. The determination of the whitening function was different due to the different assessment objects. The function used in the gray assessment method was determined abiding by the literature and the practical assessment of this study. In the present study, the risk fell to five levels. Thus, we chose the five gray assessment model [36]. The functions that can be used to construct the gray assessment matrix in the gray statistical method are listed in Table 3.Table 3
Gray whitening weight function.
The gray classLeveleFunctionThe first gray classSafe1fe=1vij=vij/9vij∈0,91vij∈9,10The second gray classRelatively safe2fe=2vij=vij/7vij∈0,72−vij/7vij∈7,10The third gray classRelatively dangerous3fe=3vij=vij/5vij∈0,52−vij/5vij∈5,100vij∉5,10The fourth gray classDangerous4fe=4vij=vij/3vij∈0,32−vij/3vij∈5,60vij∉5,6The fifth gray classExtremely dangerous5fe=5vij=1vij∈0,12−vijvij∈1,20vij∉2,10(3) Construction of Gray Assessment Matrix. It can be assumed that there are E gray classes. The whitening weight functions fe were determined by the gray statistics method. Subsequently, the whitening weights of the assessment sample dijq pertaining to the e (e = 1, 2, 3, …, E) gray classes were calculated. E of the gray class of the whitening weights was fe (dijq).The following equations represent the gray statisticsnije of the index Uij pertaining to the eth gray class and the total gray statistics nij, respectively [36]:(13)nije=∑q=1pfedijq,nij=∑e=1Enije.Based on the gray statistics and the total gray statistics, the gray assessment weightzije could be calculated by(14)zije=nijenij.In the above equation, the value ofzije indicates how strongly all experts advocate that Uij belongs to the eth gray class. The gray assessment weight vector Zi=zij1,zij2,…,zije,…,zijE of Uij for each assessment gray class can be obtained from zije. In turn, the gray assessment matrix Z of indicator Uij on each assessment gray class is expressed as(15)Z=Z1Z2⋮Zi⋮Zn=z111z112⋯z11e⋯z11Ez121z122⋯z12e⋯z12E⋮⋮⋮⋮⋮⋮zij1zij2⋯zije⋯zijE⋮⋮⋮⋮⋮⋮znni1znni2⋯znnie⋯znniEi=1,2,…,E.


## 2.4.2. Gray Relation Sensitivity Analysis

The advantage of gray relational degree analysis is that it can be easy to calculate, and there will be no inconsistency between the quantitative results and the qualitative results. The calculated steps are represented as follows.(1)
Prioritization:m represents the number of assessment samples; n represents risk assessment index;xi¯ is the mean value of the index set; and x0 is the reference sample. We set it as the final risk in the gray fuzzy method in this article. The original assessment matrix xi′ is [37](16)xi′=x′1,x′2,…,x′m,xi=xi1xi¯,xi2xi¯,…,ximxi¯,wherei=0,1,2,…,n.(2)
Absolute differenceΔik calculation:(17)Δik=x0k−xik,wherek=0,1,2,…,m.(3)
Calculation of correlation coefficientζik:(18)ζik=Δmin+ρΔmaxΔik+ρΔmax,whereρ=0.5.(4)
Gray correlationri calculation:(19)ri=1m∑k=1mζik.The greater the correlation is, the weaker the uncertainty and the less the sensitivity would be.


## 2.4.3. Comprehensive Assessment

Based on the weight vectorW and the gray assessment matrix Z obtained by the optimized combination method and the gray statistical method, respectively, their product was the comprehensive assessment vector H [24]:(20)H=W∗Z.Under the combination of the integrated assessment vectorH and the risk level vector V, the overall structural safety assessment value risk of the system was the product of the H and the risk level vector V:(21)Risk=H∗VT.During the practical assessment process, the most intuitive way was to express the risk status of the system as quantitative assessment values.Risk denotes the final risk assessment value of the system. The safety risk level of the system could be determined through the combination with the risk assessment level vector V. It laid a scientific and effective reference basis for assessing the safety of ancient building structures.


## 3. A Case Study

### 3.1. The Study Area

The Asoka Temple was initially established in the third year of Taikang emperor of the Western Jin Dynasty (282 AD) with a history of over 1,700 years, located in Yinzhou District of Ningbo. The Asoka Temple is known as the “Southeast Buddhist country.” It refers to famous 283 temples of Zen Buddhism and one of the Chinese Buddhism “five mountains.” Moreover, it is the only existing thousand-year-old temple in China named after the Indian King Asoka. The temple is notable for its treasure of Sakyamuni Buddha and exquisite pagoda. There are numerous scenic spots and historical sites close to King Asoka Temple. The plan is presented in Figure7. The Asoka Temple takes up a crucial position to inherit the favorable Buddhist cultural tradition and carry forward the Buddhist cultural thoughts in the history of Buddhism for its historical and cultural value.Figure 7
The plan of the Asoka Temple.Given the urban transportation planning, the Treasure House Station of the Ningbo rail transit 1st line 2nd phase went through the Asoka Temple. The Asoka tunnel refers to the only tunnel project in Ningbo with drilling and blasting construction methods. The construction of the tunnel went through the fault fracture zone. Moreover, the surrounding environment of this tunnel is complex. The upper soil slope section exhibits poor stability. Several parts of the tunnel exit are made up of gravel silty clay, intensely weathered rhyolite porphyry, moderately weathered rhyolite porphyry, and fault fracture zone. The rock mass was relatively cracked and underwent strong weathering. This project exhibits poor self-steady ability. The core protection area of Asoka Temple, a national-level cultural relic protection unit, is approximately 98.6 m away from the tunnel. Figure8 illustrates the relative position between the subway and the temple. Thus, blasting vibration is capable of easily affecting the safety of the Asoka Temple and the stability of the existing railways. A safety assessment is required for the Asoka Temple.Figure 8
The location map of the Asoka Temple.


### 3.2. The Weight Results and Analysis

#### 3.2.1. G1 Methods

Ten experts were invited to fill in the scoring form in Table4. Experts scored the significance of risk indicators abiding by the criteria in Table 1.Table 4
Expert scores.
IndicatorsA1A2…AmScoreXA1JXA2J…XAmJThe weight obtained by the subjective assessment method of the first index and the secondary index is listed in Table5.Table 5
Risk factor of G1 method.
The 2nd indicatorThe 2nd weightThe 3rd indicatorThe 3rd weightTotal weightUU10.4U110.150.06U120.210.084U130.080.032U140.120.048U150.110.044U160.080.032U170.050.02U180.130.052U190.070.028U20.5U210.130.052U220.150.06U230.160.064U240.180.072U250.120.048U260.110.044U270.150.06U30.1U310.320.032U320.150.015U330.320.032U340.210.021


#### 3.2.2. Risk Factor Weight Values Determined Based on Entropy Weighting Method

Ten experts scored the 20 indicators by using the safety assessment system, as listed in Table2. The score ranged from 1 to 10, with the most significance when reaching 10 and the least significance when reaching 1. Moreover, the weight calculation of the risk factors was performed with the improved order relation analysis method, and the results are listed in Table 6.Table 6
Risk index weights of entropy weight method.
The secondary indicatorsSecondary index weightTertiary indicatorsTertiary index weightUU10.562U110.17U120.26U130.07U140.08U150.11U160.07U170.06U180.11U190.07U20.316U210.16U220.13U230.13U240.16U250.12U260.12U270.18U30.122U310.35U320.11U330.32U340.22


#### 3.2.3. Optimal Assignment Weight Calculation

By normalizing the indicators, we obtained the combination coefficients with formula (5):(22)αc=0.49,0.51.The calculation brought the weights of the indicators in the safety assessment system and the combination coefficients into the formula of the combination weights to obtain the combination weights. The results of combined weights are provided in Table7.Table 7
Combined weight.
IndicatorsEntropy method weightsG1 method of weightCombined weightU110.095540.060.0774146U120.146120.0840.1144388U130.039340.0320.0355966U140.044960.0480.0465104U150.061820.0440.0527318U160.039340.0320.0355966U170.033720.020.0267228U180.061820.0520.0568118U190.039340.0280.0335566U210.050560.0520.0512944U220.041080.060.0507292U230.041080.0640.0527692U240.050560.0720.0614944U250.037920.0480.0430608U260.037920.0440.0410208U270.056880.060.0584712U310.04270.0320.037243U320.013420.0150.0142258U330.039040.0320.0354496U340.026840.0210.0238616


### 3.3. Risk Values and Analysis

In fact, this study used the Delphi method and invited 10 experts to assess 18 risk indicators based on the score criteria in Table1. Besides, the indicator matrix was constructed and then normalized. The results of experts’ assessment of the risk indexes are shown in Table 8, from which we can analyze the opinions of 10 experts on the mentioned indicators.Table 8
Risk index matrix.
IndicatorsE1E2E3E4E5E6E7E8E9E10U115.86.25.76.05.45.65.16.16.35.8U127.17.576.46.67.27.47.06.87.1U138.28.58.07.97.47.17.67.87.57.4U144.14.44.34.54.144.24.24.34.5U157.17.577.46.87.17.17.26.77.2U166.86.56.66.16.86.76.66.97.26.8U176.16.26.16.06.16.56.16.56.36.4U186.56.86.67.27.17.07.17.56.87.0U196.16.05.55.45.66.26.16.05.65.5U216.06.16.45.85.75.55.46.56.16.0U227.17.67.57.26.86.97.47.27.16.8U234.14.24.14.044.34.54.14.14.5U246.56.46.56.06.26.56.66.46.26.0U254.14.54.34.44.55.05.14.84.44.6U268.588.17.67.68.08.27.87.77.5U277.17.57.47.37.07.17.27.17.07.5U316.566.15.66.56.45.86.76.86.4U324.54.45.05.15.34.54.15.25.15.6U337.27.15.46.57.17.37.05.17.07.2U346.56.16.25.85.16.46.05.55.36.0Ei means expert i, i = 1, 2, 3, …, 10.Fuzzy assessment matrix:(23)D1=5.86.25.76.05.45.65.16.16.35.87.17.576.46.67.27.476.87.18.28.587.97.47.17.67.87.57.46.56.276.66.66.86.76.97.177.17.577.46.87.17.17.26.77.26.86.56.66.16.86.76.66.97.26.87.377.57.277.17.286.97.26.56.86.67.27.177.17.56.877.67.587.267.47.37.55.67.2.According to Table3, the gray assessment matrix weight vector can be calculated, and the total calculation results are shown in Table 9.Table 9
The total calculation results.
Risk indicatorsTotal gray statisticsGray assessment matrix weight vectorThe risk valueU1123.13010.2786,0.3582,0.3632,0,06.8308U1223.59750.3301,0.4165,0.2534,0,07.1534U1323.12000.3720,0.4325,0.1955,0,07.3530U1428.0990.1685,0.2165,0.4086,0.2064,05.6942U1523.60860.3346,0.4206,0.2448,0,07.1796U1623.58730.3156,0.4046,0.2798,0,07.0716U1723.36220.2963,0.3810,0.3227,0,06.9472U1823.62760.3273,0.4154,0.2573,0,07.1400U1923.92970.2693,0.3463,0.3510,0.0334,06.7030U2124.08730.2745,0.3173,0.3861,0.0221,06.6884U2223.56420.3376,0.4213,0.2411,0,07.1930U2325.05460.3014,0.3875,0.2985,0.0126,06.9554U2428.86990.2860,0.3464,0.3676,0,06.8368U2523.97580.3022,0.3867,0.2903,0.0208,06.9406U2622.97780.3820,0.4352,0.1828,0,07.3984U2723.58220.3402,0.4240,0.2358,0,07.2088U3123.58920.2958,0.3803,0.3154,0.0085,06.9268U3225.36690.2138,0.2748,0.3642,0.1472,06.1104U3323.98190.3100,0.3932,0.2760,0.0208,06.9834U3423.68540.2823,0.3630,0.3546,0,07.1312The correlation coefficient and ranking of risk factors are represented in Table10.Table 10
Correlation coefficient and ranking of risk factors.
Risk indicatorsCorrelation coefficientRankU110.6715U120.95U130.876U140.5118U150.932U160.867U170.7512U180.914U190.6914U210.7413U220.923U230.3520U240.8110U250.4119U260.859U270.941U310.7811U320.5917U330.868U340.6316Form a gray assessment matrix from gray assessment weight vectorsZ and obtain the comprehensive assessment vector according to formula (11):(24)H=0.29100.36340.27800.01660.The overall tunnel safety assessment level of the system from the equation:(25)Risk=H∗VT=6.6025.


## 3.1. The Study Area

The Asoka Temple was initially established in the third year of Taikang emperor of the Western Jin Dynasty (282 AD) with a history of over 1,700 years, located in Yinzhou District of Ningbo. The Asoka Temple is known as the “Southeast Buddhist country.” It refers to famous 283 temples of Zen Buddhism and one of the Chinese Buddhism “five mountains.” Moreover, it is the only existing thousand-year-old temple in China named after the Indian King Asoka. The temple is notable for its treasure of Sakyamuni Buddha and exquisite pagoda. There are numerous scenic spots and historical sites close to King Asoka Temple. The plan is presented in Figure7. The Asoka Temple takes up a crucial position to inherit the favorable Buddhist cultural tradition and carry forward the Buddhist cultural thoughts in the history of Buddhism for its historical and cultural value.Figure 7
The plan of the Asoka Temple.Given the urban transportation planning, the Treasure House Station of the Ningbo rail transit 1st line 2nd phase went through the Asoka Temple. The Asoka tunnel refers to the only tunnel project in Ningbo with drilling and blasting construction methods. The construction of the tunnel went through the fault fracture zone. Moreover, the surrounding environment of this tunnel is complex. The upper soil slope section exhibits poor stability. Several parts of the tunnel exit are made up of gravel silty clay, intensely weathered rhyolite porphyry, moderately weathered rhyolite porphyry, and fault fracture zone. The rock mass was relatively cracked and underwent strong weathering. This project exhibits poor self-steady ability. The core protection area of Asoka Temple, a national-level cultural relic protection unit, is approximately 98.6 m away from the tunnel. Figure8 illustrates the relative position between the subway and the temple. Thus, blasting vibration is capable of easily affecting the safety of the Asoka Temple and the stability of the existing railways. A safety assessment is required for the Asoka Temple.Figure 8
The location map of the Asoka Temple.


## 3.2. The Weight Results and Analysis

### 3.2.1. G1 Methods

Ten experts were invited to fill in the scoring form in Table4. Experts scored the significance of risk indicators abiding by the criteria in Table 1.Table 4
Expert scores.
IndicatorsA1A2…AmScoreXA1JXA2J…XAmJThe weight obtained by the subjective assessment method of the first index and the secondary index is listed in Table5.Table 5
Risk factor of G1 method.
The 2nd indicatorThe 2nd weightThe 3rd indicatorThe 3rd weightTotal weightUU10.4U110.150.06U120.210.084U130.080.032U140.120.048U150.110.044U160.080.032U170.050.02U180.130.052U190.070.028U20.5U210.130.052U220.150.06U230.160.064U240.180.072U250.120.048U260.110.044U270.150.06U30.1U310.320.032U320.150.015U330.320.032U340.210.021


### 3.2.2. Risk Factor Weight Values Determined Based on Entropy Weighting Method

Ten experts scored the 20 indicators by using the safety assessment system, as listed in Table2. The score ranged from 1 to 10, with the most significance when reaching 10 and the least significance when reaching 1. Moreover, the weight calculation of the risk factors was performed with the improved order relation analysis method, and the results are listed in Table 6.Table 6
Risk index weights of entropy weight method.
The secondary indicatorsSecondary index weightTertiary indicatorsTertiary index weightUU10.562U110.17U120.26U130.07U140.08U150.11U160.07U170.06U180.11U190.07U20.316U210.16U220.13U230.13U240.16U250.12U260.12U270.18U30.122U310.35U320.11U330.32U340.22


### 3.2.3. Optimal Assignment Weight Calculation

By normalizing the indicators, we obtained the combination coefficients with formula (5):(22)αc=0.49,0.51.The calculation brought the weights of the indicators in the safety assessment system and the combination coefficients into the formula of the combination weights to obtain the combination weights. The results of combined weights are provided in Table7.Table 7
Combined weight.
IndicatorsEntropy method weightsG1 method of weightCombined weightU110.095540.060.0774146U120.146120.0840.1144388U130.039340.0320.0355966U140.044960.0480.0465104U150.061820.0440.0527318U160.039340.0320.0355966U170.033720.020.0267228U180.061820.0520.0568118U190.039340.0280.0335566U210.050560.0520.0512944U220.041080.060.0507292U230.041080.0640.0527692U240.050560.0720.0614944U250.037920.0480.0430608U260.037920.0440.0410208U270.056880.060.0584712U310.04270.0320.037243U320.013420.0150.0142258U330.039040.0320.0354496U340.026840.0210.0238616


## 3.2.1. G1 Methods

Ten experts were invited to fill in the scoring form in Table4. Experts scored the significance of risk indicators abiding by the criteria in Table 1.Table 4
Expert scores.
IndicatorsA1A2…AmScoreXA1JXA2J…XAmJThe weight obtained by the subjective assessment method of the first index and the secondary index is listed in Table5.Table 5
Risk factor of G1 method.
The 2nd indicatorThe 2nd weightThe 3rd indicatorThe 3rd weightTotal weightUU10.4U110.150.06U120.210.084U130.080.032U140.120.048U150.110.044U160.080.032U170.050.02U180.130.052U190.070.028U20.5U210.130.052U220.150.06U230.160.064U240.180.072U250.120.048U260.110.044U270.150.06U30.1U310.320.032U320.150.015U330.320.032U340.210.021


## 3.2.2. Risk Factor Weight Values Determined Based on Entropy Weighting Method

Ten experts scored the 20 indicators by using the safety assessment system, as listed in Table2. The score ranged from 1 to 10, with the most significance when reaching 10 and the least significance when reaching 1. Moreover, the weight calculation of the risk factors was performed with the improved order relation analysis method, and the results are listed in Table 6.Table 6
Risk index weights of entropy weight method.
The secondary indicatorsSecondary index weightTertiary indicatorsTertiary index weightUU10.562U110.17U120.26U130.07U140.08U150.11U160.07U170.06U180.11U190.07U20.316U210.16U220.13U230.13U240.16U250.12U260.12U270.18U30.122U310.35U320.11U330.32U340.22


## 3.2.3. Optimal Assignment Weight Calculation

By normalizing the indicators, we obtained the combination coefficients with formula (5):(22)αc=0.49,0.51.The calculation brought the weights of the indicators in the safety assessment system and the combination coefficients into the formula of the combination weights to obtain the combination weights. The results of combined weights are provided in Table7.Table 7
Combined weight.
IndicatorsEntropy method weightsG1 method of weightCombined weightU110.095540.060.0774146U120.146120.0840.1144388U130.039340.0320.0355966U140.044960.0480.0465104U150.061820.0440.0527318U160.039340.0320.0355966U170.033720.020.0267228U180.061820.0520.0568118U190.039340.0280.0335566U210.050560.0520.0512944U220.041080.060.0507292U230.041080.0640.0527692U240.050560.0720.0614944U250.037920.0480.0430608U260.037920.0440.0410208U270.056880.060.0584712U310.04270.0320.037243U320.013420.0150.0142258U330.039040.0320.0354496U340.026840.0210.0238616


## 3.3. Risk Values and Analysis

In fact, this study used the Delphi method and invited 10 experts to assess 18 risk indicators based on the score criteria in Table1. Besides, the indicator matrix was constructed and then normalized. The results of experts’ assessment of the risk indexes are shown in Table 8, from which we can analyze the opinions of 10 experts on the mentioned indicators.Table 8
Risk index matrix.
IndicatorsE1E2E3E4E5E6E7E8E9E10U115.86.25.76.05.45.65.16.16.35.8U127.17.576.46.67.27.47.06.87.1U138.28.58.07.97.47.17.67.87.57.4U144.14.44.34.54.144.24.24.34.5U157.17.577.46.87.17.17.26.77.2U166.86.56.66.16.86.76.66.97.26.8U176.16.26.16.06.16.56.16.56.36.4U186.56.86.67.27.17.07.17.56.87.0U196.16.05.55.45.66.26.16.05.65.5U216.06.16.45.85.75.55.46.56.16.0U227.17.67.57.26.86.97.47.27.16.8U234.14.24.14.044.34.54.14.14.5U246.56.46.56.06.26.56.66.46.26.0U254.14.54.34.44.55.05.14.84.44.6U268.588.17.67.68.08.27.87.77.5U277.17.57.47.37.07.17.27.17.07.5U316.566.15.66.56.45.86.76.86.4U324.54.45.05.15.34.54.15.25.15.6U337.27.15.46.57.17.37.05.17.07.2U346.56.16.25.85.16.46.05.55.36.0Ei means expert i, i = 1, 2, 3, …, 10.Fuzzy assessment matrix:(23)D1=5.86.25.76.05.45.65.16.16.35.87.17.576.46.67.27.476.87.18.28.587.97.47.17.67.87.57.46.56.276.66.66.86.76.97.177.17.577.46.87.17.17.26.77.26.86.56.66.16.86.76.66.97.26.87.377.57.277.17.286.97.26.56.86.67.27.177.17.56.877.67.587.267.47.37.55.67.2.According to Table3, the gray assessment matrix weight vector can be calculated, and the total calculation results are shown in Table 9.Table 9
The total calculation results.
Risk indicatorsTotal gray statisticsGray assessment matrix weight vectorThe risk valueU1123.13010.2786,0.3582,0.3632,0,06.8308U1223.59750.3301,0.4165,0.2534,0,07.1534U1323.12000.3720,0.4325,0.1955,0,07.3530U1428.0990.1685,0.2165,0.4086,0.2064,05.6942U1523.60860.3346,0.4206,0.2448,0,07.1796U1623.58730.3156,0.4046,0.2798,0,07.0716U1723.36220.2963,0.3810,0.3227,0,06.9472U1823.62760.3273,0.4154,0.2573,0,07.1400U1923.92970.2693,0.3463,0.3510,0.0334,06.7030U2124.08730.2745,0.3173,0.3861,0.0221,06.6884U2223.56420.3376,0.4213,0.2411,0,07.1930U2325.05460.3014,0.3875,0.2985,0.0126,06.9554U2428.86990.2860,0.3464,0.3676,0,06.8368U2523.97580.3022,0.3867,0.2903,0.0208,06.9406U2622.97780.3820,0.4352,0.1828,0,07.3984U2723.58220.3402,0.4240,0.2358,0,07.2088U3123.58920.2958,0.3803,0.3154,0.0085,06.9268U3225.36690.2138,0.2748,0.3642,0.1472,06.1104U3323.98190.3100,0.3932,0.2760,0.0208,06.9834U3423.68540.2823,0.3630,0.3546,0,07.1312The correlation coefficient and ranking of risk factors are represented in Table10.Table 10
Correlation coefficient and ranking of risk factors.
Risk indicatorsCorrelation coefficientRankU110.6715U120.95U130.876U140.5118U150.932U160.867U170.7512U180.914U190.6914U210.7413U220.923U230.3520U240.8110U250.4119U260.859U270.941U310.7811U320.5917U330.868U340.6316Form a gray assessment matrix from gray assessment weight vectorsZ and obtain the comprehensive assessment vector according to formula (11):(24)H=0.29100.36340.27800.01660.The overall tunnel safety assessment level of the system from the equation:(25)Risk=H∗VT=6.6025.


## 4. Results and Discussion

Given Table7, the weight of each tertiary risk factor was ranked as follows: U32 < U34 < U17 < U19 < U33 < U13 < U16 < U31 < U26 < U25 < U14 < U22 < U21 < U15 < U23 < U18 < U27 < U24 < U11 < U12. The weights of the secondary risk factors were ranked as U1 > U2 > U3. As indicated from the weighting, the indicators of the ancient building itself exerted a critical effect on its safety assessment. According to Figure 9, among the mentioned tertiary risk indicators, the age of ancient buildings gained the maximal weight since the older the ancient buildings in China are, the more likely they would be damaged. Moreover, previous protective measures may not be sufficiently effective due to the limitations of science and technology, thereby significantly impacting the safety of the mentioned buildings. The arrangement of the correlation degree in Table 10 revealed that the risk assessment value was highly sensitive to the two factors U23 and U25, and U23 was the most sensitive.Figure 9
The combined risk weighting for ancient buildings.The weighting of risk indicators was calculated with the combined optimal method, which reduced subjectivity in the assessment process to some extent. In particular, the greater the weighting is, the more significant the effect of the method on the combined weight would be. According to the risk values of the individual risk factors obtained in Table7 and the overall risk value acquired eventually, the risk level of the building was IV (relatively safe).As indicated in Figure10, most of the risk factors of this project were in IV (relatively safe)-V (safe) risk level. However, the risk level of U14, the structure type, was III (relatively dangerous). The structure type of the building referred to a masonry-timber building’s structure. On the whole, its destruction factor included wood corrosion, moth, and building deformation. The safety of ancient buildings in masonry-timber structures was reduced attributed to long-time physical action, chemical action, and seismic factors. Moreover, the main vibration frequency of field blasting earthquakes was largely distributed in the range of 10–70 Hz, as indicated from the field data of the project. The structural dynamic response and modal analysis of the masonry tower indicate that its natural frequency ranged from 1 to 10 Hz. Thus, the two might overlap in the low-frequency region. While the blasting vibration was attenuated with the distance, the frequency of vibration tended to be in a smaller range and even overlapped the natural frequency. Consequently, the structural resonance would be caused inevitably, and then the dynamic response would be amplified. Thus, the blasting method U24 and the frequency range U22 should be considered.Figure 10
The combined risk weighting for ancient buildings.In Figure11, the range of most indicators’ risk value was between 6 and 8, the fourth range according to Figure 4. It was therefore suggested that the experts invited considered that the risk level of the mentioned factors was relatively safe given the situation provided by the actual engineering information. According to the mentioned results, dynamic blasting construction was adopted to monitor blast vibration. Such a method could maintain the security and durability of ancient buildings. Moreover, the step method, short drilling ruler method, and small dosage method were employed to regulate the risk factors according to the topographic and geological conditions of the site and the existing tunneling technology.Figure 11
The risk values of risk indicators.In the present study, the mean square root error (RMSE) acted as a convenient method to measure the deviation between the observed value and the true value. The synthetic risk value was taken as the observational value while the experts’ score was considered true. As revealed from the results in Table11, all relative errors were less than 1, thereby demonstrating that the model could be effective, which could be referenced for construction protection. Given the risk score of the expert assessment, the engineer should write the construction plan of safety protection of ancient buildings, and the constructor should take different protective measures in accordance with the risk plan and obtain assessment results to increase the construction efficiency.Table 11
The total calculation results.
Risk indicatorsRMSERelative errorU111.090.11U124.30.43U134.560.46U141.80.18U154.340.43U164.10.41U173.640.36U184.330.43U193.240.32U213.420.34U224.520.45U233.210.32U243.880.39U252.070.21U264.870.49U274.510.45U313.60.36U322.310.23U333.740.37U342.860.29


## 5. Conclusions

In this study, a set of safety assessment systems considering the complexity and fragility of ancient buildings was developed and applied to the Asoka Temple close to the Treasure House Station of Ningbo Rail Transit Line 1 Phase II Project. Several conclusions were drawn as follows:(1)
The present study improved the original G1 method and preprocessed the initial data obtained to comprehensively assess ancient buildings’ safety. The method adopted here converted quantitative data into interval numbers. Compared with the conventional analytic hierarchy process, this method could be more reasonable and accurate. The results revealed the risk scores of the tunnel construction. Besides, the risk level of the respective risk factor was determined to target the risk factors in the construction and control the risk promptly. The algorithm could exert significant application effects on the risk assessment of ancient buildings through the calculation of an example.(2)
The safety assessment model exhibited generality and could be applied to other ancient buildings in the same situation. To a certain extent, this study could effectively protect the preservation of ancient buildings and facilitate the modernization of the country and the survival of ancient buildings. It is significant to maintain the historical culture and continuously develop the advanced multiculture.(3)
The optimized combined optimal method was employed to determine the weight of risk indicators and rank them given their significance. The results were real and reliable. The method guided the construction personnel to take appropriate protective measures. They could allocate protection resources timely and provide measures to construct target safety protection projects.On the whole, this study expedited the optimization of the ancient building adjacent to the blasting safety assessment in China. It is noteworthy that this study still relied partially on the expert scoring method, so it was considered subjective. In the subsequent research, experts can exploit the fuzzy sets of images to assess the safety of ancient buildings qualitatively and quantitatively, achieve accurate and comprehensive assessment results, and then provide guidance opinions on the protection of the buildings. Furthermore, the combination of artificial neural networks and assessment methods can be employed to make the safety of buildings predictable.



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*Source: 2573201-2021-11-08.xml*