Safety risk assessment model based on comprehensive weight - set pair analysis theory for heritage buildings adjacent to metro construction

: With the rapid development of urban rail transit systems, the safety of nearby heritage buildings and historic sites is threatened. To better protect these heritage buildings and sites, it is crucial to be able to rapidly and accurately evaluate these threats, especially when a rail project has a potential impact upon numerous heritage buildings and sites in an old city. Based on set pair analysis (SPA) theory, this paper presents a risk assessment model to assess the safety of heritage buildings adjacent to metro construction. First, the risk level of adjacent heritage buildings is graded. Second, this study establishes an assessment index system comprising 16 single indexes among four categories related to heritage building, metro, soil, and management, and determines the threshold for the level of corresponding risk for each evaluation factor. To improve the reliability of the index weighting, a linear weighting method is adopted, which comprehensively considers subjective weights calculated by the analytic hierarchy process and objective weights calculated by the clustering weight method. Finally, the proposed SPA model is verified by using it to assess the structural safety risk of a heritage building adjacent to the Zhengzhou Metro Line Three. By extracting the field measured data at different survey points on the metro line, the risk levels of the heritage building in the shield tunneling process are evaluated, and the results verify the feasibility of the SPA model. The proposed SPA method can provide decision-making support for controlling risk on similar projects.


Introduction
Large underground rail transit systems have been recently built in several Chinese cities in order to avoid traffic congestion and problems lined to it [1,2]. Such underground rail development can dramatically affect the surrounding urban environment [3]: shield tunneling can easily release the stress of surrounding rocks above the roof, produce soil loss, and cause nearby ground settlement, road surface cracking, excessive building deformation, and so on [4]. Heritage buildings are irreplaceable and have especially important historic, artistic, and scientific value; so, the threats to the safety of adjacent heritage buildings due to metro construction must not be ignored [5]. For example, on September 23, 2009, in Tianjin, Metro Line Three was seriously flooded during construction, and this caused many cracks from the foundation up to the roof of the adjacent historic DD Hotel. The greatest crack was 70 cm wide, and there was a partial collapse on the northwest side of the hotel [6].
Underground rail transit construction threatens the structural integrity of adjacent heritage buildings not only in China, but throughout the world [7]. For example, the Historical Archives in Cologne (Germany) collapsed due to metro construction; on March 3, 2009, many cracks appeared in the external wall of the building, which quickly spread to the roof and triggered the collapse of the archives [8]. Nevertheless, underground rail transit projects are being vigorously promoted in big cities, and thus, it is important for engineers to be able to evaluate the risks of shield construction on the safety of adjacent heritage buildings [9].
Many research works have investigated the impact of underground rail transit construction upon adjacent buildings. The main research methods include finite element analysis (FEA) [10][11][12], empirical analysis (EA) [9,13], Bayesian networks (BNs) [14,15], information fusion (IF) [4,16], extended cloud model (ECM) [17], and the chromatography multiply assessment method (CMAM) [6,18]. All the above research methods have some advantages, and some disadvantages. For example, FEA is not only a multi-parameter and dynamic analysis method, but it can also be used for repeated simulation calculations of various working conditions with high accuracy and visualization. The method has been widely used to study the influence of tunnel environments. However, the modeling process of this method is complex, requiring a highly professional background and theoretical approach on the part of relevant users, and the time cost cannot be ignored. Especially when a metro line is built in the old part of a city, and there are many heritage buildings near the line that require an assessment of the impact of metro construction on structural safety, this method is deemed to be time-consuming and expensive. EA needs to obtain prior examples and experiences through statistical analysis of a large number of actual engineering monitoring data, so as to provide theoretical guidance for engineering, so that the results of this method can get as close as possible to the real engineering practice. Yet, this method is only applicable to similar engineering constructions in similar environmental conditions; so, its popularity and application have certain limitations. BNs is based on probabilistic reasoning, which can solve the problems of uncertainty and incompleteness, but it has high complexity and high computational demands, and its analytical quality depends on whether there is a sufficient amount of reliable prior data samples. IF is based on the Dempster-Shafer evidence theory, which can fuse a variety of data, and it is more intuitive than BNs. However, there is no solid theoretical support for the synthesis rules, so its rationality and effectiveness are controversial.
ECM can be used to evaluate the impact of metro tunnel shield construction in a simple, quick, and convenient way, but it is easy to lose important information in the calculation process. In CMAM, images are overlaid according to a chromatic principle by means of Photoshop or ArcGIS technology platform. The operation is simple and the method gives intuitive, vivid, and concise images, but the interaction between the metro tunnel and heritage building factors, as well as the contribution of soil factor and management factor, is not considered, and it is only applicable to the evaluation of metro lines during the planning stage.
In general, most of the available methods have certain limitations. This study attempts to explore from a new angle a more convenient and efficient method to evaluate heritage buildings under the impact of nearby metro tunnel shield construction, avoiding unnecessary complex numerical simulations of many of the lower risk buildings, and provide a basis for decision-makers to determine risk levels and protection measures for structural safety. It is of practical significance to create a thorough construction plan and ensure the structural safety of heritage buildings during metro construction using shield tunneling.
This study presents such a method, using factors related to heritage buildings, metro construction, soil conditions, and construction management as evaluation index factors, by using mathematical tools to build the safety assessment model, based upon set pair analysis (SPA). It simply and rapidly evaluates the risk to adjacent heritage buildings under the influence of metro shield tunneling construction. Moreover, when shield tunneling is used during the metro construction process, relevant risks can be controlled in real time by updating the data for each evaluation parameter, thus providing feedback for the adjustment and optimization of the construction plan.

Basic SPA theory
The SPA theory was first introduced in 1989 by Zhao Keqin as a new kind of systems analysis method that focuses on the study of certainty and uncertainty in a given system [19].
In this system, "identity", "opposition", and "difference" are used to describe the relationships between objects: identity and opposition represent two aspects of certainty, whereas difference represents uncertainty. Identity, opposition, and difference are interrelated and influence and restrict each other, and they transform each other under certain conditions [20].
The three can be indicated with the correlation degree shown in Eq. (1), thus transforming the dialectical understanding of uncertainty into a mathematical operation. there is a mixed degree of identity and opposition.

Standard grades of risk
According to the relevant standard specification [21] and existing literature [16,17] Table 1 lists the relationships among risk levels, effects, and safety control measures of heritage buildings. Take essential pre-reinforcement measures during construction; strengthen monitoring of surface subsidence and building displacement; conduct trend analysis weekly for building damage caused by tunneling.
Take essential pre-reinforcement measures during construction; strengthen monitoring and feedback of surface subsidence and building displacement; conduct field tests to guide the adjustment of parameters during construction; invite experts to analyze weekly the trend for building damage caused by tunneling. V Extreme Severe effect: building outdoor floor has many Conduct field tests and strengthening analyses; risk cracks (width >0.50 mm), with significant nonuniform settlement; non-structural components have many cracks (width >0.5 mm); the main structure of the building has many cracks (width >0.25 mm), lateral displacement (> H/500).
optimize the construction plan according to parametric analysis and expert opinions; strengthen monitoring and feedback of surface subsidence and building displacement; invite experts to analyze weekly the trend for building damage caused by tunneling, and make a contingency plan; after construction, repeat safety assessment.

Selection of evaluation factors
The main reason that metro construction affects the structural safety of heritage building is the loss of soil above the pipeline caused by shield tunneling construction. This leads to uneven settlement of the site in the area where the heritage buildings are located, thus threatening the structural safety of these buildings [22]. The impact that metro construction has on the structure of heritage buildings is divided into three main factors: building, soil, and metro tunnel. In addition, construction management is indispensable. Effective safety management can control risks in a timely manner and ensure the safety of the construction site and surrounding environment [23]. Therefore, the evaluation factors are mainly derived from four sources: heritage building, metro construction, soil, and management: (1) Heritage building factors( ): the importance degree( ) of the heritage building consists of protection level, historic value, scientific value and artistic value [24]. The higher the degree of importance, the greater is the loss due to disaster, and therefore, greater are the security implications. The ability of heritage buildings to resist the influence of the external environment is also important for the safety of heritage buildings; such capability comprises the geometric character( ), structure type ( ) and deterioration degree( ), as they are all related to the structural reliability parameters [21,25].
(2) Metro construction factors( ): The distance from the metro construction to a heritage building is an important factor affecting the safety of these buildings [22,26], and it includes namely, cover depth ( the vertical distance from the tunnel roof to the ground [27]); and horizontal distance( ). According to R. Peck, the land subsidence is caused by the loss of soil, with the soil loss showing a positive correlation relationship to the section size ( ) [28]. The advancing speed ( ) has a significant effect on land subsidence [29].
(3) Soil factors( ): Soil is the medium for the interaction between a building and the metro, and it is a direct factor affecting the safety of heritage building [16]. Friction angle( ), compression modulus( ), Poisson's ratio( ), and cohesion are the main parameters that describe the engineering geological characteristics [30]. X. Li et al. pointed out that Poisson's ratio was the most sensitive to surface subsidence and the cohesion was the least sensitive [31]; and Y. Zhang et al. also pointed out that cohesion was the least sensitive [32], so cohesion was not selected. Soil loss rate ( ) is the soil loss per unit of soil excavation area.
The larger the loss rate, the greater is the soil loss per unit area, the more significant is the ground subsidence, and the greater is the impact on the heritage buildings [33].
(4) Management factors( ): Construction management is a dynamic process that organically combines people, materials, machinery, law, and the environment at the construction site [34].
High-frequency and high-precision monitoring measurement( ), a perfect management system( ), an ideal contingency plan( ), and a professional monitoring engineer( ) are the key factors to ensure construction safety.
The influence of metro construction using shield tunneling upon the safety of adjacent heritage buildings can be evaluated by considering several indexes. With reference to the above analysis, this study selected the 16 indexes listed in Table 2 as our evaluation indexes, from among four categories: heritage buildings factors, metro construction factors, soil factors, and management factors.

Grade division standard of evaluation factors
The proposed safety risk evaluation index system for adjacent heritage buildings under the influence of metro construction using shield tunneling thus comprises both objective evaluation factors (construction and soil) and subjective evaluation factors (building and management). Each factor has a certain contribution to the ultimate risk level and it is, therefore, necessary to analyze the intervals of the evaluation factors. Objective factors are measured by actual values on a real project, while subjective factors are measured by the judgments of relevant experts using a 100-mark system (0-100) [16]. There is fuzziness in the determination of the grade interval of those factors. Combining with engineering practices and theoretical analysis, the reasonable intervals for each factor are recognized. The evaluation criteria are shown in Tables 3 and 4. Since there are different attribute categories for the indexes, and the unit for each index is different, the indexes are not easy to analyze; accordingly, each index is normalized to allow comparison.
where is a "the smaller the better" index (negative index), is a "the bigger the better" The values of each index in Tables 3 and 4 are normalized according to Eqs. (2) and (3), and the normalized results are listed in Table 5.

Determination of index weight
Weights can be divided into subjective weights and objective weights. The subjective weight reflects the amount of willingness on the part of the decision-maker, and the objective weight reflects the contribution of specific index data. In the present work, subjective and objective weights were obtained using the analytic hierarchy process (AHP) and the clustering weight method (CWM), respectively, and this study adopted a linear weighting method to determine the weight of each factor, which is helpful to improve the reliability of the evaluation results.

The AHP approach
The AHP decomposes elements related to evaluation problems into a target layer, criterion layer, index layer, and other layers. It is a multi-level weight analysis method that integrates people's subjective judgments and is a concise systematic analysis and evaluation method combining qualitative and quantitative analyses [35].
The AHP theory itself is very mature, so this paper will not elaborate on it; specific steps are explained in the relevant literature [36,37]. It is worth noting that consistency testing of the results should be carried out; if this testing passes, the eigenvector can be used as the weight vector; if not, the judgment matrix needs to be reconstructed until it can pass the consistency test.

The CWM approach
In the CWM approach, the clustering weight is usually calculated by means of a simple threshold method. However, this method neglects differences in the ranges of each index's standard value [38]. Therefore, this study uses a revised CWM in which the weight of each index at the different levels is determined by considering not only the measured value of the samples but also the standard value of the evaluation index at each level. The specific steps are as follows: Step 1: Construct the original decision matrix as follows.
where is the upper threshold of the index at the level.
Step 2: Calculate the weight distribution of each index as follows.
where is the weight distribution of each index, and is the normalized evaluation value of the actual sample.
Step 3: Calculate the clustering weight.
where is the clustering weight of the index.

Comprehensive weight
The comprehensive weight can be calculated by referring to Eq. (8).
where is the AHP weight, is the CWM weight, and is a weight coefficient that varies for different projects.

Determination of SPA correlation degree
The core of the SPA evaluation method is to determine correlation degree, and the key to determine correlation degree is the coefficient of the difference degree. The SPA method, which is different from the Set Membership method, is a wide-domain functional structure whose use can fully improve the information utilization rate and ensure the credibility of the comprehensive results [39]. As listed in Table 1 In Eqs. The SPA method is applied herein essentially to formulate each safety risk index (sample value) and grading criteria as a set pair, as well as to calculate the correlation degree between the safety risk index and each evaluation level.
Then, Eq. (14) is used to calculate the average degree of correlation.
where is the average correlation degree of the safety risk index on the jth evaluation level; and is the comprehensive weight of each safety risk index.
, the safety risk assessment result of the sample can be identified at the level.

Case study verification
A heritage building is located at 27 Square in the old town of Zhengzhou in Henan Province.
Built in 1971, the building is a cultural monument comprising hexagonal conjoined twin towers, and it has a reinforced concrete structure with a height of 63 meters in 14 layers. The base has three layers with a surrounding white marble fence, the tower has 11 layers, and a hexagonal bell tower 2.7 meters in diameter stands at the top of the tower (Fig. 1). The The tunnel of the Zhengzhou Metro Line Three (ZMLT) runs alongside the heritage building.
The horizontal distance between the tunnel edge and the building is only 3 m, and the vertical distance is 20.5 m; the spatial relationship is illustrated in Fig. 2.

Data acquisition
During the propulsion process for the ZMLT shield construction at the side of the heritage building, the values of each objective evaluation index were obtained by means of field detection of geological conditions and tunnel design depths at different horizontal distances.
The values of each subjective evaluation index were obtained according to the scores given by the domain experts on the heritage building and management factors. Table 6 lists the values of each evaluation index. Table 7 lists the corresponding values as normalized using Eqs. (2) and (3).

Correlation calculation
Taking the measured data set as an example, the nearest horizontal distance between the tunnel and the building was set as 3 m, and the advancing speed for the shield machine was tentatively set at 40 mm/min. The calculation process was then undertaken as follows:

Weights calculation
According to the established hierarchical structure model, combined with experience in engineering practice, a method based on a scale of 1-9 was adopted to construct the judgment matrixes of the criterion and the index layers, included as Tables 8 and 9. The CWM decision matrix thus constructed is included as Table 10.

Correlation degree calculation
According to Eqs. (9) -(13), the correlation degree of each evaluation factor with each level was calculated as shown in Table 11.
Using Eq. (14) and the comprehensive weight matrix, the average correlation degree ( ) of the safety risk assessment level for the heritage building was calculated as shown in Table 12.

Results and discussion
During the propulsion process for the shield tunneling construction of the ZMLT, the risk level for the safety impact of a heritage building corresponding to different locations and different advancing speeds are summarized in Table 13.  II  II  II  II  II  II  II  II  II  II  II  II  II  II  II   -20m  II  II  II  II  III  III  III  III  III  III  III  III  III  III  III   -15m  II  II  II  II  III  III  III  III  III  III  III  IV  IV  IV  IV   -10m  II  II  II  II  III  III  III  III  III  IV  IV  IV  IV  IV  IV   -6m  II  II  II  II  III  III  III to the heritage building. The main reason is the obvious difference in geological conditions at ±15 m.
(5) When = 25 m, has little influence on structural safety; the levels are all II. This finding is consistent with relevant standard requirements [40], namely, that when a metro structure or pipeline runs alongside an existing structure, the monitoring range is generally within 30 m of both sides of the metro structure and the pipeline.
The SPA evaluation method is conducted before the construction, with the decision-makers implementing the corresponding safety control measures according to the evaluation results.
If the risk assessment results show Level-I and Level-II risks, according to the classification requirements of Table 1, the necessary engineering measures do not need to be taken before construction. Otherwise, engineering measures should be taken to control the higher level of risk.
In the actual construction of this project, the normal advancing speed of the shield machine is 60 mm/min. Table 13 shows that metro shield construction has a very high impact on the structural safety of heritage buildings at this speed. To reduce the impact on the structure of this building while also optimizing the metro construction schedule, when <6 m, the speed should not exceed 50 mm/min, when 6-15m, the speed should not exceed 60 mm/min; when >15m, the shield construction could be carried out at the normal advancing speed of 60 mm/min. Furthermore, additional pre-reinforcement measures are required before construction, such as installing 29-m-length ⌀800@1000 mm isolation piles between the building and the metro tunnel, thereby forming an isolation curtain to limit deformation of the soil mass behind the piles [41]. During construction, the monitoring of surface subsidence and building displacement should be strengthened. The layout of on-site monitoring points is shown in Fig. 3. The shield cutter head moved into the 30 m scope of the building on April 15, 2019, and the shield tail moved away from the 30 m scope on April 29, 2019. The monitoring data for the surface subsidence are shown in Fig. 4(a), and building displacement data are shown in Fig. 4(b). The monitoring results show that the surface subsidence is 4.87 -4.79 mm, the maximum differential settlement of the building is 1.89 mm, and the gradient ≈0.13‰, conforming to the relevant control standards [21,42]. After the construction, no visible cracks or uneven settlement occurred on the outdoor floor of the building (see Fig.   5(a)), no visible cracks appeared in the main structure (see Fig. 5(b)), a few slight cracks appeared in the non-structural components (see Fig. 5(c)), and a door tilted slightly (see Fig.   5(d)).
The above analysis shows that the evaluation results are in line with objective reality, and that risk control can be effectively carried out by taking protective measures and controlling the related parameters.

Conclusions
This study have established a safety risk assessment model of the influence of metro construction on adjacent heritage buildings. The model is based upon the SPA theory and uses 16 single indexes as evaluation factors, namely, importance degree, geometric character, structure type, deterioration degree, cover depth, horizontal distance, section size, advancing speed, friction angle, compression modulus, Poisson's ratio, soil loss ratio, monitoring measurements, management system, contingency plan, and monitoring engineer. The model has been applied in practice by analyzing a heritage building in Zhengzhou, and the main conclusions are as follows.
(1) The SPA-based safety risk assessment model greatly improves the information utilization rate and guarantees the credibility of the evaluation results. Therefore, the method is suitable for multi-level and multi-objective complex decision systems.
(2) In general, when metro lines go through old cities, a large number of heritage buildings are affected. Commonly used numerical simulation methods have high precision and the workload is large if every building is included in the calculations. The SPA method can be used to conduct the evaluation of buildings one by one. It is not only very simple but also easy to operate using computer programs, making it more efficient. For buildings with higher risk level, numerical simulation is used to calculate the specific stress concentration area, and targeted protective measures can be implemented.
(3) A calculation example herein shows that the evaluation results are in line with objective reality. According to the dynamic changes to the risk levels of heritage buildings in the process of metro shield tunneling, this method can be used to control risk by slowing the advancing speed of the shield machine as appropriate, thereby improving the construction plan. The SPA method can effectively guide similar projects and is worth popularizing.
It is worth noting that the values of subjective indexes and the weights calculated by AHP, as they depend on expert knowledge and rich experience, have strong subjectivity. The question of how to carry out quantitative analysis more objectively remains for follow-up studies.
Future research work will consider sensitivity analysis of the factors of influence and the scientific selection of safety control measures, to establish a more thorough safety risk management system for heritage buildings.

Availability of data and materials
All data generated or analysed during this study are included in this published article.